Suppose you just received a shipment of ten televisions. Two of the televisions are defective. If two televisions are randomly selected without replacement, compute the probability that both televisions do not work.

Statement 3:

Reason: Law of cosines

Statement 4:

Reason: Law of cosines

Proof

We have the following situation:

Because the law of cosines,

Therefore,

The solution of the given system of equations is x = -4, y = 5 and z = 2 is the answer.

The system of equations given below:x + 2y + 3z = 11;2x + 4y + 5z = 21;3x + 5y + 6z = 27.

Here, we will solve this system of equations using inverse of the matrix method as follows:

We can write the given system of equations in matrix form as AX = B where, A = [1 2 3; 2 4 5; 3 5 6], X = [x; y; z] and B = [11; 21; 27].

The inverse of matrix A is given by the formula: A-1 = (1/ det(A)) [d11 d12 d13; d21 d22 d23; d31 d32 d33]  where,

d11 = A22A33 – A23A32 = (4 × 6) – (5 × 5) = -1,

d12 = -(A21A33 – A23A31) = -[ (2 × 6) – (5 × 3)] = 3,

d13 = A21A32 – A22A31 = (2 × 5) – (4 × 3) = -2,

d21 = -(A12A33 – A13A32) = -[(2 × 6) – (5 × 3)] = 3,

d22 = A11A33 – A13A31 = (1 × 6) – (3 × 3) = 0,

d23 = -(A11A32 – A12A31) = -[(1 × 5) – (2 × 3)] = 1,

d31 = A12A23 – A13A22 = (2 × 5) – (3 × 4) = -2,

d32 = -(A11A23 – A13A21) = -[(1 × 5) – (3 × 3)] = 4,

d33 = A11A22 – A12A21 = (1 × 4) – (2 × 2) = 0.

We have A-1 = (-1/1) [0 3 -2; 3 0 1; -2 1 0] = [0 -3 2; -3 0 -1; 2 -1 0]

Now, X = A-1 B = [0 -3 2; -3 0 -1; 2 -1 0] [11; 21; 27] = [-4; 5; 2]

Therefore, the solution of the given system of equations is x = -4, y = 5 and z = 2.

know more about matrix method

https://brainly.com/question/32106604

#SPJ11

Laurel must increase her net income to $10,000 in order to keep her housing costs at 25%.

To determine how much Laurel must increase her net income in order to keep her housing costs at 25%, we need to know the following information:

The amount of Laurel's new mortgage, which is $2500

The percentage of Laurel's net income that she wants to use for housing costs, which is 25%

To find the amount of net income that Laurel needs to maintain a housing cost of 25%, we can use the following formula:

Net income = Mortgage / (Housing cost percentage)

Substituting the values from the problem, we get:

Net income = $2500 / (25/100)

Net income = $2500 / 0.25

Net income = $10,000

To learn more about income:

https://brainly.com/question/25745683

#SPJ4

Laurel must increase her net income to $10,000 to keep her housing costs at 25%.

The amount of Laurel's new mortgage is $2500

The percentage of Laurel's net income that she wants to use for housing costs, which is 25%

To find the amount of net income that Laurel needs to maintain a housing cost of 25%, we can use the following formula:

Net income = Mortgage / (Housing cost percentage)

Substituting the values from the problem, we get:

Net income = $2500 / (25/100)

Net income = $2500 / 0.25

Net income = $10,000

Learn more about income:

brainly.com/question/25745683

#SPJ1

To determine if the bolts vary by more than the required variance, we can conduct a hypothesis test. The null hypothesis (H₀) states that the variance of the bolts is equal to or less than the required variance (σ² ≤ 0.025), while the alternative hypothesis (H₁) states that the variance is greater than the required variance (σ² > 0.025).

Next, we need to determine the critical value(s) of the test statistic. Since we are testing for variance, we will use the chi-square distribution. For a one-tailed test with α = 0.01 and 14 degrees of freedom (n-1), the critical value is 27.488.

Now, we can compare the test statistic to the critical value. The test statistic is calculated as (n-1) * s² / σ², where n is the sample size (15), s² is the sample variance (0.1587²), and σ² is the required variance (0.025).

