A human resources manager selected a random sample of 200 workers who donate to charity. The following table shows the distribution of the 200 workers.
Count Type of worker Management Other white collar 96 50 S Blue collar 54
The manager conducts a goodness-of-fit test to determine whether the proportions of workers of these types are identical to the population proportions of workers donating to charity, which are 50 percent for management, 30 percent for other white-collar workers, and 20 percent for blue-collar workers. Which of the following statements must be true about the sample?
A. The expected number of blue-collar workers donating to charity is less than 30.
B. The expected number of management workers donating to charity is 100.
C. The expected numbers of other white collar and blue-collar workers donating to charity are the same.
D. The expected number of other white-collar workers donating to charity is 50
E. The combined expected numbers of other white collar and blue-collar workers donating to charity is greater than the expected number of management workers donating to charity.

Answer:

Z

Step-by-step explanation:

Angle V is congruent to angle z because they have the same placement in the letter order.

By using trigonometry, it can be calculated that The measure of the angle is 53.13° First option is correct.

What is Trigonometry?

Trigonometry is a branch of mathematics that studies relationships between the sides and angles of triangles. It is used to calculate lengths, angles, and other geometric figures. Trigonometry has applications in many fields, including engineering, astronomy, and navigation. The most common trigonometric functions are sine, cosine, and tangent. These functions are used to solve problems related to triangles, circles, and other geometric figures. Trigonometric identities are also used to solve algebraic equations. Trigonometry is an important tool for studying the physical world, as it allows us to calculate the position and motion of objects in space.

There are six trigonometrical functions. They are

[tex]sin\theta, cos\theta, tan\theta, cot\theta, sec\theta, cosec\theta[/tex]

[tex]sin\theta = \frac{perpendicular}{hypotenuse}\\cos\theta = \frac{baser}{hypotenuse}\\tan\theta = \frac{perpendicular}{base}\\cot\theta = \frac{base}{perpendicular}\\sec\theta = \frac{hypotenuse}{base}\\cosec\theta = \frac{hypotenuse}{perpendicular}\\[/tex]

Trigonometry is a very important tool in mathematics.

Here, the trigonometric function given is

[tex]cos\theta = \frac{3}{5}[/tex]

[tex]\theta = cos^{-1}(\frac{3}{5})[/tex]

[tex]\theta = 53.13^{\circ}[/tex]

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Answer:

Below

Step-by-step explanation:

6139 * x * 3 = 798

x = 798/(3*6139) = .0433= 4.33%

Answer:

2, 13, 103

Step-by-step explanation:

These prime numbers are the ones.

2678 = 2 * 13 * 103

A prime number is a natural number that is greater than one and is not a product of smaller natural numbers. For example,  3 is a prime number and we can write it as a product, 1 * 3 or 3 * 1, which involves 3 itself.

So, prime numbers are those numbers that have only two factors, which are 1 and the number itself.

A natural number that is greater than 1 and is not a prime number, is called a composite number. Every natural number which is greater than 1, is either a prime itself or can be factorized as a product of primes that is unique up to their order.

The answer is -

    2678 = 2 * 13 * 103

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The ordered pairs to the system of linear inequality are (-1, 5), (0, 4), (-6, 7)

A system of linear inequalities in two variables consists of at least two linear inequalities in the same variables. The solution of a linear inequality is the ordered pair that is a solution to all inequalities in the system and the graph of the linear inequality is the graph of all solutions of the system.

In the problem given;

x + 5y > 8 ...eq(i)

4x - y < 6 ...eq(ii)

From eq(i)

x + 5y > 8

x > 8 - 5y ...eq(iii)

however, this can easily be solved using a graph.

Plotting the inequality in a graph line;

The ordered pairs are (-1, 5), (0, 4), (-6, 7)

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Answer:

For the first one x= 60 degrees

Second one x= 125 degrees

Step-by-step explanation:

a) To figure out this we can see that the total of angles in a 5- angled shape is 540 degrees.

