4. The circle graph shows how the annual bodget for
Smithville Community Theater. If the total annual
budget is $200,000, what amount is budgeted for
costumes and props?
Smithville Community Theater
Expenditures
20%
set
construction
25%
staff
salaries
20%
costumes
and props
15%
advertising
10% 10%
misc. physical
items
plant

Answer:

The correct answer is D. 16 + 4 - 1 = 20 - 1

Step-by-step explanation:

Option A is not a true equation because 16 + 4 - 1 = 19 and not 20.

Option B is not a true equation because we're using the relational sign "less than" that is used by inequations or inequalities.

Option C is not a true equation because 16 + 4 - 1  = 19 and is not equal to 19 - 1 = 18.

Finally, option D is a true equation because 16 + 4 - 1  = 19 and is equal to 20 - 1 = 19.

The correct answer is D. 16 + 4 - 1 = 20 - 1

Answer:

- 2 < x < 4

Step-by-step explanation:

We have to write in interval notation of the following interval.

The interval is given by (-2,4) which means the values of the variable, say x, vary from -2 (but not including -2) to 4 (but not including 4).

So, in interval notation this can be written as - 2 < x < 4 (Answer)

Therefore, the values -2 and 4 are the limiting end values of the variable x.

Answer:

r(x) = -7

Step-by-step explanation:

r(x) = -x - 7

+ 7 + 7

7 = -x

÷ -x ÷ -x

7/-1 = x

-7 = x

Answer:

294 square feet

Step-by-step explanation:

If the volume is one  side  at the 3rd power, then  If we know the volume, we calculate   the cubic root of 343  that is 7

So 1 side =7

The cube has 6 faces

1 face of the cube is 7*7=49

Six faces =

49*6= 294

Answer:

3x+15=90.

3x=75

x=25

Step-by-step explanation:

Answer:

x = 25

Step-by-step explanation:

Triangle = 180 degrees

The square indicates that the angle = 90 degrees

So we know the other two angles have to equal the remaining 90 together.

x + (2x + 15) = 90

3x + 15 = 90

3x = 75

x = 25

Answer:

The explanation is below.

Step-by-step explanation:

Given

C is the midpoint of [tex]\overline{AD}[/tex] and also C is the midpoint of [tex]\overline{EB}[/tex]

[tex]\overline{AC} = \overline{DC}\\ and\\\overline{BC} = \overline{EC}[/tex]

To Prove:

[tex]\angle A \cong \angle D[/tex]

Proof:

[tex]In\ \triangle ACB\ and\ \triangle DCE\\\overline{AC} \cong \overline{DC}\ \textrm{ C is the midpoint of AD}\\\angle ACD \cong \angle DCE\ \textrm{vertically opposite angles}\\\overline{BC} \cong \overline{EC}\ \textrm{ C is the midpoint of BE}\\\therefore \triangle ACB \cong \triangle DCE\ \textrm{ By Side-Angle-Side test}\\\therefore \angle BAC \cong \angle EDC\ \textrm{corresponding parts(angles) of congruent triangles}\\\therefore \angle A \cong \angle D\ \textrm{ Proved}[/tex]

Answer:

1/0.04 = 25

Step-by-step explanation:

Answer:

Step-by-step explanation:

well 1/4% wouldnt be 25% because they are 25% = 0.25 = 1/4

the percentage sign changes everything

since it is 1/4% rather than 1/4 by itself

1/4% = 0.25%

if you want to know the percent as a decimal you move the "." to the left twice

(or divide by 100)

so that means that the decimal of 0.25% would be 0.0025

Divide the total by 1 +  interest rate.

12,720 / 1.06 = 12,000

They invested $12,000

Answer:

i believe it would be 36

Answer:36

Step-by-step explanation:

Answer:

$3.80

Step-by-step explanation:

could be wrong though

Answer:

Step-by-step explanation:

19 divided by 5 = 3.8

3.8 to nearest hundreth is 3.80 or you could

Answer:

112 dimes and a nickel.

because, one, 110 dimes equals 11.00 (so add the2 extra dimes.)

two, the .05 is a nickel not a .5 dime.

So that's your answer. 112 dimes and 1 nickel.

The point located 3/5 of the way from point A(4, 5) to point B(-6, 0) on line segment BA is at (0, 3). This is found using the formula for division of a line segment at given ratio.

The subject of this question is Geometry, specifically finding the coordinates of a point along a line segment. Line segment BA has coordinates B(-6, 0) and A(4, 5). To find the point located 3/5 of the way from point A to point B, we will need to use the formula for the division of a line segment which is: X = x1 + r(x2 - x1) and Y = y1 + r(y2 – y1), where r is the ratio, in this case 3/5.

