The following are the ages (years) of 5 people in a room:
20, 21, 13, 22, 18
A person enters the room.
The mean age of the 6 people is now 18.
What is the age of the person who entered the room?

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:

X=72

Step-by-step explanation:

216/3= 72

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

You find the circumference and multiply it by the central angle. If the central angle is in degrees, you divide that by 360. If the central angle is in radians, you divide by 2pi.

Answer:

Function 4

Step-by-step explanation:

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:

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:

It will take 0.8333h for the mustang to catch up to the grand am.

The two cars will have traveled 66.664 miles on the turnpike

Step-by-step explanation:

The position for each car can be modeled by equations in the following format:

[tex]S(t) = S(0) + vt[/tex]

In which S(t) is the position t hours after the last car(the Ford Mustang) has left, S(0) is the position of each car when the Ford Mustang left and v is the speed of each car, in miles per hour.

Pontiac

Traveling at 50 mph, which means that [tex]v = 50[/tex].

The Ford Mustang leaves half an hour after the Pontiac. The Pontiac travels at 50 mph, which means that in this interval, the Pontiac will have traveled 0.5*50 = 25 mph. This means that S(0) = 25. So

[tex]S_{P}(t) = 25 + 50t[/tex]

Ford Mustang

Leaves from position 0, so S(0) = 0.

Travel in the same distance at 80 mph, so [tex]v = 80[/tex]. So

[tex]S_{M}(t) = 80t[/tex]

How long would it take for the mustang to catch up to the grand am ?

This is t when

[tex]S_{M}(t) = S_{P}(t)[/tex]

[tex]80t = 25 + 50t[/tex]

[tex]30t = 25[/tex]

[tex]t = \frac{25}{30}[/tex]

[tex]t = 0.8333[/tex]

It will take 0.8333h for the mustang to catch up to the grand am.

When it catch up how far will the two cars have traveled on the turnpike

This is either [tex]S_{M}(0.8333)[/tex] or [tex]S_{P}(0.8333)[/tex], since they will be in the same position. So

[tex]S_{M}(t) = 80t[/tex]

[tex]S_{M}(0.8333) = 80*0.8333 = 66.664[/tex]

The two cars will have traveled 66.664 miles on the turnpike

The Ford Mustang will catch up to the Pontiac Grand Am in 18.75 minutes and they will have traveled a total of 25 miles on the turnpike.

To find out how long it takes for the Ford Mustang to catch up to the Pontiac Grand Am, we need to determine the time it takes for the Mustang to cover the same distance that the Grand Am has already traveled. The Grand Am has a head start of half an hour at a speed of 50 mph, so it has covered a distance of:

Distance = Speed x Time = 50 mph x 0.5 hr = 25 miles

Now, we can calculate the time it takes for the Mustang to cover this distance:

Time = Distance / Speed = 25 miles / 80 mph = 0.3125 hr = 18.75 minutes

Therefore, it will take the Mustang 18.75 minutes to catch up to the Grand Am.

When the two cars catch up, they will have traveled a total distance of 25 miles, which is the distance covered by the Grand Am in the half-hour head start.

Answer:

0.9032

Step-by-step explanation:

Given that:

mean (μ) = 146 grams and standard deviation (σ) = 2.3 grams

The z score is a measurement used in statistics to calculate how far a value is from the mean in a normal distribution. The z score is given as:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

For the baseball not to weigh more than 149 grams i.e x = 149 g

[tex]z=\frac{x-\mu}{\sigma}=\frac{149-146}{2.3} =1.30[/tex]

From the probability distribution table, P(x < 149) = P(z < 1.30) = 0.9032 = 90.32%

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

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: 3 and 240

Step-by-step explanation:

Edg 2020

Answer:

The triangular prism has

✔ 3

lateral faces.

The triangular prism has a lateral area of

✔ 240

square inches.

Step-by-step explanation:

Answer:

150 miles

Step-by-step explanation:

0.15x1000=150

Step-by-step explanation:

since both objects and sides are similar, you can set each side equal, then you cross multiply, and do subtraction, then find x.

Final answer:

To find the value of x in similar polygons, justify the similarity, write an equation relating the sides, algebraically solve for x, calculate, and then check that the result is reasonable.

Explanation:

The subject of this question is Mathematics, and it is likely at the high school level, as it involves finding a missing length in similar polygons, which requires knowledge of ratios and properties of similar figures, often covered in high school geometry courses.

Steps to find the value of x:

Justify that the triangles are similar: This can typically be done by verifying that the triangles meet the criteria of similarity, such as having identical angles or corresponding sides in proportion.

Write an equation that relates the sides of the triangles: Utilize the properties of similar triangles to write ratios that compare the lengths of corresponding sides.

Algebraically isolate the unknown quantity x.

Plug in numbers and calculate the answer.

Check the answer to ensure it seems reasonable.

It's also important to remember that if two triangles are similar, their corresponding lengths are proportional, which you can express algebraically with a statement such as AB/CD = EF/GH where AB, CD, EF, and GH are corresponding sides of the similar triangles.

Answer:

The answer is 6 cups.

Step-by-step explanation:

If 20 cookies are 2 cups, that means that 10 cookies are 1 cup. If you see the pattern, the answer would easily be 6 cups.

To solve this, you need to isolate/get the variable "r" by itself in the equation:

-1 = -3r + 2r       Combine like terms(terms that have the same variable and power/exponent.)  The only like terms you can combine are -3r and 2r

-1 = -r       Divide -1 on both sides to get "r" by itself

[tex]\frac{-1}{-1} =\frac{-r}{-1}[/tex]   (two negative signs cancel each other out and become positive)

1 = r   or   r = 1

Answer:R=-1

Step-by-step explanation: You would have to first do the math for the equation, then you would have to work in the "R" and given the answer is smaller than the equation itself we can tell that the "R" is a negative. So, if we add the -3 and the 2 we get 1,so we can say that the "R" are both equal to -1 then we put it in the equation. We get -1=1 we add the "R's" then get -1

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:

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:

b then a

Step-by-step explanation:

Answer:

Step-by-step explanation:

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:

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:

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:

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:

vbighughyuogytifvyigguhui

Step-by-step explanation:

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.

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 answer to your question is $84.15

Step-by-step explanation:

Data

cost of the meal = $76.50

tip 10%

total cost = ?

Process

1.- Calculate the 10% of $76.50 using proportions and cross multiplication.

             $76.50 --------------- 100%

                   x     -----------------  10%

                      x = (10 x 76.5) / 100

                      x = 765/100

                      x = 7.65

2.- Calculate the total cost

Total cost = cost of the meal + tip

-Substitution

Total cost = $76.50 + $7.65

-Result

Total cost = $84.15

Answer:

Step-by-step explanation:

Let x represent the number of hours for which you can rent the truck.

truck rental company charges a weekend rate of $50.75 plus $8.25 for each hour a truck is rented. It means that the cost of renting the truck for x hours would be expressed as

50.75 + 8.25x

You have at most $125.00 to spend on a truck rental. Therefore, the inequality that describes the number of hours you can rent the truck is

50.75 + 8.25x ≤ 125

Answer:

  -3, 10

Step-by-step explanation:

Let s represent the smaller number. Then 7-s is the larger one.

  7-s = 16 +2s

  -9 = 3s . . . . . . . add s-16

  -3 = s

  7-s = 10

The smaller number is -3, the larger one is +10.