Question 2(Multiple Choice Worth 4 points)

(08.06)A student wants to report on the number of movies her friends watch each week. The collected data are below:

2
14
1
2
0
1
0
2


Which measure of center is most appropriate for this situation and what is its value?

Median, 1.5
Median; 3
Mean, 1.5
Mean; 3

Answer:

I'm going to assume that this is compound interest, as simple interest in this case would not make sense.

Let A be the final amount ( in this case, after 4 years). A = 20,000(1+0.042/12)^12*4. In this formula, I am assuming that the interest compounds 12 times a year, or every month. I am also assuming that he pays it off once he hits the 4-year mark.

If the assumptions are correct, he would be paying $23651.79 at the 4-year mark.

Step-by-step explanation:

Final answer:

Marco will owe approximately $23,521.93 on his unsubsidized student loan after graduation, calculated using the future value formula for a loan with compounded interest.

Explanation:

To calculate the amount Marco will owe after he graduates, we need to apply the formula for the future value of a loan when interest is compounded annually and no payments are made until after a certain period. Since Marco's unsubsidized student loan does not require payments while he is in school, the interest will be capitalized and added to the principal amount of the loan.

The formula for future value FV of a present value PV after n periods at an interest rate r is:

FV = PV * (1 + r)ⁿ

Where:

PV is the initial loan amount ($20,000)

r is the annual interest rate (4.2% or 0.042 as a decimal)

n is the number of periods (years in this case) before he starts repaying the loan (4 years)

Using the formula, we get:

FV = $20,000 * (1 + 0.042)⁴

FV = $20,000 * (1.042)⁴

F = $20,000 * 1.1760965435

FV = $23,521.93

Thus, Marco will owe approximately $23,521.93 once he graduates, before he starts making any payments on the loan.

Answer:

1. x>4

2.y>-3

Answer:

20

Step-by-step explanation:

The question tells us that line a is parallel to line b (even if they don't seem to be in the image).

∠8 = ∠4 and ∠5 = ∠1 since line t crosses the parallel lines.

We are given ∠4 = 3x and ∠5 = 6x.

Since we know ∠8 = ∠4 , we can then say

∠8 = 3x and ∠5 = 6x

Since ∠8 and ∠5 are complementary and combined they form a flat angle of 180 degrees, we can say:

3x + 6x = 180

9x = 180

x = 20

The problem involves calculating the probability of winning a prize in an art contest. The total prizes are 5 and the total students are 50. Therefore, the probability of winning a prize is 5/50 = 10%

The problem you're asking about is a classic question in the field of probability. In this case, we have 50 students entering an art contest. There are 1+1+3=5 prizes to be won. Therefore, the total number of ways of winning a prize is 5.

The total number of outcomes (which in this case is the total number of students) is 50. Thus, the probability of a student winning a prize can be calculated as the ratio of the number of ways of winning to the total number of outcomes. This gives us:

P(Winning a prize) = Number of ways of winning / Total number of outcomes = 5 / 50 = 0.1 or 10%.

So, each student has a 10% chance of winning a prize in the contest.

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The probability of winning a prize in the art contest is 1/10.

To find the probability of winning a prize in the art contest, we need to consider the total number of students and the number of prizes available.

There are 1 prize for 1st place, 1 prize for 2nd place, and 3 prizes for honorable mention.

Therefore, a total of 5 prizes are available.

The probability of winning a prize can be calculated by dividing the number of prizes by the total number of students.

So, the probability is 5/50, or 1/10.

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Answer:

She applied the exponent -2 to 4(-2) instead of applying the exponent to just -2

Step-by-step explanation:

we have the expression

[tex]\frac{4m^{-3}n^{-2}}{m^{-1} n}[/tex]

Simplify

[tex]\frac{4m^{-3}n^{-2}}{m^{-1} n}=4m^{(-3+1)}n^{(-2-1)}= 4m^{(-2)}n^{(-3)}[/tex]

Substitute the values of m and n in the expression

For[tex]m=-2, n=4[/tex]

[tex]4(-2)^{(-2)}(4)^{(-3)}=4(\frac{1}{4})* (\frac{1}{64})=\frac{1}{64}[/tex]

She applied the exponent -2 to 4(-2) instead of applying the exponent to just -2

Answer: It’s C

Step-by-step explanation:

Juss took a test

Answer:

153.86

Step-by-step explanation:

To find the area the equation is pi* radius squared

so it's 3.14*7 squared it's

3.14*49

The answer is 153.86

Answer:

(-1,4)(1,4)

2

Step-by-step explanation:

Answer:

PR = 20

Step-by-step explanation:

The perimeter is the sum of the 3 sides, thus

4z + z + 3 + 3z + 2 = 45 ← simplify left side

8z + 5 = 45 ( subtract 5 from both sides )

8z = 40 ( divide both sides by 8 )

z = 5

PR = 4z = 4 × 5 = 20

Answer:

40

Step-by-step explanation:

Using the triangle perimeter formula [P=2(l) + 2(w) / 2]:

45 = 2 (z + 3) + 2 (3z + 2) / 2

45 = 2z + 6 + 6z + 4 / 2

45 = 8z + 10 / 2

45 = 4z + 5

40 = 4z

z = 10

PR

4z

4 (10)

40

Answer:

Step-by-step explanation:

Look at the picture.

We have the triangles 45° - 45° - 90° and 30° - 60° - 90°.

The sides of those triangles are in ratio:

1 : 1 : √2 and 1 : √3 : 2

Therefore

If AC = 6√2 then AB = BC = 6

If BC = 6 then x = 6 : 2 = 3

Answer:

Alternate exterior angles

Step-by-step explanation:

Alternate exterior angles are angles that are opposite of the transversal line, but are found outside or the external side of the of the line that intersects them.

If the lines that intersect them happen to be parallel, then their measures would be congruent.

ANSWER

<1 and <8 are alternate exterior angles.

EXPLANATION

From the diagram we can trace a Z shape between the two parallel lines.

When we trace the shape, <1 and <8 will be on the exterior corners of the z-shape.

z-angles are called alternate angles.

These two angles are alternate to each other.

Hence <1 and <8 are alternate exterior angles.

the assumption here, being that it's a square pyramid, thus its base is a square, namely a 6x6, Check the picture below.

notice, the pyramid has four triangular faces with a height of 9 and a base of 6, and the squarish base, so we can simply get the area of each of those figures and sum them up.

[tex]\bf \stackrel{\textit{area of four triangles}}{4\left[\cfrac{1}{2}(6)(9) \right]}+\stackrel{\textit{area of base}}{(6\cdot 6)}\implies 108+36\implies 144[/tex]

Answer:

[tex]\large\boxed{m=\dfrac{3w-2u-z}{u+w-z}}[/tex]

Step-by-step explanation:

Use the distributive property: a(b + c) = ab + ac

[tex]u(m+2)+w(m-3)=z(m-1)\\\\um+2u+wm-3w=zm-z\qquad\text{subtract}\ 2u\ \text{from both sides}\\\\um+wm-3w=zm-z-2u\qquad\text{add}\ 3w\ \text{to both sides}\\\\um+wm=zm+3w-2u-z\qquad\text{subtract}\ zm\ \text{from both sides}\\\\um+wm-zm=3w-2u-z\qquad\text{distributive}\\\\(u+w-z)m=3w-2u-z\qquad\text{divide both sides by}\ (u+w-z)\neq0\\\\m=\dfrac{3w-2u-z}{u+w-z}[/tex]

Final answer:

The amount deducted weekly for Social Security taxes from Tomas Gomez's gross weekly pay of $750 at a tax rate of 6.2% is $46.50.

Explanation:

The question relates to calculating deductions for Social Security taxes from Tomas Gomez's weekly pay. To calculate the amount deducted weekly for Social Security taxes at a tax rate of 6.2%, you multiply the gross weekly pay by the tax rate.

Gross Weekly Pay: $750
Social Security Tax Rate: 6.2%

Calculation: $750 * 6.2% = $750 * 0.062 = $46.50

Thus, the amount deducted weekly for Social Security taxes from Tomas Gomez's gross pay is $46.50.

Answer:

[tex]x=630[/tex]

Step-by-step explanation:

The Exponential Product rule tells us that...

[tex]x^m*x^n=x^{m+n}[/tex]

Therefore, [tex]x=1+2+3...+35[/tex].

Therefore, [tex]x=630[/tex]

To find the measure of Angle B, solve the equation 5x - 15 = 2x + 21, which gives x = 12. Then, substitute x back into the expression for Angle B to get 2(12) + 21 = 45°. Thus, Angle B measures 45°.

Solve for x and find the measure of Angle B

To solve for x and find the measure of Angle B, follow these steps:

Now, substitute x back into the expression for Angle B:

Angle B = 2x + 21
= 2(12) + 21
= 24 + 21
= 45°

Therefore, the measure of Angle B is 45°.

