question the probability that a randomly selected visitor to a certain website will be asked to participate in an online survey is 0.40. avery claims that for the next 5 visitors to the site, 2 will be asked to participate in the survey. is avery interpreting the probability correctly? responses yes, because 2 out of 5 is equal to 40%. yes, because 2 out of 5 is equal to 40%. yes, because participants in the survey are selected at random. yes, because participants in the survey are selected at random. no, because there could be voluntary response bias. no, because there could be voluntary response bias. no, because only 40% of all people will visit the site. no, because only 40% of all people will visit the site. no, because 0.40 represents probability in the long run over many visits to the site.

The equation of line k is y = 1/2x - 1.

The equation y = mx + c is the general equation of any straight line, where m is the gradient of the line and c is the y -intercept.

Given that, the equation for line j can be written as y=1/2x-4. Parallel to line j is line k which passes through the point (-8, -5)

When two lines are parallel their slope are equal, so solving for c,

-5 = 1/2*-8 + c

c = -1

The equation will be,

y = 1/2x - 1

Hence, The equation of line k is y = 1/2x - 1.

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In the given triangle KLM with coordinates K(0,2) ,L(2 ,9) ,M(4,2), the sets of points which represent the dilation from the origin is K'(0,8), L'(8, 36) , M'(16, 8) multiply by scale factor 4.

As given in the question,

In the given triangle KLM,

Coordinates of the triangle KLM are given by :

K(0,2) ,L(2 ,9) ,M(4,2)

Dilation from the origin is represented by:

a. K'(0,2) , L'(8,9) , M'(16, 2)

Dilation scale factor does not effect on all the coordinates .

Not a correct option.

b. K'(0,2) , L'(2,36) , M'(16, 2)

Dilation scale factor does not effect on all the coordinates .

Not a correct option.

c. K'(0,8) , L'(8,36) , M'(16, 8)

Multiply by scale factor 4.

Dilation exist.

d. K'(4,6) , L'(6,13) , M'(8, 6)

Scale factor of addition of 4.

Dilation does not exist.

Therefore, in the given triangle KLM with coordinates K(0,2) ,L(2 ,9) ,M(4,2), the sets of points which represent the dilation from the origin is K'(0,8), L'(8, 36) , M'(16, 8) multiply by scale factor 4.

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The probability that the price of the used car is less than $65 is 0.55962.

Here it is given that the price of the used car has a mean of $50 and a variance of $100.

Since it follows normal distribution X~N(μ, σ²)

where,

μ = 50

σ = 100

Here we need to find the probability P(X < 65)
To find this we need to convert the distribution to the standard normal form, N~(0, 1)

We know,

P(X < (x - μ)/ σ) = Φ(Z)

Therefore we get

P(X < (65 - 50)/ 100)

Solving this we get the Z value

= Φ(0.15)

From the Z table, we can get our p-value.

= 0.55962

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Using simplification, the equations that are equivalent to [tex]\frac{(6x+2)}{3} =2-(3x+14)[/tex] are [tex]\frac{(6x+2)}{3 } = -3x-12[/tex] and 6x + 2 = -9x - 36

Two systems of equations are equivalent if they have the same solution(s)

In a simpler term, two equations are equivalent if they have the same solution.

Therefore, let's simplify the equation to find the equivalent solutions.

[tex]\frac{(6x+2)}{3} =2-(3x+14)[/tex]

let's open the brackets of the right side of the equation.

[tex]\frac{(6x+2)}{3}=2-(3x+14)[/tex]

[tex]\frac{(6x+2)}{3} = 2-3x-14[/tex]

[tex]\frac{(6x+2)}{3 } = -3x-12[/tex]

Therefore, let's cross multiply

6x + 2 = 3(-3x - 12)

6x + 2 = -9x - 36

Therefore, the equivalent equation are as follows:

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Answer:

The number is -36 or x = -36

Step-by-step explanation:

2x + 16 = -56
       2x = -72
         x = -36

Answer:

m=2

Step-by-step explanation:

-16=m-18

-16+18=m

2=m

The equation of a line is the mathematical function of a line thus the equation of the line that passes through the points (-4, -6) and (2, 8) will be y = (14/6)x + 10/3.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

A linear equation or function is given as ;

y = mx + c

Here, m is the slope and is given as (y₂ - y₁)/(x₂ - x₁).

