Bill is also planning to buy a condo and he needs to finance $115,000. At which mortgage lender will Bill get the better deal? How much less will Bill pay with this lender?

The probability that none of the prizes is a $10 gift certificate is; 7/99

The expected number of $20 gift certificates drawn is 2.083

This is a question of picking objects from a mixture without replacement. The modelling distribution is the hypergeometric distribution, given by the formula:

P(a) = C(A,a) * C(B,b)/C(A+B,a+b)

Where;

a = number of good objects picked

b = number of bad objects picked.

A = number of good objects in the given batch.

B = number of bad objects in the given batch.

a + b = total number of objects picked without replacement.

A + B = total number of objects in the batch.

A) In this question;

A = 4 ($10, good)

B = 3 + 5 = 8 ($20, $50, "bad")

a = 0, b = 5

a + b = 5

Thus;

P(a = 0) = C(4, 0) × C(8, 5)/C(12, 5)

P(a = 0) = 1 × 56/792

P(a = 0) = 7/99

B) $20 is the "good" prize.

Thus;

A = 5

B = 3 + 4 = 7

a + b = 5 (total number of prizes drawn)

Thus;

E[$20] = (5/(5 + 3 + 4)*5)

E[$20] = (5/12)*5

E[$20] = 25/12

E[$20] = 2.083

Complete Question is;

The door prizes at a dance are four $10 gift certificates, five $20 gift certificates, and three $50 gift certificates. The prize envelopes are mixed together in a bag, and five prizes are drawn at random.

What is the probability that none of the prizes is a $10 gift certificate?

What is the expected number of $20 gift certificates drawn?

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Answer:

  B.  180° about the origin

Step-by-step explanation:

You are given a figure and its image, and asked to determine the angle of rotation. All of the answer choices indicate the center of rotation is the origin.

__

You have two clues that the rotation is 180° about the origin:

__

To find the angle of rotation, you can look at the angle formed by a point, the center of rotation, and the image of the original point. Here, the angle UOU' is a straight angle, so the angle of rotation about O is 180°--the measure of that angle. (It can be convenient to use points close to the center of rotation, but any corresponding points on preimage and image will do.)

Answer:

0.125 times larger

Step-by-step explanation:

given the scale factor of 2 solids is k , then the volume  factor = k³

here k = 0.5 , so

volume factor = (0.5)³ = 0.125

Since cosine is negative in the second and 3rd quadrant, the required angles are 120 and 240 degrees

Trigonometry identities are expressed as a function of cosine, sine and tangent.

Given the trigonometry expression shown

4cos2θ+9=−14cosθ

Equate to zero

4cos2θ+9 + 14cosθ = 0

According to trig identity

cos2θ = 2cos²θ - 1

Substitute to have:

4(2cos²θ - 1)+9 + 14cosθ = 0

Expand

8cos²θ - 4 + 9 + 14cosθ = 0

8cos²θ+ 14cosθ + 5 = 0

let P = cosθ to have;

8P² + 14P + 5 = 0

Factorize the result

8P² + 10P + 4P + 5 = 0

2P(4P+5)+1(4P+5)=0
(2P+1) = 0 and 4P+5 = 0
2P = -1 and P = -5/4

P = -1/2 and -5/4

Recall that P = cosθ

If P = -1/2

cosθ = -1/2

θ = -60

Since cosine is negative in the second and 3rd quadrant, the required angles are 120 and 240 degrees

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Answer:

56

Step-by-step explanation:because 12345

The probability that Luisa gets 2 diamonds and 2 hearts (in any order) is:

P = 0.022

The probability of getting a particular type of card, is given by the quotient between the number of cards of that type and the total number of cards.

Here, let's assume that the 4 draws are:

diamond-diamond-heart-heart.

In that order.

First, the probability of drawing a diamond card is equal to:

p₁ = 13/52

Because there are 13 diamond cards and 52 cards in total.

Bt after that draw, there will be 12 diamond cards and 51 cards in total, so the probability of getting the second diamond card is:

p₂ = 12/51.

Now, there are 13 heart cards and 50 cards in the deck, so the probability of getting the first heart card is:

p₃ = 13/50

And the probability of getting the second one is:

p₄ = 12/49.

The joint probability will be the product of the 4 individual probabilities, but we also need to take in account the possible permutations, these are:

(using D for diamond and H for heart).

D - D - H - H

D - H - D - H

D - H - H - D

H - D - D - H

H - D - H - D

H - H - D - D

So there are 6 permutations, this means that the probability is:

P = 6*p₁*p₂*p₃*p₄ = 6*(13/52)*(12/51)*(13/50)*(12/49) = 0.022

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Beth's description of the transformation is incorrect

Beth says that the graph of g(x)=x-5+1 is a translation of 5 units to the left and 1 unit up of f(x) = x. She continues to explain that the point (0,0) on the square root function would be translated to the point (-5,1) on the graph of g(x). Is Beth's description of the transformation correct? Explain

The functions are given as:

g(x) = x - 5 + 1

f(x) = x

When the function f(x) is translated 5 units left, we have:

f(x + 5) = x + 5

When the above function is translated 1 unit up, we have:

f(x + 5) + 1 = x + 5 + 1

This means that the actual equation of g(x) should be

g(x) = x + 5 + 1

And not g(x) = x - 5 + 1

By comparison;

g(x) = x - 5 + 1 and g(x) = x + 5 + 1  are not the same

Hence, Beth's description of the transformation is incorrect

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Median is the central tendency of the data and always exists in the middle of the data set.

