please answer if you can? (This is my math from 8th grade)

The 99% confidence interval for the true population mean backpack weight is approximately (68.15, 71.85) ounces, rounded to two decimal places.

To construct a 99% confidence interval for the true population mean backpack weight, we can use the formula:Confidence Interval = Sample Mean ± (Critical Value * Standard Deviation / √Sample Size).

Since the population standard deviation is known, we can use the z-distribution and find the critical value corresponding to a 99% confidence level. The critical value for a 99% confidence level is approximately 2.576.

Given that the sample mean weight is 70 ounces, the population standard deviation is 6.4 ounces, and the sample size is 48, we can calculate the confidence interval:

Confidence Interval = 70 ± (2.576 * 6.4 / √48).

Simplifying the expression, we get:

Confidence Interval ≈ 70 ± 1.855.

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Answer:

0.85714286

Step-by-step explanation:

Answer:

x=-3

Step-by-step explanation:

Divide both sides by 2, so -4x+2=14

Subtract 2 from both sides, -4x=12

Divide both sides by -4, so x=-3

Answer:

4x2 = 28

Step-by-step explanation:

Therefore , the solution of Inverse function comes out to be of x-20 equals to x+20

A function f has an inverse function only if for every y in its range there is only one value of x in its domain for which f(x)=y. This inverse function is unique and is frequently denoted by f−1 and called “f inverse.” For an overview into the idea of an inverse function, see the function machine inverse.Steps for finding the inverse of a function fReplace f(x) by y in the equation describing the function. Interchange x and y. In other words, replace every x by a y and vice versa.

Here,

Solve for y.

Replace y by f-1(x).

y=x-20

x=y-20

Solve for y,x = y-20

x+20

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Answer:

ƒ^(-1)(x) = x + 20

Step-by-step explanation:

To find the inverse of the function ƒ(x) = x - 20, we need to switch the roles of x and y and solve for y.

Let's start by replacing ƒ(x) with y:

y = x - 20

Next, swap x and y:

x = y - 20

Now, solve for y by isolating it:

x + 20 = y

Therefore, the inverse of the function ƒ(x) = x - 20 is given by:

ƒ^(-1)(x) = x + 20

Answer:

w = -1

Step-by-step explanation:

Answer:

10045 rounded to nearest tens is10050

Answer:

-2

Step-by-step explanation:

1/2 slope

flip fraction 2/1

change sign -2/1 or -2

Given the graph represents the amount of water in the aquarium versus time.

A) As shown in the graph :

as the time increases the amount of water in the aquarium decreases

The rate of water decreasing =

so, the rate = 60 litres per minute

Answer:

0.24 pages per hour

Step-by-step explanation:

To solve this you have to divide total pages by the hours to get the speed per hour. Here is the equation;

28 / 116 = 0.2413793103448276

Hope this helps!

Answer:

55

Step-by-step explanation:

complementary angle means either of two angles whose sum is 90°.

we can use this to find that angle abc is 55 and since angle abc and ebf are opposite the measure the same

Answer:

D

Step-by-step explanation:

P(A)=0.3

P(B)=0.1

P(A)×P(B)=0.3×0.1=0.03

P(A and B)=P(A)×P(B)

They are independent.

Part A:

8t + 5h = 220

t + 5h = 112

Part B:

T-shirt cost $13.50

Hat cost $22.40

Answer:

12

Step-by-step explanation:

12 can go in both 12 and 24 without a remainder

The number that belongs in the green box using sine rule is 13.96.

The rule of sine or the sine rule states that the ratio of the side length of a triangle to the sine of the opposite angle, which is the same for all three sides.

To calculate the number that belongs in the green box, we use the formula below

Formula:

From the diagram,

Given:

Substitute these values into equation 1

Solve for x

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Answer: There is no solution to this problem.

Step-by-step explanation:

The goal test score pints are 150, 103, and 41. Let's check to see if each statement is true

A. The total points for the tests are:

Type A - 156

Type B -  98

Type C -  40

None of these matches the total points.

B. The total points for the tests are:

Type A - 39

Type B - 98

Type C - 160

None of these matches the total points.

C.

Type A - 156

Type B - 2,352

Type C - 40

None of these matches the total points.

Since none of these statements match this data, there is no solution to this chart. Hope this helps!

-From a 5th Grade Honors Student

Answer:

1.  d   (last option)

2.  a   (first option)

Step-by-step explanation:

Question 1

Rewrite \(b=\pi r^2+c\) to make r the subject.

