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3 years ago

12 The perimeter of a rectangle

Mathematics

1 answer:

Karo-lina-s [1.5K]3 years ago

4 0

Answer:

Length = 9 cm

Width = 21 cm

Step-by-step explanation:

Length = x

Width = x + 12

Perimeter = 60 cm

2 * ( length + width ) = 60

2 * (x + x +12) = 60

2x + 12 = 60/2 = 30

2x = 30 - 12 = 18

x = 18/2 = 9

Length = 9 cm

Width = 9 + 12 = 21 cm

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Suppose that the population of the scores of all high school seniors who took the SAT Math (SAT-M) test this year follows a Norm

Vlad1618 [11]

Answer:

Confidence = $1-\alpha=1-0.01=0.99$

And then the confidence level would be given by 99%

Step-by-step explanation:

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".

Assuming the X follows a normal distribution

$X \sim N(\mu, \sigma)$

The distribution for the sample mean is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

$\bar x =512$ represent the sample mean

$\sigma=100$ represent the population standard deviation

n= 100 sample size selected.

The confidence interval is given by this formula:

$\bar X \pm z_{\alpha/2} \frac{\sigma}{\sqrt{n}}$ (1)

The marginof error for this case is given by Me=25.76. And we know that the formula for the margin of error is given by:

$Me=z_{\alpha/2} \frac{\sigma}{\sqrt{n}}$

$25.76=z_{\alpha/2} \frac{100}{\sqrt{100}}$

And we can find the critical value $z_{\alpha/2}$ like this:

$z_{\alpha/2}=\frac{25.76(\sqrt{100})}{100}=2.576$

And we know that on the right tail of the z score =2.576 we have $\alpha/2$ of the total area. We can find the area on the right of the z score using this excel code:

"=1-NORM.DIST(2.576,0,1,TRUE)" or using a table of the normal standard distribution, and we got 0.004998= $\alpha/2$ , so then $\alpha=0.00498*2=0.009995 \approx 0.01$ , and then we can find the confidence like this:

Confidence = $1-\alpha=1-0.01=0.99$

And then the confidence level would be given by 99%

8 0

3 years ago

A 30% solution of fertilizer is to be mixed with a 70% solution of fertilizer in order to get 40 gallons of a 60% solution. How

Murrr4er [49]

Answer:10 gallons of 30% solution and 30 gallons of 70% solution should be mixed.

Step-by-step explanation:

Let x represent the number of gallons of the 30% solution that should be mixed.

Let y represent the number of gallons of the 70% solution that should be mixed.

The total number of gallons of the mixture to be made is 40. This means that

x + y = 40

The 30% solution of fertilizer is to be mixed with a 70% solution of fertilizer in order to get 40 gallons of a 60% solution. This means that

0.3x + 0.7y = 0.6 × 40

0.3x + 0.7y = 24- - - - - - - - - - - - - -1

Substituting x = 40 - y into equation 1, it becomes

0.3(40 - y) + 0.7y = 24

12 - 0.3y + 0.7y = 24

- 0.3y + 0.7y = 24 - 12

0.4y = 12

y = 12/0.4

y = 30

x = 40 - y = 40 - 30

x = 10

5 0

3 years ago

solve this system of linear equations separate the x- and y- values with a comma 6x=-32-10y 11x=8-10y

Evgen [1.6K]

Hello :
<span>6x=-32-10y ...(1)
11x=8-10y ....(2)
by (1) : x = -32/6 -(10/6)y .....(*)
x = -16/3-(5/3)y
subst in (2) : 11(</span>-16/3-(5/3)y)-10y .......calculate y....then x by : (*)

5 0

3 years ago

Two of the angles in a triangle measure 149° and 90. What is the measure of the third<br> angle?

Inga [223]

Third angle =180° - (149° + 9°)
= 22°
Thanks me if is correct!

7 0

3 years ago

Plz help !!!!!!!!!!!

TiliK225 [7]

Answer:

The answer is 9.

4 0

4 years ago

Read 2 more answers