in the figure below, trapezoid mnrs is made up of trapezoid mnpt, triangle tpq, and parallelogram pqrs. the area of triangle tpq is 84 square feet. the lengths of np, pq, and qr are in the ratio 2: 1.5:1. find the area of trapezoid mnrs

Using time value of money tables the following are -

(a) The future value of $450 six years from now at 7 percent is $675.33.

(b) The future value of $900 saved each year for 10 years at 8 percent is $13037.91.

(c) The amount a person would have to deposit today (present value) at an interest rate of 6 percent to have $1,000 five years from now is $747.26.

(d) The amount a person would have to deposit today to be able to take out $600 a year for 10 years from an account earning 8 percent is $8691.93.

What in annuity?

An annuity is a contract that you have with an insurance provider that calls for regular payments to be made by the insurer to you, either now or in the future.

(a) The future value of $450 six years from now at 7 percent.

FV= PV × (1 + r)n

FV= $450 × (1 + 7%)6

FV= $450 × (1.07)6

FV= $450 × 1.50073

FV= $675.33

(b) The future value of $900 saved each year for 10 years at 8 percent.

This is annuity as $900 is saved each year

Formula :: FV = PMT * (((1 + r%)n - 1) / r%)

FV = $900 × (((1 + 8%)10 - 1) / 8%)

FV= $900 × 14.4865624

FV= $13037.91

(c) The amount a person would have to deposit today (present value) at a 6 percent interest rate to have $1,000 five years from now.

PV= FV / (1 + r)n

PV= $1000 / (1 + 6%)5

PV= $1000 / 1.3382255

PV=$747.26

(d) The amount a person would have to deposit today to be able to take out $600 a year for 10 years from an account earning 8 percent.

Annuity value = $600

FV= Annuity value × Annuity factor(10%,8 year)

= $600 × (((1 + 8%)10 - 1) / 8%)

= $600 × 14.4865624

= $8691.93

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Answer:

Step-by-step explanation:

2:3 / 8/4

firt step you need factorize

2/3 /2

because 8/4 =2;

2/3:2/1

we have formula

2/3*1/2

answer is :2/6 => 2:2/6:2 => 1/3

Answer:

To convert the weight from pounds to tons, we can divide the weight by 2,000, since there are 2,000 pounds in a ton.

3.9 million pounds / 2,000 = 1,950 tons

So, a fully loaded and fueled spacecraft that weighs close to 3.9 million pounds can be said to weigh 1,950 tons.

Prove of that if the lengths of two sides of a triangle are a and b, respectively, then the lengths of the corresponding altitudes to those sides are in the ratio b.

A triangle is a three by three-sided polygon having three angles and three sides. It is one of the most fundamental and basic shapes in geometry and is used in many other fields of physical science. Triangles are also utilized in architecture and other areas of design and come in a variety of shapes.

Let, a triangle Δ ABC be given, and let its sides be BC = a and AC = b

(figure is given below)

Let, AM and BN are altitudes of corresponding sides of traingle Δ ABC.

We know that the altitude of a triangle is the perpendicular drawn from the vertex of the triangle to the opposite side.

Notice two right-triangles triangles Δ AMC and Δ BNC

We can conclude that the pairs of congruent angles are:

Δ AMC ≅ Δ BNC ≅ 90°

∠ACM ≅ ∠BCN          (common angle)

So, Δ AMC ≈ Δ BNC by the Angle-Angle Similarity Theorem

The triangles are similar and therefore their corresponding angles are congruent:

AM/BN = AC /BC = a/b

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Answer:

9800

Step-by-step explanation:

The median number is the middle term (or the average of the two middle terms, if there are an even number of terms) when sorted in an ascending order.

Sorting in ascending order:

8900, 9600, 9800, 12000, 15500

Hence, 9800 is the mean.

Hello :3

Answer:

C. what is m<ACB

Explanation:

Because you found the angles of ABC and BAC which is 35 and 115, it would only be appropriate to find ACB as well! :)

Hope this helps! ;)

The exponential model that represents the number of cell phone subscribers y (in billions), t years after 2014 is; F = 233 ( 1.06)^t

When the expression of function is such that it involves the input to be present as exponent (power) of some constant, then such function is called exponential function. There usual form is specified below. They are written in several such equivalent forms.

The general formula for an exponential growth is:

F = P( 1 + i ) ^t

where F is the future amount in t years

P is the present amount

i is the fraction of increase per time

t is the time

For the increase cellphone subscriber

P = 233

i = 0.06

Therefore,

F = 233 ( 1 + 0.06)^t

F = 233 ( 1.06)^t

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The rate of change over the interval 15 ≤ x ≤ 18 is equal to 2/3 or 0.67.

In Mathematics, the average rate of change of f(x) on a closed interval [a, b] is given by this mathematical expression:

Average rate of change = [f(b) - f(a)]/(b - a)

Next, we would determine the average rate of change of the function y(x) over the interval [15, 18]:

a = 15; g(a) = 3

b = 18; g(b) = 5

Substituting the given parameters into the average rate of change formula, we have the following;

Average rate of change = (5 - 3)/(18 - 15)

Average rate of change = 2/3

Average rate of change = 2/3 or 0.67.

