When renting a limo for prom, the number of people is inversely proportional to the cost per person. Originally there were 3 people and the cost per person was $72. If the number of people changed to 12, what would be the new cost per person?

There are 13 teams in the softball league, so there are 13 options for the first-place team. Once the first-place team is determined, there are 12 remaining teams for the second-place spot. Finally, there are 11 remaining teams for the third-place spot. Therefore, the number of different end-of-the-season rankings of first, second, and third place is possible is:

13 x 12 x 11 = 1,716

So there are 1,716 possible rankings.

Answer:

C, In many, many boxes of cereal of this type, we can expect about 75% of the boxes to contain a prize.

Step-by-step explanation:

All of them say "Expect", or "Exactly" other than this answer, but probability isn't Exact or Expected, so it is C.

Answer:

answer is 25

Step-by-step explanation:

x+2+153=180

x+155=180

x=180-155

x=25

hope this helps :)

Answer:

f(1) = 15

f(-9) = -65

f(0) = 7

Step-by-step explanation:

f(1) = 8(1) + 7

f(1) = 8 + 7

f(1) = 15

f(-9) = 8(-9) + 7

f(-9)  = -72 + 7

f(-9) = -65

f(0) = 8(0) + 7

f(0) = 7

Answer:

What sitting/laying position are you in?

Step-by-step explanation:

Answer: x=92x=−7

Step-by-step explanation:x=−b±b2−4ac2a=−±2−4√2Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.

Answer:it’s 3

Step-by-step explanation:

so what u do is multiply

Answer:

a. $256

Step-by-step explanation:

The computation of the maximum allowable recurring debt is shown below:

Given ratio = 28:36

And the monthly income is $3,200

So the maximum expense on housing = 28% of $3,200 = $896

And, the maximum expense on total debt = 36% of $3,200 = $1,152

Now the maximum alloweable recurring debt is

= $1,152 - $896

= $256

Answer:

the answer is A

Step-by-step explanation:

Answer:

0.48 of a mile in 1 minute

Step-by-step explanation:

If Amare runs 1.10 miles in 2.3 minutes, you need to find how much he runs in 1 minute. 2.3 divided by what = 1? 2.3. Divide 1.10 by 2.3 to get 0.47826. You can round this to .48 or even .5, depending on the question. So, Amare runs .48 of a mile in 1 minute.

Answer:

3.9msquare inches(round to 1dp)

Step-by-step explanation:

herons formula can be used to calculate the area of any triangle

and the triangle you mentioned is an equilateral one

the formula is A=√(s(s-a)(s-b)(s-c)) where √ means square root and abc are the sides of the triangle and s is the semi perimeter of the triangle such that a+b+c/2=s and A is the area of the triangle so,

3+3+3

=9/2

=4.5=s

√(4.5(4.5-3)(4.5-3)(4.5-3)

=√15.1875

=3.9 square inches (round to 1dp)

Answer:

more info needed

Step-by-step explanation:

The probability that an international flight leaving the US is delayed in departing given that the flight is a transpacific flight is approximately 0.1964.

We can use Bayes' theorem to calculate the probability that an international flight leaving the United States is delayed in departing given that the flight is a transpacific flight. Bayes' theorem states that:

P(D|P) = P(P|D) * P(D) / P(P)

where P(D|P) is the probability that a flight is delayed given that it is transpacific, P(P|D) is the probability that a flight is transpacific given that it is delayed, P(D) is the probability of a flight being delayed, and P(P) is the probability of a flight being transpacific.

Using the given values, we can calculate:

P(P and D) = 0.11 (the probability that a flight is both transpacific and delayed)

P(P) = 0.56 (the probability that a flight is transpacific)

P(D) = 0.28 (the probability that a flight is delayed)

To find P(D|P), we need to calculate P(P and D) / P(P):

P(D|P) = P(P and D) / P(P) = 0.11 / 0.56 = 0.1964

Therefore, the probability that an international flight is delayed in departing is approximately 0.1964 (rounded to 4 decimal places).

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--The given question is incomplete, the complete question is given

"The probability that an international flight leaving the United States is delayed in departing (event D) is .28. The probability that an international flight leaving the United States is a transpacific flight (event P) is .56. The probability that an international flight leaving the U.S. is a transpacific flight and is delayed in departing is .11. (a) What is the probability that an international flight leaving the United States is delayed in departing given that the flight is a transpacific flight? (Round your answer to 4 decimal places.)"--

Answer:

The Ratio would be 11:30

Step-by-step explanation:

peas : 11

Peppers: 30

High Hopes ^^

Barry-

Whe you need to write a number in standard form, you normally write a number between the range of 1 and 10 and then multiply it by 10 raised to the power of ___.

