In a transformation, the preimage is the original figure and the image is the figure in the new location.

False

True

Answer:

  a. $461.67

  b. $12771.73

Step-by-step explanation:

You want to know the monthly payment and total amount paid for a car that costs $12500 when $4000 is the down payment and the interest is 3.8% for 19 months.

The formula for the monthly payment is ...

  A = P(r/12)/(1 -(1 +r/12)^-n)

where P is the amount borrowed at interest rate r compounded monthly for n months.

Here, the down payment of $4000 reduces the loan amount to ...

  $12500 -4000 = 8500

So, the monthly payment is ...

  A = 8500(0.038/12)/(1 -(1 +0.038/12)^-19) ≈ 461.67

Matteo needs to pay $461.67 each month.

The total Matteo pays for the car will be the sum of the down payment and the 19 monthly payments:

  total = $4000 +19×461.67 = $12771.73

Matteo will end up paying $12771.73 for his car.

Answer:

TVM calculator: N = 40, PV = -1,075.25, PMT = 30.25, FV = 1,000; CPT I = 2.714% YTM = 2.714% × 2 = 5.43%

Step-by-step explanation:

Answer:

67.7215189873%

Step-by-step explanation:

The price of a desktop computer decreases from $3160 to $1020

Initial price of desktop =$3160

New Price= $1020

Change in price = 3160 - 1020 = 2140

Percentage decrease = [tex]\frac{2140}{3160}[/tex][tex]X[/tex][tex]100[/tex]=67.7215189873%

Hence , the answer is 67.7215189873%

Hope it helps u

A farmer needs to construct two adjoining rectangular pens with each pen is to have an area of 1200 square feet. So dimeosions will minimize the length of fencing is length = 40 ft and width = 30 ft.

For pictures of two rectangular pens, see the attachment.

Area of rectangle = length × width

A = x × y

1200 = xy

     y = 1200/x

The entire length of the fence

P = 3x + 4y

P = 3x + 4 (1200/x)

P = 3x + 4800/x

P = 3x + 4800x⁻¹

Find dimentions will minimize the length of fencing, if P' = 0.

P = 3x + 4800x⁻¹

P' = 3 - 1 × 4800x⁻¹⁻¹

0 = 3 - 4800x⁻²

4800x⁻² = 3

4800/x² = 3

4800 = 3x²

     x² = 4800/3

     x² = 1600

     x = 40

y = 1200/x

y = 1200/40

y = 30

So dimeosions will minimize the length of fencing is length = 40 ft and width = 30 ft.

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The difference between consecutive integral squares must be greater than 1000. (x+1)^2-x^2>=1000, so x>=999/2 implies x>=500. x=500 does not work, so x>500. Let n=x-500. The sum of the square of n and a number a little over 1000 must result in a new perfect square. By inspection, n^2 should end in a number close to but less than 1000 such that there exists 1000N within the difference of the two squares. Examine when n^2=1000. Then, n=10sqrt(10). One example way to estimate sqrt(10) follows.

3^2=9, so 10=(x+3)^2=x^2+6x+9. x^2 is small, so 10=6x+9. x=1/6 implies sqrt(10)\approx 19/6. This is 3.16.

Then, n approx 31.6. n^2<1000, so n could be 31. Add 500 to get the first square and 501 to get the second. Then, the two integral squares are 531^2 and 532^2. Checking, 531^2=281961 and 532^2=283024. 282,000 straddles the two squares, which have a difference of 1063. The difference has been minimized, so N is minimized N=282000 implies 282

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When the data set is extremely small, the algorithm might fail to detect the inherent clusters in the data set. When the data set has a high degree of overlap between clusters, the algorithm might generate too many clusters and fail to capture the underlying structure of the data.

Partitional clustering algorithms can automatically determine the number of clusters, which is often perceived as an advantage. However, this is not always the case. For example, when the data set is small the algorithm might be unable to detect the true clusters in the data set. Additionally, when the data set has high levels of overlap between clusters, the algorithm might generate too many clusters and fail to recognize the underlying structure of the data. In these cases, the automatic determination of the number of clusters can be disadvantageous as it fails to capture the true structure of the data.

