Segment KL has endpoints located at (0, 0) and (-4, 6) when graphed on the
coordinate plane. After a dilation about the origin, which scale factor, k, produces an
image with endpoints located at (0, 0) and (-12, 18) ?

A.k = 1/3
B.k = 3/2
C.k 3
D.k=8

Answer:

The answer is :

E - 6c + 4t < 300

Answer:

Step-by-step explanation:

To graph the functions y = sin^(-1) x and y = π - sin^(-1) x on the same coordinate-axis system, we can use the properties of the inverse sine function and the unit circle.

The inverse sine function, denoted as sin^(-1) x or arcsin x, is the inverse of the sine function. This means that if we input a value x into the inverse sine function, it will output the angle θ in radians that satisfies the equation sin θ = x.

The unit circle is a circle with radius 1 centered at the origin of a coordinate plane. The angles in the unit circle are measured in radians. On the unit circle, the x-coordinate of a point is equal to the cosine of the angle formed by the point and the positive x-axis, and the y-coordinate is equal to the sine of the angle.

Given this information, we can graph the functions y = sin^(-1) x and y = π - sin^(-1) x as follows:

For y = sin^(-1) x, we can input values of x into the inverse sine function and plot the resulting values of y on the coordinate plane. Since the range of the inverse sine function is -π/2 ≤ y ≤ π/2, we can start by plotting the points (-1, -π/2), (1, π/2), and (0, 0).

For y = π - sin^(-1) x, we can input values of x into the inverse sine function, subtract the resulting values from π, and plot the resulting values of y on the coordinate plane. Since the range of the inverse sine function is -π/2 ≤ y ≤ π/2, we can start by plotting the points (-1, π/2), (1, -π/2), and (0, π).

On the same coordinate-axis system, the graph of y = sin^(-1) x will be a curve that starts at (-1, -π/2), goes through (0, 0), and ends at (1, π/2). The graph of y = π - sin^(-1) x will be a curve that starts at (-1, π/2), goes through (0, π), and ends at (1, -π/2).

If we connect the points on the two curves, we will see that they intersect at (0, π/2) and (0, -π/2). This means that the two functions are reflections of each other about the x-axis.

A quadratic equation of at the origin, estimate the error = 0.000859M

The approximation is valid because  is very small.

Calculation of  concentration:

Since

0.85 M             0           0

(0.85-x)M         x            x

Now the value of x should be

x = 0.0000229

So based on this, the above concentration should be determined.

In order to demonstrate that the same value of x may be achieved either way, you will now solve using the quadratic formula rather than iterations. What are the values of a, b, and c and x, where a, b, and c are the coefficients in the quadratic equation [tex]ax^{2} +bx+c=0[/tex] and x is [h3o+], when using the quadratic equation to determine [h3o+] in 0.00250 m hno2? Keep in mind that ka=4.5104.

a : 1

b : 4.5x[tex]10^{-4}[/tex]

c : 1.125x[tex]10^{-6}[/tex]

[[tex]H_{3} O^{+}[/tex]] = 0.000859M

As [tex]HNO_{2}[/tex] is a weak acid, its equilibrium in water is:

[tex]HNO_{2} (aq)+H_{2} O(I)[/tex] ⇄ [tex]H_{3} O^{+} (aq)+N_{2} O^{-} (aq)[/tex]

Equilibrium constant, ka, is defined as:

ka = 4.5x[tex]10^{-4}[/tex] = [[tex]H_{3} O^{+}[/tex]]  [NO₂⁻] / [HNO₂]                    (Equation-1)

Equilibrium concentration of each specie are:

[HNO₂] = 0.00250M - x

[H₃O⁺] = x

[NO₂⁻] = x

Replacing in (1):

4.5x[tex]10^{-4}[/tex] = [tex]\frac{x*x}{0.00250M-x}[/tex]

1.125x10⁻⁶ - 4.5x10⁻⁴x = x²

0 = x² + 4.5x10⁻⁴x - 1.125x10⁻⁶

As the quadratic equation is ax² + bx + c = 0

Coefficients are:

a: 1

b: 4.5x10⁻⁴

c: 1.125x10⁻⁶

Now, solving quadratic equation:

x = -0.0013 → False answer, there is no negative concentrations.

x = 0.000859

As [H₃O⁺] = x; [H₃O⁺] = 0.000859M

Therefore,

A quadratic equation of at the origin, estimate the error = 0.000859M

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Answer: 72

Step-by-step explanation

Let's just look at the denominators for this problem.