The slope of the line passing through (-4, -6) and (2, 8) will be,

m = (8 + 6)/(2 + 4)

m = 14/6

So, y = (14/6)x + c

Substitute,  (2, 8)

8 =  (14/6)2 + c

c = 8 - 14/3 = 10/3

Therefore, y = (14/6)x + 10/3

Hence "The equation of a line is the mathematical function of a line thus the equation of the line that passes through the points (-4, -6) and (2, 8) will be y = (14/6)x + 10/3".

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Answer:

Y = 2x+8

Step-by-step explanation:

Y=mx=b equations

The equation of the parabola that similar to f(x) = [tex]7x^2[/tex] but the vertex is (3, 5) in the standard form is y = [tex]7(x-3)^2[/tex] + 5

The equation of the parabola

f(x) = [tex]7x^2[/tex]

The standard vertex form of a parabola is

y = [tex]a(x-h)^2[/tex] + k

The coordinates of the vertex of a parabola = (3, 5)

Where (h, k)  is the coordinates

From the given function of the parabola f(x) =  [tex]7x^2[/tex]

The value of a = 7

Substitute the values in the vertex form of a parabola

y = [tex]7(x-3)^2[/tex] + 5

Hence, the equation of the parabola that is similar to f(x) = [tex]7x^2[/tex] but the vertex is (3, 5) in the standard form is y = [tex]7(x-3)^2[/tex] + 5

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The solution to the difference 20 4/10 - 3 1/10 is 17 3/10

We have been given two fractions.

20 4/10 and 3 1/10

We need to find the difference 20 4/10 - 3 1/10

First we write improper fraction as a proper fraction.

20 4/10 = 204/10

3 1/10 = 31/10

So, the difference would be,

20 4/10 - 3 1/10

= 204/10 - 31/10

= 173/10

= 17 3/10

Therefore, the solution to the difference 20 4/10 - 3 1/10 is 17 3/10

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There are 45 yards of cable that will be required.

Since we have given that

Height of cable = 15 yards - 3 yards = 12 yards

Distance from pole = 9 yards

cable is the hypotenuse of the right-angled triangle.

So, it becomes,

[tex]c^{2} = b^{2}+p^{2}[/tex]

[tex]c^{2} = 12^{2}+9^{2}[/tex]

[tex]c^{2} = 144+81[/tex]

[tex]c^{2} = 225[/tex]

[tex]c = \sqrt{225}[/tex]

c=15 yards

Since the number of cables supported = 3

So, the number of yards of cable that will be required would be

= 3  x 15 = 45

Hence, there are 45 yards of cable will be required.

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The option(1) that is  g(1) is 3 is True and remaining are false.

Function of a variable is when a change in one is accompanied by a change in the other. The graph's x-axis denotes the function's domain, and the y-axis its range.

Eight distinct types of regularly used functions correspond to eight distinct types of function graphs. They include linear, power, quadratic, polynomial, rational, exponential, logarithmic, and sinusoidal function graphs.

we have,

g(x) = f(x - 3)

As graph in question,

g(1) = f(1-3) = f(-2) = 3

This option is true.

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The remainder of the long division problem (x + 1)/x is given as follows:

1.

The representation of a long division problem is given as follows:

di(x)/d(x) = q(x) + (r(x)/b(x))

In which the meaning of each symbol is listed as follows:

In the context of this problem, the operation is presented as follows:

(x + 1)/x.

This division can be separated into two divisions that are added, hence:

(x + 1)/x = x/x + 1/x = 1 + 1/x.

