The test grades of a science class are given.

78, 75, 70, 92, 69, 83, 98, 76, 75, 82, 91, 89

The grades are normally distributed with a mean of 81.5 and a standard deviation of 9.3.



What is the z-score of the highest grade in the test?

Round the answer to the nearest hundredth.

Answer:

2 6/15, 2 4/9, 2 3/5, 2 2/3

Step-by-step explanation:

Make all the fractions improper fractions. So 2 2/3= 8/3, 2 6/15= 13/15, etc.

Then make all the denominators 45 and then order them from there.

Answer:

Option C.

Step-by-step explanation:

System of the equation consists of two equations

2x + y - 4 = 0

2x + y - 4 + 4 = 0 + 4

2x + y = 4--------(1)

and 2x - y - 4 = 0

2x - y + 4 - 4 = 0 + 4

2x - y = 4------(2)

Now we will add these equations to eliminate y.

(2x + y) + (2x - y) = (4 + 4)

(2x + 2x) + (y - y) = 8

4x = 8

Therefore, resulting equation will be 4x = 8

Option C. will be the answer.

Answer:

30 miles per 1 day

Step-by-step explanation:

so 30 miles for each day and if you add 30 eight times which is the same as 30 times 8 you will get 240 miles hope it helps

Answer:

c =1.50n +2.50

Step-by-step explanation:

c=1.50(n-2)+5.50

The first step is to distribute the 1.5

c= 1.50*n -1.50*2 + 5.50

c = 1.50n - 3.0 +5.50

Now we need to combine like terms

c =1.50n +2.50

Answer:

d 5.5

Step-by-step explanation:

Answer:

D: 5.5%

Step-by-step explanation:

6(9)-8(-2)

6*9=54

8*(-2)=-16

54-16=38

38<-----

Answer:

70

Step-by-step explanation:

x=9 and y=−2, evaluate the following expression : 6x−8y

plug in

6(9) - 8(-2)

= 54 + 16

= 70

Answer: 160 miles

Step-by-step explanation:

Because if each inch is 20 miles then you multiply 20 times 8. You multiply by 8 because that how far they live from each other in inch but you want to know miles so you multiply the I with 20 and get 160 miles

Answer: A. Sun car dealers pay $18,000 to Galaxy car manufacturers for a car worth $20,000.

Step-by-step explanation:

Hi, "dealer incentives" for this case mean that a car dealer pays a reduced price for a car. This incentive allows the car dealer to make a profit.

To be an example of dealer incentive the option must state that the car dealer makes a profit.

So, with this information analyzed the correct option is A."Sun car dealers pay $18,000 to Galaxy car manufacturers for a car worth $20,000" because this option states that the Sun car dealers make a profit of $2000.

Feel free to ask for more if it´s necessary or if you did not understand something.

Answer:

-3

Step-by-step explanation:

Anything that is negative multiplied by a negative is a positive so knowing this, you can multiply -3*-3=9 or divide 9/-3=-3

Hope this helps

<> Anna <>

Answer:

The answer to linear equation 9t=-3 is t = - (1/3)

Step-by-step explanation:

9t=-3

Solving for t: Dividing both sides of the equation by 9:

9t/9=-3/9

t=-(3/9)

Simplifying the fraction on the right side of the equation dividing the numerator and denominator by 3:

t = - (3/3) / (9/3)

t = - (1/3)

Answer:

[tex]k=2[/tex]

Step-by-step explanation:

1) Rewriting:

[tex]f(x+k)=f(x)+2[/tex]

2) Suppose f(x)= ax (Linear function with b=0)

[tex]a(x+k)=ax+2\\a(x+k)=x+2\\ax+ak=x+2 \Rightarrow a=1\\x+k=x+2\\k=2[/tex]

3) Check the graph below

The correct option is D) 2.

Step-by-step explanation:

Given :

f(x) +2 and f(x +k)

Solution :

let, [tex]f(x) = ax[/tex] (linear function with b = 0)

so,   [tex]f(x+k)=a(x + k)\;\;\;at,\; x=x+k[/tex]

Rewriting,

[tex]f(x+k)=f(x) + 2[/tex]

[tex]a(x + k) = ax +2[/tex]

[tex]k = 2 \;\;\;(at,\;a=1)[/tex]

Therefore, the correct option is D) 2.