Answer:

(212 cups/2 dozen)(15 dozen) = 1,590 cups

Answer:

x = 4

Step-by-step explanation:

a = i-2j

b = 2i-xj

1 = k•2

-2 = k•(-x)

=> 1/2 = k

=> (-2)/(-x) = k

=> 1/2 = (-2)/(-x) => 1/2 = 2/x => x = 4

Answer:

$9.75 per hour

Step-by-step explanation:

243.75/25= 9.75

Hope this helps you out!

Answer:

Jeff is paid $9.75 for one hour of work.

Step-by-step explanation:

Jeff made last week = $243.75

He worked 25 hours for a week.

We have to calculate his pay per hour, so we divide his total pay by the time he worked.

total pay ÷ time he worked ( in hours)

pay per hour = 243.75 ÷ 25 = $9.75/hour

Jeff is paid $9.75 for one hour of work.

Answer:

there would be 4 vertices

Step-by-step explanation:

For this case we must find an expression equivalent to:

[tex]\frac{4\sqrt{6}}{\sqrt[3]{2}}[/tex]

We multiply by:

[tex](\frac{(\sqrt[3]{2})^2}{(\sqrt[3]{2})^2})\\\frac{4\sqrt{6}}{\sqrt[3]{2}}*(\frac{(\sqrt[3]{2})^2}{(\sqrt[3]{2})^2})=[/tex]

By definition of multiplication of powers of the same base we have:

[tex]a^n*a^m=a^{m+n}\\\frac{4\sqrt{6}*(\sqrt[3]{2})^2}{(\sqrt[3]{2})^3}=\\\frac{4\sqrt{6}*(\sqrt[3]{2})^2}{2}=[/tex]

Move the exponent within the radical:

[tex]\frac{4\sqrt{6}*\sqrt[3]{2^2}}{2}=\\\frac{4\sqrt{6}*\sqrt[3]{4}}{2}=[/tex]

We rewrite:

[tex]4^{\frac{1}{3}}=4^{\frac{2}{6}}=\sqrt[6]{4^2}\\6^{\frac{1}{2}}=6^{\frac{3}{6}}=\sqrt[6]{6^3}[/tex]

Rewriting the expression:

[tex]\frac{4\sqrt[6]{4^2}\sqrt[6]{6^3}}{2}=\\\frac{4\sqrt[6]{16*216}}{2}=\\\frac{4\sqrt[6]{3456}}{2}=\\\frac{4\sqrt[6]{2^6*54}}{2}=\\\frac{8\sqrt[6]{54}}{2}=\\4\sqrt[6]{54}[/tex]

Answer:

[tex]4\sqrt[6]{54}[/tex]

Answer:

A!!!!

12^sqrt 27/ 2

Step-by-step explanation:

Answer:

[tex]2*10^{-1}[/tex]

Step-by-step explanation:

From 0 to 1, there are 5 units, so each of the lines are 1/5.

Hence, it is  0, 1/5, 2/5, 3/5, 4/5, 1

The point P is the first line, so that is 1/5, or in decimal, 0.2

Now we check all the options:

First Choice:  2 ^ -1 = 1/2^1 = 1/2  NO

Second Choice:  2 ^ 0 = 1  (anything to the power 0 is 1)  (NO)

Third Choice:  2 ^ 1 = 2 (NO)

Fourth Choice:  2 * 10 ^ -1 = 2 * 1/10 = 1/5 or 0.2 (RIGHT)

So, last choice is correct.

Answer:

B). 5.6

Step-by-step explanation:

3.2/x = 4/7

Then, cross-multiply

4x = (3.2) 7

4x = 22.4

x = 5.6

Area of each cookie is approximately 28.3 cm2.

The area of a circle can be calculated using the formula A = πr2. Given that the diameter of each cookie is 6 centimeters, the radius would be half of the diameter, which is 3 centimeters. Plugging in the values, we get: A = 3.14 x (3 cm)2 = 3.14 x 9 = 28.26 cm2. Rounded to the nearest tenth, the area of each cookie is approximately 28.3 cm2.

Answer:

correct answer is option b.

