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1 year ago

Do the following lengths satisfy the Pythagorean Theorem? Lengths =14, 50, 48. Yes No

Mathematics

1 answer:

seraphim [82]1 year ago

6 0

Answer:

yes

Step-by-step explanation:

14² +48² = 196 +2304 = 2500 = 50²

The three lengths (14, 48, 50) are a Pythagorean triple.

<em>Additional comment</em>

The two smaller numbers correspond to side lengths. The larger one corresponds to the hypotenuse length.

We typically write the numbers of a Pythagorean triple in increasing order, but the order doesn't really matter. As sides of a triangle, the triangle formed is a right triangle, regardless of the order.

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Hayden is a manager at a landscaping company. He has two workers to landscape an entire park, Cody and Kaitlyn. Cody can complet

belka [17]

Answer: 3.4 h

Explanation:

1) The basis to solve this kind of problems is that the speed of working together is equal to the sum of the individual speeds.

This is: speed of doing the project together = speed of Cody working alone + speed of Kaitlyin working alone.

2) Speed of Cody

Cody can complete the project in 8 hours => 1 project / 8 h

3) Speed of Kaitlyn

Kaitlyn can complete the project in 6 houres => 1 project / 6 h

4) Speed working together:

1 / 8 + 1 / 6 = [6 + 8] / (6*8 = 14 / 48 = 7 / 24

7/24 is the velocity or working together meaning that they can complete 7 projects in 24 hours.

Then, the time to complete the entire project is the inverse: 24 hours / 7 projects ≈ 3.4 hours / project.Meaning 3.4 hours to complete the project.

7 0

2 years ago

Read 2 more answers

Solve the equation. 11 6 = n + 7 9 6 11 =n+ 9 7 start fraction, 11, divided by, 6, end fraction, equals, n, plus, start frac

belka [17]

Answer:

n = 19/18

Step-by-step explanation:

Given:

11/6 = n + 7/9

Find n

11/6 = n + 7/9

Subtract 7/9 from both sides of the equation

11/6 - 7/9 = n + 7/9 - 7/9

11/6 - 7/9 = n

(99-42) / 54 = n

n = 57/54

n = 19/18

4 0

2 years ago

A company wants to find out if the average response time to a request differs across its two servers. Say µ1 is the true mean/ex

lorasvet [3.4K]

Answer:

a) The null and alternative hypothesis are:

$H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2\neq 0$

Test statistic t=0.88

The P-value is obtained from a t-table, taking into acount the degrees of freedom (419) and the type of test (two-tailed).

b) A P-value close to 1 means that a sample result have a high probability to be obtained due to chance, given that the null hypothesis is true. It means that there is little evidence in favor of the alternative hypothesis.

c) The 95% confidence interval for the difference in the two servers population expectations is (-0.372, 0.972).

d) The consequences of the confidence interval containing 0 means that the hypothesis that there is no difference between the response time (d=0) is not a unprobable value for the true difference.

This relate to the previous conclusion as there is not enough evidence to support that there is significant difference between the response time, as the hypothesis that there is no difference is not an unusual value for the true difference.

Step-by-step explanation:

This is a hypothesis test for the difference between populations means.

The claim is that there is significant difference in the time response for the two servers.

Then, the null and alternative hypothesis are:

$H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2\neq 0$

The significance level is 0.05.

The sample 1, of size n1=196 has a mean of 12.5 and a standard deviation of 3.

The sample 2, of size n2=225 has a mean of 12.2 and a standard deviation of 4.

The difference between sample means is Md=0.3.

$M_d=M_1-M_2=12.5-12.2=0.3$

The estimated standard error of the difference between means is computed using the formula:

$s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{3^2}{196}+\dfrac{4^2}{225}}\\\\\\s_{M_d}=\sqrt{0.046+0.071}=\sqrt{0.117}=0.342$

Then, we can calculate the t-statistic as:

$t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{0.3-0}{0.342}=\dfrac{0.3}{0.342}=0.88$

The degrees of freedom for this test are:

$df=n_1+n_2-1=196+225-2=419$

This test is a two-tailed test, with 419 degrees of freedom and t=0.88, so the P-value for this test is calculated as (using a t-table):

$\text{P-value}=2\cdot P(t>0.88)=0.381$

As the P-value (0.381) is greater than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that there is significant difference in the time response for the two servers.

<u>Confidence interval </u>

We have to calculate a 95% confidence interval for the difference between means.

The sample 1, of size n1=196 has a mean of 12.5 and a standard deviation of 3.

The sample 2, of size n2=225 has a mean of 12.2 and a standard deviation of 4.

The difference between sample means is Md=0.3.

The estimated standard error of the difference is s_Md=0.342.

The critical t-value for a 95% confidence interval and 419 degrees of freedom is t=1.966.

The margin of error (MOE) can be calculated as:

$MOE=t\cdot s_{M_d}=1.966 \cdot 0.342=0.672$

Then, the lower and upper bounds of the confidence interval are:

$LL=M_d-t \cdot s_{M_d} = 0.3-0.672=-0.372\\\\UL=M_d+t \cdot s_{M_d} = 0.3+0.672=0.972$

The 95% confidence interval for the difference in the two servers population expectations is (-0.372, 0.972).

7 0

2 years ago

The length of a flag is 0.3 foot less than twice its width. if the perimeter is 14.4 feet longer than the width, find the dimens

dem82 [27]

3.0 by 3.6 would be the dimensions

3 0

2 years ago

Maria bought 5 tickets for $20 each. Each ticket had a $2 fee. Write an expression that shows how much Maria paid for the ticket

Tanya [424]

The algebraic expression which shows how much Maria paid for the tickets including the additional fee is y = 20(5) + 2(5)

<h3>Algebraic expression to show how much Maria paid for the tickets</h3><h3 />

Number of tickets Maria bought = 5
Cost of each tickets = $20
Additional fee per tickets = $2

let

Total amount Maria paid for the tickets = y

Total amount Maria paid for the tickets = Cost of each tickets(Number of tickets Maria bought) + Additional fee per tickets(Number of tickets Maria bought)

y = 20(5) + 2(5)

y = 100 + 10

y = $110

Therefore, the algebraic expression which shows how much Maria paid for the tickets including the additional fee is y = 20(5) + 2(5)