Evaluate the expression X - 2 + 2(4) - X when x =12

The slope is 5 and the y-intercept is -2000.

(b) The slope tells us about the rate of change in weekly profit and the y-intercept tells us about the minimum profit.

(c) The situation can be modeled as y = 5x -200. Here, y= profit per week and x= number of customers per week.

(d) If the state world roller rink reached a maximum capacity of 2,500 customers per week then the weekly profit will be $10,500.

In order to make the y-intercept (where the line crosses the vertical y-axis) and slope (steepness) immediately apparent, a line's equation must be written in the slope-intercept form. This version is frequently known as y = mx + b. the equation of a straight line in the form of y = mx + b, where m is the line's slope and b is its y-intercept. The slope intercept formula y = mx + b is used when you know the line's slope and the provided point is also the line's y-intercept (0, b).  y = mx + b, where m represents the line's slope, is the slope-intercept form of a line.

(a) Consider two points

(x₁, y₁) = (400, 0)

(x₂, y₂) = (500, 500)

The slope is given as

m = (y₂ - y₁)/ (x₂ - x₁)

= (500-0)/(500-400)

= 500/100

= 5

To find y- intercept put (x, y) = (400,0) in y= mx+b (slope-intercept form of a line)

0 = 5(400)+b

0 = 2000 + b

b= - 2000

(b) The slope tells us about the rate of change in weekly profit and the y-intercept tells us about the minimum profit.

(c) Let the number of customers per week = x

And the profit per week = y

Then, the situation can be modeled using slope-intercept form as

y = 5x -200

(d) Put x= 2500 in y = 5x -200

y = 5(2500)-2000

= 12,500-2000

= 10,500

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The values of x in the equations are as follows:

1. x = 8 or 4

2. x = 2

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.

Therefore, let's solve the equation as follows:

log₄ x² - 12x + 48 = 2

using law of logarithm

4² = x² - 12x + 48

16 = x² - 12x + 48

x² - 12x + 48 - 16 = 0

x² - 12x + 32 = 0

x² - 4x - 8x + 32 = 0

x(x - 4) - 8(x - 4) = 0

(x - 8)(x - 4) = 0

Therefore,

x = 8 or x = 4

[tex]27^{(4x-6)}=(\frac{1}{9})^{2x-7}[/tex]

[tex]27^{(4x-6)}=(3^{-2} )^{2x-7}[/tex]

[tex]3^{3(4x-6)}=3^{-4x+14}[/tex]

[tex]3^{12x-18} =3^{-4x+14}[/tex]

Cancel the base

Therefore,

12x - 18 = - 4x + 14

12x + 4x = 14 + 18

16x = 32

x = 32 / 16

x = 2

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Answer:

Real, Irrational

Step-by-step explanation:

5sqrt2 is NOT:

Natural (1,2,3...)

Whole (0,1,2,3...)

Integer (...-3,-2,-1,0,1,2,3...)

Rational (can be written like a ratio)

Imaginary (have the number i in it.)

It IS Irrational, will have neverending decimal with no repeating pattern.

5sqrt2 = 7.0710678119...

It IS REAL and IRRATIONAL.

Answer:

7.8

Step-by-step explanation:

Switch 8 and 7, it round to 8 and end in tenths.

Answer:

7.8

Step-by-step explanation:

7.8 rounds to 8, because 8 is greater than 5, and then we end in the tenths place.

solution: [tex]x > -175[/tex]

interval notation:  (-175, ∞)

explanation:

[tex]-\frac{1}{5}x + 4 < 39\\[/tex]

Subtract 4 from both sides

[tex]-\frac{1}{5}x +4-4 < 39-4\\[/tex]

Simplify

[tex]-\frac{1}{5}x < 35[/tex]

Multiply both sides by -1 (reverse the inequality)

[tex](-\frac{1}{5}x )(-1) > 35(-1)[/tex]

Simplify

[tex]\frac{1}{5}x > -35\\[/tex]

Multiply both sides by 5

[tex]5[/tex] ·[tex]\frac{1}{5}x > 5(-35)[/tex]

Simplify

[tex]x > -175[/tex]

The value of TV for the similar triangles is 25

Similar triangles are the triangles that have corresponding sides in proportion to each other and corresponding angles equal to each other. Similar triangles look the same but the sizes can be different.

