About 32% of the population in a large region are between the ages of 40 and 65, according to the country's census. However, only 2% of the 2100 employees at a company in the region are between the ages of 40 and 65. Lawyers might argue that if the company hires people regardless of their ages, the distribution of ages would be the same as through they had hired people at random from the surrounding population. Check whether the condoms for using the one proportion z-test are met.

Formula for the area of a circle:

A = πr²                   [A = area        r = radius]

The radius is [tex]\frac{1}{2}[/tex] (half) the diameter. Since the diameter = 10cm, the radius = 5cm.

You know:

r = 5cm         Substitute/plug this into the equation

A = πr²

A = π(5)²    

A = 25π  ->     A = 25(3.14)

A = 78.5cm²

The area of the circle when the diameter is 10 cm should be [tex]78.5\ cm^2[/tex].

Since the diameter is 10 cm

We know that

The diameter should be

[tex]= \pi r^2\\\\= 3.14\times 5^2\\\\= 25\times 3.14\\[/tex]

= [tex]78.5\ cm^2[/tex]

Hence, The area of the circle when the diameter is 10 cm should be [tex]78.5\ cm^2[/tex].

Learn more about circle here; https://brainly.com/question/15673093

Answer:

V = 7776 pi m^3

Step-by-step explanation:

The volume of a sphere is given by

V = 4/3 pi r^3

We need to know the radius

r = d/2 = 36/2 = 18

V = 4/3 pi (18)^3

V = 4/3 * pi *5832

V = 7776 pi

We cannot approximate pi since we want the exact answer

Answer:

7776π cubic meters.

Step-by-step explanation:

Recall the volume formula for a sphere is

V = (4/3) π r^3

r = (1/2)*diameter = (1/2)*36 m = 18 meters

V = (4/3)*π*(18)^3 = 24,429.02447 cubic meters

However the problem wants an exact answer, and not an approximation, therefore I will express the volume in terms of simplified expressions.

V = (4/3)*π*(18)^3 = (4/3)*π * (3*6)^3  =  4 *π * (1/3)*(3^3) *(6^3)

V =  4 *π * (1/3)*(3^3) *(6^3)  = 4*π * 9 * 6^3 = 7776π cubic meters.

Answer:

g(f(x)) = - x² + 4

Step-by-step explanation:

To evaluate g(f(x)), substitute x = f(x) into g(x), that is

g(f(x))

= g(- x² - 1)

= - x² - 1 + 5

= - x² + 4

Answer:

Dependent event because the sample space depends on the first event

Step-by-step explanation:

10 marbles total

4 green

6 yellow

1st pick green:  Probability=  4/10

2nd pick yellow: Probability= 6/9

Dependent event because the sample space depends on the first event

Answer:

A and B

Step-by-step explanation:

From what we know, Sandra biked 7 kilometers on Wednesday because of the statement, followed by how she biked 3x as many miles on Thursday. We do not know how many total meters she biked because it does not give us that information. Hope this helps!

Final answer:

The volume of the sphere is 113.04 cubic inches.

Explanation:

The volume of a sphere can be calculated using the formula V = (4/3)×πr³. In this case, the radius is given as 3 inches. Plugging in the value, we get:

( V)   volume of the sphere = (4/3)×3.14×3³ = (4/3)×3.14×27 = 113.04 cubic inches.

Answer:

$ 404.17 every month

Step-by-step explanation:

$19,700/2 =$9,850

$9,850-$5,000= $4,850

$4,850/12 = $404.1666666666667  

rounds to $ 404.17

Answer:

The mean is 4.5 and the standard deviation is 1.44.

Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The mean of the uniform probability distribution is:

[tex]M = \frac{(a + b)}{2}[/tex]

The standard deviation of the uniform probability distribution is:

[tex]S = \sqrt{\frac{(b-a)^{2}}{12}}[/tex]

Uniformly distributed random variable ranging from 2 to 7.

This means that [tex]a = 2, b = 7[/tex].

So

[tex]M = \frac{(2 + 7)}{2} = 4.5[/tex]

[tex]S = \sqrt{\frac{(b-a)^{2}}{12}} = \sqrt{\frac{(7 - 2)^{2}}{12}} = 1.44[/tex]

The mean is 4.5 and the standard deviation is 1.44.

