Answers
Answer:
1.a) x = g(2)
1.b) See below
2.a) See below
2.b) α = 60°
3.a) 2 + h
3.b) 2
4.a) Interval [3, 4] = 3 m/s
Interval [3, 3.1] = 2.1 m/s
4.b) 2 m/s
Step-by-step explanation:
Question 1Part (a)
Given function f(x):
[tex]f(x)=\dfrac{x}{x-2}[/tex]
If the range of f is (-∞, 1) U (1, ∞), then a value of y in the range of f is y=2.
Set the function equal to the value of y and solve for x:
[tex]\begin{aligned}y=2 \implies \dfrac{x}{x-2}&=2\\x&=2(x-2)\\x&=2x-4\\-x&=-4\\x&=4\end{aligned}[/tex]
The solution written as a function x = g(y) is:
x = g(2)Part (b)
Given function g(y):
[tex]g(y)=\dfrac{2y}{y-1}[/tex]
Verify that g is the inverse function of f by calculating g(f(x)):
[tex]\begin{aligned}\implies g(f(x)) &=\dfrac{2f(x)}{f(x)-1}\\\\&=\dfrac{2\left(\frac{x}{x-2}\right)}{\left(\frac{x}{x-2}\right)-1}\\\\&=\dfrac{2\left(\frac{x}{x-2}\right)}{\left(\frac{x-(x-2)}{x-2}\right)}\\\\&=\dfrac{\left(\dfrac{2x}{x-2}\right)}{\left(\dfrac{2}{x-2}\right)}\\\\&=\dfrac{2x}{2}\\\\&=x \quad (\text{for all $x\neq 2$})\end{aligned}[/tex]
Similarly, calculate f(g(y)):
[tex]\begin{aligned}\implies f(g(y))&=\dfrac{g(y)}{g(y)-2}\\\\&=\dfrac{\left(\frac{2y}{y-1}\right)}{\left(\frac{2y}{y-1}\right)-2}\\\\&=\dfrac{\left(\frac{2y}{y-1}\right)}{\left(\frac{2y-2(y-1)}{y-1}\right)}\\\\&=\dfrac{\left(\dfrac{2y}{y-1}\right)}{\left(\dfrac{2}{y-1}\right)}\\\\&=\dfrac{2y}{2}\\\\&=y \quad \text{(for all $y \neq 1$)}\end{aligned}[/tex]
Hence verifying that g is the inverse function of f.
Question 2[tex]\boxed{\begin{minipage}{5 cm}\underline{Trigonometric Identities}\\\\$\tan x=\dfrac{\sin x}{\cos x}$\\\\\\$\cos \left(\arctan \left(x\right)\right)=\dfrac{1}{\sqrt{1+x^2}}$\\\\\\$\sin\left(\arctan \left(x\right)\right)=\dfrac{x}{\sqrt{1+x^2}}$\\\end{minipage}}[/tex]
Part (a)
If y = arctan(x) then tan(y) = x.
Use the trigonometric identities to express sin(y) and cos(y) in terms of x.
[tex]\boxed{\begin{aligned}\tan(y) &= x\\\implies \dfrac{\sin y}{\cos y}&=x\\\sin y&=x \cos y\\ \sin y&=x \cos (\arctan x)\\ \sin y&=\dfrac{x}{\sqrt{1+x^2}}\end{aligned}}[/tex]
[tex]\boxed{\begin{aligned}\tan(y) &= x\\\\\implies \dfrac{\sin y}{\cos y}&=x\\\\\dfrac{\sin y}{x}&= \cos y\\\\ \cos y&=\dfrac{\sin(\arctan x)}{x}\\\\ \cos y&=\dfrac{\dfrac{x}{\sqrt{1+x^2}}}{x}\\\\\cos y&=\dfrac{x}{\sqrt{x^2+1}x}\\\\\cos y&=\dfrac{1}{\sqrt{x^2+1}}\end{aligned}}[/tex]
Part (b)
Given linear equation:
[tex]y=\sqrt{3}x+1[/tex]
As the slope of a linear equation y = mx + b is m, then the slope (m) of the given line is √3.
If m = tan(α) then:
[tex]\begin{aligned}\implies m&=\sqrt{3}\\\tan (\alpha)&=\sqrt{3}\\\alpha&=\arctan \sqrt{3}\\\alpha&=60^{\circ}+180^{\circ}n\\\end{aligned}[/tex]
If α is the angle the line forms with the x-axis, then α = 60°.
