You need to borrow money for gas, so you ask your mother and your sister. You can only borrow money from one of them. Before giving you money, they each say they will make you play a game. Your sister says she wants you to flip a fair coin. She will give you $9 for heads and $21 for tails. Your mother says she wants you to roll a six-sided die. She will give you $5 times the number that appears on the die. Determine the expected value of each game and decide which offer you should take.

Answer:

16x²

Step-by-step explanation:

since all sides of a square are equal, we just multiply 4x by 4x. this gives us 16x².

The area of square with side length 4x is 16x.

A square is a two-dimensional closed shape with 4 equal sides and 4 vertices.

Given,

The side length of a square is 4x

We need to find the area of square.

As we know that area of square = 4a.

Where a is the length of side of a square.

In a square all the four sides will have same length.

a=4x

Area of square=4(4x)

=16x

Hence the area of square with side length 4x is 16x.

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*see attachment for diagram

Answer:

Volume of new backpack = 1,299.84 in.³

Step-by-step explanation:

Volume of the new back pack = volume of the front pocket + volume of the main section of the backpack

✔️Volume of the front pocket = volume of rectangular prism = L*W*H

L = 8 in.

W = 4 in.

H = 2 in.

Volume of the front pocket = 8*4*2 = 64 in.³

✔️Volume of the main section of the back pack = volume of the rectangular prism + volume of the half cylinder

= L*W*H + ½(πr²h)

L = 12 in.

W = 10 in.

H = 7 in.

r = 6 in.

h = 7 in.

Plug in the values into the equation

Volume of the main section of the backpack = 12*10*7 + ½(π*6²*7)

= 840 + ½(791.68)

= 1,235.84 in.³

✅Total volume of the new backpack = 64 + 1,235.84 = 1,299.84 in.³

Answer:

a) 0.1434 = 14.34% probability that the number of U.S. adults who have very little confidence in newspapers is exactly five.

b) 0.7731 = 77.31% probability that the number of U.S. adults who have very little confidence in newspapers is at least six.

c) 0.022 = 2.2% probability that the number of U.S. adults who have very little confidence in newspapers is less than four.

Step-by-step explanation:

For each adult, there are only two possible outcomes. Either they have very little confidence in newspapers, or they do not. Adults are independent. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

66​% of U.S. adults have very little confidence in newspapers.

This means that \(p = 0.66\)

You randomly select 10 U.S. adults.

This means that \(n = 10\)

(a) exactly​ five

This is P(X = 5). So

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 5) = C_{10,5}.(0.66)^{5}.(0.34)^{5} = 0.1434\)

0.1434 = 14.34% probability that the number of U.S. adults who have very little confidence in newspapers is exactly five.

(b) at least​ six

This is:

\(P(X \geq 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)\)

So

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 6) = C_{10,6}.(0.66)^{6}.(0.34)^{4} = 0.232\)

\(P(X = 7) = C_{10,7}.(0.66)^{7}.(0.34)^{3} = 0.2573\)

\(P(X = 8) = C_{10,8}.(0.66)^{8}.(0.34)^{2} = 0.1873\)

\(P(X = 9) = C_{10,9}.(0.66)^{9}.(0.34)^{1} = 0.0808\)

\(P(X = 10) = C_{10,10}.(0.66)^{10}.(0.34)^{0} = 0.0157\)

\(P(X \geq 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.232 + 0.2573 + 0.1873 + 0.0808 + 0.0157 = 0.7731\)

0.7731 = 77.31% probability that the number of U.S. adults who have very little confidence in newspapers is at least six.

(c) less than four.

This is:

\(P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)\).

So

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 0) = C_{10,0}.(0.66)^{0}.(0.34)^{10} \approx 0\)

\(P(X = 1) = C_{10,1}.(0.66)^{1}.(0.34)^{9} = 0.0004\)

\(P(X = 2) = C_{10,2}.(0.66)^{2}.(0.34)^{8} = 0.0035\)

\(P(X = 3) = C_{10,3}.(0.66)^{3}.(0.34)^{7} = 0.0181\)

\(P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0 + 0.0004 + 0.0035 + 0.0181 = 0.022\)

0.022 = 2.2% probability that the number of U.S. adults who have very little confidence in newspapers is less than four.

Answer:

-6/49

Step-by-step explanation:

this is the answer it is very easy

Answer:

He kept 7/12 of the box.

Step-by-step explanation:

We add and convert both 1/6 and 1/4 because we cant add fractions with unlike denominators.

