The x-values at which the function f(x) is differentiable are all real numbers, excluding those values where the derivative is undefined. This can be expressed using interval notation as (-∞, -4) ∪ (-4, 0) ∪ (0, 4) ∪ (4, ∞).
The function mentioned is a continuous function on the interval 4 < x < 5, h(x), which is described in the table provided. This function has a vertical asymptote at 4 and 5, meaning that its values approach positive or negative infinity at these points.
The function's domain is 4 < x < 5, meaning that it is defined and can take a value for any x within this interval. The function's range is not specified, so it can take any value for an x within the given interval. Additionally, the function is differentiable for all values of x within the given interval, meaning that its rate of change can be calculated using derivatives.
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Southeast Electric charges $0.09 per kilowatt-hour for the first 200 kWh. The company charges $0.11 per kilowatt-hour for all electrical usage in excess of 200 kWh. How many kilowatt-hours were used if a monthly electric bill was $57.06?
Therefore , the solution of the given problem of unitary method comes out to be 555.09 kWh is the total energy used.
Define unitary method.To finish a work using the unitary strategy, multiply the amount by two after determining the size of the small slice. The unit technique, to put it simply, works to isolate a programming object from a specific group or sets of sets. For instance, 40 pens would cost 400 pounds ($1.01) and Rs. There is a chance that one nation will have complete control over the technique used to do this. Almost all living things have a unique trait. Both integration and reciprocity are possible (mathematics, algebra).
Here,
Given :
For the first 200 kWh, Electric charges $0.09 per kilowatt-hour
For any electricity usage after 200 kWh, the firm charges $0.11 per kilowatt-hour.
Thus ,
for 200kWh hour cost = 0.09 * 200 = $18
thus ,
total bill was after 200 kWh = 57.06 - 18 = 39.06
Thus,
=> 39.06/0.11 = 355.09
Thus , total Kwh used is : 355.09 + 200 = 555.09 kWh
Therefore , the solution of the given problem of unitary method comes out to be 555.09 kWh is the total energy used .
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Which of the following vectors is shown in the graph below?
The vector shown in figure is, (- 2, 1 , - 4)
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The graph of the vectors is shown below.
Now, By definition of vectors the sign of coordinates are, ( - , + , - )
Thus, By options the coordinate of vectors are,
⇒ (- 2, 1 , - 4)
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a block attached to a spring with unknown spring constant oscillates with a period of 3.4 s . parts a to d are independent questions, each referring to the initial situation.
The period of oscillation of a spring-block system is most affected by changes in the mass and the spring constant, while changes in the amplitude do not affect the period.
The period of oscillation of a spring-block system is a measure of the time it takes for the block to complete one full cycle of its motion and is dependent on the mass of the block, the spring constant, and the amplitude of the oscillation.
a. If the mass is halved, the system becomes less stiff, and the period of oscillation increases.
b. Doubling the amplitude of the oscillation only changes the magnitude of the displacement and does not affect the period of oscillation.
c. If the spring constant is doubled, the system becomes stiffer, and the period of oscillation decreases.
d. If the mass is doubled, the system becomes more massive, and the period of oscillation increases.
In conclusion, the period of oscillation of a spring-block system is most affected by changes in the mass and the spring constant, while changes in the amplitude do not affect the period.
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The correct question is :
A block attached to a spring with unknown spring constant oscillates with a period of 3.4 s. Parts a to d are independent questions, each referring to the initial situation. What is the period if
a. The mass is halved?
b. The amplitude is doubled?
c. The spring constant is doubled?
d. The mass is doubled?
The diameter of a ball bearing was measured by 12 inspectors, each using two different kinds of calipers. The results are as follows: Inspector Caliper 1 Caliper 2 0.264 1 2 0.265 0.264 0.266 3 4 5 6 0.265 0.265 0.266 0.267 0.267 0.265 0.267 0.267 0.265 0.268 0.267 0.268 0.264 7 8 9 0.265 0.265 0.267 10 11 0.268 0.268 12 0.265 0.269 (a) Is there a significant difference between the means of the population of measurements from which the two sam- ples were selected? Use a = 0.05. (b) Find the P-value for the test in part (a). (c) Construct a 95 percent confidence interval on the differ- ence in mean diameter measurements for the two types of calipers.
