The FBI wants to determine the effectiveness of their 10 Most Wanted list. To do so, they need to find out the fraction of people who appear on the list that are actually caught. In an earlier study, the population proportion was estimated to be 0.26. How large a sample would be required in order to estimate the fraction of people who are captured after appearing on the 10 Most Wanted list at the 98% confidence level with an error of at most 0.04?

Answer: 90 degrees

Step-by-step explanation:

An angle inscribed in a semicircle measures 90 degrees.

The percentage of winning if 20 winning numbers are randomly selected from numbers 1 to 80 is 12.48%.

Given There are 80 numbers from which 20 numbers are selected randomly in a game of Keno by player and after selection of 20 winning numbers again 20 numbers are selected and player wins if the player has correctly selected 3,4,or 5 of the 20 winning numbers.

Probability is the chance of happening an event among all the events possible.

Probability of winning is calculated as under:

Probability=[tex]C(20,3)C(60,17)/C(80,20)[/tex]

We have taken C(20,3) because player will win if 5 numbers are selected from 20 winning numbers.

We have taken C(60,17) because after selection of 20 numbers 60 numbers will left from 80 and after winning from 3 numbers 17  numbers left and from total 80, 20 numbers are taken.

=C(20,3)C(60,17)/C(80,20)

=(20!/3!17!  * 60!/17!43!)/80!/20!60!

=1140*387221678682300/35353161422121743200

=12.48%

Hence the probability of winning is 12.48%.

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The value of d is 27/2 when v =30

Equation is the defined as mathematical statements that have a minimum of two terms containing variables or numbers is equal

Suppose that d is directly proportional to the square of v.

So the equation is, d ∝ v² equals to d = kv², where k is a constant.

So in order to find the value of k,

d = k v²

d = 6, v = 20,

Substitue the value of d and v into the equation :

6 = k(20)²

k = 6/400

k = 3/200

Substitue the value of k and v =30 into the equation,

d = 3/200(30)²

d = 2700/200

d = 27/2

Hence, the value of d is 27/2 when v =30

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95% of the students have study hours between 10.75 and 13.25 hours and the percentage of the students have study hours that are above 12 is 92%.

Given average of 12 % studying required, population mean of 15 hours, standard deviation of 3 hours.

We have to find the confidence interval for 95% students and the percentage of the students that have studied above 12 hours.

Margin of error=z*σ[tex]\sqrt{n}[/tex]

z value for the p value 0.95 is 1.96.

Margin of error=1.96*3/[tex]\sqrt{22}[/tex]

=5.88/4.69

=1.25

Upper interval=Mean +margin of error

=12+1.25

=13.25

Lower interval=Mean- margin of error

=12-1.25

=10.75

The confidence interval (10.75,13.25).

Now we will calculate the percentage of the students that are above 12.

z value when X=12, z=12-15/15

=-3/15

=-0.2

p value of -0.2 will be =0.5+0.4207=0.9207

=0.9207*100

Percentage=92.07%

Approx=92%.

Hence the confidence interval is (10.75 , 13.25) and 92% students have studied above 12.

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Question is incomplete as it should include  sample size of 22.

[tex]P \: \div \: 7 \: = \: 14[/tex]

[tex] \frac{1}{7} P \: = \: 14[/tex]

[tex] \boxed{ \bold{P \: = \: 98}}[/tex]

Answer:

Here you go!

sorry for my writing -_-

Any confusion, you may ask me.

The amount of money that Davis has in this scenario is; $50

Let the amount of money he has be $X.

Now, if he buys 10 notebooks, he will have $10 left. Thus;

X - 10n = 10  -----(1)

If he buys 15 notebooks, he will be $10 short. Thus;

X - 15n = -10   ------(2)

Subtract eq 1 from eq 2 to get;

-5n = -20

n = -20/-5

n = 4

Thus;

X - 10(4) = 10

X = 10 + 40

n = $50

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Answer:

Looks like an obtuse scalene triangle

Step-by-step explanation:

The angle of the top vertex looks to be obtuse. It if was acute isosceles it would have 2 equal sides. If it was a right triangle it would have a right angle (which it doesn't). It was obtuse isosceles it would have equal sides. So it should be A: Obtuse Scalene Triangle

40 gallons of liquid b weighs the same as 30 gallons of liquid a.

