The sum of the three interior angles of a triangle is 180°. Suppose one angle is 68° and the remaining two angles are the same measure. Reason numerically to find the measures of the remaining angles.

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

1. If the mean is used to determine Nathan's salary, he should choose Company A.

2. If the median is used to determine Nathan's salary, he should choose Company A.

3. The center of the data for Company B is more accurately described by the Median because the data is not uniformly scattered and has extreme values or outliers.

The Mean is the average value obtained after adding up a set of values and dividing the result by the number in the set.

The Median represents the middle value in an ordered list from smallest to largest.

Salaries   Company A   Company B

Year 1                10                   10

Year 2              20                  20

Year 3              30                  70

Year 4              40                  30

Year 5              50                  40

Year 6              60                  50

Year 7              70                  60

Total             280                280

Mean              40                  40

Median           40                  35 (30 + 40)/2

Thus, Nathan should choose Company A whether the Mean or the Median is used to determine Nathan's salary.

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Answer: Company B

Company A

Median

Skewed Right

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

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

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:

hope it helpssssssss youj

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:

z = 30

Step-by-step explanation:

All angles of a triangle add up to 180:

z + 120 + 30 = 180

z + 150 = 180

z = 180 - 150

z = 30

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 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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Answer:

Step-by-step explanation:

D∩L={f}

D∪L={a,f,g,j,k}

Answer:

22 meters

Step-by-step explanation:

Let x = width of the rectangle

Let y = length of the rectangle

Equation 1

If the length of the rectangle is 6 meters shorter than four times the width then:

⇒ y = 4x - 6

Equation 2

Perimeter of a rectangle = 2(width + length)

If the perimeter is 58 inches, then:

⇒ 58 = 2(x + y)

Solve by substitution

Substitute Equation 1 into Equation 2 and solve for x:

⇒ 58 = 2(x + 4x - 6)

⇒ 58 = 2(5x - 6)

⇒ 58 = 2 · 5x - 2 · 6

⇒ 58 = 10x - 12

⇒ 58 + 12 = 10x -12 + 12

⇒ 10x = 70

⇒ 10x ÷ 10 = 70 ÷ 10

⇒ x = 7

Substitute found value of x into Equation 1 and solve for y:

⇒ y = 4(7) - 6

⇒ y = 28 - 6

⇒ y = 22

Conclusion

The dimensions of the rectangle are:

Therefore, the length of the longer side is 22 meters

The length of the longer side is 22 meters.

Let, one side of the rectangle is x meters.

According to the problem, the other side is 6 meters shorter than four times this side, which means the length of the second side is (4x - 6) meters.

The perimeter of a rectangle is given by the formula:

Perimeter = 2 * (length + width)

In this case, the perimeter is 58 meters:

58 = 2 * (x + 4x - 6)

Now, let's solve for x:

58 = 2 * (5x - 6)

58 = 10x - 12

Add 12 to both sides:

58 + 12 = 10x

70 = 10x

Now, divide both sides by 10 to isolate x:

x = 70 / 10

x = 7

So, one side of the rectangle is 7 meters.

Now, we can find the length of the longer side:

Length of the longer side = 4x - 6

Length of the longer side = 4 * 7 - 6

Length of the longer side = 28 - 6

Length of the longer side = 22 meters

Therefore, the length of the longer side is 22 meters.

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Answer:

1 28/99

Step-by-step explanation:

When a number with 1-2 digits is divided by 99, it gets repeated with two digits. For example, 2/99=0.0202020202...

Another example would be 18/99=0.18181818...

Using this information, we can determine that 1.28282828 repeating would be 1 28/99

Let me know if you have any questions! :)

Primeter=10 + 4 +10 +7 = 31 ft

Answer:

60°

Step-by-step explanation:

Arc BC and Angle BWC are the same number of degrees.

When the vertex of an angle is at the center of a circle, its called a Central Angle. A central angle and the arc it "cuts off" have the same number of degrees.

Angle AWB and Angle BWC lay together on a straight line, so they add up to 180°.

180° - 120° is 60°

Angle BWC is 60° so Arc BC is 60°

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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The statement "If the equation of a function is a rational expression the function is a rational" is true.

If the value of a numerical expression is terminating then they are the rational number then they are called the rational number and if the value of a numerical expression is non-terminating then they are called an irrational number.

If the equation of a function is a rational expression the function is a rational, the statement is true.

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The inverse function of f(x) = 3x + 3 is f-1(x) = 1/3x - 1

The equation is given as:

f(x) = 3x + 3

Express f(x) as y

y = 3x + 3

Swap the positions of y and x

x = 3y + 3

Make y the subject

3y = x - 3

Divide by 3

y = 1/3x - 1

Replace y with the inverse function

f-1(x) = 1/3x - 1

Hence, the inverse function of f(x) = 3x + 3 is f-1(x) = 1/3x - 1

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The decimal degree of the angle 12' 8" is 0.2022

The angle measure is given as:

Angle = 12' 8"

As a general rule;

Where:

' represents minutes and " represents seconds.

So, we have:

Angle = 12/60 + 8/(60 * 60)

Evaluate the expression

Angle = 0.2022

Hence, the decimal degree of the angle 12' 8" is 0.2022

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[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: 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

Answer:

See below

Step-by-step explanation:

h^2 - 5h = 84

h^2 - 5h - 84 = 0

Answer:

1. 5² is 25 yards

2. 7² is 49m

3. 8² is 64cm

4.draw a square, make one side 6 feet then do 6² which is 36feet

5. do the same thing then write 10 inches on one side and 10² is 100 inches.

6. 7x3= 21 ft

7. 5x4= 20 in.

8. 2x8= 16 yd

Step-by-step explanation:

common sense

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:

Step-by-step explanation:

Answer: Commutative property