An envelope from the post office is 7 inches wide and 8 inches long. What is the perimeter of the envelope?

Water fills a tank at a rate of 150 litres during the first hour, 350 litres during the second, 550 litres during the third and

Alborosie

Putting this as an arithmetic sequence gives:

$u_n = 150+200(n-1)$

The sum of the series = 16 x 7 x 7 = 784 m^3 = 784 000 L

The sum of an arithmetic series can be written as:

$S_n=n/2 [2a+(n-1)d] = 784 000
\\n/2[2(150)+(n-1)200] = 784 000
\\n[300+200(n-1)=1 568 000
\\300n+200n^2-200n = 1 568 000
\\200n^2+100n- 1 568 000 = 0
\\2n^2 +n- 15680 = 0

\\n= 88.2...,-88.7$

n has to be positive, so we get

n = <u>88.2 hours (3 s.f.)</u>

3 0

3 years ago

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58,927 move to the decimal left 4 place

olga nikolaevna [1]

So in the number 58,927 your decimal point starts after the 7. When you move it to the left four places (four numbers) the decimal is now right after the 5. Your new answer is 5.8927. Hope I helped :D

5 0

3 years ago

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Please help ill give brainiest

suter [353]

Answer:

Sales Tax: $12

Total Price: $312

Step-by-step explanation:

4% of 300 is 12, so that is the sales tax. Then, because it's tax, you add it on the the price before tax to get the total price, 300+12=312.

(hope this helps!)

7 0

3 years ago

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Which expression gives the x-coordinate of the solution of the system?

aalyn [17]

To find the the expression that gives the value of $x$ we are going to proceed as follows:
$5x+3y=-18$ equation (1)
$2x-4y=-28$ equation (1)

Step 1. solve for $y$ in equation (2)
$2x-4y=-28$
$-4y=-28-2x$
$y= \frac{-28-2x}{-4}$
$y=7+ \frac{1}{2} x$ equation (3)

Step 3. Replace equation (3) in equation (1) and solve for $x$
$5x+3y=-18$
$5x+3(7+ \frac{1}{2} x)=-18$
$5x+21+ \frac{3}{2} x=-18$
$\frac{13}{2} x=-39$
$x= \frac{-39(2)}{(13)}$
$x=-6$

We can conclude that the expression that gives the value of $x$ is: $x=-6$

7 0

3 years ago

A development economist is studying income growth in a rural area of a developing country. The last census of the population of

kykrilka [37]

Answer:

If we compare the p value and the significance level given $\alpha=0.01$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL reject the null hypothesis, so we can say that the population mean is not singificantly higher than 425.

Step-by-step explanation:

Data given and notation

$\bar X=433.75$ represent the mean height for the sample

$\sigma=\sqrt{2500}=50$ represent the population standard deviation for the sample

$n=100$ sample size

$\mu_o =425$ represent the value that we want to test

$\alpha=0.01$ represent the significance level for the hypothesis test.

z would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean height actually is higher than the mean height for men in 1960, the system of hypothesis would be:

Null hypothesis: $\mu \leq 425$

Alternative hypothesis: $\mu > 425$

Since we know the population deviation so is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$z=\frac{433.75-425}{\frac{50}{\sqrt{100}}}=1.75$

P-value

Since is a one right tail test the p value would be:

$p_v =P(z>1.75)=1-P(z$

Conclusion

If we compare the p value and the significance level given $\alpha=0.01$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL reject the null hypothesis, so we can say that the population mean is not singificantly higher than 425.

3 0

3 years ago