The foci of the hyperbola are ( 13 , 0) and (− 13 , 0), and the asymptotes are y = 12 x and y = − 12 x. find an equation of the conic section with the given properties. use x and y as the variables in your answer.

Answers

Answer 1

y=k+- a/b(x-h)

y=-+12x

12=a/b

a=12b

c²=a²+b²

(13,0) and (-13,0)

13²=(12b)²+b²

169=145b²

b= 13/12

169=a²+169/145

a²= 24336/145

x²/a²-y²/b²=1

145x²/24336 + 145y²/169=1

Answer 2

The equation of the conic section is [tex]\frac{145x\²}{24336} - \frac{145y\²}{169}=1[/tex]

The foci of the hyperbola are given as: (13,0) and (-13,0)

The asymptote is given as [tex]y =\pm 12x[/tex]

Divide both sides of [tex]y =\pm 12x[/tex] by x.

[tex]\frac yx = \pm 12[/tex]

Where y/x = a/b.

So, we have:

[tex]\frac ab = \pm 12[/tex]

Make a the subject

[tex]a = \pm 12b[/tex]

Recall that

[tex]c\²=a\²+b\²[/tex]

Where:

[tex]c = \pm13[/tex]

[tex]c\²=a\²+b\²[/tex] becomes

[tex](\pm 13)^2 = (\pm 12b)^2 +b^2[/tex]

[tex]169 = 144b^2 +b^2[/tex]

Evaluate like terms

[tex]169 = 145b^2[/tex]

Make b^2 the subject

[tex]b^2 = \frac{169}{145}[/tex]

Recall that [tex]a = \pm 12b[/tex]

Square both sides

[tex]a^2 = 144b^2[/tex]

Substitute [tex]b^2 = \frac{169}{145}[/tex]

[tex]a^2 = 144 \times \frac{169}{145}[/tex]

[tex]a^2 = \frac{24336}{145}[/tex]

The equation of the conic section is represented as:

[tex]\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1[/tex]

Substitute known values

[tex]\frac{x^2}{24336/145} - \frac{y^2}{169/145} = 1[/tex]

Rewrite as:

[tex]\frac{145x\²}{24336} - \frac{145y\²}{169}=1[/tex]

Hence, the equation of the conic section is [tex]\frac{145x\²}{24336} - \frac{145y\²}{169}=1[/tex]

Related Questions

Find the length of the arc shown in red, Leave your answer in terms of pi.

Answers

Answer:

The red arc has length (3/2) π

Step-by-step explanation:

* Lets revise some rules in the circle

- The measure of any arc = the measure of the central angle

subtended by this arc

- Equal central angles subtended by equal arcs

- The length of the arc is a part from the length of the circle,

it depends on the ratio between the measure of this arc

and the measure of the circle

- The measure of the circle = 360°

- The length of the circle = 2πr

* Lets solve our problem

∵ The measure of the arc = 30°

∴ The measure of its central angle 30°

∴ The central angle of the red arc = 30° by condition of

vertically opposite angles are equal in measures

∴ The measure of the red arc = 30°

- The ratio between measure the arc and the measure

of the circle is 30/360 = 1/12

∴ The arc is 1/12 from the circle

∴ The length of the arc is 1/12 from the length of the circle

∴ Length red arc = (1/12) × 2πr

∵ r = 9

∴ Length red arc = (1/12) × 2 × π × 9 = (3/2) π

* The red arc has length (3/2) π

help with this question?

Answers

The rational expression [tex]\dfrac{(x-4)(x+9)}{(x-1)(x+9)}[/tex] has a removable discontinuity at x=-9. The definition of f(x) removes the discontinuity at x=-9. However, the function remains undefined at x=1.

The appropriate choice is ...
c. continuous at every real number except x = 1.