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The expressions are solved and answered below.

Given are the expressions as shown in the image.

{ 1 } -

2[tex]$\frac{5}{6}[/tex] - 2[tex]$\frac{1}{5}[/tex]

17/6 - 11/5

17/6 - (11 x 1.2/5 x 1.2)

17/6 - 13.2/6

3.8/6

38/60

19/30

{ 2 } -

3[tex]$\frac{5}{8}[/tex] + 7/3

29/8 + 7/3

(29 x 3)/(8 x 3) + (7 x 8)/(3 x 8)

87/24 + 56/24

143/24

Similarly the remaining expressions can be evaluated.

Therefore, the expressions are solved and answered above.

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{Question in english -

Please help urgently with all the answers}

Using proportional relationships, it is found that:

1. A = 15.8, B = 5, C = 63.2.

2. A table with a rate of 0.82 represents the data.

3. Candidate B received 54 votes.

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, also called unit rate, as follows:

y = kx

here, we have,

For item 1, the constant is given as follows:

k = 31.6/4 = 7.9.

Hence the equation is:

y = 7.9x.

Then the value of A is found as follows:

A = 7.9(2)

= 15.8.

The value of B is found as follows:

7.9B = 39.5

B = 39.5/7.9

B = 5.

The value of C is:

C = 7.9(8) = 63.2.

For item 2, the rate is given as follows:

k = 35/42.5 = 0.82.

Hence a table with a rate of 0.82 represents the data.

For item 3, we have that the relation is:

B = kA.

Hence the constant is:

k = 18/15

k = 1.2.

Then the number of votes received by Candidate B is:

B = 1.2 x 45 = 54 votes.

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Answer:First, use the positive value of the

±

to find the first solution.

x

=

7

Next, use the negative value of the

±

to find the second solution.

x

=

−

7

The complete solution is the result of both the positive and negative portions of the solution.

x

=

7

,

−

7

Step-by-step explanation: First, use the positive value of the

±

to find the first solution.

x

=

7

Next, use the negative value of the

±

to find the second solution.

x

=

−

7

The complete solution is the result of both the positive and negative portions of the solution.

x

=

7

,

−

7

Answer:y = (5/4)x - 3/2

Step-by-step explanation:

Answer:

A) The verb "waddled" most accurately and vividly describes the action in this situation, as "waddle" is a verb used to describe a slow and awkward gait often associated with a heavily pregnant woman. This verb conveys the idea of the woman's awkward and unsteady movement, making it the most accurate and vivid description of her actions.

Answer:

yes

Step-by-step explanation:

Use the vertical line test to determine whether or not a graph represents a function. If a vertical line is moved across the graph and, at any time, touches the graph at only one point, then the graph is a function. If the vertical line touches the graph at more than one point, then the graph is not a function.

So if you plug in the following values for x & y, you'll get a curve crossing the Y axis at 0,0

-1,-1

-2,-2

-3,-3

0,0

1,1

2,2

3,3

Answer:

I think the coefficient is 1/3.

Because (x, y) to (1/3x, 1/3y)

Answer:

[tex]\frac{2}{3}[/tex]

Step by Step Explanation:

Convert any mixed numbers to fractions.

Reduce fractions where possible.

Then your initial equation becomes:

[tex]\frac{143}{120}[/tex] - [tex]\frac{21}{40}[/tex]

Applying the fractions formula for subtraction,

= (140 × 40) - (21 × 120)

          120 × 40

= [tex]\frac{5720 - 2520}{4800}[/tex]

= [tex]\frac{3200}{4800}[/tex]

Simplifying [tex]\frac{3200}{4800}[/tex], the answer is [tex]\frac{2}{3}[/tex].

Erin uses sugar at a faster rate than Lucia. This can be seen by comparing the equation for Lucia's cups of tea (y = 10x) to Erin's cups of tea (6, 8, 10, 4).

An equation is a statement that expresses the equality of two values. It consists of an expression containing variables, constants, and operators, and is used to solve mathematical problems. Equations are used to describe the relationships between different variables and can be used to solve for the unknown value of one of those variables. As the number of cups increases, the amount of sugar used by Erin increases at a faster rate than the amount of sugar used by Lucia.

For example, for 6 cups of tea, Erin uses 8 pounds of sugar, while Lucia uses 10 pounds of sugar. For 12 cups of tea, Erin uses 10 pounds of sugar, while Lucia uses 20 pounds of sugar.

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the four key assumptions which are required for multiple linear regression analysis are.

A regression model known as multiple linear regression uses a straight line to calculate the association between two or more independent variables and a quantitative dependent variable.

1.

the four key assumptions which are required for multiple linear regression analysis are:

A non-linear data transformation or the inclusion of a quadratic factor may be able to solve the issue if the data are heteroscedastic.

