Four times the sum of a number and eight times the number is 252. Find number

Use the distributive property to generate an equivalent expression for 2(10x-3)

mr Goodwill [35]

Answer:

20x - 6

Step-by-step explanation:

You just multiply 2 by 10x and by -3

5 0

2 years ago

Read 2 more answers

A rectangular prism has a width of 51 ft and a volume of 144 ft3. Find the volume of a similar prism with a width of 17 ft. Roun

meriva

Answer:

$5.3\ ft^3$

Step-by-step explanation:

Similar shapes with scale factor $k$ have proportional volumes with coefficient $k^3$ i.e.

$\dfrac{V_{large}}{V_{small}}=k^3,$

where

$k=\dfrac{\text{width of large prism}}{\text{width of small prism}}.$

Since

$\text{width of large prism}=51\ ft,\\ \\\text{width of small prism}=17\ ft,$

then

$k=\dfrac{51}{17}=3.$

Hence,

$\dfrac{144}{V_{small}}=3^3\Rightarrow V_{small}=\dfrac{144}{27}=\dfrac{16}{3}=5\dfrac{1}{3}\approx 5.3\ ft^3.$

7 0

2 years ago

£70 is divided between Natasha, Richard & Stephen so that Natasha gets twice as much as Richard, and Richard gets three time

Mekhanik [1.2K]

Answer:

£42

Step-by-step explanation:

The ratio of Richard's amount to Stephen's amount is ...

R : S = 3 : 1

The ratio of Natasha's amount to Richard's amount is ...

N : R = 2 : 1 = 6 : 3

Then the ratio of all three amounts is ...

N : R : S = 6 : 3 : 1

The proportion of the total that Natasha gets is ...

6/(6+3+1) = 6/10

so she gets ...

(6/10)×£70 = £42

Natasha gets £42.

5 0

2 years ago

Madison read 1/2 of a book in the morning, and she read some more at night. By the end of the day she still had 2/5 of the book

chubhunter [2.5K]

Answer: 1/10

Step-by-step explanation:

At the end of the day, she still had 2/5 of the book to read. Which meant that she had read 3/5 of the book. Since she read 1/2 of the book in the day, we would read 3/5 - 1/2 = 6/10 - 5/10 = 1/10 of the book at night.

3 0

2 years ago

Scores on a test are normally distributed with a mean of 81.2 and a standard deviation of 3.6. What is the probability of a rand

Misha Larkins [42]

Answer:

The probability of a randomly selected student scoring in between 77.6 and 88.4 is 0.8185.

Solution:

Given, Scores on a test are normally distributed with a mean of 81.2

And a standard deviation of 3.6.

We have to find What is the probability of a randomly selected student scoring between 77.6 and 88.4?

For that we are going to subtract probability of getting more than 88.4 from probability of getting more than 77.6

Now probability of getting more than 88.4 = 1 - area of z – score of 88.4

$\mathrm{Now}, \mathrm{z}-\mathrm{score}=\frac{88.4-\mathrm{mean}}{\text {standard deviation}}=\frac{88.4-81.2}{3.6}=\frac{7.2}{3.6}=2$

So, probability of getting more than 88.4 = 1 – area of z- score(2)

= 1 – 0.9772 [using z table values]

= 0.0228.

Now probability of getting more than 77.6 = 1 - area of z – score of 77.6

$\mathrm{Now}, \mathrm{z}-\text { score }=\frac{77.6-\text { mean }}{\text { standard deviation }}=\frac{77.6-81.2}{3.6}=\frac{-3.6}{3.6}=-1$

So, probability of getting more than 77.6 = 1 – area of z- score(-1)

= 1 – 0.1587 [Using z table values]

= 0.8413

Now, probability of getting in between 77.6 and 88.4 = 0.8413 – 0.0228 = 0.8185

Hence, the probability of a randomly selected student getting in between 77.6 and 88.4 is 0.8185.

4 0

2 years ago