Type the correct answer in each box. Use numerals instead of words. Please Help!

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:

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:

7/16.  

Step-by-step explanation:

The first triangle has no shading.

The second triangle has 1/4 shaded.

The third has 3/9.

The fourth has 6/16.

Based on this pattern, we can assume that the number of small triangles in each triangle are going to be squared of numbers, since the first had 1, the second 4, the third 9, the fourth 16. So, the 8th triangle would have 8^2 small triangles, or 64 triangles in total.

The first triangle has no shaded triangles. The second has 1. The third has 3. The fourth has 6. If you study the pattern, the second triangle has 1 more than the previous, the third has 2 more, the fourth has three more. And so, the fifth triangle would have 6 + 4 = 10 triangles, the sixth would have 10 + 5 = 15 triangles, the seventh would have 15 + 6 = 21 triangles, and the eighth would have 21 + 7 = 28 shaded triangles.

So, the fraction of shaded triangles would be 28 / 64 = 14 / 32 = 7 / 16.

Hope this helps!

Answer:

Group B is farther from the airport.

Step-by-step explanation:

To find the distance of each group to the airport we can use the law of cosines in the triangle created with the two movements done and the resulting total distance.

Law of cosines:

[tex]c^2 = a^2 + b^2 - 2ab*cos(angle)[/tex]

For group A, we have the sides of 200 miles and 75 miles, and the angle between the sides is (180-68) = 112°, so the third side of the triangle is:

[tex]c^2 = 200^2 + 75^2 -2*200*75*cos(112)[/tex]

[tex]c^2 = 56863.198[/tex]

[tex]c = 238.46\ miles[/tex]

For group B, we also have the sides of 200 miles and 75 miles, and the angle between the sides is (180-51) = 129°, so the third side of the triangle is:

[tex]c^2 = 200^2 + 75^2 -2*200*75*cos(129)[/tex]

[tex]c^2 = 64504.612[/tex]

[tex]c = 253.98\ miles[/tex]

The distance from group B to the airport is bigger, so group B is farther from the airport.

Answer:

The expected number of sales of this store from this sample of 30 is 6.

Step-by-step explanation:

For each prospect, there are only two possible outcomes. Either there is a trade, or there is not. Prospects are independent of each other. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

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

The expected value of the binomial distribution is:

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

A retail variety store that advertises extensively by mail circulars expects a sale with 20% probability.

This means that [tex]p = 0.2[/tex]

Suppose 30 prospects are randomly selected from a city-wide mailing.

This means that [tex]n = 30[/tex]

What is the expected number (mean) of sales of this store from this sample of 30?

[tex]E(X) = np = 30*0.2 = 6[/tex]

The expected number of sales of this store from this sample of 30 is 6.

The expected number (mean) of sales of this store from this sample of 30 is 6.

Since A retail variety store that advertises extensively by mail circulars expects a sale with 20% probability. Suppose 30 prospects are randomly selected from a city-wide mailing.

So here the expected mean should be

= 20% of 20

= 6

Hence, The expected number (mean) of sales of this store from this sample of 30 is 6.

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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:

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:

[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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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:

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:

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:

Can 1 will contain more stew

Step-by-step explanation:

diameter= 8

radius=d/2=4

height=4

therefore volume= [tex]\pi[/tex] r2 h= 201.06

Diameter= 6

radius=d/2=3

height= 7

therefore volume= [tex]\pi[/tex] r2 h= 197.92

The cylindrical can that contains more stew is the first can which has a diameter of 8 inches and a height of 4 inches.

Suppose that the radius of considered right circular cylinder be 'r' units.

And let its height be 'h' units.

Then, its volume is given as:

[tex]V = \pi r^2 h \: \rm unit^3[/tex]

Right circular cylinder is the cylinder in which the line joining center of top circle of the cylinder to the center of the base circle of the cylinder is perpendicular to the surface of its base, and to the top.

The more volume of a can is, the more stew it can store.

For first can:

Since radius = diameter/2, so radius of base = 8/2 = 4 inches.

Thus, volume of first can: [tex]V = \pi (4)^2 (4) = 64\pi \: \rm unit^3[/tex]

For second can:

Since radius = diameter/2, so radius of base = 6/2 = 3 inches.

Thus, volume of first can: [tex]V = \pi (3)^2 (7) = 63\pi \: \rm unit^3[/tex]

Thus, as π > 0, so first can can contain more stew.

Thus, the cylindrical can that contains more stew is the first can which has a diameter of 8 inches and a height of 4 inches.

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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:

b= 10.39

c = 20.79

Step-by-step explanation:

a = 60 °

b = 30°

c= 180-(60+30)

c = 180-(90)

c = 90°

Length facing angle a = 18

Let's look for length facing angle b

b/sinb = a/sin a

b/sin 30 = 18/sin 60

b =( 18 * sin30)/sin 60

b = (18*0.5)/0.8660

b = 9/0.8660

b= 10.39

Let's look for c

c/sin c = a/sin a

c/sin 90 = 18/sin 60

c = (18 * sin 90)/sin 60

c =18/0.8660

c = 20.79

Answer:

y = (x - 4)² + 2 , x ≥ 4.

Step-by-step explanation:

Finding the inverse of

f(x) = 4 + √(x - 2)

Begin by swapping the x and y variables in the equation:

x = 4 + √(y - 2)

Subtract 4 from both sides:

x - 4 = √(y - 2)

Square both sides:

(x - 4)² = y - 2

Add 2 to both sides to get your equation:

y = (x - 4)² + 2

However, the domain restriction also needs to be included since the question involves finding the inverse of a square root function. In this case, the domain restriction would be x ≥ 4.

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

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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Given that,

ABC and ADC are triangles.

The area of ΔADC is 52 m².

Suppose , AD is the median.

According to figure,

We need to find the area of ΔABC

Using theorem of triangle

[tex]\bigtriangleup ADB +\bigtriangleup ADC=\bigtriangleup ABC[/tex]

Here, Δ ADB = Δ ADC

So, [tex]2 \bigtriangleup ADC=\bigtriangleup ABC[/tex]

Put the value of Δ ADC

[tex]\bigtriangleup ABC =2\times52[/tex]

[tex]\bigtriangleup ABC = 104\ m^2[/tex]

Hence, The area of ΔABC is 104 m².

Answer:

180 degrees

Step-by-step explanation:

The sum of all the interior angles in a triangle is always equal to 180 degrees.

Answer:

The correct answer is TRUE.

Step-by-step explanation:

Find the measure of x.

Begin by setting up an equation of the five angles equal to 180°.

x + 37° + 41° + 29° + 51°  = 180° • The sum of the angles is 180°.

x + 158° = 180°       • Add the known values on the left side.

x = 22° • Subtract 158° from both sides.

The measure of angle x is 22°.

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:

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:

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:

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:

350 mL of water

Step-by-step explanation:

Well she starts with 200mL of water and there is 800 mL of acid of water.

She drains 100 mL of acid and adds 100 mL of water so there is 300 mL of water.

And she stirs meaning the compounds have mixed.

Then she drains 100 mL and she they are mixed she drains half of acid and half of water so she has 250 mL of water.

The she adds 100 mL of water so now there’s 350 mL of water left.

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:

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:

Step-by-step explanation:

y-|x|+3

y=|x|+3

vertex=(0,3)

y=|x-4|-7

vertex(4,-7)

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:

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..

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