If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the bolts vary by more than the required variance. Otherwise, we fail to reject the null hypothesis.

To learn more about Hypothesis test - brainly.com/question/29996729

#SPJ11

To determine if the bolts vary by more than the required variance, we can conduct a hypothesis test. The null hypothesis (H₀) states that the variance of the bolts is equal to or less than the required variance (σ² ≤ 0.025), while the alternative hypothesis (H₁) states that the variance is greater than the required variance (σ² > 0.025).

Next, we need to determine the critical value(s) of the test statistic. Since we are testing for variance, we will use the chi-square distribution. For a one-tailed test with α = 0.01 and 14 degrees of freedom (n-1), the critical value is 27.488.

Now, we can compare the test statistic to the critical value. The test statistic is calculated as (n-1) * s² / σ², where n is the sample size (15), s² is the sample variance (0.1587²), and σ² is the required variance (0.025).

If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the bolts vary by more than the required variance. Otherwise, we fail to reject the null hypothesis.

To learn more about Hypothesis test - brainly.com/question/29996729

#SPJ11

The slope of a line perpendicular to the line is -4

The equation is x -4y = 28

The equation for the line is

y = mx + c

where m = slope

c = y-intercept

Here the equation is x - 4y = 28

4y = x - 28

y = x/4 - 7

So the slope of this line is 1/4

Now we have to find the slope of the line perpendicular to that line.

We know that,

m1 × m2 = -1

1/4 × m2 = -1

m2 = -4

Therefore the slope of the line perpendicular to the line is -4.

To know more about the slope of the line refer to the link given below:

https://brainly.com/question/22057368

#SPJ1

The complete question is:

Find the slope of a line perpendicular to x-4y=28

Answer: to scale the base units so that they can represent anything from a very large numeric value

Step-by-step explanation:

to scale the base units so that they can represent anything from a very large numeric value

the anwser for this is true

Answer:

I also think it's true because it mostly made sense to me.

Hey there!

\(Answer:\boxed{x=\frac{-13}{3}}\)

\(Explanation:\)

\(-22=6x+4\)

Let's start off with flipping the equation.

\(6x+4=-22\)

Now we need to subtract 4 from both sides of the equation.

\(6x+4-4=-22-4\\6x=-26\)

Now in our third/last step, we will divide both sides by 6.

\(\frac{6x}{6}=\frac{-26}{6}\)

\(x=\frac{-13}{3}\)

\(\boxed{x=\frac{-13}{3}}\text{ is the answer.}\)

Hope this helps!

\(\text{-TestedHyperr}\)

Answer:

wh4t th3 0th3r p3rs0n s41d

Step-by-step explanation:

h33h33h33h33h33h33h33h33hh33h3h3h3h3h333h33hhhhh333333

To evaluate the integral ∫tan^4(x) cos^5(x) dx, we can use trigonometric identities to simplify the integrand.

We'll use the power-reducing formula for tan^4(x) and the power-reducing formula for cos^5(x) to simplify the integrand:

∫tan^4(x) * cos^5(x) dx

= ∫(tan^2(x))^2 * (cos^2(x))^2 * cos(x) * cos^2(x) dx

= ∫[(sec^2(x) - 1)^2] * [(1 - sin^2(x))^2] * cos(x) * cos^2(x) dx

Expanding the square terms, we get:

= ∫[(sec^4(x) - 2sec^2(x) + 1)] * [(1 - 2sin^2(x) + sin^4(x))] * cos(x) * cos^2(x) dx

Multiplying the terms together, we have:

= ∫[sec^4(x) - 2sec^2(x) + 1 - 2sin^2(x) + 4sin^4(x) - 2sin^6(x)] * cos^3(x) dx

Now, let's integrate each term separately:

∫sec^4(x) * cos^3(x) dx:

Using the substitution u = sin(x), we have:

∫(1 + u^2)^2 * (1 - u^2) du

Expanding the expression and integrating, we get:

= ∫(1 + 2u^2 + u^4 - u^4 - u^6) du

= u + 2/3 u^3 + 1/5 u^5 - 1/7 u^7 + C

Substituting back u = sin(x), we have:

= sin(x) + 2/3 sin^3(x) + 1/5 sin^5(x) - 1/7 sin^7(x) + C

∫-2sec^2(x) * cos^3(x) dx:

Using the substitution u = sin(x), we have:

∫-2(1 + u^2) * (1 - u^2) du

Expanding the expression and integrating, we get:

= ∫(-2 + 2u^2 - 2u^2 + 2u^4) du

= -2u + 2/3 u^3 - 2/5 u^5 + 2/7 u^7 + C

Substituting back u = sin(x), we have:

= -2sin(x) + 2/3 sin^3(x) - 2/5 sin^5(x) + 2/7 sin^7(x) + C

∫cos^3(x) dx:

Using the substitution u = sin(x), we have:

∫(1 - u^2) du

Integrating, we get:

= u - 1/3 u^3 + C

Substituting back u = sin(x), we have:

= sin(x) - 1/3 sin^3(x) + C

Putting it all together, the complete result of the integral is:

∫tan^4(x) * cos^5(x) dx

= ∫[sec^4(x) - 2sec^2(x) + 1 - 2sin^2(x) + 4sin^4(x) - 2sin^6(x)] * cos^3(x) dx

= ∫sec^4(x) *

cos^3(x) dx - 2∫sec^2(x) * cos^3(x) dx + ∫cos^3(x) dx

= (sin(x) + 2/3 sin^3(x) + 1/5 sin^5(x) - 1/7 sin^7(x)) - 2(-2sin(x) + 2/3 sin^3(x) - 2/5 sin^5(x) + 2/7 sin^7(x)) + (sin(x) - 1/3 sin^3(x)) + C

= sin(x) + 4/3 sin^3(x) - 8/5 sin^5(x) + 20/7 sin^7(x) + C

Therefore, the final result is:

∫tan^4(x) * cos^5(x) dx = sin(x) + 4/3 sin^3(x) - 8/5 sin^5(x) + 20/7 sin^7(x) + C

To learn more about integral  Click Here: brainly.com/question/31059545

#SPJ11

Answer: 12 inches

Step-by-step explanation:

The length of the rectangular box is given as follows:

1.59 inches.

The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, as follows:

Volume = length x width x height.

A rectangular box weight 2.8 pounds, and each pound has 27.68 cubic inches, hence the volume in in³ is given as follows:

V = 2.8 x 27.68

V = 77.504 in³.

The width is of 7.70 inches and the height is of 7.75 - 1.41 = 6.34 inches, hence the length is obtained as follows:

7.70 x 6.34l = 77.504

l = 77.504/[7.70 x 6.34]

l = 1.59 inches.

More can be learned about the volume of a rectangular prism at brainly.com/question/22070273

#SPJ1

Answer:

0(x-4)

Step-by-step explanation:

in my working system i mean just when i try on the place of 4 any number can be inserted

$5x-7=13x+17$,here both gives -22 as a result so

$6(x-4)$=6x-24 and to give the same result or 0

$6(x-4)$=0(x-any number )

Answer:

Step: 1

6x and 8x

Step: 2

remove the three x's on the first one and remove the one x one and 4 circles on the second and they should be even

Step-by-step explanation:

The Answer is Positive Integers (B)

The number of Chromebooks = x

The total cost of purchasing Chromebooks = c(x)

where x is the domain of c(x)

The number of Chromebooks x can be: {0, 1, 2, 3, 4, 5, 6...}. You cannot have numbers like {0.2, 0.5, 3.8 ...} or any other decimal neither can you have surds like:

Integers contain numbers like: {... , -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ...}

Positive Integer contains numbers like: {1, 2, 3, 4, 5, ...}

Rational Numbers contain numbers like: {-0.2, -0.1, -0.05, -0.005,0.2, 0.1, 0.05, 0.005,...} and also contain numbers like {... , -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ...} as in Integers.