8 and 18

8 can go into 24, 3 times but 18 does not multiply into 24

18 can go into 36, 2 times but 8 does not multiply into 36

Therefore 72 is the least common denominator.

8 times 9 = 72

18 times 4 = 72

72 is the least common denominator.

The probabilities, using the hypergeometric distribution, are given as follows:

i) Two wear the same color: 37/105: 0.35238 = 37/105.

ii) At least 2 wear red: 0.4461.

The mass probability formula is presented as follows:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are presented as follows:

The probability of two red is given as follows:

[tex]P(X = 2) = h(2,15,2,7) = \frac{C_{7,2}C_{8,0}}{C_{15,2}} = 0.2[/tex]

The probability of two green is given as follows:

[tex]P(X = 2) = h(2,15,2,6) = \frac{C_{6,2}C_{9,0}}{C_{15,2}} = 0.14286[/tex]

The probability of two white is given as follows:

[tex]P(X = 2) = h(2,15,2,2) = \frac{C_{2,2}C_{13,0}}{C_{15,2}} = 0.00952[/tex]

Then the probability of two wearing the same color is given as follows:

0.2 + 0.14286 + 0.00952 = 0.35238 = 37/105.

The probability that out of 3 people, at least 2 wear red, is given as follows:

[tex]P(X = 2) = h(2,15,3,7) = \frac{C_{7,2}C_{8,1}}{C_{15,3}} = 0.3692[/tex]

[tex]P(X = 3) = h(3,15,3,7) = \frac{C_{7,3}C_{8,0}}{C_{15,3}} = 0.0769[/tex]

Hence:

0.3692 + 0.0769 = 0.4461.

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Hence, the speed that Rick must be driving on to even with Bobby at the end of the 16th lap should be: Distance = Speed × Time16=1084× Speed Speed=16×8410=134.4 mph.

The time taken by Bobby to complete 10 laps will be:

[tex]$$\begin{aligned}\text { Distance } & =\text { Speed } \times \text { Time } \\10 & =84 \times \text { Time } \\\text { Time } & =\frac{10}{84} \text { hours }\end{aligned}$$[/tex]

Hence, the speed that Rick must be driving on to even with Bobby at the end of the 16 th lap should be:

[tex]$$\begin{aligned}\text { Distance } & =\text { Speed } \times \text { Time } \\16 & =\frac{10}{84} \times \text { Speed } \\\text { Speed } & =\frac{16 \times 84}{10}=134.4 \mathrm{mph} .\end{aligned}$$[/tex]

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The area of a rectangle with the sides of x+7 and 3x-4 is 3x² + 17x - 28.

Any shape's area can be calculated by counting how many unit squares will fit inside of it. A square with a side of 1 unit is referred to as a unit square in this context. Therefore, the quantity of unit squares that make up a rectangle's perimeter is its area. Alternately, the area of the rectangle is the area contained within the boundary of this shape. The unit-length tiles in your home are a good illustration of a rectangle form. By counting the number of tiles, you can quickly determine how much space the floor takes up. This will also enable you to calculate the rectangle floor's area.

Given

Sides = x+7 and 3x-4

Area of rectangle

Length ×Breadth

(x + 7) (3x - 4)

Multiplying,

x(3x - 4) + 7(3x - 4)

3x² - 4x + 21x - 28

3x² + 17x - 28

The area of a rectangle with the sides of x+7 and 3x-4 is 3x² + 17x - 28.

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The equivalent rate is 163.7 meters.

What is an equivalent rate?

Equivalent rates are different rates that have the same value. Similar to finding equivalent ratios, you may find an equivalent rate by multiplying or dividing the numerator and denominator by the same number.

Here, we have

Given: the height of one Tampa city center is 537 feet.

We have to convert 537 feet to meters by finding an equivalent rate.

1 feet = 0.3048 meter

So, 537 feet = 537 × 0.3048 = 163.7 meters.

Hence, the equivalent rate is 163.7 meters.

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Answer:

Hence, on a number line,-12 lies to the left of Zero.

Step-by-step explanation:

On a number line, zero lies exactly at the middle of the number line.Left to the zero, negative number lies and right to the zero, positive number lies.

The equation of the parabola is y = -1/4 x² + 3/2 x - 17/4. Where the vertex of the equation is at (3, -2) and the focus is at (3, -2 2/16) that opens downwards.

The equation of the parabola with vertex at (h, k) is

y = a(x - h)² + k

The focus of the parabola is represented by (h, k + 1/4 a).

It is given that, the vertex of the parabola is (h, k) = (3, -2)

And the focus of the parabola is (h, k + 1/4 a) = (3, -2 1/16)

From the focus point, we can calculate the value of 'a'.

