Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 3x^4 − 4x^3 − 12x^2 + 1, [−2, 3]

Answer:

0.9987 = 99.87% probability that the mean weight of 4 eggs in a package is less than 68.5g

Step-by-step explanation:

To solve this question, we use the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value 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. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean weight of 67g and a sample standard deviation of 1g.

This means that [tex]\mu = 67, \sigma = 1[/tex]

Sample of 4

This means that [tex]n = 4, s = \frac{1}{\sqrt{4}} = 0.5[/tex]

What is the probability that the mean weight of 4 eggs in a package is less than 68.5g?

This is the pvalue of Z when X = 68.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{68.5 - 67}{0.5}[/tex]

[tex]Z = 3[/tex]

[tex]Z = 3[/tex] has a pvalue of 0.9987

0.9987 = 99.87% probability that the mean weight of 4 eggs in a package is less than 68.5g

Answer:

-10

Step-by-step explanation:

Khan

Answer:

An = 32 - (4*(n-1))

Step-by-step explanation:

the starting term for this pattern is 32 (which you will need to include in the "rule")

you also know that the next term is the previous term - 4

so!

we can write this pattern as

An = 32 - (4*(n-1))

An = any number of term in the pattern

- ex). A2 = 28, A3 = 24, etc

n = the nth term

- the 3rd term = 24, the fourth term = 20, etc

Me das mas información?

Answer:

1

Step-by-step explanation:

Answer:

small is 0.018

medium is 0.016

large is 0.010

Answer:

B

Step-by-step explanation:

I'm pretty sure

Answer:

0.6892 = 68.92% of bottles are within specification.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value 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. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

On average, each bottle contains 2.07 liters of soda, with a standard deviation of 0.06 liters.

This means that [tex]\mu = 2.07, \sigma = 0.06[/tex]

The plant’s quality manager wants to determine how well the process is operating.

To do this, we find the proportion of bottles within specification.

The specification limits for a bottle of soda are 2.1 liters and 1.9 liters

This is the pvalue of Z when X = 2.1 subtracted by the pvalue of Z when X = 1.9. So

X = 2.1

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{2.1 - 2.07}{0.06}[/tex]

[tex]Z = 0.5[/tex]

[tex]Z = 0.5[/tex] has a pvalue of 0.6915.

X = 1.9

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{1.9 - 2.07}{0.06}[/tex]

[tex]Z = -2.83[/tex]

[tex]Z = -2.83[/tex] has a pvalue of 0.0023

0.6915 - 0.0023 = 0.6892

0.6892 = 68.92% of bottles are within specification.

Answer:

were is the graph lol

9514 1404 393

Answer:

  33°

Step-by-step explanation:

The law of cosines tells you ...

  a² = b² +c² -2bc·cos(A)

Solving for A, we get ...

  A = arccos((b² +c² -a²)/(2bc))

  A = arccos((15² +24² -14²)/(2·15·24)) = arccos(605/720)

  A ≈ 32.8305°

The smallest angle is about 33°.

Answer:

0.04

Step-by-step explanation:

Using absolute value |.02|+|.-02|= .04

Answer:

wssp i can help

Step-by-step explanation:

Answer:

x = 6 , y = 0   (x , y) = (6 , 0)

x = 12, y = 3   (x , y) = (12 , 3)

x = 24, y = 9   (x , y) = (24 , 9)

Step-by-step explanation:

Simply plug in a x, and find a y that would make the equation true:

When x = 6:

6 - 2y = 6

6 (-6) - 2y = 6 (-6)

-2y = 0

(-2y)/-2 = (0)/-2

y = 0

When x = 6, y = 0    (x , y) = (6 , 0)

When x = 12:

12 - 2y = 6

12 (-12) -2y = 6 (-12)

-2y = -6

(-2y)/-2 = (-6)/-2

y = 3

When x = 12, y = 3   (x , y) = (12 , 3)

When x = 24:

24 - 2y = 6

24 (-24) - 2y = 6 (-24)

-2y = -18

(-2y)/-2 = (-18)/-2

y = 9

When x = 24, y = 9   (x , y) = (24 , 9)

~

We have a linear equation here.

3 - 4x = 12

Subtract 3 from both sides.

3 - 3 - 4x = 12 - 3

-4x = 9

Divide both sides by -4 to find x.

