The percent relative average deviation for the data set is 0.30%.
((20.96 - 20.89) + (20.85 - 20.89) + (20.92 - 20.89)) / 3 / 20.89 * 100 = 0.30%
The percent relative average deviation for the given data set can be calculated by first finding the absolute differences between each value and the mean (20.89) then adding those differences together. Once the differences are added, divide that by the mean and multiply by 100. This will give you the percent relative average deviation, which in this case is 0.30%.
The percent relative average deviation for the data set is 0.30%.
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determine the values of k such that the given augmented matrix is that of a consistent linear system
a. The value of k from augmented matrix [tex]\left(\begin{array}{ccc}3&- 5&k\\- 9&15&3\end{array}\right)[/tex] is - 1.
b. The value of k from augmented matrix [tex]\left(\begin{array}{ccc}k&1&- 6\\5&- 1&6\end{array}\right)[/tex] is - 5.
The complete question is in the attachment. The augmented matrix is a consistent linear system if
Has at least one solution.The last column in the matrix is not a pivot column.a. The augmented matrix [tex]\left(\begin{array}{ccc}3&- 5&k\\- 9&15&3\end{array}\right)[/tex]
Making the second row become zero R₂ = R₂ + 3R₁
[tex]\left(\begin{array}{ccc}3&- 5&k\\- 9 \:+\: (3 \times 3)&15 \:+\: (3 \times - 5)&3 \:+\: (3 \times k)\end{array}\right)[/tex]
[tex]\left(\begin{array}{ccc}3&- 5&k\\- 9 \:+\: 9&15 \:+\: (- 15)&3 \:+\: 3k\end{array}\right)[/tex]
[tex]\left(\begin{array}{ccc}3&- 5&k\\0&0&3 \:+\: 3k\end{array}\right)[/tex]
From the second row
0x + 0y = 3 + 3k
For the system to be consistent, then
3 + 3k = 0
3k = - 3
k = - 3/3
k = - 1
b. The augmented matrix [tex]\left(\begin{array}{ccc}k&1&- 6\\5&- 1&6\end{array}\right)[/tex]
Making the second row become zero R₂ = R₂ + R₁
[tex]\left(\begin{array}{ccc}k&1&- 6\\5 \:+\: k&- 1 \:+\: 1&6 \:+\: (- 6)\end{array}\right)[/tex]
[tex]\left(\begin{array}{ccc}k&1&- 6\\k \:+\: 5&0&0\end{array}\right)[/tex]
From the second row
(k + 5)x + 0y = 0
For the system to be consistent, then
k + 5 = 0
k = - 5
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What is the circumference of a circle with a radius of 21 feet? Use 22 over 7 for π.
132 feet
66 feet
5,544 feet
1,386 feet
Answer:
Option A) [tex]132ft[/tex]
Step-by-step explanation:
It is given that,
Radius of a circle = 21ft
We know that π = [tex]\frac{22}{7}[/tex]
So the circumference of a circle = 2πr
Substituting the values,
= [tex]2X\frac{22}{7} X 21[/tex]
So we get,
[tex]= 2X22X3[/tex]
[tex]= 132ft[/tex]
The required circumference of the circle is 132 feet. Option A is correct.
What is the circumference of the circle?To find the circumference of a circle, we use the formula C = πd, where C is the circumference, π is the mathematical constant pi (approximately equal to 3.14), and d is the diameter of the circle.
Here,
The circumference of a circle with a radius of 21 feet can be found using the formula:
C = 2πr
where "C" is the circumference, "r" is the radius, and "π" is the mathematical constant pi, which is approximately equal to 22/7.
Substituting the values given, we have:
C = 2 x (22/7) x 21
C = 132 feet
Therefore, the circumference of the circle is 132 feet. Answer: 132 feet.
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Use dimensional analysis to convert the quantity to the indicated units. If necessary, round the answer to two
decimal places.
100 in. to ft
O 1200 ft
8.33 ft
O 16.67 ft
33.33 ft
The dimensional analysis conversion of 100 inch to feet is 8.33 feet.
