Type the correct answer in the box the coordinates of vertex is are blank and blank the area of rectangle pqrs is blank square units

The inverse of matrix A is given by;

A^-1 = |5/139   -189/139 29/139 |

         |-10/139 129/139 -27/139 |
         |-5/139   19/139 -3/139  |

The given matrix is A =

| -5  -10  21 |
| -2   -5   9 |
|  1    2  -4 |

To find the inverse of a matrix, first find the determinant of that matrix. The determinant of matrix A is given as;

|A| = -5(-5(-4) - 2(9)) - (-10)(-2(-4) - 1(21)) + (21)(-2(2) - 1(-5))

|A| = -5(10) + 100 - 21(9)

|A| = -50 + 100 - 189

|A| = -139

Thus, the determinant of matrix A is -139. Now, we can use the formula of inverse of a 3x3 matrix;

A^-1 = 1/|A| * |(b22b33 - b23b32)  (b13b32 - b12b33)  (b12b23 - b13b22)|
| (b23b31 - b21b33)  (b11b33 - b13b31)  (b13b21 - b11b23)|
| (b21b32 - b22b31)  (b12b31 - b11b32)  (b11b22 - b12b21)|

where b is the cofactor of each element of matrix A.

The cofactor of element aij is denoted as Aij and given as Aij = (-1)i+j|Mij|.

Thus, the cofactors of matrix A are;

|-5  -10  21|
| -2  -5  9 |
|  1   2 -4 |

M11 = | -5  9 |
         |  2 -4 |

M12 = | -2  9 |
          |  2 -5 |

M13 = | -2 -5 |

M21 = | -10 21 |
         |   2 -9 |

M22 = |  -5 -21 |
           |  -2  5 |

M23 = |  -2 -2 |

M31 = | -10 -5 |
         |  2  9 |

M32 = |  -5 -9 |
          |  2  2 |

M33 = |  -2 -2 |

Now we can find the inverse of matrix A as follows;

A^-1 = 1/-139 * |(5   189  -29)|
                      |(-10 -129  27)|
                      |(-5   19  -3) |

Hence, the inverse of matrix A is given by;

A^-1 = |5/139   -189/139 29/139 |

         |-10/139 129/139 -27/139 |
         |-5/139   19/139 -3/139  |

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a) The differential equation is y = [tex]e^{(4x)/x}[/tex] + 3 b) The particular solution is y = [tex]e^{x^3 - x}[/tex] - 1 c) The particular solution to the differential equation is given by the equations is y = 2x or y = -2x.

a) To find the general solution to the differential equation:

x(dy/dx) + 3y = [tex](e^{4x})/{x^2}[/tex]

We can start by rearranging the equation:

dy/dx = [[tex](e^{4x})/{x^2}[/tex] - 3y]/x

This equation is linear, so we can use an integrating factor to solve it. The integrating factor is given by:

μ(x) = e^(∫(1/x) dx) = [tex]e^{ln|x|}[/tex] = |x|

Multiplying both sides of the equation by the integrating factor:

|x| * dy/dx - 3|xy| = [tex]e^{(4x)/x}[/tex]

Now, let's integrate both sides with respect to x:

∫(|x| * dy/dx - 3|xy|) dx = ∫([tex]e^{(4x)/x}[/tex]) dx

Using the properties of absolute values and integrating term by term:

∫(|x| * dy) - 3∫(|xy|) dx = ∫([tex]e^{(4x)/x}[/tex]) dx

Integrating each term separately:

∫(|x| * dy) = ∫([tex]e^{(4x)/x}[/tex]) dx + 3∫(|xy|) dx

To integrate ∫(|x| * dy), we need to know the form of y. Let's assume y = y(x). Integrating ∫[tex](e^{4x)/x}[/tex] dx gives us a natural logarithm term.

Integrating 3∫(|xy|) dx can be done using different cases for the absolute value of x.

By solving these integrals and rearranging the equation, you can find the general solution for y(x).

b) To find the particular solution to the differential equation:

dy/dx = (y + 1)(3x² - 1)

subject to the condition that y = 0 at x = 0.

