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3 years ago

Finding the sum. imaginary numbers! hellpp

Mathematics

1 answer:

Neko [114]3 years ago

3 0

The "i" in this problem actually doesn't represent imaginary numbers. This is a summation problem which is asking for the sum of (2i+1) for when i = 1 to i = 7.

So (2(1) + 1) + (2(2) + 1) + (2(3) + 1) + (2(4) + 1)... etc...

The summation rules we need to know for this problem are for constants and for a single variable.

When we have a constant, the summation rule is n*c where n is the number of times.

When we have a single variable, the summation rule is n(n+1)/2.

So applying the summation rules where n = 7:

2(7)(7+1)/2 + 1(7)

(7)(8) + 7 = 63

The answer to the summation is 63.

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B The percentage change is 55%

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4 years ago

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john has us and foreign stamps in his album. the ratio of the numer of us stamps to foreign stamps is 5:2. after paul gives him

VLD [36.1K]

Answer:

The number of U.S stamp he has is 120.

Step-by-step explanation:

John has us and foreign stamps in his album. the ratio of the number of U.S stamps to foreign stamps is 5:2.

After Paul gives him 12 foreign stamps the ratio becomes 2:1.

Now, to find the number of U.S stamps.

Let the U.S stamps be $x.$

And the foreign stamps be $y.$

Now, to solve by using cross multiplication method:

So, the ratio is:

$\frac{x}{y} =\frac{5}{2}$

By cross multiplying we get:

$2x=5y$

Dividing both sides by 2 we get:

$x=\frac{5y}{2}$ ......(1)

Now, after Paul gives him 12 foreign stamps the ratio becomes:

$\frac{x}{12+y} =\frac{2}{1}$

By cross multiplying we get:

$x=24+2y$

Putting the value of $x$ as we get in above equation (1):

$\frac{5y}{2} =24+2y$

Multiplying both sides by 2 we get:

$5y=48+4y$

Subtracting both sides by 4y we get:

$y=48.$

The number of foreign stamps = 48.

Now, to get the number of U.S stamps by putting the value of $y$ in equation (1):

$x=\frac{5\times 48}{2}$

$x=\frac{240}{2}$

$x=120.$

Therefore, the number of U.S stamp he has is 120.

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4 years ago

A major department store chain is interested in estimating the average amount its credit card customers spent on their first vis

SSSSS [86.1K]

Answer: (39.424, 61.576)

Step-by-step explanation:

When population standard deviation( $\sigma$ ) unknown ,The confidence interval for population mean is given by :-

$\overline{x}\pm t^*\dfrac{s}{\sqrt{n}}$

, where n= Sample size

$\overline{x}$ = sample mean.

s= sample standard deviation

$t^*$ = Critical t-value (two-tailed)

Given : n= 15

Degree of freedom= 14 [df=n-1]

$\overline{x}=\ $50.50$

$s^2=400\\\\\Rightarrow\ s=\sqrt{400}=20$

Significance level = $\alpha=1-0.95=0.05$

For $\alpha=0.05$ and df = 14, the critical t-values : $t^*=\pm2.1448$

Then the 95% confidence interval for population mean will be :

$50.50\pm (2.1448)\dfrac{20}{\sqrt{15}}\\\\=50.50\pm(2.1448)(5.1640)\\\\\approx50.50\pm11.076\\\\=(50.50-11.076,\ 50.50+11.076)\\\\=(39.424,\ 61.576)$

Hence, a 95% confidence interval for the average amount its credit card customers spent on their first visit to the chain's new store in the mall. : (39.424, 61.576)

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4 years ago

ANSWER FOR BRAINIEST

Rina8888 [55]

THE ANSWER IS: y=3/2x+1

to find a line that is perpendicular, invert the slope and multiply by -1
so the original slope is -2/3,
invert it to get -3/2 then multiply by -1 to get 3/2

put the given point (-2,-2) and the new slope into point intercept form: y+2=3/2(x+2)

rewrite in standard form to get y=3/2x+1

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3 years ago