The P-value for the test is 1.804 and the 95 percent confidence interval on the difference in mean diameter measurements for the two types of calipers is [-0.00147, 0.00347].
a) To determine if there is a significant difference between the means of the population of measurements from which the two samples were selected, we can use a two-tailed t-test. We can calculate the t-statistic as follows:
t = (x1 - x2) / sqrt[((s1^2)/n1) + ((s2^2)/n2)]
where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.
For this example, the sample means are x1 = 0.266 and x2 = 0.267. The sample standard deviations are s1 = 0.0017 and s2 = 0.0015. The sample sizes are n1 = 12 and n2 = 12.
Plugging these values into the formula, we get:
t = (0.266 - 0.267) / sqrt[((0.0017^2)/12) + ((0.0015^2)/12)] = -0.145
The critical t-value for a two-tailed test at a significance level of 0.05 with 11 degrees of freedom is 2.201. Since our calculated t-value of -0.145 is not greater than the critical t-value, we can conclude that there is not a significant difference between the means of the population of measurements from which the two samples were selected.
b) The P-value for the test in part (a) is the probability of obtaining a test statistic as extreme as the one we calculated (or more extreme) if the null hypothesis is true. We can calculate this probability as follows:
P = 2 * P(t <= -0.145)
where P(t <= -0.145) is the cumulative probability of the t-distribution with 11 degrees of freedom at -0.145.
Using the t-distribution table, the cumulative probability of t at -0.145 is 0.902. Thus, the P-value for the test in part (a) is P = 2 * 0.902 = 1.804.
c) To construct a 95 percent confidence interval on the difference in mean diameter measurements for the two types of calipers, we can use the following formula:
CI = [x1 - x2 +/- t(alpha/2, df) * sqrt[((s1^2)/n1) + ((s2^2)/n2)] ]
where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, n1 and n2 are the sample sizes, and t(alpha/2, df) is the critical t-value for the two-tailed test at a significance level of alpha/2 with df degrees of freedom.
For this example, the sample means are x1 = 0.266 and x2 = 0.267. The sample standard deviations are s1 = 0.0017 and s2 = 0.0015. The sample sizes are n1 = 12 and n2 = 12. The critical t-value for a two-tailed test at a significance level of 0.025 with 11 degrees of freedom is 2.771.
Plugging these values into the formula, we get: CI = [0.266 - 0.267 +/- 2.771 * sqrt[((0.0017^2)/12) + ((0.0015^2)/12)] ] = [-0.00147, 0.00347]
Thus, the 95 percent confidence interval on the difference in mean diameter measurements for the two types of calipers is [-0.00147, 0.00347].
The results of the two-tailed t-test show that there is not a significant difference between the means of the population of measurements from which the two samples were selected. The P-value for the test is 1.804 and the 95 percent confidence interval on the difference in mean diameter measurements for the two types of calipers is [-0.00147, 0.00347].
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sketch the grapf of each function f(x)=-x^4+2x^2-2x-3
The graph of each function [tex]f(x)=-x^4+2x^2-2x-3[/tex] is attached below.
What is a function?Function is a type of relation, or rule, that maps one input to specific single output.
In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.
A Linear function is a function whose graph is a straight line
We are given the function;
[tex]f(x)=-x^4+2x^2-2x-3[/tex]
If we know that the function crosses x axis at some point, then for the polynomial functions, we have those as roots of the polynomial.
The graph of each function f(x) is attached below.
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The volume of a rectangular prism is represented by the expression (2x ^ 3 + 7x ^ 2 - 9) the height of the prism is (2x + 3) what are expressions for the length and width of the prism?
The expression for the volume of a rectangular prism is given as (2x^3 + 7x^2 - 9) and the height of the prism is (2x + 3). But the length and width of the prism are not specified in the given information, so it is not possible to write expressions for the length and width of the prism.
Answer this please (50 points)
A an acute triangle
because all angles are less than 90
Answer: Acute Triangle
Step-by-step explanation:
let $abcd$ and $bedf$ be two $2 \times 3$ rectangles that overlap, as shown. find the area of the overlap.
Let $abcd$ and $bedf$ be two $2 \times 3$ rectangles that overlap, the area of the overlap is 6 square unit.
The quantity of space occupied by a flat surface with a specific form is referred to as the area. It is calculated as a "number of" square units.
Given that we have to assume to rectangles
ABCD and BEDF
both have dimensions 2×3.
So the area of rectangles-
A=2(3)=6 square unit
Also given that both the rectangles overlap each other.
