Question 8 of 25
Which of the following is the quotient of the rational expressions shown here?

Hello,

"perpendicular to the line y= - 1/2x +4 "

so y = -1/2x + p

-1/2 × 6 + p = 4 ⇔ -3 + p = 4 ⇔ p = 4 + 3 = 7

y = -1/2x + 7

There are 7,800 different passwords.

Here we need to count the number of options for each of the digits of the password.

The first character has 26 options (26 letters in the alphabet).

The second character has 10 options (ditis from 0 to 9), and also does the third character

The fourth character has 3 options (%,*, or #)

The total number of different passwords that can be generated is given by the product between the numbers of options, so we have:

C = 26*10*10*3 = 7,800

There are 7,800 different passwords.

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Answer:

C. 0 ≤ y ≤ 7

Step-by-step explanation:

Range is the interval of the numbers on the y-axis. The numbers go from y-value 1 to y-value 7. Since the circles at the ends are closed, this means 0 and 7 are included in the range, so ≤ is included instead of <.

Answer:

862

Step-by-step explanation:

4 x 2 = 8

3 x 2 = 6

8 + 6 + 2 = 16

The empty cells in the table by determining all terms, constants, and coefficients for both algebraic expressions will be:

In the first expression, the equation is given as 4a² - 5a - 3 while in the second expression, the equation is given as 7(-3x + 5) + 11y.

In this second expression, the term is 7(3x + 5), 11y. The constants are -7 and 5. Lastly, the coefficients are -3, and 11.

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The answers are

We have the cost function in this question to be

C(x) = 60x+300

We have the function of the revenue to be

Revenue = 100x−0.5x²

A. The formula for revenue function is given

revenue - cost

This is expressed as

= (100x−0.5x²)-60x+300

We have to collect like terms and open the equation above.

This given us:

B. when profit = 50$

We have p = 40x-0.5x²-300

50 = 40x-0.5x²-300

Multiply the two sides by 10

This gives

500 = 400x - 5x² - 3000

This gives a quadratic equation

5x² - 400x - 3500 = 0

To solve the equation you have to make use of a quadratic calculator.

This gives us the values

c. We have  P =  40x-0.5x²-300.

at P = 2500

2500  =  40x-0.5x²-300.

Multiply the equation by 10

25000 = 400x - 5x² - 3000

collect like terms

400x - 5x2 - 3000 +28000

400x -5x2 +28000

We have to take the discriminant

-400² - 4*5*28000

= -400000

The discriminant is negative hence it is not possible.

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The amount of money that is saved by purchasing the projector at Office and beyond is $144.

The first step is to determine the price of the projector at The Office spot.

Discounted price : (1 - 0.20) x $1200

0.80 x $1200 = $960

The second step is to determine the price of the projector at the Office and Beyond.

Discounted price : (1 - 0.15) x $960 = $816

Difference in price : 960 - 816 = $144

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The forecast for week 13 is 9.7%

a) MAD without the forecast = 43.71

MAD with the forecast = 45.59

b) MAPE = 0.097

MAPE= 9.7%

642 602 656 747 663 618 731 726 679 737 664 740

Mean Absolute deviation is given as

MAD = [Σ|x - μ|]/N

We first calculate the mean

Mean = Σx/N

Mean = (642+602+656+747+663+618+731+726+679+737+664+740)/12

Mean = (8205/12)

Mean= 683.75

absolute deviations from the mean

|642-683.75| + |602-683.75| + |656-683.75| + |747-683.75| + |663-683.75| + |618-683.75| + |731-683.75| + |726-683.75| + |679-683.75| + |737-683.75| + |664-683.75| + |740-683.75|

Absolute deviations from the mean

41.75+81.75+27.75+63.25+20.75+65.75+47.25+42.25+4.75+53.25+19.75+56.25= 524.5.