A substance's density is defined as its mass per unit volume (more specifically, the volumetric mass density; also known as specific mass). Although the Latin letter D may also be used, the sign most frequently used for density is (the lower case Greek letter rho). Density is mathematically defined as mass divided by volume.

where m is the mass, V is the volume and D is the density, which is sometimes roughly characterized as weight per unit volume, while this is incorrect scientifically; this quantity is more precisely known as specific weight.

For liquid a,

8= mass/30

For liquid b,

6=mass/volume

For the two masses to be equal,

240=6*volume

volume=240/6

volume=40

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Answer:

$23.75

Step-by-step explanation:

first, we know the tie he bought is $12.50, so we want to subtract that from the total ($60). Now we have 47.50 dollars left and if he wants to buy two shirts, we divide $47.50 by 2, which is $23.75. So if the two shirts are the same price, he can pay $23.75 for each shirt.

The simplified expression of (-2)⋅n⋅(8)⋅n⋅(-n) is 16n^3

The expression is given as:

(-2)⋅n⋅(8)⋅n⋅(-n)

Express as products

(-2) * n * (8) * n * (-n)

Multiply -2 and 8

-16 * n * n * (-n)

Multiply the three n's

-16 * -n^3

Evaluate the product

16n^3

Hence, the simplified expression of (-2)⋅n⋅(8)⋅n⋅(-n) is 16n^3

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Step-by-step explanation:

when given a ratio like this 4:7, it means that one item represents 4 units, and the other 7 units.

let's assume that length is larger than width, so the given 31.5 in are these 7 units.

that means 1 ratio unit is

31.5 / 7 = 4.5 in

the width is 4 units, therefore

width = 4×4.5 = 18 in

the perimeter is

2×length + 2×width = 2×31.5 + 2×18 = 63 + 36 = 99 in

the area is

length × width = 31.5×18 = 567 in²

When the first cars hit the roads they were as much (or more) a novelty, as they were the first step in mechanized transportation for the masses. Going for a “Sunday Drive” was an actual activity, not just an analogy for someone taking their sweet time. Vehicles were lighter and slower, and there wasn’t a constant sense of urgency to get from “Point A” to “Point B”.

Fast forward a little over a century and our vehicles have transformed into an average of a 2-ton living room/office/daycare that can cover 95 feet every second traveling down the road.

A lot of talks are occurring about distracted driving, but have you ever thought “I can take my eyes off the road for 2 seconds, it's no big deal”? To change a radio station, to answer a phone call, to look for an item you’ve dropped.  Nearly every single one of us has at some point, even those who use a hands-free device.  

The more times you take your eyes off the road for just those two seconds, the increases your likelihood of an incident

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Answer:

the answer is c

Step-by-step explan

UV ⊥ AB and UV ║ ZY is the correct statement about the given figure.

A quadrilateral with the opposing sides parallel is called a parallelogram (and therefore opposite angles equal). A parallelogram with all right angles is known as a rectangle, while a quadrilateral with equal sides is known as a rhombus.

As we can observe in the graph Line ZY is parallel to the UV and WX is parallel to AB.

Similarly,  WX is perpendicular to ZY and UV(Parallel)

And AB is perpendicular to UV and ZY(Parallel)

Therefore, the correct statement is

UV ⊥ AB and UV ║ ZY

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Answer:

y = - 3x + 11

Step-by-step explanation:

the altitude is a line from the vertex A drawn perpendicular to the opposite side BC

calculate the slope of BC using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = B (- 7, 3 ) and (x₂, y₂ ) = C (- 1, 5 )

[tex]m_{BC}[/tex] = [tex]\frac{5-3}{-1-(-7)}[/tex] = [tex]\frac{2}{-1+7}[/tex] = [tex]\frac{2}{6}[/tex] = [tex]\frac{1}{3}[/tex]

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{3} }[/tex] = - 3

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept ) , then

y = - 3x + c ← is the partial equation

to find c substitute A (4, - 1 ) into the partial equation

- 1 = - 12 + c ⇒ c = - 1 + 12 = 11

y = - 3x + 11 ← equation of altitude from A

The congruence theorem that proves that △LON ≅ △LMN is: A. SSS congruence theorem

According to the SSS congruence theorem, if all three corresponding sides of two triangles are congruent, then both triangles are congruent.

