Find formulas for​ X, Y, and Z in terms of​ A, B, and C. It may be necessary to make assumptions about the size of a matrix in order to produce a formula.​
[A B C 0] [1 0 X Y] = [0 1 Z 0]
Find the formulas for​ X, Y, and Z. Note that I represents the identity matrix and 0 represents the zero matrix.

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.

Answer:

The key difference between simple interest and compound interest is that in simple interest, the interest is calculated based on the principal amount of the loan.

The formula is principal multiplied by time by rate divided by 100.

Compound interest on the other hand, has to do with the principal amount and accumulated interest on previous periods.

The difference affects the effectiveness of each because in SI, interest is calculated once, while in CI, there's accumulated interest.

Answer:

3x-11

Step-by-step explanation:

f (x) = 3x - 5

f(x-2)

Replace x in the function with x-2

f (x-2) = 3(x-2) - 5

           =3x-6 -5

           =3x-11

Answer:

The expected number of items that will be classified into group 1 is 100.

Step-by-step explanation:

For each observation, there are only two possible outcomes. Either it will be classified into group 1, or it will not. The probability of an observation being classified into group 1 is independent of any other observation, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

400 observations

This means that [tex]n = 400[/tex]

Four mutually exclusive groups. The probability of a randomly selected item being classified into any of the four groups is equal.

This means that [tex]p = 0.25[/tex]

Then the expected number of items that will be classified into group 1 is

[tex]E(X) = np = 400*0.25 = 100[/tex]

100 is the answer.

Answer:

N80

Step-by-step explanation:

One ruler is N60 and one pencil is N20.

Answer:

yes

Step-by-step explanation:

Answer:

Protein smoothie =14

Berry Smoothie= 29

Step-by-step explanation:

Let number of protein smoothie be X

Let number of berry smoothie be Y

1. X+Y=43

Y=43-X

2. 10X+6Y=314

5X+3Y= 157

5x+3(43-x)=157 (substitute)

5x+129-3x=157

2x=157-129

x=14

X+Y=43

Y=43-14

Y=29

Brainliest please~

Answer:

Enrollment at walnut junior = 142

Enrollment at walnut high = 710

Step-by-step explanation:

Let :

Enrollment at walnut junior = x

Enrollment at walnut high = 5x

Total enrollment in both schools = 852

Mathematically ;

x + 5x = 852

6x = 852

x = 142

5x = 142 * 5 = 710

Hence,

Enrollment at walnut junior = 142

Enrollment at walnut high = 710

Answer:

1/11 of a gallon

Step-by-step explanation:

He used 2/11 of 1/2 gallon

2/11 * 1/2 = 1/11 of a gallon

Answer:

[tex]\frac{1}{11}[/tex]

Step-by-step explanation:

Step 1:  Find how much of a gallon he used

[tex]\frac{2}{11} * \frac{1}{2} =\frac{2}{22}[/tex]

[tex]\frac{2}{22}=\frac{1}{11}[/tex]

Answer:  [tex]\frac{1}{11}[/tex]

Answer:

x = 12

Step-by-step explanation:

Δ ESR and Δ EGF are similar, then ratios of corresponding sides are equal, so

[tex]\frac{ES}{EG}[/tex] = [tex]\frac{ER}{EF}[/tex] , substitute values

[tex]\frac{45}{12x-3}[/tex] = [tex]\frac{55}{143}[/tex] ( cross- multiply )

55(12x - 3) = 6435 ( divide both sides by 55 )

12x - 3 = 117 ( add 3 to both sides )

12x = 120 ( divide both sides by 12 )

x = 10

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:

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.

Since this is a right triangle, we can use one of the three main trigonometric functions: sine, cosine, or tangent.

Remember: SOH-CAH-TOA

Looking from the given angle, we know the opposite side and want to know the adjacent side. Therefore, we should use the tangent function.

tan(54) = 16/BC

BC = 16/tan(54)

BC = 11.62 units

Hope this helps!

Answer:

193 in

Step-by-step explanation:

Volume of a triangular prism:

The volume of a triangular prism is the base area multiplied by the wedge, that is:

[tex]V = A_bw[/tex]

The base area is one half times the triangle base times it's height, so:

[tex]V = 0.5*b*h*w[/tex]

The wedge of cheese is 7 inches tall.

