In 2012, the U.S. population was about
314 million. How many people over the
age of 64 were in the U.S.?

The longest and shortest possible lengths of the third side of the triangle are 4.9 cm and 11.1 cm.

It states that the opposite side of a triangle is divided into segments by each angle bisector that are proportional in length to the adjacent sides.

Given:

An angle bisector divides the opposite side of the triangle into segments 6 cm and 4 cm long.

Second side of the triangle is 7.4 cm.

We have to calculate the longest and shortest possible lengths of the third side of the triangle.

By Angle Bisector Theorem we can solve this problem,

In the triangle ABC, AD is the angle that bisects angle A, placing D on side BC.

Now, BD / DC = AB / AC

BC = 6 + 4 = 10 cm

Angle bisector divides BC into 2 segments,

BD = 6 cm

CD = 4 cm

If AB = 7.4 cm,

6/4 = 7.4 / AC

AC = 7.4(4) / 6

AC = 29.6 / 6

AC = 4.94 cm (shortest possible length of the third side of the triangle)

If AC = 7.4 cm

6/4 = AB/7.4

AB = 6(7.4)/4

AB = 44.4/4

AB = 11.1 cm (longest possible length of the third side of the triangle)

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Answer:

-4

Step-by-step explanation:

14= -5c-6

+6 +6

________

20 = -5c

÷-5 ÷-5

________

-4 = c

The product when multiplying by powers of 10 is 6 ×[tex]10^{10}[/tex] = 60000000000

The fundamental concept of repeatedly adding the same number is embodied in the process of multiplication. The outcome of multiplying two or more numbers is known as the product of those numbers, and the factors that are multiplied are referred to as the factors. The process of repeatedly adding the same number is made easier by multiplication.

Finding the product of two or more numbers is done by multiplication. It is a fundamental mathematical operation that is frequently applied in everyday situations. When combining groups of similar sizes, multiplication is utilized.

Given that :The table shows the equations Ms. Valer discussed in math class Equations

6 x 10°= 6

6× 10¹ =60

6 x 10=600

6x 10³=6,000

6 ×[tex]10^{10}[/tex] = 60000000000

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Using the Law of Sines, it is found that:

Suppose we have a triangle in which:

The lengths and the sine of the angles are proportionally related as follows:

[tex]\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}[/tex]

From this relation, we have that:

In this problem, we have that:

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Answer:

1. sixty point zero three OR sixty and 3 hundredths

2. two hundred and nine point one one OR two hundred nine and 11 hundredths

The answer is D. -1,-3. i just finished and got it right

Answer:

  $29.16

Step-by-step explanation:

You want the total cost of a $27 meal after 8% tax is added.

The amount of added tax is found by multiplying the meal cost by the tax rate:

  0.08 × $27.00 = $2.16

The total cost is the meal cost plus the tax:

  $27 +2.16 = $29.16 . . . . actual cost of the meal

__

Additional comment

The sum 27 + 0.08×27 can also be found by factoring out the 27:

  = 27(1 +0.08) = 27×1.08

Answer: rotation 90° clockwise about the origin

The missing step is rotation 90° clockwise about the origin.

A translation in math moves a shape left or right and/or up or down. The translated shapes look exactly the same size as the original shape, and hence the shapes are congruent to each other. They just have been shifted in one or more directions.

In the graph, triangle 1 is translated to triangle 2.  

Triangle 1 has three transformations, rotation 90° clockwise, translation 3 units to the right and 4 units down.

Therefore, the missing step is rotation 90° clockwise about the origin.

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For the application of the law of sine the true statement is that at least one side length and opposite angle pair must be known.

The law of sine is used to solve the sides and angles of a triangle.

Law of sines defines the ratio of sides of a triangle and their respective sine angles are equivalent to each other.

In other words,  the law of sines is defined as the ratio of side length to the sine of the opposite angle.

It holds for all the three sides of a triangle respective of their sides and angles.

Therefore, the law of sine can be expressed as follows:

a / sin A = b / sin B = c / sine C

Hence, the statement that is true is at least one side length and opposite angle pair must be known.

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The current location of the submarine would be -50 feet.

The questions says that the submarine was at -20 feet already.

Now it says that it descended 30 feet. Remember that the descent refers to a fall. Hence the way that it would be represented would be through the use of a negative sign.

This would be -30

The current location of the descent of the submarine would be

-20 - 30

= -50 feet

Therefore the current location of the submarine would be -50 feet.