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Answer:

14x+41

Step-by-step explanation:

Answer:

14x + 41

Step-by-step explanation:

4(2X - 1) + 3(2X + 15)  distribute the 4 and 3.

8x - 4 + 6x + 45  Combine like terms

14x + 41  This is your answer simplified.

The length of the diagonal from point A to point G is √89.

Blank 1: Using the Pythagorean Theorem

Blank 2: Finding the AC.

Blank 3: Now use CG as a adjacent side.

Blank 4: Now AG is being Hypotenuse.

Blank 5: Now find AG.

In the given question, we have to find the length of the diagonal from point A to point G.

We would first use on the bottom of the box rectangle to find the diagonal AC.

Then we use CG as of the triangle ACG.

Blank 1: Using the Pythagorean Theorem

In this theorem; a^2+b^2=c^2

Where a=adjacent side, b=base, c=hypotenuse

Blank 2: Finding the AC.

Now in the triangle ABC, use Pythagorean Theorem

So AC = √(AB)^2+(BC)^2

AC = √(8)^2+(3)^2

AC = √64+9

AC = √73

Blank 3: Now use CG as a adjacent side.

Blank 4: Now AG is being Hypotenuse.

Blank 5: Now find AG.

Now in the triangle ACG, use Pythagorean Theorem

So AG = √(AC)^2+(CG)^2

AG = √(√73)^2+(4)^2

AG = √73+16

AG = √89

Hence, the length of the diagonal from point A to point G is √89.

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Answer:

y=-7(x+1)^2 +8

Step-by-step explanation:

Vertex as shown in vertex form, and solve for the coefficient by plugging in the point.

y=-9(x+1)^2+8

start with the vertex form of a parabola:

y=a(x-h)^2+k , "h" and "k" are the vertex coordinates, and "a" is the leading coefficient.

1. plug in the vertex coordinates

y=a(x+1)^2+8

2. to find "a", plug in the point coordinates in the function from step 1 for x and y

-1=a(-2+1)^2+8

when you solve this equation, you will find that a=-9

3. substitute "a" value in the equation from step 1

Done

Answer: 23.49

Step-by-step explanation:

Look at the thousandths place and the hundredths place.

92

Now we round 92.

1-4 it stays the same

5 or more you raise it

92 is about 90.

So you would get 23.490

You can eliminate the excess zero.

Your answer is 23.49

Answer:

y > 5x + 14

Step-by-step explanation:

5x – y > –14

–y > –5x–14

divide both sides by (–)

–(–y) > –(–5x–14)

y > 5x + 14

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Answer:

-13

Step-by-step explanation:

the pattern goes +7 - 14, so -20 + 7 = 13

The rate of change (slope) of the distance in feet below sea level with respect to time that the submarine traveled is 11 feet .

Given :

The table below shows the linear relationship between the distance in feet below sea level and the time in seconds traveled by a submarine .

From the table:

Take any two points ( 0 , 380 ) and ( 15 , 545 )

slope m = 545 - 380 / 15 - 0

= 165 / 15

= 33 / 3

= 11 / 1

= 11 feet

Hence the slope m is 11 feet .

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Step 1

We are given a homogenous rod in a cubic curve shape having two free ends, upper end B

and lower end x

The distance of the upper end from x

axis is 1m

and from y axis is 2m.

The rod is bent in a cubic curve shape between two ends and the equation for the rod is given by

[tex]y=2 x^3[/tex]

Here, [tex]$\bar{x}_1$[/tex]and [tex]$\bar{y}_1$[/tex]are the centroidal distances of the strip element from [tex]x$and $y$[/tex] axes respectively.