We can solve this equation using separation of variables. Rearranging the equation:

dy/(y + 1) = (3x² - 1) dx

Now, let's integrate both sides:

∫(dy/(y + 1)) = ∫((3x² - 1) dx)

The left-hand side can be integrated using the natural logarithm function:

ln|y + 1| = x³ - x + C1

Solving for y, we have:

[tex]y + 1 = e^{x^3 - x + C1}\\y = e^{x^3 - x + C1} - 1[/tex]

Using the initial condition y = 0 at x = 0, we can find the particular solution. Substituting these values into the equation:

0 = [tex]e^{0 - 0 + C1}[/tex] - 1

1 = [tex]e^{C1}[/tex]

C1 = ln(1) = 0

Therefore, the particular solution is:

y = [tex]e^{x^3 - x}[/tex] - 1

c) To find the particular solution to the differential equation:

x(dy/dx) - y = y

subject to the condition that y = 2 at x = 1.

We can simplify the equation:

x(dy/dx) = 2y

Now, let's separate variables and integrate:

(1/y) dy = (1/x) dx

Integrating both sides:

ln|y| = ln|x| + C2

Simplifying further:

ln|y| = ln|x| + C2

ln|y| - ln|x| = C2

ln(|y/x|) = C2

|y/x| =  [tex]e^{C2}[/tex]

Since we are given the initial condition y = 2 at x = 1, we can substitute these values into the equation:

|2/1| = [tex]e^{C2}[/tex]

2 =    [tex]e^{C2}[/tex]

C2 = ln(2)

Therefore, the particular solution is:

|y/x| = [tex]e^{ln(2)}[/tex]

|y/x| = 2

Solving for y, we have two cases:

y/x = 2

y = 2x

y/x = -2

y = -2x

So, the particular solution to the differential equation is given by the equations:

y = 2x or y = -2x.

The complete question is:

a) Find the general solution to the differential equation

x dy/dx + 3y = (e⁴ˣ)/(x²)

b) Find the particular solution to the differential equation dy/dx = (y + 1)(3x² - 1)

subject to the condition that v = 0 at x = 0

c) Find the particular solution to the differential equation

x dy/dx (y) = y

subject to the condition that y = 2 at x = 1

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Answer:  A. 4p + $17.50 = $53.50; p = $9.00

1:  17.50+4p=  Nothing further can be done with this topic. Please check the expression entered or try another topic.

17.5 + 4 p

2:  4p=53.50-17.50=  4p=53.50-17.50

Step-by-step explanation:  9

The total bill: $53.50

17.50 + 4 x = 53.50

4 x = 53.50 - 17.50

4 x = 36

x = 36 : 4

x = $9

Answer: The price of each shrub is $9.

...............................................................................................................................................

Answer:

$9

Step-by-step explanation:

Let   be the price of each shrub.

4 shrubs at    each costs    dollars

Potting soil is $17.50

Hence, total cost is the expression  

We know that total bill is $53.50, so we can equate it to the expression:

This equation can be solved for    to find cost of each shrub.

Solving for    gives us:

So price of each shrub is $9

a)

b) If the test statistic is greater than the critical value, we can reject the null hypothesis and conclude that there is evidence that the proportion is greater than 0.132.

c. Two possible explanations for the evidence that Jenna found are given below.

Solution:

a.

Identify the population, Parameter, sample, and statistic.

Population: All pennies in the container

Parameter: p = Proportion of pre-1982 copper pennies in the container

Sample: 50 randomly selected pennies from the container

Statistic: Number of pre-1982 copper pennies in the sample = 11

b.

To determine if Jenna has convincing evidence that more than 13.2% of her pennies are pre-1982 copper pennies, we can perform a hypothesis test.

Let's assume that the null hypothesis is that the proportion of pre-1982 copper pennies in the container is equal to 0.132, while the alternative hypothesis is that the proportion is greater than 0.132.

Then, we can calculate the test statistic and compare it to the critical value.

If the test statistic is greater than the critical value, we can reject the null hypothesis and conclude that there is evidence that the proportion is greater than 0.132.

c. Two possible explanations for the evidence that Jenna found could be:

1. The container has a higher proportion of pre-1982 copper pennies than the national average.

2. Jenna's sample is not representative of the container, and the sample proportion is higher than the population proportion by chance.

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The best fit line estimate for the y value when x is 100 in this case is 205.

Two or more expressions with an Equal sign is called as Equation.

To determine what the best fit line estimate for the y value is when x is 100.

Assuming that you have a linear regression model with the equation y = mx + b, where "m" is the slope and "b" is the y-intercept, you would need to know the values of "m" and "b" to estimate the y value for a given x value.

If you have these values, you can substitute x = 100 into the equation and solve for y.

The resulting value will be the estimated y value for the given x value.

If the equation of the best fit line is y = 2x + 5, then the estimated y value when x is 100 would be:

y = 2(100) + 5

y = 200 + 5

y = 205

Hence, the best fit line estimate for the y value when x is 100 in this case is 205.