To solve this problem, set up a system of equations with x and y representing the number of buttons. If there are 20 Weights of buttons in total, 20 of them weigh 12 grams and none weigh 8 grams.

To solve this problem, we can set up a system of equations. Let x be the number of buttons weighing 12 grams, and y be the number of buttons weighing 8 grams.

We can then write the following equations based on the information given:

x + y = total number of buttons

12x + 8y = total weight of the buttons

Substituting the given values, we have:

x + y = total number of buttons

12x + 8y = 240

From the first equation, we can express y in terms of x:

y = total number of buttons - x

Substituting this into the second equation:

12x + 8(total number of buttons - x) = 240

Simplifying:

12x + 8total number of buttons - 8x = 240

4x + 8total number of buttons = 240

4x = 240 - 8total number of buttons

4x = 8(30 - total number of buttons)

x = 2(30 - total number of buttons)

Since x and y represent the number of buttons, they must be whole numbers.

We can test different values for the total number of buttons to find a solution that satisfies this condition.

For example, if we assume there are 20 buttons in total:

x = 2(30 - 20) = 2(10) = 20

y = 20 - 20 = 0

Therefore, if there are 20 buttons in total, 20 of them weigh 12 grams and none weigh 8 grams.

Learn more about Weights of buttons here:

https://brainly.com/question/34128823

#SPJ3

The probable question may be:

In a box, there are two types of buttons with different weights. One type of button weighs 12 grams, and the other type weighs 8 grams. If the total weight of the buttons in the box is 240 grams, how many buttons of each type are in the box?

Final answer:

To determine the maximum number of days Jim can rent a car, set up the inequality 21d + 25 ≤ 115. Solving for 'd', Jim can rent a car for a maximum of 4 days.

Explanation:

To determine the maximum number of days that Jim can rent a car, we need to set up an inequality using the given information. Let's denote the number of days as 'd'. The rental cost per day is $21, so the total cost for 'd' days would be 21d. The cost for the miles driven is $0.10 per mile, and Jim will travel 250 miles. So the cost for the miles driven would be 0.10 * 250 = $25. Now, we can set up the inequality:

21d + 25 ≤ 115

To solve for 'd', we need to subtract 25 from both sides of the inequality:

21d ≤ 90

Now, divide both sides of the inequality by 21:

d ≤ 90/21

d ≤ 4.29 (approx)

So, Jim can rent a car for a maximum of 4 days.

Answer:

Y = 45*p(y) / (1 - p(y))    if I knew what p(y) is, we can find how many yellow marbles there are.   p(y) = probability of choosing yellow.

Step-by-step explanation:

Total marbles =  35 + 10 + yellow

If probability of choosing yellow =p(y) = yellow/Total

p(y) =  Y/(35 + 10 + Y)

Solve for Y,

p(y)*(35 + 10 + Y) = Y

45*p(y) + p(y)*Y = Y

45*p(y) = Y - p(y)*Y

Y = 45*p(y) / (1 - p(y))

To find the number of yellow marbles in the bag, set up an equation using the given probabilities. Simplify the equation and solve for the total number of marbles. Finally, substitute the value of  into the equation to determine the number of yellow marbles.

To solve this problem, we need to find the number of yellow marbles in the bag. Given that there are 35 blue marbles and 10 red marbles, we can subtract these two numbers from the total number of marbles to find the number of yellow marbles. Let's denote the number of yellow marbles as 'y'. We can set up the equation: 35 + 10 + y = total number of marbles. Since the probability of selecting a yellow marble is , we know that the ratio of yellow marbles to the total number of marbles is . This can be written as: y/total number of marbles = . Now, we can solve for 'y'.

