Jake cuts out five-pointed stars. They are different sizes, but they

Gordon buys 3 HD Tvs for $1200 each. There is a shipping charge of $90 to have the Tv s delivered to his house . How much does G

ANTONII [103]

Gordon will pay $3,960

7 0

3 years ago

Suppose that a new company that makes yo yos made 560 yoyos the first week the company overestimated its requirements. The manag

KATRIN_1 [288]

Answer:

312 yoyos in 8th week; 3407 yoyos over 8 weeks

Step-by-step explanation:

The <em>formula for the nth term</em> of a geometric sequence is

aₙ = a₁rⁿ⁻¹

In your geometric sequence, a₁ = 560 and r = 0.92.

Thus, the formula for your sequence is

aₙ = 560(0.92)ⁿ⁻¹

Eighth term

a₈ = 560(0.92)⁷ = 560 × 0.5578 = 312

The company will manufacture 312 yoyos in the eighth week.

Sum over eight weeks

The formula for <em>the sum of the first n terms</em> of a geometric series is

Sum = a₁[(1 - rⁿ)(1 - r)]

Sum = 560[(1 - 0.92⁸)/(1 - 092)]

= 560[(1 - 0.513 22)/0.08 ]

= 560 × (0.486 78/0.08)

= 560 × 6.0848

= 3407

The company will manufacture a total of 3407 yoyos over eight weeks.

4 0

3 years ago

Suppose that the epidemiologist wants to re-estimate the population proportion and wishes for her 95% confidence interval to hav

Svetllana [295]

Answer:

She needs a sample of at least 385.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

The margin of error is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

How large a sample should she take to achieve this?

She needs a sample of size at least n.

n is found when M = 0.04.

We do not know the true population proportion, so we use $\pi = 0.5$ , which is the case for which we are going to need the largest sample size.

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.05 = 1.96\sqrt{\frac{0.5*0.5}{n}}$

$0.05\sqrt{n} = 1.96*0.5$

Dividing both sides by 0.05

$\sqrt{n} = 19.6$

$(\sqrt{n})^{2} = 19.6^{2}$

$n = 384.2$

Rounding up

She needs a sample of at least 385.

3 0

3 years ago

What is the rate of change between the interval x= pi and x= 3pi/2

Romashka [77]

Answer:

$\frac{6}{\pi }$ or 1.9099

Step-by-step explanation:

Look for y values at each of those given values of "x" and apply the slope formula. When x = pi. y = -1 so the coordinate is $(\pi,-1)$ . When x = 3pi/2, y = 2 so the coordinate is $(\frac{3\pi }{2},2)$

Plug those values into the slope formula:

$\frac{2-(-1)}{\frac{3\pi }{2}-\pi}$

You need a common denominator of pi:

$\frac{3}{\frac{3\pi-2\pi}{2} }=\frac{3}{\frac{\pi }{2} }$

Do the math on that to get a slope of $\frac{6}{\pi } =1.9099$

8 0

3 years ago

What two fractions are equivalent to 3/10

d1i1m1o1n [39]

Answer:

6/20 and 9/30

Step-by-step explanation:

Any fraction that can be simplified to 3/10 by dividing the numerator and the denominator is considered equivalent. If you look at the fractions above 6/20 is literally the same thing as 3/10 but I just multiplied the 3 and 10 times 2. As long as you multiply/divide both the numerator and the denominator by the same number the answer you get should be equivalent.

8 0

3 years ago