In the image given, we have:

This means all three corresponding sides are congruent, therefore, the congruence theorem that proves both triangles are congruent is:

A. SSS.

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Answer: Option 1 or A. SSS

Step-by-step explanation: The congruence theorem that can be used to prove △LON ≅ △LMN is SSS.

Trust me!

If you are working on Edge the answer is correct. The proof is down below. I hope someone finds this helpful.

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Answer:

=Rs.10

Step-by-step explanation:

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A piece of cloth costs Rs. 200. If the piece was 5m longer and each meter of cloth costs Rs. 2 less the cost of the piece would have remained unchanged. How long is the piece and what is the original rate per meter?

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Let the length of the piece be x metres. Then, rate per metre =Rs.

x

200

New length =(x+5) metres

Since the cost remains same

New rate per metre =Rs.

x+5

200

It is given that

x

200

−

x+5

200

=2

⇒

x(x+5)

200(x+5)−200x

=2⇒

x(x+5)

1000

=2

⇒x

2

+5x=500⇒x

2

+5x−500=0$

⇒x

2

+25x−20x−500=0

⇒(x+25)(x−20)=0⇒x+25=0

orx−20=0⇒x=20orx=−25

But x cannot be negative. So, x=20

Rate per metre Rs.

x

200

=Rs

20

200

=Rs.10

The correct answer is 700 months .

Given,

         I = 105

         P = 100

            r = 0.15

Now use simple interest formula,

      [tex]S.I. = \frac{p * r* t}{100}[/tex]

105=100×(0.15)×(t)

Swap sides so t is on the left.

100 ×(0.15)×(t)=105

Divide both sides by 100.

0.15t=1.05

Divide both sides by 0.15

t=700

So, we see that it takes 700 months to earn this amount.

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The order from least to greatest is 0.8%, 0.556, 1.2 and 10/8

In order to order the given numbers, we will first have to write them as a percentage as shown.

Given the number below

10/8, 1.2, 0.556, 0.8%

Convert to percentage

10/8 = 125%

1.2 = 120%

0.556 = 55.6%

0.8%

Hence the order from least to greatest is 0.8%, 0.556, 1.2 and 10/8

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Answer:

work hours: independent

salary: dependent

Step-by-step explanation:

The independent variable is what is you're "typically" in control of, or it has a constant increase. For example time, you're not really "in control" of time, but it has a constant change. One example where you are in control, is how much money you deposit into your account, you can slightly control it (you obviously can't deposit more than you have), but it's still somewhat in your control.

The dependent variable is what changes as a result of the independent variable changing. So for example in the previous example, where the money deposited was the independent variable, the dependent variable would be the total amount of money in your account

In this case the number of hours during the week is the independent variable and the salary depends on how many hours you work in the week so that is the dependent variable

The value of x = 93 degree and value of angle A and B is 72 , 108 degree

The pair of triangles that are supplementary and they add to form 180 degree angle are called Linear Pairs.

It is given that

∠ A = x -21

∠ B = x+15

also it is given that

angle  A and B form a linear pair

∠ A + ∠ B = 180 degree

To find the value of x

x -21 + x+15 = 180

2x - 6 = 180

2x = 186

x = 93 degree

so

∠ A = x -21 = 93 -21 = 72 degree

∠ B = x+15 = 93+21 = 108 degree

Therefore the value of x = 93 degree and value of angle A and B is 72 , 108 degree.

