nicole and adam are each saving money for a car. the total amount of money nicole will save is represented by the function f(x)=36+4x. the total amount of money adam will save is represented by the function g(x)=x^2+15. after how many weeks, x, will they have the same amount of money saved? explain.

Answers

Answer 1

Answer: They will have the same amount of money after 7 weeks.

We first set these equal to each other:
36+4x=x²+15

We want to gather all of the variables on one side. Subtract 4x from both sides:
36+4x-4x=x²+15-4x
36=x²-4x+15

We want the equation to be equal to 0 to solve it, so subtract 36 from both sides:
36-36=x²-4x+15-36
0=x²-4x-21

We can factor this expression. We want factors of -21 that sum to -4; -7(3)=-21 and -7+3=-4:
0=(x-7)(x+3)

Using the zero product property, we know that x-7=0 or x+3=0; this means x=7 or x=-3. Since a negative number of weeks makes no sense, the answer is 7 weeks.

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A cylindrical package to be sent by a postal service can have a maximum combined length and girth (perimeter of a cross section) of 141 inches. Find the dimensions of the package of maximum volume that can be sent. (The cross section is circular.)
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EP-21 What is a requirement for fire extinguishers on a boat?Must be filled with water
Must be red or orange in color
Must be Coast Guard approved
Must be permanently mounted

Answers

Answer:

Must be Coast Guard approved

Step-by-step explanation:

--The use Coast Guard has a fire extinguisher requirement based on the boat size.

-The fire extinguisher on board has to be approved by the US Coast guard for protection of the engine compartment.

Answer:

Must be maintained in a fully charged usable condition.

In a random sample of 500 college students, 23% say that they read or watch the news every day. Develop a 90% confidence interval for the proportion of all students who read or watch the news on a daily basis. Interpret your results. If you wanted to develop a 95% confidence interval with a margin of error of .01, how many students would need to be surveyed?

Answers

Answer:

The 90% confidence interval is $0.199 < p < 0.261$

The sample size to develop a 95% confidence interval is $n = 2032$

Step-by-step explanation:

From the question we are told that

The sample size is n =500

The sample proportion is $\^ p = 0.23$

From the question we are told the confidence level is 90% , hence the level of significance is

$\alpha = (100 - 90 ) \%$

=> $\alpha = 0.10$

Generally from the normal distribution table the critical value of $(\alpha )/(2)$ is

$Z_{(\alpha )/(2) } = 1.645$

Generally the margin of error is mathematically represented as

$E = Z_{(\alpha )/(2) } * \sqrt{(\^ p (1- \^ p))/(n) }$

=> $E = 1.645 * \sqrt{(0.23 (1- 0.23))/(500) }$

=> $E = 0.03096$

Generally 90% confidence interval is mathematically represented as

$\^ p -E < p < \^ p +E$

=> $0.23 -0.03096 < p < 0.23 + 0.03096$

=> $0.199 < p < 0.261$

From the question we are told the confidence level is 95% , hence the level of significance is

$\alpha = (100 - 95 ) \%$

=> $\alpha = 0.05$

Generally from the normal distribution table the critical value of $(\alpha )/(2)$ is

$Z_{(\alpha )/(2) } = 1.96$

The margin of error is given as $E = 0.01$

Generally the sample size is mathematically represented as

$n = [\frac{Z_{(\alpha )/(2) }}{E} ]^2 * \^ p (1 - \^ p )$

=> $n = [(1.96 )/(0.01) ]^2 *0.23 (1 - 0.23 )$

=> $n = 2032$

If 5 added to thrice an integer is – 7, then the integer is

Answers

Answer:

The integer would be -12

Step-by-step explanation:

x + 5 = -7

-5 - 5

x = -12

-12 + 5 = -7

The management of the unico department store has decided to enclose an 834 ft2 area outside the building for displaying potted plants and flowers. one side will be formed by the external wall of the store, two sides will be constructed of pine boards, and the fourth side will be made of galvanized steel fencing. if the pine board fencing costs $6/running foot and the steel fencing costs $3/running foot, determine the dimensions of the enclosure that can be erected at minimum cost. (round your answers to one decimal place.)

Answers

The area is given by:
A = x * y = 834
The cost equation is given by:
C = 6 * (2x) + 3 * (y)
We express the equation in terms of a variable:
C (x) = 6 * (2x) + 3 * (834 / x)
Rewriting:
C (x) = 12x + 2502 / x
We derive the equation:
C '(x) = 12 - 2502 / x ^ 2
We match zero:
0 = 12 - 2502 / x ^ 2
We clear x:
x = root ((2502) / (12))
x = 14.4 feet
We look for the other dimension:
y = 834 / x
y = 834 / 14.4
y = 57.9 feet
Answer:
The dimensions of the enclosure that can be erected at minimum cost are:
x = 14.4 feet
y = 57.9 feet

For each of the following four statements, indicate whether it is possible or not according to probability theory. Explain your answer. (1) The probability that a customer will buy 5 items in a single purchase is 30% ___________________________ (2) The probability that a customer will buy 3 items in a single purchase is 101% ___________________________ (3) The probability that a customer will buy 3 items in a single purchase is 99% ___________________________ (4) The probability that a customer will buy 8 item

Answers

Answer:

a) According to probability theory, the following are possible:

(1) The probability that a customer will buy 5 items in a single purchase is 30%. This represents a 0.30 chance of the customer buying 5 items.

(3) The probability that a customer will buy 3 items in a single purchase is 99% This means that there a 0.99 chance that the customer will buy 3 items.

b) According to probability theory, the following are not possible:

2) The probability that a customer will buy 3 items in a single purchase is 101%. Probability is always equal to 1 or 100%. It cannot exceed 100%.

(4) The probability that a customer will buy 8 item. This part lacks the necessary information to solve the problem.

Step-by-step explanation:

Probability describes the likelihood or chance of an event happening out of the many possible events that can take place. The sum of all probabilities for a particular event is always equal to 1. This shows that probability does not exceed 100%.

Which decimal number is equivalent to 7/10

Answers

Answer:

0.7

Step-by-step explanation:

Answer:

0.7

Step-by-step explanation:

7/10 can also be written as 7÷10

7÷10=0.7

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