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vampirchik [111]

1 year ago

15

An adventure sports club claims to take its hot air balloon to a height of 10,020 feet. The hot air balloon’s elevation is model

ed by the equation y = x5 − 6x4 + 3x3 − 18x2 + 180x, where x is the number of minutes since the balloon took off. In how many minutes will the hot air balloon reach an elevation of 1,080 feet?
A)4 minutues
B)5 minutes
C)6 minutes
D)7 minutes

2 answers:

Rama09 [41]1 year ago

6 0

Answer: C) 6 minutes.

Step-by-step explanation: to solve the given problem we can replace the given option in the values of x, and calculate y for each option, the one that results in y=1080 feet will be the correct answer:

for option A:

$y=4^{5}-6*4^{4}+3 *4^{3}-18*4^{2} +180*4$

y=1024-1536+192-288+720

y=112 feet.

for option B:

$y=5^{5}-6*5^{4}+3 *5^{3}-18*5^{2} +180*5$

y=3125-3750+375-450+900

y=200 feet.

for option C:

$y=6^{5}-6*6^{4}+3 *6^{3}-18*6^{2} +180*6$

y=7776-7776+648-648+1080

y=1080 feet. As we can see the ballon will reach an elevation of 1080 feet in 6 minutes.

Ostrovityanka [42]1 year ago

3 0

C, six minutes, it might be D idk

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ALGEBRA Jake Duffy drove 12,568 miles

kirza4 [7]

Answer:

The cost per mile that Jack Duffy charge $0.278 per miles , i.e option B

Step-by-step explanation:

Given as :

The distance drove by Jack Duffy = d = 12,568 miles

The fixed costs totaled = $1,485.00

The variable cost totaled = $2,015.75

Let The cost per mile that Jack Duffy charge = $x cost per miles

Now, According to question

The totaled cost = The fixed costs + The variable cost

Or, The totaled cost = $1,485.00 + $2,015.75

I.e The totaled cost = $3500.75

Now,

The cost per mile that Jack Duffy charge = $\dfrac{\extrm Total cost}{\textrm Total Distance}$

I.e x = $\dfrac{3500.75}{12568}$

∴ x = $0.278 per miles

So,The cost per mile that Jack Duffy charge = x = $0.278 per miles .

Hence,The cost per mile that Jack Duffy charge $0.278 per miles , i.e option B Answer

5 0

2 years ago

A sample of 1714 cultures from individuals in Florida diagnosed with a strep infection was tested for resistance to the antibiot

Damm [24]

Answer:

a) $p$ represent the real population proportion of people who showed partial or complete resistance to the antibiotic

b) $\hat p=\frac{973}{1714}=0.568$ represent the estimated proportion of people who showed partial or complete resistance to the antibiotic

c) We are confident (95%) that the true proportion of individuals in Florida diagnosed with a strep infection was tested for resistance to the antibiotic penicillin present partial or complete resistance to the antibiotic is between 54.5% to 59.1%.

Step-by-step explanation:

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Part a

Description in words of the parameter p

$p$ represent the real population proportion of people who showed partial or complete resistance to the antibiotic

$\hat p$ represent the estimated proportion of people who showed partial or complete resistance to the antibiotic

n=1714 is the sample size required

$z_{\alpha/2}$ represent the critical value for the margin of error

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Part b

Numerical estimate for p

In order to estimate a proportion we use this formula:

$\hat p =\frac{X}{n}$ where X represent the number of people with a characteristic and n the total sample size selected.

$\hat p=\frac{973}{1714}=0.568$ represent the estimated proportion of people who showed partial or complete resistance to the antibiotic

Part c

The confidence interval for a proportion is given by this formula

$\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

For the 95% confidence interval the value of $\alpha=1-0.95=0.05$ and $\alpha/2=0.025$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=1.96$

And replacing into the confidence interval formula we got:

$0.568 - 1.96 \sqrt{\frac{0.568(1-0.568)}{1714}}=0.545$

$0.568 + 1.96 \sqrt{\frac{0.56(1-0.56)}{1714}}=0.591$

And the 95% confidence interval would be given (0.545;0.591).