Positive rational Numbers are just the positive values of Rational Numbers like: {1, 2, 3, 4, 5, ...} and {0.2, 0.1, 0.05, 0.005,...}

From the information laid out, it is obvious that the only set of values that qualify to be called the domain of c(x) is Positive Integers

The Answer is Positive Integers (B)

Answer:

The answer is $86.80. The lunch service gains $86.80 in 3 1/2 hours if they get $24.80 per hour.

Step-by-step explanation:

You have to multiply how much they earn per hour, $24.80, by the number of hours they work, 3 1/2. $24.80 times 3 1/2 equals 86.80 so the lunch service earns $86.80 in 3 1/2 hours.

Hope this helps!

Answer:

y=6+2x

Step-by-step explanation:

The amount of wood, in meters, needed to rebuild the frame is 1.8288 m.

What is amount and example?

amount to (something) : to produce (a total) when added together. The bill amounted to 10 dollars. They have debts amounting to thousands of dollars.

To calculate the amount of wood, in meters, needed to rebuild the frame, we can use the following formula:

wood (m) = (wood (ft) x 0.3048) / 6

Since each piece of wood provided measures 6 ft (approximately 1.8 to 8.7), we can calculate the amount of wood, in meters, needed to rebuild the frame as follows:

wood (m) = (6 ft x 0.3048) / 6

wood (m) = 1.8288 m      

Therefore, the amount of wood, in meters, needed to rebuild the frame is 1.8288 m.

Learn more about amount  here:

brainly.com/question/30063054

#SPJ4

Answer:

gradient = 3

Step-by-step explanation:

Calculate the gradient using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = - 6, 4) and (x₂, y₂ ) = (- 4, 10)

m = \(\frac{10-4}{-4+6}\) = \(\frac{6}{2}\) = 3

Answer:

i hope its clear . the answer is 3 .

I believe it would be x = 0.

Hope this helps!

The concept is Data Analysis,  which is the process of totally applying statistical tools to dissect data. The answer is options B, C, and D.

To help you consider data limitations, critically dissect correlations, examine the environment, and understand tool strengths and sins. Data analysis applies statistical and/ or logical ways to describe, illustrate, epitomize, and estimate data.

Data analysis helps individualities and associations make sense of data. Data analysts typically analyze raw data for insights and trends.

Limitations include:

Question

You're preparing a question-and-answer session that will follow your donation. Which styles help you to consider data limitations? elect everything that suits you.

A) exclude the outliers

B) Understand the strengths and sins of the tools

C) Critically dissect the correlations

D) Look at the environment

To know more about Data Analysis,

brainly.com/question/28264896

#SPJ4

Answer:

B

Step-by-step explanation:

Integers are like whole numbers, but they can also be negative.

Some examples of integers are -1, 2, 5 etc.

Answer:

x + y = 10

6x + 8y = 72

Step-by-step explanation:

Number of packages = 10

Total batteries = 72

For AA:

batteries per package = 6

Let number of packages = x

For AAA:

batteries per package = 8

Let number of packages = y

Number of AA packages + number of AAA packages = 10

Sum of AA + sum of AAA equals 72 batteries

x + y = 10

6x + 8y = 72

Answer:Answer:

x + y = 10

6x + 8y = 72

Step-by-step explanation:

Number of packages = 10

Total batteries = 72

For AA:

batteries per package = 6

Let number of packages = x

For AAA:

batteries per package = 8

Let number of packages = y

Number of AA packages + number of AAA packages = 10

Sum of AA + sum of AAA equals 72 batteries

x + y = 10

6x + 8y = 72

Step-by-step explanation:

it is just still 5 I believe :P hope this helps

Answer:

570240000

Step-by-step explanation:

Answer:

sorry I also dont understand

Answer:

Perpendicular!!!

Step-by-step explanation:

-3 and 1/3 are negative recopricals. This means they are perpendicular.

I would take a brainliest

Answer:

perpendicular

Step-by-step explanation:

for an equation to be parallel, the equations would have to have the same slope. for and equation to be perpendicular, the slopes have to be reciprocal, like 5/1 and 1/5, or 2/15 and 15/2. Also, one slope has to be negative. These equations match the definition of perpendicular lines.

