The result after the point is translated is (-5, -5)
How to detemrine the result of the transformationFrom the question, we have the following parameters that can be used in our computation:
Point = (-9, -2)
The transformation rule is given as
translation left 4 units and down 3 units
Mathematically, this is represented as
(x, y) = (x + 4, y - 3)
So, we have
Image = (-9 + 4, -2 -3)
Evaluate
Image = (-5, -5)
Hence, the image is (-5, -5)
Read more about transformation at
https://brainly.com/question/27224272
#SPJ1
Consider the first order differential equation y' + t/t2 + 9y = et/t - 5. For each of the initial conditions below, determine the largest interval a < t < b on which the existence and uniqueness theorem for first order linear differential equations guarantees the existence of a unique solution. y(-7) = 6. 4. help (Inequalities) y(-2. 5) = -0. 5. help (inequalities') y(0) = 0. help (inequalities') y(4. 5) = -2. 1. help ('inequalities') y(14)= 1. 7. help ('inequalities')
These intervals were calculated assuming that the differential equation coefficients and initial value are continuous on the intervals. Additional analysis may be required in practice to confirm the precise duration of existence and uniqueness.
The existence and uniqueness theorem for first order linear differential equations states that if the differential equation's coefficients and the initial value are continuous on an interval containing the initial value, then the differential equation has a unique solution on that interval.
y(-7) = 6: The existence and uniqueness theorem ensures that a unique solution exists in the interval -8 t -6.The existence and uniqueness theorem ensures the existence of a unique solution in the interval -3 t -2.y(0) = 0: The existence and uniqueness theorem ensures that a unique solution exists in the interval -1 t 1.y(4.5) = -2.1: The existence and uniqueness theorem ensures that a unique solution exists in the interval 4 t 5.y(14) = 1.7: The existence and uniqueness theorem ensures that a unique solution exists in the interval 13 t 15.It should be noted that these intervals were determined under the assumption that the differential equation coefficients and initial value are continuous on the intervals. In practice, additional analysis may be required to confirm the precise duration of existence and uniqueness.
To learn more about differential equation.
https://brainly.com/question/14620493
#SPJ4
the following questions all refer to properties of the sample mean of education () which is an estimator constructed from a random sample of size drawn from the population.
The correct option is D, The probability that the Z-transform is greater than 2 in absolute value Pr (Z] > 2) is approximately 5%.
The Empirical rule states that 2 standard deviation from mean contains 95% data.
For, Z follows standard normal distribution.
[tex]Z ~ Normal(\mu=0, \sigma=1)[/tex]
Then,
P( -2 ≤ Z≤ +2) = 0.95
Or
P(|Z| ≤ 2) = 0.95
And
P( |Z|>2) = 1 - P(|Z|≤2)
P(|Z|>2) = 1- 0.95
P(|Z|>2) = 0.05 = 5%
Probability is a mathematical concept that deals with the likelihood of events or outcomes. It is expressed as a number between 0 and 1, with 0 meaning no chance of an event occurring and 1 meaning that an event is certain to occur. In probability theory, random experiments are performed and the results are analyzed to determine the probability of specific outcomes.
For example, if you roll a dice, there are 6 possible outcomes and each outcome has a probability of 1/6. In statistics, probabilities are used to make predictions and to analyze data. The use of probabilities is essential in fields such as insurance, finance, and decision making as it provides a framework for making decisions based on uncertain information. Probability is an important tool for understanding and making decisions about the world around us.
To learn more about Probability visit here:
brainly.com/question/30034780
#SPJ4
Complete Question: -
Suppose that in a population of interest, a random variable education, which measures an individual's educational attainment in years, has a mean of 13.20 =13.2) and a variance of 9 o? = 9 ). The following questions all refer to properties of the sample mean of education ( education ) which is an estimator constructed from a random sample of size n = 100 drawn from the population. Question 4 1 pts The probability that the Z-transform is greater than 2 in absolute value Pr (Z] > 2) is approximately: O 2.5% 95% unknown O 5%
CAN SOMEONE HELP WITH THIS QUESTION?
