Raymond owns a used pickup truck that he wants to sell. A use-vehicle guide shows that its average retail value is $17,600. He adds $1,700 for 4-wheel drive, $475 for an entertainment system, $800 for a special trim package, and $225 for power locks. He also adds $125 for a sliding rear window, $325 for a towing package, $250 for power windows, and $3,125 for a diesel engine. He deducts $675 for having a manual transmission. He adds $450 for having less than the expected mileage. What is the average retail price of Raymond's vehicle?

Answers

Answer 1

The average retail price of Raymond's vehicle is $24,400.

What is Average Retail Price?

Average price is a measure of a range of prices. It is calculated by taking the sum of the values and dividing it by the number of prices being examined. The average price reduces the range into a single value, which can then be compared to any other point to determine if the value is higher or lower than what would be expected.

average retail value = $17,600

All the additions to the average retail value are;

$1,700 for 4-wheel drive

$475 for an entertainment system

$800 for a special trim package

$225 for power locks

$125 for a sliding rear window

$325 for a towing package

$250 for power windows

$3,125 for a diesel engine

$450 for less than expected mileage

Deductions

$675 for having a manual transmission

Average retail price = Average retail value + additions - deductions

Average retail price = $17,600 + ($1,700+$475+$800+$225+$125+$325+$250+$3,125+$450) - $675

Average retail price = $17,600 + $7,475 - $675

Average retail price = $24,400

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Related Questions

35 POINTS please help asap

Type the correct answer in each box. Use numerals instead of words.

This graph represents a quadratic function. What is the function’s equation written in factored form and in vertex form?

f(x) = _x(x - _)
f(x) = _(x − _)^2 + _

i know for sure the first four blanks are 2, 4, 2, and 2 but the last is NOT 8.

Answers

The quadratic equation given in the graph can be represented in these two following ways:

Factored: f(x) = 2x(x - 4).Vertex form: y = 2(x - 2)² - 8.

What is the Factor Theorem?

The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:

[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]

In which a is the leading coefficient.

In this graph, the roots are [tex]x_1 = 0, x_2 = 4[/tex], hence the factored form of the polynomial is:

f(x) = ax(x - 4).

When x = 5, y = 10, hence the leading coefficient is found as follows:

10 = 5a(5 - 4)

5a = 10

a = 2.

Hence the factored form of the polynomial is:

f(x) = 2x(x - 4).

What is the equation of a parabola given it’s vertex?

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

In this problem, the vertex is at point (2,-8), hence h = 2, k = -8 and:

y = a(x - 2)² - 8

When x = 5, y = 10, hence the leading coefficient is found as follows:

10 = a(5 - 2)² - 8

9a = 18

a = 2.

Hence the equation in vertex-form is:

y = 2(x - 2)² - 8

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If f(x) and ¹(x) are inverse functions of each other and f(x) = 2x+5, what is f¹ (8)?
-1
T MIN 700
3
8
23

Answers

Answer: 3/2

Step-by-step explanation:

[tex]f^{-1}(8)=k \implies f(k)=8\\\\\therefore 2k+5=8\\\\2k=3\\\\k=\frac{3}{2}[/tex]

PLEASE HELP QUICKLY️️️​

Answers

Answer:

first option x = 7

Step-by-step explanation:

"x" is the cathetus opposite the angle of 30°

14 is the hypotenuse

use the sine function

[tex]sin30^{0} =\frac{x}{14}[/tex]

[tex]x=14sen30^{0} =14(0.5)=7[/tex]

Hope this helps

PLS HELP FAST
Kryton -85 is a radioisotope of krypton that has a half-life of about 10.75years. This isotope is produced by the nuclear fission of uranium and plutonium in nuclear weapons and in nuclear reactors, as well as cosmic rays. An important goal of the Limited Nuclear Test Ban Treaty of 1963 was to eliminate the release of such radioisotopes into the atmosphere. At present, the activity of Krypton -85 in the atmosphere is about 135 mCi.




How much Krypton -85 will be present in the atmosphere after 12,532days?

Answers

Using an exponential function, it is found that 14.75 mCi of Krypton -85 will be present in the atmosphere after 12,532 days.

What is an exponential function?