Question 3Given function:
[tex]f(x)=x^2-1[/tex]
Part (a)
[tex]\begin{aligned}\dfrac{f(1+h)-f(1)}{h} &=\dfrac{((1+h)^2-1)-(1^2-1)}{h}\\\\&=\dfrac{(1+2h+h^2-1)-0}{h}\\\\&=\dfrac{2h+h^2}{h}\\\\&=2+h\end{aligned}[/tex]
Part (b)
Part a used differentiating from first principles to find the gradient of f(x) at x = 1. As h gets smaller, the gradient of the straight line gets closer and closer to the gradient of the curve. Therefore, as h gets close to zero, (2 + h) gets close to 2. Therefore, the slope of the tangent line to the graph of f(x) at the point where x = 1 is 2.
Question 4A particle is moving on the x-axis and its position at time is given by
[tex]x(t)=t^2-4t+3[/tex]
Evaluate the position of the particle at t = 3, t = 4 and t = 3.1:
[tex]x(3)=3^2-4(3)+3=0[/tex]
[tex]x(4)=4^2-4(4)+3=3[/tex]
[tex]x(3.1)=(3.1)^2-4(3.1)+3=0.21[/tex]
Average velocity formula
[tex]\overline{v}=\dfrac{s(t_2)-s(t_1)}{t_2-t_1}[/tex]
Therefore, the average velocity of this particle over the interval [3, 4]:
[tex]\overline{v}=\dfrac{x(4)-x(3)}{4-3}=\dfrac{3-0}{1}=3\;\; \rm m/s[/tex]
The average velocity over the interval [3, 3.1] is:
[tex]\overline{v}=\dfrac{x(3.1)-x(3)}{3.1-3}=\dfrac{0.21-0}{0.1}=2.1\;\; \rm m/s[/tex]
Part (b)
To find an equation for velocity, differentiate the given equation for displacement:
[tex]v(t)=\dfrac{\text{d}x}{\text{d}t}=2t-4[/tex]
To calculate the instantaneous velocity of the particle at time t = 3, substitute t = 3 into the equation for velocity:
[tex]v(3)=2(3)-4=2\;\; \rm m/s[/tex]
Related Questions
PLEASE HELP 10 points
Answers
The statement -
"If there is {b} ounces of water in a bottle, than (b + 5) would represent the amount of water left in the bottle after you drink 5 ounces" in option 2, cannot be represented with the help of the function given.
What is a function?An function in mathematics defines a relationship between one variable (the independent variable, {x}) and another variable (the dependent variable, {y}). Example -
y = f{x} = ax + b
Given is a function as -
y{b} = b + 5
The statement that cannot be represented with the help of this function is given below -
"If there is {b} ounces of water in a bottle, than (b + 5) would represent the amount of water left in the bottle after you drink 5 ounces".This amount of water left is represented by the expression (b - 5).Therefore, the statement "If there is {b} ounces of water in a bottle, than (b + 5) would represent the amount of water left in the bottle after you drink 5 ounces" cannot be represented with the help of the function given.
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RISE AIRLINES- WE RISE TOGETHER!
With the recent crisis in the country's airline industry failing to meet customer needs and
demand, Rise Airlines is re-evaluating its overbooking policy for its most common routes on
their small aircraft. They have hired your team to perform a study of the cost of overbooking
vs flying with empty seats using several types of demand distributions. They have provided
your team with some information about their last 60 days of flites and cancellations as well as
their estimates on demand. On average, a ticket sells for $200 and there are 50 seats on each
aircraft. The fixed cost for running their operations is $100,000 per DAY and their variable
cost of operations is $2,000 per flite, per day. Rise airlines has the current capacity to fly a
mean of 15 flites a day with a standard deviation of 12. The minimum amount of flites they can
fly per day and still maintain their gate space is 13 and the maximum they can fly before they
run out of functional aircraft is 25. Management is requesting a study of their distributions,
the breakeven point, SL and SO. Management would also like recommendations on which
distribution should be used and what other factors they should consider. In order to prepare
this analysis, you and your team have gathered information and will answer the following
questions using excel, graphs, and the case study shell:
A. What is the expression for total cost per month? Assume 30 days in the month
B. What is the expression for total revenue per month? Assume 30 days in a month
C. How many flites need to fly on a daily basis for Rise to breakeven?
D. What percentage of Rise's total flite capability must be in the air that day?
Hint- set these calculations up in excel to help make any graphics easier.
Answers
Total cost of Airline per month = 3,900,000$. Total revenue of airline per month = $ 90,000. The break even point= 55.56. Rise in flight to make end meet = 222.24%
What is percentage rise?The growth rate formula is the ratio of the increased value to the original value multiplied by 100, expressed as a percentage. As the value of something increases, the percentage of the value increases.
A. To calculate your total cost per month, you need to find the sum of your fixed and variable costs. The fixed cost is $100,000 per day and the variable cost is $2,000 per flight per day. So the formula for total cost per month is:
$100,000 * 30 + $2,000 * 15 * 30 = $3,000,000 + $900,000 = $3,900,000
B. To calculate your total revenue per month, multiply your average revenue per flight ($200) by the average number of flights per day (15), then multiply by the number of days in a month (30) is needed. So the formula for total sales per month is:
$200 * 15 * 30 = $90,000
C. To calculate your break-even point, you must determine the number of flights required per day so that your total revenue equals your total cost. We can formulate an equation for this:
$200 * x = $100,000 + $2,000 * x
200x = 100,000 + 2,000x
-1,800x = -100,000
x = 55.56 (rounded to two decimal places)
Therefore, the breakeven point is 55.56 flights per day.
