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2 years ago

Which graph has the same end behavior as the graph of f(x) = –3x^3 – x^2 + 1?

Mathematics

1 answer:

ololo11 [35]2 years ago

4 0

To find out end behavior, we always look at the largest exponent (3 in this case) and the sign of the term with the largest exponent (negative in this case). We can rule out the first two choices because since it is a cubic graph (exponent of 3) the graph will be pointing in opposite directions. Then, the negative tells us that as the x values approache infinity, the y values will approach negative infinity. So the correct answer is the last choice.

Hope this helps

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A study of 25 graduates of four-year public colleges revealed the mean amount owed by a student in student loans was $55,051. Th

Kitty [74]

Answer:

The 90% confidence interval is $52561.13 < \mu < 57540.8$

Confidence interval for the population men between <u>$52561.13</u> up to <u>$57540.8</u>

Step-by-step explanation:

From the question we are told that

The sample size is $n = 25$

The sample mean is $\= x = \$ 55,051$

The standard deviation is $\sigma = \$ 7,568$

Given that the confidence level is 90% then the level of confidence is mathematically represented as

$\alpha = 100 -90$

$\alpha = 10\%$

$\alpha = 0.10$

Next we obtain the critical value of $\frac{\alpha }{2}$ from the normal distribution table the values is

$Z_{\frac{\alpha }{2} } = 1.645$

Generally the margin of error is mathematically represented as

$E = Z_{\frac{ \alpha }{2} } * \frac{ \sigma }{\sqrt{n} }$

substituting values

$E = 1.645 * \frac{ 7568}{ \sqrt{ 25} }$

$E = 2489.9$

The 90% confidence interval is mathematically evaluated as

$\= x -E < \mu < \= x +E$

substituting values

$55051 - 2489.8 < \mu < 55051 + 2489.8$

$52561.13 < \mu < 57540.8$

6 0

2 years ago

y = x2 + 11x + 24 is equivalent to the graph of which equation? y = (x + 8)(x + 3) y = (x + 4)(x + 6) y = (x + 9)(x + 2) y = (x

Montano1993 [528]

Answer:

First option: $y=(x + 8)(x + 3)$

Step-by-step explanation:

Given the quadratic equation $y = x^2 + 11x + 24$ , you need to factor it.

To do this, you need to find two number that when you add them you get 11 and when you multply them you get 24. These numbers are: 8 and 3.

Therefore, knowing this, you can factor the quadratic equation:

$y = x^2 + 11x + 24\\\\y=(x + 8)(x + 3)$

Then, $y = x^2 + 11x + 24$ is equivalent to the graph of the equation $y=(x + 8)(x + 3)$ , which matches with the first option.

7 0

2 years ago

What is the lateral area of a cylinder which has an element of 8 inches and a right section with a perimeter of 24 inches?

Greeley [361]

3 is the answer because 24/3=8

7 0

2 years ago

A ball is thrown upward and outward from a height of 77 feet. the height of the ball, f(x), in feet, can be modeled by f left

Oksi-84 [34.3K]

From the given function modeling the height of the ball:
f(x)=-0.2x^2+1.4x+7
A] The maximum height of the ball will be given by:
At max height f'(x)=0
from f(x),
f'(x)=-0.4x+1.4
solving for x we get:
-0.4x=-1.4
x=3.5ft
thus the maximum height would be:
f(3.5)=-0.2(3.5)^2+1.4(3.5)+7
f(3.5)=9.45 ft

b]
How far from where the ball was thrown did this occur:
from (a), we see that at maximum height f'(x)=0
f'(x)=-0.4x+1.4
solving for x we get:
-0.4x=-1.4
x=3.5ft
This implies that it occurred 3.5 ft from where the ball was thrown.

c] How far does the ball travel horizontally?
f(x)=-0.2x^2+1.4x+7
evaluationg the expression when f(x)=0 we get:
0=-0.2x^2+1.4x+7
Using quadratic equation formula:
x=-3.37386 or x=10.3739
We leave out the negative and take the positive answer. Hence the answer 10.3739 ft horizontally.

6 0

2 years ago

You typically buy all of your groceries at Grocery Mart. This week, your favorite cereal is on sale there, 4 boxes for $10. At F

julia-pushkina [17]

Answer:

B. Food market

Step-by-step explanation:

You typically buy all of your groceries at Grocery Mart. This week, your favorite cereal is on sale there, 4 boxes for $10. At Food Market, where you don’t typically shop, the same cereal is on sale for $2.25 a box. Based on price, which is the better value option?

A.Grocery Mart

B. Food Market

Grocery market:

4 boxes for $10

Unit price = cost / quantity

= $10 / 4 boxes

= $2.50 per box

Food market:

Price per box = $2.25

The better value option based on price is food market because it cost less to buy a box of cereal than grocery mart

8 0

2 years ago