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Answer:

[tex]x+y=12[/tex]

[tex]21.50x+14.75y=204[/tex]

Step-by-step explanation:

Let x be the number of adult tickets and y be the number of children's tickets.

We are given that there are total 12 people. Therefore, we can set:

[tex]x+y=12[/tex]

Moreover, we are given that an adult ticket costs $21.50 and a child's ticket costs $14.75, therefore, cost of x adult tickets will be [tex]21.50x[/tex] and cost of y children's ticket will be [tex]14.75y[/tex]. We can form the second equation by setting the total cost of tickets as:

[tex]21.50x+14.75y=204[/tex]

Therefore, the required system of equations that could be used to find x and y will be:

[tex]x+y=12[/tex]

[tex]21.50x+14.75y=204[/tex]

Answer:

[tex]x+y = 12[/tex]

[tex]21.50x+14.75y=204.00[/tex]

Step-by-step explanation:

Given :

A local amusement park charges $21.50 per daily adult ticket and $14.75 per daily child's ticket.

Group of 12 people paid $204.00 for tickets.

To Find : System of equations could be used to find x, the number of adult tickets purchased, and y, the number of children's tickets purchased.

Solution :

Since group contains 12 people so no. of tickets are 12 .

Let out of 12 people no. of adults's tickets  are x.

Let out of 12 people no. of children's ticket are y .

⇒[tex]x+y = 12[/tex]

Since charge of one adult ticket = $21.50

So, charge of x adult tickets = $21.50 x

Since charge of one child ticket = $14.75

So, charge of y children tickets =$14.75 y

And we are given that total amount paid by these 12 people = $204.00

Thus [tex]21.50x+14.75y=204.00[/tex]

Hence , System of equations could be used to find x, the number of adult tickets purchased, and y, the number of children's tickets purchased:

[tex]x+y = 12[/tex]

[tex]21.50x+14.75y=204.00[/tex]

Answer:

find below

Step-by-step explanation:

7x-6 = 3x-14

4x = -8

x = -2

-2*7-6 = -14-6 = -20

-2*3-14 = -6-14 = -20

Answer:

12:5

Step-by-step explanation:

We want to find the ratio of Jeanne's tickets to Jake's tickets

Jeanne's tickets: Jake's tickets

15:36

We can simplify this ratio by dividing each side by 3

15/3:36/3

5:12

Answer:

Step-by-step explanation:

15:36

simplifies to

5:12

Jeanne: Jake

Answer:

B, C D

Step-by-step explanation:

Inequalities are the "alligators"  <   or >  or the "alligators" with lines  ≤  or ≥

<  less than

>greater than

≤  less than or equal to

≥  greater than or equal to

ANSWERS:

B) 11 > (w - 4)^2 & C) y < 3^4 & D) 5 + 9 < 5 x 9

About this > inequality sign:

About this < inequality sign:

About this > inequality sign:

About this < inequality sign:

The solution in scientific notation si:

Option D: 6.8 * 10⁵

How to give the answer in scientific notation?

Scientific notation is a way of expressing very large or very small numbers. It involves writing a number as a product of a number between 1 and 10 and a power of 10.

For example, 800,000,000 can be written in scientific notation as 8 × 10⁸.

We are given the expression:

(3.4 * 10²) * (2 * 10³)

= (3.4 * 2) * 10² ⁺ ³

= 6.8 * 10⁵

x=

D) 5  1/3

Simplify 5 6/9 to 5 2/3. Subtract 1/3 from both sides and you are left with x=5 1/3

[tex]25=12+r\\r=25-12\\r=13[/tex]

12 + r = 25      subtract 12 from both sides

12 - 12 + r = 25 - 12

Answer: C

Step-by-step explanation: |-15| is 15. |12| is 12. 15 is greater then 12.