Similar triangles are not the same as congruent triangles though.

triangle UXW and UTV are similar since line TV cuts lines UX and UW in the same proportion.

Let UV = p, it means also that WV = P. which means WU = 2p

so since the two triangles are similar, the ratio of their corresponding lengths are equal

meaning,

UV/UW = TV/XW

substituting their values, we have

p/2p = TV/50

by cross multiplying,

2p x TV = 50p

2TV = 50

TV = 50/2 = 25

In conclusion,  the value of TV is half the value of WX = 25

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The calculation of the following income statement figures are as follows:

The income statement is the first financial statement that summarizes the revenues and expenses for a business period to arrive at different profit points.

One of the profit points is the gross profit, which is the difference between the sales revenue and the cost of goods sold.

The other profit points include the operating income, income before tax, and net income.

Gross sales                            $170,000

Sales returns and allowances   9,000

Net Sales                               $161,000

Cost of goods sold:

Beginning inventory $8,000

Net purchases           18,000

Ending inventory       (5,000) $21,000

Gross profit                          $140,000

Operating expenses             (56,000)

Net Income                          $84,000

Thus, the calculation of the income statement figures shows a net income of $84,000.

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1) In figure 4, the area of the square os 16cubes. The shaded part is 7cubes, being one less than 4^2 or 4*4.  The formula is n+n-1. This can be put in for 5 too. 5+5-1=9.

2) Using the formula, 50+50-1=99. Therefor, the shaded squares in the 50th figure would be 99.

Complete sentence:

1) The formula for the number of shaded squares in the Nth figure is n+n-1.

2) There would be 99 shaded squares in the 50th figure.

explanation: Knowing that the area of a square is length*width, in this case because the figures are squares, the length and the width are both the same number. From this, we can tell that for figure 45, the length is 45 and so this the width. The one square in the corner is both the length and the width so this is why we take 1 away or -1.

By using normal distribution of probability, it can be inferred that

For [tex]x_1 = 325[/tex], z = -1.5

This means  325 is 1.5 standard deviation below the mean.

For [tex]x_2 = 366.21[/tex], z = -1.1385

This means 366.21 is 1.1385 standard deviation below the mean.

[tex]x_1 = 325[/tex] is 1.5 standard deviation below the mean.

[tex]x_2 = 366.21[/tex] is 1.1385 standard deviation below the mean.

What is normal distribution of probability?

Normal distribution of probability is a continuous type probability distribution whose probability density function is given by-

[tex]f(x) = \frac{1}{\sigma \sqrt{2\pi}}}e^{-\frac{z^2}{2}[/tex]

where  [tex]z = \frac{x - \mu}{\sigma}[/tex], [tex]\mu[/tex] is the mean and [tex]\sigma[/tex] is the standard deviation.

For [tex]x_1 = 325[/tex]

[tex]z = \frac{325 - 496}{114} = -1.5[/tex]

This means  325 is 1.5 standard deviation below the mean.

For [tex]x_2 = 366.21[/tex]

[tex]z = \frac{366.21 - 496}{114}[/tex] = -1.1385

This means 366.21 is 1.1385 standard deviation below the mean.

[tex]x_1 = 325[/tex] is 1.5 standard deviation below the mean.

[tex]x_2 = 366.21[/tex] is 1.1385 standard deviation below the mean.

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Answer:

---------------------------

Answer:

Step-by-step explanation:

1) v + 8w = 4v, for v?

→ v + 8w = 4v

→ 8w = 4v - v

→ 8w = 3v

→ [ v = (8w)/3 ]

Thus, value is (8w)/3.

2) -m + 5n = -2, for n?

→ -m + 5n = -2

→ 5n = -2 + m

→ 5n = m - 2

→ [ n = (m - 2)/5 ]

Thus, value is (m - 2)/5.

Answer:

The answer is x=4.5

Step-by-step explanation:

I hope this helps

Answer:

Step-by-step explanation:

Here by using the ascending property:

-75, -28, -3, 13, 103, 341, 619

Answer:

30

Step-by-step explanation:

3/8 is less than 1.

30 is much greater than 1.