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Answer:

No solution.

Step-by-step explanation:

First, we can simplify both sides of the equation by squaring them. This gives:

(√x+12)² = (√x + 2)²

Expanding both sides, we get:

x + 24√x + 144 = x + 4√x + 4

Moving all the terms to one side, we get:

20√x + 140 = 0

Subtracting 140 from both sides, we get:

20√x = -140

Dividing both sides by 20, we get:

√x = -7

However, this is not a valid solution for x, since the square root of a number cannot be negative. Therefore, there is no solution for x that satisfies the given equation.

Answer:

3

Step-by-step explanation:

The degree of a polynomial in two or more variables is the highest of the sum of the degrees of each variable

Here there is only one term with variables x and y: xy²

Degree of x = 1, degree of y = 2

Sum of the individual degrees = 1 + 2 = 3

Answer:

56.57 km/h.

Step-by-step explanation:

Distance traveled:

First, we need to convert the time into hours to have the same unit. 1 hour 30 minutes is equivalent to 1.5 hours.

The total time the van traveled is 2 hours + 1.5 hours = 3.5 hours.

The distance traveled during the first 2 hours is 36 km/h * 2 hours = 72 km.

The distance traveled during the next 1.5 hours is 84 km/h * 1.5 hours = 126 km.

The total distance traveled is 72 km + 126 km = 198 km.

Average speed over the whole journey:

The average speed is the total distance traveled divided by the total time traveled.

Average speed = Total distance traveled / Total time traveled = 198 km / 3.5 hours = 56.57 km/h.

Answer:

56.6km/hr

Step-by-step explanation:

2 hours with a speed of 36km/hr is with a distance of (36×2) = 72km

1.5 hours with a speed of 84km/hr = 126km

Total distance = 72+126 = 198km

Average speed = 198/ total time taken = 198/3.5 = 56.6km/hr

Therefore , the solution of the given problem of relative frequency comes out to be  nonfiltered cigarettes have a higher relative frequency of cigarettes with higher tar grades.

A class interval's frequency is the amount of observations that take place during a specific predetermined interval. In other words, the frequency for such 5–9 age range is 20 if there are 20 children between the ages of 5 and 9 in the data from our study.

Here,

Tar(mg) Rel. freq.(Non-filtered) Rel. freq.(filtered)

4 to 9              0                            0.12

10 to 15               0                    0.08

16 to 21            0.04                       0.2

22 to 27           0.08                        0.6

28 to 33          0.52                           0

34 to 39            0.32                           0

40 to 45           0.04                            0

and

Yes, since nonfiltered cigarettes have a higher relative frequency of cigarettes with higher tar grades.

Therefore , the solution of the given problem of relative frequency comes out to be  nonfiltered cigarettes have a higher relative frequency of cigarettes with higher tar grades.

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The value of a must be equal to (k + 2), and then the equation is only true if k = 6, then a = 8.

We want the equation:

(k + 2)x + 3k = ax + 18

To be true for all values of x, then we must have the same thing in both sides of our equation.

Now we wod want the dependence on x to dissapear, then:

(k + 2)x = ax

(k + 2) = a

That must be value of a, and then the equation becomes:

k*x + 2x + 3k = (k+ 2)x + 18

3k = 18

This is only true if k = 6, then:

k + 2 = a

6 + 2 = a

a = 8

That must the value of a.

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Answer:

e and b!

Step-by-step explanation:

the difference is basically a "-minus"

- meaning it's getting smaller

meaning that it's subtracting from this number so basically 12 - 20% is basically what it means but if you take those altogether it takes out the b and e

basically in your head C&D will also be an answer

is definitely out of your track with the difference between those

could you please crouwn me brainliest?

The positive number we're looking for is 5/16.

What is the Equation?

An equation is a mathematical statement that asserts the equality of two expressions.

Let's call the positive number we're looking for x. Then, the problem can be expressed as two equations:

[tex]12x^2 = 4x + 5x^2 = (4/12)x + 5/12\\\x^2 = (1/3)x + 5/12\\\\x^2 - (1/3)x = 5/12\\(4/3)x = 5/12\\x = 5/12 * (3/4)\\x = 5/16[/tex]

Hence, the positive number we're looking for is 5/16.

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The positive number we're looking for is 5/16.

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. For instance, the equation 6x + 5 = 20 consists of the two equations 6x + 5 and 20, which are separated by the 'equal' sign.

A mathematical statement that claims the equivalence of two expressions is known as an equation.

Let's call the positive number we're looking for x.

Then, the problem can be expressed as two equations:

12x² = 4x + 5x² = (4/12) x + (5/12)

x² = (1/3) x + (5/12)

x² - (1/3) x = (5/12)

(4/3) x = (5/12)

x = (5/12) × (3/4)

x = 5/16

Hence, the positive number we're looking for is 5/16.

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Answer:

155

Step-by-step explanation:

see attached.