What is dimensional analysis?Dimensional analysis is the study of the relationships between different physical quantities in engineering and science by identifying their base quantities and units of measurement and tracking these dimensions as calculations or comparisons are performed. when there is insufficient information to set up precise equations, a method of analysis in which physical quantities are expressed in terms of their fundamental dimensions. Dimensional Analysis (also known as the Factor-Label Method or the Unit Factor Method) is a problem-solving strategy that takes advantage of the fact that any number or expression can be multiplied by one without changing its value.
Here,
100 inch to feet,
=100/12
=8.33 feet
The conversion of 100 inch to feet using dimensional analysis is 8.33 feet.
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find the volume of the solid generated by revolving the region bounded by the parabola y=-(x^2)/9 and the lines y=-1 about the following lines a. the line y=-1 b. the line y=-2 c. the line y=1
The volume of the solid generated by revolving about the line y=-1 is 324π cubic units and the volume of the solid generated by revolving about the line y=-2 is 216π cubic units.
To find the volume of the solid generated by revolving the region bounded by the parabola y=-(x^2)/9 and the lines y=-1 about a line, we can use the method of cylindrical shells.
a) The line y=-1 is the axis of revolution, so the volume of the solid generated by revolving the region about this line is:
V = ∫[(-1-(x^2)/9)^2 - (-1)^2] * 2πx dx
where the integral is taken over the interval for which the parabola y=-(x^2)/9 is above the line y=-1. So the limits of the integral are from -3 to 3, the volume is:
V = ∫[(-1-(x^2)/9)^2 - (-1)^2] * 2πx dx from -3 to 3 = 324*π cubic units
b) The line y=-2 is the axis of revolution, so the volume of the solid generated by revolving the region about this line is:
V = ∫[(-2-(x^2)/9)^2 - (-2)^2] * 2πx dx
where the integral is taken over the interval for which the parabola y=-(x^2)/9 is above the line y=-2. So the limits of the integral are from -3 to -sqrt(92) = -3 to -3sqrt(2) and 3*sqrt(2) to 3 , the volume is:
V = ∫[(-2-(x^2)/9)^2 - (-2)^2] * 2πx dx from -3 to -3sqrt(2) + ∫[(-2-(x^2)/9)^2 - (-2)^2] * 2πx dx from 3sqrt(2) to 3 = 216*π cubic units
c) The line y=1 is not on the same side of the parabola y=-(x^2)/9 as the region bounded by the parabola and the lines y=-1 so there is no solid generated by revolving about this line.
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please help will mark BRAINLIEST
Read the following prompt and type your response in the space provided.
Explain how the associative property can be used to solve this problem.
8/9 / 7/5 x 3/16
The associative property shows that the value of 8/9 / 7/5 x 3/16 is 5/24.
How to calculate the value?The associative property states that the way in which we group the numbers or variables in an arithmetic operation does not affect the result. In other words, we can change the grouping of the numbers or variables by using parentheses without changing the outcome of the calculation.
In this problem, we can use the associative property to group the fractions in a way that makes it easier to simplify.
= 8/9 ÷ 7/5 x 3/16
= (8/9) ÷ (7/5) x 3/16
= 8/9 x 5/7 x 3/16
= 8/9 x 15/112
= 120/1008
= 5 / 24
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on drawing line 1/4-inch long represent a lenght of 1 foot on the same drawing what length represent 4 feet
The line represents 1 foot, so 4 feet would require a line that is 4 times as long as the 1/4 inch line, which is 1 inch.
The formula for finding the length of a line to represent a certain number of feet is L = (1/4)*F, where L is the length of the line, and F is the number of feet. In this case, to find the length of a line to represent 4 feet, the calculation would be L = (1/4)*4 = 1. Therefore, the line would need to be 1 inch long to represent 4 feet. This is because 1/4 inch of the line represents 1 foot, so 4 feet would require a line that is 4 times as long as the 1/4 inch line, which is 1 inch.Therefore, to represent a length of 4 feet on the same drawing, a line 1 inch long needs to be drawn. The calculation is as follows: 1/4 inch line = 1 foot, therefore 4/4 inch line = 4 feet. Therefore, 1 inch line = 4 feet.