MAD = [Σ|x - μ|]/N

MAD = (524.5/12)

MAD = 43.71

If we include the forecast for the 13th week

642 602 656 747 663 618 731 726 679 737 664 740 747

Mean = (8205+747)/13

Mean = 688.62

absolute deviations from the mean

|642-688.62| + |602-688.62| + |656-688.62| + |747-688.62| + |663-688.62| + |618-688.62| + |731-688.62| + |726-688.62| + |679-688.62| + |737-688.62| + |664-688.62| + |740-688.62| + |747-688.62|

Absolute deviations from the mean

=46.62+86.62+32.62+58.38+25.62+70.62+42.38+37.38+9.62+48.38+24.62+51.38+58.38

= 592.62

MAD = (592.62/13)

MAD = 45.59.

b) MAPE is used to check forecast errors

MAPE = (1/N) Σ [|x-f|/x]

where N = Sample size = 12

x = each variable

f = the forecasted value = 747

x = 642, 602, 656, 747, 663, 618, 731, 726, 679, 737, 664, 740

Σ[|xf|/x]=0.164+0.241+0.139+0+0.112+0.209+0.022+0.029+0.100+0.014+0.125+0.009

Σ [|x-f|/x] = 1.164

MAPE = (1.164/12)

MAPE = 0.097

MAPE=9.7%

The forecast for week 13 is 9.7%.

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Answer:

30-5×2 of 3+(19-3) ÷8

Step-by-step explanation:

30-5×6+(19-3)÷8

30-5×6+16÷8

30-30+8

38-30

8

Answer:

Step-by-step explanation:

b

The total number of pies they made altogether is 100.

In order to determine this value, add the number of blueberry pies with the number of apple pies.  Addition is the mathematical operation that is used to determine the sum of two or more numbers.

The total number of pies = 55 + 45 = 100 pies

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Answer:

41.83 inches

Step-by-Step Explanation:

You have to trust me. I helped my brother with this.

The length of the shortest side of the hexagon is approximately 41.83 inches

Let's denote the length of the shortest side of the hexagon as "x" inches. According to the given information, each side of the hexagon is 10 inches longer than the previous side.

So, the lengths of the sides of the hexagon can be expressed as follows:

First side: x inches

Second side: (x + 10) inches

Third side: (x + 20) inches

Fourth side: (x + 30) inches

Fifth side: (x + 40) inches

Sixth side: (x + 50) inches

To find the perimeter of the hexagon, we sum up the lengths of all the sides:

Perimeter = x + (x + 10) + (x + 20) + (x + 30) + (x + 40) + (x + 50)

We know that the perimeter is given as 401 inches, so we can set up the equation:

401 = x + (x + 10) + (x + 20) + (x + 30) + (x + 40) + (x + 50)

Simplifying the equation:

401 = 6x + 150

Subtracting 150 from both sides:

251 = 6x

Dividing both sides by 6:

x = 251/6

Therefore, the length of the shortest side of the hexagon is approximately 41.83 inches (rounded to two decimal places).

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The volume of the sawdust pile is 11,039.06 ft³.

The shape of the sawdust pile would be a cone. The diameter is always proportional to its height.

Diameter = k x height

where k is equivalent to the rate of increase of the diameter with respect to the increase in height.

25= k20

k = 25 / 20

k = 1.25

Diameter when height is 30 ft = 1.25x 30 = 35.50 feet

Volume of the sawdust = [tex]\frac{1}{3}[/tex]πr²h

Where:

[tex]\frac{1}{3}[/tex] x 3.14 x 18.75² x 30 = 11,039.06 ft³

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The reason that would support that is ∠B ≅ ∠B , the reflective property of equality.

Similar triangles are triangles that have their corresponding angles equal and the ratio of their corresponding lengths also equal.

Analysis:

triangle BDE and BAC share the same angle B

which means ∠DBE = ∠ABC.

The reflective property of equality says a number is always equal to itself. Therefore, ∠B ≅ ∠B

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The future value is $10,354.72.

The total interest earned is $754.72.

When an amount is compounded quarterly, it means that both the amount deposited and interest already earned increases in value every quarter.

The future value = quarterly deposit x annuity factor

Annuity factor = {[(1+r)^n] - 1} / r

Where:

Annuity factor = [1.01^16) - 1 ] / 0.01 = 17.26

17.26 x 600 = $10,354.72

Total interest earned = future value - total amount deposited

Total amount deposited  = $600 X 4 X 4 = 9600

$10,354.72 - 9600 = $754.72

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Step-by-step explanation:

[tex]y = log_{4}( {x}^{4} ) [/tex]

Swap x and y.

