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3 years ago

John and alisha randomly met at the local movie theater. what will affect their first impression of each other?

Mathematics

1 answer:

Vesna [10]3 years ago

7 0

How they dress, What movie they buy, and what snacks you buy

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An artist creates a cone-shaped sculpture for an art exhibit. If the sculpture is 8 feet tall and has a

nikitadnepr [17]

Answer:

192.92 ft^3

Step-by-step explanation:

volume of a cone = $\frac{1}{3}$ πr²h

π = 3.14

r = radius ]

h = height

the base of a cone is in the shape of a circle. thus, the circumference of the base is equal to the circumference of a circle

circumference of a circle= 2πr

30.144 = 2 x 3.14 x r

r = 30.144 / 6.28

r = 4.8

Volume = 1/3 x 3.14 x 4.8² x 8 = 192.92 ft^3

8 0

3 years ago

Estimate the integral ∫6,0 x^2dx by the midpoint estimate, n = 6

Anettt [7]

Splitting up the interval [0, 6] into 6 subintervals means we have

$[0,1]\cup[1,2]\cup[2,3]\cup\cdots\cup[5,6]$

and the respective midpoints are $\dfrac12,\dfrac32,\dfrac52,\ldots,\dfrac{11}2$ . We can write these sequentially as ${x_i}^*=\dfrac{2i+1}2$ where $0\le i\le5$ .

So the integral is approximately

$\displaystyle\int_0^6x^2\,\mathrm dx\approx\sum_{i=0}^5({x_i}^*)^2\Delta x_i=\frac{6-0}6\sum_{i=0}^5({x_i}^*)^2=\sum_{i=0}^5\left(\frac{2i+1}2\right)^2$

Recall that

$\displaystyle\sum_{i=1}^ni^2=\frac{n(n+1)(2n+1)}6$
$\displaystyle\sum_{i=1}^ni=\frac{n(n+1)}2$
$\displaystyle\sum_{i=1}^n1=n$

so our sum becomes

$\displaystyle\sum_{i=0}^5\left(\frac{2i+1}2\right)^2=\sum_{i=0}^5\left(i^2+i+\frac14\right)$
$=\displaystyle\frac{5(6)(11)}6+\frac{5(6)}2+\frac54=\frac{143}2$

8 0

2 years ago

Can someone help solve 1 + 2x = 7?

Yanka [14]

Answer:

Step-by-step explanation:

1+2x=7

7-1=6

2x=6

6/2=3

x=3

5 0

3 years ago

Read 2 more answers

A sheet of paper has a perimeter of 39 in. If the width of the paper is 8.5 in. What is the length of the sheet of paper?

natta225 [31]

Perimeter of a rectangle = 2L + 2W

Perimeter = 39
W = 8.5

we plug those into the perimeter equation and get
2L + 2(8.5) = 39

simplify
2L + 17 = 39

subtract 17 from both sides
2L = 22

divide both sides by 2
L = 11

therefore the length of the sheet of paper is 11 in.

7 0

2 years ago

Read 2 more answers

A teacher is making a history test composed of the same number of multiple-choice questions as short-answer questions. She estim

STALIN [3.7K]

Answer:

The inequality is $5.5n \leq 45$

Step-by-step explanation:

Total time:

The total time to complete the test is the sum of the number of multiple-choice questions multiplied by the time it takes to solve each and the number of short-answer questions multiply by the time it takes to solve each.

In this question:

Same number(n) of both.

Multiple-choice takes 2 minutes, short-answer takes 3.5 minutes. The total time is given by:

$T = 2n + 3.5n = 5.5n$

Write an inequality to determine how many questions, n, the teacher can include if the test must take students less than 45 minutes to complete.?

This means that:

$T \leq 45$

$5.5n \leq 45$

The inequality is $5.5n \leq 45$

5 0

2 years ago