This means that [tex]w = 7[/tex]

The base of the cheese is shaped like a triangle with a base of 11 and a height of 5 inches.

This means that [tex]b = 11, h = 5[/tex]

Volume:

[tex]V = 0.5*b*h*w = 0.5*11*5*7 = 192.5[/tex]

Rounding, approximately 193 in.

Answer:

Step-by-step explanation:

f(x) + g(x) = 3x + 5 + 4x^2 - 2

f(x) + g(x) = 4x^2 + 3x + 3

f(x) + g(x) - h(x) = 4x^2 + 3x + 3 - (x^2 - 3x + 1)  Remove the brackets.

f(x) + g(x) - h(x) = 3x^2 +3x + 3 - x^2 + 3x - 1     Collect like terms

f(x)+g(x) - h(x) = 2x^2 + 6x + 2

Answer:

f(x)=3x^2+6x+2

Step-by-step explanation:

Equate whats inside (arguments) [tex]\sin[/tex] with base period of sine function [tex]2\pi[/tex] and solve for x to get period,

[tex]\pi x=2\pi\implies x=2[/tex]

So the period of the graph of the given function is precisely 2.

Hope this helps :)

Answer:

Step-by-step explanation:

bvjvhvghj

Answer:

f(x) = x + 3

Step-by-step explanation:

9514 1404 393

Answer:

  C)

Step-by-step explanation:

The table that has a constant ratio between y and x values is the one that represents a proportional relationship.

A) 2/4 ≠ 4/16

B) 1/1 ≠ 4/16

C) 6/8 = 12/16 = 18/24 = 30/40, a proportional relationship

Answer: y = 30x

Step-by-step explanation:

Because we are talking about over 8 hours. The question states that you get 30$ per hour for overtime hours. That means if you work over 8 hours your dollars per hour increases to 30. So because the amount of dollars increases to 30 you can infer that all you have to do is make the same equation as the 20 dollar's per hour equation. Except you put 30 making it y = 30x.

The equation of the line is.

y = (3/8)*x - 1.5

A general linear relationship can be written as:

y = a*x + b

Where a is the slope, and b is the y-intercept.

If the line passes through the points (x₁, y₁) and (x₂, y₂), we can write the slope as:

a = ( y₂ - y₁)/(x₂- x₁)

We define the y-intercept and the x-intercept as the points where the graph intersects the y-axis or the x-axis correspondingly.

Here we know that the x-intercept is 4, or we can write this as (4, 0)

we also know that the y-intercept is -1.5, or we can write this as (0, -1.5)

So we know two points of the line, this means that we can find the slope of the line:

a = (-1.5 - 0)/(0 - 4) = (1.5)/(4) = (3/2)*(1/4) = 3/8

Then the line is:

y = (3/8)*x + b

And remember that b is the y-intercept, which we know is equal to -1.5, so we can just replace it:

Then the equation of the line is.

y = (3/8)*x - 1.5

If you want to learn more about this topic, you can read:

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The answer is always your welcome

Answer:

always

Step-by-step explanatia;won:

9514 1404 393

Answer:

  yes

Step-by-step explanation:

No x-value is repeated, so these ordered pairs do represent a function.

Option C

Because in Side Angle Side there should be 2 sides and a angle stuffed between them.

In this If CD ≅ RS then √QRS is not ≅ and We cannot use SAS

Therefore the wrong statement is Option c

Answered by Gauthmath must click thanks and mark brainliest

Because in Side Angle Side there should be 2 sides and a angle stuffed between them.

In this If CD ≅ RS then √QRS is not ≅ . Option C is correct

To determine a congruency statement that would not result in Triangle BCD being congruent to Triangle QRS, we need to find a condition that does not satisfy the congruence criteria. The congruence of two triangles can be determined by considering their corresponding angles and sides.

Here are the possible congruency statements:

Angle-Angle-Side (AAS): If we have two angles of one triangle congruent to two angles of the other triangle, and the included side between these angles congruent, we can establish congruence. This statement could result in Triangle BCD being congruent to Triangle QRS.