So (2x X 4) + x = 540 degrees

= 9x= 540

= x = 60

b) To figure out this we can see that the total of angles in a 7- angled shape is 900 degrees.

So 60+2x+x+x+x+x+90= 900

= 150 +6x= 900

= 6x= 750

= x= 125

If you are given an equation of a line and a set of points, you should determine the slope of the equation that is perpendicular to the given equation of line. Lastly, you should use the set of points to write an equation for the perpendicular line.

Mathematically, the slope-intercept or standard form of the equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

In Mathematics, a condition that must be met for two lines to be perpendicular is given by this mathematical expression:

m₁ × m₂ = -1

Assuming the given equation of a line is y = 2x, the slope of the equation that is perpendicular to this line would be calculated as follows;

m₁ × m₂ = -1

2 × m₂ = -1

Slope, m₂ = -1/2.

In conclusion, you will use the newly calculated slope alongside the set of points to determine the equation for the perpendicular line either by using the slope-intercept form or point-slope form.

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The average of the provided numbers is calculated by dividing the total number of values by the sum of all the values that different socioeconomic classes are affected differently by religion membership.

The middle number, which is determined by dividing the sum of all the numbers by the total number of numbers, is the average value in mathematics. When determining the average for a collection of data, we add up all the values and divide this sum by the total number of values. a single number (such as a mean, mode, or median) that encapsulates or depicts the overall importance of a collection of disparate data. unkind sense 1b.: a calculation that approximates the arithmetic mean. an intellectual level that is characteristic of a group, class, or series. superior than average.

[tex]65, 85, 70, 90, 105.[/tex]

Average =

[tex](65+85+70+90+105)/5\\= 415/5\\= 83\\[/tex]

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The magnitude of the acceleration of the particle is zero when the velocity of the particle is zero.

What is Acceleration ?

Acceleration is the rate of change of velocity. Usually, acceleration means the speed is changing, but not always. When an object moves in a circular path at a constant speed, it is still accelerating, because the direction of its velocity is changing.

Given,

Velocity  v= x² − 5x + 4

now, the acceleration

a = dv/dt

​a = 2x (dx/dt) - 5x(dx/dt)

​

given that, v= dx/dt =0

so, a = 2x*0−5*0

a=0 m/sec²

so, the acceleration is zero ,when the velocity is zero.

Hence ,The magnitude of the acceleration of the particle is zero when the velocity of the particle is zero.

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Answer:

Yes, your answer would be correct.

Step-by-step explanation:

That graph intersects at (0, 2), is a solid line, and the slope is -2.

Answer:

D

Step-by-step explanation:

slope of the given line :

(-4-2)/(-1-4)

-6/-5

6/5

slope of a perpendicular line : -5/6

y-7 = -5/6 (x-(-3)

y -7 = -5/6 (x+3)

y -7 = -5/6 x - 5/2

5/6 x + y - 7 + 5/2 = 0

5/6 x + y + (-14 + 5)/2 = 0

5/6 x + y - 9/2 = 0

5x + 6y - 27= 0

5x + 6y = 27

Answer:

D

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 1, - 4 ) and (x₂, y₂ ) = (4, 2 )

m = [tex]\frac{2-(-4)}{4-(-1)}[/tex] = [tex]\frac{2+4}{4+1}[/tex] = [tex]\frac{6}{5}[/tex] ← slope of graphed line

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{6}{5} }[/tex] = - [tex]\frac{5}{6}[/tex] , then

y = - [tex]\frac{5}{6}[/tex] x + c ← is the partial equation of the perpendicular line

to find c substitute (- 3, 7 ) into the partial equation

7 = [tex]\frac{5}{2}[/tex] + c ⇒ c = 7 - [tex]\frac{5}{2}[/tex] = [tex]\frac{14}{2}[/tex] - [tex]\frac{5}{2}[/tex] = [tex]\frac{9}{2}[/tex]

y = - [tex]\frac{5}{6}[/tex] x + [tex]\frac{9}{2}[/tex] ← equation in slope- intercept form

multiply through by 6 ( the LCM of 6 and 2 ) to clear the fractions

6y = - 5x + 27 ( add 5x to both sides )