Step 3

The given equation of the homogenous rod is,

[tex]\begin{gathered}y=2 x^3 \\\frac{d y}{d x}=6 x^2\end{gathered}[/tex]

The given equation of the homogenous rod is,

\begin{aligned}

[tex]& d L=\sqrt{d x^2+d y^2} \\& d L=d x \times \sqrt{1+\left(\frac{d y}{d x}\right)^2} \\& d L=\sqrt{1+\left(6 x^2\right)^2} \cdot d x \\& d L=\sqrt{1+36 x^4} \cdot d x\end{aligned}[/tex]

[tex]& d L=\sqrt{d x^2+d y^2} \\& d L=d x \times \sqrt{1+\left(\frac{d y}{d x}\right)^2} \\& d L=\sqrt{1+\left(6 x^2\right)^2} \cdot d x \\& d L=\sqrt{1+36 x^4} \cdot d x\end{aligned}[/tex]

[tex]& L=\int_{x=0}^{x=1 \mathrm{~m}} d L \\& L=\int_{x=0}^{x=1 \mathrm{~m}} \sqrt{1+36 x^4} \cdot d x \\[/tex]

[tex]& L=6 \times \int_{x=0}^{x=1 \mathrm{~m}} \sqrt{\left(x^2\right)^2+\frac{1}{36}} \cdot d x \\[/tex]

[tex]& L=6 \times\left[x^2 \sqrt{x^4+\frac{1}{36}}+\frac{1}{36} \ln \left|\left(x^2+\sqrt{x^4+\frac{1}{36}}\right)\right|\right]_0^{1 \mathrm{~m}}\end{aligned}[/tex]

Substituting the values in the above expression and solving,

[tex]& \int_L y \cdot d L=\left[\frac{\left(36 \times(1 \mathrm{~m})^4+1\right)^{\frac{3}{2}}}{108}\right]-\left[\frac{\left(0+1 \mathrm{~m}^4\right)^{\frac{3}{2}}}{108}\right] \\& \int_L y \cdot d L=\frac{224.062}{108} \mathrm{~m}^2 \\& \int_L y \cdot d L=2.075 \mathrm{~m}^2[/tex]

Now according to the formula for the center of gravity of a curve, the expression for the center of gravity of the homogenous rod is given by,

[tex]& \bar{y}=\frac{\int_L \bar{y}_1 \cdot d L}{\int_L d L} \\& \bar{y}=\frac{2.075 \mathrm{~m}^2}{2.42 \mathrm{~m}} \\& \bar{y}=0.857 \mathrm{~m}[/tex]

Therefore, the center of gravity of the given homogeneous rod is

0.857 m above the horizontal axis

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The value of the other points in each of the number line is;

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) The point P = 2¹/₂

The distance from point 0 of the number line to point P is 5 units and therefore;

Each unit = 2¹/₂/5 = ¹/₂

Thus;

M = -2¹/₂

N = -1

R = 4

b) The point N = -0.4

The distance from point 0 of the number line to point N is 2 units and therefore;

Each unit = 0.4/2 = 0.2

Thus;

M = -1

P = 1

R = 1.6

C) The point R = 200

The distance from point 0 of the number line to point R is 8 units and therefore;

Each unit = 200/8 = 25

Thus;

M = -125

P = 125

N = -50

D) The point M = -15

The distance from point 0 of the number line to point N is 5 units and therefore;

Each unit = 15/5 = 3

Thus;

N = -6

P = 15

R = 24

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1)The regression equation is Age--26.7+809 LN [(1+(R/1))/(1-(R/L))]. Hence, the value of the regression coefficients by is-26.7 and by is 809

2)The forecasted value for 0.0901 LN [(1+(RL)) (1- (RL))) is 46.103.

3)The 95% prediction interval for the age at death of Sherlock Holmes' surprise garden visitor is 41.013,51.193.

4)Yes, a man in Sherlock Holmes's neighborhood thought that the body because; the man's age comes under the age in years that is, the smaller age is 14 and the larger age is 69. Thus, this is the body of that man.

Exponential law=The first law states that to multiply two exponential functions with the same base, we simply add the exponents. The second law states that to divide two exponential functions with the same base, we subtract the exponents.

MINITAB procedure:

Choose Stat > Regression Regression

Step 2: In Responses, enter the column of Age (yrs)

Step 3: In Predictors, enter the column of LN [(1+(R/L))/ (1-(R/1))] Step 4: In Options, enter the value of Prediction interval for new observation as 0.0901

The regression equation  Age (year 26,7 809 28(13+1/233/4-1-26.7252.025 -13.20 0.00025.61 31.37 0.000)

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The appropriate distribution to use is t distribution with df = 80.