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Answer:

28.27

Step-by-step explanation:

A=πr2=π·32≈28.27433

Answer:

If you're using 3.14 for pi, it's 28.26

Step-by-step explanation:

Answer:

D) 8

Step-by-step explanation:

We're looking for [tex]x[/tex], which means the 7x and 5x will have the SAME x.

7(8) = 56

For the C corner, it is cornered as a 90 degree angle, so that means the (7x) + 34 degrees NEEDS to equal 90.

7(8) = 56 + 34 = 90!!

Now we have to see if 5(8) is correct

5(8) = 40 + 50 [The degree mark] = WHICH EQUALS 90 TOO..

Therefore, the answer is D) 8

It cant be written any way else its already in its simplest form

Answer:

Given ABCD ~ EFGH

FG = BC(EF/AB)

FG = 7(9/6)

FG = 63/6

FG = 10.5

GH = CD(EF/AB)

GH = 11(9/6)

GH = 99/6

GH = 16.5

EH = AD(EF/AB)

EH = 12(9/6)

EH = 108/6

EH = 18

Answer:

Step-by-step explanation:

Given equation:

q is independent variable, we need to solve it for s:

Correct choice is

Then, the width of the pool covered by the concrete walkway is 16 + 2c feet (2c feet on each side), and the length of the pool covered by the concrete walkway is 26 + 2c feet (2c feet on each end).

We have given a rectangular swimming pool with a length of 26 feet and a width of 16 feet. We need to find the perimeter of the wood deck that surrounds the concrete walkway of width c around the pool and extends w feet on all sides.

Let's solve the given problem as follows:Firstly, let's calculate the dimensions of the concrete walkway. Let the width of the concrete walkway be 'c' feet.

Then, the width of the pool covered by the concrete walkway is 16 + 2c feet (2c feet on each side), and the length of the pool covered by the concrete walkway is 26 + 2c feet (2c feet on each end).

So, the dimensions of the pool and concrete walkway are (26 + 2c) ft. x (16 + 2c) ft.The dimensions of the wood deck that surrounds the concrete walkway by w feet on all sides will be (26 + 2c + 2w) ft. x (16 + 2c + 2w) ft.Now, let's write the expression for the perimeter of the wood deck.P = 2(Length + Width)P = 2[(26 + 2c + 2w) + (16 + 2c + 2w)]P = 2[42 + 4c + 4w]P = 84 + 8c + 8wThe expression for the perimeter of the wood deck is 84 + 8c + 8w. Hence, the answer is 84 + 8c + 8w.

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Answer: the second one/ \/36/6

Step-by-step explanation:

Answer:

36.25 miles per gallon

Step-by-step explanation:

4/5 = .8

29/.8 = x/1

cross-multiply:

.8x = 29

x = 36.25

Answer:

394.2 ft

Step-by-step explanation:

7.8(9)=70.2

This is the measurement for the two triangular sides

9(12)(3)=324 This is the measurement for the three triangular sides

70.2 +324 = 394.2 APPROX

Answer:

a=-2

Step-by-step explanation:

3a−6=−12

Step 1: Add 6 to both sides.

3a−6+6=−12+6

3a=−6

Step 2: Divide both sides by 3.

3a/ 3 = −6/ 3

a=−2

Answer:

75

Step-by-step explanation:

Answer:

the angle that is 75 degrees

Step-by-step explanation:

Because the longest side is always opposite of the largest angle and the smallest side is always opposite of the smallest angle.

Answer:

12 cm of coastline

Step-by-step explanation:

Multiply the years (factor) by the receding amount, 3cm, (constant) BAM answer.

The probability of obtaining exactly 3 heads is 5/16.

We can find the probability of obtaining exactly 3 heads by considering the different ways in which this can happen.

First, suppose we toss the two normal coins and the biased coin with the two heads.

There is a probability of getting heads on each toss of the biased coin: 1/2

A  probability of getting heads on each toss of the normal coins: 1/2

Therefore, the probability of getting exactly 3 heads in this case is:

(1/2) * (1/2) * (1/2) = 1/8

Now suppose we toss the two normal coins and the biased coin with the two heads, but we choose to use the biased coin twice. In this case, we need to get two heads in a row with the biased coin, and then a head with one of the normal coins.