[tex]x = log_{4}( {y}^{4} ) [/tex]

Solve for y.

[tex]x= 4 log_{4}(y) [/tex]

[tex] \frac{1}{4} x = log_{4}(y) [/tex]

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

So the inverse is

[tex]4 {}^{ \frac{x}{4} } = f {}^{ - 1} (x)[/tex]

The value of f(g(7)) is 20

The functions are given as:

f(x) = x^2 + x

g(x) = x - 3

Start by calculating g(7)

g(7) = 7 - 3

Evaluate

g(7) = 4

So, we have:

f(g(7)) = f(4)

Substitute 4 for x in f(x) = x^2 + x

f(4) = 4^2 + 4

Evaluate

f(4) = 20

Hence, the value of f(g(7)) is 20

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The value of x in the equation is 2.

Indices singular index is a branch of algebra that deals with the power or exponent of variables.

Laws of indices help us to evaluate indicial expressions and equations.

Analysis:

[tex]4^{8-2x}[/tex] = 256

Here 4 is the base number while 8-2x is the exponent or index.

So for us to evaluate this, we need to write 256 in its index form having its base as 4 also.

so 256 in base 4 index form is [tex]4^{4}[/tex]

[tex]4^{8-2x}[/tex] = [tex]4^{4}[/tex]

since both sides have the same base number, we equate only their exponent

8-2x = 4

-2x = 4 - 8

-2x = -4

x = -4/-2 = 2

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Step-by-step explanation:

as speed is always

distance/time

we need to multiply speed by the time traveled to get the distance traveled.

so,

d = 95t + 65

after all, until it reached the city it traveled already 65 miles (we don't know the speed, but it does not matter for the question about the total distance traveled), which we need to add to get the total distance.

Answer:

84 degrees

Step-by-step explanation:

Angle A = 83 degrees

Angle B = x degrees

Angle C = 135 degrees

Angle CDE = 122 degrees

We know that the four inner corners of a quadrilateral should add up to 360 degrees. Two supplementary angles will add up to 180 degrees. Adjacent angles on a straight line will always be supplementary. Knowing this, just solve for <ADC and add that amount to <A and <C. Then, subtract that sum from 360 degrees.

<ADC = 180-122 = 58

58+83+135 = 276

360-276 = 84 degrees

Answer:

288

Step-by-step explanation:

[tex]26 * 8+(2^{6} +2^{4} )\\\\208+(64+16)\\208+80[/tex]

Answer:

288

Step-by-step explanation:

PEMDAS

Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.

Parentheses and Exponents:

(26) x 8+(64+16)          (28) x 8+(80)

Multiplication:

26 x 8 + 80       208+80

Addition:

208+80= 288

The factor of the polynomial f(x) = x⁴ - 4x³ + 3x² + 4x -4 are x = -1, x = 1 and x = 2.

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the function  f(x) = x⁴ - 4x³ + 3x² + 4x -4. The factor of the polynomial f(x) = x⁴ - 4x³ + 3x² + 4x -4 are x = -1, x = 1 and x = 2.

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In statistics, a Chi-squared test may be used to determine holiday choice and gender and α (alpha) is the response variable.

A statistical technique called the chi-square test is used to compare actual outcomes with predictions.

The goal of this test is to establish if a discrepancy between actual and predicted data is the result of chance or a correlation between the variables you are researching.

Whether there is a statistically significant association between categorical variables is determined by the Chi-square test of independence.

This issue is addressed by a hypothesis test. The chi-square test of association is another name for this assessment.

Hence,in stats would a test looking at gender & holiday preference yes you can do  a Chi-squared test and α(alpha) is the response variable.

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The range of the averages in a class with a maximum point of 100 point and a minimum point of 20 point is 80 points

An equation is an expression that shows the relationship between two or more numbers and variables.