Variance

Distribution

Given that:

n1 = 37

n2 = 45

The variances of the populations are not know so we can use t distribution

Degree of freedom = n1 + n2 - 2

                                = 37 + 45 - 2

                                = 80

Therefore, t distribution with df = 80

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Answer:4*3+70=840

Step-by-step explanation:

Perimeter = 2(Length + Width)

length = 4x ; width = 3x ; perimeter = 70

Perimeter = 2(Length + Width)

70 = 2(4x + 3x)

70 = 2(7x)

70 = 14x

x = 5

Perimeter = 2(Length + Width)

70 = 2(20 + 15)

70 = 2(35)

70 = 70

The solution to the system of equations is x = 3 and y = -7. The correct option is C. (3, -7).

The system of equations is given as follows:

2x + 3y = −15  ....(1)

3x + y = 2       ....(2)

Multiply Equation 2 by 3:

9x + 3y = 6      ....(3)

Now, we can subtract Equation 1 from Equation 3 to eliminate y:

(9x + 3y) - (2x + 3y) = 6 - (-15)

9x + 3y - 2x - 3y = 6 + 15

7x = 21

x = 21/7

x = 3

Substituting the value of x into Equation 2 to solve for y:

3(3) + y = 2

9 + y = 2

y = 2 - 9

y = -7

Therefore, the solution to the system of equations is x = 3 and y = -7.

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Complete question:

Solve the system of equations using elimination.

2x + 3y = −15

3x + y = 2

A. (0, 5)

B. (1, −1)

C. (3, −7)

D. (4, −10)

As there is sufficient evidence to conclude that the population mean weight is at least 16 ounces.

What is standard deviation ?

The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

Think about the following data: 2, 1, 3, 2, 4. The average and the total square of the observations' departures from the mean will be 2.4 and 5.2, respectively. This means that (5.2/5) = 1.01 will be the standard deviation.

The following null and alternative hypotheses need to be tested

H0 :  µ  = 16

Hα :  µ  < 16

This corresponds to a left-tailed test , for which a z-test for one mean, with known population standard deviation will be used.

Based on the information provided, the significance level is α = 0.1, and the critical value for the left-tailed test is [tex]Z_{c}[/tex] = -1.28

The rejection region for this left-tailed test is R = {z : z < -1.282}

The z-statistics is computed as follow

[tex]z = \frac{X - µ _{0} }{sigma / \sqrt{n} }[/tex]

   = (15.84 - 16) / (0.4 / √16)

   = -1.6

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[tex]-4-4[/tex]

[tex]-4+(-4)[/tex]

[tex]=\fbox{-8}[/tex]

[tex]-4+(-4)[/tex] on a number line:

Answer: R(7, 9), S(6, 7), T(2, 3), U(8, 5), V(5, 5)

consider the sample space given below. a die is a cube with six sides on which each side contains one to six dots. Suppose probability a blue die and a gray die are rolled together, and the numbers of dots that occur face up on each are recorded.a fraction in lowest terms. 21/36

The sample space given in the question is the set S = {11, 12, 13, 14, 15, 16, 21, 22, 23, 24, 25, 26, 31, 32, 33, 34, 35, 36, 41, 42, 43, 44, 45, 46, 51, 52, 53, 54, 55, 56, 61, 62, 63, 64, 65, 66} The event that the sum of the numbers showing face up is at least 9 is represented by the set E = {9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26}.

To compute the probability of this event, we need to count how many elements are in the set E and divide this number by the total number of elements in the set S. There are 18 elements in the set E and 36 elements in the set S. Therefore, the probability of the event is 18/36, which can be simplified to 21/36.

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The meaning of the y-coordinate of the graph when x = 15 is given as follows:

B. Erin has completed 25% of her exercise program.

The graph is a relation that represents a function between two variables.

The variables for this problem are given as follows:

One ordered pair for the graph in this problem is given as follows:

(15, 25).

