The four models each show two parallel lines cut by a transversal and some angle measures formed by the
intersection of the lines.

What are the values of angle measures a and b in Model 4?

Move the correct answer to each box. Each answer may be used more than once. Not all answers will be used.

19° 71° 90° 109° 180° 119°

The value of a is ____, and the value of b is ____.

Hello,

I hope you and your family are doing well!

A) To find the annual growth rate between 1991 and 2008, we can use the compound interest formula:

S = P(1 + r)

Where S is the final value of the house, P is the initial value of the house, and r is the annual growth rate.

Plugging in the values from the problem, we get:

165,000 = 95,000(1 + r)

Dividing both sides of the equation by 95,000 gives:

1.737 = 1 + r

Subtracting 1 from both sides of the equation gives:

0.737 = r

The annual growth rate between 1991 and 2008 is 0.737.

B) To express the growth rate in percentage form, we can multiply it by 100%:

0.737 * 100% = 73.7%

So the annual growth rate between 1991 and 2008 was 73.7%.

C) To find the value of the house in the year 2011, we can use the compound interest formula again, with the initial value of the house set to the final value in 2008:

S = P(1 + r)

Plugging in the values from the problem, we get:

S = 165,000(1 + 0.737)

Solving for S gives:

S = 165,000 * 1.737 = 285,195

So the value of the house in the year 2011 will be approximately $285,195. Rounded to the nearest thousand dollars, this is $285,000

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The vertices of a rectangle are W(1, 2) X(4, 2) Y(4, 23) and Z(1, 23) Find the perimeter of the rectangle is 16.

We could use the distance formula to find the distance between the points in this problem, but when we look we see that the sides of the rectangle are parallel to the x and y-axis for each pair of sides. The first two points have a distance of 3 because 4-1=3. Since it is a rectangle, the opposite side will have the same length. For the sides perpendicular, we look at the points with the same x coordinate. Using (4,2) and (4,-3), we can calculate the length of the side by finding the distance by adding the absolute values of the y coordinate. 2+3=5. This means that the triangle has two sides with a length of 5 and two sides with a length of 3. Adding these together, 5+5+3+3 = 16.

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The solutions of the given system of Equations are (5/2, 41/2).

The set of values for each variable in a system of linear equations is referred to as the solution set.

The intersection or meeting points of the lines or planes used to illustrate the linear equations are also known as the solutions.

The elimination method is one way of resolving a system of linear equations. To obtain the equation in one variable using this technique, simply add or subtract the equations.

Here we have

y = 9x-2 --- (1)

y = 7x+3 --- (2)

From (1) and (2)

=>  9x - 2 = 7x + 3

=>  9x - 7x = 3 + 2

=> 2x = 5

=> x = 5/2

Substitute x = 5/2 in (1)  

=> y = 9(5/2) - 2  

=> y = (45/2) - 2

=> y = (45 - 4)/2

=> y = 41/2

Therefore,

The solutions of given system of Equations are (5/2, 41/2).

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Answer:

m∠A = 60

m∠D = 60

Step-by-step explanation:

∆ABC and ∆DEF are congruent triangles

So,

m∠A = m∠D

x + 30 = 2x

2x - x = 30

x = 30

So,

m∠A = x + 30 = 30 + 30 = 60

m∠D = 2x = 2(30) = 60

Thus, m∠A and m∠D are 60°

Rate percent is 10%

A coefficient that is a quotient of two values, where the denominator is written in percentage points and has the same units as the numerator when it is multiplied by a unit of time.

According to the given information

Sum of money ( principal ) P = 5000 rupees

Interest obtained in money = 1500 rupees

Time duration T = 3 years

According to the given information

I = P × T × [tex]\frac{R}{100}[/tex]

1500 = 500 × 3 × R/100

Rate percent is 10%

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Answer:

y=2x+8

Step-by-step explanation:

-6x+3y=24

-6x+6x+3y=24+6x  ==> isolate the y variable

3y=6x+24  ==> simplify

(3y=6x+24)/3

y=2x+8  <== y=mx+b  <== slope intercept form

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For the function in the given case the constraint on domain can be written as  x ≥ 182. The correct option is (a).

A function y = f(x) is a one to one relationship between two sets X and Y where the set X is called the domain and Y the range of function f(x) ans x ∈ X and y ∈ Y.

Suppose the amount of money spent be x.

And, the number of food items be y.

Now, as per the question the function can be written as follows,

y = x/182

As the number of food items can only be positive integers, the values of x must be the multiples of 182.

Thus, the expression for the domain can be written as x ≥ 182.

Hence, the constraint on the domain is given as x ≥ 182.

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The ratio shows how many times one value is contained in another value.

The ratio of office buildings to hotels will be 9 : 4.

The ratio shows how many times one value is contained in another value.

Example:

There are 3 apples and 2 oranges in a basket.

The ratio of apples to oranges is 3:2 or 3/2.

We have,

The ratio of hotels to office buildings = 4 : 9

Now,

The ratio of office buildings to hotels will be 9 : 4.

Thus,

The ratio of office buildings to hotels will be 9 : 4.

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The total weight of the water in a filled tank will be equal to 16,336 Pounds.

Every three-dimensional item takes up space in some way. The volume of this area is what is used to describe it. The area covered within an entity's three-dimensional bounds is referred to as its volume. The object's size is another name for it.

As per the given data in the question,

Radius, r = 10/2 = 5 ft.

Use the equation of the volume of a sphere,

V = 4/3πr³

We only require half of it then,

V =  2/3πr³

V = 261.8 ft³

So, the total weight will be,

W = 261.8 × 62.4

W = 16,336 Pounds.

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Answer:

a. [tex]1 * 10^{-10}[/tex]

Explanation:

A converted to standard notation is the same number.

We can estimate the number of adult partons at 2187 by solving equations.

The equals sign is a symbol used in mathematical formulas to denote the equality of two expressions.

A function is an equation that has only one answer for y for every possible value of x.

When utilizing a function, each input of a specific type receives exactly one output.

A function is commonly referred to as f(x) or g instead of y. (x).

Because f(2) instructs us to do so, we should figure out the value of our function when x is equal to 2.

So, the total number of adults present was thus:

Let a be an adult, and b and c be kids.

Ticket totals:

a + c = 5200

c = (5200-a)

Total amount:

7.50a + 4.50c = 29961

In the first equation, swap out c with (5200-a).

7.5a + 4.5(5200-a) = 29961

7.5a + 23400 - 4.5a = 29961

7.5a - 4.5a = 29961 - 23400

3a = 6561

a = 6561/3

a = 2187

Therefore, we can estimate the number of adult partons at 2187 by solving equations.

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Answer:

Albert = $2159.07; Marie = $2244.99; Hans = $2188.35; Max = $2147.40

Marie is $10 000 richer

Step-by-step explanation:

Albert

(a) $1000 at 1.2 % compounded monthly

A = P (1 + r/n )^nt

A = 1000(1 + 0.001)¹²⁰ = $1127.43

(b) $500 losing 2%

0.98 × 500 = $490

(c) $500 compounded continuously at 0.8%

A = Pe^rt

  = 500e^0.008 * 10

 =  $541.64

(d) Balance

Total = 1127.43 + 490.00+ 541.64 = $2159.07

Marie

(a) 1500 at 1.4 % compounded quarterly

A = 1500(1 + 0.0035)⁴⁰ = $1724.99

(b) $500 gaining 4 %

1.04 × 500 = $520.00

(c) Balance

Total = 1724.99 + 520.00 = $2244.99

Hans

$2000 compounded continuously at 0.9 %

A = 2000e^0.009 * 10

  = $ 2188.35

Max

(a) $1000 decreasing exponentially at 0.5 % annually

A = 1000(1 - 0.005)¹⁰= $951.11

(b) $1000 at 1.8 % compounded biannually

A = 1000(1 + 0.009)²⁰ = $1196.29

(c) Balance

Total = 951.11 + 1196.29 = $2147.40

Marie is $10,000 richer at the end of the competition.

Hope this helps!!! :)

Answer:

Below

Step-by-step explanation:

2.42 x 10^4  = 24200

 24200

+ 23580

 47 780    or   4.778 x 10^4

Answer:

203 dollars

Step-by-step explanation:

100 percent = 145

10 percent = 14.5

30 percent = 43.5

43.5 + 14.5 + 145 = 203

Hello,

I hope you and your family are doing well!

Let's call Sydney's age x and Devaughn's age y. We know that y = 3x and x + y = 116.

Substituting the first equation into the second equation gives:

3x + x = 116

4x = 116

x = 29

So Sydney's age is 29.

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Answer:

[tex]\huge\boxed{\sf 157.1 \ units^2}[/tex]

Step-by-step explanation:

Diameter = 20

Radius = Diameter/2 = 20/2 = 10

[tex]\displaystyle =\frac{\pi r^2}{2} \\\\r = 10\\\\= \frac{\pi (10)^2}{2} \\\\= \frac{100 \pi}{2} \\\\= \frac{314.2}{2} \\\\= 157.1 \ units^2\\\\\rule[225]{225}{2}[/tex]

The confidence interval of this confidence level as calculate from the given data is 3.68 and 99% respectively.

Number of random sample (n)=28

Sample Standard deviation (S)=19.52

Confidence interval = 439.23 -  460.77 =  21.54

t = s/root of n

=19.52 /5.29

=3.68

v = n -1 = 27

now, confidence level

= 1 - alpha

= 99%

Confidence Interval, put simply, is a range within which we are confident that the genuine value exists. The probability that a confidence interval will contain the real parameter value depends on the confidence level that is chosen for the interval.

The phrase "Confidence Interval" refers to the range of values that is typically used to handle population-based data, extracting precise, important information with a given level of confidence.

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Answer:

c= 1.5t, c=t+0.5t and c=(1+0.5)t

Step-by-step explanation:

Given that, Clare scored 50% more points than Tyler, c is the number of points that Clare scored and t is the number of points that Tyler scored,According to question,c = 150% of tc = 1.5tHence, the correct options are c = 1.5t, c = t+0.5t and c = (1+0.5)t

The interest over 18 months will be $105.00 if Margo borrows $1000, agreeing to pay it back with 7% annual interest.

It is defined as the interest on the based on the principal amount, it does not include the compounded amount. The interest calculate on the initial amount or borrowed amount.

It is given that:

Margo borrows $1000, agreeing to pay it back with 7% annual interest after 9 months

I = Prt

= 1.5 x 7%

= 1.5 x .07

= 0.105

= $1000 x .105

= $105.00

Thus, the interest over 18 months will be $105.00 if Margo borrows $1000, agreeing to pay it back with 7% annual interest.

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Answer:

Step-by-step explanation:

1) x - 1 = 2x - 2

-x = -1

x = 1

2) 4x = x + 3

3x = 3

x = 1

3) x + 1 = x + 1

infinite solutions (parallel lines)

For graphing, just look at the y-intercept, in the equation y = mx + b.

b is the y-intercept, so, for you plot the y-intercpet on the y-axis. You look at m, which is the slope. For positive, you go up how many ever it says in the numerator and then to the right how many ever it says in the denominator. For a negative you do the same thing except you go down and then to the right, or up and to the left. For positive there is only up and then to the right. I hope this answers your question.

Answer:

the width of the rectangle is -5/3 inches.

Step-by-step explanation:

To find the perimeter of the rectangle, we add together the lengths of all four sides. Since the rectangle is 5 inches long and 2x inches wide, the perimeter is given by:

Perimeter = 5 + 2x + 5 + 2x = 10 + 4x

To find the area of the rectangle, we multiply the length by the width. The area is given by:

Area = 5 * 2x = 10x

Setting the perimeter equal to the area, we have:

10 + 4x = 10x

Subtracting 10 from both sides, we have:

4x = 10x - 10

Combining like terms, we have:

-6x = -10

Dividing both sides by -6, we have:

x = 10 / -6

Simplifying, we have:

x = -5/3

The expected value of this game will be 1,784.75.

In parameter estimation, the expected value is an application of the weighted sum. Informally, the expected value is the simple average of a considerable number of individually determined outcomes of a randomly picked variable.

The expected value is given below.

E(x) = np

Where n is the number of samples and p is the probability.

In a lottery game, a player picks six numbers from 1 to 28. Assuming the player matches each of the six numbers, they win 50,000 bucks. In any case, they lose $1.

Then the probability of winning (p) and losing (q) is given as,

p = 1 / 28

q = 27 / 28

Then the expected value is given as,

E(x) = 50,000 (1 / 28) - 1 (27 / 28)

E(x) = 1785.714 - 0.964

E(x) = 1,784.75

The expected value of this game will be 1,784.75.

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Answer:

6790 km

Step-by-step explanation:

move the decimal 3 places to the right.

The point which satisfies equation is (-2,4)

What is circle?

A circle could be a form consisting of all purposes during a plane that are at a given distance from a given point, the centre.

Main body:

The center of circle formula is also known as the general equation of a circle. In a circle, if the coordinates of the center are (h,k), r is the radius, and (x,y) is any point on the circle, then the center of circle formula is given below:

Formula of circle =

(x - h)² + (y - k)² = r²

According to question:

center of circle = (2,1)

diameter of circle = 10 units

radius = 5 units

equation of circle ⇒

(x - 2)² + (y - 1)² = 25

for a point to lie on circle , it need to satisfy the equation of circle:

A) (1,-3)

⇒(1 - 2)² + (3 - 1)²

⇒(-1)² +2²

⇒5

so it does not lie on circle.

B) (-2,4)

⇒(-2 - 2)² + (4 - 1)²

⇒-4²+3²

⇒ 25

so, it satisfies the equation.

hence, the point which satisfies equation is (-2,4)

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The type of the function for the given graph f(x) on the right is odd function.

An exact one of each element of Y is assigned to each element of X via a mathematical function from a set X to a set Y. The sets X and Y are denoted by the terms "domain" and "codomain," respectively.

The link between varying amounts and other variables was the foundational idea behind functions. The effect of time on a planet's position serves as an example of this. The infinitesimal calculus was used to develop the concept in the past, beginning at the end of the 17th century and continuing through the 19th century.

An odd function's graph possesses rotational symmetry with respect to the origin, which means that it doesn't change after being rotated by 180 degrees around the origin.

Therefore, The type of the function for the given graph f(x) on the right is odd function.

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4,034.06 ,5,965.94 are confidence interval for the population average wages at the factory.

What is confidence interval estimation?

Your estimate's mean plus and minus the range of that estimate's fluctuation is called a confidence interval.

                                              If you repeat your test, you can expect your estimate to fall between these numbers with a reasonable degree of certainty.  Another term for probability in statistics is confidence.

The formula for confidence interval estimation is:

μ = M ± Z(sM)

where:

M = sample mean

Z = Z statistic determined by confidence level

sM = standard error = √(s2/n)

M = 50000

Z = 2.58

sM = √(30002/64) = 375

μ = M ± Z(sM)

μ = 50000 ± 2.58*375

μ = 50000 ± 965.94

μ = 4,034.06 ,5,965.94

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Answer: To find the value of m in the equation W = 1/2 * m * v^2, you need to know the values of W and v. The variable m represents the mass of the object, and W represents the kinetic energy of the object. The equation states that the kinetic energy of an object is equal to 1/2 of its mass multiplied by its velocity squared.

If you are given the values of W and v, you can solve for m by rearranging the equation as follows:

m = 2 * W / v^2

Plugging in the values of W and v will give you the value of m.

For example, if W = 100 joules and v = 10 meters per second, the equation would be:

m = 2 * 100 joules / 10 m/s^2 = 20 kilograms

This is the mass of the object.

[tex]m=\frac{2W}{v^{2} }[/tex].

[tex]W=\frac{1}{2} mv^{2}[/tex]

[tex]\frac{W}{\frac{1}{2} v^{2} }=m\\ \\[/tex]

[tex]m=\frac{W}{\frac{1}{2} v^{2} }\\ \\m=\frac{2W}{v^{2} }[/tex].

The time needed for the account value to reach 11200 dollars is approximately 15.9 years.

Simple interest formula is expressed as;

A = P( 1 + rt )

Where A is accrued amount, P is principal, r is interest rate and t is time.

Given the data in the question;

Plug the given values into the above formula and solve for time t.

A = P( 1 + rt )

A/P = 1 + rt

( A/P - 1 ) = rt

t = ( A/P - 1 ) / r

t = ( $11200/$5400 - 1 ) / 6.75%

t = ( $11200/$5400 - 1 ) / 6.75/100

t = ( 56/27 - 1 ) / 0.0675

t = ( 29/27 ) / 0.0675

t = 15.9 years.

Therefore, the required time to reach the accrued amount is 15.9 years.

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Answer:

ANS:- 15.9

Step-by-step explanation:

5814/365 = 15.9

The expression that is equivalent to  ∛ 5 * [tex]\sqrt[5]{4}[/tex] is [tex]5^{1/3}*4^{2/5}[/tex]

A radical in mathematics is the opposite of an exponent, which is symbolized by the sign "n√" also known as root.

The number before the symbol or radical is regarded as an index number or degree, and it can either be a square root or a cube root and so on.

This equation represents exponents in fraction form and the basics for the calculation is from

x^(b/n)

[tex]\sqrt[n]{x}^{b}[/tex]

Rewriting the expression is done as below

∛ 5

= [tex]5^{1/3}[/tex]

and

[tex]\sqrt[5]{4}[/tex]

[tex]= 4^{2/5}[/tex]

combining both gives

∛ 5 * [tex]\sqrt[5]{4}[/tex]

[tex]5^{1/3}*4^{2/5}[/tex]

[tex]5^{1/3}*4^{2/5}[/tex] is the equivalent expression

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