To find out the y-intercept of the line that is
parallel to y = 0.5x - 2, what should you do?
Since the parallel line goes through the point (3,
0) substitute 3 for x and 0 for y and solve for b,
the y-intercept.
You cannot solve it because you do not know
what x and y are for the parallel line.
Since the parallel line goes through the point (3,
0) substitute 0 for x and 3 for y and solve for b,
the y-intercept.

Answer:

P = 10

Q=12

[tex]p = \frac{1}{q} [/tex]

a). p = 1/2 = 0.5

b). 1.25 = 1/Q

Q = 1/1.25 Q = 0.8

Answer:

P=6

Q= 9.6

Step-by-step explanation:

A)

y=k/x

substitute it in.

10=k/1.2

10×1.2=k

k=12

y=12/x

x=2

12/2=6

P=6.

B)

Since we know y=kx

we know k=12

you would do 12/1.25 to give u Q

12/1.25=9.6

Answer:

A. Subtract the distance between each point and the x-axis.

Step-by-step explanation:

As the two points have the same x-coordinate, x = 6, it means they lie on the vertical line x = 6.

Therefore, the distance between the points can be found by subtracting the distance between each point and the x-axis.

In the given example, the points are C(6, -4) and D(6, -8).

To find the distance between a point and the x-axis, we simply take the absolute value of the y-coordinate of the point:

Distance between point C and the x-axis = |-4| = 4

Distance between point D and the x-axis = |-8| = 8

Subtracting the distances, we get:

Distance = 8 - 4

Distance = 4

Therefore, the distance between points C and D is 4 units.

Each function operation should be matched with what it is equivalent to as follows:

f(x) + g(x) = -2x² + x + 6.

g(x) - f(x) = -2x² - 5x + 2.

f(x) · g(x) = -6x³ - 10x² + 8x + 8.

h(x) - f(x) = 3x² - 7x - 2

f(x) · h(x) = 9x³ - 6x² - 8x.

f(x) + g(x) + h(x) = x² - 3x + 6.

In order to determine the solutions of the given function, we would have to evaluate each of the function based on the required mathematical operations as follows.

From the information provided, we have the following functions:

f(x) = 3x + 2

g(x) = -2x² - 2x + 4

h(x) = 3x² - 4x

f(x) + g(x) = 3x + 2 + (-2x² - 2x + 4)

f(x) + g(x) = 3x + 2 - 2x² - 2x + 4

Next, we would rearrange the function by collecting like terms as follows:

f(x) + g(x) = -2x² + (3x - 2x) + (2 + 4)

f(x) + g(x) = -2x² + x + 6 (solution).

g(x) - f(x) = -2x² - 2x + 4 - (3x + 2)

Opening the bracket, we have:

g(x) - f(x) = -2x² - 2x + 4 - 3x - 2

Next, we would rearrange the function by collecting like terms as follows:

g(x) - f(x) = -2x² + (-2x - 3x) + (4 - 2)

g(x) - f(x) = -2x² - 5x + 2 (solution).

f(x) · g(x) = (3x + 2) × (-2x² - 2x + 4)

Opening the bracket, we have:

f(x) · g(x) = -6x³ - 6x² + 12x - 4x² - 4x + 8

Next, we would rearrange the function by collecting like terms as follows:

f(x) · g(x) = -6x³ + (-6x² - 4x²) + (12x - 4x) + 8

f(x) · g(x) = -6x³ - 10x² + 8x + 8 (solution).

h(x) - f(x) = 3x² - 4x - (3x + 2)

h(x) - f(x) = 3x² - 4x - 3x - 2

h(x) - f(x) = 3x² - 7x - 2 (solution).

f(x) · h(x) = (3x + 2) × (3x² - 4x)

f(x) · h(x) = 9x³ - 12x² + 6x² - 8x

f(x) · h(x) = 9x³ - 6x² - 8x (solution).

f(x) + g(x) + h(x) = 3x + 2 + (-2x² - 2x + 4) + (3x² - 4x)

f(x) + g(x) + h(x) = -2x² + x + 6 + 3x² - 4x

f(x) + g(x) + h(x) = x² - 3x + 6 (solution).

