Please help me answer the middle question please and thank you

You own a motel and have a pricing structure that encourages rentals of rooms in groups.

zheka24 [161]

Answer:

$41

Step-by-step explanation:

One room rents for $68,
Two rooms for $65 each,
In general, the group rate per room is found by taking $3 off the base of $68 for each extra room.

So,

$a_1=\$68\\ \\a_2=\$65\\ \\a_3=\$62\\ \\...$

where $a_n$ is the rate per nth room rented.

This is an arithmetic sequence, so

$a_n=a_1+(n-1)\cdot d$

In your case,

$a_1=68\\ \\n=10\\ \\d=-3$

Hence

$a_{10}=68+(10-1)\cdot (-3)=68-9\cdot 3=68-27=41$

This means if a group rents 10 rooms, the charge per room is $41.

5 0

3 years ago

A manufacturer is planning to sell a new product at the price of 210 dollars per unit and estimates that if x thousand dollars i

sattari [20]

Answer:

Development costs: $2757

Promotion costs: $3155

Step-by-step explanation:

This might seem like a two-variable problem, but in actuality it's not - because the demand function is a sum of two components, each being independent and using only one variable, we can solve for the two separately.

Moreover, the price per unit and cost per unit is constant, so each product yields exactly $80 ($210 - $130).

Let's solve separately.

We need to maximize:

$80 * 160y/(y+4) - 1000y = $12800 * y/(y+4) - $1000*y

$80 * 170x/(x+7) - 1000x = $13600 * x/(x+7) - $1000*x

Let's go:

$12800 * y/(y+4) - $1000*y = $12800 * (1 - 4/(y+4)) - $1000y = $12800 - $51200/(y+4) - $1000*y

we analyze the derivative. $12800 is a constant, so we can skip it. Derivative of 1/(y+4) is -(y+4)^-2, derivative of $1000y is $1000.

deriv = $51200/(y+4)/(y+4) - $1000

We find the changepoints by analyzing $51200/(y+4)/(y+4) - $1000 = $0. We don't need to worry about y+4 = 0 because we cannot spend negative money on development/advertisement.

(y+4)^2 = $51.2

y+4 ~= 7.155417528 (or -y-4 = 7.1554... but it doesn't make sense because negative budget so we don't analyze).

y ~= 3.155417528

lastly, we should check that it's actually a maximum there - but it is, the original function goes to negative infinity.

rounding $1000y to the nearest dollar gives us $3155

Let's do the same for x:

$13600 * x/(x+7) - $1000*x = $13600 * (1 - 7/(x+7)) - $1000x = $13600 - $95200/(x+7) - $1000*x

deriv = $95200/(x+7)/(x+7) - $1000

$95200/(x+7)/(x+7) - $1000 = $0

(x+7)^2 = 95.2

(x+7) ~= 9.75704873412

x ~= 2.75704...

rounding $1000x to the nearest dollar yields $2757

3 0

3 years ago

A random sample of 100 observations from a quantitative population produced a sample mean of 22.8 and a sample standard deviatio

natima [27]

Answer:

We conclude that the population mean is 24.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 24

Sample mean, $\bar{x}$ = 22.8

Sample size, n = 100

Alpha, α = 0.05

Sample standard deviation, s = 8.3

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 24\\H_A: \mu \neq 24$

We use Two-tailed z test to perform this hypothesis.

Formula:

$z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }$

Putting all the values, we have

$z_{stat} = \displaystyle\frac{22.8 - 24}{\frac{8.3}{\sqrt{100}} } = -1.44$

We calculate the p-value with the help of standard z table.

P-value = 0.1498

Since the p-value is greater than the significance level, we accept the null hypothesis. The population mean is 24.

Now, $z_{critical} \text{ at 0.05 level of significance } = \pm 1.96$

Since, the z-statistic lies in the acceptance region which is from -1.96 to +1.96, we accept the null hypothesis and conclude that the population mean is 24.

7 0

3 years ago

A car dealer just took delivery on forty new cars. He plans to put four of these cars on display at the front of the lot. In how

vagabundo [1.1K]

Answer:

B

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Are you good at maths?????????????????????????

Flauer [41]

The probability that a student, chosen at random, does not study chemistry is 20/41.

<h3>What is Probability?</h3>

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favorable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows.

Probability(Event) = Favorable Outcomes/Total Outcomes = x/n

Here, Total number of student = 41

Student who does not study chemistry = 20

So, the probability = favorable outcome / total outcomes

P(not studying chemistry) = 20 / 41

Thus, The probability that a student, chosen at random, does not study chemistry is 20/41.

Learn more about Probability from:

brainly.com/question/11234923

#SPJ1

7 0

2 years ago