D. To find the percentage of Rise's total flight capacity that needs to be in the air each day to break even, divide the number of flights required to reach breakeven into the maximum number of flights you can fly in a day. You need to divide by the number of times (25). . This can be expressed as:
55.56/25 = 2.2224
2.2224 * 100 = 222.24D
44 Therefore, about 222.24% of Rise's total flight capacity needs to be in the air that day to make ends meet.
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Need help with geometry dialation
Answers
The vertices of triangle DEF after dilation are D'(4, -M), E'(-2, M) and F'(-2, -M)
What is dilation?Dilation means changing the size of an object without changing its shape. The size of the object may be increased or decreased based on the scale factor.
Given a triangle DEF which is being dilated by a dilation factor of (2,M) we need to find the vertices of the image,
The vertices before dilation are D(2, -1), E(-1, 1) and F(-1, -1)
Since, the dilation factor is (2,M), so the new vertices are,
D'(2×2, -1×M)
D'(4, -M)
E'(-1×2, 1×M)
E'(-2, M)
F'(-1×2, -1×M)
F'(-2, -M)
Hence, the vertices of triangle DEF after dilation are D'(4, -M), E'(-2, M) and F'(-2, -M)
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a group of five students is being selected for a leadership group. they are being selected from a group of 12 nominees.
Answers
The probability of selecting a group of five students from a group of 12 nominees is 2.32 or 792 possible combinations.
The formula used to calculate the probability of a group of five students being selected from a group of 12 nominees is C(12,5) which is equal to 792. This can be calculated using the formula n!/(r!(n-r)!), where n is the number of nominees (12) and r is the number of students in the group (5).
To calculate C(12,5), first calculate 12!/5!7!. This is equal to 12x11x10x9x8/5x4x3x2x1, which is equal to 11,664. Then divide 11,664 by 7! (7x6x5x4x3x2x1) which is equal to 5040. This is equal to 2.32, which is the probability of selecting a group of five students from a group of 12 nominees.
Therefore, the probability of selecting a group of five students from a group of 12 nominees is 2.32 or 792 possible combinations.
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Management Development and Consultancy Bureau (MDCB) conducted research on the daily expenses of civil servants traveling to various cities throughout the world. In particular, MDCB published appropriate per diem totals, which represent the average costs for the typical civil servant at the management level including three meals a day in business-class restaurants and single-rate lodging in business-class hotels. If 86.65% of the per diem costs in Nairobi, Kenya, are less than $449, and if the standard deviation of per diem costs is $36, what is the average per diem cost in Nairobi?
Answers
The average per diem cost in Nairobi is $417.806.
What is standard deviation?Standard deviation is the positive square root of the variance. Standard deviation is one of the basic methods of statistical analysis. Standard deviation is commonly abbreviated as SD and denoted by 'σ’ and it tells about the value that how much it has deviated from the mean value.
Given that, 86.65% of the per diem costs in Nairobi, Kenya, are less than $449, and if the standard deviation of per diem costs is $36.
z=(x-μ)/σ
z= standard score
x= raw observed data point
μ= population mean
σ= population standard deviation.
Here, 0.8665 =(449-μ)/36
0.8665×36=449-μ
31.194=449-μ
μ=449-31.194
μ=$417.806
Therefore, the average per diem cost in Nairobi is $417.806.
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Please find the measure of CL.
Answers
Note that in the problem above, CL is 9m. This is resolved using the theorem of the Angle Bisector.
What is the Angle Bisector Theorem?The angle bisector theorem in geometry is concerned with the relative lengths of the two segments of a triangle's side that are separated by a line that bisects the opposing angle. It compares their lengths to the lengths of the other two sides of the triangle.
In geometry, the angle bisector is the ray, line, or segment that splits a given angle into two equal places.
Thus, given that, in ∆ABC, m∠C= 90° AL is an angle bisector m∠ABC = 30°, LB = 18 m,
CL is derived using the SOH principle; that is: Sine of the Angle = Opposite /Hypothenus
Sin 30° = CL/BL
⇒ 1/2 = CL/18
⇒ CL=9 m
Thus, the measure of CL is 9 m. See the attached image.
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What percentage of presidents’ ages fall within one standard deviation of the mean? (Round to 1 decimal place.)
Ages of Last 6 Presidents at Inauguration
George Bush
64
Bill Clinton
46
George W. Bush
54
Barack Obama
47
Donald Trump
70
Joe Biden
78
Answers
The mean of the given data set is 59.83.
