rectangle with area of 12 square units is dilated by a scale factor of 3. What is the area?

Answer:

Ans= 6720 ways

Step-by-step explanation:

From Combination rule from Permutation and Combination, nCr

We use 8^C3 or 8C3,

8x7x6x5x4x3x2x1

--------------------------  =6,720

3x2x1

or

8x7x6x5x4x3! /3!, here the 3! cancels each other out, and we're left with 8x7x6x5x4, which equals 6720.

Answer:

see the attachment photo!

The value of side z will be equal to 99.32 cm.

The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle are termed trigonometry.

Given that:-

In ΔXYZ, x = 27 cm, y = 79 cm and ∠Z=142°

So by applying the formula given below:-

z²   =   x²  +  y²  -  2xyCos(142)

z²   =   79²  +   27²   -  2 ( 79 x 27  x  Cos142  )

z    =    99.32  cm

Hence the value of side z will be equal to 99.32 cm.

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Answer:

QR = 15 cm

PQ = 20 cm

Step-by-step explanation:

Use the Pythagorean theorem. [tex]a^{2} +b^{2} =c^{2}[/tex]

Find QR first since you know QP are SR.

[tex]a^{2} +b^{2} =c^{2}\\12^{2} +9^{2} =c^{2}\\144+81=c^2 \\225=c^2\\\sqrt{225} = \sqrt{c^2} \\c = 15[/tex]

QR = 15 cm

Now you can find PQ. First find the length of PR by adding PS and SR together.

16 + 9 = 25

[tex]a^{2} +b^{2} =c^{2}\\a^{2} +15^{2} =25^{2}\\a^{2} +225 =625\\a^{2} +225-225 =625-225\\\a^{2} = 400\\\sqrt{a^2} =\sqrt{400} \\a = 20[/tex]

PQ = 20 cm

Answer:

1942

Step-by-step explanation:

31072 / (2^4) = 31072

Hope This Helped

Question

What is 131072 divided by 2 to the power of 4?

Solution in steps:

Answer:

Step-by-step explanation:

if I understand this correctly, then

1 was rolled 77 times

2 89 times

3 73 times

4 69 times

5 110 times

6 82 times

remember, a probability is always desired cases over total possible cases.

a)

the experimental probability to roll an odd number (1, 3, 5) is the number of desired cases (77 + 73 + 110) over the total cases (500).

260 / 500 = 26/50 = 13/25 = 0.52

b)

if the cube would be totally equal, so that every side has truly the same probability to appear we would have for every roll 6 total possible outcomes (1 .. 6), and 3 desired outcomes (1, 3, 5).

so the theoretical probability is

3/6 = 1/2 = 0.5

c)

if the cube is truly "fair" (all sides really have the same probability to show), then the first answer is true.

the more rolls of the die, the greater the likelihood that both probabilities will get closer and closer.

that is actually a main point of probabilities : to find the most likely behavior or structure of a large number of items or objects out of the structure or behavior of a smaller sample. or out of theoretical considerations that can be tested with smaller samples.

Answer:

hope it helpssssssss youj

The value of 'a' in the P(X≤a)=0.6 is 5 because at X =5 we get a probability of 0.7. a = 5 is the answer.

It 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.

From the graph:

P(X ≤ 1) = 0.05

P(X ≤ 2) = 0.1

P(X ≤ 3) = 0.15

P(X ≤ 4) = 0.2

P(X ≤ 5)= 0.2

Add all the probability:

P = 0.05+0.1+0.15+0.2+0.2 = 0.7

P(X≤a)=0.6  (that means the value of the area under the curve 'a' is 0.6)

So the value of a should be 5

Thus, the value of 'a' in the P(X≤a)=0.6 is 5 because at X =5 we get a probability of 0.7. a = 5 is the answer.

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Answer:

Put 5 in the input

The expression that represents Felipe's balance at the end of the year is 3700 x [tex]( 1 + \frac{0.059}{4}) ^{4}[/tex] x [tex](1 + \frac{0.172}{8})^{8}[/tex].