The Median is the middlemost value of the numbers arranged in the ascending orders. Median is the central tendency of the data and always exists in the middle of the data set.

The process of finding the median if the number of data points is even is as follows:

( if the number of data pints were even then we just need to arrange the numbers and cross the high/low pair and only one data point will be left which acts as the Median of the data set)

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[1] t ≥ 45

   Since Isabel exercises more ("no less") than 45 minutes a day, we will use greater than or equal to.

-> because being equal is not less, hence still "no less"

[2] f ≥ 45

   Because the vehicle's fuel is "at least" that means it can also be equal too, hence the user of greater than or equal to.

Answer:

1

Step-by-step explanation:

[tex]\text{Given that,}~ (x_1,y_1) = (-2,4)~ \text{and}~ \text{slope,}~ m = -\dfrac 32\\ \\\text{Equation of line,}~\\\\~~~~~~~y -y_1 = m(x-x_1)\\\\\implies y -4 =-\dfrac 32(x+2)\\\\\implies y-4 =-\dfrac 32x - 3\\\\\implies y = -\dfrac 32x -3 +4\\\\\implies y = -\dfrac 32x +1[/tex]

The current equation of the perpendicular line;

 ⇒ is the slope-intercept form: [tex]y= mx + b[/tex]

Now for the point-slope form, we need a point on the line and the slope of the line:

⇒ we have

Since this is the point-slope form: [tex](y-y_1)=m(x-x_1)[/tex]

 ⇒ where the (x₁,y₁) is the point on the line and m is the slope

    [tex]= > Equation: (y-4)=-\frac{3}{2}(x+2)[/tex]

To convert the equation to slope-intercept form:

  ⇒ must isolate 'y' to one side and everything to the other side

      [tex]y= -\frac{3}{2}(x+2)+4\\ y=-\frac{3}{2} x-3+4\\y=-\frac{3}{2}x+1[/tex]

Answer: [tex]y = -\frac{3}{2}x+1[/tex]

Hope that helps!

Answer:

P(5 ≤ X ≤ 8)  = a  rectangle  with a width of 3  and height of .15   = 3(.15)  = .45

P( 4 ≤ X ≤ 5)  =  a triangle  with a base of 1  and a height of (0.15 -0.05) = .10

So....this area  =   (1/2)(1)(.10)  = .05

And  another rectangle with a width of 1 and height of .05  = (1) (.05) = .05

So

Adding these areas

P( 4 ≤ X ≤ 8 )  =  .45 + .05 + .05   =  .55

Step-by-step explanation:

Hoped this helped!

Answer:

The height of the ladder is 6.9 meter

Explanation:

Given:

As opposite and hypotenuse given, use sine rule:

[tex]\rightarrow \sf sin(x) = \dfrac{opposite}{hypotenuse}[/tex]

[tex]\rightarrow \sf sin(60) = \dfrac{6}{h}[/tex]

[tex]\rightarrow \sf h = \dfrac{6}{sin(60)} = 4\sqrt{3} = 6.928 \ meters \quad \approx \ 6.9 \ meters \ \ (one \ decimal \ place)[/tex]

Answer:

3.276.799.999,9875

Step-by-step explanation:

(8 × 10)^5 - (8 × 10)^-1 = 3.276.799.999,9875

The total purchase price of the dictionary and the software package is  $61.47.

The total purchase price is the sum of the dictionary, software package and taxes.

Total cost of  the dictionary and the software package = $27.65 + $29.80 = $57.45

Total cost after the taxes = ( 1 + 0.055 + 0.015) x $57.45 = $61.47

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The correct answer is option D which is both Jason’s sample and Yolanda’s sample can be used to make inferences about the population

The complete question is given below:-

Jason and Yolanda both drew a simple random sample from a non-normally distributed population of 25,000. Jason’s sample consisted of 0.24% of the population, while Yolanda’s sample consisted of 0.32% of the population. Whose sample can be used to make inferences about the population?

neither Jason’s sample nor Yolanda’s sample

only Jason’s sample

only Yolanda’s sample

both Jason’s sample and Yolanda’s sample

Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Since we have given that

Total number of population = 25000

Percent of a sample of Jason = 0.24%

Percent of a sample of Yolanda's = 0.32%

So, the number of the population according to Jason's sample is given by

= ( 0.24 / 100 ) x 25000

= 60

The number of the population according to Yolanda's sample is given by

= ( 0.32 / 100 ) x 25000

= 80

Both the sample can be used to make inferences about the population

Hence, the Last Option is correct.