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let f be the function given by , where k is a constant. for what values of k, if any, is f strictly decreasing on the interval (-1, 1)?
For any k ∈ (-∞, o), function f is strictly decreasing on the interval (-1, 1).
In mathematics, a function is a relationship or mapping between two sets of elements, known as the domain and the codomain, that assigns each element from the domain to a unique element in the codomain. It describes how inputs from the domain are transformed or related to corresponding outputs in the codomain.
The given function is f = [tex]\frac{kx}{x^2+1}[/tex] ...(1),
Differentiate (1) w.r.t. x,
[tex]\dfrac{d}{dx}f = \dfrac{d}{dx}\frac{kx}{x^2+1}[/tex]
f' = [tex]k\frac{1-x^2}{(x^2 + 1)^2}[/tex]
Since f is decreasing on (-1, 1),
therefore
f' < 0 on (-1, 1),
[tex]k\frac{1-x^2}{(x^2 + 1)^2}[/tex] < 0 on (-1, 1).
As [tex]\frac{1-x^2}{(x^2 + 1)^2}[/tex] > 0 on (-1, 1),
k < 0 for f' < 0.
Therefore, k ∈ (-∞, o) for f to be strictly decreasing on (-1, 1).
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The complete question is as follows:
Let f be the function given by [tex]\frac{kx}{x^2+1}[/tex], where k is a constant. For what values of k, if any, is f strictly decreasing on the interval (-1, 1)?
There is a stack of eight cards each given a different number from 1 to 8. Suppose we select a card randomly from the stack, replace it, and then randomly select another card. What is the probability that the first card isn’t even number and the second card is less than five
The probability that the first card isn’t even number and the second card is less than five is given as follows:
1/4 = 0.25 = 25%.
How to obtain the probability?A probability is obtained with the division of the number of desired outcomes by the number of total outcomes.
The probabilities for each event in this problem are given as follows:
First card isn't even: 4/8 = 1/2. (1, 3, 5 and 7 are not even).Second card is less than five: 4/8 = 1/2. (1, 2, 3 and 4 are less than 5).The events are independent, hence the probability is obtained with the multiplication of the two probabilities, as follows:
1/2 x 1/2 = 1/4 = 0.25 = 25%.
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A fuel pump at a gasoline station doesn't always dispense the exact amount displayed on the meter. When the meter reads 1.000 L, the amount of fuel a certain pump dispenses is normally distributed with a mean of 1 L and standard deviation of 0.05 L. Let X represent the amount dispensed in a random trial when the meter reads 1.000 L Find P(0.9
The value of P(x < 1) is 0.5.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
We have,
Mean = 1
Standard deviation = 0.05
The P-value of Z when x = 1.
z = (x - mean) / standard deviation
z = (1 - 1)/0.05
z = 0
The P-value when z = 0 is 0.5.
So,
P(x < 1) = 0.5
Thus,
P(x < 1) is 0.5.
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Martin's mom has a large box of toys. The box contains 80 different toys. She wants to divide the large box into smaller boxes. She wants each of the smaller boxes to have 10 toys. After she divided the toys, she put 28 more toys into one of the boxes. How many toys are in that box?
Answer: 38 toys
If each of the smaller boxes has 10 toys, and Martin's mom added 28 more toys into only one of the boxes, that box would have a total of 38 toys.
10 + 28 = 38 toys
All of the following are true statements. According to your Mini-Lesson, which of them is the more formal definition of a function? A Function is a rule where every input has only one output and every input has an output. A Function describes a particular relationship between two quantities: an input quantity and an output quantity. A Function defines a relationship between two Quantities. A Function is a rule that assigns a single, unique output value to each input value. A Function, when graphed, must pass the vertical line test.
A function is a rule that generates one unique output value for every specified input value. Therefore, the fourth statement is true.
In mathematics, the function is something that relates an input to an output. The output obtained will somehow be related to the input. We write the function as f(x). For example, consider f(x) = x². This means that the function f takes the value of x and squares this value. Like when we input x=4. Then the output is f(x)=4²=16.
