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2 years ago

10

Ms. Casey grades 4 tests during her lunch. She grades 1/3 of the remainder after school. If she still has 16 tests to grade afte

r school, how many tests are there?

1 answer:

CaHeK987 [17]2 years ago

6 0

Answer:30 tests

Step-by-step explanation:

16=2/3 -4

20=2/3

10=1/3

30tests

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The table shows how an elevator 500 feet above the ground is descending at a steady rate.

Snezhnost [94]

We are given that the elevator is descending, so the coefficient of t must be negative. The elevator's initial position is 500 feet above the ground, so this is a positive value of +500. Therefore the only choice that fits these is h(t) = -5t + 500.

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1 year ago

Read 2 more answers

The fraction of defective integrated circuits produced in a photolithography process is being studied. A random sample of 300 ci

Olenka [21]

Answer:

The correct answer is

(0.0128, 0.0532)

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence interval $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

Z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$

For this problem, we have that:

In a random sample of 300 circuits, 10 are defective. This means that $n = 300$ and $\pi = \frac{10}{300} = 0.033$

Calculate a 95% two-sided confidence interval on the fraction of defective circuits produced by this particular tool.

So $\alpha$ = 0.05, z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{300}} = 0.033 - 1.96\sqrt{\frac{0.033*0.967}{300}} = 0.0128$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{300}} = 0.033 + 1.96\sqrt{\frac{0.033*0.967}{300}} = 0.0532$

The correct answer is

(0.0128, 0.0532)

4 0

1 year ago

The scale factor of a room for a scale drawing is 2.3. The actual length of a wall in the room is 46 feet and the actual width o

dimaraw [331]

Answer:

There's two ways to solve this.

Step-by-step explanation:

First way:

Let's divide the width and length by 2.3.

46÷2.3=20

69÷2.3=30

20×30

600 ft²

Second Way:

Let's find the area of the actual room.

46×69

3,174 ft²

Let's find the scale drawing squared.

2.3²=5.29

3,174÷5.29

600 ft²

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2 years ago

Read 2 more answers

There is a 0.9991 probability that a randomly selected 31-year-old male lives through the year. A life insurance company charge

jarptica [38.1K]

Answer:

a) Monetary values corresponding to the two events are:

-In case of surviving the year = -166$

-In case of a death in the year = 89834$

b) Expected value of the purchasing the insurance is -85 $

c) Yes, insurance company can make a profit with this policy.

Step-by-step explanation:

<em>a)</em> The man need to pay 166$ first to enroll the insurance policy. If he survives within a year, he will lose 166$. Otherwise, if he dies within a year he will profit 89834$.

<em>b)</em> Expected value of the purchasing the insurance as following:

<u>-In case of surviving the year: </u>

Value: -166$

Probability: 0,9991

<u>-In case of death in a year </u>

Value: 89834$

Probability: 0,0009

Expected value is E(x) = -166×0,9991 + 89834×0,0009 = -85 $

<em>c)</em> Lets consider that 10000 different 31 year old man enrolled to this insurance policy. According to probability of death, 9 out of 10000 man expected to be dead within the year. Therefore, company need to pay 9*90000 = 810000$ to their costumers. But, company will collect 10000*166=1660000$ from their costumers in the beginning of the year

So, it is expected that company is going to profit 1660000-810000=850000$ per year.

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2 years ago

A rectangular exercise mat has a perimeter of 36 feet. The length of the mat is twice the width. Write and solve an equation to

Karo-lina-s [1.5K]

<h2>Hello!</h2>

The answers are:

- Length

$length=2width=12feet$

- Width

$width=6feet$

- Area

$Area=72feet^{2}$

<h2>Why?</h2>

We are given the perimeter of a rectangular mat, and we are asked to find the area, and write an equation to determine the length, if feet, of the mat. To solve this problem we need to remember the equation of the perimeter of a rectangle, which is:

$Perimeter=2length+2width$

Using the given information we have,

$36feet=2length+2width$

Also, we know that the length is twice the width, so:

$length=2width$

Then, substituting the second equation into the first equation, we can find the width of the mat.

Substituting, we have:

$36feet=2(2width)+2width$

$36feet=4width+2width$

$36feet=6width$

$[tex]\frac{36feet}{6} =width$ \\width=\frac{36feet}{6} =6feet[/tex]

Then, substituting the width into the second equation, we can find the length of the mat,

Substituting, we have:

$length=2width$

$length=2(6feet)=12feet$

Then, finding the area, we have:

$A=length*width=12feet*6feet=72feet^{2}$

Have a nice day!

7 0

2 years ago