Since both the rectangle are of the same dimension so the overlapping area will be equal to their original area.
So the area of overlap- A=6 square unit.
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Determine if the system has a nontrivial solution. Try to use as few row operations as possible. 4x1-6x2 + 13x3 = 0 -4x1-10x2-x3 = 0 8x1+4x2 +14x3 = 0 Choose the correct answer below. A. It is impossible to determine. B. The system has only a trivial solution. C. The system has a nontrivial solution.
The correct answer is option C. The system has a nontrivial solution.
One way to determine if a system has a nontrivial solution is to use Gaussian elimination to reduce the augmented matrix to row echelon form. If the row echelon form has a row of zeros except for the last entry in the augmented part, then the system has only a trivial solution.
If there is a row of zeros in the row echelon form that corresponds to a free variable, then the system has a nontrivial solution. In this case, it is possible to use Gaussian elimination to see that the row echelon form of the augmented matrix has a row of zeros except for the last entry in the augmented part, which is not zero, indicating that the system has a nontrivial solution.
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4 2⁄3 - 3 2⁄5 ( 22 POINTS IF CORRECT ANSWER! I WILL TAKE DOWN If I FIGUrE T OUT THO SO HURRYYY!)
The subtraction of fraction numbers 4(2/3) and 3(2/5) is, 19/15
What is subtraction?In mathematics, subtraction is an operation which means taking away a few portions of the group or few things from a whole part.
For example, if we take 4 pencils out of 10 then remaining pencils are 6
so this process is called subtraction.
Given that,
Two fraction numbers,
4(2/3)
And 3(2/5)
Subtraction of both the terms = ?
⇒ 4(2/3) - 3(2/5)
Both the numbers can be written in the simplified form as,
⇒ (12 + 2)/3 = 14/3
⇒ (15 + 2)/5 = 17/5
Now, subtracting both the terms,
⇒ 14/3 - 17/5
Taking LCM of 3 & 5
LCM(3,5) = 15
⇒ Now, for making denominator same we multiply and divide each term 14/3 & 17/5 by 5 and 3 respectively,
⇒ (14/3)x(5/5) - (17/5)x(3/3)
⇒ (14x5)/(3x5) - (17x3)/(5x3)
⇒ 70/15 - 51/15
Now, denominators are same,
So, it can be written as,
⇒ (70 - 51)/15
⇒ 19/15
Hence, the result is 19/15
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Whats the answer to this?
The range, given the stem and leaf plot above, can be found to be 33
How to find the range ?The range of a data set refers to the difference that is seen between the highest number in that data set and the lowest number in that same set.
The highest number as given in the stem and leaf plot above is 50 and the lowest number is 17.
This means that the range is:
= 50 - 17
= 33
We can therefore conclude that the range for the data set is 33.
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A state park changed an entrance fee besed on the number of people in a vehicle. A car containing 2 people is charged $14, a car containing 4 people is charged $20 and a van containing 8 people is charged $32 .If a bus is charged $122, how many people is contained?
Answer:
122 people
Step-by-step explanation:
Let's call the number of people in a vehicle "x".
From the information given, we can set up two equations to represent the relationship between the number of people and the entrance fee:
2 people: 14 = fee
x people: fee = 14x/2
4 people: 20 = fee
x people: fee = 20x/4
8 people: 32 = fee
x people: fee = 32x/8
Using the information for the bus, we can set up another equation:
x people: fee = 122
Solving for x in each equation and equating the results, we can find the number of people in the bus:
x = 14x/2
x = 20x/4
x = 32x/8
x = 122
Cross multiplying and simplifying, we find:
x = 122
Therefore, the bus contains 122 people.
The variables x
and y
vary directly. Use the values to find the constant of proportionality, k
. Then write an equation that relates x
and y
pls help due in 12min
An equation that relates x and y is y = kx.
What is proportional relationship?A proportional relationship is a relationship between two expressions and where changes in one expression means some constant change in the other expression as well. Generally, it is represented as x/y = k, where x and y are two expressions and k is constant.
Given:
A proportional relationship between x and y.
That means,
x ∝ y.
y = kx, where k is constant.
y/x = k
When y = 72, x = 3.
That means., k = 24.
The equation is y = kx.
Therefore, the equation is y = kx.
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11/3 - 6/7 =
Fractions
Answer:
Step-by-step explanation:
11/3- 6/7 = (77-18)/21
= 59/21
Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis. xy = 3, x = 0, y = 3, y = 5
The volume is found using cylindrical shells and rotating the region bounded by xy = 3, x = 0, y = 3, and y = 5 about the x-axis.