The greater solution of x is x = -12 + 2√3 ÷ 3, and the lesser solution is x = -12 ± 2√3 ÷ 3.
What is differentiation?Apart from integration, differentiation is one of the two key ideas in calculus. A technique for determining a function's derivative is differentiation. Mathematicians use a process called differentiation to determine a function's instantaneous rate of change based on one of its variables. The most typical illustration is velocity, which is the rate at which a distance changes in relation to time. Finding an antiderivative is the opposite of differentiation.
The given function [tex]f(x) = \frac{x}{x + 4}[/tex].
The differentiation of the function is:
[tex]f'(x) = \frac{g(x)f'(x) - f(x)g'(x)}{g(x)^2} \\\\f'(x) = \frac{(x+4)(1) - x(1)}{(x+1)^2}\\\\f'(x) = \frac{x + 4 - x}{(x+4)^2} \\\\f'(x) = \frac{4}{(x+4)^2}[/tex]
The value of f'(x) = 3:
Thus,
3 = 4/ (x + 4)^2
3(x + 4)^2 = 4
3(x² + 8x + 16) = 4
3x² + 24x + 48 - 4 = 0
3x² + 24x + 44= 0
Use the quadratic formula to find the roots of the equation:
x = -12 ± 2√3 ÷ 3
Hence, the greater solution of x is x = -12 + 2√3 ÷ 3, and the lesser solution is x = -12 ± 2√3 ÷ 3.
Learn more about differentiation here:
https://brainly.com/question/24898810
#SPJ1
4. Ettienne wants to calculate the cost of his electric bill. He is on a standard use plan that has a
graduated fee schedule.
Standard Use Plan
8.5 cents/kWh for the first 400 kWh
12 cents/kWh for the next 400 kWh
14.5 cents/kWh for anything over 800 kWh
How much will his bill be if he uses 1,895 kWh? Round to the nearest dollar.
The total cost for the electric bill is given by the equation A = $ 241
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the total cost for the electric bill be A
Now , the equation will be
The amount of electricity used by Ettienne = 1,895 kWh
And , the standard plan is
8.5 cents/kWh for the first 400 kWh
12 cents/kWh for the next 400 kWh
14.5 cents/kWh for anything over 800 kWh
So , for the first 400 kWh , the cost is = 400 x 8.5 = 3,400 cents
And , for the next 400kWh , the cost is = 400 x 12 = 4,800 cents
And , the remaining units of electricity is = 1,895 - 800 = 1,095 kWh
So , for the next 1,095kWh, the cost is = 1,095 x 14.5 = 15,877.5 cents
Therefore , the total cost for 1,895kWh = 3,400 cents + 4,800 cents + 15,877.5 cents
On simplifying the equation , we get
The total cost for 1,895kWh A = 24,077.5 cents
The total cost for 1,895kWh A = $ 240.77
The total cost for 1,895kWh A = $ 241
Hence , the equation is A = $ 241
To learn more about equations click :
https://brainly.com/question/19297665
#SPJ1
A dressmaker needs to cut 12-inch pieces of ribbon from rolls of ribbon that are 3 feet in length. How many 12-inch pieces can the dressmaker cut from 10 of these rolls of ribbon?
Before you try that problem, answer the question below.
How many inches of ribbon does the dressmaker have, in total?
The 12-inch pieces the dressmaker can cut from 10 of these rolls of ribbon will be 30 strips.
What is the unitary method?The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
Given a dressmaker has a ribbon of 3 feet in length,
and he has a total of 10 rolls,
total length of ribbon = 10*3 = 30 feet
and 1 feet = 12 inches
30 feet = 12*30 inches
30 feet = 360 inches
the dressmaker has 360 inches of ribbon.
The dressmaker needs to cut 12-inch pieces of ribbon from rolls of ribbon that are 3 feet in length.
The number of rolls she has = 10 rolls
so,
12 inches strips from 360 inches of ribbon
= 360/12 = 30 strips.
Hence the dressmaker can make 30 strips of 12 inches from 360 inches of total ribbon.
Learn more about the unitary method;
brainly.com/question/23423168
#SPJ1
consider the expression\[x^2 \boxed{\phantom{00}}x 100.\] find all possible values for the missing number that make this expression the square of a binomial.