Answer:

A) 210

Step-by-step explanation:

The percentage of students who have a cell phone plan with company x is student with plan x over total.The total is 130

P(x) = 70/130

The number of students with cell phone  company x is  found by multiplying the total number of students times   the percentage of students with company x

Students with company x = total * P(x)

                                          = 390 * 70/130

                                             = 210

Answer:

A) 210

Step-by-step explanation:

70 students have company X, out of the sample size 130. This forms the fraction 70/130.

n students have company X, out of the population 390. The n is simply a placeholder for a number. This forms the fraction n/390

Equate the two fractions, cross multiply, then divide both sides by 130 to solve for n

Doing all that gives us the following

70/130 = n/390

70*390 = 130*n ..... cross multiply

27300 = 130n

130n = 27300

130n/130 = 27300/130 ...... divide both sides by 130

n = 210

Out of the entire population, the best approximation to the number of students who have company X is 210 people.

Answer:

The bill total is $27.32

Step-by-step explanation:

how to figure out tax amount: 25.30 x .08 = $2.024

add tax to cost of meal : 25.30 + 2.024 = $27.32

To calculate the total cost of the meal including an 8% tax, multiply the cost of the meal by the tax rate and add this to the original meal cost. The tax comes to $2.02. So, the total cost of the meal, including tax, is $27.32.

The question asks how much the total bill is for Michael and Imani when they go out to eat for lunch. The food and beverages cost $25.30 and there is an 8% meal tax. To calculate the total cost of the meal including the tax, we can multiply the cost of the meal ($25.30) by the tax rate (8%) and add this to the original cost for the meal.

First, let's convert the tax rate from a percentage to a decimal. 8% is equivalent to 0.08 as a decimal. Then, we multiply $25.30 by 0.08:

$25.30 * 0.08 = $2.02

This amount ($2.02) is the tax on the meal. To get the total cost, add this tax amount to the cost of the meal:

$25.30 + $2.02 = $27.32

So, Michael and Imani's bill, including the 8% meals tax, will be $27.32.

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Answer:

17 seconds

Step-by-step explanation:

The rescue helicopter travels down for 100 seconds at a speed of 10.5 feet per second.

So, the distance it covered = 100(10.5) = 1050 feet.

It then travels directly up for 150 seconds at a speed 5.2 feet per second.

So, the distance = 150(5.2) = 780 feet

Now, the distance from sea level = 1050 - 780 = 270 feet.

It will reach this distance with a maximum speed of 15.8 feet per second.

Hence, the time required to reach this distance = [tex]\frac{distance}{speed}[/tex]

= [tex]\frac{270}{15.8}[/tex]

≈ 17 seconds

Answer:

23.3%

Step-by-step explanation:

so 5 by 6 is 30

so to find the fraction or desimal or persent u need to put 7/30

and that would be .23 reapeating then time it by 100 to get

23.3% ps the 3 is reapeating

Final answer:

The probability that Ari will select a sold-out item is 7/30 or approximately 23.33%.

Explanation:

The question asks about the probability that Ari will select an item that is already sold out from a candy machine with a certain configuration and number of sold-out items. To calculate this probability, we need to know the total number of items in the machine and how many are sold out.

There are five rows with six items each, giving a total of 30 items. With seven items sold out, there are 30 - 7 = 23 items available for purchase. The probability of selecting a sold-out item is the number of sold-out items divided by the total number of items. In this case, it's 7/30, which simplifies to 7/30.

So, if Ari randomly pushes a button on the candy machine, the probability that he will select an item that is already sold out is 7/30, or approximately 23.33%.

Answer:

a= 14

b= 111

just took it

Answer:

Part a) The area of the figure is [tex]\frac{9}{2}(4+\pi )\ cm^{2}[/tex]

Part b) The perimeter of the figure is [tex]3(2+2\sqrt{2}+ \pi)\ cm[/tex]

Step-by-step explanation:

Step 1

Find the area of the figure

In this problem we have that

The figure ABC is the half of a square and the other figure is a semicircle

Find the area of the figure ABC

we have

[tex]AB=6\ cm, BC=6\ cm[/tex]

The area of the half square ABC is equal to find the area of triangle ABC

so

[tex]A1=\frac{1}{2}*6*6=18\ cm^{2}[/tex]

