You buy a house for $230,000. It appreciates at a rate

On a particular day, the wind added 4 miles per hour to Jaime's rate when she was rowing with the wind and subtracted 4 miles pe

larisa [96]

Nice so
remember
t=d/s
a(b+c)=ab+ac

time=distance/speed

lets say s=jamie's normal speed
speed agains wind=s-4
speed with wind=s+4

30 miles is agains wind
distance is 54 with wind

t=d/s
t=30/(s-4)
t=54/(s+4)

since they are both equal to t, set them equal to each other

30/(s-4)=54/(s+4)
multipliy both sides by (s+4)(s-4)
30(s+4)=54(s-4)
distribute
30s+120=54s-216
subtract 30s from both sides
120=24s-216
add 216 to both sides
336=24s
divide both sides by 24
14=s

answer is 14 miles per hour without wind

8 0

3 years ago

A farmer has 520 feet of fencing to construct a rectangular pen up against the straight side of a barn, using the barn for one s

Setler [38]

Answer:

$310\text{ feet and }210\text{ feet}$

Step-by-step explanation:

GIVEN: A farmer has $520 \text{ feet}$ of fencing to construct a rectangular pen up against the straight side of a barn, using the barn for one side of the pen. The length of the barn is $310 \text{ feet}$ .

TO FIND: Determine the dimensions of the rectangle of maximum area that can be enclosed under these conditions.

SOLUTION:

Let the length of rectangle be $x$ and $y$

perimeter of rectangular pen $=2(x+y)=520\text{ feet}$

$x+y=260$

$y=260-x$

area of rectangular pen $=\text{length}\times\text{width}$

$=xy$

putting value of $y$

$=x(260-x)$

$=260x-x^2$

to maximize $\frac{d \text{(area)}}{dx}=0$

$260-2x=0$

$x=130\text{ feet}$

$y=390\text{ feet}$

but the dimensions must be lesser or equal to than that of barn.

therefore maximum length rectangular pen $=310\text{ feet}$

width of rectangular pen $=210\text{ feet}$

Maximum area of rectangular pen $=310\times210=65100\text{ feet}^2$

Hence maximum area of rectangular pen is $65100\text{ feet}^2$ and dimensions are $310\text{ feet and }210\text{ feet}$

5 0

3 years ago

Several years ago, 39% of parents who had children in grades K-12 were satisfied with the quality of education the students r

BaLLatris [955]

<h2>Answer with explanation:</h2>

Let p be the population proportion of parents who had children in grades K-12 were satisfied with the quality of education the students receive.

Given : Several years ago, 39% of parents who had children in grades K-12 were satisfied with the quality of education the students receive.

Set hypothesis to test :

$H_0: p=0.39\\\\H_a :p\neq0.39$

Sample size : n= 1055

Sample proportion : $\hat{p}=\dfrac{466}{1055}=0.441706161137\approx0.44$

Critical value for 95% confidence : $z_{\alpha/2}=1.96$

Confidence interval : $\hat{p}\pm z_{\alpha/2}\sqrt{\dfrac{p(1-p)}{n}}$

$0.44\pm (1.96)\sqrt{\dfrac{0.39(1-0.39)}{1055}}\\\\0.44\pm0.0299536805135\\\\0.44\pm0.03\\\\=(0.44-0.03, 0.44+0.03)\\\\=(0.41,\ 0.47)$

Since , Confidence interval does not contain 0.39.

It means we reject the null hypothesis.

We conclude that 95% confidence interval represents evidence that parents' attitudes toward the quality of education have changed.

8 0

3 years ago

Could someone help me with 2, 9, 10, 11, 12 13, and 14?

shutvik [7]

Answer:

13. (1) x + 8x = 32

14. $337.5

Step-by-step explanation:

14. $270 x 0.25 = 67.5

270 + 67.5 = 337.5

I am sorry. I only got these-

7 0

3 years ago

Read 2 more answers

<img src="https://tex.z-dn.net/?f=%20%7B3%7D%5E%7B2%20%7D%20" id="TexFormula1" title=" {3}^{2 } " alt=" {3}^{2 } " align="absmid

expeople1 [14]

Answer: 9

Step-by-step explanation:

To square a number, you multiply it by itself twice.

In this case, your answer would be 3 x 3 = 9.

Hope it helps! :)

3 0

3 years ago