The equation that can be used to determine future value with compounding is:

FV = P (1 + r)^nm

3700 x [tex]( 1 + \frac{0.059}{4}) ^{4}[/tex] x [tex](1 + \frac{0.172}{8})^{8}[/tex].

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Step-by-step explanation:

after subtracting the monthly fee (which she has to pay, even if she does not make a single call) we have

66.9 - 15 = $51.90

for actual phone call minutes.

1 minute is $0.05

so, in the month with the lowest charge she had used

51.9 / 0.05 = 1038 minutes for calls.

since this was the minimum, for all the numbers of minutes m she used in a month we have

m >= 1038 minutes

The conversion from degree to radian will be 180° = π radian. Then the measure of angle 75° is 1.31 radians.

Conversion means to convert the same thing into different units.

Convert the degree measure to the radian measure.

⇒ 75°

We know the conversion is given as

180° = π radian

   1° = π/180°

Then we have

75° = 75° x π/180° radian

75° = 1.30899 radian

75° ≅ 1.31 radian

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When Jax drew an angle that turns through 80 one-degree angles, the measure of the angle will be 80°.

It should be noted that when an angle turns through a particular degree, it'll be said to have an identical degree.

In this case, when Jax drew an angle that turns through 80 one-degree angles, the measure of the angle will be 80°.

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Answer:

Step-by-step explanation:

Answer:

2(x-5)

Step-by-step explanation:

Hope this helps

Answer:

2 · (x - 5)

Step-by-step explanation:

2 · (x - 5)

2 ·

"2 times"

when multiplication- or "times" is said, it can be shown in multiple ways. Multiplication can be shown as a×b , a·b , (a)(b)

(x - 5)

"difference of x and 5"

when difference is noted, the first number listed is the one written first. The difference between 2 and x is ( 2 - x ); the difference between x and 2 is ( x - 2).

Step-by-step explanation:

x = number of bottles Paula sold

y = number of bottles Pedro sold

x + y = 72

x = 72 - y

x/y = 3/5

(72 - y)/y = 3/5

5(72 - y) = 3y

360 - 5y = 3y

360 = 8y

y = 45

x + y = 72

x + 45 = 72

x = 27

so,

Paula sold 27 water bottles, and Pedro sold 45.

The  letters of the word "UNDERDOG" can be arranged in 144 ways.

There are only two letters that are the same which are D, then the remaining letters are 6 letters.

V, E, O are vowels

         N  R  G

The vowels are not joined together

For N, R, G  A³3

There are 4 openings A³4

Hence:

A³4· A³3=4×3×2×3×2×1

A³4· A³3=144

Therefore the  letters of the word "UNDERDOG" can be arranged in 144 ways.

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Answer: 75 people

Step-by-step explanation:

1).

we have percentage of people who invested in 18-29 year category

=31%

we need

n=40 people

this is

30% of x =40

or

0.3x=40

x=40/0.3 =133.33 or 134 people

2).

in 65+ category

percentage =54%

we need

n=40

this is

54% of x =40

or

0.54x=40

or

x=40/0.54 =70.07 or 75 people

The size of the unknown angle "x"

We'll have to check which one is appropriate from SOHCAHTOA.

In this question hypotenuse and adjacent is given so, we'll have to use cos.

[tex]\large\boxed{Formula: cos \: (A)= \frac{adj}{hyp}}[/tex]

Let's solve!

Let's substitute the values according to the formula.

[tex]cos \: x= \frac{8}{11}[/tex]

We'll have to use cos inverse.

[tex]x= {cos}^{-1}( \frac{8}{11} )[/tex]

[tex]x= 43.34175823[/tex]

Now we'll have to round off to 1 decimal place.

The value in hundredths place is less than 5 so we won't have to round up.