1/6 = 2/12  | 1/4 = 3/12

then add.

2/12 + 3/12 = 5/12.

we subtract this from a whole, which is 12/12.

12/12 - 5/12 = 7/12

he keeps 7/12 of the box

hope this helped!

Answer:The price of a bond can be calculated using the formula:

Price = Maturity Value / (1 + r)^n

Where:

Maturity Value = $12,000

r = the annual interest rate as a decimal (7.25% / 100 = 0.0725)

n = the number of years to maturity (11 years)

So the price of the bond is:

Price = $12,000 / (1 + 0.0725)^11

By solving this equation we get the price of bond is $7,065.87 approximately.

Note: The bond price is the amount you pay to buy the bond and receive the maturity value at the end of the bond term.

Step-by-step explanation:

Answer:

-5

Step-by-step explanation:

(i^2) = -1 so -1 -1 + 3x = 3x - 2. If x = i^2 = -1, then 3x = -3. -3 - 2 = -5

Answer:

Step-by-step explanation:

The answer is 198.416

The average rate of change of the function over the interval is -6

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

The graph

The interval is given as

From x = 2 to x = 4

The function is a quadratic function

This means that it does not have a constant average rate of change

So, we have

f(2) = -3

f(4) = -15

Next, we have

Rate = (-15 + 3)/(4 - 2)

Evaluate

Rate = -6

Hence, the rate is -6

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Answer:

0.0451

Step-by-step explanation:

Answer:

451/10000 or 0.0451 in decimal form

Step-by-step explanation:

Hope this helps :)

xfgxfsdfxcxcxAnswer:

Step-by-step explanation:

Answer:

x = 2

Step-by-step explanation:

Five multiplied by a certain number is added to two

 5          *                          x                        +             2

equals four times the number plus four

  =          4       *              x          +       4

---------------------------------------------

5x + 2 = 4x + 4

Subtract 4x from both sides

x + 2 = 4

Subtract 2 from both sides

x = 2

Answer:

  168

Step-by-step explanation:

You are given one equation that can be used to solve this problem. The other equation you need is ...

  b = 82

Using this value in the given equation, you can find "a".

  10.50a +3.75b = 2071.50 . . . . . . . given

  10.50a +3.75·82 = 2071.50 . . . . . .using 82 for b

  10.50a +307.50 = 2071.50 . . . . . . evaluated

  10.50a = 1764 . . . . . . . subtract 307.50

  a = 168 . . . . . . . . . . . . . divide by 10.50

168 adult tickets were sold.

Answer:

168 Adult tickets were sold

Step-by-step explanation:

Make me brainliest

Answer:

-48

Step-by-step explanation:

we can see each number is getting doubled but flipped from negative and positive and vise versa. aka getting multiple by negative 2

we can also double check our work by multiplying each number in the sequence we have by -2 and make sure it follows the sequence.

Answer:

1/12 gallons

Step-by-step explanation:

We can determine how much more hot chocolate than apple cider die Joe serve by subtracting 1/12 from 1/6.

Step 1:  Since 1/12 has the bigger denominator and 6 * 2 = 12, let's give 1/6 the same denominator as 1/12 by multiplying the entire fraction by 2/2

(1/6) * (2/2) = 2/12

Step 2:  Now we can subtract 1/12 from 2/12:

2/12 - 1/12 = 1/12

Thus, Joel served 1/12 more gallons of hot chocolate than apple cider.

Answer:

-11

Step-by-step explanation:

g(-5)=-5^2+8(-5) +4

=25+-40+4

=-11

Answer:

To one decimal place,

y = 16.3 m

Step-by-step explanation:

Using SOHCAHTOA,

In this case we need to use CAH,

WE know the angle = 25 and the hypotenuse H = 18,

so,

y = adjacent

\(cos(angle) = y/H\\y = (18)(cos(25))\\y = 16.3135\\y = 16.3\)

Answer: 16.3 in.

Step-by-step explanation:

use SOH CAH TOA

cos x = adj/hyp

cos 25  = y/18

18 cos 25  = y

y= 16.3

Answer:

Let your two numbers be n and n-1. Then: 2n+n²-2n+1=51 n²=50 n=5√2 n-1=5√2-1

Hope that helps <3

Answer: 125

Step-by-step explanation: product of 5 and 75 = 5*75 = 375 divided by 3 which is 375/3 = 125.

