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3 years ago

Rewrite 8x - 7 as the product of two factors

Mathematics

1 answer:

kykrilka [37]3 years ago

8 0

Answer:

factors are any group of number or expressions which, when multiplied, produce another number or expression.

Basic example: 4 can be broken into 2 factors---2 and 2. 2 times 2 = 4

Example using an unknown:

2X + 6 = 2 * (X + 3)

In the given problem, there is no whole-number common factor. A normal convention would be to factor based on the unknown term----thus 8X is factored into 8 and X.

So: 8X + 7 = 8 ( X + 7/8 )

The following would also be correct:

8X + 7 = 4 ( 2X + 7/4 )

Step-by-step explanation:

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Factorise fully the following:<br> a) 3x^3-9x<br> b) 4x^2+28^3

Leokris [45]

Answer:

3 x(x^2-3)

4x(x^2+5488)

Step-by-step explanation:

3 0

3 years ago

Write a division number story with an answer of 1/4

Rasek [7]

Answer:

Once upon a time I had 4 candies. there were 4 kids to share to (including me). what fraction of the candies does each child get

Step-by-step explanation:

4÷4=1

1/4

7 0

3 years ago

Read 2 more answers

Standard Error from a Formula and a Bootstrap Distribution Sample A has a count of 30 successes with and Sample B has a count of

tia_tia [17]

Answer:

Using a formula, the standard error is: 0.052

Using bootstrap, the standard error is: 0.050

Comparison:

The calculated standard error using the formula is greater than the standard error using bootstrap

Step-by-step explanation:

Given

Sample A Sample B

$x_A = 30$ $x_B = 50$

$n_A = 100$ $n_B =250$

Solving (a): Standard error using formula

First, calculate the proportion of A

$p_A = \frac{x_A}{n_A}$

$p_A = \frac{30}{100}$

$p_A = 0.30$

The proportion of B

$p_B = \frac{x_B}{n_B}$

$p_B = \frac{50}{250}$

$p_B = 0.20$

The standard error is:

$SE_{p_A-p_B} = \sqrt{\frac{p_A * (1 - p_A)}{n_A} + \frac{p_A * (1 - p_B)}{n_B}}$

$SE_{p_A-p_B} = \sqrt{\frac{0.30 * (1 - 0.30)}{100} + \frac{0.20* (1 - 0.20)}{250}}$

$SE_{p_A-p_B} = \sqrt{\frac{0.30 * 0.70}{100} + \frac{0.20* 0.80}{250}}$

$SE_{p_A-p_B} = \sqrt{\frac{0.21}{100} + \frac{0.16}{250}}$

$SE_{p_A-p_B} = \sqrt{0.0021+ 0.00064}$

$SE_{p_A-p_B} = \sqrt{0.00274}$

$SE_{p_A-p_B} = 0.052$

Solving (a): Standard error using bootstrapping.

Following the below steps.

Open Statkey
Under Randomization Hypothesis Tests, select Test for Difference in Proportions
Click on Edit data, enter the appropriate data
Click on ok to generate samples
Click on Generate 1000 samples ---- <em>see attachment for the generated data</em>

From the randomization sample, we have:

Sample A Sample B

$x_A = 23$ $x_B = 57$

$n_A = 100$ $n_B =250$

$p_A = 0.230$ $p_A = 0.228$

So, we have:

$SE_{p_A-p_B} = \sqrt{\frac{p_A * (1 - p_A)}{n_A} + \frac{p_A * (1 - p_B)}{n_B}}$

$SE_{p_A-p_B} = \sqrt{\frac{0.23 * (1 - 0.23)}{100} + \frac{0.228* (1 - 0.228)}{250}}$

$SE_{p_A-p_B} = \sqrt{\frac{0.1771}{100} + \frac{0.176016}{250}}$

$SE_{p_A-p_B} = \sqrt{0.001771 + 0.000704064}$

$SE_{p_A-p_B} = \sqrt{0.002475064}$

$SE_{p_A-p_B} = 0.050$

5 0

3 years ago

A boat is 122 meters from the base of a lighthouse. The lighthouse is 34 meters tall. The angle formed with the lighthouse and s

mojhsa [17]

Answer:

about 16°

Step-by-step explanation:

Make sure your calculator is in degree mode.

Drawing the right triangle, we see that the shorter leg is 34 meters, and the longer leg is 122 meters. So the angle of elevation is:

$\tan( \alpha ) = \frac{34}{122}$

$\alpha = { \tan }^{ - 1} \frac{34}{122} = 15.57$

3 0

2 years ago

A 72° sector in a circle has an area of 16.4π yd². What is the area of the circle? Use 3.14 for pi.

Dmitry [639]

The area of a sector of a circles is calculated by the equation A = πr^2 (theta/360). From the data of the sector, we determine the radius of the circle. THen, we can calculate for the area of the circle.

16.4π = πr^2 (72/360)
r = 9.06

Area of circle = πr^2
Area of circle = π(9.06)^2
Area of circle = 82π

6 0

3 years ago