Norma plans to rent a car for her vacation. The cost to rent the car is $39
plus $0.15 per mile she drives. Write a function rule for the total cost of
the rental.

In order to prove that two triangles are congruent, the following cases of congruency can be used:

SSS (all three sides congruent)

SAS (two sides and the angle between them congruent)

ASA (two angles and the side between them congruent)

AAS (two angles and the side not between them congruent)

The other cases (AAA and SSA) are not congruency theorems.

Answer:

If f(x) =3x^3+10x^2-13x-20 and f(-4)=0, then find all of the zeros of f(x) algebraically

Answer:

4 and 40

Step-by-step explanation:

the answer is 36

45/100 multiplied by 81.21

Answer:squares area is. 24

Step-by-step explanation:

6×4 = 24

Using the normal distribution, there is a 0.0781 = 7.81% probability that a randomly selected cyclist will take between 2.35 and 2.45 hours to complete the race.

The z-score of a measure X of a normally distributed variable with mean \(\mu\) and standard deviation \(\sigma\) is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The mean and the standard deviation are given, respectively, by:

\(\mu = 2.5, \sigma = 0.5\).

The probability that a randomly selected cyclist will take between 2.35 and 2.45 hours is the p-value of Z when X = 2.45 subtracted by the p-value of Z when X = 2.35, hence:

X = 2.45:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{2.45 - 2.5}{0.5}\)

Z = -0.1

Z = -0.1 has a p-value of 0.4602.

X = 2.35:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{2.35 - 2.5}{0.5}\)

Z = -0.3

Z = -0.3 has a p-value of 0.3821.

0.4602 - 0.3821 = 0.0781.

0.0781 = 7.81% probability that a randomly selected cyclist will take between 2.35 and 2.45 hours to complete the race.

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Answer:

Hey there, Lets solve this step by step.  

A number t divided by 82  

Let the number be represented by y.  

t divided by 82 = t / 8  

Therefore-  

In algebraic expressions, "y" is normally used as the dependent variable and "x" is normally used as the independent variable, instead of other variables. So that is why i used the variable y in the equation.

Step-by-step explanation:

Answer:

for 5 minutes

Explanation:

35%/ 100 20 times 5 is 100. so I thought it would be 5

Answer:

57.1428 minutes

Step-by-step explanation:

Power : Time

100 : 20

35 : x

if POWER increase then TIME decrease, it means both are inversely proportional to each other

x/20 = 100/35

x = (100/35) * 20

x = 400 / 7

x = 57.1428

where x is basically the time in minutes, So time = 57.1428 minutes

Answer: x=-3, x=3

Step-by-step explanation:

Answer:

4-[x]=1

-4.    -4

-[x]=-3

x=3

Answer:

3√3v/3x V

Step-by-step explanation:

d/dt[32/3π, sin (tim), 3√3v/3x, V]

The least among all 4 integers such that they sum up to 100 will be 22.

An integer is a whole number irrespective of the sign that the integer is all whole numbers that are going from 0 to infinite or 0 to minus infinite.

Integer; ....-2 , -1 , 0 , 1 , 2 , .....

Integers are non-decimal numbers and all integers are rational numbers.

Suppose the first integer is x.

The next three digits will be, x + 2, x + 4, and x + 6 correspondings.

Sum x + x + 2 + x + 4 + x + 6 = 100

(x + x + x + x) + (2 + 4 + 6) = 100

4x + 12 = 100

4x = 88

x = 22

Hence"The smallest of the four integers that add up to 100 is 22".

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\(\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta r^2}{2} ~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ \theta =\frac{\pi }{2}\\[1em] r=\frac{8}{3} \end{cases}\implies A=\cfrac{1}{2}\cdot \cfrac{\pi }{2}\cdot\left( \cfrac{8}{3} \right)^2 \\\\\\ A=\cfrac{1}{2}\cdot \cfrac{\pi }{2}\cdot \cfrac{64}{9}\implies A=\cfrac{16\pi }{9}\implies A\approx 5.59\)

Answer:

151.5 cm = 1.515 m

151.5 cm = 1515/1000 m

The sample should be taken to provide a 95% confidence interval is 200.

A confidence interval is made up of the mean of your estimate plus and minus the estimate's range. This is the range of values you expect your estimate to fall within if you repeat the test, within a given level of confidence.

Confidence is another name for probability in statistics.

Given the planning value for the population proportion,

probability, p = 0.25

q  = 1 - p = 1 - 0.25

q = 0.75

margin of error = E = 0.06

value of z at 95% confidence interval is 1.96,

the formula for a sample is,

n = (z/E)²pq

n = (1.96/0.06)²*0.25*0.75

n = 200.08

n = 200 approx

Hence sample size is 200.

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Answer:

The answer would be 100^32

Answer:

x=6

Step-by-step explanation:

This is a vertical line going through (6,0).  If you take this point and the point given and calculate the slope you find the change in y over the change in x.  

0-(-3)/6-6  The slope is undefined because the denominator of the slope would be zero.

Answer:

3692.64 cm³

Step-by-step explanation:

9514 1404 393

Answer:

  240 cars

Step-by-step explanation:

The x-coordinate of the vertex of the quadratic function ax^2 +bx +c is found at ...

  x = -b/(2a)

The vertex is the point at which the cost function is a minimum. So, we're interested in the value of x there.

  x = -(-432)/(2(0.9)) = 432/1.8 = 240

240 cars must be made to minimize the unit cost.

The interval over which the graphed function is positive is given as follows:

(3, ∞).

