In 2009 the bureau of labor statistics reported a surge in volunteerism. At this time there were a reported 63,361 volunteers in the us. The pie chart below shows the different categories in which these people volunteered. Find the number of people who volunteered in an educational capacity. Round your answer to the nearest whole number

Question:

If cos(θ) =-8/17 and sin(θ) is negative, then sin(θ) = ___  and tan(θ) =___.

Answer:

[tex]Sin\theta = \frac{-15}{17}[/tex]

[tex]Tan\theta = \frac{15}{8}[/tex]

Step-by-step explanation:

Given

cos(θ) =-8/17

Required

sin(θ) = __

tan(θ) =__

The first step is to determine the length of the third side

Given that

[tex]cos(\theta) = \frac{Adj}{Hyp}[/tex]

Where Adj and Hyp represent Adjacent and Hypotenuse

[tex]cos(\theta) = \frac{-8}{17}[/tex]

By comparison

[tex]Adj = -8\ and\ Hyp = 17[/tex]

Using Pythagoras

[tex]Hyp^2 = Adj^2 + Opp^2[/tex]

By Substitution

[tex]17^2 = (-8)^2 + Opp^2[/tex]

[tex]289 = 64 + Opp^2[/tex]

Subtract 64 from both sides

[tex]289 - 64 = 64 - 64 + Opp^2[/tex]

[tex]225 = Opp^2[/tex]

Take square roots of both sides

[tex]\sqrt{225} = \sqrt{Opp^2}[/tex]

[tex]\sqrt{225} = Opp[/tex]

[tex]15 = Opp[/tex]

[tex]Opp = 15[/tex]

The question says that sin(θ) is negative; This implies that θ is in the third quadrant and as such

[tex]Opp = -15[/tex]

From trigonometry

[tex]Sin\theta = \frac{Opp}{Hyp}[/tex]

[tex]Sin\theta = \frac{-15}{17}[/tex]

Also from trigonometry

[tex]Tan\theta = Sin\theta / Cos\theta[/tex]

[tex]Tan\theta = \frac{-15}{17} / \frac{-8}{17}[/tex]

[tex]Tan\theta = \frac{-15}{17} * \frac{-17}{8}[/tex]

[tex]Tan\theta = \frac{-15 * -17}{17 * 8}[/tex]

[tex]Tan\theta = \frac{15 * 17}{17 * 8}[/tex]

[tex]Tan\theta = \frac{15}{8}[/tex]

Answer:

Option (C)

Step-by-step explanation:

Given question is incomplete; here is the complete question.

Consider the expression [tex]0.8^{x-3}[/tex] . Which of the following is an equivalent expression?

A- [tex]0.8^{\frac{x}{3}}[/tex]

B- [tex]0.8^{\frac{3}{x}}[/tex]

C- [tex]\frac{0.8^{x}}{0.8^3}[/tex]

D- [tex]\frac{0.8^{3}}{0.8^{x}}[/tex]

Given expression is [tex]0.8^{x-3}[/tex]

[tex]0.8^{x-3}=0.8^{x}\times 0.8^{-3}[/tex] [Since [tex]x^{b+c}=x^{b}\times x^{c}[/tex]]

          [tex]=\frac{0.8x^{x}}{0.8^{3} }[/tex] [Since [tex]a\times b^{-1}=\frac{a}{b}[/tex]]

Therefore, Option C will be the equivalent expression.

Answer:

Consider the expression 0.8X-3.  Which of the following is an equivalent expression?

A.

B.

C.  <<<<correct

D.

Step-by-step explanation:

eDGE 2021

Answer:

volume of the sphere

=4/3π × r³

=4/3π × 3 × 3 × 3

=4/3π × 27

=36π ( c )

The value of volume of the sphere shown with a radius of 3 is,

⇒ 36π units³

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Since, We know that;

volume of the sphere is,

V = 4/3π × r³

Here, We have;

r = 3

Hence, We get;

V = 4/3π × 3 × 3 × 3

= 4/3π × 27

=36π

Thus, The value of volume of the sphere shown with a radius of 3 is,

⇒ 36π units³

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Answer:

Let's start first with sin(x+y) :

Now with sin(x)+sin(y) :

We can see that both expressions are far away from being equal

We can prove the given expression, sin(x + y) ≠ sin x + sin y by taking the value of x and y as 90 respectively.