Rhombus A has base of 7 inches and an area of 35 square inches. Rhombus B has a Base and Height that are three times the base and height of Rhombus A. Find the area of Rhombus b and compare it to the area of rhombus A Explain

Answers

Final answer:

Rhombus B, which has dimensions three times larger than Rhombus A, has an area that is nine times larger than the area of Rhombus A.

Explanation:

This question is based on geometry and compares the areas of two rhombuses. Firstly, remember that the area of a rhombus is obtained by the formula A = base x height. For Rhombus A, with a base of 7 inches and area 35 square inches, this implies that its height is 5 inches (since 7 x 5 = 35). Therefore, the height of Rhombus B which is three times larger than that of Rhombus A would be 15 inches, and its base would be 21 inches (three times that of Rhombus A).

Now applying these values into the formula for the area of a rhombus, for rhombus B we get A = 21 x 15, which equals 315 square inches - this is the area of Rhombus B. Comparing this with the area of Rhombus A (35 square inches), we find that Rhombus B is 9 times larger than Rhombus A (because 315 divided by 35 equals 9).

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Final answer:

By increasing the base and height of Rhombus A by three times, the resulting area of Rhombus B is nine times the area of Rhombus A. The area of Rhombus A is 35 square inches and the area of Rhombus B is 315 square inches.

Explanation:

The subject of this question is area of rhombuses. A key concept to remember is that the area of a rhombus is calculated by the formula: Area = base x height.

Rhombus A has base of 7 inches and an area of 35 square inches. This means the height h of Rhombus A is A/base = [tex]35/7 = 5[/tex] inches.

The base and height of Rhombus B are three times the base and height of rhombus A. So, Rhombus B has a base of [tex]7 * 3 = 21[/tex] inches and height of [tex]5 * 3 = 15[/tex] inches.

To find the area of Rhombus B, you apply the same formula, Substituting the values we get, B = base x height = [tex]21 * 15 = 315[/tex] square inches. Therefore, the area of Rhombus B is nine times the area of Rhombus A since 315/35 = 9.

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identify the type of conic section that has the equation 4x^2+25y^2=100 and identify its domain and range.

Answers

To obtain the domain and the range, I will give you the graph of the section so that you can understand better.
4x^2+25y^2=100
The range:
set y=0, and solve for x:
4x^2=100
x^2=25
x=+/-5
thus the domain is:
[-5,5]

Range:
set x=0 and solve for y:
25y^2=100
y^2=4
y=+/-2
thus the range is:
[-2,2]

Final answer:

The equation given represents an ellipse, a type of conic section. The domain of this particular conic section is -5 to 5, and its range is -2 to 2.

Explanation:

The equation given represents an ellipse, which is one kind of conic section. The general form of the equation of an ellipse is[tex]x^2/a^2 + y^2/b^2 = 1,[/tex] where a and b are the lengths of the semi major and minor axes respectively. The equation you provided, [tex]4x^2+25y^2=100,[/tex]when arranged to fit into the general form of ellipse becomes [tex]x^2/25 + y^2/4 =1.[/tex] Thus, it is clear that the given equation represents an ellipse.

The domain of the function described by this elliptical equation includes all the x-values that the ellipse covers, and for this particular equation, is -5 to 5. The range includes all the y-values that the ellipse covers, which in this case is -2 to 2.

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You have the opportunity to lease space for your business with a fixed-rate lease. The property owner has proposed a five-year lease with a rent of $4,000 per month. How much is the rent per year? How much is the rent over the life of the lease?

Answers

$48,000/year, $240,000 total

Is 28 cups greater or less than 14 Pints

Answers

Short answer: NO.

28 cups is exactly equal to 14 pints. (There are 2 cups per pint.)

Matt has $550 in his savings account. He is eager to know how much interest the bank will pay him for the whole year. He knows that the bank pays a 3 percent interest rate. He sits down with a pen, paper, and calculator to find out the simple interest

Answers

Nice story.

We suppose the question is, "what is the amount of interest Matt will be paid?"