What is a mean?Mean is defined as the ratio of the sum of the number of data sets to the total number of data. In statistics, the mean is the product of all the values in a set of data divided by the total number of values in the data for a given set of observations.
The given data set is:-
George Bush
64
Bill Clinton
46
George W. Bush
54
Barack Obama
47
Donald Trump
70
Joe Biden
78
The mean of the data set is calculated as:-
Mean = ( 64 + 46 + 54 + 47 + 70 + 78 ) / 6
Mean = 359 / 6
Mean = 59.83
Hence, the mean of the data set is 59.83.
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y-6≤-3(x+4) in slope intercept form WITH STEPS!!!
Answers
Answer:
y≤-3x-6
Explaination:
First you distribute the -3 to the x and -6.
So you would then have y-6≤-3x-12.
Then you would add 6 to each side.
After doing this you will have y≤-3x-12+6.
Then you combine like terms which are -12 and 6 to get -6. Then you are left with your final answer of y≤-3x-6.
I hope this helped :) (I believe I did it correctly based off of my knowlege)
which of the following is the largest unit? group of answer choices meter micrometer kilometer millimeter decimeter
Answers
A kilometer is the largest unit.
In the International System of Units, a kilometer represents one mile (SI). The symbol for it is km. Km is typically used to describe a location's or a piece of land's distance. It is possible to measure length and distance in kilometers or "km." The measurement unit "kilometer," which is also used to measure geographic distances, is comparable to the measurement unit "mile." Kilometers are a common measurement unit for length and distance in many nations. 1000 meters make up one kilometer.
the distance between two points along an object's longest side or length; often used to describe a specific component of an object: a length of rope; the boat is 20 feet long.
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6(2d-3) but we don't know what d is
Answers
D is zero
Answer:12d-18
Step-by-step explanation:
graph g has vertex set {v1, v2, v3, v4, v5} and end edge set {e1, e2, e3, e4}, with edge point function as follow:
Answers
Graph H is a simple undirected graph, meaning that it has no self-loops or multiple edges between the same pair of vertices. The vertex set is {v1, v2, v3, v4, v5}. The edge set is {e1, e2, e3, e4}.
To draw the graph, we start by placing the vertices on a plane and then connecting them with edges according to the edge-endpoint function.
For example:
Edge e1 connects vertex v1 to itself. This means that v1 has a self-loop.Edges e2 and e3 connect vertices v2 and v3. This means that v2 and v3 are adjacent and there is an edge between them.Edge e4 connects vertices v1 and v3. This means that v1 and v3 are adjacent and there is an edge between them.Note that v4 and v5 are not included in the edge-endpoint function and are not part of the graph.
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Complete Question:
Graph H has a vertex set {v1, v2, v3, v4, v5}, edge set {e1, e2, e3, e4} and edge-endpoint function: Edge Endpoints e1 {v1} e2 {v2, v3} e3 {v2, v3} e4 {v1, v3} Draw the graph.
The graph below shows the solution set of which inequality?
-
OA. Ixl < 100
OB. Ix|>1
OC. Ix ≤ -5
OD. Ix ≥ 5
OE. x > -5
OF. x < -5
2 3
SUBMIT
Answers
The solution set of the inequality is shown in the graph as the set of all points to the left of the line x = -5. This represents the solution set for the inequality x < -5. So correct option is F.
What do you mean by inequality?An inequality is a mathematical statement that represents a relationship between two values or expressions. It is used to express that one value is greater than, less than, or equal to another value. Inequalities are written using symbols such as ">", "<", "≥", or "≤". For example, the statement "x < 10" represents the inequality that the value of x is less than 10. Inequalities are used in many areas of mathematics, including algebra, geometry, and calculus, to model real-world situations and solve problems. They are also used in many scientific and engineering fields, such as economics, physics, and engineering, to model and analyze complex systems and relationships.
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(50 POINTS AND BRAINLYEST)
Answers
Answer:
Question 1:
Diameter: 10
radius: 5
circumference: 15.70796
Area: 78.53981
Question 2:
98 Gallons of paint
Step-by-step explanation:
Question 1:
Diameter: 10
radius: 5
circumference: 2π x 5
= 15.70796
Area: π x [tex]5^{2}[/tex]
= 78.53981
Question 2:
To find the radius of the sphere: r=(3V4π)⅓
=(3·66844·π)⅓
≈11.68555
To find the surface area of the sphere: A=4πr2
=4·π·11.692
≈1715.96403
Since surface area is 1715.96403 and each gallon of paint can cover 350 square feet the number of gallons of paint needed to paint the water tower is:
1715.96403÷35x2
=98 gallons of paint is needed to paint the entire water tower twice
Answer: x = 666
Step-by-step explanation:
solve for the area while doing pi squared and then solve it with the hypotenuse of the area
Decide whether the relation determines a function
7x=14-5y
Answers
Answer:
yes, it is a funtion
Step-by-step explanation:
we can rewrite the equation as,
y = 14/5 - 7x/5
there us only one value of y for every real no of x
The relation 7x = 14 - 5y is a function.
