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3 years ago

A rabbit can run 35 miles per hour.A fox can run 21 miles in half an hour.Which animal is faster and how much

Mathematics

1 answer:

Pachacha [2.7K]3 years ago

6 0

Answer:

Step-by-step explanation:

The fox is faster. Because he is a fox.

Also because he can (assuming he doesn't fatigue or get caught by hounds in the second half of the hour) run 42 miles in 1 hour.

The rabbit runs 35 miler per hour.

Velocity = Distance/time

Fox velocity = 21 miles/0.5 hour

Dividing by 0.5 is the same as multiplying by 2, so...

Fox velocity = 42 miles/hour

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If you can answer 5 questions in an hour, how many questions can you complete in 3 hours? HINT: Use the proportion 5 questions :

Stella [2.4K]

Answer:

Step-by-step explanation:

1 hr: 5

2 hr: 10

3 hr: 15

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4 years ago

An actor invested some money at 5% simple interest, and $41,000 more than 4 times the amount at 9%. The total annual interest ea

NARA [144]

Answer:

The amount invested at 5%=$77,000
The amount invested at 9%=$349,000

Step-by-step explanation:

Let the amount invested at 5% simple interest =$x

He invested $41,000 more than 4 times the amount at 9%.

This amount is: $(4x+41000)

Total Annual Interest Earned = $35,260

Therefore, Time=1 year

Simple Interest $=\frac{Principal X Rate X Time}{100}$

Therefore, his total interest

=Interest from Investment 1 + Interest from Investment 2

$35260=\left(\frac{x*5*1}{100} \right)+\left(\frac{4x+41000*9*1}{100} \right)\\35260=0.05x+(0.36x+3690)\\35260-3690=0.05x+0.36x\\31570=0.41x\\\text{Divide both sides by 0.41}\\x=\$77000$

Therefore:

The amount invested at 5%=$77,000

The amount invested at 9%=$(4*77,000+41000)=$349,000

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3 years ago

Why do you think you need to add zero pairs to get the -1- tiles to fit in the rectangle?

Olin [163]

You will need. 1- to fit the rectangle tile in

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3 years ago

PLEASE HELP ME!!!! WILL MARK BRAINLIEST

FromTheMoon [43]

Answer:

Step-by-step explanation:

Pythagoras's theorem dictates that a squared + b squared = c squared when talking about sides on right angled triangles with a and b being flat sides and c being the hypotenuse which gives us the forumula below

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3 years ago

Read 2 more answers

A study was conducted and two types of engines, A and B, were compared. Fifty experiments were performed using engine A and 75 u

USPshnik [31]

Answer:

a) -6 mpg.

b) 2.77 mpg

c) The 95% confidence interval for the difference of population mean gas mileages for engines A and B and interpret the results, in mpg, is (-8.77, -3.23).

Step-by-step explanation:

To solve this question, we need to understand the central limit theorem, and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Gas mileage A: Mean 36, standard deviation 6, sample of 50:

$\mu_A = 36, s_A = \frac{6}{\sqrt{50}} = 0.8485$

Gas mileage B: Mean 42, standard deviation 8, sample of 50:

$\mu_B = 42, s_B = \frac{8}{\sqrt{50}} = 1.1314$

Distribution of the difference:

Mean:

$\mu = \mu_A - \mu_B = 36 - 42 = -6$

Standard error:

$s = \sqrt{s_A^2+s_B^2} = \sqrt{0.8485^2+1.1314^2} = 1.4142$

A. Find the point estimate.

This is the difference of means, that is, -6 mpg.

B. Find the margin of error

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1 - 0.95}{2} = 0.025$

Now, we have to find z in the Ztable as such z has a pvalue of $1 - \alpha$ .

That is z with a pvalue of $1 - 0.025 = 0.975$ , so Z = 1.96.

Now, find the margin of error M as such

$M = zs = 1.96*1.4142 = 2.77$

The margin of error is of 2.77 mpg

C. Construct the 95% confidence interval for the difference of population mean gas mileages for engines A and B and interpret the results(5 pts)

The lower end of the interval is the sample mean subtracted by M. So it is -6 - 2.77 = -8.77 mpg

The upper end of the interval is the sample mean added to M. So it is -6 + 2.77 = -3.23 mpg

The 95% confidence interval for the difference of population mean gas mileages for engines A and B and interpret the results, in mpg, is (-8.77, -3.23).

8 0

3 years ago