Consider the pair of points below.
(-5, -4)
(-1,8)
Find the slope of the line passing through the pair of points.
m =

Wayne's Actual ACT score is 19.2 where mean is 21, standard deviation is 5 and the Z - score is -0.6.

Standard Deviation:

Standard deviation is  a measure of the dispersion of a set of numerical values from their mean.

The general form of the standard deviation is,

[tex]SD=\sqrt{\frac{\sum (x_i-\bar{x})}{n} }[/tex]

where

xi is each value in the data set,

x-bar is the mean, and

n is the number of values in the data set.

Given,

Mean = 21.

Standard deviation = 5

Wayne's standardized score on the act = −0.6 .

Here we need to find the Wayne's Actual ACT score.

Let x be the Wayne's Actual ACT score.

So,
=> z-score = (x - mean)/SD

Apply the values on it,

=> -0.6 = (x - 21) / 3

=> -1.8 = x - 21

=> x = 21 - 1.8

=> x = 19.2

Therefore, Wayne's Actual ACT score is 19.2

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the composition of functions gives:

g(f(0)) = -6

Here we have the two functions:

f(x) = 3(x - 7)/4

g(x) = 2x  - 1

The problem in the answer is in the third step, where the distribution is done incorrectly.

g(f(x)) = 3*( (2x - 1) - 7)/4

g(f(x)) = 3*( 2x - 8)/4

g(f(x)) = ( 6x - 24)/4

Evaluating in x = 0 we get:

g(f(0)) = ( 6*0 - 24)/4 = -24/4 = -6

That is the solution of the composition of functions.

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Answer:

The mistake is in the third step

The solutions to the given equation containing absolute value term |3x-7| - 7 = x are 0 and 7.

Given the equation in question;

|3x-7| - 7 = x

First, add 7 to both sides.

|3x-7| - 7 + 7 = x + 7

|3x-7|  = x + 7

Next, remove the absolute value term, this creates a ± on the right side of the question.

|3x-7|  = x + 7

3x-7  = ±( x + 7 )

The complete solution is the result of both the negative and positive portions of the solution.

For the first solution, use the positive of ±.

3x-7  = ( x + 7 )

3x - 7  =  x + 7  

3x - x = 7 + 7

2x = 14

x - 14/2

x = 7

For the second solution, use the negative of ±.

3x-7  = -( x + 7 )

3x-7  = -x - 7

3x + x = -7 + 7

4x = 0

x = 0/4

x = 0

Therefore, the solutions to the given equation containing absolute value term |3x-7| - 7 = x are 0 and 7.

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Answer: -19.7        

Step-by-step explanation:

62.7 - 82.4=

-(82.4-62.7)= -19.7        ==> switch the numbers and negate the expression to get the same answer

Only function 2 represent a linear function.

Herein we find four cases of functions, of which we are asked to determine if each function is linear or not. A function is linear if and only if the change between every pair of two consecutives values of x and y is the same. Now we proceed to check each case:

Function 1

Δx = - 1 - (- 3) = 2; Δy = 6 - 2 = 4

Δx = 1 - (- 1) = 2; Δy = 18 - 6 = 12

Δx = 3 - 1 = 2; Δy = 54 - 18 = 36

The function is not linear.

Function 2

Δx = 5 - 1 = 4; Δy = - 1 - 1 = - 2

Δx = 9 - 5 = 4; Δy = - 3 - (- 1) = - 2

Δx = 13 - 9 = 4; Δy = - 5 - (- 3) = - 2

The function is linear.

Function 3

Δx = 5 - 4 = 1; Δy = - 10 - (- 5) = - 5

Δx = 6 - 5 = 1; Δy = - 13 - (- 10) = - 3

Δx = 7 - 6 = 1; Δy = - 15 - (- 13) = - 2

The function is not linear.

Function 4

Δx = 1 - (- 2) = 3; Δy = 5 - 4 = 1

Δx = 4 - 1 = 3; Δy = 6 - 5 = 1

Δx = 7 - 4 = 3; Δy = 1 - 6 = - 5

The function is not linear.