Range is the difference between the maximum value and minimum value of a data set. Hence:

Range = Maximum - Minimum

Let us assume that the maximum point is 100 point and the minimum point is 20 point, hence:

Range = 100 - 20 = 80 points

The range of the averages in a class with a maximum point of 100 point and a minimum point of 20 point is 80 points

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Answer:

4^2+4

Step-by-step explanation:

one 2 and two 4s

so 4^2+4=16+4=20

so 4^2+4

(calculation)

Answer:

a & c

Step-by-step explanation:

Answer:

B) Point (1, 1) is a solution because it is one of the points on the line already graphed.

D) Point (20, 58) is a solution because it results in a true statement when the point values are substituted into the equation of the line.

E) When the other line in the system is graphed, it will share all points with the line already graphed.

Step-by-step explanation:

x is powering both numbers so it can be outside the parenthesis.

We have given that 3^x.

An expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

The first one isn't an answer because 3^x is exponential while x^3 is a cubic function.

If you draw them you will see that they are very different.

B is correct because we can divide both numerator and denominator by 6 and we get 3^x.

C is not correct because x is not powering 3 so we cannot divide both by 6D is correct because 3^(x-1) is the same as

and when multiplied by 3 we get 3^x

3^x*3^(-1) = 3^x/3

E is not correct.

will understand after the explanation in DF is correct.

x is powering both numbers so it can be outside the parenthesis.

The question is incomplete the complete question is,

Which expressions are equivalent to the one below? Check all that apply.

3^x

A. x^3

B.(18/6)^x

C.18^x/3

D.3(3^(x-1))

E.3(3^(x+1))

F.18^x/6^x

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The required  exponential function that contains the points (3,24) and (4,48) is y = 3(2)^x

The standard exponential function is expresses as y = ab^x

Given the coordinate points (3,24) and (4,48), the equivalent equations are:

24 = ab^3 ......... 1

48 = ab^4

Take the ratios

48/24 = b^4/b^3

2 = b

Substitute b = 2 into equation 1

24 = a(2)^3

8a = 24

a = 3

Hence the required  exponential function that contains the points (3,24) and (4,48) is y = 3(2)^x

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Answer:

a. 17

b. 30

c. 5

Step-by-step explanation:

English (E) = 28 - 15 (10+8-3) = 13

Amharic (A) = 30 - 10 (8+5-3) = 20

Afan Oromo (AO) = 42 - 12(10+5-3) = 30

E+AO = 10

E + A = 8

A + AO = 5

A + AO + E = 3

a. 13 people spoke just English+ 20 people who just spoke Amharic + 30 people who just spoke Afan Oromo+ The multilingual people (10+8+5-3=20) which is 83, so that means that 17 learned no language.

b. 42 People learned Afan Oromo, but only 30 of them learned that language separately. 10 People learned it along with English, and 5 learned it with Amharic. However, 3 of those people were the same, so 12 people of those 42 spoke multiple languages. Therefore, only 30 people spoke just Afan Oromo.

c. This one is kinda just a trick question, they want you to overthink it because of the 3 who learned all, but it's just 5 like it says in the question.

Answer: x>-5

Step-by-step explanation:

add 4 to both sides

5x-4+4<11+8x+4

simplify

5x<8x+15

subtract 8x from both sides

5x-8x<8x+15

simplify

-3x<15

divide both sides by -3 and switch inequality sign

-3x/-3>-15/-3

x>-5

[tex]\large\displaystyle\text{$\begin{gathered}\sf 5x-4 < 11+8x \end{gathered}$}[/tex]

Simplify both sides of the inequality.

[tex]\large\displaystyle\text{$\begin{gathered}\sf 5x-4 < 8x+11 \end{gathered}$}[/tex]

Subtract 8x from both sides.

[tex]\large\displaystyle\text{$\begin{gathered}\sf 5x-4-8x < 8x+11-8x \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf -3x-4 < 11 \end{gathered}$}[/tex]

Add 4 to both sides.

[tex]\large\displaystyle\text{$\begin{gathered}\sf -3x-4+4 < 11+4 \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf -3x < 15 \end{gathered}$}[/tex]

Divide both sides by -3.

[tex]\large\displaystyle\text{$\begin{gathered}\sf \frac{-3x}{-3} < \frac{15}{-3} \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf x > -5 \ \ \iff \ \ \ Answer \end{gathered}$}[/tex]