A distribution of measurements is relatively mound-shaped with a mean of 60 and a standard deviation of 14. Use this information to find the proportion of measurements in the given interval. between 46 and 74

Answers

Answer 1

Answer:

Approximately 68.26% of the measurements fall between 46 and 74 in this distribution.

To find the proportion of measurements between 46 and 74 in a normal distribution with a mean (μ) of 60 and a standard deviation (σ) of 14, we can use the standard normal distribution (z-score) and the cumulative distribution function (CDF).

First, we need to convert the interval endpoints to z-scores using the formula:

z = (x - μ) / σ

Where x is the value in the interval, μ is the mean, and σ is the standard deviation.

For x = 46:

z₁ = (46 - 60) / 14

z₁ = -1

For x = 74:

z₂ = (74 - 60) / 14

z₂ = 1

Using the Excel functions:

=NORM.S.DIST(-1) and =NORM.S.DIST(1)

The probabilities are 0.1587 and 0.8413 respectively.

Now, we want the proportion of measurements between z₁ and z₂, which is:

Proportion = 0.8413 - 0.1587

≈ 0.6826

To learn more about the z-score;

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Which statements are true? Select three options. The line x = 0 is perpendicular to the line y = –3. All lines that are parallel to the y-axis are vertical lines. All lines that are perpendicular to the x-axis have a slope of 0. The equation of the line parallel to the x-axis that passes through the point (2, –6) is x = 2. The equation of the line perpendicular to the y-axis that passes through the point (–5, 1) is y = 1.
How do you do this question?
PLEASE HELP!!! According to the synthetic division below, which of the following statements are true?

What is mZSVT?
Enter your answer in the box.

Answers

Answer:

The measure of ∠SVT is 79°

Step-by-step explanation:

In the given figure

∵ US ∩ RT at V

∴ ∠SVT and ∠UVR are vertically opposite angles

∵ The vertically opposite angles are equal in measures

∴ m∠SVT = m∠UVR

∵ m∠SVT = (5y + 9)°

∵ m∠UVR = (8y - 33)°

→ Equate them

∴ 8y - 33 = 5y + 9

→ Add 33 to both sides

∴ 8y - 33 + 33 = 5y + 9 + 33

∴ 8y = 5y + 42

→ Subtract 5y from both sides

∴ 8y - 5y = 5y - 5y + 42

∴ 3y = 42

→ Divide both sides by 3

∵ $(3y)/(3)$ = $(42)/(3)$

∴ y = 14

→ Substitute the value of y in the measure of ∠SVT

∵ m∠SVT = 5(14) + 9

∴ m∠SVT = 70 + 9

∴ m∠SVT = 79°

∴ The measure of ∠SVT is 79°

In your own words, describe how to graph the linear equation y = -1/5x + 3. Step by step

Answers

Answer:

Steps given below and graph is attached.

Step-by-step explanation:

First Step:

Find out $y-intercept$ by substituting $x=0$

$y=-(1)/(5)* 0+3\n\ny=3\n\nHence\ line\ passes\ through\ (0,3).$

Second Step:

Find out $x-intercept$ by substituting $y=0.$

$0=-(1)/(5)x+3\n\n(1)/(5)x=3\n\nx=15\n\nHence\ line\ passes\ through\ (15,0).$

Third Step:

Draw a line passing through $(0,3)\ and\ (15,0)$ .

Graph is attached.

Greatest comment factor of 14^3 and 13^4

Answers

Answer:

14^3 = 2,744. Common factors are 1,2,4,7,8,14,28,49,56...

13^4 = 2,197. Common factors are 1, 13, 169, and 2197.

A tank contains 22 gallons of water when all of a sudden the water begins draining at a constant rate of 2 gallons per hour. Let t represent the number of hours since the water begun draining and let v represent the volume of water in the tank. Write a formula that expresses y in terms of t .

Answers

Answer:

V= 22-2t

Step-by-step explanation:

I guess the alphabet should be v instead of y. So I am working using v

The rate at which water is draining from the tank is 2gallons/hour. This is the rate of water removal from the tank. So after an hour, 2 × 1= 2 gallons would have drained. After 5 hours, 2×5 =10 gallons would have drained

Therefore to obtain the amount of water in gallons that have been removed from the tank, you will multiply the rate by the time in hours after which the draining started.

Amount (gallons) =2×t

The amount of water remaining in the tank will be obtained by subtracting the amount of water drained after some hour (2×t) from the initial amount of water in the tank (22)

Therefore, the amount of water present in the tank (v)= 22-2t or 2(11-t) gallons

Final answer:

The formula to express volume of the water v in terms of time t is v = 22 - 2t, where 22 is the initial volume and 2t represents the rate at which the water is draining.

Explanation:

This problem is a mathematical representation of a real-world scenario using a linear equation. The volume of water v in the tank can be represented in terms of time t through the equation v = 22 - 2t. This equation illustrates the initial volume of water in the tank (22 gallons) and accounts for the constant rate at which the water is draining (2 gallons per hour).

When time t = 0 (meaning no time has passed since the water started draining), the volume of water v = 22 (the initial volume). As time increases, the volume gradually decreases at a rate of 2 gallons per hour, represented by the term -2t.

Learn more about Linear Equation here:

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Mariana tried to drink a slushy as fast as she could. She drank the slushy at a rate of 4.5 milliliters per second. After 17 seconds, 148.5 milliliters of slushy remained.How much slushy was originally in the cup?