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Answer:

If you add up all those hours that makes 6.5 hours

Answer:7.5

Step-by-step explanation:

Just add them

Answer:

thank me that's is my answer

The number of players in the team will be 18.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Total cost to go to a tournament = $1885.50

Rent for bus = $949.50

Budget for meal for each player = $52

Now,

Let the number of players = x

So, We can formulate;

⇒ $949.50 + $52x = $1880.50

Solve for x, as;

⇒ $949.50 + $52x = $1880.50

Subtract 949.50 both side, we get;

⇒ $949.50 + $52x - $949.50 = $1880.50 - $949.50

⇒ $52x = $931

⇒ x = $17.90

After round we get;

⇒ x = $18

Thus, The number of players in the team will be 18.

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The value of x is 12.

Given on a line lie three points e, f and g.

therefore, ef = x ₋ 4

fg = 2x ₋ 9 and

eg = 13

we can say that ef and fg must add upto eg.

⇒ ef ₊ fg = eg

⇒ x ₋ 4 ₊ 2x ₋ 19 = 13

⇒ 3x ₋ 23 = 13

⇒ 3x = 13 ₊ 23

3x = 36

x = 36/3

x = 12

hence we get the value of x as 12.

now substitute x value to get ef and fg values.

ef = x ₋ 4  = 12 ₋ 4 = 8

fg = 2x ₋ 19 = 2(12) ₋ 19 = 24 ₋ 19 = 5

Hence we get the value of x as 12.

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Answer:

Hope this helps :)

If it is seven and three thousandths then the answer would be...

7.003

This is because after the decimal the first place is tenths, then, hundredths, and lastly, thousandths. So the 3 would be in the thousandths place. Also, 7 is in the ones place which is before the decimal.

Answer:

135

Step-by-step explanation:

135 > 13.1 > 13.09 > √169 (√169 = 13)

I hope I could help ^^

Answer:

Step-by-step explanation:

Favorite hobby is gaming

Favorite activity is football

Zeros of a Polynomial Function

An important consequence of the Factor Theorem is that finding the zeros of a

polynomial is really the same thing as factoring it into linear factors. In this section we

will study more methods that help us find the real zeros of a polynomial, and thereby

factor the polynomial.

Rational Zeros of Polynomials:

The next theorem gives a method to determine all possible candidates for rational zeros

of a polynomial function with integer coefficients.

Rational Zeros Theorem:

If the polynomial ( ) 1

1 1 ... n n P x ax a x ax a n n

− = + ++ − + 0 has integer

coefficients, then every rational zero of P is of the form

p

q

where p is a factor of the constant coefficient 0 a

and q is a factor of the leading coefficient n a

Example 1: List all possible rational zeros given by the Rational Zeros Theorem of

P(x) = 6x

4

+ 7x

3

- 4 (but don’t check to see which actually are zeros) .

Solution:

Step 1: First we find all possible values of p, which are all the factors

of . Thus, p can be ±1, ±2, or ±4. 0 a = 4

Step 2: Next we find all possible values of q, which are all the factors

of 6. Thus, q can be ±1, ±2, ±3, or ±6. n a =

Step 3: Now we find the possible values of p

q by making combinations

of the values we found in Step 1 and Step 2. Thus, p

q will be of

the form factors of 4

factors of 6 . The possible p

q are

12412412412

, , , , , , , , , , ,

11122233366

± ± ± ± ± ± ± ± ± ± ±±

4

6

Total 330 four-digit numbers can be formed if the number is odd and greater than 6000.

Let's tackle the problem in three steps.

First, take into account the numbers with "6" as the first digit on the left.

Then take the first eight digits of the numbers as the leftmost digit.

Last but not least, we'll use the numbers that begin with "7" as the leftmost digit.

1. As the leftmost digit, think of the numbers that begin with "6."

Any one of the final four odd digits—1, 3, 5, or 7—is acceptable (and recommended).