A decaying exponential function is modeled by:

[tex]A(t) = A(0)(0.5)^\frac{t}{h}[/tex]

In which:

A(0) is the initial value.h is the half life, in years.t is the time, in years.

In this problem, the parameters are:

A(0) = 135, h = 10.75, t = 12532/365 = 34.334.

Hence the amount is:

[tex]A(t) = A(0)(0.5)^\frac{t}{h}[/tex]

[tex]A(t) = 135(0.5)^\frac{34.334}{10.75}[/tex]

A(t) = 14.75.

14.75 mCi of Krypton -85 will be present in the atmosphere after 12,532 days.

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Which systems of equations have no real number solutions? Check all that apply.
Oy=x² + 4x + 7 and y = 2
□ y=x²-2 and y=x+5
-Oy=-x²-3 and y = 9 + 2x
y=-3x-6 and y = 2x² - 7x
y=x² and y = 10 - 8x

Answers

Answer + Step-by-step explanation:

Recall That the number of solution

of a quadratic equation ax² + bx + c = 0

depends on the discriminant b² - 4ac :

if b² - 4ac > 0 , the equation has two distinct solutions.

if b² - 4ac = 0 , the equation has only one solution.

if b² - 4ac < 0 , the equation has no solutions.

=======================================

System 1 :

y = x² + 4x + 7  and y = 2

⇔ x² + 4x + 7 = 2

⇔ x² + 4x + 5 = 0

→ b² - 4ac = 4² - 4×1×5 = 16 - 20 = -4 < 0

Then the quadratic equation has no solutions

Therefore the system has no solutions.

System 2 :

y = x² - 2  and y = x + 5

⇔ x² - 2 = x + 5

⇔ x² - x - 7 = 0

→ b² - 4ac = (-1)² + 4×7 = 29 > 0

Then the quadratic equation has two solutions

Therefore the system has two solutions.

System 3 :

y = -x² - 3  and y = 9 + 2x

⇔  -x² - 3 = 9 + 2x

⇔ -x² - 2x - 12 = 0

→ b² - 4ac = (-2)² - 4×(-1)×(-12) = 4 - 48 = -44 < 0

Then the quadratic equation has no solutions

Therefore the system has two solutions.

System 4 :

y = -3x - 6  and y = 2x² - 7x

⇔  -3x - 6 = 2x² - 7x

⇔ 2x² - 4x + 6 = 0

→ b² - 4ac = (-4)² - 4×(2)×(6) = 16 - 48 = -32 < 0

Then the quadratic equation has no solutions

Therefore the system has two solutions.

System 5 :

y = x² and y = 10 - 8x

⇔ x² = 10 - 8x

⇔ x² + 8x - 10 = 0

→ b² - 4ac = 8² - 4×1×(-10) = 64 + 40 = 104 > 0

Then the quadratic equation has two solutions

Therefore the system has two solutions.

Find the area of the polygon with the coordinates (1, 2), (3, 2), (3, 0), and (1, 0)

Answers

The area of the polygon is 4 square units

How to determine the area of the polygon?

The vertices are given as:

(1, 2), (3, 2), (3, 0), and (1, 0)

The area is then calculated as:

A = 0.5 * |x1y2 - x2y1 +x2y3 - x3y2 + ....... |

So, we have:

A = 0.5 * |1 * 2 - 3 * 2 + 3 * 0 - 2 * 3 + 3 * 0 - 0 * 1 + 1 * 2 - 0 * 1|

Evaluate

A = 0.5 * |-8|

Remove the absolute bracket

A = 0.5 * 8

This gives

A = 4

Hence, the area of the polygon is 4 square units

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Module 1: directions: respond to this question to demonstrate your understanding of the topic/content. be sure to provide adequate and relevant details learned in the module to support your response. pay close attention to organizing your response so it makes sense and uses correct grammar. your response should be at least 5-7 sentences at a minimum. question: given the two points (1,5) and (-2, -4), write a set of instructions for your younger cousin that determines the equation of the line in slope-intercept form (y=mx+b). be sure to write the equation.

Answers

The slope intercept form of the line whose points are (1,5) and (-2,-4) is y=3x+2.

Given two points of a line (1,5) and (-2,-4).

We have to form an equation in slop intercept form.