So, here see the function assigns a single and a unique output value of 16 for the input value of 4. Therefore, option 4 is correct. That is function gives every input value a unique, separate output value.
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a room 27 feet by 32 feet is to be carpeted all to wall. the width of the carpet is 27 inches. the length, in yards, of the carpet needed for this room is
The length in yards, of the carpet needed for this room is 128 yards.
length of the room = 32 ft
breadth of the room = 27 ft
so we find area now,
area = length X breadth
area = 32 X 27
area = 864ft^2
The width of the carpet in feet is = 2.25ft
so , to find the length of the carpet needed, you must apply the formula for calculate the area of a rectangle and solve for the length, as following,
area = length X width
864 = length X 2.25
length = 864/ 2.25
length = 384ft
length = 128yards
so the length, in yards, of the carpet needed for this room is 128 yards.
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how to solve 5 3/8 + m = 8
Answer:
m=21/8
Step-by-step explanation:
5 /38+m=8
Move the constant to the right.
43/8+m=8
m=8-43/8
m=21/8
Help!
Lauren and Shayla have ½ pound of skittles. They want to share the Skittles between themselves and 2 friends.
How many pounds of skittles will each of them receive?
Answer:
0.125 pounds of skittles
Step-by-step explanation:
Lauren and Shayla have a total of ½ pound of skittles and they want to share them with 2 friends, including themselves, so the total number of people is 2+2 = 4
If they want to divide the ½ pound of skittles equally among 4 people, each person will receive ½ pound / 4 = 0.125 pounds of skittles.
Solve please? I really need help
Could you also make sure I’m right for these?
The area and heights and bases of the figures are: 8.9, 54 in², 35cm²,20.25m², 168 ft², 6cm, 37.8in² and 5mm respectively
How to find the areas?The figures include triangles and trapezoids. The areas are the floor spaces the figures occupy
1) Area of a triangle = 1/2 *b*h
b = 14.3*2 = 28.6
h=8.9
Area = 1/2 *28.6 * 8.9
Area = 127.27 cm²
2) Area of a trapezoid = 1/2(a+b)h
Area = 1/2 (12+6)*6
Area = 1/2*18*6
= 54in²
3) Area of a trapezoid = 1/2(a+b)h
Area = 1/2 (8+6)*5
= (14*5)/2 = 35cm²
4) Area of a triangle = 1/2 *b*h
Area = 1/2 * 9 * 4.5
=20.25m²
5) Area of a trapezoid = 1/2(a+b)h
Area = 1/2 (18+24)*8
= 168ft²
6) Area of a triangle = 1/2 *b*h
38.4 = 1/2*b*12.8
Making b the subject of the relation we have
76.8 = 12.8b
b=6cm
7) Area of a triangle = 1/2 *b*h
Area = 1/2*8.4*9
=37.8in²
8) Area of a trapezoid = 1/2(a+b)h
35=1/2(6+8)*h
70=14h
Making h the subject we have
h= 5 mm
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Question 15 of 25
Which relation is not a function?
OA. X 126
18 24 36
y 6 12 6 30 24
OB. ((7,3), (3, 7), (1, 5), (5, 4), (0, 6)}
OC. {(6,5), (3, 2), (2, 4), (6, 3), (1, 0))
O D.
·0€
7
34
Answer:
Step-by-step explanation:oc (6,5), (3,2), (2,4) (6, 3), (1, 0)
Convert 13/30 to a decimal and a percent.
Answer:
0.43, 43%
Step-by-step explanation:
You use beads to make design. Of the beads, 1/3 are red and 1/6 are blue. The rest are white. What fraction of the beads are red red or blue?
Answer:
Step-by-step explanation:
1/3 is 2/6
2/6 + 1/6 = 3/6
3/6 = 1/2
answer 1/2 or half
Answer:
It is 1/2
Step-by-step explanation:
You make 1/3 the same denominator so it becomes 2/6.
2/6+1/6=3/6
Now when you simplify this you get 1/2.
Whats HL? Please help. Thanks
The measure of the length HL will be 18.5 units for the given figure.
