Assume that Y is normally distributed with mean μ and standard deviation σ. After observing a value of Y, a mathematician will construct a rectangle with length L = |Y|and width W = 3 |Y|. Let A denote the area of the resulting rectangle. What is E(A)?

Answer:

1/36

Step-by-step explanation:

P(2 then 1) = 1/6 x 1/6 = 1/36

Answer:

good question

Step-by-step explanation:

Answer:

Step-by-step explanation:

The formula to find the angle between 2 vectors is

[tex]cos\theta=\frac{u*v}{|u||v|}[/tex] which is the dot product of u*v over the (magnitude of u times the magnitude of v). We also know that θ = [tex]\frac{\sqrt{2} }{2}[/tex]. Filling in that formula requires us to find the dot product of u and v, which is

u·v = (2×(-6)) + (a×8) so

u·v = -12 + 8a. Then we need the magnitudes of both u and v:

[tex]|u|=\sqrt{2^2+a^2}=\sqrt{4+a^2}[/tex] and

[tex]|v|=\sqrt{(-6)^2+8^2}=\sqrt{100}=10[/tex]

Putting all of together looks like this:

[tex]\frac{\sqrt{2} }{2}=\frac{-12+8a}{10\sqrt{4+a^2} }[/tex] . Cross multiply to get

[tex]10\sqrt{2}(\sqrt{4+a^2})=2(-12+8a)[/tex] which is tricky to simplify. You really need to know the rules for multiplying radicals to do this correctly. The simplification is

[tex]10\sqrt{8+2a^2}=-24+16a[/tex] and we need to solve for a. Begin by squaring both sides to get rid of the square root to get:

100(8 + 2a²) = 256a² - 768a +576 and simplify some more by distributing through the parenthesis to get

800 + 200a² = 256a² -768a + 576. Combine like terms to come up with

0 = 56a² - 768a - 224 and we need to factor that. Assuming since you're this far in math (pre-calc or maybe late algebra 2) you know how to factor, when you do, you get values for a of - .285714... and 14.

Therefore, the value for a is 14. I checked it...it works

Answer:

a = 14, U = (2, 14)

Step-by-step explanation:

the other answer is correct.

just to add the solution path for the quadratic equation

0 = 56a² - 768a - 224

in general, a quadratic equation usually expressed in x

0 = ax² + bx + c

has its solution as

x = (-b ± sqrt(b² - 4ac))/(2a)

for us here this looks like this then

a = (768 ± sqrt(768² - 4×56×-224))/(2×56) =

= (768 ± sqrt(589824 + 4×56×224))/112 =

= (768 ± sqrt(589824 + 50176))/112 =

= (768 ± sqrt(640000))/112 = (768 ± 800)/112

a1 = (768 + 800)/112 = 1568/112 = 14

a2 = (768 - 800)/112 = -32/112 = -0.29

and the negative solution would be for a vector solution in the wrong direction (down instead of up). as V is pointing up left, and the angle is only 45 degrees (pi/4), also U has to point up.

so, 14 is the solution for U.

Answer:

C) 5.66

Step-by-step explanation:

For a 45-45-90 triangle, the length of each leg length (not including the hypotenuse) is congruent to each other. If 8=y√2, then y=8/√2=4√2=5.66

Answer:

5.66

Step-by-step explanation:

take 45 degree as reference angle

using cos rule

cos 45 =adjacent /hypotenuse

[tex]\frac{1}{\sqrt{2} }[/tex] =y/8

[tex]\frac{1}{\sqrt{2} } *8=y[/tex]

[tex]\frac{8}{\sqrt{2} }=y[/tex]

[tex]4\sqrt{2} =y[/tex]

5.66=y

Answer:

both apply

Step-by-step explanation:

i guessed just do it

See the graph in the attached image.

Answer:

334.4 m²

Step-by-step explanation:

The formula for the area of a sector is given as:

1/2 × r² × θ

Where θ = Central angle

Area of a Circle = 700 m²

The formula for the area of a circle = πr²

r = Radius of a circle

r² = Area / π

r = √Area / π

r = √700/π

r = 14.927053304 m

Approximately, r = 14.93 m

Therefore, the area of the sector

= 1/2 × r² × θ

= 1/2 × 14.93² × 3 rad

= 334.35735 m²

Approximately, Area of the sector = 334.4 m²

Answer:

Maybe Plants products...

Answer:

120 free throws

Step-by-step explanation:

If she misses 15% of her free throws, that means she makes 85% of them.

Find how many she attempted by dividing 102 by 0.85:

102/0.85

= 120

So, she attempted 120 free throws

The number of free throws that were attempted is 120 free throws.

Since the basketball player missed 15% of her free throws, This means that the percentage scored will be:

= 100% - 15% = 85%

Therefore, 85% of x = 102

0.85x = 102

x = 102/0.85.

x = 120

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Answer:

S>1

Step-by-step explanation:

5s + 2 > 7

Subtract 2 from both sides

5s>5

Divide 5 from both sides

S>1

Solution of the inequality is s>1.

In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to one another.

Adding the same amount to each side, taking the same amount away from each side, multiplying or dividing each side by the same positive integer, and other operations can be used to solve the inequality.

