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xxTIMURxx [149]

3 years ago

7

A farmer has some chickens and rabbits. There are 60 eyes and 100 legs altogether. How many chickens and how many rabbits are th

ere?

2 answers:

expeople1 [14]3 years ago

8 0

Answer:

20 rabbits, 10 chickens

Step-by-step explanation:

Because chickens and rabbits each have 2 eyes, the number of animals is 60 ÷ 2 = 30.

Let's say that all of the 30 animals are chickens. There would be a total of 30 × 2 = 60 legs.

So the extra (100 – 60) = 40 legs must have come from the rabbits.

Every rabbit has (4 – 2) = 2 more legs than a chicken.

So there are 40 ÷ 2 = 20 rabbits and 30 – 20 = 10 chickens.

slamgirl [31]3 years ago

3 0

Answer:

20 rabbits and 10 chicks

Step-by-step explanation:

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What is the solution?. 1/2x2 – x + 5 = 0

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1/2 x^2 - x + 5 = 0
Multiply through by 2 to get:
x^2 - 2x + 10 = 0
$x= \frac{-b\pm\sqrt{b^2-4ac}}{2a}$ ; where a = 1, b = -2 and c = 10
$x=\frac{-(-2)\pm\sqrt{(-2)^2-(4\times1\times10)}}{2\times1}\\=\frac{2\pm\sqrt{4-40}}{2}\\=\frac{2\pm\sqrt{-36}}{2}\\=\frac{2\pm6i}{2}\\=1\pm3i$
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3 years ago

When the sample size and the sample proportion remain the same, a 90 percent confidence interval for a population proportion p w

deff fn [24]

Answer:

A 90% confidence interval for <em>p</em> will be <u>narrower </u>than the 99% confidence interval.

Step-by-step explanation:

The formula to compute the (1 - <em>α</em>) % confidence interval for a population proportion is:

$CI=\hat p\pm z_{\alpha /2}\sqrt{\frac{\hat p(1-\hat p)}{n}}$

Here $\hat p$ is the sample proportion.

The margin of error of the confidence interval is:

$MOE= z_{\alpha /2}\sqrt{\frac{\hat p(1-\hat p)}{n}}$

The MOE is dependent on:

Confidence level
Standard deviation
Sample size

The MOE is directly related to the confidence level and standard deviation.

So if any of the two increases then the MOE also increases, thus widening the confidence interval.

And the MOE is inversely related to the sample size.

So if the sample increases the MOE decreases and vice versa.

It is provided that the sample size and the sample proportion are not altered.

The critical value of <em>z</em> for 90% confidence level is:

$z_{\alpha/2}= z_{0.10/2}=z_{0.05}=1.645$

And the critical value of <em>z</em> for 99% confidence level is:

$z_{\alpha/2}= z_{0.05/2}=z_{0.05}=1.96$

So as the confidence level increases the critical value increases.

Thus, a 90% confidence interval for <em>p</em> will be narrower than the 99% confidence interval.

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3 years ago

Which equation could be used to solve the problem? Sarah spent $160 on lunch in 10 weeks. If she spent the same amount every wee

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The correct answer would be A, because 160/10 is getting you your unit rate, or the amount Sarah spent every week.

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3 years ago

How to write it in quotient + remainder/divisor form

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4 years ago

A geometric sequence is defined by the equation an = (3)3 − n.

Delvig [45]

PART A

The geometric sequence is defined by the equation

$a_{n}=3^{3-n}$

To find the first three terms, we put n=1,2,3

When n=1,

$a_{1}=3^{3-1}$

$a_{1}=3^{2}$

$a_{1}=9$
When n=2,

$a_{2}=3^{3-2}$
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$a_{2}=3$

When n=3

$a_{3}=3^{3-3}$

$a_{3}=3^{0}$
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The first three terms are,

$9,3,1$

PART B

The common ratio can be found using any two consecutive terms.

The common ratio is given by,
$r= \frac{a_{2}}{a_{1}}$
$r = \frac{3}{9}$

$r = \frac{1}{3}$

PART C

To find
$a_{11}$

We substitute n=11 into the equation of the geometric sequence.

$a_{11} = {3}^{3 - 11}$

This implies that,

$a_{11} = {3}^{ - 8}$

$a_{11} = \frac{1}{ {3}^{8} }$

$a_{11}=\frac{1}{6561}$

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3 years ago