Equation is relationship between two or more variables which are expressed in equal to form.Equations of two variables looks like ax+by=c.

Point slope form of an equation is y=x+mc where m is slope of the line.

From two points the formula of equation is as under:

(y-[tex]y_{1}[/tex])=[tex](y_{2} -y_{1} )/(x_{2} -x_{1} )[/tex]*(x-[tex]x_{1}[/tex])

where [tex](x_{1} ,y_{1} ) and (x_{2} ,y_{2} )[/tex] are the points.

Putting the values of [tex]x_{1}[/tex]=1, [tex]x_{2}[/tex]=-2, [tex]y_{1}[/tex]=5 and [tex]y_{2}[/tex]=-4.

y-5=(-4-5/-2-1)*(x-1)

y-5=-9/-3*(x-1)

y-5=3(x-1)

y-5=3x-3

y=3x-3+5

y=3x+2

Hence the slope intercept form of the line having points (1,5)(-2,-4) is y=3x+2.

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Circle U is shown. Chords R T and Q S intersect at a point forming 4 angles. The top left angle is angle 1, and the top right angle is angle 2. Arc R Q is 53 degrees and arc S T is 47 degrees. Angle 1 intersepts arc R Q. Angle 2 intersepts arc R S.

What are the measures of angles 1 and 2?

m∠1 =

°

m∠2 =
°

Answers

Answer:

∠1 = 50°∠2 = 130°

Step-by-step explanation:

The relation between intercepted arcs and angles at crossing chords can be used to find the angles of interest. That relation tells you the angle where the chords cross is half the sum of the intercepted arcs.

Angle 1

The arcs intercepted by the chords making angle 1 are given as 53° and 47°. Half their sum is the measure of angle 1:

  ∠1 = (53° +47°)/2 = 100°/2

  ∠1 = 50°

Angle 2

Angles 1 and 2 form a linear pair, so angle 2 is the supplement of angle 1.

  ∠2 = 180° -∠1 = 180° -50°

  ∠2 = 130°

Based on the calculations, the measures of angles 1 and 2 are 50° and 135° respectively.

What is the theorem of intersecting chord?

The theorem of intersecting chord states that when two (2) chords intersect inside a circle, the measure of the angle formed by these chords is equal to one-half (½) of the sum of the two (2) arcs it intercepts.

By applying the theorem of intersecting chord to circle U shown in the image attached below, we can infer and logically deduce that angle 1 will be given by this formula:

m∠1 = ½(53 + 47)

m∠1 = ½(100)

m∠1 = 50°.

Since angles 1 and 2 are linear pair, they are supplementary angles. Thus, we have:

m∠1 + m∠2 = 180°

m∠2 = 180 - m∠1

m∠2 = 180 - 50

m∠2 = 130°.

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In the diagram AB/BC = AD/DE
Substitute the known values into the proportion and solve for DE

Answers

Answer:

[tex]\huge\boxed{\sf DE = 9}[/tex]

Step-by-step explanation:

From the figure,

AB = 2

BC = 3

AD = 6

Substitute in the given formula

[tex]\displaystyle \frac{AB}{BC} =\frac{AD}{DE} \\\\\frac{2}{3} = \frac{6}{DE} \\\\Cross \ Multiply \\\\2 \times DE = 6 \times 3\\\\2DE = 18\\\\Divide \ 2 \ to \ both \ sides\\\\DE = 18/2\\\\DE = 9\\\\\rule[225]{225}{2}[/tex]

Find x such that the matrix is singular. A = 3 x −6 −4 x =

Answers

The matrix A becomes singular when x is equal to ±√8 (positive or negative square root of 8).

We have,

Matrix A becomes singular (i.e., its determinant is zero).

The given matrix A is:

A = | 3x  -6 |

      | -4  x |

Using the determinant formula for a 2x2 matrix, we have:

det(A) = (3x * x) - (-6 * -4)

Simplifying the expression:

det(A) = 3x^2 - 24

To find the value of x for which det(A) = 0, we set the determinant equal to zero:

3x^2 - 24 = 0

Now, we can solve this quadratic equation for x:

3x^2 = 24

x^2 = 8

x = ±√8

Therefore,

The matrix A becomes singular when x is equal to ±√8 (positive or negative square root of 8).

