Find the volume of the given prism. round to the nearest tenth if necessary.

Answers

Answer 1

Answer: Volume of triangular prism = area of triangle x length.
Here, the triangle is an equilateral triangle with sides 14yds
Area of the triangle = 1/2 x 14 x 14 x sin 60 = 84.87 square yds
volume of the triangular prism = 84.87 x 25 = 2,121.8 cubic yds

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How do i solve 3x² - 8x + 2 = 0 using quadratic formula?

Answers

$3x^2 - 8x + 2 = 0\n \na=3 , \ \ b=-8 , \ \ c=2 \n \nx_(1)=(-b-√(b^2-4ac))/(2a) =(8-√( (-8)^2-4 \cdot 3\cdot 2))/(2 \cdot 3) =(8-√( 64-24 ))/(6) =\n \n =(8-√(40 ))/(6) = ( 8-√(4\cdot 10 ) )/(6) = ( 8-2√( 10 ))/(6) = (2 (4-√( 10 )))/(6) = ( 4-√( 10 ) )/(3)$

$x_(2)=(-b+√(b^2-4ac))/(2a) =(8+√( (-8)^2-4 \cdot 3\cdot 2))/(2 \cdot 3) = ( 4+√( 10 ) )/(3)$

$x = (-b +/- √(b^2 - 4ac))/(2a)$

$x = (-(-8) +/- √((-8)^2 - 4(3)(2)))/(2(3))$

$x = (8 +/- √(64 - 24))/(6)$

$x = (8 +/- √(40))/(6)$

$x = (8 +/- 6.31)/(6)$

$x = (14.32)/(6)$ x ≈ 2.39

$x = (1.68)/(6)$ x ≈ 0.28

Population since 2000 has been approximately linear. In 2006 the population was 1148 and in 2014 the population was 1348. What is the rate of population growth?

Answers

Answer:

2.03% Rate of Population Growth.

Step-by-step explanation:

According to the Question,

Given, In 2006 the population was 1148 and in 2014 the population was 1348.

2006⇒2014 (8 Years)

So, $1148 * (1+(x)/(100) )^(8) = 1348$

$(1+(x)/(100) ) = \sqrt[8]{1.1742}$

(1 + x/100) = 1.0202

x/100 = 0.020276

x = 2.03% Rate of Population Growth

The two-way table shows the distribution of book style to genre. Miguel claims that given that the book is paperback (PB) does not affect the outcome that the book is nonfiction (NF).

Answers

Answer:

Yes, the two events are independent because P(NF|PB)=P(NF).

Step-by-step explanation:

Xian and his cousin Kai both collect stamps, and Kai has 68 stamps. The boys recently joined different stamp collecting clubs. Xian’s club sill send him 12 new stamps per month. Kai’s club will send him 8 new stamps per month. After how many months will Xian and Kai have the same number of stamps? How many stamps will each have?

Answers

Assuming that Xian starts with 0 stamps, you set the equations equal to each other to find what month they have the same amount of stamps.

(68 from Kai's original stamps) (8 from how many per month)
(0 from Xian's original stamps) (12 from how many per month)
68+8m=0+12m
solve for m in this equation and you get 68=4m
and 68/4 = 17 months

For how many stamps each will have, you plug in 17 into m in Xian's equation (you could do either but Xian's is easier):
0+12m
0+12(17)=204
204 stamps.

Hope this helped, it was kinda long lol

A 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 4.5, 6.75, 10.125, 15.1875.What is the multiplicative rate of change of the exponential function represented in the table?

1.5
2.25
3.0
4.5

Answers

The rate of change for the given function is 2.25. Therefore, option B is the correct answer.

What is rate of change of a function?

The rate of change, or the slope, is calculated as Δy/Δx , or (y2−y1)/(x2−x1). The slope-intercept equation of a line is y=mx+b , where m is the slope and b is the initial value.

From the given table, we have (1, 4.5), (2, 6.75), (3, 10.125) and (4, 15.1875).

Using coordinate points (1, 4.5) and (2, 6.75), we get

Rate of change = (6.75-4.5)/(2-1)

= 2.25

Therefore, option B is the correct answer.

Learn more about the rate of change here:

brainly.com/question/8223651.

#SPJ6

Answer:

its 3.0

Step-by-step explanation:

ik bc i took the test