A company produces 2 types of computers; desktops and laptops

Answer:

a) 0.0038 = 0.38% probability that the mean weight of the sample is less than 5.97 ounces.

b) Given a mean of 6.05 ounces, it is very unlikely that a sample mean of less than 5.97 ounces, which means that the true mean must be recalculated.

Step-by-step explanation:

To solve this question, we need to understand 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 z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes 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 of 6.05 ounces and a standard deviation of .18 ounces.

This means that [tex]\mu = 6.05, \sigma = 0.18[/tex]

Sample of 36:

This means that [tex]n = 36, s = \frac{0.18}{\sqrt{36}} = 0.03[/tex]

a. Find the probability that the mean weight of the sample is less than 5.97 ounces.

This is the p-value of z when X = 5.97. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{5.97 - 6.05}{0.03}[/tex]

[tex]Z = -2.67[/tex]

[tex]Z = -2.67[/tex] has a p-value of 0.0038.

0.0038 = 0.38% probability that the mean weight of the sample is less than 5.97 ounces.

b. Suppose your random sample of 36 cans of salmon produced a mean weight that is less than 5.97 ounces. Comment on the statement made by the manufacturer.

Given a mean of 6.05 ounces, it is very unlikely that a sample mean of less than 5.97 ounces, which means that the true mean must be recalculated.

9514 1404 393

Answer:

  6

Step-by-step explanation:

The number of distinct zeros in the product will be the union of the sets of zeros. Duplicated values are not distinct, so show in the union of sets only once.

  F = {-2, 3, 7}

  G = {-3, -1, 4, 7}

  F∪G = {-3, -2, -1, 3, 4, 7} . . . . . . a 6-element set

The product has 6 distinct zeros.

_____

As you may notice in the graph, the duplicated zero has a multiplicity of 2 in the product.

Answer:

75cedis

[tex]50 = 40\% \\ 60\%[/tex]

The amount of money Kofi earned today from mowing lawns is 30 cedis.

Percentage can be described as a fraction of a number multiplied by 100. Percentage is represented with this sign - %.

In order to determine the amount Kofi earned today, this formula would be used:

Percentage Kofi earned today x amount Kofi earned yesterday

60% x 50 cedis

0.6 x 50 cedis

= 30 cedis

To learn more about percentages, please check: https://brainly.com/question/92258?referrer=searchResults

Step-by-step explanation:

xx is the Roman number of 20

Answer:

[tex][1, -4 ,5][/tex]

Step-by-step explanation:

In this question we are multiplying together two matrices. When we multiply a (1 x 3) matrix with a (3 x 3) matrix, we get a (1 x 3) matrix.

To compute each value, all you need to do is take the each value in each row in the first matrix, and multiply it by each value in each column of the second matrix and add up the result. So let's do that.

[tex]a = (2 * 1) + (1 * -1) + (0 * 0) = 2 - 1 + 0 = 1[/tex]

[tex]b = (2 * -1) + (1 * -2) + (0 * 1) = -2 -2 = -4[/tex]

[tex]c = (2 * 2) + (1 * 1) + (0 * 1) = 4 + 1 + 0 = 5[/tex]

Answer:

3 pants are $20.55

4 shirts are $47.9

Step-by-step explanation:

a pant is $6.85 × 3= $20.55

68.45 - 20.55 = $47.9

$47.9 ÷ 4 = $11.98 a shirt

Answer:

b(-2,-5)

Step-by-step explanation:

Answer:

a. These four vectors are dependent because there are columns of 3 by 4 matrix with one free variable.

b. If one is a multiple of other

c. c1v1 + c20 = 0 has nontrivial solution.

Step-by-step explanation:

Any set of 4 or more vectors must be linearly dependent. The non trivial combination of vector may produce zero as the set is linearly dependent. The vector v1 and v2 will be dependent if one is the multiple of the other.

Hi there!

[tex]\large\boxed{\frac{1}{18}}[/tex]

1/3x = 6

Begin by multiplying both sides by 3 to cancel the fraction:

1/x = 18

Take the reciprocal of both sides:

x = 1/18

Answer:

1/18

Step-by-step explanation:

I N E E D P O I N T S :O)

Answer:

[tex]B =102[/tex]

[tex]Y = 32[/tex]

Step-by-step explanation:

Solving (47):

To solve for B, we have:

[tex]B + 50 + 28 = 180[/tex] --- sum of angles in a triangle

This gives

[tex]B + 78 = 180[/tex]

Collect like terms

[tex]B =- 78 + 180[/tex]

[tex]B =102[/tex]

Solving (48):

To solve for Y, we have:

[tex]X + Y+ Z = 180[/tex] --- sum of angles in a triangle

This gives

[tex]Y = 180 - X - Z[/tex]

Where

[tex]W+ X=180[/tex] -- angle on a straight line

Solve for X

[tex]X=180 -W[/tex]

[tex]X=180 -100 = 80[/tex]

So, we have:

[tex]Y = 180 - X - Z[/tex]

[tex]Y = 180 - 80 - 68[/tex]

[tex]Y = 32[/tex]

What do you personaly feel like is most dificult.