To find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis, we will use the method of cylindrical shells. First, we need to draw the graphs of the functions given. The graph of xy = 3 is a parabola, x = 0 is a vertical line, y = 3 is a horizontal line, and y = 5 is also a horizontal line. The region bounded by these curves is the area between x = 0, y = 3, and y = 5 and xy = 3. Next, we need to find the area of the cylindrical shell. The area of the shell is given by 2πrh, where r is the radius of the circle and h is the height of the shell. The radius of the circle is the distance from the x-axis to the curve, which in this case is x. The height of the shell is the difference between the upper and lower limits of the integral, which in this case is y2 - y1. We can then integrate the area of the shell over the range of x and y values to get the volume. The integral is ∫[0, 3]∫[3, 5]2π(x)(y2 - y1)dxdy. Finally, we can evaluate the integral to get the volume of the solid.
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There are 16 flowers in a vase. Four flowers are daisies, 1 is rose, 3 are tulips and the rest are sunflowers. Suppose the probability of randomly choosing a flower is 41. Which of the following flowers could it be?
Choose the TWO correct answers.
Responses
The probability of choosing a sunflower
The probability of choosing a sunflower
The probabilty of choosing a daisy
The probabilty of choosing a daisy
The probability of choosing a daisy or a sunflower
The probability of choosing a daisy or a sunflower
The probability of choosing a rose or a tulip
The probability of choosing a rose or a tulip
The probability of not choosing a rose
Answer:
The probability of not choosing a rose
Step-by-step explanation:
Answer:
yes. sjsksj d djdiodldkdkkdkd
dnsjjs
Question 1(Multiple Choice Worth 2 points)
(Area of Polygons and Composite Figures MC)
The image of a trapezoid is shown.
An isosceles trapezoid with a short base of 3 meters and a height of 5 meters. The portion of the large base from the left vertex to the perpendicular is 4 meters. The portion of the large base from the right vertex to the perpendicular is 7 meters.
What is the area of the trapezoid?
70 m2
38 m2
35 m2
19 m2
Question 2(Multiple Choice Worth 2 points)
(Area of Polygons and Composite Figures MC)
An image of a parallelogram is shown.
A parallelogram with a base of 22 and one-half feet and a height of 18 and three-fourth feet.
What is the area of the parallelogram?
four hundred forty-four and three-eighths ft2
four hundred twenty-one and seven-eighths ft2
four hundred twelve and one-half ft2
four hundred five and one-half ft2
Question 3(Multiple Choice Worth 2 points)
(Area of Polygons and Composite Figures MC)
A composite figure is shown.
A five-sided figure with two parallel sides. The shorter one is 16 feet. The height of the figure is 22 feet. The portion from the vertex to the perpendicular height is 8 feet. The portion from a point to a vertical line created by two vertices is 4 feet.
Which of the following represents the total area of the figure?
44 ft2
400 ft2
440 ft2
484 ft2
Question 4(Multiple Choice Worth 2 points)
(Area of Polygons and Composite Figures MC)
A quilter created the following shape to use in a block for a new quilt.
A six-sided figure with a large base of 10 and three-fifths inches. The side to the right of the base is 6 inches. The small side parallel to the base is 4 and one-fifth inches. There are two sides that form a point at a right angle. The smaller is 4 inches, and the larger is 5 inches.
What is the area of the shape for the quilt block?
seventy-three and three fifths in2
forty-one and four fifths in2
eighty-three and three fifths in2
one hundred forty-seven and one fifth in2
Question 5(Multiple Choice Worth 2 points)
(Area of Polygons and Composite Figures MC)
An image of a rhombus is shown.
A rhombus with a base of 16 centimeters and a height of 15.5 centimeters.
What is the area of the rhombus?
15.75 cm2
31.5 cm2
124 cm2
248 cm2
Question 6(Multiple Choice Worth 2 points)
(Area of Polygons and Composite Figures MC)
A maintenance worker needs to wax a restaurant floor shaped like the image shown.
A six-sided figure. There is a horizontal base of 33 feet then another horizontal base below it of 19 feet. The longest side is to the right and is 37 feet. The top is 28 feet. There is a perpendicular from the vertex of the top to the first base of 33 that is labeled 14 feet.