Answer:

m=0

Step-by-step explanation:

the slope is calculated using two points on the line and the formula

m = (y2 - y1) ÷ (x2 - x1)

where

x1 and y1 are the coordinates of point 1

x2 and y2 are the coordinates of point 2

for example, you can take

point 1 = (x1;y1) = (-2;3)

point 2 = (x2;y2) = (-1;3)

then your slope is

m = (3 - 3) ÷ (-1 - (-2)) = 0

notice that x1 is always at the left of x2 on the x axis

and it makes sense that your slope is 0 because for each x your y is the same

as there are 30 children and from 30 children 2 will be picked (which will than be 2/30)

but if we simplify that by 2, than that will lead to the ANSWER OF: 1/15

Answer:

So the diameter of the pipe with the insulation around it is approximately 18.84 inches / 2 = 9.42 inches.

Step-by-step explanation:

To find the diameter of the pipe with the insulation around it, we can use the formula for the circumference of a circle:

C = 2 * π * r

Where:

· C = circumference of the pipe

· π = the mathematical constant approximately equal to 3.14

· r = the radius of the pipe

Using the given information, we know that the pipe’s diameter is 2.5 inches and that the insulation around the pipe is 0.5 inch thick. Therefore, the radius of the pipe with the insulation around it is:

r = 2.5 inches + 0.5 inch = 3 inches

Plugging in the values:

C = 2 * π * 3

C = 6.28 * 3

C = 18.84 inches

Note that this is only an approximation, as the thickness of the insulation is slightly larger than the diameter of the pipe. To obtain a more accurate result, we would need to use a geometric area formula or a numerical integration technique.

Answer:

30.5

Step-by-step explanation:

Let L = the larger number

Let S = the smaller number

L + S = 144

L - S = 73

L = S + 73

S + S + 73 = 144

2S = 71

S = 30.5

The constant of proportionality is a crucial aspect of a proportional relationship, as it tells us how much one variable changes in relation to the other. It can be calculated from the equation of the relationship, or from the slope of the graph if it is a linear relationship.

A proportional relationship is a mathematical equation that expresses two variables that are in proportion to one another. In this type of relationship, if one variable is multiplied by a certain constant factor, then the other variable will be multiplied by the same constant factor. For example, if the cost of 3 books is $15, then the cost of 6 books will be $30. In this case, the number of books and the cost of the books are in proportion to one another.

The constant of proportionality is the constant factor by which the two variables are multiplied to obtain each other. In other words, it is the ratio between the two variables that remain constant in a proportional relationship. It can be represented by the letter k, and is calculated by dividing one variable by the other.

To find the constant of proportionality from a graph, we need to look at the slope of the line. The slope is the ratio between the change in the y-values and the change in the x-values, which is also known as the rise over run. If the graph shows a proportional relationship, then the slope will remain constant throughout the graph.

For example, if the graph shows the relationship between the number of hours worked and the amount of money earned, and the slope is 10, then the constant of proportionality is 10. This means that for every hour worked, the person earns $10. The equation for this proportional relationship can be written as y = 10x, where y represents the amount of money earned and x represents the number of hours worked.

In conclusion, the constant of proportionality is a crucial aspect of a proportional relationship, as it tells us how much one variable changes in relation to the other. It can be calculated from the equation of the relationship, or from the slope of the graph if it is a linear relationship.

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Answer:

dream is cool................

Answer:

Not equal to.

Step-by-step explanation:

Answer:

A)

\(\left \{ {{80} \atop {20}} \} * \left \{ {{60} \atop {20}} \} * \left \{ {{40} \atop {20}} \} * \left \{ {{20} \atop {20}} \}\)

B)

\(\left \{ {{20+4-1} \atop {4-1}} \} = \left \{ {{23} \atop {3}} \}\)

C)

= \(\left \{ {{17+4+1} \atop {4-1}} \} = \left \{ {{20} \atop {3}} \}\)

D)

= \(\left \{ {{20} \atop {3}} \} - \left \{ {{17} \atop {3}} \}\)

Step-by-step explanation:

A) How many ways can you put all Jellybeans in a row

Total number of Jellybeans = 80

The first jellybeans = 20 yellow , second is 20 orange jellybeans , third is 20 red jellybeans , fourth is 20 green jellybeans

Therefore the number of ways the Jellybeans can be put in a row is :

\(\left \{ {{80} \atop {20}} \} * \left \{ {{60} \atop {20}} \} * \left \{ {{40} \atop {20}} \} * \left \{ {{20} \atop {20}} \}\)