(h, k + 1/4 a) = (3, -2 1/16)

⇒ k + 1/4 a = -2 1/16 = -33/16

⇒ -2 + 1/4 a = -33/16

⇒ 1/4 a = -33/16 + 2

⇒ 1/4 a = -1/16

⇒ a = -1/16 × 4

∴ a = -1/4

Since a is negative the parabola is downwards.

Now, the equation of the parabola is

y = a(x - h)² + k

On substituting the values, we get

y = -1/4(x - 3)² - 2

  = -1/4(x² - 6x + 9) - 2

  = -1/4 x² + 3/2 x -9/4 - 2

  = -1/4 x² + 3/2 x - 17/4

Therefore, the equation of the parabola is y = -1/4 x² + 3/2 x - 17/4.

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The options that represent binomial random variable  are;

A. Take a random sample of 30 tours and let L = the number of tours that result in a sale.

B. Take a random sample of 3 tours and let K = the number of tours that result in a sale.

There are 4 primary conditions for a random variable to be classified as binomial random variable and they are;

1. The number of observations n is fixed.

2. Each observation is independent.

3. Each observation represents one of two outcomes ("success" or "failure").

4. The probability of "success" p is the same for each outcome.

No, in this case, since 5% of home tours result in a sale, it therefore tells us that number of home tours is the independent variable while the amount of sales generated is the dependent variable.

From the above, we can access the given options and say that the last option is not a binomial random variable because the variable M is dependent and so does not satisfy one of the four conditions.

However, options A and B satisfy the 4 conditions and we say they are binomial random variables.

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it can be inferred that there is a 95% probability that the true value falls within that range.

A confidence interval, in statistics, refers to the probability that a population parameter will fall between a set of values for a certain proportion of times. Analysts often use confidence intervals than contain either 95% or 99% of expected observations.

Thus, if a point estimate is generated from a statistical model of 10.00 with a 95% confidence interval of 9.50 - 10.50,

it can be inferred that there is a 95% probability that the true value falls within that range.

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1405 in base 7 = 544 in base 10

What is base-7 number system ?

The heptimal system is another name for base-7 numbers. Base 7 numbers are represented by the digits 0, 1, 2, 3, 4, 5, and 6.

The digits of a Base 10 number, on the other hand, are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. If there isn't a subscript at the supplied number, Base 10 is used to write that number. The decimal system is sometimes known as base-10 numbers. Currently, in daily life, we frequently use numbers in the base 10 range.

base 7 to  base 10 conversion:

Multiply each digits by the powers of 7 as follows:

Base 7 digits:   1         4        0         5

Multiply by:      7^3      7²      7^1      7^0

  ( 1*7^3) + (4*7² ) + (0* 7^1 )+ ( 5 *   7^0)

= 343 + 196 + 0 + 5

= 544

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Answer: The coefficient of the term with t^3 and q^14 in the expansion of (3t - q)^17 is 816 / 3.

Step-by-step explanation: The coefficient of the term with a certain power of t and a certain power of q in the expansion of a binomial raised to a power can be found using the binomial formula. The formula is given by:

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(a + b)^n = sum_{k=0}^n choose(n, k) * a^(n-k) * b^k

In this case, we have a = 3t, b = -q, and n = 17. We want to find the coefficient of the term with t^3 and q^14, which means we need to find the coefficient of the term with a^(n-k) = t^3 and b^k = q^14. Plugging these values into the formula, we get:

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(3t - q)^17 = sum_{k=0}^17 choose(17, k) * 3^(17-k) * (-1)^k * t^(17-k) * q^k

To find the coefficient of the term with t^3 and q^14, we need to find the value of choose(17, k) for k = 3. The binomial coefficient choose(n, k) is equal to the number of ways to choose k items from a set of n items. It can be calculated using the formula:

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choose(n, k) = n! / (k! * (n-k)!)

where n! is the factorial of n, which is the product of all positive integers less than or equal to n. For example, 5! = 5 * 4 * 3 * 2 * 1 = 120.

In our case, we have n = 17 and k = 3, so the coefficient we are looking for is:

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choose(17, 3) = 17! / (3! * (17-3)!) = 17 * 16 * 15 * 14 * 13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 / (3 * 2 * 1 * 14 * 13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) = 17 * 16 / 3 = 816 / 3

Therefore, the coefficient of the term with t^3 and q^14 in the expansion of (3t - q)^17 is 816 / 3.