The missing number must make the expression a perfect square trinomial in the form [tex](a + b)^2[/tex].
This means that the missing number must be equal to the product of the two factors outside the parentheses, minus the square of the number inside the parentheses.
In this case, the missing number must be equal to [tex]100x^2 - x^2, or 99x^2[/tex].
Using the FOIL method (First, Outer, Inner, Last), we can expand [tex](x + x)^2 to get x^2 + 2x^2 + x^2[/tex]. Since the expression we are working with is [tex]100x^2 + 2x^2 + x^2[/tex], the missing number is [tex]99x^2[/tex].
Therefore, the missing number that makes this expression the square of a binomial is [tex]99x^2[/tex].The missing number must make the expression a perfect square trinomial in the form [tex](a + b)^2[/tex].
Learn more about perfect square trinomial here:
https://brainly.com/question/88561
#SPJ4
Select the equation and solution for the number of weeks, x, it takes her to have $150 left to pay. -18.75x + 600 = 150 Clarissa's sister will have $150 left to pay after 24 weeks. 18.75x − 150 = 600 Clarissa's sister will have $150 left to pay after 8 weeks. 18.75x − 600 = 150 Clarissa's sister will have $150 left to pay after 8 weeks. -18.75x + 150 = 600 Clarissa's sister will have $150 left to pay after 24 weeks.
Clarissa's sister will have $150 left to pay after 24 weeks.
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 the equation as -
- 18.75x + 600 = 150
The given equation is -
- 18.75x + 600 = 150
- 18.75x = - 450
x = (450/18.75)
x = 24 weeks
Therefore, Clarissa's sister will have $150 left to pay after 24 weeks.
To solve more questions on functions, visit the link below -
brainly.com/question/26182329
#SPJ1
An urn contains 4 blue and 8 red balls. Two balls are selected randomly. We define E as the event that the first ball is blue and F as the event that the second ball is blue. Which one of the following statements is correct? E and F are always independent E and F are independent if after selecting the first ball we do not place it back in the urn (without replacement). E and F are independent if after selecting the first ball we place it back in the urn (with replacement).
The correct statement is: "E and F are independent if after selecting the first ball we do not place it back in the urn (without replacement)."
An event is independent if the occurrence of one event does not affect the probability of the other event.
In this case:
E and F are not always independent, because the occurrence of E (the first ball is blue) does affect the probability of F (the second ball is blue).
E and F are independent if after selecting the first ball we do not place it back in the urn (without replacement). In this case, the probability of F remains constant, regardless of the occurrence of E.
E and F are not independent if after selecting the first ball we place it back in the urn (with replacement). In this case, the occurrence of E affects the number of blue balls in the urn, and hence affects the probability of F.
For more questions on Probability
https://brainly.com/question/24756209
#SPJ4
need help on This question I’ll give you brainliest
The area swept by the blade in model 3 is 66932 square feet.
What is area?An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure. The word "area" refers to a free space. A shape's length and width are used to calculate its area. Unidimensional length is expressed in terms of feet (ft), yards (yd), inches (in), etc. But a shape's area is a two-dimensional measurement.
The blade length for model 3 is r = 146.
The area of the circle is given by:
A = pi(r)²
A= (3.14) (146)²
A = 66932
Hence, the area swept by the blade in model 3 is 66932 square feet.
Learn more about area here:
https://brainly.com/question/27683633
#SPJ1
How many 1 1/2 foot pieces can be cut from a 12 foot length of ribbon. what was diedred’s first error
Answer:11
Step-by-step explanation: yup
FILL IN THE BLANK the reason why response scales are generally limited to less than_________ options is that anything over this number creates meaningless distinctions.
The reason why response scales are generally limited to less than ten options is that anything over this number creates meaningless distinctions.