The formula that applies is
I = Prt
I = $550*0.03*1 = $16.50

Matt will be paid $16.50 in interest for the year.

NEED HELP WILL GIVE OUT BRAINLIEST AND POINTS

11. Find the area. The figure is not drawn to scale.

12. Find the area of the kite. The figure is not drawn to scale.

Answers

part 1) Find the area

we know that
the area of the triangle is
A=b*h/2
in this problem
b=9
h=12
so
A=9*12/2-----> A=54 units²

the answer part 1) is
Area=54 units²

Part 2) Find the area of the kite

see the picture attached with letters to better understand the problem

we know that
The area of a Kite is half the product of the diagonals

step 1
find CB
applying Pythagoras Theorem
AB²=AC²+BC²------> BC²=AB²-AC²-----> BC²=5²-3²----> BC²=16
BC=4
so
the diagonals are
(10+4) and (3+3)---------> 14 and 6
Area=(1/2)*[14*6]----> Area=42 units²

the answer Part 2) is
the area of a kite is 42 units²

John paid 5% sales tax on his television, which cost $769 before taxes. What did the television cost in total?

Answers

For this case we can make the following rule of three:
$ 769 ---------> 100%
x --------------> 105%
From here, we clear the value of x.
We have then:
x = (105/100) * (769)
x = 807.45 $
Answer:
the television did cost 807.45 $ in total

An airliner travels 45 miles in 5 minutes. What is it’s speed in miles?

Answers

9 miles per minute. Divide 45 by 5

F(x, y, z) = yz i + xz j + (xy + 18z) k c is the line segment from (1, 0, −1) to (5, 6, 1) (a) find a function f such that f = ∇f. f(x, y, z) = (b) use part (a) to evaluate c ∇f · dr along the given curve
c.

Answers

[tex]\nabla f(x,y,z)=\dfrac{\partial f}{\partial x}\,\mathbf i+\dfrac{\partial f}{\partial y}\,\mathbf j+\dfrac{\partial f}{\partial z}\,\mathbf k=\mathbf f(x,y,z)[/tex]

[tex]\displaystyle\int\frac{\partial f}{\partial x}\,\mathrm dx=\int yz\,\mathrm dx[/tex]
[tex]\implies f(x,y,z)=xyz+g(y,z)[/tex]
[tex]\dfrac{\partial f}{\partial y}=xz+\dfrac{\partial g}{\partial z}=xz[/tex]
[tex]\implies\dfrac{\partial g}{\partial z}=0[/tex]
[tex]\implies g(y,z)=h(z)[/tex]

[tex]\dfrac{\partial f}{\partial z}=xy+\dfrac{\mathrm dh}{\mathrm dz}=xy+18z[/tex]
[tex]\implies\dfrac{\mathrm dh}{\mathrm dz}=18z[/tex]
[tex]\implies h(z)=9z^2+C[/tex]

[tex]\implies f(x,y,z)=xyz+9z^2+C[/tex]

[tex]\implies\displaystyle\int_{\mathcal C}\mathbf f\cdot\mathrm d\mathbf r=f(5,6,1)-f(1,0,-1)=30[/tex]

Final answer:

Through anti-derivatives, we find a function f(x, y, z) in part (a) of the problem. We then use the fundamental theorem of line integrals in part (b) to evaluate the line integral of ∇f ∙ dr along a curve c, using the function f we found.

Explanation:

This problem lies within the field of vector calculus, specifically dealing with gradient fields and line integrals. Part (a) requires us to find a function f(x, y, z) such that the gradient of f (∇f) is equal to the field F. Since ∇f yields the vector field (Fx, Fy, Fz), we find the anti-derivatives of each component of F to solve for f. For this particular function f, the anti-derivatives are 1/2 * yz^2 + C1 for Fx = yz, 1/2 * xz^2 + C2 for Fy = xz, and 1/2 * xy^2 + 9z^2 + C3 for Fz = xy + 18z. Therefore, the function that satisfies the requirement is 1/2 * yz^2 + 1/2 * xz^2 + 1/2 * xy^2 + 9z^2 + C, where C is a constant.

