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3 years ago

The sum of twice a number and 4 is equal to the sum of the number and 8

Mathematics

1 answer:

zalisa [80]3 years ago

3 0

Answer:

Step-by-step explanation:

Variable: X = Unknown Number

2x + 4 = x + 8

2x - x = 8 - 4

x = 4

Check:

2(4) + 4 = 4 + 8

8 + 4 = 12

12 = 12

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2 years ago

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Answer:

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2 years ago

Solve this rational equation 1/x-4 + x/x-2 = 2/x^2-6x+8

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3 years ago

Find the area of the shape shown below.

vlabodo [156]

Answer:

6 $cm^{2}$ (assuming the units is in centimetres)

Step-by-step explanation:

Hi, hope this helps!

Method 1:

Calculate this shape as a trapezium. This is a trapezium because it has one pair of parallel sides. The way to calculate the area of a trapezium is this:

- Half the sum of the parallel sides

- Multiply the perpendicular height between them

In this case, 4 and 2 are parallel, so we add them together (4 + 2 = 6) then we divide by two (6 ÷ 2 = 3). Then we multiply our answer by the perpendicular length between the two parallel sides (assuming the side on the left is at a right-angle, 3 x 2 = 6).

Method 2:

Calculate this shape as a rectangle + a triangle. If you split the shape so the pointy bit on the right becomes a triangle and the left becomes a square, you can calculate the area without knowing the formula for calculating a trapezium (see above ^).

- Area of the square / rectangle = length x width = 2 x 2 = 4

- Area of the triangle = 1/2 x length x width = 2 x 2 x 1/2 = 4 x 1/2 = 4 ÷ 2 = 2

Then we add the two areas together (4 + 2 = 6).

I hope this helped and I wasn't waffling on :)

Bluey

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3 years ago

Read 2 more answers

83 random samples were selected from a normally distributed population and were found to have a mean of 32.1 and a standard devi

arlik [135]

Answer:

$\frac{(82)(2.4)^2}{104.139} \leq \sigma^2 \leq \frac{(82)(2.4)^2}{62.132}$

$4.525 \leq \sigma^2 \leq 7.602$

Now we just take square root on both sides of the interval and we got:

$2.127 \leq \sigma \leq 2.757$

Step-by-step explanation:

Information given

$\bar X=32.1$ represent the sample mean

$\mu$ population mean (variable of interest)

s=2.4 represent the sample standard deviation

n=83 represent the sample size

Confidence interval

The confidence interval for the population variance is given by the following formula:

$\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma^2 \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}$

The degrees of freedom given by:

$df=n-1=8-1=7$

The confidence level is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a table to find the critical values.

The excel commands would be: "=CHISQ.INV(0.05,82)" "=CHISQ.INV(0.95,82)". so for this case the critical values are:

$\chi^2_{\alpha/2}=104.139$

$\chi^2_{1- \alpha/2}=62.132$

The confidence interval is given by:

$\frac{(82)(2.4)^2}{104.139} \leq \sigma^2 \leq \frac{(82)(2.4)^2}{62.132}$

$4.525 \leq \sigma^2 \leq 7.602$

Now we just take square root on both sides of the interval and we got:

$2.127 \leq \sigma \leq 2.757$

5 0

2 years ago