The inequality sign must be reversed if either side is multiplied or divided by a negative number.

5s+2 > 7

Subtracting 2 on both side,

5s > 5

s>1

Therefore, the solution set of inequality is s>1.

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Answer:

[tex]( {x}^{2} + 12)(x + 2)[/tex]

Step-by-step explanation:

[tex] {x}^{3} +2 {x}^{2} +12x+24[/tex]

[tex]( {x}^{3}+2 {x}^{2} )+12x+24[/tex]

[tex] {x}^{2} (x+2)+12(x+2)[/tex]

[tex]( {x}^{2} + 12)(x + 2)[/tex]

Answer:

24 per day

Step-by-step explanation:

'x' = days, so since 24 is with x, the rate of change is 24

Answer:

38

Step-by-step explanation:

Have a nice day :)

Answer:

A) 3 ways

B) sorry don't know.

Step-by-step explanation:

2 P and 2 N

3P and 1 N

4P

So 3 ways.

Answer: Graph B

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

Explanation:

Point A appears to be at (2.5, -1)

If we shift 6 units to the left, then we subtract 6 from the x coordinate. So the new x coordinate is now 2.5-6 = -3.5

If we shift 4 units up, then we add 4 to the y coordinate to go from -1 to -1+4 = 3

Overall, the point A(2.5, -1) moves to A'(-3.5, 3)

Graph B is the answer because of this. The other points B and C will follow the same pattern as point A does.

Answer:

Step-by-step explanation:

A customer satisfaction survey refers to a questionnaire that's designed by a company in order for businesses to know what customers think about their products.

Since the manager of a local car dealership wants to conduct a customer satisfaction survey, then the group of people should make up a sample of the population will be the people who bought cars from the dealership

Answer:

c

Step-by-step explanation:

Answer:

f(x) = x^2 ( x -4i) (x+4i)

Step-by-step explanation:

f(x) = x^4 + 16x^2

Factor out x^2

f(x) = x^2 ( x^2 +16)

f(x) = x^2 ( x^2 - -16)

The square root of -16 is 4i and -4i

Using the difference of square (a^2 - b^2) = (a-b)(a+b)

f(x) = x^2 ( x -4i) (x+4i)

Answer:

14 (B)

Step-by-step explanation:

Area = L * h

L = 7 in^2

h = 2

Area = 7 * 2

Area = 14 in^2

Answer:

14

Step-by-step explanation:

Did lesson

Given:

x-intercepts of the hyperbola are ±4.

The foci of hyperbola are [tex]\pm 2\sqrt{5}[/tex].

Center of the hyperbola is at origin.

To find:

The equation of the hyperbola.

Solution:

The general equation of a hyperbola:

[tex]\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1[/tex]            ...(i)

Where, (h,k) is the center of the hyperbola, ±a are x-intercepts, [tex](\pm c,0)[/tex] are foci.

Center of the hyperbola is at origin. So, h=0 and k=0.

x-intercepts of the hyperbola are ±4. So,

[tex]\pm a=\pm 4[/tex]

[tex]a=4[/tex]

The foci of hyperbola are [tex]\pm 2\sqrt{5}[/tex].

[tex]\pm c=\pm 2\sqrt{5}[/tex]

[tex]c=2\sqrt{5}[/tex]

We know that,

[tex]a^2+b^2=c^2[/tex]

[tex](4)^2+b^2=(2\sqrt{5})^2[/tex]

[tex]16+b^2=20[/tex]

[tex]b^2=20-16[/tex]

[tex]b^2=4[/tex]

Taking square root on both sides, we get

[tex]b=\sqrt{4}[/tex]                    [b>0]

[tex]b=2[/tex]

Substituting [tex]h=0,k=0,a=4,b=2[/tex] in (i), we get

[tex]\dfrac{(x-0)^2}{4^2}-\dfrac{(y-0)^2}{2^2}=1[/tex]

[tex]\dfrac{x^2}{4^2}-\dfrac{y^2}{2^2}=1[/tex]

Therefore, the correct option is (d).

Answer:

60

[tex]2^{2} * 3 * 5[/tex]

Step-by-step explanation:

Answer:

44.94

Step-by-step explanation:

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

Explanation:

Let x be the net winnings the customer gets

Saying something like x = 24 means you've walked away with $24. This occurs when you pay $1, and get $25 back in prizes, so 25-1 = 24 dollars overall.

The probability of this event occurring is 1/100 since there's only one ticket with the $25 prize

Make a table as shown below. It represents all the possible x values which are all the possible net winnings. Note how 1/100 = 0.01, 3/100 = 0.03 and 95/100 = 0.95

The third column is x*p(x) which is the product of the first two columns. Adding everything in the third column (that isn't highlighted in yellow) gets us the value -0.45 which is the expected value for the customer.

This represents a loss of $0.45, aka a loss of 45 cents. This is from the perspective of the customer.

Flipping things around, the pizza company will see this is as a gain of $0.45 or a gain of 45 cents.