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what ac is equal to

Answers

Answer:

AC = 10

Step-by-step explanation:

Formula

(x + 1) + (x + 3) + 2x = 40                Remove the brackets

Solution

x + 1 + x + 3 + 2x = 40                    Collect like terms

4x + 4 = 40                                     Subtract 4 from both sides

4x +4 -4 = 40 - 4                             Combine

4x = 36                                            Divide both sides by 4

4x/4 = 36/4

x = 9

AC = x + 1

AC = 9 + 1

AC = 10

Quick algebra 1 question for 15 points!


Only answer if you know the answer, quick shout-out to Yeony2202, tysm for the help!

Answers

The cost per person if number of students is 100 given the inverse variation is $46.75

Inverse variation

Cost per person = CNumber of students = n

C = k / n

where,

k = constant of proportionality

If n = 55 and C = $85

C = k / n

85 = k / 55

85 × 55 = k

4,675 = k

Find C if n = 100

C = k / n

= 4,675 / 100

C = $46.75

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Were the non-violent, civil disobedience tactics used by civil rights leaders like dr. king effective at creating change and ending injustice? why or why not

Answers

Yes, the non-violent, civil disobedience tactics used by civil right leaders were effective to a great extent at creating change and ending injustice.

How were the civil disobedience tactics effective?

Martin Luther King, Jr.'s and other civil right leaders' leadership and vision were shaped by their steadfast faith in the efficacy of nonviolence and civil disobedience. Although it permitted civil rights protesters to avoid harsher legal penalties, it also had a deeper significance. America only learned about the effectiveness of nonviolent protest as a result of the work of Martin Luther King, Jr. and his civil disobedience allies.

Civil Disobedience Tactics

The Civil Rights Act of 1964 and the Voting Rights Act of 1965 were primarily made possible thanks to King. The Civil Rights Act outlawed discrimination on the basis of "race, color, religion, or national origin" in the workplace and in public places. African Americans' right to vote is safeguarded by the Voting Rights Act.

Inspired by Gandhi, King and other non-violent leaders, utilized civil disobedience to pressure governments to change. It manifested as widespread, nonviolent defiance of official orders. Civil disobedience is the act of refusing to comply with governmental orders or demands and remaining unaffected by the arrest and punishment that may follow.

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In the 1980’s, a clinical trial was conducted to determine if taking an aspirin daily reduced the incidence of heart attacks. Of 22,071 medical doctors participating in the study, 11,037 were randomly assigned to take aspirin and 11,034 were randomly assigned to the placebo group. Doctors in this group were given a sugar pill disguised to look like aspirin. After six months, the proportion of heart attacks in the two groups was compared. Only 104 doctors who took aspirin had a heart attack, whereas 189 who received the placebo had a heart attack. Can we conclude from this study that taking aspirin reduced the chance of having a heart attack? the purpose of this study was to determine whether taking an aspirin daily reduces the proportion of heart attacks.

Answers

There is enough evidence to conclude that taking aspirin cannot  reduces the chance of cancer.

Given sample size of patients take aspirin 11037, sample size of patients who have assigned placebo group be 11034. 104 doctors who take aspirin had a heart attack, 189 doctors had placebo had heart attacks.

First we have to form hypothesis.

[tex]H_{0} :p{1} -p_{2} =0[/tex]

[tex]H_{1}:p_{1} -p_{2} < 0[/tex]

We have to find the respective probabilities.

[tex]p_{1}[/tex]=104/11037

=0.0094

[tex]p_{2}[/tex]=189/11034

=0.0171

Now their respective margin of errors.

[tex]s_{1}[/tex]=[tex]\sqrt{ {(0.0094*0.9906)/11037}[/tex]

=0.0009

[tex]s_{2}[/tex]=[tex]\sqrt{0.0171*0.9829}[/tex]

=0.0011

Hence the distribution of the differences,they are given by:

p=[tex]p_{1} -p_{2}[/tex]

=0.0094-0.0171

=-0.0077

S=[tex]\sqrt{s_{1} ^{2}+s_{2} ^{2} }[/tex]

=[tex]\sqrt{(0.0009)^{2} +(0.0011)^{2} }[/tex]

=0.00305

z=(p -f)/S (In which f=0 is the value tested at the null hypothesis)

=(-0.0077-0)/0.00305

=-2.52

p value will be 0.005.

p value of 0.05 significance level.

z=1.96.

