John is 4 years older than becky, and john’s and becky’s combined ages is 58. how old are becky and john?

the length of the highway is 1500 miles. If 1 inch represents 150 miles, what is the length of the highway on the map?

NeX [460]

Answer:

10 inches.

Step-by-step explanation:

If 1 inch represents 150 miles, and there are 1500 miles covered by the map, then the length of the highway on the map is 10 inches.

4 0

2 years ago

Which of the following equations is equivalent to log(y)= 3.994 ?

Kisachek [45]

Answer:

The correct answer is option D: $y = 10^{3.994}$

Step-by-step explanation:

Given:

log(y)= 3.994

Solution:

A logarithm base b of a positive number x satisfies the following definition:

$y =log_b(x) => b^y =x$

For $x > 0, b >0, b \neq 1$

Also if no base b is indicated, the base of the logarithm is assumed to be 10 .

Thus, in log(y)= 3.994 base b is not indicated. so its base is assumed to be 10

now

$log_{10}(y)= 3.994$

Then

$y = 10^{3.994}$

4 0

2 years ago

Samantha received a loan from the bank of 4500 she’s plans on paying off the loan and for years at the end of four years Samanth

zheka24 [161]

At the end it will be 20% interest.

6 0

2 years ago

6. It took Juan 48 minutes to drive 12 miles, Calculate his speed in miles per hour,

GREYUIT [131]

Answer:

15 miles per hour

Step-by-step explanation:

First, lets find the number of miles he goes in 1 minutes.

That would be found by dividing the number of miles (12) by the number of minutes (48), so we have:

12/48 = 0.25 miles per minute

We want the speed in miles PER HOUR.

So, how many minutes are in an hour??

That is 60 mins = 1 hr

So, we need to multiply this by 60.So,

0.25 miles per minute * 60 minutes (1 hr) = 15 miles per hour

3 0

2 years ago

Jason swam 3 and one-half miles, then another 3 1/4th miles in one day. On the same day, Rachel swam 2 2/3rd miles, then another

Fynjy0 [20]

<h2>Hello!</h2><h2>The answer is:</h2>

Rachel swam $\frac{5}{12}$ miles or 0.42 miles more than Jason.

To calculate how many miles did Rachel swim more than Jason, we need to write the following equation:

$Difference=RachelMiles-JasonMiles$

Where,

Difference, is equal to the number of Miles that Rachel did more than Jason

RachelMiles, is equal to 2 2/3rd miles plus 4.5 miles.

Jason Miles, is equal to 3.5 miles plus 3 1/4th miles.

Also, we need to remember the following:

- How to convert mixed fractions to improper fractions,

$a\frac{b}{c}=a+\frac{b}{c}$

- How to add or subtract fractions and whole numbers.

$a+\frac{b}{c}=\frac{ac+b}{c}$

Now, we are given the following information:

Jason's miles:

$JasonMiles=3\frac{1}{2}+3\frac{1}{4} =(3+\frac{1}{2})+(3+\frac{1}{4})\\\\JasonMiles=(3+\frac{1}{2})+(3+\frac{1}{4})=(\frac{(2)*(3)+1}{2})+(\frac{(3)*(4)+1}{4})\\\\JasonMiles=(\frac{(2)*(3)+1}{2})+(\frac{(3)*(4)+1}{4})=\frac{7}{2}+\frac{13}{4}\\\\JasonMiles=\frac{(7)*(4)+(2)*(13)}{8}=\frac{28+26}{8}=\frac{54}{8}\\\\JasonMiles=\frac{54}{8}=\frac{27}{4}miles$

Rachel's miles:

$RachelMiles=2\frac{2}{3}+4\frac{1}{2}=(2+\frac{2}{3})+(4+\frac{1}{2})\\\\RachelMiles=(2+\frac{2}{3})+(4+\frac{1}{2})=(\frac{(2)*(3)+2}{3})+(\frac{(4)*(2)+1}{2})\\ \\RachelMiles=(\frac{(2)*(3)+2}{3})+(\frac{(4)*(2)+1}{2})=\frac{6+2}{3} +\frac{8+1}{2}\\\\RachelMiles=\frac{6+2}{3} +\frac{8+1}{2}=\frac{8}{3}+\frac{9}{2}\\\\RachelMiles=\frac{8}{3}+\frac{9}{2}=\frac{(8)*(2)+(3)*(9)}{(3)*(2)}\\\\RachelMiles=\frac{(8)*(2)+(3)*(9)}{(3)*(2)}=\frac{16+27}{6}=\frac{43}{6}miles$

Now, substituting the miles swam by Rachel and Jason into the equation, we have:

$Difference=\frac{43}{6}-\frac{27}{4}=\frac{(43)*(4)-(6)*(27)}{24}\\\\Difference=\frac{(43)*(4)-(6)*(27)}{24}=\frac{172-162}{24}\\\\Difference=\frac{172-162}{24}=\frac{10}{24}=\frac{5}{12}miles=0.42miles$

Hence, we found that Rachel swam 0.42 miles more than Jason.

Have a nice day!

7 0

2 years ago