5x + 6y = 27 ← equation of perpendicular line in standard form

The perimeter of the figure with side length of 5 units is 50 units

From the question, we have the following parameters that can be used in our computation:

Shape = rectangle

Smaller shapes = squares

Side lengths = 5 units

The perimeter of the figure is calculated as

Perimeter  = Number of visible sides * Side length of the square shape

In this case, we have

Number of visible sides = 10

Substitute the known values in the above equation, so, we have the following representation

Perimeter  = 10 * 5

Evaluate the products

Perimeter  = 50 units

Hence, the perimeter is 50 units

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Answer:

84

Step-by-step explanation:

EFD is an iscosilies triangle therefore angle F = angle D = 48

and therefore angle E= 180-48-48=84

Answer:

CHECKING

let W = 10

C = W/2

C = 10/2

C = 5

C = 5     W = 10

Step-by-step explanation:

Answer:

R = (3, 14 )

Step-by-step explanation:

given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint M is

( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] ) ← midpoint formula

calculate the midpoint of PR using this formula and equate x and y coordinates to the coordinates of the given midpoint

let coordinates of R be (x, y ) and P = (- 15, 4 ) , then

[tex]\frac{x-15}{2}[/tex] = - 6 ( multiply both sides by 2 )

x - 15 = - 12 ( add 15 to both sides )

x = 3

and

[tex]\frac{y+4}{2}[/tex] = 9 ( multiply both sides by 2 )

y + 4 = 18 ( subtract 4 from both sides )

y = 14

the coordinates R = (3, 14 )

Answer:

x = 3.66

Step-by-step explanation:

Area of a rectangle = length * width

In this case:

(x+10)x = 50

x*x + x*10 = 50

x² + 10x - 50 = 0

x = {-10±√((10²) -(4*1*-50))} / (2*1)

x = {-10±√(10² + 200)} / 2

x = {-10±√(100+200)} / 2

x = {-10±√300} / 2

x = {-10±17.321} /2        aprox,

It is a geometric figure so only the positive value is taken.

x = {-10+17.321} / 2

x = 7.321/2

x = 3.66

Check:

3.66(3.66+10) = 50

3.66*13.66 = 50

Answer:

A:Infinite solutions

Step-by-step explanation:

1.2 ( 3x + 5 ) = 3.6x + 6

1.2 ( 3x ) + 1.2 ( 5 ) = 3.6x + 6

3.6x + 6 = 3.6x + 6

Answer: A

Step-by-step explanation:

Answer:

684.

Step-by-step explanation:

To calculate how much money David will have in this account after 5 years, we first need to find out how much interest the account earns each year. To do this, we need to multiply the interest rate by the amount of money in the account. In this case, the interest earned each year would be $800 * 0.023 = $18.40.

Next, we need to calculate how much interest the account earns over the 5-year period. Since the interest is compounded semiannually, this means that the interest is earned twice per year. Therefore, the total amount of interest earned over 5 years would be $18.40 * 2 * 5 = $184.

Finally, we need to add the interest to the original amount of money in the account to find out how much money David will have after 5 years. In this case, the total amount of money David will have after 5 years is $800 + $184 = $984.

Therefore, if David keeps the money in this account for 5 years, he will have $984.

Answer:

$897

Step-by-step explanation:

We know:

P = 800

n = 2

r = 2.3

t = 5

Write Equation:

[tex]F = 800(1+\frac{\frac{2.3}{100} }{2} )^{2(5)}[/tex]

Evaluate:

896.9

Thus the answer is $897

Step-by-step explanation:

whenever you see a variable ( a letter )  without a number in front of it, add a 1 ! It means the same thing...

y is the same as 1y

1). 3y + y = ?

Add that 1!

3y + 1y = ?

This problem is the same as 3 + 1

3y + 1y = 4y

2). b + b = ?

