A postal service will accept a package if its length plus its girth is not more than 96 inches. Find the dimensions and volume of the largest package with a square end that can be mailed.

The inverse of the given permutation matrix A is

                          [tex]\[ A^{-1} = \begin{bmatrix}0 & 0 & 0 & 1 \\0 & 0 & 1 & 0 \\1 & 0 & 0 & 0 \\0 & 1 & 0 & 0 \\\end{bmatrix} \][/tex]

To find the inverse of the given permutation matrix A:

[tex]\[ A = \begin{bmatrix}0 & 0 & 1 & 0 \\0 & 0 & 0 & 1 \\0 & 1 & 0 & 0 \\1 & 0 & 0 & 0 \\\end{bmatrix} \][/tex]

Utilize the concept that the inverse of a permutation matrix is its transpose.

Therefore, the inverse of matrix A is:

[tex]\[ A^{-1} = A^T \][/tex]

Taking the transpose of matrix A, gives

[tex]\[ A^{-1} = \begin{bmatrix}0 & 0 & 0 & 1 \\0 & 0 & 1 & 0 \\1 & 0 & 0 & 0 \\0 & 1 & 0 & 0 \\\end{bmatrix} \][/tex]

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Answer:

[tex]\frac{dy}{dx}[/tex] = - 21[tex]x^{6}[/tex] + 6x² + 1

Step-by-step explanation:

Differentiate each term using the power rule

[tex]\frac{d}{dx}[/tex] (a[tex]x^{n}[/tex] ) = na[tex]x^{n-1}[/tex]

Given

y = - 3[tex]x^{7}[/tex] + 2x³ + x , then

[tex]\frac{dy}{dx}[/tex] = (7 × - 3 )[tex]x^{6}[/tex] + (3 × 2)x² + (1 × 1 )[tex]x^{0}[/tex]

    = - 21[tex]x^{6}[/tex] + 6x² + 1

Hey there! :)

Answer:

D: [8, 12].

R: [-10, -6].

Step-by-step explanation:

Notice that the endpoints of the graph are closed circles. This means that square brackets will be used:

The graphed equation is from x = 8 to x = 12. Therefore, the domain of the function is:

D: [8, 12].

The range goes from y = -10 to -6. Therefore:

R: [-10, -6].

Answer:

D: [8 , 12]

R: [-10 , -6]

Step-by-step explanation:

Well for this parabola domain and rage are acttually limited because of the solid dots you see on the graph.

So first things first, what is range? Well range is the amount of y values on a line or anything in a graph.

And what’s domain? Domain is the amount of x values on a line or whatnot.

So let’s do domain first.

On the parabola the first x value is 8 and the last is 12 so we have to write this in interval notation which is  [8 , 12].

Now for range the lowest y value is -10 and the highest is -6 so in interval notation it is [-10 , -6].

Answer:

Yes, it's also true about the confidence interval method.

Step-by-step explanation:

The confidence interval includes all the null hypothesis values for the population mean that would be accepted by the hypothesis test at the significance level of 5%. Now, it means this assumes a two-sided alternative.

Now, when testing claims about

population​ proportions, the critical method and the​ P-value method are equivalent due to the fact that they always produce the same result. Similarly, a conclusion based on a confidence interval estimate will be the same as a conclusion based on a hypothesis test.

So, Yes the confidence interval method and the​ P-value or critical methods will always lead to the same conclusion when the tested parameter is the standard deviation.

Answer:

The sample size required is, n = 502.

Step-by-step explanation:

The (1 - α)% confidence interval for population proportion is:

[tex]CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p\cdot (1-\hat p)}{n}}[/tex]

The margin of error is:

[tex]MOE=z_{\alpha/2}\sqrt{\frac{\hat p\ \cdot (1-\hat p)}{n}}[/tex]

Assume that 50% of the people would support this political candidate.

The margin of error is, MOE = 0.05.