Answer: 30

Answer:30 is greater

Step-by-step explanation:

A solution to this inequality |y + 4| < 1 in as an interval is: A. −5 < y < –3.

An inequality simply refers to a mathematical relation that can be used to compare two (2) or more numerical values, numbers, and variables in an algebraic equation, especially based on any of the following inequality symbols:

Adding -1 to both sides of the inequality, we have:

|y + 4| + (-1) < 1 + (-1)

|y + 4| - 1 < 0

Evaluating the absolute value function, we have the following:

y + 4 < ±1

For the positive interval, we have:

y < -4 + 1

y < -3

For the negative interval, we have:

y < -4 - 1

y < -5

Finally, we would express the solution to this inequality as an interval as follows:

-5 < y < -3.

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Complete Question:

What is a solution to this inequality |y + 4| < 1?

A. −5 < y < –3

B. –3 < y < 5

C. –4 < y < 1

D. 1 < y < 4

1) y = 3x+2, where slope is 3 and point is(3, -5).

2) y+6 = 4(x-5) is the equation for the given slope and point.

                      y = mx + b

                       Slope = m = tan θ = (y2 - y1)/(x2 - x1)

1) y + 5 = 3(x-1)x-x

Compare this equation to y - y₁ = m(x - x₁)

y = 3x - 3 + 5

y = 3x + 2

2) Given:

Slope = 4; point (5, -6)

y - y₁ = m(x - x₁)

y + 6 = 4(x -5 )

Option A

Hence, i) y = 3x+2, where slope is 3 and point is(3, -5) and ii) y+6 = 4(x-5) is the equation for the given slope and point.

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The money was spent on a pass and lunch for each student is $28.07

It was stated that the the school spends 654.84 dollars on passes for 32 students and 2 teachers while the school also spends 281.92 dollars on lunch for just the students.

Therefore the amount spent on pass will be:

= Total amount / Number of people

= 654.84 / 34

= 19.26

The amount spent on each student will be:

= 281.92 / 32

= 8.81

The amount spent in pass and lunch will be:

= 19.26 + 8.81

= $28.07

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a) The test statistic is: t = -7.44.

b) The p-value is: < 0.0001.

c) The conclusion is that the null hypothesis is rejected.

d) The final conclusion is that there is sufficient evidence to conclude that the mean prediction error is different of zero.

From the pop-up shown at the complete problem given by the image at the end of the answer, the test statistic and the p-value are given as follows:

The conclusion regarding the null hypothesis is to reject the null hypothesis, as the test statistic has an absolute value less than the critical value, as we are using a two-tailed test, comparing if the mean is different of zero.

Considering that the null hypothesis is rejected, and also that the p-value is less than the significance level of 0.05, there is sufficient evidence to conclude that the mean prediction error is different of zero.

The pop-ups with the information of the test are given by the image at the end of the answer.

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The amount that $100 will be able to buy in 20 years, given an inflation rate of 4% is $44.20

When given the inflation rate, know that this rate is the rate at which the value of money decreases per year.

If given a rate of 4% as inflation, then the value of a dollar would decrease by 4% a year.

In 20 years therefore, the value of $100 would be:

Value in 20 years = Value today x (1 - inflation rate) ^ number of years

= 100 x (1 - 4%) ²⁰

= $44.20

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The y-intercept of a line that has a slope of and passes through points (8, 3) is (0,1).

what is the slope-intercept?

A method of formulating a line's equation that makes it simple to identify the slope and y-intercept is known as the slope-intercept form. The point where the line crosses the y-axis is known as the y-intercept, and the slope refers to how steep the line is.

The slope-intercept form: y = mx + b

m - a slope

b - y-intercept

Here, we have

A slope m = 1/4.

Substitute: y = 1/4 x + b

We know that

the line passes through the point (8, 3) → x = 8, y = 3.

Put the values of x and y into the slope of the line:

1/4 · 8 + b = 3

2 + b = 3 |-2

b = 1

Hence, the y-intercept is (0, 1)

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Answer:_______________________________

Answer: f (x)= -2x + 4

As per the concept of transformation, the image of the polygon after a reflection in the line y = - x is has vertices at A(0,-2), B(-4,-3), C(-4,-6), D(0,-5) as shown in the diagram attached below.