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After evaluating the limit we have came to find that the limit of      [tex]\lim_{x\rightarrow 2 }\frac{\sqrt{x-1} -1}{x-2}[/tex]as x approaches 2 is 0.5

As an input or as an index approaches a specific value in mathematics, a limit is the value that the function, sequence, or index approaches. The definitions of continuity, derivatives, and integrals all require limits, which are fundamental to calculus and mathematical analysis.

In addition to having a connection to the category theory concepts of limit and direct limit, the idea of a limit of a sequence is further generalized to include the idea of a limit of a topological network.

A limit of a function is typically expressed in formulas as

[tex]{\displaystyle \lim _{x\to c}f(x)=L,}[/tex]

To find the limit we will use L'Hôpital's Rule

Find the derivative

⇒ [tex]\lim_{x\rightarrow 2 }\frac{\sqrt{x-1} -1}{x-2}[/tex]

⇒ [tex]\lim_{x\rightarrow 2 } \frac{1/2(x-1)^{-1/2}}{1}[/tex]

⇒ [tex]\lim_{x\rightarrow 2 } \frac{1}{2\sqrt{x-1} }[/tex]

Evalúe 2 as x

⇒ [tex]\frac{1}{2\sqrt{(2)-1} }[/tex]

⇒ [tex]\frac{1}{2\sqrt{1} }[/tex]

⇒ [tex]\frac{1}{2}[/tex]

⇒ 0.5

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By using the elimination method,  the numbers are 11 and 30

Consider the first number as x and the second number as y

Sum of 5 times the first number and 6 times the second number is 235

The linear equation will be

5x+6y = 235

The difference between 7 times the first number and 17 is 2  times the second number

7x-17 = 2y

Rearrange the terms

7x-2y = 17

The both equations are

5x+6y = 235

7x-2y = 17

Multiply the first equation by 2 and second equation by 6

10x+12y = 470

42x-12y = 102

Here we have to use the elimination method

Add both equation and y term will cancelled

10x+42x = 470+102

52x = 572

x = 11

Substitute the value of x in any equation

5x+6y =235

5(11)+6y = 235

55+6y = 235

6y = 180

y = 30

Hence, by using the elimination method,  the numbers are 11 and 30

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The 2 conservative numbers whose square differs by 25 are 12 and 13.

It should be noted that consersative numbers simply refer to the numbers hat follow each other continuously in a particular order. They include 1, ,2, 3, etc.

In this case, the two conservative numbers whose square differs by 25 are 12 and 13. This will be illustrated as:

= 13² - 12²

= 169 - 144

= 25

Therefore, the numbers are 12 and 13

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The expression m = a + n + p can be written as a = m - n - p after making the subject a.

It is defined as the combination of constants and variables with mathematical operators.

The expression is:

m = a + n + p

To solve for a make the subject as a:

a = m - n - p

Thus, the expression m = a + n + p can be written as a = m - n - p after making the subject a.

The question is incomplete.

The complete question is:

Solve for a, if the expression is m = a + n + p.

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Answer:

Defined: M-N

Not defined: Q+P, M+P, L-N

Step-by-step explanation:

Just took the test

Answer:

I don't know

Step-by-step explanation:

I don't know

The given table shows that does not show a proportional relationship, as the ratio between the output and the input is not the same for all terms of the table.

A direct proportional relationship is a function in which the output variable is given by the multiplication of the input variable and the constant of proportionality k, as defined below.

y = kx

In this problem, we have that:

To verify if it shows a proportional relationship, we have to divide the output by the input in each case, hence:

Due to the different constant for 4 pounds, the table does not show a proportional relationship,

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A small order coffee company charges $12 for each bag of coffee +3 dollars shipping no matter how many bags are ordered. Describe the function that this situation gives rise to. make a table for this function, sketch a graph for this function, and find an equation for this function. Is the function linear or not? How can you tell?

Step 1

Describe the function,

.