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Let [tex]a[/tex] be the first term in the series and [tex]r[/tex] the common ratio. Then the infinite series converges to

[tex]a + ar + ar^2 + ar^3 + ar^4 + ar^5 + \cdots = \dfrac a{1-r}[/tex]

Removing the first three terms from the left side effectively multiplies the right side by 27, so

[tex]ar^3 + ar^4 + ar^5 + \cdots = \dfrac{27a}{1-r}[/tex]

By elimination,

[tex]a + ar + ar^2 = -\dfrac{26a}{1-r}[/tex]

Solve for [tex]r[/tex]. We can eliminate [tex]a[/tex] so that

[tex]1 + r + r^2 = -\dfrac{26}{1-r} \\\\ \implies 1-r^3 = -26 \\\\ \implies r^3 - 27 = 0 \\\\ \implies r^3 = 27 \implies \boxed{r=3}[/tex]

The actual payment Eric made to the bank at 175.00 for 36 months is 6,300

Actual payment to bank = Monthly payment × Number of months

= 175.00 × 36

= 6,300

Therefore, the actual payment made to the bank is 6,300.

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The length of xy  in the triangle XYZ is 9 units if xyz is dilated to create triangle x prime, y prime and z prime.

Given triangle xyz is dilated to create x prime, y prime and z prime.The length of oz is 2, the length of Zz Prime is 4,the length of x prime y prime is 9 and the length of side y prime z prime is 12.

Dilation is basically technique of creating similar shapes. Each point is streched outwards from the center point by multiplying the scale.

After dilation the side of the shape used to reduce according to factor. It is reduced by number of times of factor.

The line xy is equal to 9 units after dilation by a factor of 3. So the length of xy is 9/3.

=3 units.

Hence the length of side xy is 3 units if xyz is dilated to create x prime, y prime and z prime.

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Answer: 3

Step-by-step explanation: just did it on edge

The maximum earning is v(r,b)

Let v(r,b) be the expected value of the game for the player, assuming optimal play, if the remaining deck has r red cards and b black cards.

Then v(r,b) satisfies the recursion

and

The stopping rule is simple: Stop when v(r,b)=0.

To explain the recursion . . .

If r,b>0, and the player elects to play a card, then:

Thus, if r,b>0, electing to play a card yields the value f(r,b).

But the player always has the option to quit, hence, if r,b>0, we get v(r,b)=max(0,f(r,b)).

Implementing the recursion in Maple, the value of the game is

v(26,26)=41984711742427/15997372030584

v(26,26)  ≈2.624475549

and the optimal stopping strategy is as follows . . .

So, The maximum earning is v(r,b)

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Answer:

Horizontal line -   y=3

Vertical line -  x=5

Step-by-step explanation:

See both graphs below

Answer: 47

Step-by-step explanation:

There are 6720 ways by 8 distinguishable books be placed in 5 shelves.

According to statement

The number of books (n) is 8

The number of shelves (r) is 5

Now, we find the ways by which the 8 books be placed in 5 distinguishable shelves

From Permutation formula

P(n,r) = n! / (n-r)!

Substitute the values then

P(n,r) = 8! / (8-5)!

P(n,r) = (8*7*6*5*4*3*2*1) / (3*2*1)

P(n,r) = 8*7*6*5*4

P(n,r) = 6720

So, there are 6720 ways by 8 distinguishable books be placed in 5 shelves.

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The division of 1987 by 12 when solved gives a quotient of; 165.5

We want to divide 1,987 by 12. This can be expressed as;

1987 ÷ 12

Now, it must be noted that when dividing, we have the divisor and the dividend. Where the number that is being divided is the dividend which is the numerator, while the number by which we divide is the divisor which is the denominator. Thus, in this question, we have;

Dividend = 1987

Divisor = 12

Thus;

1987/12 = 165.5

Thus, we can conclude that when we divide 1987 by 12, we get 165.5

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According to AAA Chicago, 58 percentage of crashes involving teen drivers are instigated by distracted driving.

What does AAA study tell about the distracted driving of teens?

According to the AAA Foundation for Traffic Safety's review of over 1,700 crash films, distracted driving causes 58 percent of car accidents involving juvenile drivers. According to the foundation, this figure is four times higher than earlier projections derived from police records.

The investigation identified 12 different kinds of distracted driving that contributed to collisions, with passenger interaction accounting for 15% of crashes. Twelve percent of the collisions were caused by using a cellphone, which was followed by reaching for something, looking inside the vehicle, gazing outside while not paying attention to the road, singing or dancing, and looking at something outdoors.

According to the study, young drivers were prey to distracted driving by calls, texts, or other mobile device use for an average of 4.1 seconds in the final six seconds before a catastrophic crash.

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