We are confident that about 54.5% to 59.1% of individuals in Florida diagnosed with a strep infection was tested for resistance to the antibiotic penicillin present partial or complete resistance to the antibiotic.

5 0

2 years ago

Dan is fourteen years older than Marge. Eight years ago, Dan was three times as old as Marge. Find their present age.

34kurt

Answer:

<u>Marge's</u> present age = 14 ; <u>Dan's</u> present age = 29

Step-by-step explanation:

Present age

Let Marge's present age be = M

Dan's present age [D] : 14 years elder than Marge = M + 14

8 years ago

Marge Age = M - 8

Dan's Age = D - 8 = (M + 14) - 8 = M + 6

{Given} : Dan's age = 3 times Marge's age

M + 6 = 3 (M - 8)

M + 6 = 3M - 24

6 + 24 = 3M - M

30 = 2M

M = 30/2

M = 15 [Marge's present age]

Dan's present age [D] = M + 14 = 29

5 0

1 year ago

g In a survey of 500 residents, 300 were opposed to the use of the photo-cop for issuing traffic tickets.The standard error of t

Evgesh-ka [11]

Answer:

Z-score 1.96

Margin of error d= 0.04323

Step-by-step explanation:

Hello!

The study variable in this case is

X: Number of people that oppose the use of photo-cop for issuing traffic tickets in a sample of 500.

n= 500

The parameter of interest is the proportion of people that opposes it.

The estimated proportion is p'= 300/500= 0.6

To estimate the population proportion per Confidence interval you have to approximate the distribution of the sample proportion p' to normal:

p'≈N(p;p(1-p)1/n)

The mean of this distribution is p and the variance is p*(1-p)*1/n

To construct the Confidence interval, since the value of the population proportion is unknown, an estimated variance is used:

p'(1-p')*1/n ⇒ then the estimated standard error is √(p'(1-p')*1/n)

The formula for the confidence interval is:

p' ± $Z_{1-\alpha /2}$ * $\sqrt{\frac{p'(1-p')}{n} }$

Where " $Z_{1-\alpha /2}$ * $\sqrt{\frac{p'(1-p')}{n} }$ " represents the margin of error of the interval.

Now for a confidence level of 0.95 the value of Z is $Z_{0.975}= 1.965$

The estimated standard error is already calculated: $\sqrt{\frac{p'(1-p')}{n} } = 0.022$

The margin of error (d) is then:

d= $Z_{1-\alpha /2}$ * $\sqrt{\frac{p'(1-p')}{n} }$ = 1.965 * 0.022

d= 0.04323

I hope it helps!

7 0

1 year ago

High-power experimental engines are being developed by the Stevens Motor Company for use in its new sports coupe. The engineers

mamaluj [8]

Answer:

The 95% confidence interval the average maximum power is (596.0 to 644.0)

Step-by-step explanation:

Average maximum of the sample = x = 620 HP

Standard Deviation = s = 45 HP

Sample size = n = 16

We have to calculate the 95% confidence interval. The value of Population standard deviation is unknown, and value of sample standard deviation is known. Therefore, we will use one sample t-test to build the confidence interval.

Degrees of freedom = df = n - 1 = 15

Critical t-value associated with 95% confidence interval and 15 degrees of freedom, as seen from t-table = $t_{\frac{\alpha}{2}}$ = 2.131

The formula to calculate the confidence interval is:

$(x-t_{\frac{\alpha}{2} } \times \frac{s}{\sqrt{n} }, x+t_{\frac{\alpha}{2} } \times \frac{s}{\sqrt{n} })$

We have all the required values. Substituting them in the above expression, we get:

$(620-2.131 \times \frac{45}{\sqrt{16} }, 620+2.131 \times \frac{45}{\sqrt{16} })\\\\ =(596.0 , 644.0)$

Thus, the 95% confidence interval the average maximum power is (596.0 to 644.0)

7 0

2 years ago