The critical value of z for 97.5% confidence level is:

z = 2.24

Compute the sample size as follows:

[tex]MOE=z_{\alpha/2}\sqrt{\frac{\hat p\ \cdot (1-\hat p)}{n}}[/tex]

       [tex]n=[\frac{z_{\alpha/2}\times \sqrt{\hat p(1-\hat p)}}{MOE}]^{2}[/tex]

           [tex]=[\frac{2.24\times \sqrt{0.50(1-0.50)}}{0.05}]^{2}\\\\=501.76\\\\\approx 502[/tex]

Thus, the sample size required is, n = 502.

Answer:

  (2/5)√5 ≈ 0.894427

Step-by-step explanation:

You require the y-coordinate of the point that satisfies two equations:

  x^2 +y^2 = 1

  y = 2x

Substituting for x, we have ...

  (y/2)^2 +y^2 = 1

  y^2(5/4) = 1

  y^2 = 4/5

  y = (2/5)√5 ≈ 0.894427

The sine of the angle is (2/5)√5 ≈ 0.894427.

Answer:

The answer would be C.

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

(3,15) and (4,12)

Answer:

C or (3, 15) and (4, 12)

Step-by-step explanation:

I just took the test on Edge 2020

Answer:

Step-by-step explanation:

[tex] - \frac{4}{9} + \frac{7}{12} + ( - \frac{ 3}{8} )[/tex]

When there is a (+) in front of an expression in parentheses, the expression remains the same:

[tex] - \frac{4}{9} + \frac{7}{12} - \frac{3}{8} [/tex]

[tex] \frac{ - 4 \times 8 + 7 \times 6 - 3 \times 9}{72} [/tex]

Calculate the sum of difference

[tex] \frac{ - 32 + 42 - 27}{72} [/tex]

[tex] \frac{10 - 27}{72} [/tex]

[tex] - \frac{17}{72} [/tex]

Hope this helps..

Good luck on your assignment...

Answer:

Step-by-step explanation:

1). [tex](\frac{-4}{9})\times (\frac{7}{4})=(-1)(\frac{4}{9})(\frac{7}{4} )[/tex]

                [tex]=-\frac{7}{9}[/tex] [Negative]

2). [tex](-2\frac{3}{4})(-1\frac{1}{5})=(-1)(2\frac{3}{4})(-1)(1\frac{1}{5})[/tex]

                        [tex]=(-1)^2(2\frac{3}{4})(1\frac{1}{5})[/tex]

                        [tex]=(2\frac{3}{4})(1\frac{1}{5})[/tex] [Positive]

3). (3)(-3)(-3)(-3)(-3) = 3.(-1).3.(-1).3.(-1).3(-1).(3)

                              = (-1)⁴(3)⁵

                              = (3)⁵ [Positive]

4). [tex](-\frac{1}{6})(-2)(-\frac{3}{5})(-9)[/tex] = [tex](-1)(\frac{1}{6})(-1)(2)(-1)(\frac{3}{5})(-1)(9)[/tex]

                                   = [tex](-1)^4(\frac{1}{6})(2)(\frac{3}{5})(9)[/tex]

                                   = [tex](\frac{1}{6})(2)(\frac{3}{5})(9)[/tex] [Positive]

5). [tex](-\frac{4}{7})(-\frac{3}{5})(-9)=(-1)(\frac{4}{7})(-1)(\frac{3}{5})(-1)(9)[/tex]

                            [tex]=(-1)^3(\frac{4}{7})(\frac{3}{5})(9)[/tex]

                            [tex]=-(\frac{4}{7})(\frac{3}{5})(9)[/tex] [Negative]

6). [tex](-\frac{10}{7})(\frac{8}{3})=(-1)(\frac{10}{7})(\frac{8}{3})[/tex]

                    [tex]=-(\frac{10}{7})(\frac{8}{3})[/tex] [Negative]

Answer:

[tex] \boxed{\sf x \degree = 62 \degree} [/tex]

Step-by-step explanation:

An exterior angle of a triangle is equal to the sum of the opposite interior angles.