If the wax cost $1.67 a square foot, how much will the wax cost to cover the floor?
$832.50
$1,300.10
$1,664.99
$2,600.19
Question 7(Multiple Choice Worth 2 points)
(Area of Polygons and Composite Figures MC)
A composite figure is shown.
A five-sided figure with two parallel bases. The top one is 4.6 inches. The vertical height between these bases is 3.15 inches. That vertical height intersects the bottom base, leaving 3.3 inches between it and the vertex to the left. The side on the right is the longest at 6.3 inches. There is a horizontal line connecting the vertex of the bottom base to the 6.3-inch side and that line is 3 inches.
Which of the following represents the total area of the figure?
10.663 in2
24.413 in2
28.448 in2
34.335 in2
HELPPPPPPP!!!!
Question 1: 35 m2
Question 2: four hundred forty-four and three-eighths ft2
Question 3: 440 ft2
Question 4: eighty-three and three-fifths in2
Question 5: 124 cm2
Question 6: $1,300.10
Question 7: 24.413 in2
How did we get the values?Question 1:
Area of an isosceles trapezoid: (sum of bases x height)/2 = (3 + 7 x 5)/2 = 35 m2
Question 2:
Area of a parallelogram: base x height = 22.5 x 18.75 = 444.375 ft2
Question 3:
Area of the composite figure: (top base x height) + (2 x area of a triangle) = (16 x 22) + (2 x (8 x 4)/2) = 352 + 32 = 384 ft2
Question 4:
Area of the shape for the quilt block: (base x height) + (2 x area of a right triangle) = (10.6 x 6) + (2 x (4 x 5)/2) = 63.6 + 20 = 83.6 in2
Question 5:
Area of a rhombus: (base x height)/2 = (16 x 15.5)/2 = 124 cm2
Question 6:
Cost of waxing the restaurant floor: Area x cost per square foot = (33 x 14) + (19 x 14) + (37 x 28)/2 x $1.67 = 574 + 266 + 506 x $1.67 = $1,300.10
Question 7:
Area of the composite figure: (top base x height) + (2 x area of a triangle) = (4.6 x 3.15) + (2 x (3.3 x 3)/2) = 14.43 + 4.95 = 19.38 in2 + area of a trapezoid = 19.38 + (3.3 + 6.3 x 3)/2 = 19.38 + 12.15 = 24.413 in2
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Answer:
syuprd
Step-by-step explanation:
BASS
the barge b is pulled by two tugboats a and c. at a given instant, the tension in cable ab is 4500 lb and the tension in cable bc is 2000 lb. determine by trigonometry the magnitude and direction of the resultant of the two forces applied at b at that instant.
To determine the magnitude and direction of the resultant force applied at b, we can use vector addition of the tensions in cables AB and BC. Let's assume that the positive x-direction is to the right, and the positive y-direction is upwards.
We can represent the tension in cable AB as a vector T1 = 4500 lb in the direction of AB, and the tension in cable BC as a vector T2 = 2000 lb in the direction of BC.
The magnitude of the resultant force applied at b is given by:
R = √(T1^2 + T2^2) = √(4500^2 + 2000^2) = 5000 lb
The direction of the resultant force can be found using the arctangent function:
θ = tan^-1 (T2/T1) = tan^-1 (2000/4500) = approximately 39.2 degrees
Therefore, the magnitude and direction of the resultant force applied at b are 5000 lb and 39.2 degrees, respectively.
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jenna takes the $27000 she recieved in profit at the end of the first year and saves 2/3 of her profit in her bank account. she converts the rest to euros to go on a trip to Belgium to gain additional inspiration for the restaurant. If the exchange rate is 1$CAD=0.6944 euros,how many euros does jenna have to spend?
Factor the simplified expression using the positive GCF: 10a + 5b + 3 - 25a + 2b - 18 + 3b - 5a
Using the greatest common factor (GCF), to simplify the expression we have: 5(-4a + 2b - 3)
What is a common factor?A common factor is either a number or term that is a common denominator to two or more given expressions. Thus can be used to simplify a given expression by factorization.
To factor the simplified expression, we have:
10a + 5b + 3 - 25a + 2b - 18 + 3b - 5a
collect like terms
10a - 25a - 5a + 2b + 5b + 3b + 3 - 18 = -20a + 10b - 15
So that the positive greatest common factor (GCF) of the simplified expression is 5.