This means that when Erin spends 15 minutes exercising, she has completed a percentage of 25% of her exercise program, and thus option B is correct.

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Answer:

Go and look up your tables and read below

Step-by-step explanation:

To solve the problem 5 x 4 using the multiplication table, you would look up the corresponding entries in the table for the numbers 5 and 4. In the row labeled 5 and the column labeled 4, you would find the product 20, which is the answer to the problem 5 x 4.

answer

Step-by-step explanation:

The object is undergoing uniform circular motion. The radius of the circular path is equal to 0.50 meters. The centripetal force, F, acting on the object can be calculated using the equation F= mv^2/r in hporizontal circular path

m is the mass of the object, v is the velocity of the object and r is the radius of the circular path.

F = (1.0 kg) (5.0 m/s)^2 / 0.50 m

F = 50.0 kg m/s^2

The object is undergoing uniform circular motion, which means it is moving at a constant speed in a circular path with its center at point O. The radius of the circular path is equal to 0.50 meters. The force acting on the object is known as the centripetal force, and can be calculated by using the equation F= mv^2/r. This equation requires the mass of the object (m), its velocity (v), and the radius of the circular path (r). In this case, the mass is 1.0 kg, the velocity is 5.0 m/s, and the radius is 0.50 m. Plugging these values into the equation gives the centripetal force acting on the object as 50.0 kg m/s^2.

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The exact value of x (in ft) so that the greatest possible amount of light is admitted is 8.96 ft

According to the question,

A norman window has the shape of a rectangle surmounted by a semicircle.

Let The width of rectangle be x and height be y

It is given that  the diameter of the semicircle is equal to the width of the rectangle

Therefore , Diameter of circle = x

Radius = x/2

Perimeter of window  = 32 = Perimeter of rectangle + Perimeter of semi-circle

=> 32 = Width + 2height + πr

=> x + 2y + πx/2 = 32

=> 2x + 4y +  πx = 64

Solving for y,

=> 4y = 64 - 2x - πx

=> y = 64  - 2x - πx/ 4 ----------(1)

Area of the window = Area of rectangle + area of semi-circle

=> A = Width × hiegth +  πx²/8

=> A = xy + πx²/8

Substituting the value of y from equation (1)

=> A =  x (  64  - 2x - πx/ 4  ) + πx²/8

[tex]A = x ( \frac{64 - 2x -\pi x}{ 4} ) + \frac{\pi x^2}{8}\\A = ( \frac{ 64x - x^2 ( 2 + \pi)}{4 } ) + \frac{\pi x^2}{8}[/tex]

Differentiating A w.r.t x

=> [tex]\frac{dA}{dx} = (\frac{64 - 2x(2 + \pi)}{4} ) + \frac{\pi x}{4}[/tex]

Now , To find a maximum area

dA/dx = 0

=> [tex]\frac{dA}{dx} = (\frac{64 - 2x(2 + \pi)}{4} ) + \frac{\pi x}{4} = 0[/tex]

Solving for x ,

64 - 4x - 2π + πx = 0

=> x = 64 / 4 + π ------(2)

Differentiating A again w.r.t x

=> d²A / dx² = -2(2 + π)/4 + π/4

=> -π+4 / 4 which is less than zero

Therefore,

Area is maximum when x = 64 / 4 + π

The exact value of x (in ft) so that the greatest possible amount of light is admitted is  8.96 ft

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The polynomial f(x) of degree 3 is

f(x) = x³ + x² - 20x

Polynomial is an equation written as the sum of terms of the form kx^n.

where k and n are positive integers.

We have,

The zeroes of the polynomial are 0, -5, and 4.

This can be written as,

x = 0, x

x = -5, (x + 5)

x = 4, (x - 4)

x(x + 5)(x - 4)

(x² + 5x)(x - 4)

x³ - 4x² + 5x² - 20x

x³ + x² - 20x

Thus,

The polynomial is f(x) = x³ + x² - 20x

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Answer:

hey

4y = 2x – 8

Step-by-step explanation:

2x – 4y = 8

–4y = –2x + 8

multiply both sides by (–)

–(–4y) = –(–2x + 8)

4y = 2x – 8

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