Part (b) then requires the evaluation of the line integral of ∇f ∙ dr along a curve c, from point (1,0,-1) to (5,6,1). According to the fundamental theorem of line integrals, if a vector field is conservative (as it is in this case because we found a function f such that F = ∇f), the line integral of a vector field F along a curve c from a to b is simply f(b) - f(a). Therefore, using the function f found in part a, you can substitute the coordinates of points a and b to find the solution to the line integral equation.

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How does an earthquake of magnitude 7.9 compare in intensity with an earthquake of magnitude of 3.7 on the Richter scale? The larger earthquake's intensity was nothing times as great as the smaller earthquake's intensity. (Round to the nearest whole number as needed.)

Answers

Answer:

15,849

Step-by-step explanation:

Final answer:

A magnitude 7.9 earthquake releases approximately 2.7 million times more energy than a 3.7 magnitude earthquake, as the Richter scale is logarithmic and represents a 32-fold increase in energy release for each unit increase in magnitude.

Explanation:

The Richter scale is logarithmic, which means that each whole number increase represents a tenfold increase in amplitude and roughly a 32-fold increase in the energy released by an earthquake.

Therefore, when comparing a magnitude 7.9 earthquake to a magnitude 3.7 earthquake, there is a difference of 4.2 on the Richter scale.

This corresponds to a tenfold increase in amplitude 4.2 times, which would be 10 to the power of 4.2 in terms of amplitude.

However, if we consider the energy, which increases by a factor of 32 for each whole number increase, we're looking at 32 to the power of 4.2, which is approximately 2,704,156 times greater in terms of energy release.

To determine the intensity difference in a more simplified manner, taking the base-10 logarithm of the energy ratio is effective.

The simplified comparison tells us that the larger quake's intensity is about 2.7 million times greater than the smaller quake's intensity.

After rounding to the nearest whole number, we find that the intensity is 2,704,156 times as great.

400,000 + 80,000 + 4,000 + 50 + 9 Write the standard form of the number shown above.

Answers

Add:

400,000
80,000
4,000
59
--------------
484,059 (answer)

Hello there, and thank you for posting your question here on brainly.

Short answer: 484,059

Why?

This equation shown is an expanded form of a number. 400k is the largest number, so that'd go first. 80k is the second largest, so that would go next to the largest number, 4. (400k) 4k is the third largest, so that'd go next to the first and second largest numbers, 48. (480k) Now, we have 484,000. Since there is no hundred, we put a zero there. Now, add a 59 at the end of the zero. Which gives us the number 484,059.

Hope this helped you! ♥

hey can some one look at this?

Answers

I'm just going to give you a very quick answer, but I can answer the question
1 foot = 12 inches.
x feet = 60 inches.

1 foot * 60 inches = 12 * x divide by 12

60 / 12 = 5

So the person is at least 5 feet tall. The height you want is 5 feet 4 inches.

So add 4 inches to 5 feet.
or
Add 4 inches to 60 inches.
you get 64 inches.

There are 20 entries all together. 2 people are 64 inches tall.

P(64) = 2/20 = 1/10 = 0.1

Answer P(64) = 0.1

I would check all of this if I were you. I'm not sure I counted either one correctly.

Of the 5th grade boys, 2/3 play sports. Of the boys who play sports, 1/4 play baseball. what fraction of the 5th grade boys play baseball?

Answers

So, to find this rate, we simply multiply the two fractions together:
2/3 * 1/4
2/12
Simplify:
1/6 of the 5th grade boys play baseball

If the typos are randomly distributed over the 10 pages, find the probability of having a single typo on each page

Answers

1/10 assuming there is are 10 typos in total

What is the mean of 20, 37, 43, 54, 83, 102, 117, 160, 208?