You are given four options.

You can use any of the remaining 8-1-1 = 6 digits for the second and third digit.

In all, it gives you 4×6×5  = 120 choices/numbers.

2.  Consider  the leftmost digit as the number starting with "6."

You have 120 more options/numbers using the same logic and analysis.

Everything is going well thus far, and you only need 120 + 120 = 240 numbers.

3.  Consider the numbers starting with "7" as leftmost digit.

Any of the final three odd digits—1, 3, and 5—may (and ought to) be used.

You have three options.

Any of the remaining 8-1-1 = 6 digits can be used for the second and third digit.

In all, it gives you 3×6×5  = 90 choices/numbers.

4. You have 120 + 120 + 90 = 330 numbers/options when everything is added up.

Hence we get 330 choices to create four digit numbers.

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Your question is incomplete. Please find the missing content below.

A four-digit number is formed using four of the eight digits 1, 2, 3, 4, 5, 6, 7, 8. No digit can be used more than once. Find how many different four-digit numbers can be formed if the number is odd and greater than 6000.

Notice the pattern:

10² = 100, so 10² - 9 = 91 with a digital sum of 9 + 1 = 10

10³ = 1000, so 10³ - 9 = 991 with a digital sum of 2•9 + 1 = 19

10⁴ = 10000, so 10⁴ - 9 = 9991 with a digital sum of 3•9 + 1 = 28

Then for an arbitrary power of 10, we have

[tex]10^n = 1\underbrace{00\ldots000}_{n\,\rm 0s} \implies 10^n - 1 = \underbrace{999\ldots99}_{n-1\,\rm9s}1 \\\\ \implies \text{digital sum} = 9(n-1)+1 = 9n - 8[/tex]

When [tex]n=51[/tex], the digital sum is 9•51 - 8 = 451.

No, the triangle with vertices (-1, -1), (2, 3), (-4, 3) is not equilateral.

An equilateral triangle is a triangle that has all three sides of equal length, also known as a "regular" triangle.

Now, as per the given question.

The vertices are given as (-1, -1), (2, 3), (-4, 3).

Find the distance between the two corresponding vertices.

First, find distances between (-1, -1), (2, 3) lets say 'c'.

c² = (-1-3)² + (-1-2)²

c² = 4² + 3²

c² = 16 + 9

c² = 25

c = 5

Now, find the distance between (2, 3), (-4, 3), let say it 'd'.

d² = (-4-2)² + (3-3)²

d² = 36

d = 6

Now, find the distance between (-1, -1), (-4, 3) say it 'p'

p² = (-1-(-4 ))² +(-1-3)²

p² = 3² +4²

p² = 25

p = 5

As, all three distances are not same. Thus, the given vertices does not form equilateral triangle.

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The correct question is-

An equilateral triangle has sides of equal length. Determine whether the triangle with vertices (-1, -1), (2, 3), (-4, 3) is equilateral.

The parametric equation of our line is;

x = 1 + 3t

y = -1 + 3t

z = 4 + 8t

We want to find parametric equations for the line through (3, 3, 8) that is perpendicular to the plane x − y + 4z = 5

A vector perpendicular to the plane ax + by + cz + d = 0 is given by (a, b, c).

So a vector perpendicular to the plane x − y + 4z - 5 = 0 is (1, -1, 4)

The parametric equation of a line through (x₀, y₀, z₀) and parallel to the vector (a, b, c) is;

x = x₀ + ta

y = y₀ + tb

z = z₀ + tc

So the parametric equation of our line is;

x = 1 + 3t

y = -1 + 3t

z = 4 + 8t

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!!Figure is not clear!! Formulae is provided below.

To fence the triangular section Mr. Johnson has to find the perimeter of the triangular field.

To find the perimeter of the triangle one has to add the length of all the three sides of the triangle.

Similarly we can also find the perimeter of other plane figures by adding the lengths of all the sides of the figure.

Suppose if the length of the sides of a triangle is a,b and c units.

