Gina is a tour boat operator and she wants to know the mean age of all the people in her tour group.

She randomly selects 8 people in the group and asks them for their ages. Their responses are 19, 27, 25, 21, 44, 22, 45, and 34.

What is the best estimate of the mean age of all the people in the tour group?



Round to the nearest whole number.

Enter your answer in the box.

___ years

-40*.15 + 150*(1-.15)= 121.50

Given the probabilities of sunny and rainy days and the respective profits, the Sudsy car wash's expected net profit per day, considering the rain probability, is $121.5.

The subject of the question is about Expected Value, a concept in Probability Theory. Considering the Sudsy car wash's situation, we know that it loses $40 on rainy days and gains $150 on sunny days. The probability of having a rainy day is given as 15%, which means the probability of having a sunny day is 85% (100% - 15%).

The expected value of the net profit can be calculated by the formula for Expected Value: E[X] = ∑[x*P(X=x)]. In the context of this problem, we can write out the expected value E[N] of the net profit N as E[N] = (-$40 * 0.15) + ($150 * 0.85) = -$6 + $127.5 = $121.5. So, it is expected that the Sudsy car wash will have a net profit of $121.5 per day, on average.

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Answer:

Step-by-step explanation:

No, you're not an idiot.  You are just misunderstanding pi.  Pi is an irrational number, meaning it goes on forever.  Literally, forever, with no end.  Some weird guy actually memorized the first 100,000 places of it or something crazy like that.  Anyway, if you use 3.14 you have rounded so incredibly, that you lose a lot of your precision.  Your calculator uses the first 9 places of the decimal or something like that.

[tex] \frac{4x + 12}{32} = \frac{15}{8} \\ ( = )32x + 96 = 480 \\ ( = )x = 12[/tex]

Answer:

x = 12

Step-by-step explanation:

Since the triangles are similar then the ratio of corresponding sides are equal, that is

[tex]\frac{4x+12}{15}[/tex] = [tex]\frac{32}{8}[/tex] = 4, thus

4x + 12 = 4 × 15 = 60 ( subtract 12 from both sides )

4x = 48 ( divide both sides by 4 )

x = 12

Gabriel Mouton

Early development. Most historians agree that Gabriel Mouton, the vicar of St. Paul's Church in Lyons, France, is the “founding father” of the metric system. He proposed a decimal system of measurement in 1670.

Answer:

5/2 kg

Step-by-step explanation:

The ratio here is 2:6.  2 plus 6 is 8.

Then (2/8) times 10 kg represents the amount of compost needed; that comes to 20/8 kg, or 10/4 kg, or 5/2 kg.

Gabriel should use 2.5 kilograms of compost to create a 10-kilogram mix that has a ratio of 2 parts compost to 6 parts potting soil.

Gabriel is making a mixture for a special plant which requires a ratio of 2 parts compost to 6 parts potting soil. He aims to make 10 kilograms of this mix in total. To calculate the amount of compost he should use, we first have to find the total number of parts in the mix:

Add the parts of compost to the parts of potting soil: 2 parts (compost) + 6 parts (soil) = 8 parts (total).

Determine the weight of each part: 10 kilograms (total mix) / 8 parts = 1.25 kilograms per part.

Multiply the weight of each part by the number of parts for compost: 1.25 kilograms per part × 2 parts (compost) = 2.5 kilograms of compost.

Therefore, Gabriel should use 2.5 kilograms of compost for his special plant mix.

Answer:

0.25

Step-by-step explanation:

The probability that a football player has suffered more than 3 broken bones is equal to the probability they suffered 4 or 5.

P(x>3) = P(4 or 5)

P(x>3) = P(4) + P(5)

P(x>3) = 0.10 + 0.15

P(x>3) = 0.25

1. Same length.

2.vertically opposite angle.

3.BAC =BDE

4.AC = DE

Hope this helps you ___!!❤

Answer:

x⁷ + 9x⁴ - 9x³ - 81

Step-by-step explanation:

(f⋅g)(x) is just another way of writing f(x) ⋅ g(x).

f(x) ⋅ g(x)

(x⁴ - 9) (x³ + 9)

If you wish to simplify:

x⁷ + 9x⁴ - 9x³ - 81

Answer:

  A. product 1

Step-by-step explanation:

An exponential function (with a base larger than 1) will eventually exceed the value of any polynomial function. Product 1 has a price described by an exponential function, so its price will exceed all others. (One only need to compute the values for x=4 to see this.)

_____

The attachment extends the table and plots the functions up to the point where Product 1 exceeds the others.

It the second equation. I used subsitution to find that out.

The second one y = 1/2x + 3/4 is the correct answer. I first graphed the two points then started graphing the equations to find which line went through those two points.

Answer:

Step-by-step explanation:

Let s represent the length of the shortest side. Then the other two sides are ...

The perimeter is the sum of the lengths of the three sides, so is ...

  56 ft = s + (s+6) + (2s-6) = 4s . . . . collect terms

  14 ft = s . . . . . . . divide by the coefficient of s

The shortest side is 14 ft; the second side is 20 ft; the third side is 22 ft.