By cross multiplying the ratio equation, we have: y = total number of marbles * . Now we can substitute this value of 'y' in the first equation: 35 + 10 + (total number of marbles * ) = total number of marbles. Simplifying this equation, we find: 45 + (total number of marbles * ) = total number of marbles. Rearranging the equation, we have: (total number of marbles * ) - total number of marbles = -45. Factoring out 'total number of marbles' from the left side, we get: total number of marbles * ( - 1) = -45. Dividing both sides of the equation by ( - 1), we find: total number of marbles = 45 / ( - ). Plugging in the value of , we can evaluate the expression: total number of marbles = 45 / ( - ) = - . Therefore, there are - yellow marbles in the bag.

https://brainly.com/question/22962752

#SPJ3

Answer:

3000 N

Step-by-step explanation:

The work done by a force on an object is given as the product of the force applied on the object and the distance moved by the object.

Mathematically:

W = F * d

The force applied by the man is 150 N and the distance moved is 20 m. Hence, the work done by the man is:

W = 150 * 20 = 3000 J

The work done by the man is 3000 Joules.

Answer: 3,4,7

Step-by-step explanation:

Answer:

a) v=6

b) s= u^2 - v^2 : -2a

Step-by-step explanation:

v^2=u^2+2as

u=12, a=-6, s=9

a)

(12)^2= 12 * 12= 144

v^2=u^2+2as

v^2=(12)^2+ 2*(-6)*9

v^2=144+(-12)*9

v^2=144+(-108)

v^2=36

v=6

b)

v^2=u^2+2as

-2as=u^2 - v^2

s= u^2 - v^2 : -2a

check for s

s= 144 - 36 : -2(-6)

s= 108 : 12

s=9 (equal vs the given)

Answer:

x = 9.3

Step-by-step explanation:

The Law of Cosines

[tex] c^2 = a^2 + b^2 - 2ab \cos C [/tex]

[tex] x^2 = 15^2 + 13^2 - 2(15)(13) \cos 38^\circ [/tex]

[tex] x^2 = 225 + 169 - 2(15)(13) \cos 38^\circ [/tex]

[tex] x^2 = 394 - 390(0.7880) [/tex]

[tex] x^2 = 86.6758 [/tex]

[tex] x = \sqrt{86.6758} [/tex]

[tex] x = 9.3 [/tex]

Answer:

x = 42   i hope this helps!   :)

Step-by-step explanation:

given   5(3x + 2) = 8(2x - 4)

distribute the 5 to both the 3x and the 2   15x + 10 = 8(2x - 4)

now distribute the 8 to both the 2x and the -4   15x + 10= 16x - 32

subtract 15x from both sides   10 = x - 32

add 32 to both sides   42 = x

flip the equation around so the x is first   x = 42

answer   x = 42

Answer:

The amounts of money each has are:

Joe = $92

Charlie = $29

Leila = $23

Step-by-step explanation:

To solve this, we will convert the statements into an equation, and use that to solve for the unknowns, as follows:

total amount = $144

Let Leila's share be S

Joe's share = 4 times Leila's = 4S

Charlie's share = $6 + Leila's share = 6 + S

Joe's share + Charlie's Share + Leila's Share = $144

4S + (6 + S) + S = 144

4S + 6 + S + S = 144

4S + 2S + 6 = 144

6S + 6 = 144

6S = 144 - 6 = 138

S = 138 ÷ 6 = $23

Therefore Leila's share 'S' = $23

Joe share= 4S = 4 × 23 = $92

Charlie's share = 6 + 23 = $29

Answer:

y=2/3x

Step-by-step explanation:

First, we have to find the slope, which is [tex]\frac{(y_{1} -y_{2})}{(x_{1}-x_{2}}[/tex]

(-3-1)/(-2-4)

-4/-6

2/3 is slope.

y=2/3x+-___

substitute in -3 from first point

y=-2+__=-2

y=2/3x+0

y=2/3x

Answer:

y + 2 = (3/2) (x+3)    (point slope form)

Step-by-step explanation:

(see attached for reference)

Given

(x₁, y₁) = (-3,-2)

(x₂, y₂) = (1,4)

Since we are given 2 points, it would be easiest to express the equation of the line in point-slope form (see attached)

(y - y₁) = m (x - x₁)

we already have the values for x₁ and y₁, hence we only need to find the slope m (see 2nd attached graphic)

m = (y₂-y₁) / (x₂ - x₁)