[tex] \sf \implies x \degree + 38 \degree = 100 \degree \\ \\ \sf \implies x \degree + (38 \degree - 38 \degree) = 100 \degree - 38 \degree \\ \\ \sf \implies x \degree = 100 \degree - 38 \degree \\ \\ \sf \implies x \degree = 62 \degree[/tex]

In the given figure, the value of x is 62°.

An angle is the formed when two straight lines meet at one point, it is denoted by θ.

The given angles are,

x°, 38° and 100°.

To find the value of angle x, use exterior angle property.

According to exterior angle property,

The  sum of two interior angles is equal to exterior angle.

Since, 100° is the exterior angle of x and 38.

x + 38 = 100

x = 100 - 38

x = 62.

The required value of angle x is 62°.

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The first ordered pair is   ( -4 , -3 )

The second ordered pair is   ( 8, 3 )

=================================================

Explanation:

The first point is (x,-3) where x is unknown. It pairs up with y = -3 so we can use algebra to find x

x-2y = 2

x-2(-3) = 2 ... replace every y with -3; isolate x

x+6 = 2

x = 2-6

x = -4

The first point is (-4, -3)

---------------------------

We'll do something similar for the other point. This time we know x but don't know y. Plug x = 8 into the equation and solve for y

x-2y = 2

8-2y = 2

-2y = 2-8

-2y = -6

y = -6/(-2)

y = 3

The second point is (8, 3)

Answer:

200√3

Step-by-step explanation:

The triangle given here is a special right triangle, one with angles measuring 30-60-90 degrees. The rule for triangles like these are that the side opposite the 30° angle can be considered x, and the side opposite the 60° angle is x√3, while the hypotenuse, or side opposite the right angle, is 2x. All we need to know here are the two legs to find the area.

Since b is opposite the 30° angle, it is x, while side RS is opposite the 60° angle, meaning it is equal to x√3, meaning that the area of the triangle is 1/2*x*x√3. We can substitute in 20 for x, making our area 1/2*20*20√3. Multiplying we get 10*20√3, or 200√3.

Answer:

  3 square units

Step-by-step explanation:

Put the numbers in the formula and do the arithmetic.

  A = 12(1/2)² = 12(1/4) = 3 . . . square units

__

Comment on the working

It might be helpful to you to see how this works when the units of the number are attached to the number.

  A = 12(1/2 unit)² = 12(1/2 unit)(1/2 unit) = 12(1/2)(1/2)(unit)(unit) = 3 unit²

I often choose to keep the units with the numbers, just to make sure that the numbers and units are correct. For example, you can multiply inches by feet, but you get in·ft, which is not square inches and not square feet. You have to do a conversion to get the result in square units.

Answer:

20 Lizard lollies.

Step-by-step explanation:

There are 10 lizard lollis.  This is out of 10+4+6 = 20 total treats.  This makes the probability of drawing a lizard lollis 10/20 = 1/2.

This means out of 40 treats handed out, we can expect him to give out 1/2(40) = 20 lizard lollis.

Answer:

58.1 and 17

Step-by-step explanation:

For the first triangles the similarity ratio is 1:7 so x is 8.3 × 7 = 58.1

For the second triangles the similarity ratio is 1:5 so x is 3.4 × 5 = 17

Answer:

hello your question is incomplete here is the complete question

Use cylindrical coordinates Find the volume of the solid that lies within both the cylinder x^2 + y^2=16 and the sphere x^2 + y^2 + Z^2= 81

Answer : [tex]\frac{4 \pi }{3} [729 - 65\sqrt{65} ][/tex]

Step-by-step explanation:

The given data

cylinder  = x^2 + y^2 = 16

sphere = x^2 + y^2 +z^2 = 81

from the given data the solid is symmetric around the xy plane hence we will calculate half the solid volume above the plane then  multiply the sesult by 2