What is geometry?One of the earliest areas of mathematics is geometry, along with arithmetic. It is concerned with spatial characteristics like the separation, shape, size, and relative placement of objects.
Given that in the quadrilateral the two sides are Jk = 12 and GF = 25. The value of HL can be calculated by the theorem,
HL = ( 1 / 2 ) x GF x JK
HL = ( 1 / 2 ) x 25 x 12
HL = 18.5
Therefore, the length of section HL will be 18.5 units.
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jared knows that distance his cars travels equals the rate at which he drives multiplied by the time he drives the car on one occasion he drove 15 miles in 0.5 hours what equation can jared use to find the rate at which he drove
Answer:
The equation Jared can use to find the rate at which he drove is:
rate (r) = distance (d) / time (t)
So in this case, Jared can plug in the values he knows into the equation:
r = 15 miles / 0.5 hours
Solving for r, he can find the rate at which he drove:
r = 30 miles per hour.
So Jared drove at a rate of 30 miles per hour.
Step-by-step explanation:
PLEASE GIVE BRAINLIEST
A new company president is saidto uave causethe company to do180. Before the new president, the company was losing 10,000 per month. What is the company most likely doing under the new president?
The company, under the new president, is most likely, earning a profit of $ 10, 000 per month.
What does it mean to do a 180 ?When a person is said to have done a 180, it means that they are now doing the opposite of what they used to do. For example, a person who was eating only fast foods doing a 180 would end up eating only healthy food.
This means that the new president doing a 180, means that the company is doing the opposite of what they were doing and instead of making losses of $ 10, 000 monthly, they are making profits of $ 10, 000 every month.
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Square ABCD is perfectly inscribed in the circle pictured above. If minor arc AD measures 2π, what is the approximate area of the shaded region?
A. 110
B. 72
C. 36
D. 18
E. 9
The area of the circle is πr², where r is the radius. The area of the shaded region is half the area of the circle.
The area of the circle is πr², where r is the radius. The area of the shaded region is half the area of the circle.
Therefore, Area of the shaded region = πr²/2
Given that minor arc AD measures 2π, the radius of the circle is 2.
Therefore, Area of the shaded region = π(2)²/2 = 4π = 72
The area of the shaded region is half the area of the circle, which is πr²/2. The minor arc AD measures 2π, so the radius of the circle is 2, and the area of the shaded region is 4π, or 72.
The area of the circle is πr², where r is the radius. The area of the shaded region is half the area of the circle.
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2. Which of these gives the better price for a item priced at $150: a 10/10/10
discount or a 15/15 discount?
Answer:
10/10/10
Step-by-step explanation:
According to mars, the makers of m&ms their factory produces 25%blue 25%orange, 12.5% for each remaining colors . How do the observed values based on the entire lasso compare to these?25 blue, 25 orange, 12.5 yellow, 12.5 green, 12.5 brown and 12.5 red
Answer: According to Mars, the makers of M&Ms, their factory produces 25% blue, 25% orange, and 12.5% for each of the remaining colors, which are yellow, green, brown, and red.
The observed values based on the entire lasso are 25 blue, 25 orange, 12.5 yellow, 12.5 green, 12.5 brown, and 12.5 red. These values match the expected values according to the manufacturer, which is 25% blue, 25% orange, and 12.5% for each of the remaining colors.
So, the observed values based on the entire lasso compare to the expected values from the manufacturer. The proportion of colors in the observed sample is the same as the proportion of colors that the factory produces, meaning that the factory is producing the expected ratio of colors.
Step-by-step explanation:
Write a multiplication equation to show an equivalent fraction of 15 using fifteenths.
Explain how the two fractions are equivalent.
A multiplication equation to show an equivalent fraction of 15 using fifteenths would gives 10/75
What is a fraction?A fraction consisting of a quotient and remainder is a mixed fraction. we can convert the mixed fraction to improper fraction by first dividing the numerator by denominator and then taking the quotient as whole number and remainder as the numerator of proper fraction keeping the denominator same.
We have to write an equivalent fraction of 15 using fifteenths.
2/15
So let multiply by 5 .