B) How many ways are there to select a handful of 20 jellybeans

lets assume:

yellow jellybeans = a , orange jellybeans = b , red jellybeans = c , green jellybeans = d

a + b + c + d = 20

This is the number Non-negative integer solutions

= \(\left \{ {{20+4-1} \atop {4-1}} \} = \left \{ {{23} \atop {3}} \}\)

C) This is also the number of Non-negative integer solutions but in this case the value of C ≥ 3

hence the number of ways to select a handful of 20 jellybeans that contains at least 3 red

= \(\left \{ {{17+4+1} \atop {4-1}} \} = \left \{ {{20} \atop {3}} \}\)

D) In this case the value of C ≥ 3 and B ≤ 2

Hence the number of ways to select a handful of 20 jellybeans that contains at least 3 red and at most 2 orange

= \(\left \{ {{20} \atop {3}} \} - \left \{ {{17} \atop {3}} \}\)

Answer:

Step-by-step explanation:

try substituting the points into both of the equations like it's a slope equation.

Answer:

Step-by-step explanation:

From the given information:

Let X be the random variable;

The mean survival time is E(X):

E(X) = μ

E(X) = ∝β

E(X) = 5 × 10

E(X) = 50

To find the standard deviation, we must first determine the variance:

\(V(X) = \sigma ^2\)

\(V(X) = \alpha \beta ^2\)

\(V(X) = 5 \times (10)^2\)

\(V(X) = 5 \times 100\)

\(V(X) = 500\)

The standard deviation is:

\(\sigma =\sqrt{V(X)}\)

\(\sigma =\sqrt{500}\)

\(\sigma =22.361\)

The standard deviation of survival time = 22.361

(c)

P(X>30) = 1 - P(X ≤ 30)

\(= 1 - \int \limits ^{30}_{0} \ f(x) \ dx\)

\(= 1 - \int \limits ^{30}_{0} \dfrac{1}{\beta^{\alpha} \Gamma \alpha }x^{a-1} e ^{-x/\beta } \ dx\)

\(= 1 - \int \limits ^{30}_{0} \dfrac{1}{\beta^{\alpha} \Gamma (5)}x^{5-1} e ^{-x/10 } \ dx --- (1)\)

So, if:

\(y = \dfrac{x}{10}\)

\(dy = \dfrac{dx}{10}\)

10dy = dx

and limits of y are 0 and 3.

because;

for x = 0

\(y = \dfrac{0}{\beta}\)

y = 0

For x = 30

\(y = \dfrac{30}{10}\)

y = 10

From (1);

\(P(X> 30) = 1 - \int \limits ^{30}_{0} \dfrac{1}{\beta^{\alpha} \Gamma (5)}x^{5-1} e ^{-x/10 } \ dx\)

\(P(X> 30) = 1 - \int \limits ^{3}_{0} \dfrac{(10y)^4}{10^{5} \Gamma (5)}e ^{-y } \ dy\)   since y = x/β

\(P(X> 30) = 1 - \int \limits ^{3}_{0} \dfrac{10^4 y^4 \ e^{-y} }{10^{4} \Gamma (5)} \ dy\)

\(P(X> 30) = 1 - \int \limits ^{3}_{0} \dfrac{y^4 \ e^{-y} }{ \Gamma (5)} \ dy\)

Since;

\(F(a, \alpha )= \int \limits ^a_0 \dfrac{y^{a-1}e^{-y}}{\Gamma (\alpha )} dy\)

Then;

P(X> 30) = 1 - F(3,5)

From the table of incomplete gamma function;

P(X > 30) = 1 - 0.185

P(X > 30) = 0.815

Thus, the probability that an animal survives more than 30 weeks is 0.815

a)The mean survival time of a randomly selected animal of the type used in the experiment is 50.

b)Standard deviation of survival time is 22.36

The standard deviation of a random variable, sample, statistical population, data set, or probability distribution is the square root of its variance.

Suppose x is the random variable.

It is given that α= 5 and β=10.

So, the mean survival E(x)=α β

The mean survival E(x) =5*10

The mean survival E(x) =50

We know that Variance =α β²

So, Variance = 5*10²

Variance =500

We know that standard deviation σ = √Variance

σ = √500

σ = 22.36

Therefore, a)the mean survival time of a randomly selected animal of the type used in the experiment is 50.

b)Standard deviation of survival time is 22.36

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The standard deviation is:

The standard deviation of survival time = 22.361