Answers

Answer is 91.56 You add all the numbers up and divide by 9(There are 9 numbers in the sequence).

Suppose x is a normal random variable with μ = 35 and σ = 10. find p(55.5 < x < 69.7).

Answers

Answer:

[tex]\boxed{\boxed{P(55.5 < X< 69.7)=0.01992}}[/tex]

Step-by-step explanation:

We know that,

[tex]Z=\dfrac{X-\mu}{\sigma}[/tex]

where,

Z = z-score,

X = raw score,

μ = mean,

σ = standard deviation.

So,

[tex]=P(55.5 < X< 69.7)[/tex]

[tex]=P(55.5-35 < X-35< 69.7-35)[/tex]

[tex]=P(\dfrac{55.5-35}{10}< \dfrac{X-35}{10}< \dfrac{69.7-35}{10})[/tex]

[tex]=P(\dfrac{55.5-35}{10}< Z< \dfrac{69.7-35}{10})[/tex]

[tex]=P(2.05< Z<3.47)[/tex]

[tex]=P(Z<3.47)-P(Z<2.05)[/tex]

[tex]=0.99974-0.97982\\\\=0.01992[/tex]

Let μ = 160 and σ = 16. find the z-score for the score, x = 150.

Answers

Put the given values in the formula
[tex]z=\dfrac{x-\mu}{\sigma}[/tex]
and evaluate.
z = (150 -160)/16 = -10/16
z = -5/8

The z-score for the score x=150 is -5/8 = -0.625.

What does same amount means?

Answers

This means two numbers that equal the same amount

How many terms are there in a geometric series if the first terms is 2, the common ratio is 4, and the sum of the series is 2,730 ?

Answers

The sum of n terms of a geometric series is given by
[tex]S_{n}=a_{1}\dfrac{r^{n}-1}{r-1}[/tex]

Substituting the given numbers, you have
[tex]2730=2\dfrac{4^{n}-1}{4-1}\\\\2730\dfrac{3}{2}=4^{n}-1\\\\4096=4^{n}\\\\\dfrac{\log(4096)}{\log(4)}=n=6[/tex]

There are 6 terms in the series.

The continuous function f is defined on the interval -4 ≤ x ≤ 3. there is no point c, -4 ≤ c ≤ 3, for which

Answers

We can say that there is no point c, which is not defined on this function's domain. Indeed, the intervals of this function and the interval of c coincide.

does anyone know the answer???

Answers

The slope of line AB is
slope = (change in y)/(change in x)
slope = (14 -(-3))/(7 -(-10)) = 17/17 = 1

The slope of line CD is the negative reciprocal of that, -1/1 = -1.
The point-slope form of the equation for line CD can be written as
y = -1(x -5) +12
y = -x +17

The x-intercept is the value of x when y = 0.
0 = -x +17
x = 17
The x-intercept is ...
(17, 0)

Another way to write the equation for line CD is "standard form." For this, we add x to the slope-intercept form to get ...
x + y = 17

For the second part of your question, we can find the answer by adding the x- and y-coordinates to see which sum is 17.
-5 +24 = 19
-2 +19 = 17 . . . . . . . . . the point (-2, 19) is the correct choice
7 +(-10) = -3
8 +11 = 19

I need help on this one please

Answers

Try this solution (see the attachment).

Starting at home, ishaan traveled uphill to the grocery store for 121212 minutes at just 151515 mph. he then traveled back home along the same path downhill at a speed of 303030 mph. what is his average speed for the entire trip from home to the grocery store and back?

Answers

The average speed is defined as the total distance covered divided by the time interval.