To determine whether the relation 7x = 14 - 5y represents a function, we need to check if each value of x corresponds to a unique value of y.
First, let's isolate y in terms of x:
7x = 14 - 5y
Subtract 14 from both sides:
7x - 14 = -5y
Divide by -5:
(7x - 14) / -5 = y
Simplifying further:
y = (-7x + 14) / 5
Since we have found a formula for y in terms of x, this relation represents a function.
For each value of x, there is a unique corresponding value of y based on the equation y = (-7x + 14) / 5.
Therefore, the relation 7x = 14 - 5y is a function.
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Which equation below does not show equivalent expressions when y = 2
Answers
The equations 5y+25= 5*(y+4) are not equivalent.
Linear Function
An equation can be represented by a linear function. The standard form for the linear equation is: y= mx+b , for example, y=5x+9. Where:
m= the slope.
b= the constant term that represents the y-intercept
For the given example: m=5 and b=9.
Algebraic expressions or linear equations are considered equivalent when they are equal.
For solving this question, you should:
replace the variable y with the number 2, since y=2. solve the algebraic expression for both sides. If the result is different, the expressions are not equivalent.1 .Expression y+4y= y(1+4)
2+4*2=2*5
2+8=10
10=10
The equations are equivalent.
2. Expression y+y+y= 3y
2+2+2=3*2
6=6
The equations are equivalent.
3. Expression 5y+25= 5*(y+4)
5*2+25=5*(2+4)
10+25=5*(6)
35≠30
The equations are not equivalent.
4. Expression 2*(y+2)=2y+4
2*(2+2)=2*2+4
2*4=4+4
8=8
The equations are equivalent.
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2.
-6
5
-2
-1
2
0
-5
3
5
Vertex (give me the x and y coordinate):
Max or Min?:
Domain:
Range:
Zeroes (just tell me how many):
Axis of Symmetry:
Y-Intercept:
TE
Answers
Max or Min: Min
Domain: infinite
Range: y ≤ 0
Zeros: 1
Axis of Symmetry: -1
Y-intercept: -3
This should all be correct based on the picture
The Bureau of Economic Analysis estimates that in 2015, personal consumption expenditures of American totaled $12.3 trillion. The major categories of these expenditures were durable goods ($1.36 trillion: for example, cars, furniture, recreational equipment), nondurable goods ($2.66 trillion: for example, food, clothing, fuel), and services ($8.3 trillion: for example, health care, education, transportation).
a. What was the approximate annual per capita spending on personal consumption? Assume a population of 321 million.
B. What was the approximate daily per capita spending on personal consumption?
c. On average, about what percentage of personal consumption spending was devoted to services? Is this figure consistent with your own spending ?
d. Spending on health care was estimated to be $2.1 trillion. About what percentage of all personal consumption spending was devoted to health care?
e. In 2000, the total spending on personal consumption was $6.8 trillion, while health care spending was $918 billion. Compare the percentage increase in total spending and health care spending between 2000 and 2015.
Answers
From 2000 to 2015, total spending on personal consumption increased by 77.5%, while health care spending increased by 129.9%.
a. The approximate annual per capita spending on personal consumption in 2015 was $38,218. This figure was calculated by dividing the estimated total personal consumption expenditure of $12.3 trillion by the population of 321 million.
b. The approximate daily per capita spending on personal consumption in 2015 was $104.89. This figure was calculated by dividing the approximate annual per capita spending of $38,218 by 365 days.
c. Services accounted for approximately 67.2% of personal consumption spending in 2015. This figure was calculated by dividing the estimated total spending on services of $8.3 trillion by the total personal consumption expenditure of $12.3 trillion. This figure is consistent with my own spending, as the majority of my expenditure is devoted to services such as transportation, food delivery, and entertainment.
d. Health care accounted for approximately 17.1% of all personal consumption spending in 2015. This figure was calculated by dividing the estimated total spending on health care of $2.1 trillion by the total personal consumption expenditure of $12.3 trillion.
e. The percentage increase in total spending between 2000 and 2015 was 77.5%, while the percentage increase in health care spending between 2000 and 2015 was 129.9%. This was calculated by first subtracting the total spending on personal consumption in 2000 of $6.8 trillion from the total spending on personal consumption in 2015 of $12.3 trillion, and then dividing the result by the total spending in 2000. This was done for both total spending and health care spending, and the results were then multiplied by 100 to get the percentage increase.
From 2000 to 2015, total spending on personal consumption increased by 77.5%, while health care spending increased by 129.9%.