-4x/-4 = 9/-4

x = -9/4

The value of solution of expression is,

⇒ x = - 9 / 14

WE have to given that;

A mathematical expression is,

⇒ 3 - 4x = 12

Now, WE can simplify as;

⇒ 3 - 4x = 12

Add 4x both side,

⇒ 3 - 4x + 4x = 12 + 4x

⇒ 3 = 12 + 4x

Subtract 12 both side, we get;

⇒ 3 - 12 = 14x

⇒ - 9 = 14x

⇒ x = - 9 / 14

Thus, The value of solution of expression is,

⇒ x = - 9 / 14

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ6

Answer:

The 99% confidence interval to estimate the mean breaking weight for this type cable is between 772.9 lb and 785.1 lb.

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 46 - 1 = 45

99% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 45 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.99}{2} = 0.995[/tex]. So we have T = 2.69

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 2.69\frac{15.4}{\sqrt{46}} = 6.1[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 779 - 6.1 = 772.9 lb

The upper end of the interval is the sample mean added to M. So it is 779 + 6.1 = 785.1 lb

The 99% confidence interval to estimate the mean breaking weight for this type cable is between 772.9 lb and 785.1 lb.

Answer:

B

Step-by-step explanation:

Put "Volume of a Cone" in your browser and all you have to do is type the height and radius.

Answer:

Y = 13

Step-by-step explanation:

You can use the sine rule to solve this.  The sine rule states that:

Sin(a) / A = Sin(b) / B = Sin(c) = C

In other words the sine of the angle in any corner in a triangle, divided by the length of the opposite side, will be equal to that of the other two sides as well.  

In this case, we can take the ratio between the sine of the right angle, and each of our hypotenuses, and state them as equal, giving us the solution:

sin(90) / (5y + 13) = sin(90) / 6y

1 / (5y + 13) = 1 / 6y

5y + 13 = 6y

6y - 5y = 13

y = 13

Answer:

abdef (those are the answers)

Step-by-step explanation:

Answer:

all but C

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

60x9 =540

Answer:

option D

the set of all points that are a fixed distance from a given point

hope it helps

Answer:

on   math  way you can take a picture of your problem. hope those helps

Step-by-step explanation:

Answer:

77°

Step-by-step explanation:

As we can see ABCD is a cyclic quadrilateral so opposite angles of a cyclic quadrilateral is supplementary.

< A + <B = 180° { being opposite angles of cyclic quadrilateral }

2x + 9° + 3x + 1° = 180°

5x + 10° = 180°

5x = 180° - 10°

5x = 170°

x = 170° / 5

x = 34°

Now

< A = 2x + 9°

= 2 * 34° + 9°

= 77°

Hope it will help :)❤

Answer:

52 pounds

Step-by-step explanation:

2 x 26= 52

Answer:

C. Acute; isosceles

Step-by-step explanation:

As you can see 2 sides of the triangle are equal to 10 which means they are congruent. It's an isosceles triangle because it has two congruent sides.

You can also see that none of the angles form 90 degrees or more which means they are acute angles.

Hope that helps

Answer:Some functions have asymptotes because the denominator equals zero for a particular value of x or because the denominator increases faster than the numerator as x increases.

Step-by-step explanation:

Answer:

The school sold 130 candles

Step-by-step explanation:

Given that the plants sold for $12.50 each and the  candles sold for $3.75 each. If the  school raised raised $3,987.50 and sold 410 candles and plants altogether then the number of candles and plants sold may be computed simultaneously as follows:

Let the number of candles sold be c and the number of plants sold be p. If the school sold 410 candles and plants altogether

p + c = 410

p = 410 - c

if the plants sold for $12.50 each and the  candles sold for $3.75 each and the school raised raised $3,987.50

12.5p + 3.75c = 3,987.50

12.5(410 - c) + 3.75c = 3,987.50

5125 -12.5c +3.75c = 3,987.50

-8.75c = 3,987.50 - 5125

-8.75c = -1137.5

c = -1137.5/-8.75

= 130

Answer:

48 ounces

Step-by-step explanation:

16 ounces per pound

3 x 16 = 48 ounces

Answer:

The appropriate alternative hypothesis if he wanted to substantiate his suspicion would be [tex]H_{a}: \mu > 238[/tex]

Step-by-step explanation:

At the null hypothesis, we test that the mean is equal to a certain value.

At the alternate hypothesis, we test that the mean is different, less than or more than the mean value tested at the null hypothesis.

The historical U.S. mean unemployment insurance benefit was reported to be $238 per week.

This means that the null hypothesis is:

[tex]H_{0}: \mu = 238[/tex]

A researcher in the state of Virginia anticipated that sample data would show evidence that the mean weekly unemployment insurance benefit in Virginia was above the national level.

This means that the alternate hypothesis is:

[tex]H_{a}: \mu > 238[/tex]