Which word in the sentence below is an interrogative pronoun?

as a salesperson, jonathan is paid $50 per week of the total amount he sells. this week, he wants to earn at least $100. write a

erastova [34]

Answer: 1/5

Step-by-step explanation:50%50=1

100%50=0.5

7 0

4 years ago

The area of a triangular block is 49 square inches. If the base of the triangle is twice the height, how long are the base and t

andrezito [222]

1) Formula: area = height * base / 2

2) Call x the height:

height = x

base = 2x

3) State the equation:

(x)(2x) = 49 in^2

4) Solve the equation:

2x^2 = 49 in^s

x^2 = (49/2) in^2

x = √(49/2) in

x = 7√2 / 2 in = 3.5 √2 in

5) Solution:

height = 3.5 √2 in and base = 7√2 in

6) Verification: area = (7√2 in) (3.5√2 in) = 49 in^2

Answer: height = 3.5√2 in and base = 7√2 in.

5 0

3 years ago

Evaluate 1^3 + 2^3 +3^3 +.......+ n^3

Molodets [167]

Notice that

$(n+1)^4-n^4=4n^3+6n^2+4n+1$

so that

$\displaystyle\sum_{i=1}^n((n+1)^4-n^4)=\sum_{i=1}^n(4i^3+6i^2+4i+1)$

We have

$\displaystyle\sum_{i=1}^n((i+1)^4-i^4)=(2^4-1^4)+(3^4-2^4)+(4^4-3^4)+\cdots+((n+1)^4-n^4)$

$\implies\displaystyle\sum_{i=1}^n((i+1)^4-i^4)=(n+1)^4-1$

so that

$\displaystyle(n+1)^4-1=\sum_{i=1}^n(4i^3+6i^2+4i+1)$

You might already know that

$\displaystyle\sum_{i=1}^n1=n$

$\displaystyle\sum_{i=1}^ni=\frac{n(n+1)}2$

$\displaystyle\sum_{i=1}^ni^2=\frac{n(n+1)(2n+1)}6$

so from these formulas we get

$\displaystyle(n+1)^4-1=4\sum_{i=1}^ni^3+n(n+1)(2n+1)+2n(n+1)+n$

$\implies\displaystyle\sum_{i=1}^ni^3=\frac{(n+1)^4-1-n(n+1)(2n+1)-2n(n+1)-n}4$

$\implies\boxed{\displaystyle\sum_{i=1}^ni^3=\frac{n^2(n+1)^2}4}$

If you don't know the formulas mentioned above:

The first one should be obvious; if you add $n$ copies of 1 together, you end up with $n$ .
The second one is easily derived: If $S=1+2+3+\cdots+n$ , then $S=n+(n-1)+(n-2)+\cdots+1$ , so that $2S=n(n+1)$ or $S=\dfrac{n(n+1)}2$ .
The third can be derived using a similar strategy to the one used here. Consider the expression $(n+1)^3-n^3=3n^2+3n+1$ , and so on.

7 0

4 years ago

10. Each day, Valerie charges her lunch

Tomtit [17]

Simple, 3*15= 45

Answer= 45

hope this helped!

4 0

3 years ago

Read 2 more answers

A college student would like to investigate the prices of sandwiches offered near the campus. A sample of 50 shops that sell san

elena-14-01-66 [18.8K]

The interval from $9 to $10 contains the largest number of sandwich prices. Option B

<h3>Which is a correct statement regarding sandwich prices, based on the histogram?</h3>

Generally, A graph known as a histogram displays the frequency of occurrence of numerical data via the use of rectangles. The frequency of a variable's distribution is shown by its position along the vertical axis, which is the height of a rectangle (the amount, or how often that variable appears).

In conclusion, The greatest number of sandwich costs may be found in the range from $9 to $10. Alternative B