Then the perimeter of the triangular field will be = (a + b + c) units.

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Answer:

D

Step-by-step explanation:

Area equal LxWxH

2x2.5x3.5=17+5

The amount of material needed to make the box is 41.5 ft².

The surface area of a figure is the number of unit squares it takes to cover the entire surface without gaps or overlaps. If a three-dimensional figure has flat sides, the sides are called faces. The surface area is the total of the areas of the faces.

Given that, a rectangular storage box is to be made with length is 3.5 feet, the width is 2 feet, and the height is 2.5 feet.

For finding the same, we will find the surface area of the box,

Surface area of the box = 2(length·width + width·height + height·length)

Therefore,

SA = 2(3.5x2+2x2.5+3.5x2.5)

SA = 2 x 20.75

SA = 41.5

Hence, the amount of material needed to make the box is 41.5 ft².

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Answer:

It is 0.4 and 40%

Step-by-step explanation:

Because if you divide 2 by 5 you get 0.4 and 0.4 is the same and 40% however, 4/100 is 0.04 or 4%

Answer:

0.4 and 40%

Step-by-step explanation:

0.4 and 40% can both be expressed as 2/5, however 4/100 cannot, as the simplified form of that is 1/25.

A compound inequality that represents the leg lengths of the cyclists the shop 18 ≤ 0.6x ≤ 26.

For the given question;

Let the cyclist's legs length be 'x'.

Then 0.6 times of cyclist's legs length will be 0.6x.

Now, the condition is;

The height ranging for the bikes is 18 inches and 26 inches.

It means the height of cyclist's legs length must be greater or equal to this value.

Thus,

18 ≤ 0.6x

And the maximum height of bike is 26 inch.

Thus, cyclist's legs length must be less than or equal to this length.

0.6x ≤ 26

Combining the two;

18 ≤ 0.6x ≤ 26 is the requires compounded inequality.

Thus, for, the value of x such that the range of the leg length lies between the 18 and 26 including both, the bike is provided otherwise NOT.

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The equation of Leo's line is given by: 3 (y - G) = ( F - x)

Given: An equation of a line on a grid, about which another line is perpendicularly.

To find: Equation of the perpendicular line.

Finding:

=> m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] = [tex]\frac{4-1}{2-1}=\frac{3}{1} = 3[/tex]

The equation of the line becomes:  [tex]y-y_0=3(x-x_0)[/tex]

    2. Since the line passes through (1,1), the final equation of the line can be given by:

=> y - 1 = 3 ( x - 1)

=> y = 3x - 3 + 1

=> y = 3x - 2

=> m' = -1/m

=> m' = -1/3

=> [tex]3(y-y_0)=(x_0-x)[/tex]

    2. Since the perpendicular line passes through the point (F,G), the equation of the line will be: 3 (y - G) = ( F - x).

Hence, The equation of Leo's line is given by: 3 (y - G) = ( F - x).

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Answer:

Scale factor = 1/2

Explanation below

Explanation belowHope this helps :)

Step-by-step explanation:

If the second figure is turned correctly then all the numbers will correspond.

10 × 1/2 = 5

6 × 1/2 = 3

8 × 1/2 = 4

The simplified expression of 6(d - 6f) -6f- 3(-7f + 8d) is - 18d- 21f

The expression is given as

6(d - 6f) -6f- 3(-7f + 8d)

Expand the brackets

6(d - 6f) -6f- 3(-7f + 8d) = 6d - 36f - 6f + 21f - 24d

Collect the like terms

6(d - 6f) -6f- 3(-7f + 8d) = 6d  - 24d- 36f - 6f + 21f

Evaluate the like terms

6(d - 6f) -6f- 3(-7f + 8d) = - 18d- 21f

Hence, the simplified expression of 6(d - 6f) -6f- 3(-7f + 8d) is - 18d- 21f

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Answer:

121°

Step-by-step explanation:

These are supplemental angles.  a straight angle is 180 degrees.