= [4 - (-2) ] / [1 - (-3)]

= (4+2) / (1+3)

= 6/4

= 3/2

substituting the value for m and the values for x₁ and y₁:

(y - y₁) = m (x - x₁)

[y - (-2)] = (3/2) [x - (-3)]

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

Answer:

True mean population distraction time with 90% confidence is

C.I[103.34 ,112.66] at 108

Step-by-step explanation:

Given:

Study Average hrs =2.1 =2.1 *60=126 minutes

For sample mean =1.8 *60= 108 minutes

S.D=20  and n=50

To Find:

True mean population distraction time with 90% confidence,

Solution:

90% C.I. means 90 % will fall in true mean and other will not .

So for that calculating the

Standard error=S.D/Sqrt(n)

S.E=20/Sqrt(50)

S.E=2.828

For 90% Confidence interval Z=1.65

C.I= mean±Z*Standard error

C.I=108±1.65*2.828

C.I=108±4.662

Hence C.I will range from 103.34 to 112.66

Study mean =126 minutes .

Here  it ranges from 103.34 to 112.66

In this exercise we have to use the knowledge of probability to calculate this we will use percentage as:

[tex]C.I= 108[/tex]

Given the following information in the text we find that:

Then calculating the probability we find that:

[tex]Standard error=S.D/\sqrt(n)\\ S.E=20/\sqrt(50)\\ S.E=2.828\\ Z=1.65\\ C.I=108+4.662 [/tex]

See more about probability at brainly.com/question/795909

Answer:

•The subset consists of all of the outcomes where the team is made up of one boy and one girl

• the subset consists of all of the outcomes where the team is not made up of all boys and not made up of all girls.

Answer:

A & D

Step-by-step explanation:

KHAN

Answer:

Infinitely many solutions

Step-by-step explanation:

5-x= -(x - 5) ➡ 5 - x = -x + 5 add x to both sides and subtract 5 from both sides

5 - x - 5 + x = -x + x - 5 + 5 ➡0 = 0 in this case we say the equation has infinitely many solutions because whatever value you give for x there will always be a solution.

Final answer:

The probability of Tim teeing off with a white ball and putting with an orange ball is 0.0331. The events are dependent.

Explanation:

To calculate the probability of Tim teeing off with a white ball and putting with an orange ball, we need to consider the total number of balls in the bag and the number of white and orange balls.

There are a total of 9 white balls, 6 yellow balls, 1 orange ball, and 1 pink ball in the bag. The probability of Tim teeing off with a white ball is 9 out of 17, since he can choose any of the 9 white balls out of the total 17 balls. After Tim tees off with a white ball, there are now 8 white balls left in the bag.

Next, Tim needs to putt with an orange ball. The probability of Tim putting with an orange ball is 1 out of 16, since there is 1 orange ball left in the bag and a total of 16 balls.

To find the probability of both events happening, we multiply the two probabilities:

P(white, then orange) = P(white) × P(orange|white) = 9/17 × 1/16 = 9/272 = 0.0331 (rounded to four decimal places).

The events of teeing off with a white ball and putting with an orange ball are dependent events, as the outcome of the first event affects the probability of the second event.

Answer:

5

Step-by-step explanation:

(15)(x+3) = (12)(2x) -->

15x + 45 = 24x -->

45 = 9x -->

5 = x

Answer:

Correct option: A

(x + 7)^2 + (y + 10)^2 = 13

Step-by-step explanation:

First we need to find the center of the circle. We can find it calculating the midpoint of the diameter.

the x-coordinates of the diameter are -4 and -10, so the midpoint is:

(-4 -10)/2 = -7

the y-coordinates of the diameter are --8 and -12, so the midpoint is:

(-8 -12)/2 = -10

Now we need to find the radius of the circle, so we find the diameter and then  find half of it.