Using the formula, the x coordinate of the point can be calculated as: X = (-6) + 3/5 [(4) - (-6)] = -6 + 3/5 * 10 = -6+6 = 0. The y coordinate of the point can be calculated as: Y = 0 + 3/5 [(5) - 0] = 0 + 3 = 3. Therefore, the point is at (0,3) which is located 3/5 of the way from point A to point B on the line segment.

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Final answer:

The coordinates of the point located 3/5 of the way from point A to point B are (0, 3), calculated by finding the weighted average of the x and y coordinates of the endpoints.

Explanation:

To find the coordinates of the point located 3/5 of the way from point A to point B, we need to calculate the weighted average of the endpoints. The coordinates of point B are (-6, 0) and the coordinates of point A are (4, 5).

The x-coordinate of the point is calculated as follows:
(-6) + ((4 - (-6)) × (3/5)) = (-6) + (10 × (3/5)) = (-6) + 6 = 0.

The y-coordinate of the point is calculated as follows:
0 + ((5 - 0) × (3/5)) = 0 + (5 × (3/5)) = 3.

Therefore, the coordinates of the point located 3/5 of the way from point A to point B are (0, 3).

[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$4000\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semiannually, thus twice} \end{array}\dotfill &2\\ t=years\dotfill &5 \end{cases} \\\\\\ A=4000\left(1+\frac{0.03}{2}\right)^{2\cdot 5}\implies A=4000(1.015)^{10}\implies A\approx 4642.16[/tex]

Answer:The value of f is;

Step-by-step explanation:

f=1/t

Answer:

For more than 500 minutes

Step-by-step explanation:

Let x be the number of minutes.

First company charges:

$0.029 per minute, then $0.029x for x minutes

and a $2 monthly fee.

In total, $(0.029x+2)

Second company charges:

$0.033 per minute, then $0.033x for x minutes

with no monthly fee.

If the charges for the first company are cheaper, then

[tex]0.029x+2<0.033x[/tex]

Multiply this inequality by 1,000:

[tex]29x+2,000<33x\\ \\33x-29x>2,000\\ \\4x>2,000\\ \\x>500[/tex]

Answer:

n= Total number of packages on trucks= 6096

n = T x P (Model Equation)

Step-by-step explanation:

No. Of delivery trucks = T = 127

Package on each truck = P = 48

Total number of packages on trucks =n= ?

Each truck contains 48 packages and total trucks were 127, to find total number of packages on trucks , we just need to multiply the number of trucks with the number of package on each truck.

Total number of packages on trucks =n= (No. Of delivery trucks) x (Package on each truck)

n = T x P (Model Equation)

n= 127 x 48

n= 6096 (Total number of packages on trucks)

To have $18,000 in 2 years with a 20% annual interest rate compounded continuously, you need to invest approximately $12,065.76.

To determine the amount of money you need to invest to have $18,000 in 2 years with a 20% annual interest rate compounded continuously, we can use the formula:

A = P * e^(rt)

Where:

Substituting the values into the formula:

18,000 = P * e^(0.20*2)

Simplifying:

18,000 = P * e^(0.40)

P = 18,000 / e^(0.40)

Using a calculator to evaluate the exponential term:

P ≈ 12,065.76

Therefore, you need to invest approximately $12,065.76 to have $18,000 in 2 years.

None of the given expressions (0.375 x 0.5, 0.625 x 0.5, 0.5 x 0.5, 4/5 x 1/2, 3/8 x 1/2) have the same product as 3 x 0.5, which equals 1.5.

To find out which expressions have the same product as 3 x 0.5, we first need to determine the product of 3 x 0.5. This is easy to do: 3 x 0.5 equals 1.5.

Now, let's check the given expressions:

As we can see, none of these expressions equals 1.5. Thus, none of them have the same product as 3 x 0.5.

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Answer:

C(-4,-2), D(3,-7)

[tex]Ar=35unit^{2}[/tex]

Step-by-step explanation:

we procced to identify points:

A(-4,-7), B(3,-2)

for being the sides of a rectangle parallel to the axes, we find the other two vertices (VIEW GRAPH)

C(-4,-2), D(3,-7);  Area of the rectangle Ar=b*h, where

[tex]b=(X_{D}-X_{A}); h=(Y_{B}-Y_{D})[/tex]

So Ar=(3-(-4))*(-2-(-7)) = (3+4)*(-2+7)=7*5=[tex]35unit^{2}[/tex]

Final answer:

The other two vertices of the rectangle are (3, -7) and (-4, -2), and the area of the rectangle is 35 square units.

Explanation:

To find the coordinates of the other two vertices of a rectangle given two vertices on the coordinate plane, use the fact that the sides of the rectangle are parallel to the axes.

The two given vertices are (3, -2) and (-4, -7). A rectangle has opposite sides of equal length, so the x-coordinates of the opposite vertices must be the same for one pair, and the y-coordinates must be the same for the other pair. Therefore, the other two vertices will have coordinates (3, -7) and (-4, -2).