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The overall profit of the corporation as during time period is $ 2.5 x 10⁷

As the question expressed-

Earned profit - $2. 5 x 10 to the 4th power

In scientific notation - $2. 5 x 10⁴

Number of days - 1 x 10 to the 3rd power

In scientific notation - 1.0 x 10³

Total profit = Earned profit x Number of days

Total profit = $2. 5 x 10⁴ x 1.0 x 10³

Total profit = $ 2.5 x 10⁷

Thus, the overall profit of the corporation as during time period is $ 2.5 x 10⁷.

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In the given parabola equations, the third equation [tex]y = 2x - 3x^{2}[/tex] has a maximum value.

What is the Maximum parabola?

If a parabola opens up, it has the lowest point, and if it opens down, it has the highest point. For a parabola to have a maximum value, it must be the case that the parabola opens down. Algebraically, this means that the leading coefficient in the equation of a parabola is negative (a < 0).

We have,

                              [tex]y = 0.1x^{2} - 3x\\\\y = 4x^{2} + 24x +23\\\\y = 2x - 3x^{2}\\\\y = x^{2} + 2x + 20[/tex]

For a parabola to have a maximum value, the parabola must open downward. Algebraically, this means that the leading coefficient in a parabola equation is negative (a < 0).

By Simplifying the third equation we get its leading coefficient is negative (a < 0).

                              [tex]y = -3x^{2} + 2x[/tex]

Hence in the given parabola equations, the third equation has a maximum value.

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Answer: b= (0,4)

Step-by-step explanation:

The 'b' value in a line is the y-int. of a linear equation. That means you need to determine where the linear equation intersects with the y-axis. In this scenario it intersects at the point (0,4)

The pack of hot dogs that the shopper should buy that would be cheaper is six - pack of hot dogs

If the shopper decided to buy the six-pack of hot dogs for $2.10, their total cost to be able to get 48 hot dogs would be:

= Cost per six pack of hot dogs x ( Number of hot dogs needed / Number of hot dogs in pack)
=2.10 x (48 / 6)

= 2.10 x 8

= $16.80

The cost if the shopper wants the eight pack is:

= 3.12 x (48 / 8)

= $18.72

The shopper should pick the six - pack of hot dogs because it is cheaper.

The rest of the question is:

Which option would be cheaper to the shopper?

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The p-value of the distribution of population standard deviation of 33.17 texts per day is 0.9435

The test statistic's "p-value" measures how likely it is that future results will be at least as extreme as the one your sample yielded. You must understand that the null hypothesis is the underlying presumption to compute this probability.

The parameters are as follows:

The sample mean ([tex]\bar x[/tex]) = 118.4

The population standard deviation ([tex]\sigma[/tex]) = 33.17

The sample size (n) = 30

Calculate the z-score first.

[tex]z = \bold{ \frac{x - \bar x}{\frac{\sigma}{\sqrt{n} } } }[/tex]

according to the entire question, x = 128

So, we have:

[tex]z = \bold{ \frac{x - \bar x}{\frac{\sigma}{\sqrt{n} } } }\\\\z = \bold{ \frac{9.6}{\frac{33.17}{\sqrt{30} } } }\\\\z = \bold{ \frac{9.6}{\frac{33.17}{5.477 } } }\\\\z = \bold{ \frac{9.6}{ 6.056} }\\\\z = 1.5852[/tex]

As determined by the z table of probability, p = 0.9435395

or p = 0.9435 (approx.)

Consequently, the distribution's p-value is 0.9435.

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Answer: D

Step-by-step explanation:

Take the equation and substitute the variables for the numbers given

-7(-4-4(-6))=-140

Hope this helps :)

Answer: 7£

Step-by-step explanation:
1. Firstly, we need to subtract the single sign up fee from the total cost. This would be 141-57 =84 pounds
2. We know that you pay a regular amount every month, so therefore we can divide 84 by 12 as there are 12 months in a year.
3. 84/12 = 7. Thus, the answer is 7 pounds a month.

Answer:

£7

Step-by-step explanation:

Given information:

To find the cost of the monthly payments, find the difference between the total cost and the sign-up fee, then divide the result by 12 (as there are 12 months in one year).

The difference between the total cost and the sign-up fee is:

[tex]\implies 141-57=84[/tex]

Therefore, the cost of each monthly payment is:

[tex]\implies \textsf{Monthly fee}=\dfrac{84}{12}=7[/tex]

The value of x is 5 for the given equation 5/3 = x/3.