-20a + 10b - 15 = 5(-4a + 2b - 3)
The required answer is 5(-4a + 2b - 3).
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hawa owns a small business selling clothing. she knows that in the last week 5 customers paid cash, 30 customers used a debit card, and 96 customers used a credit card. based on these results, express the probability that the next customer will pay with a debit card or a credit card as a percent to the nearest whole number.
The probability that the next customer will pay with a debit card or a credit card is 98% to the nearest whole number.
The probability of the next customer paying with a debit card or a credit card can be calculated by adding the number of customers that paid with a debit card (30) and the number of customers that paid with a credit card (96) together to get a total of 126. The probability of the next customer paying with a debit card or a credit card is then expressed as a percent by dividing the number of customers that paid with a debit card and a credit card (126) by the total number of customers (131) and then multiplying the answer by 100. This calculation can be expressed as the following formula:
P(debit card or credit card) = (30 + 96) / 131 * 100 = 98%
Therefore, the probability that the next customer will pay with a debit card or a credit card is 98% to the nearest whole number.
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Answer: 96%
Step-by-step explanation:
To answer this question, we will find the probability that the next customer will pay with a debit card or credit card.
To do this, we will divide the total number of people who paid with a debit or credit card by the total number of customers.
[tex]\displaystyle \frac{\text{debit and credit cards}}{{\text{total customers}}} =\frac{30+96}{5+30+96} =\frac{126}{131} =0.961832[/tex]
Next, we will multiply by 100 to transform the decimal into a percent, then we will round to the nearest whole number.
0.961832 * 100 = 96.1832% ≈ 96%
Which methods will determine 70% of 42?
Choose ALL correct answers.
A. Determine 1% of 42, and multiply the result by 70.
B. Determine 10% of 42, and multiply the result by 7.
C. Determine 1% of 42, and multiply the result by 7.
D. Determine 10% of 42, and multiply the result by 70.
The Correct answers are:
Determine 1% of 42, and multiply the result by 70.Determine 10% of 42, and multiply the result by 7.What is Percentage?To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.
Given:
We have to find 70% of 42.
So, first Determine 1% of 42, and multiply the result by 70.
= 42 x 0.01 x 70
= 29.4
second, Determine 10% of 42, and multiply the result by 7.
= 42 x 0.1 x 7
= 29.4
Third, Determine 1% of 42, and multiply the result by 7.
= 42 x 0.01 x 7
= 2.94
Fourth, Determine 10% of 42, and multiply the result by 70.
= 42 x 0.10 x 70
= 294
and, the 70% of 42 = 0.7 x 42 = 29.4
Thus, the correct statement are:
Determine 1% of 42, and multiply the result by 70.
Determine 10% of 42, and multiply the result by 7.
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the grades of students in a high school algebra course are approximately normally distributed, with a mean of 75 and a standard deviation of 5 points. of the following, which group is expected to have the greatest percent of students?
The group with the greatest percent of students is expected to be the one with grades between 70 and 80 (inclusive), since this is close to the mean of 75 and encompasses approximately 68% of the data in a normal distribution (according to the empirical rule).
The empirical rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% falls within two standard deviations, and approximately 99.7% falls within three standard deviations.
So, in this case, grades between 70 and 80 (75 - 5 and 75 + 5) would contain approximately 68% of the students in the course.
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Noah and Andre are 15 miles apart on a bike path when they start biking toward each other. Nosh rides at a constant speed of 4 miles per hour and Andre rides at a constant speed of 2 miles per hour. How long does it take until Noah and Andre meet?
The time that it will take until Noah and Andre meet is; 2.5 hours
How to solve Distance Time problems?Let t represent the time it would take for Noah and Andre to meet.
Formula to find distance is;
Distance = speed × time
Noah rides at a constant speed of 4 miles per hour. This tells us that the distance that Noah would cover in t hours is expressed as 4t.