1.96>0.005

So we will reject the null hypothesis which means it cannot reduce the whole chance of becomming a heart attack.

Hence there is enough evidence to conclude that taking aspirin cannot  reduces the chance of cancer.

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can someone please help mee

Answers

Answer:

5/13

Step-by-step explanation:

sine=opposite/hypotenuse

cosine=adjacent/hypotenuse

opposite=-12 (I know that this is not possible)

hypotenuse=13

These are ratios, not real lengths

using the Pythagorean theorem, the other leg is 5

cos (theta)=5/13

Write the equation of the sinusoidal function shown.
A) y = cos x - 1
B)y=sin x - 1
C) y=2 sin x - 1
D) y = 2 cos x - 1

Answers

Answer:

A. y= cos x - 1

Step-by-step explanation:

short answer: this is basically the parent graph cos(x), just vertically shifted down 1 unit.


longer answer:

standard form is y = a cos(bx-c) +d

a = amplitude

b = 2pi/period

c = horizontal shift

d = vertical shift (also equal to midline)


for this graph

a=1

period is 2pi, so b=1

there is no horizontal shift so c=0

d= -1 because it is shifted down one unit from axis (midline is at -1)

An ice cream store charges $3.00 per scoop,$2.00 per topping and $0.75 for each add syrup flavor

a) Write an algebraic expression to represent the cost of the ice cream.

b) Rafael orders 3 scoops of ice cream with added chocolate and marshmallows and peanut syrup and chocolate syrup Use the formula to solve for the cost of the ice cream. show your work

Answers

The algebraic expression for the ice cream is 3x + 2y + 0.75z.

The cost of Rafael ice cream is 12 dollars

How to find the algebraic expression that represent cost of the ice cream?

The algebraic expression that represent the cost of an ice cream is as follows:

let

number of scoop = x

number of topping = y

number of added syrup = z

Hence,

cost of the ice cream = 3x + 2y + 0.75z

Therefore,

The cost of ice cream Rafael ordered is as follows:

cost of ice cream = 3(3) + 0.75(4)

cost of ice cream = 9 + 3

cost of the ice cream = 12

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Can someone please help me with this? I'll give brainliest :)


Based on the information given find the slope from [2,5] Is interval notation and means from x=2 to x=5.
16. y = 3x - 4
17. y = 2x^2-4x - 2


Answers

The slope of y = 3x - 4 on the interval [2, 5] is 3 and the slope of y = 2x^2-4x - 2 on the interval [2, 5] is 10

How to determine the slope?

The interval is given as:

x = 2 to x = 5

The slope is calculated as:

[tex]m = \frac{y_2 -y_1}{x_2-x_1}[/tex]

16. y = 3x - 4

Substitute 2 and 5 for x

y = 3*2 - 4 = 2

y = 3*5 - 4 = 11

So, we have:

[tex]m = \frac{11 - 2}{5 - 2}[/tex]

[tex]m = \frac{9}{3}[/tex]

Divide

m = 3

Hence, the slope of y = 3x - 4 on the interval [2, 5] is 3

17. y = 2x^2-4x - 2

Substitute 2 and 5 for x

y = 2 * 2^2 - 4 * 2 - 2 = -2

y = 2 * 5^2 - 4 * 5 - 2 = 28

So, we have:

[tex]m = \frac{28 + 2}{5 - 2}[/tex]

[tex]m = \frac{30}{3}[/tex]

Divide

m = 10

Hence, the slope of y = 2x^2-4x - 2 on the interval [2, 5] is 10

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Using the quadratic formula, solve the
equation below to find the two possible
values of t.
6x^2-35=-11x
Give each value as a fraction in its
simplest form.

Answers

The two possible solutions to the given equation ( 6x^2-35 = -11x ) are x = 5/3 and x = -7/2

What are the two possible solution to the equation?