Comparing to the standard symbols, we have that:

The expression is:

(x + 1)/x.

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Answer:

B 1

Step-by-step explanation:

The simple interest earned on a 2,000 principal at 8% interest for 5 years is I = $1,937.50.

Therefore,

I = Prt

First, converting R percent to r a decimal

r = R/100 = 3.875%/100 = 0.03875 per year,

then, solving our equation

I = 10000 × 0.03875 × 5 = 1937.5

I = $ 1,937.50

The simple interest accumulated

on a principal of $ 10,000.00

at a rate of 3.875% per year

for 5 years is $ 1,937.50.

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Answer:

Step-by-step explanation:

b) The value of 12⁰ will be?

→ 12⁰ = ?

→ 12⁰ = 1

Hence, the solution is 1.

c) The value of (3)^(-2) will be?

→ (3)^(-2) = ?

→ (3)^(-2) = 0.1

Hence, the solution is 0.1.

Answer:

A

Step-by-step explanation:

using the rule of radicals

[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex] , then

[tex]\sqrt{12}[/tex]

= [tex]\sqrt{4(3)}[/tex]

= [tex]\sqrt{4}[/tex] × [tex]\sqrt{3}[/tex]

= 2[tex]\sqrt{3}[/tex]

Then

[tex]\sqrt{144}[/tex] + 18[tex]\sqrt{12}[/tex] - 5[tex]\sqrt{64}[/tex]

= 12 + 18(2[tex]\sqrt{3}[/tex] ) - 5(8)

= 12 + 36[tex]\sqrt{3}[/tex] - 40

= - 28 + 36[tex]\sqrt{3}[/tex]

The number of days that it will take to sell his box of 35 is 21 days.

Ratio simply demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).

In this case, Nigel is selling candy bars for his outdoor club and he is averaging 4 bars every 3 days.

Let the number of days be x.

This will be:

3/x = 4/35

Cross multiply

4x = 3 × 35

x = (3 × 35)/4

x = 105 / 4

x = 21

It will take 21 days

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Answer: [tex]x=7[/tex]

Step-by-step explanation:

[tex]3^x=2187\\\\x=\log_{3} (2187)\\\\x=7[/tex]

Coppinger Corp is using Scenario Analysis.

Given, that Coppinger Corp is considering the use of a computer to assign probability distributions to the input variables used in the analysis.

The computer would then randomly select input variables from their distributions and calculate npvs based on those selections

Now, A scenario analysis consists of multiple inputs. For eg. a Company may consider how an increase in available fuel can impact their number of goods sold etc.

Here, also Coppinger Corp is assigning multiple values to the computer and getting outputs.

So, this can be the Scenario Analysis.

Hence, Coppinger Corp is using Scenario Analysis.

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The histogram that shows a left-skewed distribution is given by:

A. A bar chart plots data points (1, 1), (2, 4), (3, 1), (4, 2), (5, 3), (6, 4) and (7, 3).

An histogram is a graph that shows the number of times each element x was observed on the data-set.

Hence, the meaning of a point (x,y) on the histogram is given as follows:

Observation x was observed y times on the data-set.

The skewness of a distribution can be explained as follows:

Hence in this problem, for the left-skewed histogram, we want an "increasing" histogram, hence option A is correct.

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Order of greatest y intercept to least y intercept,

1). A linear function has been given as,

   y = [tex]\frac{1}{2}[/tex]x + 4

   Y intercept = 4

2). The graph,

    Y intercept = (2)

3). Graph represented by table

    Y intercept = 1

4). A line passes through two points (-2, -3) and (4, 0)

    Y intercept = -2

It is the total distance from the origin and the intersection of y axis and the formed line. It may be positive, negative or zero.