180 - 59 = 121

Answer: m2=121 degrees

Step-by-step explanation:

m1+m2=180 ==> m1 and m2 are on a straight line. Straight lines measure 180 degrees and are called straight angles. m1 and m2 are supplementary angles, so they add up to 180 degrees.

59+m2=180

59-59+m2=180-59

m2=180-59

m2=121 degrees

Answer:its 180 cm

Step-by-step explanation:

Tony have to get to pay $187.5.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

There are two cases in Unitary Method

Let's start with finding the price of one ice cream. Divide the entire cost of ice cream by the total number of ice creams to get at that. A single ice cream will cost you 125 divided by the amount of ice creams, or 25 cents. Consequently, 1 ice cream costs $25.

Step 2: To calculate the price of three ice creams, multiply the price of one ice cream by the quantity. Cost of 1 ice cream x number of ice creams = 25 x 3 = $75 is the price of 3 ice creams. The final cost is $75, which is the price of three ice creams.

Given:

For 1 1/2 or 3/2 hours tony charges = $37.50

For 1 hour tony charges = 37.50 * 2/3

                                        = 12.5 * 2

                                        = $25

Now, for 7 1/2 hours tony charges

= 15/2 * 25

= $187.5

Hence, tony charges $187.50 for tutoring 7 1/2 hours.

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Asking questions, formulating a hypothesis, testing the hypothesis, drawing conclusions, and reporting the results are steps in the: scientific method.

Scientific method refers to a process that has been the hallmark of natural science since the 17th century and entails systematic observation, measurement, and experiment as well as the creation, examination, and change of hypotheses.

Now,

Hence, Asking questions, formulating a hypothesis, testing the hypothesis, drawing conclusions, and reporting the results are steps in the: scientific method.

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The correct option is c. True.

If the intquantity and decprice variables contain the numbers 3 and 15.75, respectively, the condition if intquantity > 0 and also intquantity < 10 or else decprice > 20 will evaluate to "True."

C++ is an object-oriented programming (OOP) language that many consider to be the best for developing large-scale applications.

C++ is a subset of the C programming language. Java is a programming language that is similar to C++ but is optimized for the dispersion of program objects over a such as the Internet.

Now, as per the question, construct a program in C++.

#include <iostream>

using namespace std;

int main()

{

  int intQuantity = 3;

  int decPrice = 15.75;

    if (intQuantity >0 && intQuantity <10 || decPrice>20){

      cout<<"True";

   }

   else{

      cout<<"False";

   }

  return 0;

}

Because the condition if (intQuantity >0 && intQuantity 10 || decPrice >20) evaluates to true, the output from in this program will be "True." The reason for this is that in programming, the Logical Or (| |) evaluates to true when either or both conditions are met.

Although the condition decPrice>20 is false in the question, the very first condition intQuantity >0 && intQuantity 10 is true, so the OR evaluates to true.

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The complete question is -

If the intQuantity and decPrice variables contain the numbers 3 and 15.75, respectively, the condition If intQuantity > 0 And Also intQuantity < 10 OrElse decPrice > 20 will evaluate to ____.

a.No

b.Yes

c.True

d.False

If a chip is randomly drawn from the bag, the probability it will be a red or a blue one is P(red or blue) = 10/19.

Probability of an event A is the number of event A divided by all possible outcomes. Mathematically,

P(A) = n(A)/n(S)

where:

n(A) = number of event A

n(S) = number of all possible outcomes or sample space.

Suppose A and B are independent outcomes, then:

P(A or B) = P(A) + P(B)

In the given problem:

Number of chips:

Blue = 3

Red = 7

Yellow = 4

Green = 5

Total chips = 3 + 7 + 4 + 5 = 19

If a chip is randomly drawn, the probability it will be a red one is:

P(red) = 7/19

Similarly,

P(blue) = 3/19

Using the probability formula for independent outcomes:

P(red or blue) = P(red) + P(blue)

                      = 7/19 + 3/19 = 10/19

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