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3 years ago

The rectangle below has an area of x^2-7x+10square meters and a width of x - 5 meters.

Mathematics

1 answer:

timofeeve [1]3 years ago

5 0

The area of a rectangle is:

$\sf A=lw$

Plug in what we know:

$\sf x^2-7x+10=l(x-5)$

Factor the left side:

$\sf (x-2)(x-5)=l(x-5)$

Divide (x - 5) to both sides:

$\sf l=\boxed{\sf x-2}$

So the length is x - 2 meters.

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A high school had 2,300 students in 2010 which increased by 33% in the following four years. How many students are there in 2014

mr Goodwill [35]

Students in 2014 = (100% + 33%) × 2,300
students in 2014 = 133% × 2,300
students in 2014 = 133/100 × 2,300
students in 2014 = 3,059

There are 3,059 students in 2014

4 0

3 years ago

Assume that the paired data came from a population that is normally distributed. using a 0.05 significance level and dequalsxmin

Artemon [7]

"Assume that the paired data came from a population that is normally distributed. Using a 0.05 significance level and d = (x - y), find $\bar{d}$ , $s_{d}$ , the t-test statistic, and the critical values to test the claim that $\mu_{d} = 0$ "

You did not attach the data, therefore I can give you the general explanation on how to find the values required and an example of a random paired data.

For the example, please refer to the attached picture.

A) Find $\bar{d}$
You are asked to find the mean difference between the two variables, which is given by the formula:
$\bar{d} = \frac{\sum (x - y)}{n}$

These are the steps to follow:
1) compute for each pair the difference d = (x - y)
2) sum all the differences
3) divide the sum by the number of pairs (n)

In our example:
 $\bar{d} = \frac{6}{8} = 0.75$ 

B) Find $s_{d}$
You are asked to find the standard deviation, which is given by the formula:
 $s_{d} = \sqrt{ \frac{\sum(d - \bar{d}) }{n-1} }$

These are the steps to follow:
1) Subtract the mean difference from each pair's difference
2) square the differences found
3) sum the squares
4) divide by the degree of freedom DF = n - 1

In our example:
$s_{d} = \sqrt{ \frac{101.5}{8-1} }$
= √14.5
= 3.81

C) Find the t-test statistic.
You are asked to calculate the t-value for your statistics, which is given by the formula:
$t = \frac{(\bar{x} - \bar{y}) - \mu_{d} }{SE}$

where SE = standard error is given by the formula:
$SE = \frac{ s_{d} }{ \sqrt{n} }$

These are the steps to follow:
1) calculate the standard error (divide the standard deviation by the number of pairs)
2) calculate the mean value of x (sum all the values of x and then divide by the number of pairs)
3) calculate the mean value of y (sum all the values of y and then divide by the number of pairs)
4) subtract the mean y value from the mean x value
5) from this difference, subtract $\mu_{d}$
6) divide by the standard error

In our example:
SE = 3.81 / √8
= 1.346

The problem gives us $\mu_{d} = 0$ , therefore:
t = [(9.75 - 9) - 0] / 1.346
= 0.56

D) Find $t_{\alpha / 2}$
You are asked to find what is the t-value for a 0.05 significance level.

In order to do so, you need to look at a t-table distribution for DF = 7 and A = 0.05 (see second picture attached).

We find $t_{\alpha / 2} = 1.895$ 

Since our t-value is less than $t_{\alpha / 2}$ we can reject our null hypothesis!!

7 0

3 years ago

How many cubic centimeters of water can this paper cone cup hold?

Igoryamba

Answer:

150.72 cubic centimeter

Step-by-step explanation:

Given:-

Height of cone (h) = 9cm

Diameter of cone(d)=8cm

radius of cone(r)= $\frac{d}{2}$ = $\frac{8}{2} =4cm$

To calculate= Volume of cone( $V_{cone}$ )

$Volume\ of\ cone(V_{cone}) =\frac{1}{3} \times \pi \times r^{2} \times h$

$=\frac{1}{3} \times 3.14\times 4^{2} \times 9$

Volume of cone( $V_{cone}$ ) $=150.72\ cubic\ centimeter$

Therefore paper cone cup can hold 150.72 cubic centimeter of water.

5 0

3 years ago

What is 54 percent as a fraction in simplest form

atroni [7]

54% is 54 out of 100.
There for the numerator is 54 and the denominator is 100.

$\frac{54}{100}$

Now, both the top and the bottom can be divided by 2. So:

$\frac{54~divided~by~2}{100~divided~by~2}$ = $\frac{27}{50}$

$\frac{27}{50}$ can't be simplified anymore, therefore, 27/50 is 54% as a fraction.

~Hope this helped :)

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3 years ago

Read 2 more answers

an employee at a pet shop randomly selects fish from a tank for their 5 Guppies 4 platy fishes and 3 rasbora what is the probabi

noname [10]

The probability is 4/12 or 1/3
because the total of fish is 12 and the platy fish is 4 or 4 parts of the total 12.

5 0

3 years ago