Select the correct equation for each situation in the table

Answer:

$139,200

Step-by-step explanation:

To find the total cost of the subsidized loan, we need to calculate the total amount of interest that will be added to the loan over the 10-year repayment period. We can use the formula for simple interest:

I = Prt

Where:

I = Interest

P = Principal (the original loan amount)

r = Interest rate (expressed as a decimal)

t = Time (in years)

In this case:

I = 80,000 * 0.074 * 10 = 59,200

The total cost of the loan would be the sum of the principal and the interest:

80,000 + 59,200 = $139,200

So the total cost of the subsidized loan is $139,200.

Yes, xk/yk converges to x/y. This can be proven mathematically using the definition of a limit.

If xk converges to x and yk converges to y, then the limit of xk/yk as k approaches infinity is equal to the limit of x/y. This can be expressed algebraically as limk→∞xk/yk = limk→∞x/y, which is equal to x/y. Thus, xk/yk converges to x/y.

To calculate this, we can take a sequence of xk an yk values, and divide every xk by its corresponding yk. For example, if xk = {2, 4, 8, 16, 32} and yk = {1, 2, 4, 8, 16}, then the sequence xk/yk = {2/1, 4/2, 8/4, 16/8, 32/16} = {2, 2, 2, 2, 2}. This sequence converges to 2, which is equal to x/y. Therefore, xk/yk converges to x/y.

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Bob would take 5 hours to mow the law by himself.

Let us consider, the area of the lawn to be mowed to be x inch².

It is given that the law can be mowed by Abe alone in 3 hours.

We know that,

Rate of work = Work/Time

⇒ rate of work of Abe = area to be mowed(work)/time taken

                                     = (x/3) inch²/hour

Now,

Abe has been working alone for 1/3 hour

⇒work done by Abe alone = rate of work of Abe x time

                                             = (x/3) inch²/hour x 1/3 hour

                                             = x/9 inch²

Remaining work = x - x/9 = 8x/9 inch²

Let, the rate of work of Bob be y inch²/hour.

It is given that the time taken by Abe and Bob to complete the remaining work together is  1 and 2/3 hours, i.e, 5/3 hours.

Therefore,

The rate of work of Abe and Bob when working together

= work ÷ time

=(8x/9) ÷ (5/3)

=8x/15 inch²/hour

⇒ Rate of work of Abe + Rate of work of Bob = 8x/15

⇒ x/3 + y = 8x/15

⇒ y = (8x/15) - (x/3)

⇒ y = 3x/15 = x/5 inch²/hour

Thus, the time taken by Bob to mow the law by himself

= work ÷ rate of work

= x inch² ÷ (x/5) inch²/hour

= 5 hours

So, it would take 5 hours for Bob to mow the lawn alone.

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The surface of the smaller cubic package is 150 squared inches.

Remember that for a cube of side length S, the surface area is given by:

A = 6*S^2

In this case,w we know that the surface area of the larger cube is 384 in^2, replacing that we will get:

384 in^2 = 6*S^2

S = √(384 in^2/6) = 8in

And the edge of the smaller package is 3 inches shorter, then its sidelength is:

s = 8in - 3in = 5in

Then its surface area is:

A = 6*(5in)^2 = 150 in^2

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x = 5/2 is a zero of the function f(x) = 2x³ - 5x² - 6x + 15.

What is a function?

A function in mathematics from a set X to a set Y allocates precisely one element of Y to each part of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.

Here, we have

Given: x = 5/2 is a zero of the function f(x) = 2x³ - 5x² - 6x + 15,

f(x) = 2x³ - 5x² - 6x + 15

When we f(x) = 2x³ - 5x² - 6x + 15 by x-5/2 we get

Remainder = -10

Quotient = 2x² - 6

Divisor = x - 5/2

2x³ - 5x² - 6x + 15 = 2x² - 6 - 10/(x - 5/2)

Hence, x = 5/2 is a zero of the function f(x) = 2x³ - 5x² - 6x + 15.

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The z-score for a weight of 10.7 kg is 1.50, which means that the weight is 1.50 standard deviations above the mean of 10.4 kg.

Height and weight are two measurements used to track a childs development an organization measures child development by comparing the weights of children who are the same height and the same gender in a certain year weights for all 80 cm girls in the reference population had a mean

μ = 10.4 kg

and standard deviation

σ = 0.2 kg.

Weights are normally distributed.

X ~ N(10.4, 0.2). Calculate the z-scores that correspond to the following weights and interpret them. (Round your numerical answers to two decimal places.)

Weight = 10.7 kg

Z-score = 1.50

This means that the weight of 10.7 kg is 1.50 standard deviations above the mean of 10.4 kg.

First, calculate the difference between the weight (10.7 kg) and the mean (10.4 kg):

x - μ = 10.7 - 10.4 = 0.3

Then, divide the difference by the standard deviation:

(x - μ)/σ = 0.3/0.2 = 1.50

The z-score is 1.50, which means that the weight of 10.7 kg is 1.50 standard deviations above the mean of 10.4 kg.

The z-score for a weight of 10.7 kg is 1.50, which means that the weight is 1.50 standard deviations above the mean of 10.4 kg.

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the change in net working capital during the year will be $6,935.

The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

Given, Rousey Incorporated, had a cash flow to creditors of $16,830 and a cash flow to shareholders of $7,370 over the past year.

Cash flow from assets:

= Cash flow to creditors + Cash flow to shareholders

= $16,965 + $7,559

= $24,524

Since

Net capital spending = Net fixed assets at the end - Net fixed assets at the beginning + Depreciation expense

Cash flow from financial assets = Operating cash flow - Net capital spending - Change in working capital

$24,524 = $51,136 - ($57,130 - $49,705 + $12,252) - Change in working capital

$24,524 = $51,136 - $19,677 - Change in working capital

$24,524 = $31,459 - Change in working capital

Change in working capital = $31,459 - $24,524

                                           = $6,935

Therefore, the change in net working capital during the year will be $6,935.

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The other number can be represented as 123-x.

The parent function is the simplest form of the type of function in the graph is g(x) = 1/x

What is graph ?

In mathematics, a graph is a collection of points, called vertices, and lines, called edges, that connect the vertices. Graphs are used to represent networks of communication, data organization, computational devices, the flow of computation, and more. Graphs are one of the most fundamental concepts in mathematics, and they are used to model many real-world problems and situations.

The transformation from the first equation to the second one can be found by finding a, h and k for each equation.

y = a / x-h   +   k

Find  a, h and k for

g(x)= 1/x

a = 1

h=0

k = 0

The horizontal shift depends on the value of h and The horizontal shift is described as :

f(x) = f(x+h)  The graph is shifted to the left h units

f(x) = f(x-h) The graph is shifted to the right h units.

Horizontal shift depends on the value of k and The horizontal shift is described as :

f(x) = f(x+k)  The graph is shifted to up k units

f(x) = f(x-k) The graph is shifted down k units.

Vertical shift : none.

The sign of a describes the reflection across the x-axis. −a means the graph is reflected across the x-axis.

Reflection about the x-axis: None

To find the transformation, compare the two functions and check to see if there is a horizontal or vertical shift, reflection about the x-axis, and if there is a vertical stretch.

Parent Function: g(x) = 1/x

Horizontal Shift: None

Vertical Shift: None

Reflection about the x-axis: None

Hence, The parent function is the simplest form of the type of function g(x) = 1/x .

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Answer:

4. 0.50g+2=15

Step-by-step explanation:

Answer:

226.1 [tex]in^{2}[/tex]

Step-by-step explanation:

Each sampling distribution becomes more leptokurtic as sample sizes increase due to a reduction in its variety. The sampling distribution's range is smaller than the initial population's range.

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Answer:

0/-2 or zero slope

Step-by-step explanation:

(4,8), (2,8)

x1 y1 x2 y2

y2- y1

_____

x2 - x1

↓

8-8

___= 0/ -2

2-4

the slope is 0/-2, making it equal 0 slope

The area of the circle having a radius of 10 ft will be 100π.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the circle in a two-dimensional plane is called the area of the circle.

Given that the radius of the circle is 10 ft. The area of the circle is calculated by the formula written as below,

Area of the circle = πr²

Substitute the value of the radius in the formula and calculate the area of the circle.

Area of the circle = πr²

Area of the circle = π x ( 10 ) ²

Area of the circle = 100π square ft

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Answer: 133.5

Step-by-step explanation:

Add the weights together and, for some reason, you get 133.5

Answer:

------------------------------------

Add the four numbers together to get the total weight:

It doesn't match any options, please double check if they are (or given weights) correct.

Answer:

True

Step-by-step explanation:

An obtuse angle is an angle that is greater than 90 degrees but less than 180 degrees. An obtuse angle is also called a reflex angle. A reflex angle is formed when the arms of an angle point in opposite directions. The degree of an obtuse angle is between 91 and 179 degrees. Therefore, it's true.

Hope it helps! :)

Answer:

True

Step-by-step explanation:

An obtuse angle measures more than 90 degrees and 180 degrees. So 179 is greater than 90 degrees and less than 180 degrees.

The function that best models the number of game consoles sold in millions since 2009 is g(x) = (25.5)(0.6)ˣ.

The correct option is B.

An exponential function's curve is created by a pattern of data called exponential growth, which exhibits higher increases over time.

y = a(1+r)ˣ,

where a is the initial population and r is the rate in decimals and sx is the time period.

Given:

The graph shows the number of game consoles sold in millions since 2009.

Let the function is,

g(x) = abˣ.

And graph passes through two points (0, 25.5) and (1, 15.3).

So,

when x = 0 then g(x) = 25.5.

That means, a = 25.5

And, when x = 1 then g(x) = 15.3.

That means,

15.3 = (25.5)b.

b = 0.6

Therefore, the function is g(x) = (25.5)(0.6)ˣ.

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A rule for a histogram that decides into endpoint convention class intervals subjects is placed if their value is on the boundary between two intervals.

Endpoints are defined as physical devices that connect to and exchange information with a computer network.

There are some examples of endpoints:

They are mobile devices, desktop computers, virtual machines, embedded devices, and servers.

Internet-of-Things devices like cameras, lighting, refrigerators, security systems, smart speakers, and thermostats are also examples of endpoints.

When a device connects to a network, the flow of information between, for instance, a laptop and a network, is much like a conversation between two people over the phone.

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Answer:

375 square units

Step-by-step explanation:

Area = (1/2) h (a+b)

=1/2 × 10 (49+26)

= 5 × 75

= 375 square units

hope it helps you <3

The factors of the polynomial x³ - 5x² - 12x + 36 are (x-5) and -12(x+3).

What is the Factorisation of Polynomial?

The factors are the polynomials that are multiplied to produce the original polynomial.

The polynomial x³ - 5x² - 12x + 36 can be factored by grouping. We can factor a common factor of x out of the first two terms and the last two terms.

x³ - 5x² - 12x + 36= x(x² - 5x) -12x(1) +36(1)

= x(x-5)(x+1) -12(x+3)

So, the factors of the polynomial x³ - 5x² - 12x + 36 are (x-5)(x+1) and -12(x+3).

We can also factorize this polynomial by using polynomial division.

we can divide x² - 5x by x, remainder will be -5x and we can divide -12x+36 by x+3, remainder will be 0

x³ - 5x² - 12x + 36 = (x(x-5) -12(x+3))

Hence, the factors of the polynomial x³ - 5x² - 12x + 36 are (x-5) and -12(x+3).

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The value of the expression (c² - d²) / (d² + cd - 2c²) in the simplified form will be negative (c + d) / (d + 2c).

When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expression is given below.

⇒ (c² - d²) / (d² + cd - 2c²)

Factorize the numerator and denominator, then we have

⇒ (c² - d²) / (d² + cd - 2c²)

⇒ (c² + cd - cd - d²) / (d² + 2cd - cd - 2c²)

⇒ [c(c + d) - d(c + d)] / [d(d + 2c) - c(d + 2c)]

⇒ [(c + d)(c - d)] / [(d - c)(d + 2c)]

⇒ - [(c + d)(d - c)] / [(d - c)(d + 2c)]

⇒ - (c + d) / (d + 2c)

The value of the expression (c² - d²) / (d² + cd - 2c²) in the simplified form will be negative (c + d) / (d + 2c).

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Answer:

Step-by-step explanation:

To find the value of f(g(-2)), we first need to substitute g(-2) for x in the equation for f(x).

g(-2) = (-2) + 7 = 5

So, f(g(-2)) = f(5)

Now we can substitute 5 for x in the equation for f(x) to find the final value:

f(x) = 3x² - 7x + 15

f(5) = 3(5)² - 7(5) + 15

f(5) = 75 - 35 + 15

f(5) = 55

So, f(g(-2)) = 55

Answer:5

Step-by-step explanation:55

Answer: Height = 20 inches, Width = 36 inches

Step-by-step explanation:

Let the height be [tex]h[/tex] and the width be [tex]h+16[/tex].

Using the formula for the perimeter of a triangle,

[tex]2(h+h+16)=112\\\\2(2h+16)=112\\\\2h+16=56\\\\2h=40\\\\h=20 \implies h+16=36[/tex]

The value of the expression: (5 + √3)/(2- √3) = 13 +7√3

The given surd to be rationalized is (5 + √3)/(2- √3)

Using a²-b² = (a+b)(a-b)

You can rewrite the value 1 in many ways as 2/2, 16/16, or 1 = (5 + √3)/(2-+√3)

Multiplying by 1 but in the form 1 = (2 + √3)/(2- √3) given

(5 + √3)/(2- √3) * (2 + √3)/(2-+√3)

⇒ (5 + √3)(2+√3) / [2² - (3√2)²]

Simplifying the surd to have

(10+ (5 + √3 + 2√3 + 3)/4-1

Therefore this gives 13 + 7√3

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Correct question:

How do you simplify  (5 + √3)/(2- √3)?

The sample proportion based on the question that we have here is 0.85

What is sample proportion?

The sample proportion (p) indicates the percentage of people in a sample who exhibit a particular quality or attribute. Divide the number of individuals (or items) who have the desired attribute by the overall sample size to obtain the sample proportion.

P=X/N, where X represents the number of successes and N represents the sample size, yields the sample proportion.

Hence from the question, we see that 85% of the passengers booked for flights actually show up.  hence the proportion is 0.85.

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Answer:

a= 17

Step-by-step explanation:

Since all sides are equal length, all angles must be equal. Since all of the angles of every triangle sum to 180*, 180/3= 60*. Therefore, (4a-8)*=60*

From there, we can solve for a by adding 8 to both sides:

(4a-8)+8=60+8

4a=68

Then we can divide both sides by 4 to get

(4a)/4= 68/4

a=17

Answer:

a = 17

Step-by-step explanation:

This seems to be an equilateral triangle, so the angle is 60 degrees. 68 - 8 is 60. 4a represents 4 × a, and we know 4 × a has to be 68. 68 / 4 is 17, meaning a = 17.

Answer:

2356

Step-by-step explanation:

slope = (y2 - y1)/(x2 - x1) = (13 - 5)/(-2-0) = 8/-2 = -4

Answer:

-4

Step-by-step explanation:

From the given data, using perimeter of rectangle, Length(L) = 6 × 11 - 7 of the rectangular field.

The length of a shape's outline is its perimeter. You must add the lengths of all four sides of a rectangle or square to determine its perimeter. In this instance, x represents the rectangle's length and y its width. P = x+x+y+y, where P is the perimeter.

Let length of the rectangular field = L

Width of rectangular field = W

Given,

length of a rectangular field is 7 feet less than six times its width

perimeter is 140 feet,

According to the question,

L = 6W - 7

Perimeter of the rectangle = 2 (L + W)

140 = 2 (6W - 7 + W)

140 = 2 (7W - 7)

70 = 7 W - 7

77 = 7 W

W = 11

L = 6 × 11 - 7

Length = 59

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In an apple orchard, the density of planting determines how many of apples a single tree will produce.  An illustration of this is Y=X².

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