Transformation:

Transformation refers the movement of a point from the initial location to a new location. Types of transformation is rotation, reflection, translation and dilation.

Given,

Here we have the vertices A(2, 0), B(3, 4), C(6, 4), D(5, 0) and the equation for line y = -x.

Now we have to plot the graph  with the given vertices and its image after a reflection in the line y = -x .

Here reflection refers flipping of a figure.

Therefore, if a point A(x, y) is reflected about the line y = - x, the new point would be at A'(-y, -x)

For the given the polygon with vertices at A(2, 0), B(3, 4), C(6, 4), D(5, 0) and the image of the polygon after a reflection in the line y = -x has vertices at:

A(0,-2), B(-4,-3), C(-4,-6), D(0,-5)

The image of the polygon is attached below.

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The unit rate of the equation y = -4x + 2 is -4

From the question, we have the following equation

y = -4x + 2

The above equation is a linear equation

Linear equations are represented as

y = mx + c

Where

When the equations y = mx + c and y = -4x + 2 are compared, we have

Unit rate, m = -4

Y-intercept, c = 2

Note that all linear equations have a constant rate of change

Hence, the unit rate in the linear equation is -4

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By doing addition and subtraction of integers, the result obtained is

Mohammed had $5290 at the end of the month

What is addition and subtraction of integers?

At first it is important to know about integers

Integers are those numbers which has no fractional part. Integer can be positive, negative and zero is also an integer.

Suppose there are many integers, and we need to find the sum total of all those integers, then the operation used in this case is called addition.

To find how big or small one integer is from the other, then the operation used is called subtraction of integers.

Here we will use addition and subtraction of integers

Bank balance of Mohammed = $8376

Amount of money taken out by Mohammed next month to buy a car = $4595

Amount of money needed to buy new tires for his car = $1200

Amount of salary received by Mohammed next day = $2709

Amount of money Mohammed had at the end of the month =

$(8376 - 4595 - 1200 + 2709)

= $5290

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Answer:

I = (2350)(0.0277)(6)

Step-by-step explanation:

We're told the principal, rate, and time so we just plug in.

We must convert the 2.77% to a decimal by moving the period two places to the left to get the rate 0.0277

The equation of line passing through points (4,−2) and (8, 3) is 4y - 5x + 28 = 0

A straight line can be written in the form of equation as, y = mx + c.

Two straight lines intersect each other only at one point.

When two straight lines are parallel to each other the angle between them is zero.

Given pair of points are  (4,−2) and (8, 3).

The equation of line passing through two points (x₁, y₁) and (x₂, y₂) is given as,

y = ((x - x₁) / (x₁ - x₂)) (y₁ - y₂) + y₁

Substitute the respective values to get the equation of line as,

y = ((x - 4 ) / (4 - 8)) (-2 - 3) + (-2)

y = ((x - 4 ) / 4) × 5 - 2

4(y + 2) = 5(x - 4)

4y - 5x + 28 = 0

Hence, the equation of line for the given points is 4y - 5x + 28 = 0.

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The number of cupcakes sold will be 4.

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, in the first hour, Brady sold 1/3 cupcakes and Jaquan sold 3/8 cupcakes. During the second hour, they sold 2 cupcakes. During the third hour, they sold 75% of the remaining cupcakes. During the fourth hour, they sold the remaining 3 cupcakes.

The number of cupcakes sold will be,

N = (1/3) + (3/8) +[(2-1/3-3/8)]+3

N = (1/3)+(3/8) + (7/24)

N = 96 / 24

N = 4

Therefore, the number of cupcakes sold will be 4.

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Answer:

??

Step-by-step explanation:

where are the equations ?

Answer:

Step-by-step explanation:

Answer: 231 thousand

Step-by-step explanation:

given,

total number of undergraduate students enrolled = 414000

let us take number of total number of male students as, X

then, total number of female students will be X + 48000

now we get,

total number of male students + total number of female students = total number of students enrolled.

X + (X + 48000) = 414000

X + X + 48000 = 414000

2X = 414000 - 48000

X = 366000/2

X = 183000

total number of male students is 183000

total number of female students is

X + 48000

183000 + 48000 = 231000