Note : we are restricting our attention to the cylinder  x^2 + y^2 = 16 and also finding the volume inside the sphere which gives bound on the z-coordinate as well

the r parameter goes from 0 to 4

ATTACHED IS THE REMAINING PART OF THE SOLUTION

showing the integration

Answer:

  D.  65°

Step-by-step explanation:

The measure of the angle at crossed chords is the average of the measures of the intercepted arcs:

  m∠XYZ = (1/2)(arc XZ +arc WV)

  m∠XYZ = (1/2)(86° +44°) = 130°/2

  m∠XYZ = 65°

Answer:

Step-by-step explanation:

For a geometric sequence

U(n) = ar^n - 1

Where

n is the number of terms

r is the common ratio

a is the first term

From the sequence

a = 2

r = - 6 /2 = -3

U(n) = 2(-3) ^ n - 1

For the 7th term

U(7) = 2(-3) ^ 7 - 1

= 2(-3)^6

The final answer is

= 1458

Hope this helps you

Answer:

a) P(1) = 0.1637

b) [tex]P(x\geq 2) = 0.0176[/tex]

c) E(x) = 0.2

Step-by-step explanation:

If X follows a poisson distribution, the probability that a disk has exactly x missing pulses is:

[tex]P(x)=\frac{e^{-m}*m^x}{x!}[/tex]

Where m is the mean and it is equal to the value of lambda. So, replacing the value of m by 0.2, we get that the probability that a disk has exactly one missing pulse is equal to:

[tex]P(1)=\frac{e^{-0.2}*0.2^1}{1!}=0.1637[/tex]

Additionally, the probability that a disk has at least two missing pulses can be calculated as:

[tex]P(x\geq 2)=1-P(x<2)[/tex]

Where [tex]P(x<2)=P(0)+P(1)[/tex].

Then, [tex]P(0)[/tex] and [tex]P(x\geq 2)[/tex] are calculated as:

[tex]P(0)=\frac{e^{-0.2}*0.2^0}{0!}=0.8187\\P(x\geq 2) = 1 - (0.8187 + 0.1637)\\P(x\geq 2) = 0.0176[/tex]

Finally, In the poisson distribution, E(x) is equal to lambda. So E(x) = 0.2

Answer:

Solve for y in the first equation.

Step-by-step explanation:

Given

3x+y=9

15x-3y = 1

Required

Determine the first step to avoid fractions

From the list of given options, the option that best answered the question is to Solve for y in the first equation.

Solving for y will let you substitute the expression for y in the second equation

Going by that:- Solve for y in the first equation.

[tex]3x + y = 9[/tex]

Subtract 3x from both sides

[tex]3x - 3x + y = 9 - 3x[/tex]

[tex]y = 9 - 3x[/tex]

Substitute 9 - 3x for y in the second equation

[tex]15x - 3y = 1[/tex] becomes

[tex]15x - 3(9 - 3x) = 1[/tex]

[tex]15x - 27 + 9x = 1[/tex]

Collect like terms

[tex]15x + 9x = 1 + 27[/tex]

[tex]24x = 28[/tex]

Divide both sides by 24

[tex]\frac{24x}{24} = \frac{28}{24}[/tex]

[tex]x = \frac{28}{24}[/tex]

Divide numerator and denominator by 4

[tex]x = \frac{7}{6}[/tex]

Substitute 7/6 for x in the [tex]y = 9 - 3x[/tex]

[tex]y = 9 - 3 * \frac{7}{6}[/tex]

[tex]y = 9 - \frac{7}{2}[/tex]

Solve fraction

[tex]y = \frac{18-7}{2}[/tex]

[tex]y = \frac{11}{2}[/tex]

Answer:

It's B (the one above is right)

Step-by-step explanation:

Answer:

The valid point is (5/2, 5)

Step-by-step explanation:

In order to check which ones are valid we will apply all of them to the expression.

(5,15):

[tex]\frac{2}{5}x - \frac{1}{5}y \geq 0\\\\\frac{2}{5}5 - \frac{1}{5}15 \geq 0\\\\-1 \geq 0[/tex]

False.

