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4 years ago

For the data in the table, does y vary directly with x? If it does, write an equation for the direct variation.

Mathematics

1 answer:

Trava [24]4 years ago

7 0

11 = 1.375 * 8
22 = 1.375 * 16
33 = 1.375 * 24
Therefore y varies directly with x.
Answer: C ) yes; y = 1.375 x

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The 17th term of an Arithmetic sequence is 51. If the commons difference is 7, what is the first term ?

vovikov84 [41]

Answer:

The first term is:

$a_1=-61$

Step-by-step explanation:

The arithmetic sequence is defined by

$a_n=a_1+\left(n-1\right)d$

where

$a_1$ is the first term

$d$ is the common difference

the 17th term of an arithmetic sequence is 51.

i.e. $a_{17}=51$

$a_n=a_1+\left(n-1\right)d$

$a_{17}=a_1+\left(17-1\right)d$

$51=a_1+\left(17-1\right)7$ ∵ $n = 17$ , $a_{17}=51$ , $d=7$

$a_1+112=51$ ∵ $\left(17-1\right)\cdot \:\:7=112$

$a_1=-61$

Therefore, the first term is:

$a_1=-61$

8 0

3 years ago

A.11.1<br><br> B.12.7<br><br> C.9.2<br><br> D.8.5

Bad White [126]

Answer: B. 12.7

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Solve the following system of inequalities graphically on the set of axes below. State the coordinates of a point in the solutio

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3 years ago

URGENT: statistics: A researcher wishes to estimate the percentage of adults who support abolishing the penny what size sample s

irina1246 [14]

Using the margin of error for the z-distribution, the sample sizes are given as follows:

a) 822.

b) 1068.

<h3>What is a confidence interval of proportions?</h3>

A confidence interval of proportions is given by:

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

The margin of error is given by:

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

In which:

$\pi$ is the sample proportion.

z is the critical value.

n is the sample size.

We have a 95% confidence level, hence $\alpha = 0.95$ , z is the value of Z that has a p-value of $\frac{1+0.95}{2} = 0.975$ , so the critical value is z = 1.96.

Item a:

The estimate is of $\pi = 0.26$ , hence we solve for n when M = 0.03.

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

$0.03 = 1.96\sqrt{\frac{0.26(0.74)}{n}}$

$0.03\sqrt{n} = 1.96\sqrt{0.26(0.74)}$

$\sqrt{n} = \frac{1.96\sqrt{0.26(0.74)}}{0.03}$

$(\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.26(0.74)}}{0.03}\right)^2$

n = 821.2

A sample of 822 is needed.

Item b:

No prior estimate, hence $\pi = 0.5$ .

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

$0.03 = 1.96\sqrt{\frac{0.5(0.5)}{n}}$

$0.03\sqrt{n} = 1.96\sqrt{0.5(0.5)}$

$\sqrt{n} = \frac{1.96\sqrt{0.5(0.5)}}{0.03}$

$(\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.5(0.5)}}{0.03}\right)^2$

n = 1067.11

A sample of 1068 is needed.

More can be learned about the z-distribution at brainly.com/question/25890103

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4 0

2 years ago

How do i complete these patterns

Ghella [55]

For a, each time it is taking away 2 places. 3,400,000, taking away 2 zeros is 34,000. Like they have in the example. So you need to take away 2 places for the first blank. For the second blank you need to move the decimal place 2 places to the left. For b, it's taking away 1 place, so do the same thing but with one place. For the first blank, add a place.

7 0

3 years ago