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question which statement best describes a graph of paired points that form a proportional relationship? responses a straight line can be drawn through all the points, and the line passes through the point (3,0). a straight line can be drawn through all the points, and the line passes through the point , begin ordered pair 3 comma 0 end ordered pair, . a straight line cannot be drawn through all the points, but the line passes through the point (0,0). a straight line cannot be drawn through all the points, but the line passes through the point , begin ordered pair 0 comma 0 end ordered pair, . a straight line can be drawn through all the points, and the line passes through the point (0,0). a straight line can be drawn through all the points, and the line passes through the point , begin ordered pair 0 comma 0 end ordered pair, . a straight line can be drawn through all the points, and the line passes through the point (0,3).
Answers
A statement which best describes a graph of paired points that form a proportional relationship include the following: F. a straight line can be drawn through all the points, and the line passes through the point, begin ordered pair 0 comma 0 end ordered pair.
What is a proportional relationship?In Mathematics, a proportional relationship is a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical expression:
y = kx
Where:
k is the constant of proportionality.y and x represent the variables in a proportional relationship.Generally speaking, the graph of any proportional relationship such as the linear equation is characterized by a straight line that passes through all the points and the origin, which is denoted by the ordered pair (0, 0).
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A) William is 3 feet 1 inch tall and would like to ride a roller coaster. Riders must be at least 42 inches tall to ride the coaster. Write an addition inequality to determine how much taller William must be to ride the coaster. Let x be the variable representing how much taller William must be.
B)
Solve the inequality found in Part A.
Answers
Answer:Multiply 3 times twelve and add one. You will get 37 inches tall. He needs to be 42 inches tall. subtract 42 - 37 and you will get 5. William needs to be five inches taller.
Step-by-step explanation:
An addition inequality to find the how much taller William to ride the coaster is, Height of William + x ≥ 42.
Inequality can be defined relation that compares two numbers or other mathematical expressions in an unequal way.
We are Given, Riders should be at least 42 inches tall to ride the coaster, and 'x' be the variable representing how much taller William should be.
Therefore,
The inequality which may be used to calculate how much taller William has to be in order to ride the coaster.
Height of William + x ≥ 42
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The area in square feet of a rectangular field is x² - 70x+1200. The width, in feet, is x - 30. What is the length, in feet?
The length, in feet, is
Answers
Explanation: 22-7ox+1200
=(1-30)(1-40)
So the length, in feet, is 2-40
I Factorization ef polynomials. 3
Find an equation of the line passing through the given points. Use function notations to write the equation. (-3,11) and (1,-1)
Answers
Considering the expression of a line, the equation of the line passing through the points (-3,11) and (1,-1) is y=-3x +2.
What is a Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin.Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope of the line can be calculated using:
m= (y₂ - y₁)÷ (x₂ - x₁)
Substituting the value of the slope and the value of one of the points, the value of the ordinate to the origin can be obtained.
Equation in this caseIn this case, being (x₁, y₁)= (-3, 11) and (x₂, y₂)= (1, -1), the slope can be calculated as:
m= (-1 - 11)÷ (1 - (-3))
m= (-1 - 11)÷ (1 + 3)
m= (-12)÷ 4
m= -3
Considering point 2 and the slope, you obtain:
-1= (-3)×1 + b
-1= -3 + b
-1 +3= b
2= b
Finally, the equation of the line is y=-3x +2.
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suppose f ( t ) represents the particles' combined distance from the wall in feet t seconds after they started moving. define the function f in terms of a and b .
Answers
The function f(t) can be represented as f(t) = a + bt, where a and b are constants that depend on the initial position and velocity of the particles.
In this function, a represents the initial distance from the wall when t = 0 and b represents the rate of change of the distance from the wall over time. The value of a and b can be determined from the initial conditions and the velocity of the particles.
The function f(t) is a linear function that models the combined distance of the particles from the wall as a function of time. As t increases, the value of f(t) increases linearly with a slope of b, representing the increase in distance from the wall over time.
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I need help with this question
Answers
The procedure used to show the converse of the Pythagorean Theorem is given as follows:
D. Knowing that 3² + 4² = 5², draw the 3-foot side and the 4-foot side with a right angle between them. The five foot side will fit to form a right triangle.
What is the Pythagorean Theorem?The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.
Hence:
h² = 3² + 4²
h² = 25
h = 5.
The hypotenuse has the larger side length, hence the sides that are connected by the right triangle must be the two smaller sides, the three foot side and the four foot side, hence option D is correct.