  From the graph,

    y-intercept = (2)

A line passes through two points (-2, -3) and (4, 0),

Slope of the line = [tex]\frac{y2 - y1}{x2 - x1}[/tex]

                           = [tex]\frac{0-(-3)}{4-(-2)}[/tex]

                           = 1/2

Equation of a line passing through a point (x', y') and slope = m

y - y' = m(x - x')

If the point is (4, 0) and slope = 1/2

y - 0 = 1/2 ( x - 4 )

y = 1/2x - 2

y-intercept of this line = (-2)

A linear function has been given as,

y = [tex]\frac{1}{2}[/tex]x + 4

Comparing it with the slope intercept equation,

y = mx + b

b = y-intercept = 4

From the given table,

For x = 0, f(x) = 1

Therefore, y-intercept = 1

Order of greatest y intercept to least y intercept,

1). A linear function has been given as,

   y = [tex]\frac{1}{2}[/tex]x + 4

Y intercept = 4

2). The graph,

Y intercept = (2)

3). Graph represented by table

Y intercept = 1

4). A line passes through two points (-2, -3) and (4, 0)

Y intercept = -2

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The solutions for the quadratic equation:

2x^2 + 12x + 18 = 0

are:

x₋ =  -5.55

x₊  = -0.4

Remember that for a general quadratic equation:

a*x^2 +b*x + c = 0

The solutions are of the form:

[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a}[/tex]

Here we have the quadratic:

2x^2 + 12x + 18 = 0

Then using the formula for the solutions we will get:

[tex]x = \frac{-12 \pm \sqrt{12^2 - 4*2*18} }{2*2} \\\\x = \frac{-12 \pm 10.2}{4}[/tex]

The two solutions of the quadratic equation are:

x₋ = (-12 - 10.2)/4 =  -5.55

x₊ = (-12 + 10.2)/4 = -0.4

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After using proportion method 325 calories will she get if she drinks the larger 20 oz. size.

What is proportion?

 Ratio and fractions are the main bases on which proportion is explained. Two ratios are equal when they are expressed as a fraction in the form of a/b, ratio a:b, and then a proportion. In this case, a and b can be any two integers. The ratio and proportion are important building blocks for understanding the numerous ideas in science and mathematics. Numerous challenges in daily life can be solved with proportion, including those in business when handling transactions or in the kitchen, among other situations. It creates a relationship between two or more quantities and aids in comparing them.

Here 16 oz medium size has 260 calories.

Then

=> [tex]\frac{size of coffee}{ calories}[/tex]

=>[tex]\frac{16}{260}=\frac{20}{x}[/tex]

=>x=[tex]\frac{20*260}{16}[/tex]

=> x = 325

Hence 325 calories will she get if she drinks the larger 20 oz. size.

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Ruth must have an initial deposit of $12000 in order to have the same simple interest at the same rate within the same time as Carter

Simple Interest (S.I) is the method of calculating the interest amount for some principal amount of money. Simple interest is a quick and easy method of calculating the interest charge on a loan. Simple interest is determined by multiplying the daily interest rate by the principal by the number of days that elapse between payments.

The formula of simple interest is given as

S.I = PRT

We can set up equivalent equations since both interest are equal.

S.I = P(1 + RT)

S.I = 12000(1 + 0.019 * 1)

S.I = 12228

But since they earned the same interest at the same rate within the same period, their principal or initial amount invested must be equal

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The probability that it toys will be shipped is option b ) 0.6691 .

Hypergeometric Distribution will be used

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

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

According to question,

N = 17

k = 2

n = 3

To find : P ( X = 0 ) ,

P ( X = 0 ) = h ( 0 , 17 , 3 , 2 )

                = [tex]C_{2,0} C_{15,3} / C_{17,3}[/tex]

                 = 455 / 680

         = 0.6691

So there is 66.91 % probability that toys will be shipped .

Hence , option b ) 0.6691 is the correct answer .

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Answer:

80

Step-by-step explanation:

Answer: 81

Step-by-step explanation:

[tex]v=\sqrt{2gh}\\\\g=32, v=72\\\\\implies 72=\sqrt{2(32)h}\\\\5184=64h\\\\h=81[/tex]