So, the equation is:

Now, solve for x as follows:

Therefore, the value of x is 5 for the given equation 5/3 = x/3.

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Correct question:

Solve for x. 5/3= x/3

The equation of the parabola from the vertex is f(x) = 7(x - 3)² + 5

The equation of the function is given as

f(x) = 7x²

Also, we have

Vertex = (3, 5)

The form of the equation is given as

f(x) = a(x - h)² + k

Where

Vertex = (h, k)

This means that

Vertex = (h, k) = (3, 5)

Substitute (h, k) = (3, 5) in the equation f(x) = a(x - h)² + k

So, we have

f(x) = a(x - 3)² + 5

This also means that

f(x) = 7(x - 3)² + 5

The 7 is gotten from f(x) = 7x²

Hence, the equation of the parabola is f(x) = 7(x - 3)² + 5

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Check the picture below.

All the inequality given are all non strict inequalities

Inequality           classification

3x - 2 < 1          non strict inequality    

3x - > 1             non strict inequality

3x - 2 > 1          non strict inequality

3x - 2 < 1          non strict inequality

Inequality refers to a way of representing relationships between variables at the left hand side of equation to the variables to the right hand side of an equation.

The signs used in inequality are of 4 types namely

The strict inequality are those inequality that the equation fails when equality sign is used to represent the relationship of the left and right hand side of an equation.. The inequality sign used here is only less than or greater than

The non strict inequality maintains the balance between both sides of the equation whether the equality is used or not

None of the given expression has the "less than or equal to" OR "greater than or equal to" signs hence they are all strict inequality

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The fraction of all the circles in the shapes  is 23/90

Given that the:

Ratio of the number of white shapes to the number of black shapes is 7:3

Ratio of the number of white circles to the number of white squares is 2:7

Ratio of the number of black circles to the number of black squares is 1:2

Total share for both white and black shape = 7+3 = 10

share for white shape = 7/10 and share for black shape = 3/10

Total share for white circles and white squares = 2+7 = 9

share for white circles = 2/9 and share for white squares = 7/9

Total share for black circles and black squares = 1+2 =3

share for black circles = 1/3 and share for black squares = 2/3

White circles will take 2/9 of white colors i.e. 2/9 x 7/10 =   14/90 = 7/45

Black circles will take 1/3 of  black colors i.e. 1/3 x 3/10 = 3/30 = 1/10

Fraction of circles = 7/45 + 1/10

                              =  14+9/ 90

                             = 23/90

Therefore, the fraction of all the shapes that are circles is 23/90

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The probability that exactly two will be replaced under warrant is 0.1937.

The possibility of an event occurring is determined by the probability formula. The ratio of positive outcomes to the total number of outcomes serves as the basis for calculating an event's probability. The probabilities are always between 0 and 1. A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

Given,

W = Warranty

V = Replaced

P(W) = 20/100

P(W) = 0.20

P(U/W) = 0.40

P(W ∩ U)

= P(U/W) × P(W)

= 0.40 × 0.20

0.-08

P( exactly two will be replaced under warranty)

Using binomial distribution:

= P(X = 2)

= 10/2 (0.0.8)² (0.9)⁸

= 0.1937

The probability that exactly two will be replaced under warrant is 0.1937.

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Answer: The volunteers are unaware of which surgery they receive.

Step-by-step explanation:

Answer:

Step-by-step explanation:

A=P(1+r/n)^nt

Let the Beth deposite is x.Here r and n will be 1.

A=x(1+1/1)^5

Similarly
B=2x(1+1/n)^nt

B=2x(1+1/1)^5

There combined interest is:
A+B=x(1+1/1)^5+2x(1+1/1)^5

21=32x+64x

21=96x

x=21/96 is the beth deposite.