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Next assume that Mr. Hyper Chonder cannot get perfect information, but that he can consult a doctor. After a medical exam, the doctor evaluates Mr. Hyper Chonder as fit or unfit for travel. Mr. Hyper Chonder believes that if the doctor finds that he will stay healthy, there is an 80 percent chance that the doctor also evaluates him as fit to travel and a 20 percent chance that he evaluates him as unfit to travel. These subjective conditional probabilities are: P(Fit Healthy) = 0.8 P(Unfit Healthy) = 0.2 Likewise, Mr: Hyper Chonder believes that if the doctor finds that he will become sick, there is still a 40 percent chance that the doctor evaluates him as fit to travel and a 60 percent chance that he evaluates him as unfit to travel. These subjective conditional probabilities are: P(Fit | Sick) = 0.4 P(Unfit Sick) = 0.6 - Fit p(Fit Healthy)=0.8 Healthy 120 p(Healthy)-0.25 Travel Unfit p(Unfit Healthy)=0.2 Fit p(Fit | Sick)=0.4 Sick -40 p(Sick)=0.75 Home 20 Unfit p(Unfit | Sick)=0.6 With which probability does Mr. Hyper Chonder expect to receive a "Fit for travel" evaluation, which is P(Fit)= 0.25 0.5 0.75 None of the above. With which probability does Mr. Hyper Chonder expect to receive an "Unfit for travel" evaluation, which is P(Unfit)= O 0.25 0.5 0.75 None of the above. Assume that the doctor tells Mr. Hyper Chonder that he is fit for travel, which probability does Mr. Hyper Chonder now assign to staying healthy, which is P(Healthy Fit) = 0.3 00.4 0.5 n Assume that the doctor tells Mr. Hyper Chonder that he is unfit for travel, which probability does Mr. Hyper Chonder now assign to staying healthy, which is P(Healthyl Unfit) = O 0.05 O 0.1 0 0.2 00.4 Assume that the doctor tells Mr. Hyper Chonder that he is unfit for travel, which probability does Mr. Hyper Chonder now assign to getting sick, which is P(Sick | Unfit) = 0.3 O 0.6 O 0.9 0.95 Assume the doctor tells Mr. Hyper Chonder that he is fit to travel, what will Mr. Hyper Chonder do? He will travel and expect 24 utils He will travel and expect 28 utils He will travel and expect 32 utils He will not travel. Assume the doctor tells Mr. Hyper Chonder that he is unfit to travel, what will Mr. Hyper Chonder do? He is now indifferent between travelling and staying home He will travel and expect 22 utils He will travel and expect 24 utils He will not travel.
Answers
If the doctor tells Mr. Hyper Chonder that he is fit for travel, he will travel and expect 28 utils, and if the doctor tells him that he is unfit for travel, he will not travel and expect 24 utils.
Mr. Hyper Chonder expects to receive a "Fit for Travel" evaluation with a probability of P(Fit) = 0.25 and an "Unfit for Travel" evaluation with a probability of P(Unfit) = 0.75. He believes that if the doctor finds that he will stay healthy, there is a P(Fit Healthy) = 0.8 chance of being evaluated as fit to travel and a P(Unfit Healthy) = 0.2 chance of being evaluated as unfit to travel. If the doctor finds that he will become sick, there is a P(Fit | Sick) = 0.4 chance of being evaluated as fit to travel and a P(Unfit | Sick) = 0.6 chance of being evaluated as unfit to travel.
If the doctor tells Mr. Hyper Chonder that he is fit for travel, he assigns a probability of P(Healthy | Fit) = 0.8 to staying healthy. If the doctor tells him that he is unfit for travel, he assigns a probability of P(Healthy | Unfit) = 0.2 to staying healthy and a probability of P(Sick | Unfit) = 0.8 to getting sick.
If the doctor tells Mr. Hyper Chonder that he is fit for travel, he will travel and expect a utility of 28 utils. If the doctor tells him that he is unfit for travel, he will not travel and expect a utility of 24 utils.
If the doctor tells Mr. Hyper Chonder that he is fit for travel, he will travel and expect 28 utils, and if the doctor tells him that he is unfit for travel, he will not travel and expect 24 utils.
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Estimate the value of x that results in y=2
Answers
Answer:
I believe it is about 3
Step-by-step explanation:
Go to y=2 then move across until you hit the line.
HELPP PLEASE
Line M goes through the points (-2, -8) and (1, 1). Which pair of points lies on a straight line that intersects Line M?
