Angad, Caroline and Sarah share some sweets in the ratio 1:4:2. Angad gets 5 sweets. How many did Sarah get?

Which expression uses the greatest common factor and the distributive property to rewrite the sum 42 + 72?

wlad13 [49]

Answer:

The answer is 6(7 + 12) ⇒ 1st answer

Step-by-step explanation:

* Lets explain how to solve the problem

- Factors are the numbers you multiply together to get another number

- Ex: 4 × 5 = 20 ⇒ 4 and 5 are the factors of 20

- Factors of a number n are the numbers that can multiplied together

to give the number n

- Ex: The factors of 6 are 1 , 2 , 3 , 6 because 1 × 6 = 6 and 2 × 3 = 6

- The distributive property lets you multiply a sum by multiplying each

term separately and then add the products

- Ex: a(b + c) = ab + ac

* Lets solve the problem

- We want to find the greatest common factor in 42 + 72

∵ 42 = 1 × 42 , 2 × 21 , 3 × 14 , 6 × 7

∴ The factors of 42 are 1 , 2 , 3 , 6 , 7 , 14 , 21 , 42

∵ 71 = 1 × 72 , 2 × 36 , 3 × 24 , 4 × 18 , 6 × 12 , 8 × 9

∴ The factors of 72 are 1 , 2 , 3 , 4 , 6 , 8 , 9 , 12 , 18 , 24 , 36 , 72

- The common factors between 42 and 72 are the bold numbers

∵ The common factors between 42 and 72 are 1 , 2 , 3 , 6

∵ The greatest one of them is 6

∴ The greatest common factor of 42 and 72 is 6

- In the distributive property we have a number multiplying by a sum

of two numbers

∵ 42 ÷ 6 = 7 and 72 ÷ 6 = 12

- We can write 42 + 72 as 6 × 7 + 6 × 12 and take 6 as a common factor

∵ 42 + 72 = 6 × 7 + 6 × 12

- Take 6 as a common factor

∴ 42 + 72 = 6(7 + 12)

6 0

4 years ago

A researcher surveyed 150 high school students and found that 68% played a musical insturment. What would be a reasonable range

maria [59]

Answer:

The reasonable range for the population mean is (61%, 75%).

Step-by-step explanation:

The interval estimate of a population parameter is an interval of values that consist of the values within which the true value of the parameter lies with a certain probability.

The mean of the sampling distribution of sample proportion is, $\hat p$ .

One of the best interval estimate of population proportion is the 95% confidence interval for proportion,

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

Given:

n = 150

$\hat p$ = 0.68

The critical value of <em>z</em> for 95% confidence level is:

$z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96$

Compute the 95% confidence interval for proportion as follows:

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

$=0.68\pm1.96\sqrt{\frac{0.68(1-0.68)}{150}}\\\\=0.68\pm 0.0747\\\\=(0.6053, 0.7547)\\\\\approx (0.61, 0.75)$

Thus, the reasonable range for the population mean is (61%, 75%).

5 0

4 years ago

Slope passing through the points of (3,-3) and (2,-5)

umka2103 [35]

Answer:

Use the slope formula (y2-y1)÷(x2-x1)

Step-by-step explanation:

(-5-(-3))÷2-3

= (-2.5,-1)

4 0

3 years ago

Using the distributive property, which number completes the statement correctly?

12345 [234]

You just have to find what will make both sides equal. So calculate -4 x (-6+ 5.7)

4 0

3 years ago

the number line goes from 0 to 1 and is subdivided into tenths Describe where youd locate the point 15/25

Vlada [557]

Answer:

6/10

Step-by-step explanation:

Simplify 15/25 by dividing by 5/5

15/25 ÷ 5/5 = 3/5

Multiply 3/5 by 2/2 to convert to tenths

3/5 × 2/2 = 6/10

5 0

3 years ago