Given the equation; 6x² - 35 = -11x

The quadratic formula is expressed as;

x = [ -b±√( b² - 4(ac)  ]/2a

First, we re-arrange our equation in the form of ax² + bx + c = 0

6x² + 11x - 35 = 0

a = 6b = 11c = -35

We substitute into the formula.

x = [ -b±√( b² - 4(ac)  ]/2a

x = [ -11±√( 11² - 4( 6 × -35 )  ]/2×6

x = [ -11±√( 121 + 840 ]/12

x = [ -11±√961 ]/12

x = [ -11 ± 31 ]/12

x = (-11 + 31)/12,  (-11 + 31 )/12

x = 20/12,  -42/12

x = 5/3, -7/2

Therefore, the two possible solutions to the given equation ( 6x^2-35 = -11x ) are x = 5/3 and x = -7/2

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PLEASE HELP ME AS SOON AS POSSIBLE

Answers

a) The linear function that models the population in t years after 2004 is: P(t) = -200t + 29600.

b) Using the function, the estimate for the population in 2020 is of 26,400.

What is a linear function?

A linear function is modeled by:

y = mx + b

In which:

m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

The initial population in 2004, of 29600, is the y-intercept. In 12 years, the population decayed 2400, hence the slope is:

m = -2400/12 = -200.

Hence the equation is:

P(t) = -200t + 29600.

2020 is 16 years after 2004, hence the estimate is:

P(16) = -200(16) + 29600 = 26,400.

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Which is a function?
look at pic

Answers

Answer:

option 2 {(12, 3), (11,2), ...}

Step-by-step explanation:

For functions, multiple x-values can have the same y-value but each y-value must have a unique x-value. The second option matches this criterion.

Can u guys pls help me with this homework

Answers

The value of √(7 * 23 - 1)/8 is 4.47, the values of a, b and c are -14/11, -10/11 and 3, respectively and the area of the shape is 5√5 + 5 square meters

How to evaluate the radical expression?

The question goes thus:

If √5 = 2.236, evaluate √(7 * 23 - 1)/8

We have:

√(7 * 23 - 1)/8

Evaluate the product of 7 and 23

√(7 * 23 - 1)/8 = √(161 - 1)/8

Evaluate the difference of 161 and 1

√(7 * 23 - 1)/8 = √160/8

Evaluate the quotient of 160 and 8

√(7 * 23 - 1)/8 = √20

Express 20 as the product 4 and 5

√(7 * 23 - 1)/8 = √(4 * 5)

Expand the product

√(7 * 23 - 1)/8 = √4 * √5

Express √4 as 2

√(7 * 23 - 1)/8 = 2 * √5

Substitute √5 = 2.236

√(7 * 23 - 1)/8 = 2 * 2.236

Evaluate the product

√(7 * 23 - 1)/8 = 4.472

Approximate

√(7 * 23 - 1)/8 = 4.47

Hence, the value of √(7 * 23 - 1)/8 is 4.47

How to simplify the radical expression?

The expression is given as:

(3√2 + 5√6)/(3√2 - 5√6)

Rationalize the above expression

(3√2 + 5√6)/(3√2 - 5√6) * (3√2 + 5√6)/(3√2 + 5√6)

Evaluate the product

(3√2 + 5√6)²/((3√2)² - (5√6)²)

Simplify the denominator

(3√2 + 5√6)²/(18 - 150)

This gives

[(3√2)² + (5√6)² + 2 *(3√2) * (5√6)]/(-132)

Simplify the numerator

[168 + 120√3]/(-132)

Simplify the fraction

-14/11 - 10√3/11

Hence, the values of a, b and c are -14/11, -10/11 and 3, respectively

How to determine the area?

The area is calculated as:

A = 1/2 * (Sum of parallel bases) * Height

So, we have:

A = 1/2 * (4 + 3√5 + 6 - √5) * √5

Evaluate the like terms

A = 1/2 * (10 + 2√5) * √5

Evaluate the product

A = (5 + √5) * √5

Evaluate the product

A = 5√5 + 5

Hence, the area of the shape is 5√5 + 5 square meters

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Help please you don’t know how much this means to me

Answers

Problem 6:a)

[tex]a(0) = 1 \: \: \: \: \: \: b(0) = 2 \: \: \: \: \: c(0) = 3 \\ a(1) = b(0) + c(0) = 2 + 3 = 5 \\ b(1) = a(0) + c(0) = 1 + 3 = 4 \\ c(1) = a(0) + b(0) = 1 + 2 = 3 \\ \\ a(2) = b(1) + c(1) = 4 + 3 = 7 \\ b(2) = a(1) + c(1) = 5 + 3 = 8 \\ c(2) = a(1) + b(1) = 5 + 4 = 9[/tex]