Trigonometry is a branch of mathematics that deals with the relationship between the sides and angles of a right-angle triangle. The trigonometric ratio is defined as the ratio of the pair of a right-angled triangle.

It is given that the expression is"sin(x + y) sin(x+y)

Suppose, x=0 and y=90

We have to prove the following expression,

sin(x + y) ≠ sin x + sin y

Left-hand side,

=sin(x + y)

=sin(90+90)

=sin 180

=0

Right-hand side,

=sin x + sin y

=sin90+sin90

=1+1

=2

As a result,

sin(x + y) ≠ sin x + sin y

Thus, we can prove the given expression, sin(x + y) ≠ sin x + sin y by taking the value of x and y as 90 respectively.

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Answer:

u = 14

t =8

Step-by-step explanation:

To make the triangles congruent

3u = u+28

Subtract u

3u-u = u+28-u

2u = 28

Divide by 2

2u/2 = 28/2

u = 14

12t = 16t -32

Subtract 16t

12t-16t = 16t-32-16t

-4t = -32

Divide by -4

-4t/-4 = -32/-4

t = 8

Answer:

t = 8

u = 14

Step-by-step explanation:

For the triangles to be congruent, the sides must be equal.  Set each side on the first triangle equal to the corresponding side on the second triangle.  

Solve.

u + 28 = 3u

28 = 2u

14 = u

12t = 16t -32

-4t = -32

t = 8

The two values for t and u are 8 and 14, respectively.

Answer: 9.53x10^-5

Step-by-step explanation:

Scientific notation means the coefficient must be between 0 and 10 and preferably without zeros because they are implied. move the decimal 5 times to the right to get 9.53 as your coeifficient and state the movement of the decimal

Answer:

Hello!

____________________-

0.000095 = 9.53 x 10^-5

Step-by-step explanation:

Hope this helped you!

Answer:

Step-by-step explanation:

The constant term of x^2 + 13x – 48 factors into either (3)(-16) or (-3)(16).

Note how 16 - 3 = 13, which is the coefficient of the middle term.  Thus, the factors are

(x + 16)(x - 3) which is equivalent to x^2 + 16x - 3x - 48, or x^2 + 13x - 48.

The factored form of the given polynomial  is (x - 3)(x + 6)

Since the equation is [tex]x^2 + 13x - 48[/tex]

Now

The four-term polynomial is

[tex]x^2 + 16x - 3x - 48[/tex]

x(x + 16) - 3(x + 16)

(x - 3)(x + 6)

Here polynomial represents the expression that includes the additions, subtraction, etc

Therefore, The factored form of the given polynomial  is (x - 3)(x + 6)

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Based on the information given, the composition of transformations that will bring about a pair of similar, not congruent triangles is D. a rotation, then a dilation.

A congruent triangle simply means when two triangles have exactly the same side and angles.

Therefore, the composition of transformations that will bring about a pair of similar, not congruent triangles is a rotation, then a dilation.

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Answer:

Step-by-step explanation:

Let s represent the speed of the bus.

From the information given, the bus needs to cover a distance of 240 km in less than 5 hours. The formula for calculating the speed of the bus, s is expressed as

Speed, s = distance covered by the bus/ time taken to cover the distance

Therefore,

Speed, s = 240/5 = 48 km/hr

A higher speed would ensure the bus covers the distance in less than 5 hours. Therefore, the inequality that represents the speed (s) of the bus would be

s ≥ 48

Answer:

The answer is option D.

Step-by-step explanation:

Because -3/-5 = 3/5 since the negative sign cancel each other.

Hope this helps you

Answer:

The fourth  option

Step-by-step explanation:

-3/5 is the same as - 3/5 or 3/-5 (it doesn't matter where the negative sign goes-on the side, numerator, or denominator)

-(-3/-5) is basically negative of -3/-5

-3/-5 is the not the same as -3/5

Answer:

(B)the alternate interior angles theorem.