Subtract c from both sides:

\(\implies b-c=\pi r^2\)

Divide both sides by \(\pi\) :

\(\implies r^2=\dfrac{b-c}{\pi}\)

Square root both sides:

\(\implies r=\pm\sqrt{\dfrac{b-c}{\pi}}\)

Question 2

Rewrite \(d=\sqrt{\dfrac{h}{6.752}}\) to make h the subject.

Square both sides:

\(\implies d^2=\dfrac{h}{6.752}\)

Multiply both sides by 6.752:

\(\implies h=6.752d^2\)

Answer:

9%

Step-by-step explanation:

(20*9)/2000=0.9

Answer:

If you have ownership of something it means that you are the owner; it belongs to you. ... The term does not only refer to people, but also to other entities. For example, the government is the owner of a state company. Also, a holding company owns its subsidiary businesses.

Answer:

a. 587

b. 543

Step-by-step explanation:

a. Mean = sum / number of numbers

To find the sum, we can add the numbers up.

432 + 543 + 348 + 788 + 823 = 2934

There are 5 numbers. Our mean is thus

2934/5 = 586.8, or 587 when rounding up. We round up because we have a .8 at the end, and 8 ≥ 5

b. To find the median, we first must order the numbers. The numbers ordered are this:

348 ,  432 , 543 , 788 , 823

To find the median, we can cross off one number on each side until we are left with one or two numbers.

348 ,  432 , 543 , 788 , 823

cross out one number from each endpoint

432 , 543 , 788

cross out one number from each endpoint

543

Hello :

    3/8 = x/(15 + x)

⇔ 3(15 + x)/8 = x

⇔ (45 + 3x)/8 = x

⇔ 45 + 3x = 8x

⇔ 8x - 3x = 45

⇔ 5x = 45

⇔ x = 45/5

⇔ x = 9

Answer: 60%

Step-by-step explanation:

You would first need to write the questio into fractio form. (12/20)

\(\frac{12}{20} = 0.6\)

This would then equal 0.6, but since percentages are out of 100, you have to multiply this decimal by 100. This in turn, gives you 60.

The mean, mean deviation mode, median standard deviation, and coefficients of variation, CV, are as follows;

1. The mean deviation about the mean, median mode are;

2.653, 3.709, and 3.709, respectively

The coefficients of variation are;

0.364, 0.337, 0.337, respectively

The variance is about 9.462

The standard deviation is about 3.076

2. Section A has a higher relative dispersion than section B

3. City 2

4. a. Mean ≈ 43.85

b. Mode 40 - 54 inches

c. Median ≈ 45.16

The variance ≈ 125.8056

Standard deviation ≈ 11.216

Coefficient of variation ≈ 0.268

The coefficient of variation of a data quantifies or is a measure of the variability of the values in the set of data.

The mean for the data can be calculated as follows;

Mean  = (3×10 + 6×15 + 11×25 + 2×6 + 4×4 + 10×3 + 5×2 + 7×8 + 8×9 + 9×4)/(10+15+25+6+4+3+2+8+9+4) ≈ 7.29

The median is the 86/2 value = 43rd value

10 + 15 + 25 = 50

Therefore, the median is in the class with a frequency of 25, which is 11

The mode of the data, which is the value with the highest frequency in the data set is 11

The mean deviation from the mean is therefore;

(|3 - 7.29|×10 + |6 - 7.29|×15 + |11 - 7.29| ×25 + |2 - 7.29| ×6 + |4 - 7.29| ×4 + |10 - 7.29| ×3 + |5 - 7.29| ×2 + |7 - 7.29|×8 + |8 - 7.29| ×9 + |9 - 7.29| ×4)/(10+15+25+6+4+3+2+8+9+4) ≈ 2.653

The coefficient for the mean deviation about the mean is therefore; 2.653/7.29 ≈ 0.364

The mean deviation about the median is therefore;

(|3 - 11|×10 + |6 - 11|×15 + |11 - 11| ×25 + |2 - 11| ×6 + |4 - 11| ×4 + |10 - 11| ×3 + |5 - 11| ×2 + |7 - 11|×8 + |8 - 11| ×9 + |9 - 11| ×4)/(10+15+25+6+4+3+2+8+9+4)