The lenght of the diameter is the distance of the endpoints:

D = sqrt((-4+10)^2 + (-8+12)^2) = 7.21

radius = 7.21/2 = 3.605

The generic equation of the circle is:

(x - xc)^2 + (y - yc)^2 = r^2

So we have:

(x + 7)^2 + (y + 10)^2 = 13

Correct option: A

Answer:

18.75

Step-by-step explanation:

To identify the vertices of this triangle, you need to find the x intercepts of both lines, as where their solutions match. Let's start with setting them equal to each other. If you subtract 10 from both sides of the second equation, then both equations are left equaling zero.  You can also multiply both sides of the equation by -1 for easier solving later Now:

3x-2y=-2y-x+10

4x=10

x=2.5

y=3.75

This shows that the height of this triangle is 3.75. Now, to find the x intercepts of both equations, we simply have to plug in the y value as 0. For the first one, 3x-0=0, so x=0 as well and the coordinates are (0,0). For the second one, x+0=10, so x=10 and the coordinates are (10,0). This shows that the base is 10-0=10 units long. The formula for the area of a triangle is [tex]\frac{bh}{2}=\frac{10\cdot3.75}{2}=18.75[/tex]. Hope this helps!

Answer:

150 miles

Step-by-step explanation:

0.15x1000=150

Given:

Points on the line are (-2, 4) and (-4, -8).

To find:

The equation of a line.

Solution:

[tex]x_1=-2, y_1=4, x_2=-4, y_2=-8[/tex]

Slope of the line:

[tex]$m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the given points.

[tex]$m=\frac{-8-4}{-4-(-2)}[/tex]

[tex]$m=\frac{-12}{-4+2}[/tex]

[tex]$m=\frac{-12}{-2}[/tex]

m = 6

Point-slope formula:

[tex]y-y_1=m(x-x_1)[/tex]

Substitute [tex]x_1=-2, y_1=4[/tex] and m = 6

[tex]y-4=6(x-(-2))[/tex]

y - 4 = 6(x + 2)

Substitute [tex]x_1=-4, y_1=-8[/tex] and m =6 in point-slope formula.

[tex]y-(-8)=6(x-(-4))[/tex]

y + 8 = 6(x + 4)

Option A and Option D are the correct answers.

Therefore y - 4 = 6(x + 2) and y + 8 = 6(x + 4) are the equations describes the shown line.

The question is:

A cake recipe calls for 550 grams of flour. About how many pounds of flour do you​ need? Use the conversion factors (1 ounce)/(28.4 grams) and (1 pound)/(16 ounces).

Answer:

About 1.2 pounds of flour is needed.

Step-by-step explanation:

Given that the cake recipe calls for 550 grams, we want to determine about how many pounds of flour we need.

This simply means we want to convert 550 grams to pounds.

First, we were given (1 ounce)/(28.4 grams)

This implies that

1/28.4 = x/550 ..............................(1)

Where x is 550 grams in ounce.

Solving (1)

28.4x = 550

=> x = 550/28.4

≈ 19.3662

That is 550 grams is equal to 19.3662 ounce

Next, we are given the ratio (1 pound)/(16 ounce). We then convert 19.3662 ounce to pound

Let y be 19.3662 ounce in pound

=> 1/16 = y/19.3662

16y = 19.3662

y = 19.3662/16

≈ 1.2

That is 19.3662 ounce is equal to 1.2 pounds.

Therefore, 550 grams is equal to 1.2 pounds, and it is the amount of flour needed.

You would need approximately 1.210 pounds of flour for the cake recipe.

To convert grams to pounds, we can use the conversion factor:

1 pound = 16 ounces

And we also have the conversion factor:

1 ounce = 28.4 grams

First, we'll convert grams to ounces, and then ounces to pounds.

Given that the recipe calls for 550 grams of flour, let's calculate the amount in pounds.

Step 1: Convert grams to ounces.

550 grams x (1 ounce / 28.4 grams) = 19.366 ounces

Step 2: Convert ounces to pounds.

19.366 ounces x (1 pound / 16 ounces) = 1.210 pounds

Therefore, you would need approximately 1.210 pounds of flour for the cake recipe.

Learn more about conversion factor click;

https://brainly.com/question/32020768

#SPJ6

Answer:

b then a

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

The width is 8 yards.

Step-by-step explanation:

[tex]\frac{461.76}{7.8\cdot7.4}=8[/tex]. Hope this helps!