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3 years ago

Consider the first four terms of the sequence below.

Mathematics

1 answer:

Lelu [443]3 years ago

8 0

Answer:

a₈ = - 1 / 128

Step-by-step explanation:

Given:

First four terms of the sequence

a₁= 1, a₂= - 1/2, a₃= 1/4 and a₄= -1/8

First we recognize that this is a geometric series (sequence) and we must calculate quotient q.

q = a₂/a₁ = a₃/a₂ = (-1/2)/1 = (1/4)/(-1/2) = - 1/2

q = - 1/2

Formula for calculating n-th term is:

aₙ = a₁ · qⁿ⁻¹

According to this:

a₈ = 1 (-1/2)⁷ = - 1/ 128

God with you!!!

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At a sale on winter clothing,Cody bought two pairs of gloves and four hats for $43.00. Tori bought two pairs of gloves and two h

lara31 [8.8K]

First do 43 - 30= $13 for two hats
so for one hat you do 13 divided by 2 which equals= $6.50 for one hat

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3 years ago

The article "Students Increasingly Turn to Credit Cards" (San Luis Obispo Tribune, July 21, 2006) reported that 37% of college f

Sloan [31]

Answer:

Step-by-step explanation:

Hello!

There are two variables of interest:

X₁: number of college freshmen that carry a credit card balance.

n₁= 1000

p'₁= 0.37

X₂: number of college seniors that carry a credit card balance.

n₂= 1000

p'₂= 0.48

a. You need to construct a 90% CI for the proportion of freshmen who carry a credit card balance.

The formula for the interval is:

p'₁± $Z_{1-\alpha /2}*\sqrt{\frac{p'_1(1-p'_1)}{n_1} }$

$Z_{1-\alpha /2}= Z_{0.95}= 1.648$

0.37±1.648* $\sqrt{\frac{0.37*0.63}{1000} }$

0.37±1.648*0.015

[0.35;0.39]

With a confidence level of 90%, you'd expect that the interval [0.35;0.39] contains the proportion of college freshmen students that carry a credit card balance.

b. In this item, you have to estimate the proportion of senior students that carry a credit card balance. Since we work with the standard normal approximation and the same confidence level, the Z value is the same: 1.648

The formula for this interval is

p'₂± $Z_{1-\alpha /2}*\sqrt{\frac{p'_2(1-p'_2)}{n_2} }$

0.48±1.648* $\sqrt{\frac{0.48*0.52}{1000} }$

0.48±1.648*0.016

[0.45;0.51]

With a confidence level of 90%, you'd expect that the interval [0.45;0.51] contains the proportion of college seniors that carry a credit card balance.

c. The difference between the width two 90% confidence intervals is given by the standard deviation of each sample.

Freshmen: $\sqrt{\frac{p'_1(1-p'_1)}{n_1} } = \sqrt{\frac{0.37*0.63}{1000} } = 0.01527 = 0.015$

Seniors: $\sqrt{\frac{p'_2(1-p'_2)}{n_2} } = \sqrt{\frac{0.48*0.52}{1000} }= 0.01579 = 0.016$

The interval corresponding to the senior students has a greater standard deviation than the interval corresponding to the freshmen students, that is why the amplitude of its interval is greater.

8 0

3 years ago

Find the missing side. 6 is A^2 10 is B^2 what is the missing side

topjm [15]

Answer:

Step-by-step explanation:

This is a right triangle, which fits the Pythagorean Theorem, a^2 +b^2 = c^2. The variables a, b, and c all are sides of the triangle, while a and b are the two legs and c is the hypothenuse.

In this problem, we see that 6 and x are the legs and 10 is the hypothenuse. We put 6 as "a" and x as "b" (but it doesn't matter which is a and b) and 10 is c. Therefore, we have the equation:

6^2 + x^2 = 10^2

which further simplifies to:

36 + x^2 = 100

x^2 = 64

and so x would equal 8 (or -8, but it is impossible to have a side length of -8).

Therefore, the missing side is 8.

7 0

3 years ago

Read 2 more answers

Determine the length of the leg of a 45o – 45o – 90o triangle with a hypotenuse length of 15 inches. ( ANSWER NEEDS TO BE IN RED

SIZIF [17.4K]

Answer:

The lenghts of both legs: $\frac{15\sqrt{2}}{2}\ inches$

Step-by-step explanation:

By definition, when a triangle has angles that measures 45°, 45° and 90°, its legs are congruent.

Then, knowing the lenght of the hypotenuse, we can find the lenght (in inches) of any leg of the given triangle by applying the Trigonometric Identity $sin\alpha=\frac{opposite}{hypotenuse}$ :