First of all we need to convert the time interval from minutes to hours, so:

[tex]121212min(\frac{1h}{60min}) = 2020.2h[/tex]

We know that the distance, speed and time are related as follows:

[tex]d = vt[/tex]

Thus, the distance covered from home to the grocery store is:

[tex]d = 151515(2020.2)=306090603mi[/tex]

So, the total distance covered for the entire trip from home to the grocery store and back is:

[tex]d_{t} = 2(306090603) = 612181206mi[/tex]

We need to the total time interval, that is:

[tex]t = t_{1} + t_{2} = 2020.2h + t_{2}[/tex]

So, it is necessary to find [tex]t_{2} [/tex] as:

[tex]t_{2} = \frac{306090603mi}{303030mph} = 1010.1h[/tex]

In this way:

[tex]t = 2020.2h + 1010.1h = 3030.3h [/tex]

Finally, his average speed for the entire trip from home to the grocery store and back is:

[tex]v_{a} = \frac{d_{t}}{t} = \frac{612181206mi}{3030.3h} = 202020,ph[/tex]

Answer: The average speed for the entire trip from home to the grocery store and back is 20 mph.

Step-by-step explanation:

Since we have given that

Ishan traveled uphill to the grocery store for 12 minutes at just 15 mph.

So, Time taken by him = 12 minutes

Speed = 15 mph

So, distance traveled = Speed × time

So, Distance becomes [tex]15\times \dfrac{12}{60}=\dfrac{180}{60}=3\ miles[/tex]

Again, he traveled back home along the same path downhill = 180 miles

Speed of covering downhill = 30 mph

so, Time taken [tex]\dfrac{Distance}{Speed}=\dfrac{3}{30}=\dfrac{1}{10}\ hours[/tex]

Since we know the formula for "Average speed ":

[tex]\dfrac{Total\ distance}{Total\ Time}\\\\\\=\dfrac{3+3}{\dfrac{12}{60}+\dfrac{1}{10}}\\\\\\=\dfrac{6}{\dfrac{1}{5}+\dfrac{1}{10}}\\\\\\=\dfrac{6\times 10}{2+1}\\\\\\=\dfrac{6\times 10}{3}\\\\\\=20\ mph[/tex]

Hence, the average speed for the entire trip from home to the grocery store and back is 20 mph.

Stocks are units of ownership in a company. The stock market is a place where stocks are bought and sold. When you buy a stock, you own a part of the company. If the company’s profits go up, the stock value goes up. If the profits fall, so does the value of the stock. Stock prices rise and fall every day. Last week, Isabelle bought stock in a toy company. Since then, the price of the stock had a change of -3 dollars. What is the absolute value of -3?

Answers

The absolute value is three.
Think of it like this. Whenever the absolute value is there, the number or expression inside, whether negative or positive takes a shower. When they are done showering, they are clean. The clean equals positive, all numbers after absolute value are positive so the answer is three.

Answer:

The absolute value is three!

Step-by-step explanation:

have a nice day/night!

Grace has one $10 bill and three $5 bills she spends 9.30 on a belt and $4.20 on snack how much money does grace have left

Answers

Total amount = 1 x 10 + 3 x 5 = $25

Amount spent = $9.30 + $4.20 = $13.50

Amount left = $25 - $13.50 = $11.50

Answer: $11.50

The correct answer is 11.50. 25-9.30-4.20=
11.50
GIVE ME BRAINLIEST PLZZZZ

what problem does the model show?

Answers

4/8 which is the same as 1/2 (one half)

1/2 is the fraction represents the diagram.

What is Fraction?

A fraction represents a part of a whole.

Fractions are of three types.

Proper fraction, improper fraction and mixed fraction.

A proper fraction is a fraction which has its numerator value less than the denominator.

An improper fraction is a fraction where the numerator is greater than or equal to the denominator.

A fraction represented with its quotient and remainder is a mixed fraction

In the diagram there are 8 boxes in whole, the number of boxes shaded are 4 out of 8.

4/8 is the fraction represents the diagram, 1/2 is another way of representing 4/8.

Hence, 1/2 is the fraction represents the diagram.