Step-by-step explanation:

The diagram for the question is attached below:

In the diagram:

BC is parallel to AD; and

AB is parallel to DC.

Effectively, the shape is a parallelogram.

The Alternate Interior Angles Theorem states that, when two parallel lines are cut by a transversal, the resulting alternate interior angles are congruent.

Therefore:

∠BCA ≅ ∠DAC and ∠BAC ≅ ∠DCA by the alternate interior angles theorem.

Answer:

You've given Uncle Sam an interest-free loan of your money for a full year. ... If you had received your expected refund incrementally as part of your pay, you could have used it to pay bills, start an emergency fund or save for something special.You are at the mercy of the IRS, which already is at the mercy of a frequently late-acting Congress when it comes to tax laws. If Congress and the IRS are slow, then so is your receipt of your refund.

Answer:

Use a graphing calculator.

Step-by-step explanation:

Graph:

f(x) = -4√x

━━━━━━━☆☆━━━━━━━

▹ Answer

f(x)  = -4√x

▹ Step-by-Step Explanation

You can use a graphing calculator as the previous answer suggested as well. The image is attached below.

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

Answer:

x = 6

Step-by-step explanation:

2x - 5 = 7

Add 5 on both sides.

2x - 5 + 5 = 7 + 5

2x = 12

Divide both sides by 2.

2x/2 = 12/2

x = 6

Step-by-step explanation:

Plug in each value of x into the equation and find y:

[tex]\left[\begin{array}{cc}x&y\\-2&(-2)^{2}-2(-2)+5=13\\-1&(-1)^{2}-2(-1)+5=8\\0&(0)^{2}-2(0)+5=5\\1&(1)^{2}-2(1)+5=4\\2&(2)^{2}-2(2)+5=5\\3&(3)^{2}-2(3)+5=8\end{array}\right][/tex]

Answer:

tanΘ = [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

tanΘ = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{6}{8}[/tex] = [tex]\frac{3}{4}[/tex]

Answer:

0.03333333333333

Step-by-step explanation:

1/6 = 0.1666666666666

0.16666666666666 / 5 = 0.03333333333

Answer:

380 square inches

Step-by-step explanation:

We are given the measurements of the Rectangular Prism as

8 inches by 9 inches by 10 inches

Where based on the order of arrangement:

8 inches = Length

9 inches= Width

10 inches = Height

Step 1

Find the amount of wrapping paper needed

Perimeter = 2L + 2W

= 2 × 8 + 2 ×9

= 16 + 18

= 34 inches

Base = L × W

= 8 × 9

= 72 inches

Surface Area of the Rectangular Prism =PH + 2B

Where P = Perimeter

H = Height

B = Base

= 34 × 10 + 2× 72

= 340 + 144

= 484 square inches

The area of the Rectangular prism = 484 square inches

Step 2

So we were told that she used wrapping paper the measured 2 feet by 3 feet.

We would convert the values in feet to inches

1 ft = 12 inches

Length = 2 ft = 2 × 12 = 24 inches

Width = 3 ft = 3 × 12 = 36 inches

We find the area of the wrapping paper

Length × Width = 24inches × 36 inches = 864 square inches.

Step 3

The amount of square inches of wrapping paper left over is calculated as:

Area of the wrapping paper used - Area of the Rectangular prism

= 864 square inches - 484 square inches

= 380 square inches.

Therefore, the amount of square inches of wrapping paper left over is 380 square inches.

Answer:

OC is not a function

Step-by-step explanation:

It's not a function because the x cannot repeat.