Response scales are generally limited to no more than ten options because any more than this creates meaningless distinctions. If there are too many options, it becomes difficult to make meaningful comparisons between the responses. Additionally, it becomes more difficult to interpret the data when there are too many options. By having fewer options, it is easier to make more accurate comparisons and more meaningful interpretations. This number helps to make sure that the data collected is accurate and useful. Having fewer options also helps to reduce the amount of time it takes to collect and analyze the data.
learn more about number here
https://brainly.com/question/10547079
#SPJ4
additive inverse for 10x-1
Answer: -10
Step-by-step explanation:
What is the value of n? 30 POINTSS!
10 < n < 12 gives the equivalent solution to the given system of equation.
Inequality expressionsInequality expressions are expressions not separated by an equal sign.
From the given expression, the equivalent inequalities are given as:
n > 0
2n > 20
5n > 60
For the expression 2n > 20
n > 20/2
n > 10
Similarly;
5n < 60
n < 60/5
n < 12
Hence the solution to the given expressions are 10 < n < 12
Learn more on inequality here: https://brainly.com/question/24372553
#SPJ1
If f(x) = 2x2 − 3x + 4, then f(x + 3) is equal to
a.
2x2 − 3x + 7
b.
2x2 − 3x + 13
c.
2x2 + 9x + 13
d.
2x2 + 9x + 25
Answer:
B
Step-by-step explanation:
please refer to the sketch for details
Select the correct answer equation and then solve for x
Answer:
Step-by-step explanation:
27/x
A trailer weighs one and one-half tons. There are 200 pounds of hay on
Answer:
3200
Step-by-step explanation:
1 1/2 US tons is 3000 pounds. Add the 200 pounds of hay and you get 3200. Hope this helps.
It takes 1100 J of work to stretch a spring from its natural length of 1 m to a length of 6 m. Find the force constant of the spring. The spring's force constant is N/m. (Type a simplified fraction.)
The spring constant for the stretched spring is 62.86 N/m.
The formula to be used for calculation of spring constant is -
W = 1/2kx², where W is work done, k is spring constant and x refers to stretched distance. For the mentioned question, x will be -
x = (final x² - initial x²)
Keep the values in formula to find the value of k
1100 × 2 = k (6² - 1²)
Performing multiplication on Left Hand Side and taking square on Right Hand Side of the equation
2200 = k (36 - 1)
k = 2200/35
Performing division on Right Hand Side of the equation
k = 62.86 N/m
Learn more about spring constant -
https://brainly.com/question/22712638
#SPJ4
find the minimum value of the function f(x)=2x^2+8.1x+15.4 to the nearest hundredth.
The minimum value of the function f(x) = 2x^2 + 8.1x + 15.4 is 15.96 to the nearest hundredth.
What is minimum value ?Minimum value is the lowest y-value the function reaches.
The minimum value of a parabolic function like f(x) = 2x^2 + 8.1x + 15.4 is achieved at the vertex of the parabola.
The x-coordinate of the vertex is given by the formula:
x = -b / (2a
where a = 2, b = 8.1, and c = 15.4.
Plugging in these values, we get:
x = -8.1 / (2 * 2) = -2.05
So, the x-coordinate of the vertex is -2.05. To find the y-coordinate (i.e., the minimum value of the function), we plug in this x-coordinate and solve for y:
y = f(-2.05) = 2(-2.05)^2 + 8.1(-2.05) + 15.4 = 15.96
So, the minimum value of the function f(x) = 2x^2 + 8.1x + 15.4 is 15.96 to the nearest hundredth.
Learn more about minimum value here: brainly.com/question/16381250
#SPJ1
Use the composite figurine to estimate the area of the figure the grid has squares with side lengths of 1 cm
The area of the composite figure is 40.65 cm².
What is a rectangle?A rectangle is a two-dimensional shape where the length and width are different.
The area of a rectangle is given as:
Area = Length x width
We have,
The composite figure can be made into two shapes.
a) Rectangle with a length of 4 cm and breadth = 3 cm
b) Two semicircles with diameters of 3 cm and 4 cm.
So,
r = 3/2 cm and r = 4 cm
Now,
Area of the rectangle.
= length x breadth
= 4 x 3
= 12 cm²
Area of the one semicircle with r = 3/2 cm
= 1/2 x πr²
= 1/2 x 3.14 x (3/2)²
= 1/2 x 3.14 x 9/4
= 3.53 cm²
Area of the one semicircle with r = 4 cm
= 1/2 x πr²
= 1/2 x 3.14 x 4²
= 1/2 x 3.14 x 16
= 25.12 cm²
Now,
Area of the composite figure.