Step-by-step explanation:

so Ashley has markdown one item by 15%

and mark up other items by 10% to get $3.77

assuming she marked ceiling fan mark down by 15%

if each  item is sold

  =  0.85 ×  $64.79 +1.1 × $51.49 +1.1 ×  $45.99 + 1.1 × $37.39

  = $203.4285

profit

= $203.4285 - $64.79 -$51.49 - $45.99 -$37.39

=$3.7685   ≅$3.77

hence ceiling fan price will be draw down by 15%

hence correct answer is option b.

The item that was marked down was the b. ceiling fan, from $64.79 to $55.07.

A markdown reduces the cost or price of an item by the percentage markdown.

A markup, on the other hand, increases the cost of the item.

Markdown = 15%

Markup = 10%

Items                   Prices

Power drill          $51.49

Ceiling fan           64.79

Circular saw        45.99

Screwdriver set   37.39

Total price       $199.66

Increase in the price = $3.77

New price = $203.43 ($199.66 + $3.77)

Most likely, Ashley will mark down the Ceiling fan to attract customers to purchase other items.

Therefore, the new prices after applying the changes will be:

Items                   Prices    Markup/down

Power drill          $51.49      $56.64 ($51.49 x 1.1)

Ceiling fan           64.79        55.07 ($64.79 x 0.85)

Circular saw        45.99       50.59 ($45.99 x 1.1)

Screwdriver set   37.39         41.13 ($37.39 x 1.1)

Total price       $199.66  $203.43

New total price = $203.43

Old total price = $199.66

Increase in cost = $3.77 ($203.43 - $199.66)

Thus, the item that was marked down was the b. ceiling fan.

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Answer:$2700

Step-by-step explanation: Really depends on the kind of interest, but you would take the initial amount, and multiply it by the APR for the amount of interest, then add the interest to the initial amount.

To repay the full principle and interest in the first year of the loan with an interest rate of 8%, David borrowed $2500 from his local bank, would need to pay a total of $2700 to the bank.

To answer your question, we first need to calculate the interest David needs to pay. The formula used to calculate the interest on a loan is: Principal sum x Annual interest rate. David's principal sum is $2500 and the annual interest rate is 8%.

Here's the calculation step-by-step:

So, if David pays the full principle and interest in the first year of the loan, he will pay a total of $2700 to the bank.

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Answer:

£ 1.96

Hope this helps :)

Have a great day !

5INGH

Step-by-step explanation:

1 kg = £ 4.90

( ÷ 10 )

100 g = £ 0.49

( × 4 )

400 g = £ 1.96

Answer:

£1.96

Step-by-step explanation:

1kg = 1000g

1 kg = £4.90

1000g = £4.90

1000g = £4.90

100 g = 4.90 ÷ 10 = £0.49

100g = £0.49

400g = 0.49 x 4 = £1.96

Answer:

y = -|x| +3

Step-by-step explanation:

Answer:

-/x/-3

Step-by-step explanation:

Answer:260

53×5=260

Step-by-step explanation:

265 paving stones will be needed if it is 53 for each project

Answer: 15 cookies and 5 brownies will be required.

Step-by-step explanation:

Given in the question is Eder needs 6 cookies and 2 brownies for 4 plates.

We have to calculate the cookies and brownies required for 10 plates.

Let's first calculate the cookies by unitary method.

⇒ 4 plates required cookies = 6 cookies

⇒  1 plate will require cookies = 6/4

⇒ 10 plates will require cookies = 6×10/4 = 15

Similarly we will calculate the brownies.

⇒ 4 plates required number of brownies = 2

⇒1 plate will require = 2/4 brownies

⇒10 plates will require = 2×10/4 = 5 brownies

⇒Therefore 15 cookies and 5 brownies will be required for 10 plates.

* Hopefully this helps:)

~ 234483279c20~

For 4 plates, an editor needs 1.5 cookies and 0.5 brownies. Thus, for ten plates, they will require 15 cookies and 5 brownies.

Let's start by determining the amount of cookies and brownies the editor needs for 4 plates. As per the given information, the editor needs 6 cookies and 2 brownies for every 4 plates. Therefore, for each plate, the editor will need to have 1.5 cookies (6/4 = 1.5) and 0.5 brownies (2/4 = 0.5).

Now, let's compute how much this would translate to if we have ten plates. Using the ratio we determined earlier, for ten plates the editor would need:

This is the simplest way to figure out how many cookies and brownies are needed for a given number of plates, provided you know how much is needed per plate.

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Answer:

Y=-2.9x+120

Step-by-step explanation:

The most simple way to solve is plug any x value into each equation and see if it works

Answer:

2nd option choice or third