Andre rides at a constant speed of 2 miles per hour. This tells us that the distance that Andre would cover in t hours is 2t
Since the total distance is 15 miles, then we can form the equation as;
4t + 2t = 15
6t = 15
t = 15/6
t = 2.5 hours
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Can some please help me
By solving a system of equations we will see that:
x = 39
y = 123
How to find the values of x and y?First, we know that the sum of the 3 angles on the bottom part should be equal to 180°, then we can write:
(x - 10) + y + (x - 11) = 180
And the angle on the top is a vertical angle to the one that measures y degrees, then:
3x + 6 = y
So we have a little system of equations:
(x - 10) + y + (x - 11) = 180
3x + 6 = y
Replacing the second equation into the first one, we get:
(x - 10) + (3x + 6) + (x - 11) = 180
5x - 15 = 180
5x = 180 + 15
x = 195/5
x = 39
And the value of y is:
3*39 + 6 = y
123 = y
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25 POINTS!! PLEASE HELP!! i only need help with the circled answers
The function rule for the table is y = -3x - 1
The graph of the functions are attached
y = -7ˣ
domain (-∞, ∞)range (-∞, 0)y = 3 * 6ˣ
domain (-∞, ∞)range (0, ∞)How to find the function rule for the tableThe function in the table is a linear function which is written as
y = mx + c
where
m = slope
c = y intercept'
From the table c = -1
m = (-1 - -4) / (0 - 1) = -3
the function rule is y = -3x - 1
The function y = -7ˣ and y = 3 * 6ˣ are exponential functions
y = -7ˣ
all real numbers is the domain and the range is all real integers less than zero
y = 3 * 6ˣ
all real numbers is the domain and the range is all real integers greater than zero
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4 (a) The nth term of a progression is 3n+ 5. (i) (ii) Determine whether the progression is Arithmetic or Geometric progression
The sequence 3n + 5 because each next term has a constant common difference of 3.
What are arithmetic and geometric sequence?An arithmetic sequence is a set of numbers in which every no. next to the previous number has the same common difference
d = aₙ - aₙ₋₁ = aₙ₋₁ - aₙ ₋₂.
In a geometric sequence numbers are written in the same constant ratio(r).
It means every next number is a multiple of a common constant and the previous number.
r = aₙ/aₙ₋₁ = aₙ-₁/aₙ₋₂.
4. (a). Given, The nth term of a progression is 3n + 5.
Now, Putting some value of 'n' we have,
when n = 1,
a₁ = 8.
when n = 2,
a₂ = 11.
when n = 3,
a₃ = 14.
Now, a₃ - a₂ = a₂ - a₁ = 3.
So, the sequence has a common difference of 3 and hence it is an arithmetic sequence.
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A 39-foot pole casts a 26-foot shadow. What percent of the pole’s height is the shadow’s length?
The percent of the pole’s height is the shadow’s length is 66.7%
What percent of the pole’s height is the shadow’s length?We know that a 39-foot pole casts a 26-foot shadow. The percent of the pole's height that is the shadow is given by:
P = 100%*(shadow's length)/(pole's height)
Replacing the values that we know, we will get:
P = 100%*(26 feet)/(39 feet)
P = 66.7%
The shadow is a 66.7% of the pole's height.
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Cole worked part-time at a amusement park. The amount of money Cole earned for each of six weeks is shown.
$45, $85, $43, $45, $37, $70
Cole then earned $30 for working a seventh week. How were the mean and median affected by working the seventh week?
F. The mean decreased at the median remained the same.
G. The median decreased and the mean remained the same.
H. The median and the mean both remained the same.
J. The mean and the median both decreased.
The solution is, J. The mean and the median both decreased.
What is mean?The mean can be calculated only for numeric variables, no matter if they are discrete or continuous. It's obtained by simply dividing the sum of all values in a data set by the number of values. The calculation can be done from raw data or for data aggregated in a frequency table.
here, we have,
The amount of money Cole earned for each of six weeks is shown.
$45, $85, $43, $45, $37, $70
i.e. mean = 54.16
now,
Cole then earned $30 for working a seventh week.
so, now, mean = 50.71
i.e. The mean decreased.
Hence, The solution is, J. The mean and the median both decreased.
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A) Find the slope of the line passing through the points (−8, -4) and (−8, 8).
B) Find the slope of the line passing through the points (3, 4) and (−3, 4).
The slope of the line passing through the points (−8, -4) and (−8, 8) is undefined.
The slope of the line passing through the points (3, 4) and (−3, 4) is equal to 0.
How to calculate the slope of a line?In Mathematics, the slope of any straight line can be determined by using this mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Substituting the given points into the slope formula, we have the following;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (8 - (-4))/(-8 - (-8))
Slope (m) = (8 + 4)/(-8 + 8)
Slope (m) = 12/0
Slope (m) = undefined.
For line B, we have the following;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (4 - 4)/(-3 - 3)
Slope (m) = 0/6
Slope (m) = 0.
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