What percentage of a dollar is the value of 1 nickel and 3 pennies?

A runner covers 55 yards in 5.5 seconds. Find the runner's average speed in miles per hour.

marusya05 [52]

$V=\frac{s}{t},where\ V-speed,\ s-distence\ ,t-time\\\\V=\frac{55y}{5,5s}=10\frac{y}{s}=10\frac{0,000568m}{\frac{1}{3600}h}=\frac{0,00568m}{\frac{1}{3600}h}=0,00568\cdot3600\frac{m}{h}=\\\\=20,448\frac{m}{h}$

7 0

4 years ago

In a fruit cocktail, for every 15 ml of orange juice you need 25 ml of apple juice and 10 ml of coconut milk. What proportion of

frosja888 [35]

Answer:

3/10 is orange juice.

Step-by-step explanation:

Step 1: Find the total mL in the concoction

15 + 25 + 10 = 50 mL in a fruit cocktail

Step 2: Find the proportion of orange juice in 1 serving (50 mL) of cocktail

15/50 = 3/10

8 0

3 years ago

Please help on two math questions. I don’t understand how to do them.

Sidana [21]

When you represent intervals on the number line, you're including full dots, excluding empty dots, and you're considering numbers highlighted by the line.

In the first case, you've highlighted everything before -2 (full dot, thus included), and everything after 1 (empty dot, excluded). So, the set would be

$x\leq -2 \lor\ x>1$

or, in interval notation,

$(-\infty,-2]\cup (1,\infty)$

In the second case, you are looking for all numbers between -3 and 5. This interval is symmetric with respect to 1: you're considering all numbers that are at most 4 units away from 1, both to the left and to the right.

This means that the difference between your numbers at 1 must be at most 4, which is modelled by

$|x-1|\leq 4$

where the absolute values guarantees that you'll pick numbers to the left and to the right of 1.

3 0

3 years ago

Write out the first few terms of the series Summation from n equals 0 to infinity (StartFraction 2 Over 3 Superscript n EndFract

anyanavicka [17]

Answer:

$\sum\limits_{n=0}^{\infty} \frac{2}{3^n}\frac{(-1)^n}{5^n} = 15/8$

Step-by-step explanation:

The sum you are trying to understand is this.

$\sum\limits_{n=0}^{\infty} \frac{2}{3^n}\frac{(-1)^n}{5^n}$

Remember that in general when you have a geometric series

$\sum\limits_{n = 0}^{\infty} a*r^n$ you have that

$\sum\limits_{n = 0}^{\infty} a*r^n = \frac{a}{1-r}$ and that equality is true as long as $|r| < 1$ .

Therefore here we have

$\sum\limits_{n=0}^{\infty} \frac{2}{3^n}\frac{(-1)^n}{5^n} = \sum\limits_{n=0}^{\infty} 2* \big(\frac{-1}{3*5} \big)^n = \sum\limits_{n=0}^{\infty} 2* \big(\frac{-1}{15} \big)^n$ and $\big|\frac{-1}{15} \big| = \frac{1}{15} < 1$