= 12 + 3.53 + 25.12
= 40.65 cm²
Thus,
The area of the composite figure is 40.65 cm².
Learn more about rectangles here:
https://brainly.com/question/15019502
#SPJ1
g use the method of cylindrical shells to find the volume v generated by rotating the region bounded by the given curves about the y-axis. y
Cylindrical shells: finding volume by rotating region around y-axis by integrating thin cylindrical shell area with height dr and radius f(x) over an interval.
To find the volume generated by rotating a region about the y-axis using the method of cylindrical shells, you need to integrate the area of a thin cylindrical shell with height dr and radius f(x) (where f(x) is the equation of the boundary curve) over the interval of x.
The volume generated by rotating the region bounded by the given curves can be found using the following formula:
[tex]V=\pi \int\limits[a,b] {(f(x))^{2} } \, dr[/tex]
Here, a and b are the lower and upper limits of the interval, and f(x) is the equation of the boundary curve. The integration should be performed over the given interval to obtain the volume.
In essence, the method of cylindrical shells involves wrapping the region around the y-axis to form a series of cylindrical shells and finding the volume of each shell, then summing up all the volumes to get the final volume.
Learn more about volume here:
https://brainly.com/question/13807002
#SPJ4
Nick divides 527 baseball cards evenly into 17 stacks. How many baseball cards are in each stack? Use the mode
Answer:
31
Step-by-step explanation:
I'm not sure if it's possible to use mode in this equation. To find the number of cards in each stack, you just need to divide 527 by 17 and you'll find your answer.
527/17 = 31
A survey of 300 SPC students was taken at registration. Of those surveyed:
52 students had signed up for a Language Arts course
40 students had signed up for a Humanities course
23 students had signed up for both a Math and Language Arts course
6 students had signed up for both a Math and Humanities course
8 students had signed up for both a Language Arts and Humanities course
3 students had signed up for all three courses
8 students did not sign up for any of these classes
How many students signed up for only Math (of these three)?
243 students signed up for only Math.
What are sets?The way that sets are represented by a person is always the same: as a group of clearly defined objects or elements. A capital letter designates a set. The cardinal number of a set is the number of elements in the finite set.
Given A survey of 300 SPC students
let L denote language, H for humanities, and M for maths,
and given, n(L ∪ H ∪ M) = 300
n(L) = 52, students had signed up for a Language Arts course
n(H) = 40, students had signed up for a Humanities course
n(M) = students signed up for only Math
LM = 23, students had signed up for both a Math and Language
MH = 6, students had signed up for both Math and Humanities
LH = 8, students had signed up for both a Language Arts and Humanities
n(LHM) = 3 students had signed up for all three courses
n(LM) = 23 + 3 = 26
n(MH) = 6 +3 = 9
n(LH) = 8 + 3 = 11
8 students did not sign up for any of these classes
using the formula of triple intersection,
n(L ∪ H ∪ M) = n(L) + n(H) + n(M) - n(LM) - n(MH) - n(LH) + n(LHM).
300 - 8 = 52 + 40 + n(M) - 26 - 9 - 11 + 3
n(M) = 292 - 49
n(M) = 243
Hence 243 students signed up for only Math.
Learn more about sets;
brainly.com/question/8053622
#SPJ1
Simplify the expression
3/4 (z+2/5) + 2z
The simplified form of the expression 3/4 (z+2/5) + 2z is (37z + 6)/20.
What is an expression?One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is the number used before a phrase.
Given:
An expression,
3/4 (z+2/5) + 2z.
Simplifying,
= 3/4 (5z + 2)/5 + 2z.
= (15z + 6)/20 + 2z
= (37z + 6)/20
Therefore, the expression is (37z + 6)/20.