The intervals for which a function is positive are the intervals for which the function graph lies above the x-axis.

For this problem, the function crosses the x-axis at x = 3, and then is positive for the entire remaining domain, hence the interval is given as follows:

(3, ∞).

This means that the correct option is given by option D.

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The total weight of the liquid in the tank is approximately 12,628 pounds.

To calculate the weight of the liquid, we need to determine the volume of the hemisphere and then multiply it by the density of the liquid. The formula for the volume of a hemisphere is V = (2/3)πr³, where r is the radius of the hemisphere.

In this case, the diameter of the tank is given as 24 feet, so the radius is half of that, which is 12 feet. Plugging this value into the formula, we get V = (2/3)π(12)³ ≈ 904.78 cubic feet.

Finally, we multiply the volume by the density of the liquid: 904.78 cubic feet * 92.5 pounds per cubic foot ≈ 12,628 pounds. Therefore, the total weight of the liquid in the tank is approximately 12,628 pounds.

In summary, to calculate the weight of the liquid in the tank, we first determine the volume of the hemisphere using the formula V = (2/3)πr³. Then, we multiply the volume by the density of the liquid.

By substituting the given diameter of 24 feet and using the appropriate conversions, we find that the total weight of the liquid is approximately 12,628 pounds.

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Answer:

Step-by-step explanation:

110

Answer:

The product of the matrices A and X is the identity matrix. Therefore, X and A are inverses of each other.

Step-by-step explanation:

Answer:

N = 20

Step-by-step explanation:

5/3 = 1 2/3

20/12 = 1 8/20

They are equivalent

Answer:

\(P(z<\frac{a-\mu}{\frac{\sigma}{\sqrt{n}}})=0.1\)

And replacing the value obtained we got:

\(z=-1.282<\frac{a-410000}{\frac{\sigma}{\sqrt{200}}}\)

And if we solve for a we got

\(a=410000 -1.282*\frac{65000}{\sqrt{200}}=404107.68\)

Step-by-step explanation:

Let X the random variable that represent the average home prices of a population, and for this case we know the distribution for X is given by:

Where \(\mu=410000\) and \(\sigma=65000\)

For this part we want to find a value a, such that we satisfy this condition:

\(P(X>a)=0.90\)   (a)

\(P(X<a)=0.10\)   (b)

We want to find a value who accumulate 0.10 of the area on the left and 0.90 of the area on the right of the normal standard distributon and for this case it's z=-1.282

And using the distribution for the sample mean we can do this:

\(P(X<a)=P(\frac{X-\mu}{\frac{\sigma}{\sqrt{n}}}<\frac{a-\mu}{\frac{\sigma}{\sqrt{n}}})=0.10\)  

\(P(z<\frac{a-\mu}{\frac{\sigma}{\sqrt{n}}})=0.1\)

And replacing the value obtained we got:

\(z=-1.282<\frac{a-410000}{\frac{\sigma}{\sqrt{200}}}\)

And if we solve for a we got

\(a=410000 -1.282*\frac{65000}{\sqrt{200}}=404107.68\)

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

y = (x-1)²

vertex (1,0)

y-intercept = (0-1)² = 1

Answer:

two column

Step-by-step explanation:

you need to flow to get what you want

His bottom line was a gain from selling and 3% commission is $257.50.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

The cost price of 200 shares of BUI is (19.50×200) = $3900.

The selling price of 200 shares of BUI is (20.75×200) = $4150.

The net gain is (4150 - 3900) = $250 and with 3% commission it is,

= (103/100)×250.

= $257.50.

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The equation that represents the balance of the loan, y, if he borrows the money for x years is presented as follows;

\(y = 5000\cdot e^{0.089\cdot t}\)

A continuous compounding interest involves finding the accrued interest and repeat reinvestment of the interest in which the number of periods is infinite.

The formula for the amount of a compound interest loan compound continuously is expressed as follows;

\(A(t) = P_0\cdot e^{r\cdot t}\)

Where;

P₀ = The principal amount = The amount loaned

r = The interest rate

t = The duration of the loan

The amount of loan Landis is taking, P₀ = $5,000

The interest rate compounded continuously, r = 8.9%

Where, y = The balance of the loan, and x = The number of years the loan is borrowed, we get;

P₀ = $5,000

r = 8.9% = 0.089

y = A(t)

x = t

Therefore; \(y = 5000\times e^{0.089 \times t}\)

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1) The dimensions of the 4 walls are:

Two walls are 20 feet long and 8 feet tall.

Two walls are 25 feet long and 8 feet tall.

2) Total area to be covered:

= 720 square feet.

3) You will need 1.8 gallons of paint to cover all four walls of the room.

Now, The dimensions of the 4 walls are:

Two walls are 20 feet long and 8 feet tall.

Two walls are 25 feet long and 8 feet tall.

And, The total area to be covered is:

For the two 20 feet long walls:

A = 20 feet x 8 feet

A = 160 square feet each.

And, For the two 25 feet long walls:

A = 25 feet x 8 feet

A = 200 square feet each.

Hence, Total area to be covered:

= (160 + 160 + 200 + 200) square feet

= 720 square feet.

For the number of gallons of paint needed, divide the total area to be covered by the area covered by one gallon of paint:

Number of gallons of paint needed = Total area to be covered / Area covered by one gallon of paint

Number of gallons of paint needed = 720 square feet / 400 square feet per gallon

Number of gallons of paint needed = 1.8 gallons

Therefore, you will need 1.8 gallons of paint to cover all four walls of the room.

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Answer:   About the building of his bed