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

Here's another way to see why this works:

The pizza company earns $100 in revenue since 100 tickets are sold for a dollar each. The company pays out 25+15+3*5 = 55 dollars in prizes overall. That means the company will make a profit of 100-55 = 45 dollars. So the average profit per ticket is 45/100 = $0.45 aka 45 cents and this is from the viewpoint of the pizza company (not the customer). The positive average profit represents a gain.

Answer: 0.973

Step-by-step explanation:

The probability mass function of geometric distribution is

[tex]f(x)=(1-p)^{x-1}p,\ \ \ x=1,2,3,...[/tex], p= probability of success on a trial.

As per given, we have

p=0.7

The probability that we'll have at most 3 orders [tex]P(X\leq3)=P(x=1)+P(x=2)+P(x=3)[/tex]

[tex]=(1-0.7)^{1-1}(0.7)+(1-0.7)^{2-1}(0.7)+(1-0.7)^{3-1}(0.7)\\\\=0.7+0.21+0.063\\\\=0.973[/tex]

hence, the required probability = 0.973

The probability that we'll have at most 3 orders will be "0.973".

According to the question,

→ [tex]x \sim Geometric (p)[/tex]

here,

p = 0.7

then,

→ [tex]P(X=x) = (1-p)^{x-1}\times p[/tex]

By putting the given values, we get

                   [tex]= (1-0.7)^{x-1}\times 0.7[/tex]

hence,

The probability that we'll have at most 3 orders will be:

→ [tex]P(X \leq 3)=P(X=1)+P(X=2)+P(X=3)[/tex]

                   [tex]=0.7+0.21+0.063[/tex]

                   [tex]=0.973[/tex]

Thus the above response is correct.

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Answer: You didnt mention how much Dan mows in 1 hour, but just do that divided by 60

Step-by-step explanation:

Answer:

[tex]\% = 11.96\%[/tex]

Step-by-step explanation:

Given

See attachment for box plot

Required

Percentage greater than or equal to 233

From the box plot, the maximum is:

[tex]Max = 244[/tex]

The minimum is:

[tex]Min = 152[/tex]

Percentage greater than 233 is calculated as:

[tex]\% = \frac{Max - 233}{Max - Min}[/tex]

[tex]\% = \frac{244 - 233}{244-152}[/tex]

[tex]\% = \frac{11}{92}[/tex]

Express as percentage

[tex]\% = \frac{11}{92}*100\%[/tex]

[tex]\% = \frac{1100}{92}\%[/tex]

[tex]\% = 11.96\%[/tex]

Answer:

There are more females dropping than males each year and that there are more females than males

Answer:

Step-by-step explanation:

The element decay percentage rate of change 2.22% per minute.

Radioisotope, radionuclide, or radioactive nuclide, any of several species of the same chemical element with different masses whose nuclei are unstable and dissipate excess energy by spontaneously emitting radiation in the form of alpha, beta, and gamma rays.

Here, mass decreases by 73% every hour.

Weight of element X is 680 grams.

According to question,

f(t) = 680 (1 - 73%)ⁿ

f(t) = 680 (1 - 0.73)ⁿ

f(t) = 680 X 0.27ⁿ

f(t) = 680 X 0.9778ⁿ

f(t) = 680 X (1 - 0.02322)ⁿ

Thus, the element decay percentage rate of change 2.22% per minute.

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Answer:

Percentage of U.S resident who used the Internet for e-mail were Hispanic=9.19%

Step-by-step explanation:

We are given that

Population was Caucasian=64%

Population was African-American=11%

Population was Hispanic=10%

Let the population of U.S=10000

Now,

Population was Caucasian=[tex]\frac{64}{100}\times10000=6400[/tex]

Population was African-American=[tex]\frac{11}{100}\times 10000=1100[/tex]

Population was Hispanic=[tex]\frac{10}{100}\times 10000=1000[/tex]

Population of others=10000-(6400+1100+1000)=1500

Population of Caucasians used the Internet for e-mail=86% of 6400

Population of Caucasians used the Internet for e-mail=[tex]\frac{86}{100}\times 6400[/tex]

Population of Caucasians used the Internet for e-mail=5504

Population of African-American used the Internet for e-mail=77% of 1100

Population of African-American used the Internet for e-mail=[tex]\frac{77}{100}\times 1100=847[/tex]

Population of Hispanics used the Internet for e-mail=77% of 1000

Population of Hispanics used the Internet for e-mail=[tex]\frac{77}{100}\times 1000=770[/tex]

Population of others used the Internet for e-mail=84% of 1500

Population of others used the Internet for e-mail=[tex]\frac{84}{100}\times 1500=1260[/tex]

Total population used the Internet for e-mail=5504+847+770+1260

Total population used the Internet for e-mail=8381

Percentage of U.S resident who used the Internet for e-mail were Hispanic

=[tex]\frac{Population \;of \;Hispanics \;used \;the \;Internet \;for \;e-mail}{total\;population\; used \;the \;Internet \;for\; e-mail}\times 100[/tex]

Percentage of U.S resident who used the Internet for e-mail were Hispanic=[tex]\frac{770}{8381}\times 100[/tex]

Percentage of U.S resident who used the Internet for e-mail were Hispanic=9.19%