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Lie detectors have a 15% chance of concluding that a person is lying even when they are telling the truth. a bank conducts interviews of job applicants with the use of the lie detector. there are 15 applicants who are interviewed.
a.assuming all 15 applicants tell the truth, what is the probability that the lie detector will conclude that all 15 are telling the truth?
b.assuming all 15 applicants tell the truth, what is the probability that the lie detector will conclude that at least one is lying?
c.what are the mean and standard deviation of the 15 applicants the lie detector concludes are lying?
d.what is the probability that the number of truthful applicants classified as liars is greater than the mean?

Answers

Part A:

Given that lie detectors have a 15% chance of concluding that a person is lying even when they are telling the truth. Thus, lie detectors have a 85% chance of concluding that a person is telling the truth when they are indeed telling the truth.

The case that the lie detector correctly determined that a selected person is saying the truth has a probability of 0.85
Thus p = 0.85

Thus, the probability that the lie detector will conclude that all 15 are telling the truth if all 15 applicants tell the truth is given by:

[tex]P(X)={ ^nC_xp^xq^{n-x}} \\ \\ \Rightarrow P(15)={ ^{15}C_{15}(0.85)^{15}(0.15)^0} \\ \\ =1\times0.0874\times1=0.0874[/tex]

Part B:

Given that lie detectors have a 15% chance of concluding that a person is lying even when they are telling the truth. Thus, lie detectors have a 85% chance of concluding that a person is telling the truth when they are indeed telling the truth.

The case that the lie detector wrongly determined that a selected person is lying when the person is actually saying the truth has a probability of 0.25
Thus p = 0.15

Thus, the probability that the lie detector will conclude that at least 1 is lying if all 15 applicants tell the truth is given by:

[tex]P(X)={ ^nC_xp^xq^{n-x}} \\ \\ \Rightarrow P(X\geq1)=1-P(0) \\ \\ =1-{ ^{15}C_0(0.15)^0(0.85)^{15}} \\ \\ =1-1\times1\times0.0874=1-0.0874 \\ \\ =0.9126[/tex]

Part C:

Given that lie detectors have a 15% chance of concluding that a person is lying even when they are telling the truth. Thus, lie detectors have a 85% chance of concluding that a person is telling the truth when they are indeed telling the truth.

The case that the lie detector wrongly determined that a selected person is lying when the person is actually saying the truth has a probability of 0.15
Thus p = 0.15

The mean is given by:

[tex]\mu=npq \\ \\ =15\times0.15\times0.85 \\ \\ =1.9125[/tex]

Part D:

Given that lie detectors have a 15% chance of concluding that a person is lying even when they are telling the truth. Thus, lie detectors have a 85% chance of concluding that a person is telling the truth when they are indeed telling the truth.

The case that the lie detector wrongly determined that a selected person is lying when the person is actually saying the truth has a probability of 0.15
Thus p = 0.15

The probability that the number of truthful applicants classified as liars is greater than the mean is given by:

[tex]P(X\ \textgreater \ \mu)=P(X\ \textgreater \ 1.9125) \\ \\ 1-[P(0)+P(1)][/tex]

[tex]P(1)={ ^{15}C_1(0.15)^1(0.85)^{14}} \\ \\ =15\times0.15\times0.1028=0.2312[/tex]

expand (x^2-3/2)^9 using binomial process

Answers

Use the Binomial expansion theorem to find and simplify each term.

[tex] x^{18} - \frac{ 27x^{6} }{2}+ 81x^{14}- \frac{ 567x^{12} }{2}+ \frac{ 5103x^{10} }{16}- \frac{ 15309x^{8} }{16}+ \frac{ 15309x^{6} }{16} - \frac{ 59049x^{2} }{256}- [/tex][tex] \frac{19683}{512} [/tex]

Man that was a lot to type out, hopefully i helped, and Gosh I hope I get a brainly for all that freaking typing. hehe~ ^.^

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