To learn more about the expression;
brainly.com/question/24242989
#SPJ1
Give the value of c in the interval [0,2] that satisfies the conclusion of the mean value theorem for g(x) = -3 root x + 2. a) 0 b) 2 c) 1/2 d) 3/2 e) 5/2
There exists a value of c in the interval [0,2] such that g(c) = 1, and that value is c = 1/2. (option c)
The mean value theorem states that for any continuous function over a closed interval, there exists a point at which the value of the function is equal to the average of the minimum and maximum values of the function. In this case, the interval is [0,2] and the function is g(x) = -3√x + 2.
To find the value of c, we need to find the average of the minimum and maximum values of g(x) in the interval [0,2]. The minimum value of g(x) in the interval is g(0) = 2, and the maximum value is g(2) = -3√2 + 2 = 0. The average of the minimum and maximum values is (0 + 2)/2 = 1. Hence, there exists a value of c in the interval [0,2] such that g(c) = 1, and that value is c = 1/2.
Learn more about the mean value theorem:
https://brainly.com/question/30403137
#SPJ4
Find the slope of a line parallel to the line whose equation is 2x + 2y = -12. Fully
simplify your answer.
Safeco growth rate for the future is 8% recent dividends 1.76
What is the value of the stock when the required return is 10%
The value of the stock at 10 percent is given as 88 dollars
How to solve for the value of the stock
The value of a stock can be estimated using the Gordon Growth Model, which takes into account the company's future growth rate, recent dividends, and the required return of the investor. The formula for the Gordon Growth Model is:
Stock Price = Dividend / (Required Return - Growth Rate)
Plugging in the given values, we have:
Stock Price = 1.76 / (0.10 - 0.08)
Stock Price = 1.76 / 0.02
Stock Price = 88
Therefore, the estimated value of the Safeco stock is $88 when the required return is 10%. This estimate assumes that the company's future growth rate and dividends will remain constant at 8% and 1.76, respectively.
Read more on value of the stock here:https://brainly.com/question/25765493
#SPJ1
Solve for x and graph the solution on the number line below. x+6≥16
Answer:
x≥10
Step-by-step explanation:
Answer:
x ≥ 10
Step-by-step explanation:
To solve for x, we simply have to subtract 6 from both sides.
x + 6 ≥ 16
- 6 - 6
x ≥ 10
Then, we can graph this inequality on the number line.
(See the attached image)
The graph shows the number of pies produced at a bakery as a function of time.Calculate the rate of change.Explain what the rate of change means in context to the situation.
Answer:
15
Step-by-step explanation:
since the graph is proportional we can divide 30 by 2 we get 15
to double check we will divide 60 by 4 and we also get 15
so 15 pies are produced every hour
I need the answer for only 1c and explanation of what happens to the numerator.
The solution is, by integrating ∫(3-2x)^10 dx using substitution, we get, -1/22.(3-2x)^11 +C.
What is integration?In mathematics, an integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data. The process of finding integrals is called integration.
here, we have,
∫(3-2x)^10 dx
now, let, 3-2x=u
so, -2. dx = du
i.e. by substitution we get,
∫u^10 du/-2
=1/-2 . ∫u^10 du
we know, ∫x^n= x^n+1/ (n+1) +c
so, we get,
⇒1/-2.1/11. u^11 +C
=-1/22.(3-2x)^11 +C
where, c=constant.
Hence, The solution is, by integrating ∫(3-2x)^10 dx using substitution, we get, -1/22.(3-2x)^11 +C.
To learn more on integration click:
https://brainly.com/question/26568631
#SPJ1
An analyst constructed the following frequency distribution on the monthly returns for 50 selected stocks. Class (in percent) Frequency –10 up to 0 8 0 up to 10 25 10 up to 20 15 20 up to 30 2 The proportion of stocks with returns of less than 10% is _____
The proportion of stocks with returns of less than 10% is 43%.
To find the proportion of stocks with returns of less than 10%, we add up the frequencies of the first two classes in the frequency distribution: 8 + 25 = 33. This number represents the total number of stocks with returns of less than 10%. To find the proportion, we divide this number by the total number of stocks (50) and multiply by 100%: (33/50) * 100% = 66%. This means that 66% of the stocks had returns less than 10%.
Learn more about Frequency Distribution here:
https://brainly.com/question/17114842
#SPJ4