A school librarian surveyed a random sample of $50$ students to find out which library resources students value most. The table below shows the results.

Library Resources Number of Students
Books 24
Study Areas 10
Classes 6
Movies 10

Which statements are best supported by the data?

Select all that apply.

A It is expected that $15\%$ to $25\%$ of all students will value movies the most.

B It is expected that $20\%$ to $30\%$ of all students will value books the most.

C In a group of $25$ students, it is expected that around $5$ students will value study areas the most.

D In a group of $100$ students, it is expected that around $6$ students will value classes the most.

E In a group of $200$ students, it is expected that $20$ students will value study areas the most, and $20$ students will value movies the most.

Answer:

[tex](a)\ (x+6)^2 + (y-5)^2 = 25[/tex]

[tex](b)\ Area = 16.75cm^2[/tex]

Step-by-step explanation:

Solving (a):

Given

[tex](a,b) = (-6,5)[/tex]

[tex]r = 5[/tex]

Required

The equation of the circle

This is calculated as:

[tex](x-a)^2 + (y-b)^2 = r^2[/tex]

So, we have:

[tex](x--6)^2 + (y-5)^2 = 5^2[/tex]

[tex](x+6)^2 + (y-5)^2 = 25[/tex]

Solving (b):

Given

[tex]r = 8cm[/tex]

[tex]\theta = 30^o[/tex] --- Missing from the question

Required

The area of the sector

This is calculated using:

[tex]Area = \frac{\theta}{360} * \pi r^2[/tex]

So, we have:

[tex]Area = \frac{30}{360} * 3.14 * 8^2[/tex]

[tex]Area = \frac{1}{12} * 200.96[/tex]

[tex]Area = 16.75cm^2[/tex]

Answer:

B. 5070π in³

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Geometry

Volume of a Cylinder Formula: V = πr²h

Step-by-step explanation:

Step 1: Define

Identify variables

r = 13 in

h = 30 in

Step 2: Find Volume

Answer:

[tex]\large\fbox{B. 5070 π inches³}[/tex]

Step-by-step explanation:

The Volume of cylinder

Volume of cylinder = π × r ² × h

Where,

Using Formula

➛Volume of cylinder = π × r ² × h

substitute the values into the formula

➛ Volume of cylinder = π × ( 13 inches)² × 30 inches.

Evaluate exponent

➛ Volume of cylinder = π × 169 inches ² × 30 inches.

multiply, we get

➛ Volume of cylinder = 5070 π inches ³.

Therefore, option B which is 5070 π inches³ is the correct ☑ answer.

Answer:

A   y ≥ (1/2)x + 5

Step-by-step explanation:

The shaded area is above the solid line

the correct symbol is ≥

Answer:

Its C

Step-by-step explanation:

Answer:

1/3

Step-by-step explanation:

Probability calculates the likelihood of an event occurring. The likelihood of the event occurring lies between 0 and 1. It is zero if the event does not occur and 1 if the event occurs.

For example, the probability that it would rain on Friday is between o and 1. If it rains, a value of one is attached to the event. If it doesn't a value of zero is attached to the event.

Experimental probability is based on the result of an experiment that has been carried out multiples times

probability of landing on the orange section = proportion of the orange section / total proportions of all the colours

= 1/3

Answer:

26

Step-by-step explanation:

Problem: f(x) = 28 + x + 7

Plug in f(-9)

New equation: f(-9) = 28 + (-9) + 7

Simplify: f(-9) = 26

Answer: f(-9) = 26

Answer:

all i know is that the answer is

above 2,400

Step-by-step explanation:

Answer:

[tex] q = 2(t - 5) [/tex]

Step-by-step explanation:

[tex]t = \frac{q}{2} + 5 \\ \\ t - 5 = \frac{q}{2} \\ 2(t - 5) = q[/tex]

hope this helps you.

Have a nice day!

Answer:

2 ( t - 5 ) = q

Step-by-step explanation:

subtract 5 from both side

multiply each side by 2.

Answer:

Y = -1x - 1

Step-by-step explanation:

I used desmos graphing calculator and tried until I got a line that worked.  It passes through (2, -3) and has a slope of -1

Hope this helped :)

Answer:

El pastel se debe dividir en 6 partes iguales, de las cuales Santiago debe tomar 3 y Alba debe tomar 2.

Step-by-step explanation:

Dado que Santiago quiere comer la mitad de un pastel y Alba quiere un tercio del mismo pastel, para repartirlo bien se deben reducir las fracciones a su común denominador. Así, para determinar en cuántas partes iguales deben dividir el pastel y cuántas partes debe tomar cada uno se deben realizar los siguientes cálculos:

Santiago = 1/2

Alba = 1/3

2 x 3 = 6

Santiago = 1/2 = 3/6

Alba = 1/3 = 2/6

Por lo tanto, el pastel se debe dividir en 6 partes iguales, de las cuales Santiago debe tomar 3 y Alba debe tomar 2.

Answer:

[tex]4x\left(x^2-3x+1\right)[/tex]

[tex]Distribute\:parentheses[/tex]

[tex]\mathrm{Apply\:minus-plus\:rules}[/tex]

[tex]Simplify[/tex]

Answer:

2.58 saved

Step-by-step explanation:

To find the discount, take the amount and multiply the discount percent

10.30 * 25%

10.30 *.25

2.575

Round to the nearest cent

2.58

Answer:

Step-by-step explanation:

2.58 saved

Answer: -5/4

Step-by-step explanation: Cosecant is hypotenuse divided by the opposite side. The hypotenuse is 5 units, while the opposite side is 4 units. The answer has to be negative because the opposite side is below y=0.