Final answer:

Using the given information about the sides of the triangular deck and its perimeter, we set up an equation to solve for the shortest side and then used that to find the lengths of the other two sides. The three sides of the triangular deck are 14 feet, 20 feet, and 22 feet.

Explanation:

To solve the problem, we need to set up an equation based on the given information. Let's define the shortest side of the triangle as x feet. According to the problem, the second side is x + 6 feet, and the third side is 2x - 6 feet. The perimeter of the triangle is the sum of the lengths of all three sides, which is given as 56 feet.

We can set up the following equation:

x + (x + 6) + (2x - 6) = 56

Combining like terms, we get:

4x = 56

Divide both sides by 4:

x = 14

Now we can find the lengths of the sides:

The shortest side: 14 feet

The second side: 14 + 6 = 20 feet

The third side: 2(14) - 6 = 22 feet

ANSWER

[tex]4(x + 6)(x - 2)[/tex]

EXPLANATION

The given rational expression is:

[tex] \frac{1}{ {x}^{2} + 4x - 12} + \frac{3x}{4x - 8} [/tex]

We can factor the denominators to obtain:

[tex] \frac{1}{(x + 6)(x - 2) } + \frac{1}{4(x - 2)} [/tex]

The common denominator is least common multiples of the denominators.

The common denominator is of the given rational expression is

[tex]4(x + 6)(x - 2)[/tex]

Answer:

B: triangle AEH

C:triangle DAE

E: triangle GDH

F: triangle CFG

H: triangle BCF

Step-by-step explanation:

just took the unit test  hope it helps ;)

Right angle triangles are triangle AEG ,  triangle AEH , triangle DAE ,  triangle BFH , triangle CFG , triangle BCF  .

Right angle triangle :

A  Right triangle states that if one of the angles of a triangle is a right angle - 90º .

So , In the figure given below we get :

→  In triangle AEG  : the angle between AE and AG is 90 ^ º .

→  In triangle AEH : the angle between  AE and EH is 90 ^ º .

→ In triangle DAE :  the angle between DA  and AE  is 90 ^ º .

→ In triangle BFH :  the angle between BF  and FH  is 90 ^ º .

→ In triangle GDH :  the angle at G , D and H is 60 ^ º .

→ triangle CFG :  the angle between CG  and GF is 90 ^ º .

→  triangle DFH : the angle between sides is not  90^ º .

→  triangle BCF :  the angle between BC  and BF is 90 ^ º .

learn more about the right angle triangles here :

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Answer:

w = 54°

Step-by-step explanation:

w is the inscribed angle subtended on the same arc with measure of 108°

w is half the size of the central angle, that is

w = 0.5 × 108° = 54°

Answer:

The approximate lateral area of the prism is [tex]831\ in^{2[/tex]

Step-by-step explanation:

we know that

The lateral area of the prism is equal to

[tex]LA=PH[/tex]

where

P is the perimeter of the base of the prism

H is the height of the prism

Find the perimeter of the hexagonal base

Remember that the area of the hexagonal base is equal to

[tex]A=\frac{1}{2} P(a)[/tex]

where

P is the perimeter

a is the apothem

we have

[tex]A=346.41\ in^{2}[/tex]

[tex]a=10\ in[/tex]

substitute and solve for P

[tex]346.41=\frac{1}{2} P(10)[/tex]

[tex]P=346.41/5=69.282\ in[/tex]

Find the lateral area

[tex]LA=PH[/tex]

we have

[tex]P=69.282\ in[/tex]

[tex]H=12\ in[/tex]

substitute the values

[tex]LA=(69.282)(12)=831\ in^{2[/tex]

Answer:

831 In^3

Step-by-step explanation:

Edge 2020

Answer:

slope = -0.5

Step-by-step explanation:

Answer:

slope = change in y / change in x

slope = 0 -3.5 / 7 -0

slope = -3.5 / 7

slope = -.5

Step-by-step explanation:

Answer:

Your answer is 7.0

Step-by-step explanation:

If the circles are congruent and RQ measures 35.6, then so does CB.  That means that half of it (the radius XD which measures 26 cuts the length of CB in half) is 17.8.  If the base of that right triangle is 17.8 and the hypotenuse is 26, then Pythagorean's Theorem tells us that the height of the triangle is 18.95151709.  Subtract that from the radius length of 26 and you'll have the length of DE

The value of length ED would be, 7.0

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

⊙X≅⊙Y

And, Length of RQ = 35.6

Now, We get;

⇒ CB = RQ = 35.6

Hence, EB = 1/2CB

                 = 1/2 (35.6)

                 = 17.8

Applying Pythagoras theorem,

⇒ XE² = XB² - EB²

⇒ XE² = 26² - 17.8²

⇒ XE² = 19

Thus, The length of ED is,

⇒ ED = XD - XE

⇒ ED = 26 - 19

⇒ ED = 7.0

Therefore, The value of length ED would be, 7.0

Learn more about the circle visit:

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Answer:

May 6

Step-by-step explanation:

20 x 2 = 40 40 x 2 = 80 80 x 2 = 160 x 2 = 320 320 x 2 = 640 after 5 days on may 6 it will surpass 500 meters.

