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2 years ago

6

Please help, I am having some difficulty with this problem! The Varners live on a corner lot. Often, children cut across their

lot to save walking distance. The diagram to the right represents the corner lot. The children's path is represented by a dashed line. Approximate the walking distance that is saved by cutting across their property instead of walking around the lot. right triangle, the hypotenuse is 42 feet, short leg is x and long leg is x+4
help will be very much appreciated! :)

1 answer:

Kipish [7]2 years ago

7 0

Answer:

17.262 feet

Step-by-step explanation:

Assuming they are cutting through using the hypotenuse, the distance they save is x+4+x-42, and is thus 2x-38.

The triangle can be solved using pythag to find the exact distance.

17.262 feet

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Clark Heter is an industrial engineer at Lyons Products. He would like to determine whether there are more units produced on the

larisa [96]

Answer:

No, at the 0.05 significance level, the number of units produced on the night shift is not larger.

Step-by-step explanation:

We are given that the mean number of units produced by a sample of 54 day-shift workers was 345. The mean number of units produced by a sample of 60 night-shift workers was 351.

Assume the population standard deviation of the number of units produced on the day shift is 21 and 28 on the night shift.

Let $\mu_1$ = population mean number of units produced on the day shift

$\mu_2$ = population mean number of units produced on the night shift

So, <u>Null Hypothesis</u>, $H_0$ : $\mu_1-\mu_2\geq0$ or $\mu_1\geq\mu_2$ {means that the mean number of units produced on the night shift is same or lesser on the day shift}

<u>Alternate Hypothesis,</u> $H_A$ : $\mu_1-\mu_2$ or $\mu_1$ {means that the mean number of units produced on the night shift is larger}

The test statistics that will be used here is <u>Two-sample z test statistics</u> as we know about population standard deviations;

T.S. = $\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{\sqrt{\frac{\sigma_1^{2} }{n_1}+\frac{\sigma_2^{2} }{n_2} } }$ ~ N(0,1)

where, $\bar X_1$ = sample mean number of units produced by a sample of 54 day-shift workers = 345

$\bar X_2$ = sample mean number of units produced by a sample of 60 night-shift workers = 351

$\sigma_1$ = population standard deviation of the number of units produced on the day shift = 21

$\sigma_2$ = population standard deviation of the number of units produced on the day shift = 28

$n_1$ = sample of day-shift workers = 54

$n_2$ = sample of night-shift workers = 60

So, <em><u>test statistics</u></em> = $\frac{(345-351)-(0)}{\sqrt{\frac{21^{2} }{54}+\frac{28^{2} }{60} } }$

= -1.302

Now at 0.05 significance level, the z table gives critical value of -1.6449 for left-tailed test. Since our test statistics is more than the critical value of z as -1.302 > -1.6449 so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.

Therefore, we conclude that the mean number of units produced on the night shift is same or lesser than those produced on the day shift.

4 0

2 years ago

Use the graph to write an explicit function to represent the data and determine how much money Amy earned in week 5.

zalisa [80]

Answer:

3rd option

$f(n)=5(3)^{n-1}$

$f(5)=405$

Step-by-step explanation:

So we are given the following points:

(1,5)

(2,15)

(3,45)

(4,135)

This is a geometric sequence because there is a common ratio, 3. That is you can keep multiply 3 to a previous y-coordinate to get the next y-coordinate.

The formula for a geometric sequence is $f(n)=a_1 \cdot r^{n-1}$

where $a_1$ is the first term and r is the common ration.

So we have

$f(n)=5 \cdot (3)^{n-1}$ .

If you want to know the fifth term, just plug in 5:

$f(5)=5 \cdot (3)^{5-1}$

Simplifying:

$f(5)=5 \cdot 3^4$

$f(5)=5 \cdot 81$

$f(5)=405$

3 0

2 years ago

Read 2 more answers

Katherine is landscaping her home with juniper trees and pansies. She wants to arrange 15 pansies around each of 8 trees. Each t

Doss [256]

Let
X-----------------> number of pansies
y-----------------> number of trees

we know that
x=15*8----------> x=120 pansies
y=8 trees

cost of each trees is----------> $<span>20.75
</span>cost of each pansies is------> $2.50/6------> $5/12

[<span>expression to find Katherine’s final cost]=[cost trees]+[cost pansies]
</span>[cost trees]=y*$20.75
[cost pansies]=x*($5/12)

[expression to find Katherine’s final cost]=y*($20.75)+x*($5/12)
[expression to find Katherine’s final cost]=8*($20.75)+120*($5/12)

[expression to find Katherine’s final cost]=$166+$50
[expression to find Katherine’s final cost]=$216

the answer is
[expression to find Katherine’s final cost]=y*($20.75)+x*($5/12)
[expression to find Katherine’s final cost]=8*($20.75)+120*($5/12)

Katherine’s final cost is $216

5 0

2 years ago

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Find the first partial derivative:<br><br> f(x, y) = y^5 -3xy

Romashka-Z-Leto [24]

Partial derivative is derivative over only 1 variable.
here we have 2 variables so it depends on which variable you want to make partial derivative.

case 1.
df/dx = -3y

case 2
df/dy = 5y^4 - 3x

8 0

2 years ago

Binks needs to raise at least $3600. He was given $200 and plans to save $50 a week. Select all of the inequalities that represe

kherson [118]

Answer:

I'm pretty sure it is 50n+200 <u><</u> 3600

Step-by-step explanation:

Im to fully sure tho

5 0

1 year ago