[tex]a(3) = b(2) + c(2) = 8 + 9 = 17\\ b(3) = a(2) + c(2) =7 + 9 = 16 \\ c(3) = a(2) + b(2) = 7 + 8 = 15 \\ \\ a(4) = b(3) + c(3) = 16 + 15 = 31 \\ b(4) = a(3) + c(3) = 17 + 15 = 32 \\ c(4) = a(3) + b(3) = 17 + 16 = 33[/tex]

[tex]a(5) = 32 + 33 = 65 \\ b(5) = 31 + 33 = 64 \\ c(5) =31 + 32 = 63 \\ \\ a(6) = 64 + 63 = 127 \\ b(6) = 65 + 63 = 128 \\ c(6) = 65 + 64 = 129 \\ [/tex]

[tex]a(7) = 128 + 129 = 257 \\ b(7) = 127 + 129 = 256 \\c (7) = 127 + 128 = 255 \\ \\ a(8) = 256 + 255 = 511 \\ b(8) = 257 + 255 = 512 \\ c(8) = 257 + 256 = 513[/tex]

[tex]a(9) = 512 + 513 = 1025 \\ b(9) = 511 + 513 = 1024 \\ c(9) = 511 + 512 = 1023 \\ \\ a(10) = 1024 + 1023 = 2047 \\ b(10) = 1025 + 1023 = 2048 \\ c(10) = 1025 + 1024 = 2049[/tex]

b)

[tex]a(n) + b(n) + c(n) = \\ 2(a(n - 1) + b(n - 1) + c(n - 1)) \\ 6 \times 2 {}^{n } [/tex]

c)

[tex]6 \times 2 {}^{n} > 100 \: 000 \\ 2 {}^{n} > \frac{100 \: 000}{6} \\ n > log {}^{2} ( \frac{100 \: 000}{6} ) \\ n > 14.02468 \\ n = 15[/tex]

Sa = 2(pi)(r)(h) + 2(pi)(r^2) v = (pi)(r^2)(h) find the surface area and the volume.

Answers

If Sa=2πrh+2π[tex]r^{2}[/tex]v=π[tex]r^{2}h[/tex] then the surface area is π[tex]r^{2} h[/tex] and volume is

(rh-2h)/2r.

Given Sa=2πrh+2π[tex]r^{2} v[/tex]=π[tex]r^{2}h[/tex].

We have to find surface area and volume from the given expression.

Volume is basically amount of substance a container can hold in its capacity.

First we will find the value of v from the expression. Because they are in equal to each other, we can easily find the value of v.

2πrh+2π[tex]r^{2}[/tex]v=π[tex]r^{2}[/tex]h

Keeping the term containing v at left side and take all other to right side.

2π[tex]r^{2}[/tex]v=π[tex]r^{2}h[/tex]-2πrh

v=(π[tex]r^{2}[/tex]h-2πrh)/2π[tex]r^{2}[/tex]

v=π[tex]r^{2} h[/tex]/2π[tex]r^{2}[/tex]-2πrh/2π[tex]r^{2}[/tex]

v=h/2-h/r

v=h(r-2)/2r

Put the value of v in Sa=2πrh+2π[tex]r^{2} v[/tex]

Sa=2πrh+2π[tex]r^{2}[/tex]*h(r-2)/2r

=2πrh+2πrh(r-2)/2

=2πrh+πrh(r-2)

=2πrh+π[tex]r^{2}[/tex]h-2πrh

=π[tex]r^{2}[/tex]h

Hence surface area is π[tex]r^{2}[/tex]h and volume is h(r-2)/2.

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Half of a set of the parts are manufactured by machine A and half by machine B. Eight percent of all the parts are defective. Two percent of the parts manufactured on machine A are defective. Find the probability that a part was manufactured on machine A, given that the part is defective. (Round your answer to 4 decimal places.)

Answers

The probability that a part was manufactured on machine A, given that the part is defective is P ( A | D ) = 0.024.