The mean deviation about the median = 319/86 ≈ 3.709

The coefficient ≈ 3.709/11 ≈ 0.337

The median = The mean deviation about the mode ≈ 3.709

The coefficient is about 0.337

The variance = (10×(3 - 7.29)² + 15×(6 - 7.29)² + 25×(11 - 7.29)² + 6×(2 - 7.29)² + 4×(4 - 7.29)² + 3×(10 - 7.29)² + 2×(5 - 7.29)² + 8×(7 - 7.29)² + 9×(8 - 7.29)² + 4×(9 - 7.29)²)/(10+15+25+6+4+3+2+8+9+4) ≈ 9.462

The standard deviation, s ≈ √(9.462) ≈ 3.076

2. The coefficient of variation, CV, can be used to compare the variability of the datasets comprising of different scales as follows;

CV = Standard deviation/( The mean of the data)

Therefore; CV for section A = 23/79 ≈ 0.2911

CV for section B = 11/64 ≈ 0.172

The higher CV value for section A indicates that the scores of section A have a higher relative dispersion than the scores for the section B

3. The consistency values can be obtained by finding the standard deviation for the values in the data for each city, using a web based tool as follows;

City 1; Mean = 23

Variance = 50/4

Standard deviation, City 1 = (√(50))/2 = 5·√2/2

City 2; Mean = 21.8

Sample variance = 2.2

Standard deviation, City 2 = √(2.2) ≈ 1.483

City 3; Mean = 29.2

Sample variance = 18.7

Standard deviation, City 3 = √(18.7) ≈ 4.324

The standard deviation of city 2, which is the smallest compared tom the other cities, indicates that the City 2, has the most consistent temperature

4. The mean of the data obtained from the data using the midpoint of the data, is; Mean = ∑fx/∑f

Therefore; The mean obtained using an online tool is; 43.85

The mode is the data that occurs most frequently, which is the data with the value; 40 - 54 inches

The median is the value at the middle of the data set, which is the value with a frequency of 53, and in the interval 40 - 54 inches

The median is; 39.5 + (54.5 - 39.5) × (50 - 30)/53 ≈ 45.16

The standard deviation found for the grouped data, using an online tool is as follows;

Variance, σ² ≈125.8056

The standard deviation, σ ≈ √(125.8056) ≈ 11.216

The coefficient of variation is; 11.216/41.83 ≈ 0.268

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Answer:

B

Step-by-step explanation:

The probability that \($A + B = C$\) is \(\boxed{\frac23\ \text{(D)}}\)

Since \($a$\) and \($b$\)are chosen independently between \($0$\) and \($1$\), each of the intervals \($(0,\frac12)$\) and \($(\frac12,1)$\) is equally likely to contain either of the two numbers. Let's consider each case separately:

\($(0,\frac12)$\) and \($(0,\frac12)$\): In this case, \($c$\) is between \($0$\) and \($1$\), so \($C=1$\) and \($A=B=0$\).

\($(0,\frac12)$\)and \($(\frac12,1)$\): In this case, \($c$\) is between \($\frac12$\) and \($1\frac12$\), so \($C=2$\) and \($A=0$\), \($B=1$\) or \($A=1$\) , \($B=0$\).

\($(\frac12,1)$\) and \($(\frac12,1)$\): In this case, \($c$\) is between \($1$\) and \($2$\), so \($C=2$\) and \($A=B=1$\).

Out of these three cases, two of them result in \($A+B=C$\), so the probability of this happening is \($\frac23$\).

Therefore, the answer is \(\boxed{\frac23\ \text{(D)}}\)

This is a probability problems that try to find the probability that the sum of the rounded values of two random numbers between \($0$\) and \($1$\) is equal to the rounded value of their sum. The question involves rounding numbers to the nearest integer, which is why it is a probability question and not simply an algebraic one.

The solution involves considering each possible combination of intervals for the two random numbers and calculating the probability that the sum of the rounded values is equal to the rounded value of their sum.

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Answer:24ounces

Step-by-step explanation:

Multiply 20 ounces by .20 (The percent) then add your answer to the 20 ounces.

Answer in fraction form = -3/2

Answer in decimal form = -1.5

=========================================

Work Shown:

\(m = \frac{g(b)-g(a)}{b-a}\\\\m = \frac{g(1)-g(-3)}{1-(-3)}\\\\m = \frac{0-6}{1-(-3)}\\\\m = \frac{0-6}{1+3}\\\\m = \frac{-6}{4}\\\\m = -\frac{3}{2}\\\\m = -1.5\\\\\)

Effectively, we're finding the slope through the points (-3, 6) and (1, 0)

The g(b)-g(a) represents how y changes when going from x = a to x = b.