Angle-Side-Angle (ASA): If we have two angles of one triangle congruent to two angles of the other triangle, and a side adjacent to one of these angles congruent, we can establish congruence. This statement could result in Triangle BCD being congruent to Triangle QRS.

Side-Angle-Side (SAS): If we have two sides of one triangle congruent to two sides of the other triangle, and the included angle between these sides congruent, we can establish congruence. This statement could result in Triangle BCD being congruent to Triangle QRS.

Side-Side-Side (SSS): If we have all three sides of one triangle congruent to the corresponding sides of the other triangle, we can establish congruence. This statement could result in Triangle BCD being congruent to Triangle QRS.

Based on these congruency statements, there is no option that would not result in Triangle BCD being congruent to Triangle QRS. All four statements have the potential to establish congruence between the two triangles.

To know more about  Angle , here

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Answer:

The two squares are 81 and 100, and their difference is 19

Step-by-step explanation:

Hey there!

Let's take out the square of 1st ten natural numbers to find out the exact answer.

1² = 1

2² = 4

3² = 9

4² = 16

5² = 25

6² = 36

7² = 49

8² = 64

9² = 81

10² = 100

Now; You can take any of these numbers and subtract from their squares.

So, let's check 6² and 5²

36-25 = 11 which is not equal to 19

Again check for 10²-9²

100 - 81 = 19 (True value)

Therefore, 19 can be expressed as the difference of square of 10 and 9.

Hope it helps!

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:

-4,-6

Step-by-step explanation:

x = y-2

2y = 4x+16

2y = 4(y-2) + 16

2y = 4y -8 + 16

-2y = 8

y = -4

x = -6

Công thức xác định tuổi thọ KL

Answer:

ytre

Step-by-step explanation:

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

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Answer:

See Below.

Step-by-step explanation:

We have the equation:

[tex]\displaystyle y = \left(3e^{2x}-4x+1\right)^{{}^1\! / \! {}_2}[/tex]

And we want to show that:

[tex]\displaystyle y \frac{d^2y }{dx^2} + \left(\frac{dy}{dx}\right) ^2 = 6e^{2x}[/tex]

Instead of differentiating directly, we can first square both sides:

[tex]\displaystyle y^2 = 3e^{2x} -4x + 1[/tex]

We can find the first derivative through implicit differentiation:

[tex]\displaystyle 2y \frac{dy}{dx} = 6e^{2x} -4[/tex]

Hence:

[tex]\displaystyle \frac{dy}{dx} = \frac{3e^{2x} -2}{y}[/tex]

And we can find the second derivative by using the quotient rule:

[tex]\displaystyle \begin{aligned}\frac{d^2y}{dx^2} & = \frac{(3e^{2x}-2)'(y)-(3e^{2x}-2)(y)'}{(y)^2}\\ \\ &= \frac{6ye^{2x}-\left(3e^{2x}-2\right)\left(\dfrac{dy}{dx}\right)}{y^2} \\ \\ &=\frac{6ye^{2x} -\left(3e^{2x} -2\right)\left(\dfrac{3e^{2x}-2}{y}\right)}{y^2}\\ \\ &=\frac{6y^2e^{2x}-\left(3e^{2x}-2\right)^2}{y^3}\end{aligned}[/tex]

Substitute:

[tex]\displaystyle y\left(\frac{6y^2e^{2x}-\left(3e^{2x}-2\right)^2}{y^3}\right) + \left(\frac{3e^{2x}-2}{y}\right)^2 =6e^{2x}[/tex]

Simplify:

[tex]\displaystyle \frac{6y^2e^{2x}- \left(3e^{2x} -2\right)^2}{y^2} + \frac{\left(3e^{2x}-2\right)^2}{y^2}= 6e^{2x}[/tex]

Combine fractions:

[tex]\displaystyle \frac{\left(6y^2e^{2x}-\left(3e^{2x} - 2\right)^2\right) +\left(\left(3e^{2x}-2\right)^2\right)}{y^2} = 6e^{2x}[/tex]

Simplify:

[tex]\displaystyle \frac{6y^2e^{2x}}{y^2} = 6e^{2x}[/tex]

Simplify:

[tex]6e^{2x} \stackrel{\checkmark}{=} 6e^{2x}[/tex]

Q.E.D.