OA (0, 2), (1, 5)
OB. (-2, -1), (3, 14)
O C. (2, 1), (-5, -20)
OD. (-3, -2), (2, 6)
Answers
first off let's find the slope of M
[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{-8})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{1}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{1}-\stackrel{y1}{(-8)}}}{\underset{\textit{\large run}} {\underset{x_2}{1}-\underset{x_1}{(-2)}}} \implies \cfrac{1 +8}{1 +2} \implies \cfrac{ 9 }{ 3 } \implies \text{\LARGE 3}[/tex]
now, any line that intersects M will have a different slope than M, and since they're both lines and going to infinity, they will intersect at some point, so let's check those points for their slope, who is different than M's
[tex]\boxed{A}\qquad (\stackrel{x_1}{0}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{5}-\stackrel{y1}{2}}}{\underset{\textit{\large run}} {\underset{x_2}{1}-\underset{x_1}{0}}} \implies \cfrac{ 3 }{ 1 } \implies 3 ~~ \bigotimes \\\\[-0.35em] ~\dotfill[/tex]
[tex]\boxed{B}\qquad (\stackrel{x_1}{-2}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{14}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{14}-\stackrel{y1}{(-1)}}}{\underset{\textit{\large run}} {\underset{x_2}{3}-\underset{x_1}{(-2)}}} \implies \cfrac{14 +1}{3 +2} \implies \cfrac{ 15 }{ 5 } \implies 3 ~~ \bigotimes \\\\[-0.35em] ~\dotfill[/tex]
[tex]\boxed{C}\qquad (\stackrel{x_1}{2}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{-5}~,~\stackrel{y_2}{-20}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-20}-\stackrel{y1}{1}}}{\underset{\textit{\large run}} {\underset{x_2}{-5}-\underset{x_1}{2}}} \implies \cfrac{ -21 }{ -7 } \implies 3 ~~ \bigotimes \\\\[-0.35em] ~\dotfill[/tex]
[tex]\boxed{D}\qquad (\stackrel{x_1}{-3}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{6}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{6}-\stackrel{y1}{(-2)}}}{\underset{\textit{\large run}} {\underset{x_2}{2}-\underset{x_1}{(-3)}}} \implies \cfrac{6 +2}{2 +3} \implies \cfrac{ 8 }{ 5 } ~~ \textit{\LARGE \checkmark}[/tex]
Solve the inequality: −u² ≤ −2u+5
Give answer in interval notation.
I put DNE as the answer but I got it wrong and don't know where I went wrong
Answers
The solution to the inequality 0 ≤ u² - 2u + 5 is all real numbers.
What is the solution of the inequality?
The solution of the inequality is calculated by applying the following method as shown below.
−u² ≤ −2u + 5
0 ≤ u² - 2u + 5
Now, to find the zeros of this quadratic equation, we can use the quadratic formula:
u = (-b ± √(b² - 4ac)) / 2a
where;
a = 1,
b = -2, and
c = 5.
u = (2 ± √(2² - (4 x 1 x 5)) / (2 x 1 )
u = (2 ± √(-16)) / 2
Since the square root of a negative number is not defined in real numbers, this means that the quadratic equation has no real zeros.
But we can still find the solution to the inequality by using the fact that a parabolic function y = ax² + bx + c is greater than or equal to 0 when it has x-intercepts that are both real and positive.
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Determine whether y varies directly with x. If so find the constant of variation k and write the equation.
x y
4 6.4
7. 11.2
10 16
13. 20.8
Please show the steps
Answers
In this situation, y varies directly with x since the constant of variation, k, is 1.6 and can be represented by the equation, y = 1.6x.
What is the constant of variation?The constant of variation refers to the ratio or unit rate (slope) between two variables in a direct variation.
In an inverse variation, the constant of variation is the product of the two variables of interest.
In this situation, the constant of variation is the quotient of the division operation between y and x.
x y Ratio
4 6.4 1.6 (6.4/4)
7. 11.2 1.6 (11.2/7)
10 16 1.6 (16/10)
13. 20.8 1.6 (20.8)
Thus, as y increases, x directly increases at a constant rate of 1.6.
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1
0
5
2 points
Determine whether 0.34567 is rational or irrational
irrational
rational
Previous
Answers
Answer:
eefawdfa
Step-by-step explanation:
to do cool u do cool 69696969
Last year, the numbers of skateboards produced per day at a certain factory were normally distributed with a mean of 20,300 skateboards and a standard deviation of 60 skateboards. On what percent of the days last year did the factory produce 20,420 skateboards or fewer? On what percent of the days last year did the factory produce 20,240 skateboards or fewer? On what percent of the days last year did the factory produce 20,480 skateboards or more?
Answers
The percentages are given as follows:
20,240 skateboards or fewer: 15.87%.20,420 skateboards or fewer: 97.72%.20,480 skateboards or more: 0.13%.How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation for this problem are given as follows:
[tex]\mu = 20300, \sigma = 60[/tex]
The proportion of 20,240 of fewer is the p-value of Z when X = 20240, hence:
Z = (20240 - 20300)/60
Z = -1
Z = -1 has a p-value of 0.1587.
The proportion of 20,420 of fewer is the p-value of Z when X = 20420, hence:
Z = (20420 - 20300)/60
Z = 2
Z = 2 has a p-value of 0.9772.
The proportion of 20480 or more is one subtracted by the p-value of Z when X = 20480, hence:
Z = (20480 - 20300)/60
Z = 3
Z = 3 has a p-value of 0.9987.
1 - 0.9987 = 0.0013.
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