Answer:

y = 3x + 11

Step-by-step explanation:

y = mx + b

y = 3x + b

2 = 3(-3) + b

2 = -9 + b

b = 11

y = 3x + 11

Answer:

Amy has to pay $600 every month for rent.

Step-by-step explanation:

To take 1/4 of a number is to multiply 1/4 and said number.

So you can do 0.25*number

or number/4.

For this problem, the number is 2400 because Amy is going to pay 1/4 of 2400 for rent.

[tex]rent = 2400/4\\rent = 600[/tex]

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when retail cost of the computer is 37% of the wholesale price then Retail price is 1.37times wholesale price

Retailers who acquire products in bulk are subject to wholesale pricing.

Selling products at a greater price than what it costs to produce them allows businesses to turn a profit.

Retail pricing is what merchants decide to charge customers as their ultimate selling price.

Consumers are the primary focus of retail pricing.

According to the question,

The retail cost of a computer is 37% more than its wholesale cost

Let Retail cost be "x" and wholesale cost be "y"

So , x = y + 0.37y

=> x = 1.37y

Therefore , The retail price is 1.37times the wholesale price

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The angles after solving the equations will be equal to 50°, and both angles will be the same as the corresponding angles. Hence, option B is correct.

An angle results from the intersection of two lines at a point. The term "angle" describes the width of the "gap" that exists between these two rays. It's represented by the symbol.

Angles are most frequently measured in degrees and radians, a measurement of roundness or rotation. Angles are a part of everyday existence.

As per the given information in the question,

The equations for the angles are:

7x + 1 = 6x + 8

7x - 6x = 8 - 1

x = 7

So, the angles will be,

7x + 1 = 7(7) + 1 = 50°

6x + 8 = 6(7) + 8 = 50°

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The correlation coefficient for the data is positive 57,72,69,58,47,84,62 with coefficient being 1.

In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data.

Correlation is a measure of a monotonic association between 2 variables. A monotonic relationship between 2 variables is a one in which either (1) as the value of 1 variable increases, so does the value of the other variable; or (2) as the value of 1 variable increases, the other variable value decreases.

In the given question, the number of fires in 7 years is given as: 57,72,69,58,47,84,62.

Similar is the number of acres burned: 57,72,69,58,47,84,62

This shows total positive correlation , with it's coefficient being 1 .

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Least time required to reach the point Q as per the distance and the speed rate is equal to 2 hours.

As given in the question,

Nearest point on the coast is 2 miles far away

rate of the row = 1mile per hour

Walk at the rate of 3 miles per hour

Let 'x' hours be the least time to reach point Q.

Time = distance / speed

Time taken to reach the point Q = [√ 1 + ( 3 - x)² ]/ 3

Time taken to reach the coast = (√ 4 + x² ) / 1

Total  time taken 't' = (√ 4 + x² ) / 1 + [√ 1 + ( 3 - x)² ]/ 3

To find least time dt/dx = 0

t  = (√ 4 + x² ) / 1 + [√ 1 + ( 3 - x)² ]/ 3

⇒dt/dx = [ x / √ 4 + x² ] + ( 3 - x) / √( 10 -6x + x² )

⇒x / √ 4 + x² = ( x - 3) / √( 10 -6x + x² )

Squaring both the side we get,

x² / (4 + x²) = ( x - 3)² / ( 10 -6x + x² )

⇒3x² -24x +36 =0

⇒ x² -8x + 12 = 0

⇒ x = 2 or 6 hours

Therefore , the least time taken to reach the point Q is equal to 2 hours.

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50 feet each dimensions of the rectangular dog park producing the greatest enclosed area given 200 feet of fencing.

For an area to be the maximum of any rectangle the difference in length and breadth must be minimal. So, in such case, the length must be ceil (perimeter / 4) and the breadth will be floor(perimeter /4). Hence the maximum area of a rectangle with a given perimeter is equal to ceil(perimeter/4) * floor(perimeter/4).

Let X be the length and Y be the width of the rectangle. 200 ft of fencing material, so the maximum perimeter is 200 ft. Therefore first equation can be, 2X + 2Y = 200 => X + Y = 100 => Y = 100 — X

Equation of area of rectangle =>

A = X×Y => A = X(100–X) => A = 100X — X^2

Differentiate with respect to X on both sides

A' = 100 — 2X

Critical point => 100 — 2X = 0 => 2X = 100, X = 50

So maximum area is generated when the length and width of the fence are 50 feet each, which makes it a square. In mathematical terms, the square can be considered a rectangle.

50 feet each dimensions of the rectangular dog park producing the greatest enclosed area given 200 feet of fencing.

