What is the prime factorization of 72?
22 × 32
22 × 33
23 × 32
23 × 33

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:

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:

It will take 44 practices for Scott to have sprinted a total of 2 miles combined

Step-by-step explanation:

This question can be solved using rules of three.

First step:

Scott practice is measured in yards.

We want to know how many practices it will take for him to have sprinted 2 miles.

So we pass 2 miles to yards

Each mile has 1760 yards.

So 2 miles is 1760*2 = 3520 yards.

A practice:

4 sprints of 20 yards each.

So 4*20 = 80 yards.

A practice is 80 yards. How many practices for 3520 yards?

1 practice - 80 yards

x practices - 3520 yards

80x = 3520

x = 3520/80

x = 44

It will take 44 practices for Scott to have sprinted a total of 2 miles combined

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:

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 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.

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: 3,4,7

Step-by-step explanation:

Answer:

150 miles

Step-by-step explanation:

0.15x1000=150

Answer:

b then a

Step-by-step explanation:

Answer:

Step-by-step explanation:

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:

•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:

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:

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.

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:

56.55

Step-by-step explanation:

The formula to find the volume of a cylinder is V=πr2h so you would just need to plug the numbers in to get 56.55.

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:

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.

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!

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:

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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?

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:

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

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.

Answer:

The width is 8 yards.

Step-by-step explanation:

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

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:

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!

Answer: 8.3

Step-by-step explanation: 37 divided by=12.3 then 12.3 - 4

Answer: the taxi travelled 11 miles

Step-by-step explanation:

Let x represent the number of miles that the taxi traveled.

The cost of the taxi was 4 dollars plus 3 dollars for each mile traveled. It means that the total cost of renting and driving the taxi over x miles is

4 + 3x

The Lopez rented the taxi and when they arrived at their destination, the total cost 37 dollars. It means that

4 + 3x = 37

3x = 37 - 4

3x = 33

x = 33/3

x = 11 miles

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:

$ 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