2 / 15 x 5/ 5 = 10/75
Thus, 10/75 is equivalent expression.
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Question 2 Multiple Choice Worth 2 points)
(04.05 MC)
There are 200,000 households in Point City. A local computer repair shop takes a random sample of 50 households and finds that the average number of computers per
household from the sample last year that needed to be repaired was 1.15 0.49. Which of the following is an estimate of the total number of computers that needed repairing
last year in Point City?
Between 66 and 164 computers
Between 115 and 49 computers
Between 132,000 and 328,000 computers
Between 230,000 and 98,000 computers
n
The estimate of the total number of computers that needed repairing last year in Point City is given as follows:
Between 132,000 and 328,000 computers.
How to obtain the estimate?The estimate is obtained applying the proportions in the context of this problem.
The confidence interval is given as follows:
1.15 plus/minus 0.49.
Hence the bounds of the interval are given as follows:
Lower bound: 1.15 - 0.49 = 0.66.Upper bound: 1.15 + 0.49 = 1.64.Hence, out of 200,000 households, the lower bound of the estimate is given as follows:
0.66 x 200,000 = 132,000.
The upper bound is of:
1.64 x 200,000 = 328,000.
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When the function f(x) is divided by x-1, the quotient is 1x^2+x-8 and the remainder is -2. Find the function f(x) and write the result in standard form.
Answer: When a polynomial is divided by x-1, the quotient is of the form of ax^2 + bx + c and the remainder is of the form of r. The quotient and the remainder are related by the formula:
f(x) = (x-1)(ax^2 + bx + c) + r
Given that the quotient is 1x^2+x-8 and the remainder is -2, we can substitute these into the above equation:
f(x) = (x-1)(1x^2+x-8) + (-2)
f(x) = x^3 - 9x^2 + (1-8)x +(-2)
f(x) = x^3 - 9x^2 - 7x - 2
Therefore the function f(x) is x^3 - 9x^2 - 7x - 2 in standard form.
Step-by-step explanation:
In the 30-60-90 triangle below, side s has a length of________ and side q has a length of_______
A. 16√3, 5
B. 8-5, 16
C. 4, 8√3
D. 4√2, 4√2
E. 4, 4 √3
F. 16√3, 16√3
Answer: Option (E)
4, 4√3
===========================================================
Reason:
The hypotenuse is 8. Half of that is 8/2 = 4, which is the value of "s".
This is the short leg of the right triangle. The short leg is opposite the 30 degree angle. Smallest side opposite the smallest angle.
Then use this 30-60-90 triangle template formula
[tex]\text{long leg} = (\text{short leg})*\sqrt{3}\\\\\text{long leg} = 4\sqrt{3}\\\\[/tex]
Each year, the newspaper America at a Glance writes an article about the performance of students on a particular nationwide math test. Included in t
this year was the following frequency distribution. It summarizes the test scores from a study which looked at 49 students who completed preperacion
for the test.
Mathematics test score
550 to 599
600 to 649
650 to 699
700 to 749
750 to 799
Frequency
5
11
14
12
7
Based on the frequency distribution, using the midpoint of each data class, estimate the mean mathematics test score for the students in the study for your
intermediate computations, use four or more decimal places, and round your answer to one decimal place.
Answer: To find the mean test score, we need to calculate the sum of the product of each score and its corresponding frequency, and divide it by the total number of students.
To estimate the mean mathematics test score, we can use the midpoint of each data class as the value for each score and multiply it by the corresponding frequency.
For the first class, 550 to 599, the midpoint is (550+599)/2 = 574.5
For the second class, 600 to 649, the midpoint is (600+649)/2 = 624.5
For the third class, 650 to 699, the midpoint is (650+699)/2 = 674.5
For the fourth class, 700 to 749, the midpoint is (700+749)/2 = 724.5
For the fifth class, 750 to 799, the midpoint is (750+799)/2 = 774.5
The mean test score is:
(5574.5 + 11624.5 + 14674.5 + 12724.5 + 7*774.5) / 49 = 669.3
Therefore, the estimate of the mean mathematics test score for the students in the study is 669.3.
Step-by-step explanation: