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Question 9

The amount of money an account with simple interest at an annual rate of 4.2% would be $3738 after 1 month and 7476 dollar after 2 month.

Simple interest is a method of calculating the interest charge. Simple interest can be calculated as the product of principal amount, rate and time peroid.

Simple Interest = (Principal × Rate × Time) / 100

Given that loan Amy is 89000 monthly payment is 479.66 rate is 4.2

Amount = $89000

Rate = 4.2 %

Time =  1 month

Therefore, Simple Interest = (Principal × Rate × Time) / 100

Simple Interest = 89000 × 4.2% × 1

Simple Interest = 3738

Also,

Simple Interest = 89000 × 4.2% × 2

Simple Interest = 7476

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No, h is not a vector space. It fails to satisfy property (b), closed under vector addition.

For a set to be a vector space, it must satisfy three properties: contains the zero vector, closed under vector addition and closed under multiplication by scalars.

For a set to be closed under vector addition, the sum of any two vectors in the set must also be in the set. In this case, the set h contains the points (s, s-1).

When two points are added, the result is (2s, 2s-2), which is not in the set h. Therefore, h fails to satisfy property (b) and is not a vector space.

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If the midpoint of AB with A (2, 4) and B (- 6, 8) is at point  (-2, 6)

The formula to determine the center point of a straight line using the coordinates of its endpoints is known as the midpoint formula in coordinate geometry.

The formula is of the form

X= (x₂ + x₁)/2

Y = (y₂ + y₁)/2

solving for the midpoint

X= (2 - 6) / 2

X = -4 / 2

X = -2

Y = (y₂ + y₁)/2

Y = (4 + 8) / 2

Y = 12 / 2

Y = 6

The midpoint is (-2, 6)

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The division of the given polynomial is [tex]\frac{20x^3+12x^2+17x-17}{5x^2-2x}=4x+4+\frac{25x-17}{5x^2-2x}[/tex].

What is a long division of polynomials?

A long-division polynomial is an algorithm for dividing polynomials by another polynomial of the same or a lower degree. The long division of polynomials also consists of the divisor, quotient, dividend, and the remainder as in the long division method of numbers.

The given expression is (20x³ + 12x² + 17x - 17) ÷ (5x² - 2x)

[tex]=\frac{20x^3+12x^2+17x-17}{5x^2-2x}\\\\=4x+\frac{20x^2+17x-17}{5x^2-2x}\\\\=4x+4+\frac{25x-17}{5x^2-2x}\\[/tex]

Hence, the division of the given polynomial is [tex]\frac{20x^3+12x^2+17x-17}{5x^2-2x}=4x+4+\frac{25x-17}{5x^2-2x}[/tex].

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Answer:

  (b)  0.058 or 5.8%

Step-by-step explanation:

Given a normal distribution with mean 10.72 and standard deviation 0.14, you want the probability that a value is less than 10.5.

A suitable probability calculator needs to know the mean, standard deviation, and set of values of interest. Here, ...

  mean = 10.72

  standard deviation = 0.14

  P(X < 10.5)

The calculator shows it to be 0.058, or 5.8%.

The probability of event A occurring is 1/2, the probability of event B occurring is 1/3, and the probability of event C occurring is 1/6.

in order for a sum of two dice to be even, the numbers on the two dice must add up to an even number. The possible combinations of two dice that add up to an even number are (1,3), (3,1), (2,4), (4,2), (5,5). Therefore, the probability of event A occurring is 1/2.

In order for the sum of two dice to be at least 10, the numbers on the two dice must add up to 10, 11, 12. The possible combinations of two dice that add up to 10, 11, 12 are (4,6), (6,4), (5,5), (5,6), (6,5). Therefore, the probability of event B occurring is 1/3.

In order for the red die to come up 5, the number on the other die does not matter. Therefore, the probability of event C occurring is 1/6.

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The transformation from the parent function is a translation by 8 units right and 4 units up

From the question, we have the following function that can be used in our computation:

f(x) = x³

g(x) = (x − 8)³ + 4

First, we have the transformation to be:

From f(x) = x³ to f'(x) = (x − 8)³

This means the function is translated right by 8 units

Next, we have:

From f'(x) = (x − 8)³ to g(x) = (x − 8)³ + 4

This means the function is translated up by 4 units

Hence, the transformation is 8 units right and 4 units up

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In the proof, The reason for (5) ΔVWX ≅ ΔXYZ is ASA

Two triangles are congruent when their three angles and three sides are equal to each other. The two triangles need to be of the same size and shape to be congruent. Both the triangles under consideration should superimpose on each other.

There are 4 property we use to congruent two triangles ( ASA , RHS , SSS and SAS)

According to the question,

Given = V W║Z Y

W X=Y X

We have to prove :  ΔVWX ≅ ΔXYZ

Proof =>

It is given that V W║Z Y ,

Using parallel line property ,

(1) ∠W = ∠Y (interior alternate angles )

(2) ∠V = ∠Z ( Interior angle property)

(3) W X=Y X (given)

Therefore , By using ASA property

ΔVWX ≅ ΔXYZ

Hence , In the proof, the reason for (5) is ASA

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The value of the equation A = ( 2/3 ) ( 2 - 6 ) is A = -8/3

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

A = ( 2/3 ) ( 2 - 6 )   be equation (1)

On simplifying the equation , we get

A = ( 2/3 ) ( 2 - 6 )

A = ( 2/3 ) ( -4 )

Multiply by -4 on the numerator , we get

A = ( 2 x -4 ) / 3

A = -8 / 3

Therefore , the value of A is -8/3

Hence , the value of the equation is -8/3

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Answer: Both points are not a solution.

Step-by-step explanation:

        This says that the graph will be every y-value less than -1. Both 5 (in the point (-2, 5)) and 2 (in the point (6, 2)) are greater than -1, meaning they are both not a solution.

        See attached for a graph with the coordinate points graphed as well. Since these points are not in the shaded region, they are not solutions.

Answer:

cos(π/2)+isin(π/2)

Step-by-step explanation:

hopefully that's the answer you're looking for, haven't done problems like this in a while-

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For the given isosceles triangle when we solve m < 2 = 12x - 4 we get the value of x = 4.5 degrees.

It is known that two sides are equal so it is a isosceles triangle so the two angles are equal, that is

m<2 = 50

50 = 12x - 4

50 + 4 = 12x

54 = 12x

Divide by 12 on both sides

54 / 12 = 12 x / 12

x = 54 / 12

= 27 / 6

= 9 / 2

= 4.5 degrees

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The ordered pairs of the solution to the system of equation are (-5, -3).

System of equation can be solved using methods like substitution method, elimination method and graphical method.

Let's solve the system of equation by substitution method.

Therefore,

-3x + 2y = 9

x - 3y = 4

Hence,

x = 3y + 4

Substitute the value of x in equation(i)

-3x + 2y = 9

-3(3y + 4) + 2y = 9

-9y - 12 + 2y = 9

-7y = 9 + 12

-7y = 21

y = 21 / -7

y = -3

Let's find x using equation(ii)

x = 4 + 3y

x = 4 + 3(-3)

x = 4 - 9

x = -5

Hence, x = -5 and y = -3

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Answer: D its 50

Step-by-step explanation:

The range of the function will be  0 ≤ y ≤ 960

The range of a function is the set of all its outputs. Example: Let us consider the function f: A→ B, where f(x) = 16x and each of A and B = {set of natural numbers}. Here we say A is the domain and B is the co-domain. Then the output of this function becomes the range. The range = {set of even natural numbers}.

Generally, the range of a function is the possible values of y in the that function and can be from -negative infinity to positive infinity.

In the given question, the function y = 16x models the situation and the capacity of the the container is 960 ounces

The range will fall between 0 ≤ y ≤ 960

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Answer:

9x-63

Step-by-step explanation:

9*(x-7)

9x-63

x= 101°.

Theory of triangles states that the sum of all inner angles of a triangle should equal 180°. Hence, you can make an equation that gives the missing value of "x" in this problem.

[tex]x+30+49=180[/tex]

[tex]x=180-30-49\\ \\x=101[/tex]

x= 101°.

Answer:

First is option B)

Second is option B)

I hope my answer helps you.

The direct framed(mapped) cache in the given hexadecimal has all the miss.

Given cache parameters

b block size( given no. of words)

Cache capacity 16 words

( a) Direct mapped cache with b = 1 word

Address mapping = Total = 8 bits

Index = 4 bits

Offset = 0 bit

Tag(Label) = remaining bits = 4 bits

illustration of mapping = 74---> 01110100

where 0111 is the label and the rest is the index

Sequencing of law addressing = 0 * 74 to binary = 01110100

Then, word offset = log₂( b) = log₂( 1) = 0 bit

Line offset = log₂(16/1) = 4

Label(tag) is the remaining bit

b) completely associative cache with b = 2 words

# of lines = 16/2 W = 8

Address mapping Offset = log ₂( 2) = 1 bit

Remaining bit = 01110100

where 0 is offset and the rest is a label

In this cache design, line no. isn't needed to map the data as we directly compare CPU- generated markers with existing markers in the cache controller.

Still, apply the LRU algorithm, if the cache is full.

c) Two- way set associative cache with b = 2 words

#sets = #lines/ p- way = (16/2)/ 2 = 4

Address mapping

Set offset = log₂( 4) = 2

Word offset = log₂( 2) = 1

Tag(label) = remaining bits

ADDRESS       INDEX         OFFSET       HIT/MISS

74                       10                    0                MISS

A0                      00                    0               MISS

78                      00                    0               MISS

38C                    10                    0               MISS

AC                      10                    0               MISS

84                       10                    0               MISS

88                       00                    0               MISS

8C                       00                    0               MISS

7C                       00                    0               MISS

34                        00                    0               MISS

38                        00                    0               MISS

13C                      00                    0               MISS

388                      00                    0               MISS

18C                       00                    0               MISS

Replacement policy(which is default) LRU

( d) Direct planned or mapped cache with b = 4 words( each instruction size = AW)

Line offset = log₂( 4) = 2 bit

Word offset = log₂( 4) = 2 bit

Tag(Label) = remaining bits

# lines = 16/ W = 4

0 * 74-----> 01110100

where,

01 is the line offset

00 is the word offset

0111 is the tag(label).

Therefore, the tag, line offset and line offset of the hexadecimal is given to be in a binary number.

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Answer:

3.12

Step-by-step explanation:

1 number after the decimal - tenths place.

2 numbers after the decimal - hundredths place.

3 numbers after the decimal - thousandths place.

4 numbers after the decimal - ten thousandths place.

5 numbers after the decimal - hundred thousandths place.

Answer:

3.12

Step-by-step explanation:

3.122 rounds up to 3.12 because 2 is less than 5, so the number rounds down.

The linear equation and the definition of the parts of the equation  of the motion of the balloon are as follows;

A. The equation is; h = 800 - 100·m

B. The rate of change is 100 ft/min. The rate of change represents the height the balloon descends in one minute

C. The y-intercept is 800 (feet). The y-intercept represents the initial height of the balloon

D. The x-intercept is 8 (minutes). The x-intercept represents the time it takes the balloon to reach the ground

A linear equation is one that has a straight line graph.

The initial height of the balloon = 800 feet

Height of the balloon after 1 minute = 700 feet

A. The change in height of the balloon in one minute = 100 feet

The rate of change of the height of the balloon = -100 feet per minute (the height reduces by 100 feet after each minute)

The linear equation for the balloon, can therefore be obtained from the following details;

The initial height of the balloon = The y-intercept of the linear equation, c = 800 feet

The rate of change of the height of the balloon = The slope of the linear equation, m = -100 ft/min

The linear equation in the form, y = m·x + c, that can be used to find the  height of the balloon is therefore;

h = -100·m + 800

B. The rate of change is the rate at which the height of the balloon changes, which is 100 feet per minute

C. The y-intercept is the point at which the linear equation intersects the y-axis which is the point at which the input variable, m, is zero, indicating the height at which the balloon started its descent.

D. The x-intercept is the point at which the graph intersects the x-axis, and at which the y-value (value of the output variable) is zero, and the x-intercept can be specified by the x-value at the point of the intersection.

At the x-intercept, therefore, h is zero, which is the ground level, and m is the time it takes the balloon to reach the ground.

At the x-intercept, therefore, we het;

h = 0 = 800 - 100·m

100·m = 800

m = 800 ÷ 100 = 8

The x-intercept is m = 8 minutes

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The value of the other points in the number line for each case are;

a) M = -2¹/₂

N = -1

R = 4

b) M = -1

P = 1

R = 1.6

c) M = -125

P = 125

N = -50

d) N = -6

P = 15

R = 24

a) We are given that P = 2¹/₂

From the point 0 of the number line to point P is 5 units and as such;

Each unit = 2¹/₂/5 = ¹/₂

Thus;

M = -2¹/₂

N = -1

R = 4

b) We are given that N = -0.4

From the point 0 of the number line to point N is 2 units and as such;

Each unit = 0.4/2 = 0.2

Thus;

M = -1

P = 1

R = 1.6

C) We are given that R = 200

From the point 0 of the number line to point R is 8 units and as such;

Each unit = 200/8 = 25

Thus;

M = -125

P = 125

N = -50

D) We are given that M = -15

From the point 0 of the number line to point N is 5 units and as such;

Each unit = 15/5 = 3

Thus;

N = -6

P = 15

R = 24

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As per the forecast, the updated forecast for the amazon sales accounting for trend, seasonality and adjusted for the serial correlation using the AR(1) model is 75.243.

In statistics, the term correlation defines the degree to which two variables move in coordination with one another.

Here we have Quarterly Amazon Sales (billion dollars) starting in Quarter 3 of 2013 through Quarter 2 of 2021 . And assume in Quarter 2 of 2021 the Amazon Sales were 96.6 billion dollars.

Now we have to use the output provided below to report the updated forecast for the Amazon Sales for Quarter 3 of 2021.

Here the variable time period is coded in the following way:

Start with

t=1 for Quarter 3 of 2013,

t=2 for Quarter 4 of 2013 .

Then the value of t will increase by 1 for each subsequent quarter.

Here in this example we have created indicator variables for Quarters 1, 2 and 3. Quarter 4 is the base level.

Now, by using the output here for the model accounting for trend and seasonality as well as the output for the AR(1) model report the updated forecast for Amazon Sales in Quarter 3 of 2021.

Here the subset of the output posted below: Response Revenues Bivariate Fit of Residual Revenues $2 By Lag residuals Parameter Estimates

Therefore, the Updated forecast for the Amazon Sales accounting for Trend, Seasonality and Adjusted for the Serial Correlation using the AR(1) model is 75.243

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The statement that best describes triangles UVW and XYZ is; They are similar, but not congruent.

We are given that;

Angles VUW and ZXY are congruent.

Angles UWV and XZP are congruent.

Angles UVW and ZYX are congruent.

Now, the length of side UV is 50, the length of VW is 60, and the length of UW is 40. The length of side ZY is 48, the length of YX is 40, and the length of ZX is 32.

Here the triangles are similar by the AAA similarity and the length of the first triangle is in the ratio 40:50:60 = 4:5:6 .

The side of the second triangle is also in the ratio 32:40:48 = 4:5:6 .

Therefore, the triangles UVW and XYZ are similar but not congruent.

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Answer:

B. They are similar, but not congruent

3x2-3(y+1)+9x2+12; reflection in the y-axis, a vertical stretch by a factor of 3, and a translation 1 unit down

The reflection in the y-axis can be achieved by changing the sign of the x-terms while leaving the y-term unchanged. Afterwards, the function needs to be stretched vertically by a factor of 3. This means that all terms will be multiplied by 3. Lastly, the function requires a translation 1 unit down. This can be done by adding a -1 to the y-term. Therefore, the final equation is 3x2-3(y+1)+9x2+12 which includes the reflection in the y-axis, vertical stretch by a factor of 3, and translation 1 unit down.

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The whole match lasts for 45 minutes + 45 minutes + 30 minutes = 120 minutes. Answer: 120 min.

The amount Harry has in his account is $2,694.50

The amount Sally has in his account is $2,714.23.

Sally made the best investment.

It is the interest we earned on the interest.

The formula for the amount earned with compound interest after n years is given as:

A = P [tex](1 + r/n)^{nt}[/tex]

P = principal

R = rate

t = time in years

n = number of times compounded in a year.

We have,

Harry:

P = $2500

T = 3 years

r = 2.5%

n = 12

A = 2500 [tex](1 + 0.208)^{36}[/tex]

A = 2500 x [tex]1.208^{36}[/tex]

A = $2,694.50

Sally:

P = $2500

T = 3 years

r = 2.75%

n = 4

A = 2500 [tex](1 + 0.69)^{12}[/tex]

A = 2500 x [tex]1.69^{12}[/tex]

A = $2,714.23

Thus,

Harry has $2,694.50 in his account.

Sally has $2,714.23 in his account.

Sally made the best investment.

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