To find the area of the rectangle, calculate the difference in the x-coordinates (length) and the difference in the y-coordinates (width), then multiply these together.

The length is |3 - (-4)| = 7 and the width is |-2 - (-7)| = 5,

so the area is 7 × 5 = 35 square units.

Answer:

y=x^2+4x+7

Step-by-step explanation:

y=(x+2)(x+2)-3

y=x^2+2x+2x+4-3

y=x^2+4x+7

Answer:

C. y = x² + 4x + 1

Step-by-step explanation:

y = (x + 2)² - 3

y = x² + 4x + 4 - 3

y = x² + 4x + 1

Answer:

The value of x is 25.

Step-by-step explanation:

Given:

side AB = [tex]3x-5[/tex]

side BC = [tex]2x+20[/tex]

side AC = [tex]4x-30[/tex]

In Δ ABC is an equilateral triangle.

In equilateral triangle all three angles are same and also the sides are same.

Hence side AB = side BC

Substituting the values for side AB and side BC we get,

[tex]3x-5=2x+20\\3x-2x=20+5\\x=25[/tex]

Hence the value of x = 25.

Answer:

The value of x for the given figure is 95 And 1.67

Step-by-step explanation:

From Given figure :

Sin angle = [tex]\dfrac{\textrm perpendicular}{\textrm Hypotenuse}[/tex]

or ,  Sin C =  [tex]\dfrac{\textrm 3x - 5}{\textrm 4 x - 30}[/tex]

Cos angle =  [tex]\dfrac{\textrm Base}{\textrm Hypotenuse}[/tex]

or ,  Cos C =  [tex]\dfrac{\textrm 2x + 20}{\textrm 4 x - 30}[/tex]

Or, Cos c = [tex]\sqrt{1 - sin^{2}C }[/tex]

Or, [tex]\dfrac{\textrm 2x + 20}{\textrm 4 x - 30}[/tex] = [tex]\sqrt{1-(\frac{3x - 5}{4 x + 20} })^{2}[/tex]

or, [tex](\frac{2x+20}{4x-30}) ^{2}[/tex] = 1 - [tex](\frac{3x-5}{4x-30} )^{2}[/tex]

[tex]\frac{4x^{2}+400+80x}{16x^{2}+900-240x}[/tex]= 1- ( [tex]\frac{9x^{2}+25-30x}{16x^{2}+900-240x}[/tex] )

Or, 4x²+400+80x = [tex]16x^{2}+900-240x[/tex] - 9x² -25 +30x

or, 4x²+400+80x = 7 x² + 875 -210x

or, 3 x² + 475 -290 x = 0

Or, Solving the equation

3 x² - 285 x - 5 x + 475 = 0

or, 3 x ( x - 95 ) - 5 ( x - 95 ) = 0

or, ( x - 95 ) ( 3 x - 5 ) = 0

∴ x = 95  and x = 1.67

Hence The value of x for the given figure is 95 And 1.67  Answer

Answer:

v172

Step-by-step explanation:

This might be wrong. Because 172=289 you can substituite 289 for 172.

To solve for the two numbers that sum to -102, with one number being 62 less than the other, we use algebraic methods to find the numbers as -20 and -82.

To find the two numbers that sum to -102 and where one number is 62 less than the other, we can set up the following system of equations based on the given information:

Substitute y from the second equation into the first equation:

Now that we have x, we can find y by substituting x back into the equation y = x - 62:

Therefore, the two numbers are -20 and -82.

Answer:

x = 4

Step-by-step explanation:

Using "number sense"

2x=8​

Double a number is 8.

What is half of 8? 4.

Double of 4 is 8.

Therefore the number, x, is 4.

Check:

2x = 8

x = 8/2

x = 4

2x = 8

2(4) = 8

8 = 8

Answer:

f(2k)=0

Step-by-step explanation:

Let's suppose f(x) is such that (x-2k) is one of its factors. We can write it as

f(x)=(x-2k).g(x)

Where g(x) is any other function of x, and g(x) in non-divisible by (x-2k). If we replace x=2k into f, we get

f(2k)=(0).g(2k)=0

f(2k)=0

Answer:

A

Step-by-step explanation:

took the test

Answer:

(8, -4)

Step-by-step explanation:

Answer: The answer is x = 12

Step-by-step explanation:

Answer:

x = 12

Step-by-step explanation:

1. Get all x varibles to one side.

-7x - 11 = 25 - 10x

+ 10x            +10x

2. Get all constants to one side.  

3x - 11 = 25

+ 11         +11

3. Divide on both sides to get x alone.

3x = 36

÷3    ÷3

x = 12

Answer:

The answer would be 5.03x10^-3   ^-^

Step-by-step explanation:

Answer:

-3.

Step-by-step explanation:

Counting the digits after the point until we get to the 5:

The count is 3.

The power is -3:

5.03 * 10^-3.