For me its rembering minus signs

Answer:

31) 4d + 28            33) 10 + 5

Step-by-step explanation:

31) 4 ( d + 7) = 4 x 7 = 28 = 4d + 28

33) 5 ( 2m + 1 ) = 5. 2m + 5 . 1: 10m + 5

Answer:

C

Step-by-step explanation:

Since the triangles are similar, the scale factor is 100/5=20. So L/15=20, L=300

9514 1404 393

Answer:

  C)  12 cm

Step-by-step explanation:

In a 30°-60°-90° triangle, the ratios of side lengths are ...

  1 : √3 : 2

This means the hypotenuse (AC) is 2/√3 times the length of the long side (AB).

  (10 cm)(2/√3) = 20/√3 cm ≈ 11.55 cm

Rounded to the nearest cm, the length of AC is 12 cm.

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

The question is somewhat poorly posed because the equation doesn't involve θ at all. I assume the author meant to use x.

sec(x) = csc(x)

By definition of secant and cosecant,

1/cos(x) = 1/sin(x)

Multiply both sides by sin(x) :

sin(x)/cos(x) = sin(x)/sin(x)

As long as sin(x) ≠ 0, this reduces to

sin(x)/cos(x) = 1

By definition of tangent,

tan(x) = 1

Solve for x :

x = arctan(1) + nπ

x = π/4 + nπ

(where n is any integer)

In the interval 0 ≤ x ≤ 2π, you get 2 solutions when n = 0 and n = 1 of

x = π/4   or   x = 5π/4

Answer:

a) 0.1295

b) The 95% confidence interval for the population proportion of disks which are defective is (0.1071, 0.1519).

Step-by-step explanation:

Question a:

112 out of 865, so:

[tex]\pi = \frac{112}{865} = 0.1295[/tex]

Question b:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 865, \pi = 0.1295[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].  

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1295 - 1.96\sqrt{\frac{0.1295*0.8705}{865}} = 0.1071[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1295 + 1.96\sqrt{\frac{0.1295*0.8705}{865}} = 0.1519[/tex]

The 95% confidence interval for the population proportion of disks which are defective is (0.1071, 0.1519).

Answer:

Option (D) x≥ 0 is absolutely correct

Step-by-step explanation:

The reason is that the square root function is defined for only non negative numbers.

Answer: x is greater than or equal to 0

Step-by-step explanation:

Step-by-step explanation:

Measure of Angle 1 is 115 due to corresponding angles postulate

Measure of Angle 2 is 65 is linear pair postulate.

Answer:

only 4 is incorrect...

1,450,000 = 1.45 x [tex]10^{6}[/tex] NOT

1,450,000 = 1.45 x [tex]10^{7\\}[/tex]

Step-by-step explanation:

Answer:

Answer is D.

Step-by-step explanation:

Let the inverse be m:

[tex]{ \sf{m = \sqrt{x} - 8 }} \\ { \sf{m + 8 = \sqrt{x} }} \\ { \sf{x = {(m + 8)}^{2} }} \\ { \bf{f {}^{ - 1} (x) = {(x + 8)}^{2} }}[/tex]

Domain:

[tex]{ \sf{x \geqslant - 8}}[/tex]

Answer:

2

Step-by-step explanation:

33

Answer:

(c) (f-g ) (x) = 6x*3 -2x*2 +4x -8

Answer: y = -3/2x + 5

Step-by-step explanation:

Slope-intercept form: y = mx + b

y = -3/2x + 5

Answer:

y = -3/2x + 5 totally

Step-by-step explanation:

Answer:

77

Step-by-step explanation:

Currently:

Talk to 8 customers per hour, work 8 hours, so:

Talk to 8*8 = 64 customers.

With the increase:

Has to increase by 20%, so 64 is multiplied by 1 + 0.2 = 1.2. Then

64*1.2 = 76.8

Rounding up, 77 is the answer.

Answer:

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