So 400 becomes

4 x 100

4 x 10^2

Answer:

{x,y} ={0,-7}

Step-by-step explanation:

[1]  3 x - 2 y = 14

[2] 5 x 6 y =42

Inequality can be used to determine x, the greatest number of 120-kilogram crates that can be loaded onto the shipping container is  8000 + 120C <= 27500

An inequality is a relationship that allows us to contrast two or more mathematical expressions.

Knowing that;

Each carton weighs 120 kg.

The container's maximum weight when loaded is 27500 kg.

Weight of the container as it is currently loaded: 8000 kg

Now that we have merged, we have;

Solution

because 8000 grams have already been loaded kilograms

into the container

each crate weighs 120 kilograms.

so 8000 + 120C <= 27500

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Percentage Of people Prefers to die at home in developed countries is 30%

Lets have Brief explanation

What is scientific research?

Scientific research is research carried out using organised, constructed scientific techniques for data collection, analysis, and interpretation.

There is growing scientific research regarding the choices people would prefer to make regarding their care as they approach death.

According to a number of studies, between 50% and 70% of patients undergoing treatment for a serious illness also state that they would prefer to die at home.

Even though many people would prefer to get care and pass away at home, hospital death is nonetheless common in many nations.

According to the research, between 25% and 30% of people want to die at home, and the classic scenario involves 30% of people.

Percentage Prefer to die at home = 30%

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Step-by-step explanation:

remember, when multiplying 2 expressions, you need to multiply every term of one expressing with every term of the other expression and then add the individual results together (while observing their signs, of course).

so, e.g. 5(x - 4) = 5x - 5×4 = 5x - 20

therefore,

1)

5x - 20 = 2x + 10

5x - 2x = 10 + 20

3x = 30

x = 10

2)

-12s - 6 = 6s + 30

-12s - 6s = 30 + 6

-18s = 36

s = -2

3)

12c - 21 = -2c + 7

12c + 2c = 7 + 21

14c = 28

c = 2

4)

-10p + 30 = -10

-10p = -10 - 30

-10p = -40

p = 4

5)

8x = -2x - 20

8x + 2x = -20

10x = -20

x = -2

6)

21 + 6a - 5 - 2a = 8

4a + 16 = 8

4a = -8

a = -2

Null hypothesis (H0): The mean monthly rent for an apartment in the city is still $800 this year.

Alternate hypothesis (Ha): The mean monthly rent for an apartment in the city is higher than $800 this year.

The appropriate null and alternate hypothesis are:

Symbolically,

H0: µ = 800

Ha: µ > 800

Here, µ represents the population mean rent for apartments in the city.

The null hypothesis (H0) is a statistical hypothesis that assumes there is no significant difference or relationship between two variables or sets of data. In other words, it suggests that any observed differences or relationships are due to chance or random variation.

The null hypothesis assumes that there has been no change in the population mean rent, while the alternate hypothesis suggests that the population mean rent has increased.

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Answer:

what should we have to do here

I don't understand

Answer:

x = -3

Step-by-step explanation:

The equation of any linear function is y = mx + c, where m is the gradient and c is the y-intercept

The equation of the function is y = -x + 4

The gradient is negative one (hence 1x) and the y-intercept is 4

We need to find what x equals when the y = 7

7 = -x + 4

Rearrange

7 - 4 = -x

-x = 3

x = -3

Answer:

Slope = -5/3

Step-by-step explanation:

Parallel lines have the same slope, so the slope will be -5/3.

Hope this helps!!

Answer:

-5/3x

Step-by-step explanation:

its the same slope

The number of times of rolling a 5 or a 6 in the fair die is 24

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

Fair 6-sided die = 72 times

In a 6-sided die, we have

P(5 or 6) = 2/6

When evaluated, we have

P(5 or 6) = 1/3

So, when the die is rolled 72 times, we have

Expected value = 1/3 * 72

Evaluate

Expected value = 24

Hence, the number of times is 24

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Answer: 55

Step-by-step explanation:

Let the number of cars washed last year be denoted as x.

This year, he washed 14 fewer cars than during last year's car wash. This will be denoted as x-14.

We can then represent them in an equation as:

x + (x - 14) = 96

2x - 14 = 96

2x = 96 + 14

2x = 110

x = 110/2

x = 55

Therefore, he washed 55 cars this year

The limit of the expression \(\lim_{x \to 0}\) [(7x² - 70x) / (x² - 100)] which x tends to 0 is equal to 0.

To find the limit of the given expression as x approaches 0,

Simplify the expression and apply algebraic methods.

Let's proceed step by step,

\(\lim_{x \to 0}\) [(7x² - 70x) / (x² - 100)]

First, factorize the numerator and denominator,

\(\lim_{x \to 0}\) [7x(x - 10) / (x + 10)(x - 10)]

Now we can cancel out the common factors of (x - 10) in the numerator and denominator,

\(\lim_{x \to 0}\) [7x / (x + 10)]

Now, substitute x = 0 into the expression,

[7(0) / (0 + 10)] = 0 / 10 = 0

Therefore, the limit of the given expression as x approaches 0 is 0.