Let

x, the number of bags

shipping = 3 dollars

Charges=$12 for each bag, then

charges=12*x

Now, the total is

total=charges + shipping

total=12x +3

now, we have a function ( the total (y) depends on the number of bags)

where

y is the total charge, and x is the numbers of bags

Step 2

assume values for x, replace and find y

x=-3

then y=12(-3)+3, y=-36+3, y=-33

so, when x=-3, y=-33

2

then y=12(-2)+3, y=-24+3, y=-21

so, when

x=-2, y=-21

1

then y=12(-1)+3, y=-12+3, y=-9

so, when

x=-1, y=-9

0

then y=12(0)+3, y=+3, y=3

so, when

x=0, y=3

1

then y=12(1)+3, y=12+3, y=15

so, when

x=1, y=15

the table is

x y

-3 -33

-2 -21

-1 -9

0 3

Step 3

, just sepick two cooridnadinates from the table mak, then mark those pintsoints, and finally, dwr in the planeaaw a line conceeecting he connectingnts

Step 4

as you can see, when we take the points of the table and we unite them, a line appears

so , this is a linear function

Also, the exponent of the variable ( x) is cero, which means it is a linear function.

Answer:

The answer to the first question is the first option

The answer to the second question is the third option

the answer to the third one is the second option

Step-by-step explanation:

*I'm not 100% sure about these but it's probably right*

Answer:

1. First one

2. Third one

3. Second on

Step-by-step explanation:

(★ ω ★)

Answer:3

Step-by-step explanation:

The recipe of the junk calls for 16/7 cups of sugar

From the question, the given parameters are:

Total number of cups = 8

Let the number of cups of sugar be x and the number of cups of flour be y

So, we have the following equation

x + y = 8

Also, we have:

The recipe uses 1/4 cup more sugar, so the amount of sugar equals half the amount of flour

This means that

(1 + 1/4) * x = 1/2 * y

Evaluate the sum and the products

So, we have

5/4x = 1/2y

Make y the subject

y = 5/2x

Substitute y = 5/2x in x + y = 8

x + 5/2x = 8

Evaluate the sum

3.5x = 8

Divide by 3.5

x = 16/7

Hence, the cups of sugar is 16/7

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Answer:

0

Step-by-step explanation:

Answer:

3/26

Step-by-step explanation:

you simply divide both numbers by there largest lcm which is 3

9/3=3

78/3=26

Together 3/26

Answer:

It would take 75 minutes for Susan to run 10 miles.

Step-by-step explanation:

10 miles divided by 4 = 2.5

30 min. x 2.5 = 75 minutes

List 3 points that are on the line 5y= 3x - 7.

We know that the y-intercept is (0, -7)

We know that slope = 3 and slope = rise / run or 3 y for every 1 x

We can add 1 for the x and 3 for the y: (0, -7) to (1, -4).

We can do that again:add 1 for the x and 3 for the y: (1, -4) to (2, -1).

(0, -7)

(1, -4)

(2, -1)

When an image is dilated by a factor of 3, the statement about the image of the figure that is true is Both the area and the perimeter increase.

When a shape is dilated, the effect on the shape is that its dimensions are made to be longer. For instance, a shape dilated by 2 would see all its dimensions increase by 2.

In the case of a figure that is dilated by a factor of 3, it means that the shape would increase by 3 in size.

The effect of this is that the perimeter would increase by 3. The area of the figure would also increase thanks to the increase in dimensions by 3.

Options for this question include:

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Using it's concept, the probability that the subject​ lied, given that the test yields a positive result is of 9/11 = 0.8182 = 81.82%.

The probability of an event in an experiment is calculated as the number of desired outcomes of the experiment divided by the number of total outcomes of the experiment.

In this problem, we want to find the probability that the subject​ lied, given that the test yields a positive result, hence:

From the table, we have that:

Hence the probability is given as follows:

p = 45/55 = 9/11 (simplifying by 5)

p = 9/11 = 0.8182 = 81.82%.

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The average monthly rating is 91.25.

         Average = Sum of the Observations/Number of Observations

Given:

The received ratings are 85, 90, 100, and 90.

Average monthly rating = Sum of ratings/ total number of ratings

                                       = (85 + 90 + 100 + 90)/ 4

                                       = 365/ 4

                                       = 91.25

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If y varies directly with x, that means there is going to be a constant that connects both the x and y variable.

The appropriate direct variation equation is stated above, and that is;

y = 8/3x

Your rate is temporarily fixed for a total of five years under a 5/1 ARM, indicated by the "5".

A loan for a home is a mortgage with an adjustable interest rate (ARM). An ARM's initial interest rate is fixed for a specific period of time.

The "1" indicates the number of times the rate may change after the initial fixed-rate term expires; in this instance, the "1" equals one year, therefore the rate changes once a year.

The "5" in the word represents the period during which the rate will be fixed, and the "1" denotes the interval between adjustments after that (once per year). Therefore, it is already apparent how crucial insurance is.

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