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Using the current equation:

C = V/I

We will get the current c = (4.7 + 0.3i) volt/ohm

We know that the equation that relates voltage V, current C and I impedance is:

V = C*I

Solving this for the current, we will get:

C = V/I

Here we know that:

V = (24 - 8i) volts

And the impedance is:

I = (5 - 2i) ohms

Replacing that in te current equation we will get:

C = (24 - 8i)/(5 - 2i)   volt/ohm

If we multiply and divide by the complex conjugate of the denominator, which is:

(5 + 2i)

We will get:

C = [(5 + 2i)* (24 - 8i)]/[ (5 + 2i)*(5 - 2i)]   volt/ohm

C = [ 5*24 + 5*(-8i) + (2i)*24 + (2i)*(-8i)]/(5^2 + 2^2)   volt/ohm

C = [120  - 40i + 48i + 16]/(29)  volt/ohm

C = [136 + 8i]/29  volt/ohm

C = (4.7 + 0.3i) volt/ohm

That is the current for the given case.

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Answer:

Yes, there are many people who can help you with a finance question. Some of the people who can help you include: financial advisors, accountants, financial planners, and financial analysts. Additionally, there are many online resources available such as personal finance forums, websites, and blogs.

Step-by-step explanation:

Answer:

x = [tex]\frac{5-3y}{2}[/tex]

Step-by-step explanation:

2x + 3y = 5

isolate variable: 2x = 5-3y

divide by 2: x = [tex]\frac{5-3y}{2}[/tex]

The generating function for the number of ways the coefficients on and in this generating function .

Given :

the generating function for the number of ways to distribute blank scratch paper to alice, bob, carlos, and dave so that alice gets at least two sheets, bob gets at most three sheets, the number of sheets carlos receives is a multiple of three, and dave gets at least one sheet but no more than six sheets of scratch paper.

Alice = x^2 + x^3 + ...... so on

Bob = 1 + x + x^2 + x^3

Carlos = 1 + x^3 + x^6+ ..... ... so on

Dave = x + x^2 + x^3 + x^4 + x^5 + x^6

The product of these could be a generating function that may be one idea to explore though  if you need separate variables to know who got how many sheets or not.

The minimum term in the product will be x^3 as Alice gets 2 sheets and Dave gets 1 sheet is the minimal solution.

Then i wonder  if the x^2 is x^2 or x^2 as there are a couple of ways to see where a 2 could go here.

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Part 1

[tex]-4.9t^2 +18.24t+0.8=-1.43t+4.26\\\\-4.9t^2 +19.67t-3.46=0\\\\\Delta =(19.67)^2 -4(-4.9)(-3.46)=319.0929 > 0[/tex]

Therefore, the blocker can knock down the punt.

Part 2

Using the quadratic formula,

[tex]t=\frac{-19.67 \pm \sqrt{319.0929}}{2(-4.9)}\\\\t \approx 0.18437, 3.82992[/tex]

Considering the graphs, it is clear to take the smaller solution. Thus, the point of intersection is [tex](0.18437, h(0.18437))=\boxed{(0.18437, 3.99635)}[/tex].

Answer:

1000

Step-by-step explanation:

If any of the digits 0-9 can be used then there are 10^3 possible codes.

10^3 = 1000

The value of 'a' can be 20. The correct option is C, 20.

As per the triangle inequality theorem, the sum of any two sides of the triangle should be greater than the third side.

As per triangle inequality theorem, the sum of the two sides of the triangle should be greater than the third side of the triangle.

As per the triangle inequality theorem, if 'a' is the longest side of the triangle then,

21 + 6 > a

27 > a

If a is not the longest side of the triangle,

21 + a > 6

a > -21 + 6

a > -15

6 + a  > 21

a > 21 - 6

a > 15

Therefore, the value of a should be greater than 15 and less than 27. Since the only option under this condition is 20.

Hence, The correct option is C, 20.

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Answer:

Step-by-step explanation:

Answer:

Leo can spend $18 on each shirt.

Step-by-step explanation:

The size of the velocity of the ball in the direction of the wind is 2 units

To find the size of the velocity of the ball in the direction of the wind, we can take the dot product of the ball's velocity vector and the wind velocity vector.

The dot product is defined as:

v1 • v2 = (x1 × x2) + (y1 × y2)

Substituting the coordinates of the ball's velocity vector and the wind velocity vector, we get:

(2, 1) • (3, -4) = (2 ×3) + (1 × (-4))

= 6 - 4

= 2

Therefore, the size of the velocity of the ball in the direction of the wind is 2. This represents the component of the ball's velocity that is aligned with the wind.

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