Answer:

The number itself is 508.231

Step-by-step explanation:

Any multiplying each of the numbers, we will have the specific places

Hundreds

5 * 100 = 500

Tenths

0 * 10 = 0

ones

8 * 1 = 8

Tenths = 2 * 1/10 = 2/10 = 1/5 = 0.2

Hundredths = 3/100 = 0.03

Thousandths = 1/1000 = 0.001

So we simply sum all these to get the number itself as follows

500 + 8 + 0.2 + 0.03 + 0.001 = 508.231

Answer:

La oferta más conveniente es la C, pues en ella se pagará menos dinero que en las dos anteriores.

Step-by-step explanation:

Dado que una empresa, para comprar ropa de trabajo para su personal, tiene un presupuesto de $ 10.000, y la empresa pide cotizaciones y recibe las siguientes propuestas: a) pagar $ 5.000 al contado y $ 5.000 en 90 días; b) pagar $ 3.000 al contado; $ 3.000 en 30 días y $ 4.000 en 90 días; y c) pagar $ 2.000 al contado, $ 4.000 en 30 días y $ 4.000 en 84 días, si la tasa de interés es del 24% anual, para determinar cuál oferta le conviene aceptar se debe realizar el siguiente cálculo:

90 días = 1/4 año

30 días = 1/12 año

84 días = 23/100 año

365 = 1

85 = X

84 / 365 = 0.23

A) 5,000 + (5,000 x 1.06) = 5,000 + 5,300 = 10,300

B) 3,000 + (3,000 x 1.02) + (4,000 x 1.06) = 3,000 + 3,060 + 4,240 = 10,300

C) 2,000 + (4,000 x 1.02) + (4,000 x 1.023) = 2,000 + 4,080 + 4,092 = 10,172

Por lo tanto, la oferta más conveniente es la C, pues en ella se pagará menos dinero que en las dos anteriores.

The answer is D.

the blue parabola is 1 y value up from red. So you have a +1. It is 4 values to the right of red, but when x is in the format of (x + a) ^2, then the sign of operation is opposite of the action in graph. So positive means subtracting and negative means adding. So you put in x - 4

Answer:

Step-by-step explanation:

Answer:△LMK △MNK △LNM

im pretty sure thats it

Answer:

the mean is 9.

Step-by-step explanation:

7

Answer:

(9, 13, 22)

Step-by-step explanation:

We can use the triangle inequality theorem to help us solve this problem. We know that the two shortest sides of a traingle added up (their sum) needs to always be greater than the longest side of the triangle. Taking that information, we can figure out that 9+13=22. 22=22, not 22>22. This means that is the right answer, hopefully that helps!

Answer:

D=1

Step-by-step explanation:

g(x)=x³-9x²+27x-25

g(2)=(2)³-9(2)²+27(2)-25

=8-36+54-25

=1

Step-by-step explanation:

Since g(f(x))=x g ( f ( x ) ) = x , f−1(x)=2x f - 1 ( x ) = 2 x is the inverse of f(x)=12x f ( x ) = 1 2 x .

Replace f(x)f(x) with yy.

y=12xy=12x

Interchange the variables.

x=12yx=12y

Solve for yy.

Rewrite the equation as 12y=x12y=x.

12y=x12y=x

Multiply both sides of the equation by 22.

2⋅12⋅y=2⋅x2⋅12⋅y=2⋅x

Simplify 2⋅12⋅y2⋅12⋅y.

Cancel the common factor of 22.

Cancel the common factor.

2⋅12⋅y=2⋅x2⋅12⋅y=2⋅x

Rewrite the expression.

1⋅y=2⋅x1⋅y=2⋅x

Multiply yy by 11.

y=2⋅xy=2⋅x

Solve for yy and replace with f−1(x)f-1(x).

Replace the yy with f−1(x)f-1(x) to show the final answer.

f−1(x)=2xf-1(x)=2x

Set up the composite result function.

g(f(x))

Answer:

Step-by-step explanation:

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Answer:

Below:

Step-by-step explanation:

y = -0.5x + 2

m = -0.5

b = 2

Answer:

x² - 9x + 20

You are correct.

None of the listed choices are correct.

-----------------------------

I think the question originally had 5 and -4 as the solutions

https://www.jmap.org/Worksheets/A.APR.B.3.ZerosofPolynomialsPR1.pdf

x = {-4, 5}

(x + 4)(x - 5) = 0

x² - 5x + 4x - 20 = 0

x² - x - 20 = 0     Answer E

Step-by-step explanation:

x = {4, 5}

y = (x - 4)(x - 5)

y = x² - 5x - 4x + 20

y = x² - 9x + 20

Answer:

[tex]\text{C. }1.3[/tex]

Step-by-step explanation:

The area of a rectangle with width [tex]w[/tex] and length [tex]l[/tex] is given by [tex]A=lw[/tex].

What we're given:

Substituting given values, we get:

[tex]1.04=0.8w,\\w=\frac{1.04}{0.8}=\boxed{\text{C. }1.3}[/tex]