Add those 1's !

1b + 1b = ?

this is the same as 1 + 1

1b + 1b = 2b

Remember to keep the variable !

Part B is like a puzzle and the instructions give us hints.

It is telling us, when we see an r, we replace it with the number 3

and when we see t , we replace it with the number 9

Let's solve these puzzles!

8). [tex]\frac{r}{t} = ?[/tex]

We see and r and a t, let's plug in 3 and 9

Now we have ...

[tex]\frac{3}{9} = ?[/tex]

Divide using a calculator!

We get ....

[tex]\frac{3}{9} = \frac{1}{3}[/tex] or 0.33

9). [tex]rt = ?[/tex]

When variables are right next to each other, this means they are being MULTIPLIED!

Let's replace r and t with 3 and 9 and multiply them together!

[tex]rt =[/tex] 3 × 9

3 × 9 = 27

We do similar things for Part C

12). [tex]ab = ?[/tex]

It tells us a = 5 and b = -4

Let's plug it in

[tex]ab =[/tex]  5 × -4

5 × - 4 = -20

USE THESE EXAMPLES AND TIPS TO COMPLETE THE REST OF THE PROBLEMS AND I WILL CHECK THEM FOR YOU.

COMMENT THEM BELOW

The like terms to make a simpler expression is   19 x^2-6 x+9 n-6

Group like terms

What is simpler expression?

Solving a math problem is the same thing as simplifying an expression. You basically strive to write an expression as simply as you can when you simplify it. At the conclusion, there shouldn't be any more multiplication, dividing, adding, or subtracting to be done.

[tex]=12 x^2+7 x^2+7 x-3 x-11 x+3 n+6 n-7+1+5-5[/tex]

Add similar elements[tex]: $12 x^2+7 x^2=19 x^2$[/tex]

[tex]=19 x^2+7 x-3 x-11 x+3 n+6 n-7+1+5-5[/tex]

Add similar elements: [tex]$7 x-3 x-11 x=-7 x$[/tex]

[tex]=19 x^2-7 x+3 n+6 n-7+1+5-5[/tex]

Add similar elements: [tex]$3 n+6 n=9 n$[/tex]

[tex]=19 x^2-7 x+9 n-7+1+5-5[/tex]

Add the numbers: [tex]$-7+1+5-5=-6$[/tex]

[tex]=19 x^2-7 x+9 n-6[/tex]

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Answer: 3/5

Step-by-step explanation:

Let x be the required solution:

so, x= 3- (12/5)

⇒ 5x = 15-12 (Multiplying both sides 5 so that the denominator is the same)

⇒ 5x = 3

∴ x = 3/5

Answer:

7/12

Step-by-step explanation:

I set up the equation, but I first had to find the common denominator which is 12 so I multiplied 3/4 by 3 (top and bottom) and I multiplied 1/6 by 2   (also top and bottom) So I got 9/12-2/12 and when I subtracted I got 7/12

(hope you understood how I got my answer..)

36% of the animals in the shelter are hamsters.

[tex]\frac{27}{75}= 0.36[/tex]

0.36 = 36%.

36% of the animals in the shelter are hamsters.

im not sure if you made a mistake and meant hundredths or not but if you are adding hundreds it would be 59.031 but if you adding hundredths is would be 0.621.

There is an effective change of 50% in the school.

What is Percentage?

A percentage is a relative figure that represents the hundredth part of any amount. One percent (symbolised 1%) is one hundredth part; consequently, 100 percent denotes the complete amount and 200 percent defines twice the supplied amount.

Solution:

To find the net/effective change we can the use the formula:

(a + b + ab/100)

here a and b are the rate of change

a = 25% and b = 20%

Net change = (25 +20 + 500/100) = 45 + 5 = 50%

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Answer:

point

vertex

one

face

face

circular

length

area

volume

Answer: -5/3

Down -5

right 3

Step-by-step explanation: count the distance between the 2 dots looking from the y axis (up and down)and from the x axis (left to right)