Answer: The answer is given below

Step-by-step explanation:

From the question, we are informed that the money m (in £) Xavier has to spend each week is his wage w (in £) subtract the tax t (in £) he pays on his income. Therefore, the formula for the money he can spend will be:

m = w - t

The amount of money that he has to spend if he earns £120 a week and pays £41 in tax will be:

m = w - t

m = £120 - £41

m = £79

Answer:

x² + 2x + 3

Step-by-step explanation:

(f + g)(x) = f(x) + g(x), thus

f(x) + g(x)

= 4x + 5 + x² - 2x - 2 ← collect like terms

= x² + 2x + 3

Answer:

The yearly growth percentage is 5%

The worth of the company in 2010 is 433 million of dollars approximately

Step-by-step explanation:

The annual growth percentage;

We can write the equation of w as follows;

W = 266 (1 + 0.05)^t

Compare this with ;

W = I(1 + r)^t

Where W is the worth at a particular year

I is the initial worth at year 2000

r is the rate of increase per year

and t is the time since 2010

where it is the 0.05 that represents the yearly growth percentage (r)

0.05 as a percentage is 5/100 which is 5%

Now, we want to calculate the worth of the company in the year 2010

The first thing to do here is to calculate the value of t.

The value of t is the difference between the years 2000 and 2010 and that is 2010-2000 = 10 years

Now to find the worth at 2010, simply substitute that value of t = 10 in the equation

Thus;

W = 266(1.05)^10

W = 433.2859707228

Which is approximately 433

Answer:

False

Step-by-step explanation:

If you were to divide a negative number by a negative number, or multiply a negative number by a negative number, you would change the sign to positive as two negatives make a positive.

Answer:

False

Step-by-step explanation:

if you multiply two negative integers, you will get a positive result

For example

(-1) x (-2) = 2   (the sign of the answer is different from the sign of the two negative integers that we multiplied)

Answer:

The constant term is 240. It represents the initial daily revenue.

Step-by-step explanation:

It is given that Tico's Taco Truck is trying to determine the best price at which to sell tacos, the only item on the menu,  to maximize profits.

The owner can calculate the daily revenue using the polynomial  expression

where x is the number of $1 increases in the taco price.

Constant term does not contain any variable.

In the given expression 240 is free from variable x. So, the constant term is 240.

The value of expression is 240 for x=0. Since x is the number of $1 increases in the taco price, therefore 240 is the daily revenue when the taco price is not increased or the taco price increased by 0.

Therefore the constant term is 240 and it represents the initial daily revenue.

Answer:

Step-by-step explanation:

Stephan can run

3 miles in 15.75 minutes

1 miles in 15.75/3 minutes

1 miles in 5.25 minutes

Kelsha can run

5 miles in 226 minutes

1 miles in 226/5 minutes

1 miles in 45.2 minutes

Stephan can run faster, since 5.25 < 45.2

Stephan can run faster, than Kelsha since 5.25 < 45.2.

Speed is defined as the ratio of the distance traveled by the body to the time taken by the body to cover the distance. The unit of speed is measured in a meter per second, Miles per second, etc. Speed is a scalar quantity and does not require direction.

The speed for Stephan will be calculated as below:-

3 miles in 15.75 minutes

1 mile in 15.75/3 minutes

1 mile in 5.25 minutes

The speed for Kelsha will be calculated as below:-

5 miles in 226 minutes

1 mile in 226/5 minutes

1 mile in 45.2 minutes

Therefore, Stephan can run faster, than Kelsha since 5.25 < 45.2.

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Answer:

Range: y ≥ -1

Step-by-step explanation:

The are no limits on the domain because x can be any value

( x-3) ^2 must be greater than or equal to zero since it is squared

0 -1 = -1

The smallest value the range can be is -1

y ≥ -1

Answer:

1. no solution

2. (0,3)

3. IMS (Infinitely Many Solutions)

Step-by-step explanation:

First graph has parallel lines, which means the lines will never intersect, therefore it will be impossible to get a solution.

Second Graph has 2 lines that intersect at points (0,3) which will give only one solution.

Third Graph has 1 line that overlaps at every point, which means that any point which is on the that line is a solution.

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Infinite solutions No Solution (0,3)

Answer:

71

Step-by-step explanation:

Because this triangle is an isosceles, the base angles are equal

the top angle is 38 and triangles add up to 180

so 180-38=142

then divide that by 2

which is 71 so x=71