All categories

3 years ago

Evaluate the following limit.

Mathematics

1 answer:

Rus_ich [418]3 years ago

7 0

Answer:

-191

Step-by-step explanation:

A limit is the value that a function approaches as the input approaches some value.

We say $\displaystyle \lim_{x\rightarrow a}f(x)=L$ if f(x) approaches to L as x approaches to a.

To find: $\displaystyle \lim_{x\rightarrow -4}2x^3-4x^2+2x+9$

Solution:

Let $f(x)=2x^3-4x^2+2x+9$

On putting x = -4 in function $f(x)=2x^3-4x^2+2x+9$ , we get

$\displaystyle \lim_{x\rightarrow -4}2x^3-4x^2+2x+9\\=2(-4)^3-4(-4)^2+2(-4)+9\\=2(-64)-4(16)-8+9\\=-128-64-8+9\\=-128-63\\=-191$

You might be interested in

What is the slope of this line? A. 1/3 B. 1/2 C. 1 D. 2

HACTEHA [7]

Slope = rise / run

so answer is

C. 1

6 0

3 years ago

Read 2 more answers

I need help with this

maksim [4K]

Answer:

The answer is B

Step-by-step explanation:

6 0

2 years ago

A sample of n = 4 scores is obtained from a population with a mean of 70 and a standard deviation of 8. If the sample mean corre

jeka57 [31]

Answer:

The value of the sample mean is 78.

Step-by-step explanation:

We are given that a sample of n = 4 scores is obtained from a population with a mean of 70 and a standard deviation of 8.

Also, the sample mean corresponds to a z score of 2.00.

Let $\bar X$ = sample mean

The z-score probability distribution for a sample mean is given by;

Z = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\mu$ = population mean = 70

$\sigma$ = standard deviation = 8

n = sample size = 4

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

Now, we are given that the sample mean corresponds to a z score of 2.00 for which we have to find the value of sample mean;

So, z-score formula is given by ;

z-score = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ = $\frac{\bar X-70}{\frac{8}{\sqrt{4} } }$

2.00 = $\frac{\bar X-70}{\frac{8}{\sqrt{4} } }$

2.00 = $\frac{\bar X-70}{4 } }$

$\bar X = 70+(2 \times 4)$

$\bar X$ = 70 + 8 = 78

Therefore, the value of the sample mean is 78.

3 0

3 years ago

Can someone please help I appreciate it

kompoz [17]

Answer:

answer =6

Step-by-step explanation:

mark me as brainliest

5 0

3 years ago

Read 2 more answers

g People between the ages of 65 and 70 were studied to see if those who exercise more were healthier. One measure of health was

liubo4ka [24]

Answer:

If the person selected had high blood pressure, the probability that he or she did not exercise is P=0.643.

Step-by-step explanation:

We have a group of people between agss of 65 and 70.

They are divided in two groups regarding their amount of exercise: "none", "moderate" and "high".

The response variable is blood pressure, that was categorized as "normal"or "high".

Then, we have the frequencies table as:

Amount of exercise None Moderate High

Blood pressure High 54 23 7

Blood pressure Normal 86 76 32

We have to calculate the probability that, given that the person had high blood pressure, he or she did not exercise.

If the person had high blood pressure, it can be of the any of the 3 groups of exercise amount. There are 54 people with high blood pressure that did not exercise, 23 that did moderate amount of exercise, and 7 that did a high amount.

Then, the probability can be calculated dividing the amount of people that had high blood pressure and did not exercise, by all the people that have high blood pressure (regarding the amount of exercise):

$P(N | HP)=\dfrac{54}{54+23+7}=\dfrac{54}{84}=0.643$

If the person selected had high blood pressure, the probability that he or she did not exercise is P=0.643.

5 0

3 years ago