The probability of getting two heads in a row with the biased coin is: 1/2, and the probability of getting a head with one of the normal coins is: 1/2. Therefore, the probability of getting exactly 3 heads in this case is:

(1/2) * (1/2) * (1/2) = 1/8

Finally, suppose we use the biased coin and one of the normal coins twice each. In this case, we need to get two heads in a row with the biased coin, and then two tails in a row with the normal coin. The probability of getting two heads in a row with the biased coin is: 1/2,

and the probability of getting two tails in a row with the normal coin is :

(1/2) * (1/2) = 1/4.

Therefore, the probability of getting exactly 3 heads in this case is:

(1/2) * (1/2) * (1/4) = 1/16

Adding up the probabilities from each case, we get:

1/8 + 1/8 + 1/16 = 5/16

Therefore, the probability of obtaining exactly 3 heads is 5/16.

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Answer:

Unbiased

Step-by-step explanation:

If b^ is equal to B this means that it is an unbiased estimator. When there is an absence of bias, we have an unbiased estimator. As an unbiased estimator it gives accurate information most of the time. The result it gives is not over estimated and also it is not underestimated.

Expected value = true value

Parameter estimates are correct on average

Thank you

Step-by-step explanation:

(FE+BC)/2=<FDE

<FDE=<BDC

it is basically the average of x and 70.

(x+70)/2=104

x=138

Hope that helps :)

Answer:

The answer is probly 70 degrees

i might be wrong

i just hope this works

good luck

To determine the intervals on which the function [tex]f(x) = x^4 - 4x^3 + 3[/tex] is concave up or concave down, we need to find the second derivative of the function and analyze its sign.

First, let's find the first derivative of f(x):

[tex]f'(x) = 4x^3 - 12x^2[/tex]

Next, let's find the second derivative of f(x) by taking the derivative of f'(x):

[tex]f''(x) = 12x^2 - 24x[/tex]

To determine the intervals of concavity, we need to find where f''(x) is positive (concave up) or negative (concave down). We can do this by analyzing the sign of f''(x).

Now, let's find the values of x for which f''(x) = 0, as these will give us potential inflection points:

[tex]12x^2 - 24x = 0[/tex]

12x(x - 2) = 0

x = 0 or x = 2

The potential inflection points are x = 0 and x = 2.

To analyze the concavity of the function, we'll use test points within the intervals between the potential inflection points and beyond.

For x < 0, let's choose x = -1 as a test point:

[tex]f''(-1) = 12(-1)^2 - 24(-1) = 12 + 24 = 36[/tex]

Since f''(-1) = 36 > 0, the function is concave up for x < 0.

For 0 < x < 2, let's choose x = 1 as a test point:

[tex]f''(1) = 12(1)^2 - 24(1) = 12 - 24 = -12[/tex]

Since f''(1) = -12 < 0, the function is concave down for 0 < x < 2.

For x > 2, let's choose x = 3 as a test point:

[tex]f''(3) = 12(3)^2 - 24(3) = 108 - 72 = 36[/tex]

Since f''(3) = 36 > 0, the function is concave up for x > 2.

In summary:

The function is concave up for x < 0 and x > 2.

The function is concave down for 0 < x < 2.

The inflection points are x = 0 and x = 2.

I hope this clarifies the concavity and inflection points of the given function. Let me know if you have any further questions!

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Answer:

Im so sorry im late! The answer is A i just took the quiz!

Step-by-step explanation:

The correct dot plot is given in option 1.

Any data that may be shown as dots or tiny circles is called a dot plot. Given that the height of the bar created by the dots indicates the numerical value of each variable, it is comparable to a bar graph or a simple histogram. Little amounts of data are shown using dot plots.

As per the given data:

There are 4 options, with each option represented by a diagram also the number and frequency table is given

Number:     3 4 5 7 8

Frequency: 3 2 4 2 3

We can find the correct diagram of the dot plot by observing the number of cross against each value of the number on the line and then matching the obtained value with the given number and frequency table.

Hence, the correct dot plot is given in option 1.

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In a two-way between subjects ANOVA, a significant main effect for B means that option A - the mean for B1 is not equal to the mean for B2.

In a two-way ANOVA, we are examining the effects of two independent variables (factors) on a dependent variable. One of the factors is referred to as factor A, and the other as factor B. A main effect for B indicates that there is a significant difference between the means of the levels of factor B. Therefore, if we observe a significant main effect for B, it implies that the mean for B1 (one level of factor B) is not equal to the mean for B2 (another level of factor B). This suggests that the variable represented by factor B has a significant influence on the dependent variable, and there is a difference in the outcome between the two levels of factor B.

