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3 years ago

Draw a square with one vertex on the origin (-3, 5) and a perimeter of 20.

Mathematics

1 answer:

vampirchik [111]3 years ago

5 0

Answer:

Coordinates:

(-3, 5)

(2, 5)

(-3, 10)

(2, 10)

Step-by-step explanation:

Perimeter formula:

length + width + length + width

Insert known value(s):

l + w + l + w = 20

Squares must have the same value for all 4 sides, so what number × 4 will equal 20? 5.

5 + 5 + 5 + 5 = 20

This means coordinates will be 5 units apart:

(-3 + 5, 5) = (2, 5)

(-3, 5 + 5) = (-3, 10)

Mark these coordinates on your grid as you go to double check the shape turns becomes a square:

(2, 5 + 5) = (2, 10)

Counting between them should equal 5 units for each side: I checked using the desmos graphing calculator online.

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ratelena [41]

Answer:

The no. of possible handshakes takes place are 45.

Step-by-step explanation:

Given : There are 10 people in the party .

To Find: Assuming all 10 people at the party each shake hands with every other person (but not themselves, obviously) exactly once, how many handshakes take place?

Solution:

We are given that there are 10 people in the party

No. of people involved in one handshake = 2

To find the no. of possible handshakes between 10 people we will use combination over here

Formula : $^nC_r=\frac{n!}{r!(n-r)!}$

n = 10

r= 2

Substitute the values in the formula

$^{10}C_{2}=\frac{10!}{2!(10-2)!}$

$^{10}C_{2}=\frac{10!}{2!(8)!}$

$^{10}C_{2}=\frac{10 \times 9 \times 8!}{2!(8)!}$

$^{10}C_{2}=\frac{10 \times 9 }{2 \times 1}$

$^{10}C_{2}=45$

No. of possible handshakes are 45

Hence The no. of possible handshakes takes place are 45.

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3 years ago

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Step-by-step explanation:

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3 years ago

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labwork [276]

Answer:

WHere is the question??

Step-by-step explanation:

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4 years ago

A construction company uses the function f(x), where x is the number of people working on a project, to model the amount of mone

Liono4ka [1.6K]

Answer:

Positive integers

Step-by-step explanation:

The domain is the people and the range is the money spent

People would be counted as positive integers, only the last answer choice considers this.

<u>So the answer is:</u>

Positive integers

8 0

3 years ago

Read 2 more answers

The second sample was the same size as the first, and the proportion of sales identified as organic was 0.4. How does the 95 per

enot [183]

Answer:

The summer interval is wider and has a greater point of estimate

Step-by-step explanation:

Assuming this problem: "An environmental group wanted to estimate the proportion of fresh produce sales indentified as organic in a grocery store. In the winter, the group obtained a random sample of sales from the store and used the data to construct a 95percent z-interval for a proportion (0.087,0.133). Six months later in the summer, the group obtained a second random sample of sales from the store. The second sample was the same size as the first, and the proportion of sales identified as organic was 0.4. How does the 95 percent z-interval for a proportion constructed from the summer sample compare to the winter interval? "

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

The confidence interval would be given by this formula

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

For the 95% confidence interval the value of $\alpha=1-0.95=0.05$ and $\alpha/2=0.025$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=1.96$

We can find the margin of error from the interval given on this case would be:

$ME= \frac{0.133-0.087}{2}=0.023$

And the point of estimate for the proportion obtained would be:

$\hat p = 0.133-0.023=0.11$

The margin of error for the proportion interval is given by this formula:

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

And on this case we have that $ME =0.023$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

And replacing into equation (b) the values from part a we got:

$n=\frac{0.11(1-0.11)}{(\frac{0.023}{1.96})^2}=710.95$

And rounded up we have that n=711

Now we know that we use the same sample size for the new confidence interval. And replacing into the confidence interval formula we got:

$0.4 - 1.96 \sqrt{\frac{0.4(1-0.4)}{711}}=0.364$

$0.4 + 1.96 \sqrt{\frac{0.4(1-0.4)}{711}}=0.436$

And the new 95% confidence interval would be given (0.364;0.436) has a width of 0.436-0.364=0.072. And the width for the previous confidence interval is 0.133-0.087= 0.046. So then the best answer is:

The summer interval is wider and has a greater point of estimate

7 0

3 years ago