Find the area of the semicircle

The area of the semicircle is equal to

[tex]A2=\pi r^{2}/2[/tex]

we have that

[tex]r=6/2=3\ cm[/tex]

substitute

[tex]A2=\pi (3)^{2}/2[/tex]

[tex]A2=(9/2) \pi\ cm^{2}[/tex]

The area of the figure is equal to

[tex]18\ cm^{2}+(9/2) \pi\ cm^{2}= \frac{9}{2}(4+\pi )\ cm^{2}[/tex]

Step 2

Find the perimeter of the figure

The perimeter of the figure is equal to

[tex]P=AB+AC+length\ CB[/tex]

we have

[tex]AB=6\ cm[/tex]

Applying Pythagoras theorem

[tex]AC=\sqrt{6^{2}+6^{2}}\\AC=6\sqrt{2}\ cm[/tex]

Remember that

the circumference of a semicircle is equal to

[tex]C=\frac{1}{2}2\pi r=\pi r[/tex]

[tex]r=6/2=3\ cm[/tex]

[tex]C=\pi(3)[/tex]

[tex]C=3 \pi\ cm[/tex]

The perimeter of the figure is equal to

[tex]P=6\ cm+6\sqrt{2}\ cm+3 \pi\ cm[/tex]

Simplify

[tex]P=3(2+2\sqrt{2}+ \pi)\ cm[/tex]

Answer:

$12.50

Step-by-step explanation:

1) Mutliply 6 with 2

6*2= 12

2) multiply 1/4 with 2

1/4 * 2 =1/2

3) add 12 and 1/2

12+1/2 = 12.50

By converting the mixed number of pizzas sold to an improper fraction and multiplying by the price per whole pizza, we find the food booth made $100 in one hour from selling pizzas.

To determine how much money was made at the food booth in the given hour, we need to calculate the total sale of pizzas. Since 1/8 of a pizza costs $2, an entire pizza would cost 8 times that amount, which is $16 per pizza. It was stated that 6 1/4 pizzas were sold in that hour. To find the total, we multiply the price per pizza by the number of pizzas sold.

First, convert the mixed number 6 1/4 to an improper fraction to simplify the calculation: 6 1/4 is the same as (6 × 4 + 1) / 4, which is 25/4. Then, multiply the cost per pizza, which is $16, by the number of pizzas sold, which is represented by the fraction 25/4.

The equation for total money made is then $16 ×  {25}/ {4} = $100.

So, the food booth made $100 in that hour from selling pizzas.

Answer:

$5750

Step-by-step explanation:

Property damage insurance = $20,000

Comprehensive insurance = $5,000

Deductible = $500

Amount of Property damage caused by him by hitting a parked car = $4,500

Amount of Damage caused to his own car = $1,750

Since, the property damage of $4500 is within the property damage insurance limit of $20,000 and own damage of $1,750 is also within the comprehensive insurance limit of $5000, he'll be paid the entire amount excluding the compulsory deductible of $500.

So,

The amount paid by the insurance company to fix both cars = 4500+1750 - 500

= 6250 - 500

= $5750

The insurance will cover a total of $5,750 for the damages caused by Saheel's accident. It will completely cover the $4,500 worth of damage to the parked car that he hit, and will cover $1,250 of the $1,750 damage to his own car after the deductible.

In this case, Saheel has coverage for both property damage ($20,000) and comprehensive and collision insurance ($5,000 with a $500 deductible). When he slid on ice and hit a parked car, causing $4,500 worth of damage, his property damage insurance will cover this cost since it is under the $20,000 limit.

As for the $1,750 damage to his own car, his comprehensive and collision insurance can cover this after he pays the $500 deductible. So, his insurance will pay $1,250 ($1,750 - $500 deductible) towards the repair of his own car.

Therefore, the total money that the insurance company will pay to fix both cars would be $5,750 ($4,500 for the parked car's damages and $1,250 for Saheel's car damages after deductible).

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Answer:

120 pounds

-hope this helps

Answer:

£111.43

Step-by-step explanation:

100% represents the original cost of the phone

30% off is then (100 - 30) = 70% of the original cost

divide the cost by 70 to find 1% then multiply by 100 for original cost

original cost = [tex]\frac{78}{70}[/tex] × 100 = £111.43