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Answer:

b - 5 = c

Step-by-step explanation:

if you take the number of cookies before the visit (B) and then you eat 5, that would be (B - 5). after you eat the cookies, C is the amount left. so it’s a subtraction problem without 2 numbers. so the equation would be

b - 5 = c

or

before - 5 = after

Answer:

3=20

4=15

5=12

Step-by-step explanation:

The exact distance between the points (8, -3) and (-2, 4) can be calculated using the distance formula in mathematics.

The formula for finding the distance between two points (x1, y1) and (x2, y2) in a two-dimensional Cartesian coordinate system is given by: Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2). Using the coordinates (8, -3) and (-2, 4), we can substitute the values into the distance formula: Distance = sqrt((-2 - 8)^2 + (4 - (-3))^2) = sqrt((-10)^2 + (7)^2) = sqrt(100 + 49) = sqrt(149) ≈ 12.207

Therefore, the exact distance between the points (8, -3) and (-2, 4) is approximately 12.207 units.

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Answer:

see the explanation below

Step-by-step explanation:

The expression for the cost can be given as

y=mx+c

where x= the distance

           m= the cost to move x distance

            c= the fixed cost

Therefore the total cost to ship the cost will be y

The mean is 1, variance is 0.9, and standard deviation is 0.948, rounded to three decimal places. Given data: Of all the registered automobiles in Colorado, 10% fail the state emissions test.

Ten automobiles are selected at random to undergo an emissions test.a. Find the probability:

1) That exactly three of them fail the test.

For the number of success (x) and number of trials (n),

the probability mass function (PMF) for binomial distribution is given by: [tex]P(X = x) = C(n, x) * p^{(x)} * q^{(n-x)},[/tex]

where [tex]C(n, x) = (n!)/((n-x)! * x!) ,[/tex]

p and q are the probabilities of success and failure, respectively. Here, the probability of success is the probability of an automobile to fail the test, p = 0.10 and the probability of failure is q = 1 - p = 0.90.

Now, X is the number of automobiles that fail the test.

Thus, n = 10, x = 3, p = 0.10, and q = 0.90.

Using the above formula:

[tex]P(X = 3) = C(10, 3) * (0.10)^{(3)} * (0.90)^{(10-3)}\\= 0.057[/tex]

The required probability is 0.057, rounded to three decimal places.

1) That fewer than three of them fail the test.

The required probability is P(X < 3).P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) Using the above formula:

[tex]P(X = 0) = C(10, 0) * (0.10)^{(0)} * (0.90)^{(10)}[/tex]

= 0.3487P(X = 1)

= [tex]C(10, 1) * (0.10)^{(1) }* (0.90)^{(9)}[/tex]

= 0.3874P(X = 2) = [tex]C(10, 2) * (0.10)^{(2)} * (0.90)^{(8)}[/tex]

 = 0.1937

Now, P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

= 0.3487 + 0.3874 + 0.1937

 = 0.9298

The required probability is 0.9298, rounded to three decimal places.

1) That at least eight of them fail the test.

The required probability is

P(X ≥ 8).P(X ≥ 8) = P(X = 8) + P(X = 9) + P(X = 10) Using the above formula:

[tex]P (X = 8) = C(10, 8) * (0.10)^{(8)} * (0.90)^{(2) }[/tex]

= 0.0000049

[tex]P(X = 9) = C(10, 9) * (0.10)^{(9)} * (0.90)^{(1) }[/tex]

= 0.0000001

[tex]P(X = 10) = C(10, 10) * (0.10)^{(10)} * (0.90)^{(0)}[/tex]

= 0.0000000001

Now,

P(X ≥ 8) = P(X = 8) + P(X = 9) + P(X = 10)

= 0.0000049 + 0.0000001 + 0.0000000001 = 0.000005

The required probability is 0.000005,

rounded to three decimal places.

b. Find the mean, variance, and standard deviation of the number of automobiles fail the test.

The mean (μ) for binomial distribution is given by: μ = n * p,

where n is the number of trials and p is the probability of success.

The variance ([tex]= 1 \sigma ^ 2 = n * p * q = 10 * 0.10 * 0.90 ^2[/tex]) for binomial distribution is given by: [tex]\sigma ^2 = n * p * q[/tex]

The standard deviation (σ) for binomial distribution is given by:

σ = √(n * p * q)

Here, n = 10 and p = 0.10.

Thus, q = 0.90.

Using the above formulas:

μ = n * p = 10 * 0.10

[tex]= 1\sigma ^2 = n * p * q = 10 * 0.10 * 0.90[/tex]

= 0.9σ = √(n * p * q)

= √(10 * 0.10 * 0.90)

= 0.948

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