In this question, we were given five relations and asked to determine if they are reflexive, symmetric, and/or transitive.

(a) The relation Ri on R is reflexive, symmetric, and transitive.

(b) The relation R on A is not reflexive, not symmetric, and transitive.

(c) The relation Rs on Z is not reflexive, not symmetric, and transitive.

(d) The relation R, on Z is not reflexive, not symmetric, and not transitive.

(e) The relation Rs on Z is reflexive, not symmetric, and transitive.

A reflexive connection is a relationship between items of a set A in which each element is related to itself. As the name implies, the image of each element of the set is its own reflection. In set theory, a reflexive relation is an essential concept.

(a) Ri is reflexive, symmetric, and transitive.

- Reflexive: For any x ∈ R, (x, x) ∈ Ri since |x - x| = 0 < 1.

- Symmetric: For any (x, y) ∈ Ri, we have |x - y| < 1, which implies |y - x| < 1. Therefore, (y, x) ∈ Ri.

- Transitive: For any (x, y), (y, z) ∈ Ri, we have |x - y| < 1 and |y - z| < 1. Adding these inequalities, we get |x - z| < 2, which implies (x, z) ∈ Ri.

(b) R is not reflexive, symmetric, or transitive.

- Not reflexive: For any x ∈ A, (x, x) ∉ R since x - x = 0 is not a positive integer.

- Not symmetric: For any distinct x, y ∈ A, if (x, y) ∈ R, then x - y = 1, which implies y - x = -1 is not a positive integer. Therefore, (y, x) ∉ R.

- Not transitive: Let A = {1, 2, 3} and R = {(1, 2), (2, 3)}. Then (1, 3) is not in R since 3 - 1 = 2 is not a positive integer.

(c) R3 is not reflexive, symmetric, or transitive.

- Not reflexive: For any x ∈ Z, (x, x) ∉ R3 since x * x = x^2 is not greater than 0.

- Symmetric: For any (x, y) ∈ R3, we have xy > 0, which implies yx > 0. Therefore, (y, x) ∈ R3.

- Not transitive: Let x = -1, y = 2, and z = -1. Then (x, y) ∈ R3 and (y, z) ∈ R3, but (x, z) = (-1, -1) ∉ R3 since xz = 1 is not greater than 0.

(d) R, is not reflexive, symmetric, or transitive.

- Not reflexive: For any y ∈ Z, (y, y) ∉ R, since 3 does not divide y + 2y = 3y.

- Not symmetric: For y = 1 and z = 2, we have (2, 1) ∉ R, but (1, 2) ∈ R since 3 divides 1 + 4 = 5.

- Not transitive: Let x = 2, y = 1, and z = 5. Then (x, y) ∈ R, (y, z) ∈ R, but (x, z) = (2, 5) ∉ R since 3 does not divide 2 + 10 = 12.

(e) Rs is the relation on Z given by Rs = {(x,y) ⬠Zx Z: there exists k ⬠N such that elyk and yak).

- Reflexive: This relation is not reflexive because (1, 1) ∉ Rs as there does not exist k such that 1 x k = 1.

- Symmetric: This relation is not symmetric because, for example, (1, 2) ∈ Rs but (2, 1) ∉ Rs since there does not exist k such that 2 x k = 1.

- Transitive: This relation is not transitive. For example, let x = 1, y = 2, and z = 4. Then (x, y) ∈ Rs and (y, z) ∈ Rs, but (x, z) ∉ Rs since there does not exist k such that 1 x k = 4.

In short, in this question, we were given five relations and asked to determine if they are reflexive, symmetric, and/or transitive.

(a) The relation Ri on R is reflexive, symmetric, and transitive.

(b) The relation R on A is not reflexive, not symmetric, and transitive.

(c) The relation Rs on Z is not reflexive, not symmetric, and transitive.

(d) The relation R, on Z is not reflexive, not symmetric, and not transitive.

(e) The relation Rs on Z is reflexive, not symmetric, and transitive.

Learn more about reflexive relation on:

https://brainly.com/question/30105703

#SPJ4