What is probability?Probability is the branch of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely it is that a claim is true. The probability of an event is a number between 0 and 1, with 0 indicating impossibility and 1 indicating certainty.

To find the probability that a part was manufactured on machine A, given that the part is defective:

The probability that a part was manufactured on machine A given that part is defective:

P ( A | D )

P ( A | D ) = [P (A) * P ( D | A )]/ P ( D )

Where: P (A) is the probability that the part is manufactured in machine A which is 0.2 (half of the parts are manufactured in machine A)

P (D/A) is the probability of a defective part given that the part was manufactured in machine A which is 2% or 0.02

And finally, the probability of defective part in the production is 8% or 0.08 hence :

P ( A | D ) = [ ( 0.2 ) * 0.02 ] / 0.08

P ( A | D ) = 0.024

Therefore, the probability that a part was manufactured on machine A, given that the part is defective is P ( A | D ) = 0.024.

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What is the sum of the 12th square number and the 9th square number

Answers

Answer: 225

Step-by-step explanation:

What is a square number?

A square number is a product of a number times itself

So, the 12th square number would be 12 * 12, or 12²

The 9th square number would be 9 * 9, or 9²

The equation would be 12² + 9²

So:

12² + 9²

= 144 + 81

= 225

So, the answer is 225

Which point is the solution to the inequality shown in this graph?? Help pls
a.(0,5)
b.(-3,-1)
c.(0,0)
d.(3,3).​

Answers

Answer:

only (0,5)

Step-by-step explanation:

(0,5) is in the shaded region on the graph, so it is a solution.

One other point is in the unshaded region so it is NOT a solution. The other two points are on the dashed line, so they are NOT solutions. If the line was solid (not dashed) they would work, but since the line is dashed they are NOT solutions.

Answer:

A. (0,5)

Step-by-step explanation:

Which terms could be used as the first term of the expression below to create a polynomial written in standard form? Select five options.

+ 8r2s4 – 3r3s3
Which statement is true about the polynomial
5s6t2 + 6st9 – 8s6t2 – 6t7 after it has been fully simplified?

It has 3 terms and a degree of 9.
It has 3 terms and a degree of 10.
It has 4 terms and a degree of 9.
It has 4 terms and a degree of 10.

Answers

The polynomial + 8r²s⁴ – 3r³s³ can have a possible first term of -rs⁵

The polynomial 5s⁶t² + 6st⁹ – 8s⁶t² – 6t⁷ has three terms with a degree of 10.

What is an equation?

An equation is an expression that shows the relationship between two or more variables and numbers.

Given the polynomial + 8r²s⁴ – 3r³s³. The polynomial is of degree  6, hence the possible first term could be -rs⁵

Also, the polynomial 5s⁶t² + 6st⁹ – 8s⁶t² – 6t⁷

= 6st⁹ - 3s⁶t² - 6t⁷

It has three terms with a degree of 10.

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Initially, there were only 86 weeds in the garden. The weeds grew at a rate of 8% each week. The following function represents the weekly weed growth: f(x) = 86(1.08)x. Rewrite the function to show how quickly the weeds grow each day.

f(x) = 86(1.08)7x; grows approximately at a rate of 5.6% daily
f(x) = 86(1.087)x; grows approximately at a rate of 0.56% daily
f(x) = 86(1.01)x; grows approximately at a rate of 0.1% daily
f(x) = 86(1.01)7x; grows approximately at a rate of 1% daily

Answers

The function is f(x) = 86(1.01)^7x; grows approximately at a rate of 1% daily

How to rewrite the function?

The function is given as:

f(x) = 86(1.08)^x

There are 7 days in a week.

This means that:

1 day = 1/7 week

So, x days is

x day = x/7 week

Substitute x/7 for x in

f(x) = 86(1.08)^(x/7)

Rewrite as:

f(x) = 86(1.08^1/7)^x

Evaluate

f(x) = 86(1.01)^x

In the above, we have:

r = 1.01 - 1

Evaluate

r = 0.01

Express as percentage

r = 1%

Hence, the function is f(x) = 86(1.01)^7x; grows approximately at a rate of 1% daily

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Answer: the answer is d

Step-by-step explanation:

if the price of an object with 13% vat is Rs 5650 find the net price of the object​

Answers

€%%% 14% object
=-98
Answer
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