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The above question is incomplete, the complete question is:

Use properties of limits and algebraic methods to find the limit, if it exists. (If the limit is infinite, enter '∞ ' or ' -∞ ', as appropriate. If the limit does not otherwise exist, enter DNE.)

lim x→0 [( 7x² -70x )/(x² -100)]

Since we can't have a fraction of a year, we need to round up to the equation nearest whole number. Therefore, it will take at least 7 years for the value of the car to be less than $3,000.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the number "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.

V(1) = 0.85 * 12,900 = $10,965

V(2) = 0.85 * 10,965 = $9,320.25

\(V(n) = 0.85^n * 12,900\\0.85^n * 12,900 < 3,000\\n > log(3,000/12,900) / log(0.85)\\n > 6.48\\\)

Since we can't have a fraction of a year, we need to round up to the nearest whole number. Therefore, it will take at least 7 years for the value of the car to be less than $3,000.

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Answer:

9 years

Step-by-step explanation:

As the car depreciates at a constant rate of 15% each year, we can use the exponential decay formula to find the value of the car after t years.

\(\boxed{f(t)=a(1-r)^t}\)

where:

Given the purchase price of the car is $12,900, a = 12900.

Given the car will depreciate at a rate of 15%, r = 0.15.

Substitute the values of a and r into the formula to create a function for the value of car after t years is:

\(f(t)=12900(1-0.15)^t\)

\(f(t)=12900(0.85)^t\)

To calculate after how many years the value of the car will be less than $3,000, substitute f(t) < 3000 and solve for t.

\(\implies 12900(0.85)^t < 3000\)

Divide both sides by 12900:

\(\implies (0.85)^t < \dfrac{3000}{12900}\)

\(\implies (0.85)^t < \dfrac{10}{43}\)

Take natural logarithms of both sides:

\(\implies \ln (0.85)^t < \ln\left(\dfrac{10}{43}\right)\)

Apply the log power law:

\(\implies t \ln (0.85) < \ln\left(\dfrac{10}{43}\right)\)

Divide both sides by ln(0.85), remembering to change the direction of the inequality sign since ln(0.85) is negative:

\(\implies t > \dfrac{\ln\left(\dfrac{10}{43}\right)}{\ln (0.85)}\)

\(\implies t > 8.9750695...\)

We need to round up to 9 years, since we can't have a fraction of a year.

Therefore, the value of the car will be less than $3,000 after 9 years.

Answer:

20 feet

Step-by-step explanation:

\(\frac{80 feet}{40 seconds}\)  = \(\frac{x feet}{10 seconds}\)

Simplify \(\frac{80}{40}\)

\(\frac{80}{40}\) = \(\frac{2}{1}\)

Every 1 second, a person will walk 2 feet.

\(\frac{x}{10}\) = \(\frac{20}{10}\)

X = 20 feet

Answer:

20 feet

Step-by-step explanation:

We can solve this two different ways:

The 1st and easiest way would be to first divide \(40/10\) to get \(4\), and then divide \(80/4\) to get \(20\).

This method works well in this situation because all the numbers are easily divisible, but in some situations this method may give you decimals which would make things more difficult.

In a situation like that, you would create a simple equation using this format: \(y=m(x)\) in which \(y\) represents the total number of feet walked, \(m\) represents the number of seconds, and \(x\) represents number of feet walked per minute.

You would start by finding out the number of feet walked per minute. You do this by plugging the information you know into the equation. We know that the person walks 80 feet in 40 seconds so the equation would look like this: \(80=40x\)

To solve for \(x\), you would then divide 40 on both sides to get \(2=x\)

Now that we know that the person walks 2 feet every second, we can plug the information into a new equation to find out how far they go in 10 seconds. This equation will look like this: \(y=10(2)\) and we can solve it to learn that \(y=20\). This means that the person will walk 20 feet in 10 seconds.

Answer:

14.45 feet

Step-by-step explanation:

The set up is a right angled triangle;

The length of the ladder = hypotenuse = 15foot

The base of the ladder is the adjacent = 4feet

The height of th house is the opposite = x

Using the pythagoras theorem;

hyp² = opp² + adj²

15² = opp²+4²

opp² = 15²- 4²

opp² = 225 - 16

opp² = 209

opp = 14.45feet

Hence the ladder reaches 14.45 feet up the house

Answer:

x = -4/7

Step-by-step explanation:

-5/2x + 1 = x + 3

-7/2x = 2

(-2/7)-7/2x = 2(-2/7)

x = -4/7