2x=2*21/96 is the Reena deposite

Ella answer makes sense because the value of  ? is 4

Given: the equation 32 divided ? =8 she says the value of ? is 4

32 / ? = 8    

Let x represent ? in the equation, thus:

32 / x = 8         cross multiply

8x = 32

x = 32/8

x = 4

Since x = 4. This implies ? = 4

Also, the value that divides 32 to give is 4

Since the value of ? is 4. Therefore, Ella's answer makes sense

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The probability that the transistor will last between 12 and 24 weeks is 0.424

the probability that a transistor will last at most 24 weeks is 0.567

The median of the lifetime distribution is less than 24

X= lifetime of the transistor in weeks E(X)= 24 weeks

O,= 12 weeks

The anticipated value, variance, and distribution of the random variable X were all provided to us. Finding the parameters alpha and beta is necessary before we can discover the solutions to the difficulties.

a) X~gamma([tex]\alpha , \beta[/tex])

E(X)= [tex]\alpha \beta[/tex]             [tex]\beta[/tex] =[tex]12^{2}/24[/tex] =6 weeks

V(x)=[tex]\alpha \beta ^{2}[/tex]                 [tex]\alpha[/tex]=24/6= 4

Now we can find the solutions:

The excel formula used to create Figure one is as follows:

=gammadist(X,[tex]\alpha[/tex] ,[tex]\beta[/tex] , False)

P([tex]12\leq X\leq 24[/tex])

P([tex]12/6 \leq X\leq 24/6[/tex])

P([tex]2\leq X\leq 4[/tex])

P= 0.424

Therefore, the probability that the transistor will last between 12 and 24 weeks is 0.424

b) For this case we want this probability:

[tex]P(X\geq 24)=1-P(X\leq 24)[/tex]

In order to find this probability we can use excel with the following code:

=1-GAMMA.DIST(24,4,6,TRUE)

And we got:

[tex]P(X\geq 24)=P(1-X\leq 24)= 0.567[/tex]

c) For this case the median of the lifetime distribution is less than 24

[tex]P(X\leq \alpha )[/tex] = 0.5  (by definition)    So [tex]\alpha[/tex]< 24 because P([tex]X\leq 24[/tex])=0.567 which is greater than 0.5

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Answer:

y= 38 + 0.20x

The equation will be y=38+0.20x where x is the number of texts and y is in dollars.

An equation is a relationship between the variables and constants representing how they are related to each other. It includes equal to "=" sign.

It is known that the fixed payment is of $38 and each text costs $0.20.

Assume Colette sends x texts in a month and y be the total cost.

Determine the monthly cost equation.

Total cost= Fixed cost+ x(cost of each text)

y=38+0.20x

So, the total monthly cost will be represented by the equation, y=38+0.20x.

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The value of [tex](x_{1},y_{1})= (-9,-6)[/tex] and the value of [tex](x_{2},y_{2})= (-1,-12)[/tex],according to the question.

What do you mean by XY coordinates?

The x and y coordinates are a component of the x-axis and y-axis in a 2D space in the Cartesian coordinate system. The x and y coordinates for a point in space are expressed as an ordered pair (x, y). The position of the point on the x-axis is shown by the first number, while its location on the y-axis is indicated by the second number.

According to the data in the given question,

We have:

The coordinates of points A are (-9,-6).

The coordinates of points W are (-1,-12).

In this question,

[tex](x_{1},y_{1})= (-9,-6)[/tex]

[tex](x_{2},y_{2})= (-1,-12)[/tex]

Therefore, the value of [tex](x_{1},y_{1})= (-9,-6)[/tex] and the value of [tex](x_{2},y_{2})= (-1,-12)[/tex].

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Main answer:

a) 18 millions of dollars/year

b) 6 millions of dollars/year

Step-by-step explanation:

a) the average rate of change of annual sales between 2001 and 2002 millions of dollars/year

Average rate = (Final year - Initial year) / (Sales on Final year - Sales on Initial year)

                     = (417 - 399) / (2001 - 2002)

                     = 18 / 1

                     = 18 millions of dollars/year

b) the average rate of change of annual sales between 2001 and 2006 millions of dollars/year

Average rate = (Final year - Initial year) / (Sales on Final year - Sales on Initial year)

                      = (369 - 399) / (2006 - 2001)

                      = 30 / 5

                      = 6 millions of dollars/year

The average rate of change of annual sales between 2001 and 2002 is 18 millions of dollars/year ,  between 2001 and 2006 is 6 millions of dollars/year

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Answer:

A and D

Step-by-step explanation:

8(6) means 8x6 so that's 48

and 12(4) is the same as 4(12) so that should be simple enough

The cost of publishing the 300 copies of the book is $6500.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that a small publishing company is planning to publish a new book. Let C be the total os of publishing the book(in dollars). Let N be the number of copies of the book produced. For the first printing, the company can produce up to 300 copies of the book. Suppose that c=20N+500 gives C as a function of N during the first printing.