The oil spill, doubling in size each day from an initial 20 square meters, will exceed 500 square meters on the 6th of May.

Based on the information provided, let's calculate how long it will take for the oil spill to exceed 500 square meters if it doubles in size each day starting from an initial size of 20 square meters. On May 1, the spill is 20 square meters. On May 2, it would be 40 square meters (20*2). If we continue this pattern, we can find the day the spillage area will exceed 500 square meters:

Therefore, the area of the oil spill exceeds 500 square meters on May 6.

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Answer:

  27,409.308

Step-by-step explanation:

Compute the given sum. If you're really stuck, your calculator can help you.

Answer:

y = 13

Step-by-step explanation:

If it's a parallelogram then its consecutive angles are supplementary (add up to 180°).

6x - 12 + 132 - x = 180°,

5x + 120 = 180

5x = 60

 x = 12

6x - 12 = 6(12) - 12 = 72 - 12 = 60

Parallelogram, opposite angles are equal

so

6y + 18 = 6x - 12

6y - 18 = 60

6y = 78

  y = 13

Answer:

216

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

30% of 50 is 15 because 30 % means 30out of 100

and if you half 100 you also half 30

Valentina, with a 30% probability, can expect to draw a blue marble 15 times out of 50 draws. This is calculated by multiplying the total number of draws by the probability of drawing a blue marble.

The question revolves around the concept of probability. The probability of an event is the measure of the likelihood that the event will occur. In Valentina's case, she has a 30% chance of drawing a blue marble. Therefore, if she were to draw a marble 50 times, we would expect her to draw a blue marble 30% of those 50 times. Probability is often expressed as a fraction or decimal, and in this case, 30% translates to 0.30 in decimal form.

To calculate how many times we can expect Valentina to draw a blue marble, we multiply the total number of draws (50) by the probability of drawing a blue marble (0.30).

So, 0.30 * 50 = 15.

Therefore, Valentina can expect to draw a blue marble 15 times out of 50 draws.

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Answer:

1,352.32

Step-by-step explanation:

If you take 7.6 and multiply it to 16,412.05 (.076)(16,412.05), you get 1,247.32. You then add the overhead cost of 105 to get 1352.32. (Apex verified too)

The drivers insurance premium is:

                $ 1352.3158

The probability of a driver getting into an accident is 7.6%.

The average cost of an accident is $16,412.05.

This means that the expected amount that will be paid to each of the driver by the company on accident will be:  0.076×16412.05

                                                       = $ 1247.3158

Also, the overhead cost for an e company per insured driver is $105.

This means that the insurance premium of driver is:

       =   105+1247.3158

     =    $ 1352.3158

Answer:

C. 279.3

Step-by-step explanation:

To find the mean of a set of numbers you have to add all of them together and divide them by how manys numbers there are

If we add all the numbers together it equals 2514

There are 9 numbers here

2514/9=279,333333

Therefore, the answer is C

The mean is the same as the average!

To find mean ...

121+

347+

45+

21+

300+

614+

312+

333+

421

__________________

2,514

[tex]\frac{2,514}{9}  = 279.33[/tex]

Final answer is D. (279.3)

Answer:

[tex][g\circ f](x)=-2[/tex]

Step-by-step explanation:

By the definition

[tex][g\circ f](x)=g(f(x))[/tex]

You are given

[tex]f(x)=2x-1\\ \\g(x)=-2[/tex]

So,

[tex][g\circ f](x)=g(f(x))=g(2x-1)=-2[/tex]

Answer: -3/2x + 7/2

Step-by-step explanation:

for parallel lines; m₁ = m₂

the gradient of the given line is -3/2

2y= -3x + 4

y = -3/2x + 2

therefore the gradient of the parallel line is -3/2

hence the equation is y-y₁ = m(x-x₁)

y-5 = -3/2(x+1)

y - 5 =-3/2x - 3/2

y = -3/2x -3/2 + 5

y = -3/2x + 7/2

Abra is the best shooter because 9/10 is almost a 1 where 3/4 is .75.

Answer:

$6,524.96

Step-by-step explanation:

Take the commission total which is $1631.24 divide it by 25% or .25.

$1,631.24 ÷ .25=$6,524.96 cost of the used car

Check your answer by taking your answer and multiple it by 25%.

$6,524.96 (cost of the car) × .25 =$1,631.24 commission

Answer:

$6,524.96

Step-by-step explanation:

Step One: Because the amount she is paid is the 25% commission, multiply the 1,631.24 by 4 ( 4 because she is paid 1 out of 4 parts of the total selling price)

Step Two: the answer is 6,524.96

Answer:

The quotient is [tex]2x^2-5x+2[/tex]

Step-by-step explanation:

We want to simplify:

[tex]\frac{6x^4-15x^3+10x^2-10x+4}{3x^2+2}[/tex]

We factor the numerator to get:

[tex]\frac{(x-2)(2x-1)(3x^2+2)}{3x^2+2}[/tex]

We cancel out the common factors to get:

[tex](x-2)(2x-1)[/tex]

Therefore the quotient is [tex]2x^2-5x+2[/tex]