(1/2, 5):

[tex]\frac{2}{5}x - \frac{1}{5}y \geq 0\\\\\frac{2}{5}\frac{1}{2} - \frac{1}{5}5 \geq 0\\\\-\frac{4}{5} \geq 0[/tex]

False.

(5/2, 5):

[tex]\frac{2}{5}x - \frac{1}{5}y \geq 0\\\\\frac{2}{5}\frac{5}{2} - \frac{1}{5}5 \geq 0\\\\0 \geq 0[/tex]

True.

(2,5):

[tex]\frac{2}{5}x - \frac{1}{5}y \geq 0\\\\\frac{2}{5}2 - \frac{1}{5}5 \geq 0\\\\-\frac{1}{5} \geq 0[/tex]

False

(-1,0):

[tex]\frac{2}{5}x - \frac{1}{5}y \geq 0\\\\\frac{2}{5}(-1) - \frac{1}{5}0 \geq 0\\\\-\frac{2}{5} \geq 0[/tex]

False.

Answer:

1:3

Step-by-step explanation:

10 red cards, 10 black cards, and 20 blue cards

We want the ratio of red to other cards

red : blue and black

10 : 10+20

10 : 30

Divide each side by 10

10/10 : 30/10

1:3

Answer:

1/5k-2/3j and -2/3j+1/5k

Step-by-step explanation:

This is because the sign of both of the terms stay the same and the fractions and variables stay the same for each term as well.

Answer:

Step-by-step explanation:

y-|x|+3

y=|x|+3

vertex=(0,3)

y=|x-4|-7

vertex(4,-7)

Answer:

Step-by-step explanation:

Let d represent the number of dimes. Then d-9 is the number of nickels. The total value (in cents) is ...

  10d +5(d-9) = 180

  15d -45 = 180 . . . . . simplify

  d -3 = 12 . . . . . . . . . .divide by 15

  d = 15

  15 -9 = 6 = number of nickels

Sue has 15 dimes and 6 nickels.

Answer:

15 dimes, 6 nickels

Step-by-step explanation:

D = # of dimes, and N = # of nickels

10D + 5N = 180

D = N + 9

Substitute:

10 (N + 9) + 5N = 180

10N + 90 + 5N = 180

15N = 90

N = 6

D = 15

Answer:

Length = 45 m

Width = 185 m

Step-by-step explanation:

Given:

Perimeter of rectangular rug = 460 m

width of the rug is five meters more than 4 times the length

To find:

Width and length of rug = ?

Solution:

Let the length = [tex]l[/tex] m

As per given statement,

Width = [tex]4l+5[/tex] m

Formula for perimeter of a rectangle = [tex]2\times (Length +Width)[/tex]

[tex]460=2\times (l+4l+5)\\\Rightarrow 230 = 5l+5\\\Rightarrow l = \dfrac{225}{5} = 45\ m[/tex]

Width = [tex]4l+5[/tex] m

Width = [tex]4\times 45+5 = 185\ m[/tex]

So, the answer is:

Length = 45 m

Width = 185 m

Answer:

His final velocity is 48.03 m/s

Step-by-step explanation:

Using SI units  (m, kg, s)

a = 3.7

x0 = 25

x1 = 300

v0 = 16.5

Apply kinematics formula

v1^2 - v0^2 = 2a(x1-x0)

solve for v1

Final velocity

v1 = sqrt(2a(x1-x0)+v0^2)

= sqrt( 2(3.7)(300-25)+16.5^2) )

= 48.03 m/s

Answer:

The answer's A 1/52

Step-by-step explanation:

That's because there's only one ace of hearts in a deck of 52 cards.

Answer: A) 1/52

Step-by-step explanation:

There is 52 cards in a whole deck, and the probability of getting that ace card is 1/52 because there is only 1 ace card in an entire deck of cards.

Hence, the answer is 1/52

Answer:

Slope: 1

y-intercept: 8

Step-by-step explanation:

x, y

-8,0

0,8