The cost of 300 copies will be calculated as,

c=20N+500

c = ( 20 x 300 ) + 500

c = 6000 + 500

c = 6500

Therefore, the cost of publishing the 300 copies of the book is $6500.

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The graph represents the system of equations -3x + y = 3 and -x + 2y = -4 is option (b) On a coordinate plane, 2 lines intersect at (negative 2, negative 3).

The system of equation are

-3x + y = 3

-x + 2y = -4

Here we have to use the substitution method

-3x + y = 3

y = 3 + 3x

Substitute the value of y in the second equation

-x + 2(3 + 3x) = -4

-x + 6 + 6x = -4

-x + 6x = -4-6

5x = -10

x = -10/5

x = -2

Substitute the value of x in the first equation

-3x + y = 3

-3(-2) + y = 3

6 + y = 3

y = 3 - 6

y = -3

Hence, the graph represents the system of equations -3x + y = 3 and -x + 2y = -4 is option (b) On a coordinate plane, 2 lines intersect at (negative 2, negative 3).

The complete question is:

Which graph represents the system of equations –3x + y = 3 and –x + 2y = –4?

a) On a coordinate plane, 2 lines intersect at (3, 0).

b) On a coordinate plane, 2 lines intersect at (negative 2, negative 3).

c) On a coordinate plane, 2 lines intersect at (negative 1.5, 1).

d) On a coordinate plane, 2 lines intersect at (1.5, 2.5).

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Answer:

B

Step-by-step explanation:

both point intersect at ( -2, -3)

The distance between two points on a 2D coordinate plane can be found using the following distance formula. d = √ (x 2 - x 1) 2 + (y 2 - y 1) 2. where (x 1, y 1) and (x 2, y 2) are the coordinates of the two points involved. The order of the points does not matter for the formula as long as the points chosen are consistent.

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Answer:

it is 5 units!

As, in our question we are doing 20 trials to get the number of on-time flights. Hence, this is a binomial experiment.

The value of p=0.8 and n=20

The probability that exactly 12 flights are on time = 0.1772

The probability that exactly fewer than 12 flights are on time =  0.1049

The probability that at least 12 flights are on time = 0.8951

The probability that between 10 and 12 flights, are on time = 0.1795

(a) Binomial probability is the probability of exactly 'k' successes on 'n' repeated trials in an experiment which has two possible outcomes.

As, in our question we are doing 20 trials to get the number of on-time flights. Hence, this is a binomial experiment.

(b) As, the probability of success on an individual trial is p and here success means the flight is on-time so the value of p be,

p = 80% = 0.8

As, we made 20 trials and n is the total number of trials then,

the value of n be,

n = 20

(c) Now, if the probability of success on an individual trial is p ,

Then the binomial probability is C(n,x)⋅p^x⋅(1−p)^(n−x)

The probability that exactly 12 flights are on time, be

P(X=12) = C(20,12)⋅(0.8)^12⋅(1−0.8)^(20-12)

P(X=12) = C(20,12)⋅(0.8)^12⋅(0.2)^(8)

P(X=12) = 10,07,760×0.0687×0.00000256

P(X=12) = 0.1772

(d) Now, the probability that exactly fewer than 12 flights are on time, be

P(X<12) = 1 - P(X>12)

So, P(X>12) = P(X=13)+P(X=14)+P(X=15)+P(X=16)+P(X=17)+P(X=18)+P(X=19)+P(X=20)

So, P(X>12) = 0.0545 + 0.0364 + 0.1746 + 0.2182 + 0.2054 + 0.1369 + 0.0576 + 0.0115

P(X>12) = 0.8951

P(X<12) = 1 - 0.8951

P(X<12) = 0.1049

(e)  Now, the probability that at least 12 flights are on time, be

P(X>12)=0.8951

(f) The probability that between 10 and 12 flights, are on time, be

P(X=10)+P(X=11)+P(X=12) = 0.0020 + 0.0003 + 0.1772

P(X=10)+P(X=11)+P(X=12) = 0.1795

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