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Answer:

reason 1.) This is the original expression

reason 2.) you subtract 4 from both sides

reason 3.) you divide both sides by 2 to get x=5

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$100000\\ P=\textit{original amount deposited}\\ r=rate\to 6.6\%\to \frac{6.6}{100}\dotfill &0.066\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semiannually, thus two} \end{array}\dotfill &2\\ t=years\dotfill &20 \end{cases}[/tex]

[tex]100000=P\left(1+\frac{0.066}{2}\right)^{2\cdot 20}\implies 100000=P(1.033)^{40} \\\\\\ \cfrac{100000}{1.033^{40}}=P\implies 27288.97\approx P[/tex]

Answer: 36

Step-by-step explanation:

[tex]g(2)=2^{2}=4\\g(3)=3^{2}=9\\g(2) \cdot g(3)=4 \cdot 9=\boxed{36}[/tex]

The complete question is

"A theater production group is making frames to support wall-like props. Three-foot beams form right triangles with 10-foot beams to allow them to stand, as shown in the image.

What is x, the angle at which the diagonal beam meets the 10-foot beam at the top of the frame?

16.7°, 17.5°, 72.5°,73.3°"

The value of angle x would be 16.7 degrees.

A right-angle triangle is a triangle that has a side opposite to the right angle the largest side and is referred to as the hypotenuse.

The angle of a right angle is always 90 degrees.

In order to find the value of x, a tan would be used.

This is because we have given the opposite and adjacent sides as 10 ft and 3 ft.

Tan Ф = opposite / adjacent

Tan Ф =  (3/10)

= 16.7 degrees

The value of angle x would be 16.7 degrees.

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Answer: the answer is 16.7°.

Step-by-step explanation: it show below.

Using it's concept, it is found that the range of the function [tex]f(x) = 9^x[/tex] is given by:

all real numbers greater than 0.

It is the set that contains all possible output values for the function.

In this problem, the function is:

[tex]f(x) = 9^x[/tex]

For exponential functions without vertical shifts, as is the case in this problem, the range is given by:

all real numbers greater than 0.

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Answer:

D.

Step-by-step explanation:

0.45*5=2.25

0.25*9=2.25

2.25*2=4.50

Hope this helps!

If not, I am sorry.

The range of the exponential function will be y ≥ 250,0003. Then the correct option is B.

The domain means all the possible values of x and the range means all the possible values of y.

The Population Of Center City Is Modeled By Exponential Function F, Where X Is The Number Of Years After The Year 2015.

The graph is given below.

We know that the exponential function is given as

y = abˣ

For x = 0, y will be 250,000

250,000 = a

For x = 40, y will be 400,000

400,000 = 250,000b⁴⁰

           b = 1.0118

Then we have

y = 250,000 (1.0118)ˣ

Then the range of the exponential function will be y ≥ 250,0003.

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Answer:

14

29  as a fraction

Step-by-step explanation:

Based on the given conditions, formulate:

14=19+14+6）

2 Calculate

14

9+14+6

Calculate

14

23+6

Calculate the sum or difference

14

29

X

Calculate the sum or difference

14

29

Alternative forms

~ 0.482759, ~ 48.275862%,

4.827586 × 10

Hope it help :)

Answer:

x = 100

Step-by-step explanation:

[tex]4x^{2} -371=29\\[/tex]

      + 371   +371

[tex]4x^{2} =400[/tex]

[tex]\sqrt{4x^{2} } =\sqrt{400}[/tex]

[tex]4x=400[/tex]

Divide both sides by 4.

x = 100

Hope it helps!

Answer:

Computer game designer.

Step-by-step explanation:

If you want to design a game, you need to have some basic shapes and stuff in it. I'm not sure what else needs to be explained here lol

Answer:

375 plates were sold

Step-by-step explanation:

$2400 (profit) - $150 (advertising) = $6 (profit per plate $8 cost - $2 expense) times x

2400 - 150 = 6x

Simplify the left side: 2400 - 150 = 2250

2250 = 6x

Divide both sides by 6

2250/6 = 375

Answer:

19.1 ft³

Step-by-step explanation:

Hello!

Volume of a cylinder: [tex]V = \pi r^2h[/tex]

We can plug in the values and solve.

The volume is approximately 19.1ft³

Step-by-step explanation:

[tex]\pink{\large{\underline{\underline{\sf Given:-}}}}[/tex]

[tex]\pink{\large{\underline{\underline{\sf To\:find:-}}}}[/tex]

[tex]\pink{\large{\underline{\underline{\sf Solution:-}}}}[/tex]

We know that,

[tex]\underline{\boxed{\sf Volume_{cylinder}=πr^2h}}[/tex]

[tex]\longmapsto \sf 3.14×(1.5)^2×2.7[/tex]

[tex]\longmapsto \sf 3.14×2.25×2.7[/tex]

[tex]\longmapsto \sf 3.14×6.075[/tex]

[tex]\longmapsto \sf 19.0755≈19.1\: cubic\:feet[/tex]

The probability that a shirt picked at random is red and the size is medium is 48 / 165.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability that a shirt picked at random is red and the size is medium = number of red shirts that a medium size / total number of shirts

48 / 165.

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Answer:

The probability that a shirt picked at random is red and the size is medium is 48 / 165.

Step-by-step explanation:

because it is