How many miles is 2/3

the length of a rectangular garden is 3 m greater than the width. The area of the garden is 70m squared. find the dimensions of

Lerok [7]

A = l x w

so you know that the length is 3m longer than the width, so you could use a formula to represent that

w = l + 3

you then substitute the second equation into the first to solve for l

70 = l x (l +3)
70 = l^2 + 3l

you could then rearrange the formula and solve for l using the quadratic formula

0 = l^2 + 3l - 70

l = -3 +- (square root (3)^2 - 4(1)(70)) / 2(1)
l = -3 +- (square root 9 + 280) / 2
l = -3 +- (square root 289) / 2
l = -3 +- 17 / 2

then you solve for the two seperate roots

l = -3 + 17 /2
l = 14 / 2
l = 7

or

l = -3 - 17 / 2
l = -20 / 2
l = -10

since a length cannot be negative, this root is not viable. therefore l = 7

to solve for w you would use

w = l + 3
w = 7 + 3
w = 10

hope this helps! if you did not understand a step or concept please let me know!

4 0

3 years ago

-5=x/3-8 plz someone help me plz

Flura [38]

Isolate x by adding 8 to both sides.
3 = x/3
Then, multiply by 3 on both sides.
9 = x
To prove that this is right, you can imput 9 into the equation and it equals -5.

5 0

2 years ago

Do political science classes require less writing than history classes? The 55 randomly selected political science classes assig

tia_tia [17]

Answer:

No, political science classes does not require less writing than history classes.

Step-by-step explanation:

We are given that the 55 randomly selected political science classes assigned an average of 19.6 pages of essay writing for the course. The standard deviation for these 55 classes was 4.8 pages.

The 50 randomly selected history classes assigned an average of 20.2 pages of essay writing for the course. The standard deviation for these 50 classes was 3.3 pages.

Let $\mu_1$ = mean writing required by political science classes

$\mu_2$ = mean writing required by history classes

SO, Null Hypothesis, $H_0$ : $\mu_1-\mu_2\geq0$ or $\mu_1\geq \mu_2$ {means that political science classes require more or equal writing than history classes}

Alternate Hypothesis, $H_A$ : $\mu_1-\mu_2$ or $\mu_1$ {means that political science classes require less writing than history classes}

The test statistics that will be used here is Two-sample t test statistics as we don't know about the population standard deviations;

T.S. = $\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{s_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }$ ~ $t__n__1+_n__2-2$

where, $\bar X_1$ = sample average writing for political science course= 19.6 pages

$\bar X_2$ = sample average writing for history course= 20.2 pages

$s_1$ = sample standard deviation for political science classes = 4.8 pages

$s_2$ = sample standard deviation for history classes = 3.3 pages

$n_1$ = sample of selected political science classes = 55

$n_2$ = sample of selected history classes = 50

Also, $s_p=\sqrt{\frac{(n_1-1)s_1^{2}+(n_2-1)s_2^{2} }{n_1+n_2-2} }$ = $\sqrt{\frac{(55-1)\times 4.8^{2}+(50-1)\times 3.3^{2} }{55+50-2} }$ = 4.154

So, the test statistics = $\frac{(19.6-20.2)-(0)}{4.154 \times \sqrt{\frac{1}{55}+\frac{1}{50} } }$ ~ $t_1_0_3$

= -0.739

Now at 0.01 significance level, the t table gives critical value of -2.367 at 103 degree of freedom for left-tailed test. Since our test statistics is more than the critical value of t as -0.739 > -2.367, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that political science classes require more or equal writing than history classes.

8 0

2 years ago

2. Finance Planners recommend no more than 30% of your income should be your rent.

sattari [20]

If she brings home 2,000 a month, she she spend around 600$ on rent because $2000 • 30% = $600.

She needs to make $5810 a month to have her 1743$ rent be 30% of her income because 30/100 = 1743/x
x= 5810

6 0

1 year ago

If x=0 how would i do this problem 2x + x - 3x + 4 = ?

horsena [70]

2(0) + (0) - 3(0) +4= 4

*My bad

3 0

2 years ago

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