So, the final answer is:

[tex]\large\boxed{x= 43.3°}[/tex]

Therefore, the size of the unknown angle "x" is 43.3°

Answer:

3600 ways

Step-by-step explanation:

person A has 7 places to choose from :

→ He has 2 places ,one to the extreme left of the line ,the other to the extreme right of the line

If he chose one of those two ,person B will have 5 choices and the other 5 persons will have 5! Choices.

⇒ number of arrangements = 2×5×5! = 1 200

→ But Person A also , can choose one of the 5 places in between the two extremes .

If he chose one of those 5 ,person B will have 4 choices and the other 5 persons wil have 5! Choices.

⇒ number of arrangements = 5×4×5! = 2 400

In Total they can be arranged in :

1200 + 2400 = 3600 ways

Answer:

See below

Step-by-step explanation:

h^2 - 5h = 84

h^2 - 5h - 84 = 0

Using function concepts, it is found that the correct statement is given by:

all of the x-intercepts of f(x) are common to those of g(x).

They are the values of x when x = 0, hence:

Hence, the first statement is correct, and the x-intercept x = -1 of f(x) is common to the x-intercept x = -1 of g(x).

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The total amount of water that Kiesha drinks in 12 days is 20 quarts

The average amount of water she drinks per day is 1 2/3 quarts

The number of days that Keshia drinks at least the average amount of water is 6 days

If she drinks 1 quart of day 13, the average reduces.

The total amount of water drank in the 12 days can be determined by adding the quarts for each day together. When they are added together, the number is 20 quarts.

Average = total amount drank / number of days 1 2/3 quarts

New average = 20 + 1 / 13 = 21 / 13 = 1 7/13 quarts

The average reduces because the quart drank on the 13th day is less than the amount of water drank on the other days.

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Since I don't see the graphs:

 ⇒ I am going to answer by the general format of what you should see

The function has zeros at -3, 4:

 ⇒ which means that the function must interest the x-axis at x = -3 and

      x = 4

Hope that helps!

      ⇒look at the image I uploaded which shows a possible answer

Answer:

4.97

Step-by-step explanation:

h(x) = -3x² + 5

h(0.1)

x = 0.1

h(0.1) = -3(0.1)² + 5

0.1² = 0.01

-3(0.01) + 5

-3(0.01) = -0.03

-0.03 + 5 = 4.97

Answer:

A and B are arithmetic sequences. they have a set and consistent increase/decrease in each term.

Step-by-step explanation:

Answer:

1.8 ounces

Step-by-step explanation:

Let :

⇒ weight of a can of juice = x

⇒ weight of an energy bar = y

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

Equations formed :

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

Multiply Equation 1 by 2 :

⇒ 2 × (3x + 2y) = 2 × 33.6

⇒ 6x + 4y = 67.2 [Equation 3]

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

Subtract : Equation 3 - Equation 2

⇒ 6x + 4y - 4y - 2x = 67.2 - 27.2

⇒ 4x = 40

⇒ x = 10

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

Finding the weight of an energy bar :

⇒ 3(10) + 2y = 33.6

⇒ 2y = 3.6

⇒ y = 1.8 ounces

[tex]\large\boxed{Formula:\frac{sum \: of \: interior \: angles}{n}}[/tex]

n means the number of sides.

Sum of interior angles of a dodecagon is 1800°

Let's substitute the values according to the formula.

[tex]\frac{1800}{12}[/tex]

[tex]\large\boxed{ = 150°}[/tex]

Now, we can find the size of one exterior angle.

[tex]\large\boxed{Formula:\frac{360}{n}}[/tex]

n means the number of sides.

A dodecagon has 12 sides.

Let's substitute the values according to the formula.

[tex]\frac{360}{12}[/tex]

[tex]\large\boxed{ = 30°}[/tex]

Hence, the size of 1 interior angle of a dodecagon is 150° and 1 exterior angle is 30°

Answer:

( 3, -2 )

Step-by-step explanation:

3, -2 is on the line so it is a solution

the rest of the points aren't in the shaded area or on the line therefore they are not a solution

Have a great day! :)