Bob bought a sofa on sale for $134.40. This price was 68% less than the original price. What was the original price?

The equation of line b that passes through the point (-3,2) is  y=-1/4x+5/4

to get the equation of a line given a point and its slope.

Recognize the slope.

Decide on the point.

In the point-slope form, y y 1 = m (x x 1), substitute the values. y − y 1 = m (x − x 1) .

Slope-intercept form should be used to write the equation.

There are three major forms of linear equations: point-slope form, standard form, and slope-intercept form.

In the above question we see that,

The line b passes through the point (-3,2)

the equation of line should satisfy this point

In the given option the only line that satisfy the point is

option C

y=-1/4x+5/4

hence option C ,y=-1/4x+5/4 is the answer

To learn more about lines, click the following link:-

https://brainly.com/question/18831322

#SPJ1

Answer:

a) (7-2x) +3 = 10 - 2X

b) x = y + 3 <=> y = x-3

c) (x-3).-2 +7 = -2x +6 +7 => -10 + 13 = 3

The graph of the inequality y > 4x - 3  , 3y - x ≤ 9 . is shown below.

In the question ,
the inequalities are given ,

we have to graph given inequalities ,

the inequalities are y > 4x - 3

3y - x ≤ 9 .

in the first inequality , y > 4x - 3

we put x = 0 , y is = -3 .

we put y = 0 , x is = 3/4 .

So ,the points for the line will be  (0,-3) and (3/4,0) .

since the inequality does not have equal to  sign , the line will be a dotted line .

in the second inequality ,3y - x ≤ 9 .

we put x = 0 ,  y is = 3 .

we put y = 0 ,  x is = -9 .

the points for the line will be (0,3) and (-9,0).

Since the inequality has equal to sign . Thus, line will be solid line .

Therefore , the for the given inequality is shown below.

Learn more about Inequality here

https://brainly.com/question/22922637

#SPJ4

Step-by-step explanation:

-1/2h(2h+3) = 0

Seperate the equation:

-1/2 = 0

h = 0

(2h+3) = 0

Subtract 3 from both sides:

2h+3 = 0

2h+3-3 = 0

Simply:

2h = -3

Final Answer:

h = 0

h = -3/2

Answer:

12 row plans

Step-by-step explanation:

the first seat has two possible options , the two directors. The second seat has another two options. With each director comes 2 options for the second seat so 2×2=4 possible options for the first and second seat . The 3rd seat has three options, that means for each combination of the 1st and 2nd seat three possible options 2×3=12 combinations

Answer:

26

Step-by-step explanation:

To find the value of the expression 2|x-4|-3y³ when x=3 and y=-2, we need to substitute the values of x and y into the expression and then simplify. The absolute value part of the expression, |x-4|, is the distance between the number x and 4 on the number line. When x=3, this distance is |3-4|=1. So the expression becomes 2*1-3(-2)³ = 2-3(-8) = 2+24 = 26. Therefore, when x=3 and y=-2, the value of the expression 2|x-4|-3y³ is 26.

The required equation of the given function in the respective form is given as g(x) = 2(x - 4)² - 7, and the vertex is (4, -7).

The graph is a demonstration of curves that gives the relationship between the x and y-axis.

Here,
g(x) = 2x² - 16x + 25
g(x) = 2[x² - 8x] + 25
g(x) = 2[x² - 8x + 16 -16] + 25
g(x) = 2(x - 4)²  - 32 + 25
g(x) = 2(x - 4)² - 7

Now, the vertex is given as (h, k) = (4, -7).
And the graph of the given function is shown.

Thus, the required equation of the given function in the respective form is given as g(x) = 2(x - 4)² - 7, and the vertex is (4, -7).

Learn more about graphs here:

brainly.com/question/16608196

#SPJ1

By using the method of eigenvalues and eigenvectors, the long-term probability that a given marked rat is in room 4 is 1/3

Here we have given that Forty rats are placed at random in a house having 4 rooms. There is one door between rooms 1 and 2, one door between rooms 1 and 4, one door between rooms 2 and 4, one door between rooms 2 and 3, and two doors between rooms 3 and 4 see the book for a picture). There are no doors between rooms 1 and 3. After each minute, a rat may change rooms, or stay still.

And we need to find the the long-term probability that a given marked rat is in room 4.

By using the eigenvalues method, we know that

Room 4 has the 3 exits that is from Room 1, Room 2 and Room 3.

So, here we have 3 possibilities for the exit so, the rat can choose any one these three ways,

So, the probability can be written as,

=> 1/3

To know more about Probability refer to:

http://brainly.com/question/11234923

#SPJ4

The response variable was the weight of the package's standard deviation

a)the generator for this design is E=-ABCD

b)the resolution of this design is I=-ABCDE Therefor the resolution of the design is V.

c)estimate the factor effects there is 3 larger effcts namely E=-0.4700,BE=-0.4050,DE=-0.3150

d)Construct a linear regrassion model.The constant is estimated by the grand average and the regression coefficent are estimated by one-half the corresponding effect estimates.

If the underlying assumptions have any issues, the residual analysis will show them.

Y=1.22625+0.04375x₂-0.01875x₄+0.2350x₅-0.08125x₂x₄-0.1575x₄x₅

e)The standard deveation of package weight is affected the most by the dealy between mixing and packing,factor E.Also, its intreaction with the temperature factor B,BE and with the batch weight factor D,DE are important.

Learn more about standard deveation here:

brainly.com/question/28210741

#SPJ4

The grade needed by Kim on the fourth test to have the average of 80% is 89%  , the correct option is (d)  .

In the question ,

it is given that ,

the scores that Kim got in the first three tests are 82% , 75% , 74% .

let the grade required by Kim to score average of 80% be = x% .

Since Kim needs to score average of 80% in all the four tests ,

that means ,

(82 + 75 + 74 + x)/4 = 80

After Simplifying further further ,

we get ,

(231 + x)/4 = 80

231 + x = 80 × 4

231 + x = 320

x = 89% .

Therefore , Kim needs to score 89% in the fourth test .

Learn more about Average here

https://brainly.com/question/14685333

#SPJ4

The domain of the function is: [0,∞), the range of the function is: [3500,∞)

Domain and Range: The set which contains all the first elements of all the ordered pairs of relation R is known as the domain of the relation. The set which contains all the second elements, on the other hand, is known as the range of the relation.

The potential input and output values of a function are its domain and range, respectively.

The formula for the function is C=130S+3500.

the region

This is a list of the function's potential S values.

Due to the fact that S refers to a physical quantity, it cannot be less than 0. (i.e. tons of sugar)

The domain of the function is [0,∞)

Since S can have any value larger than 0.

The variety

This represents the function's potential C values.

The formula for the function is C=130S+3500.

Assuming S = 0, the following is true: C=130*0+3500=3500.

C must be more than 3500.

Any number higher than 3500 can be used as the value of C.

Consequently, the function's range is [3500,∞)

To learn more about Domain and Range visit:

brainly.com/question/28135761

#SPJ4

Answer:

12.244 cm long

Step-by-step explanation:

The area of a rectangle is equal to its height times its width, so if the piece of cardboard has an area of 66 square centimeters and is 5 centimeters longer than it is tall, we can write the following equation to represent the dimensions of the piece of cardboard:

height * (height + 5) = 66

To solve this equation, we can first divide both sides of the equation by the height of the piece of cardboard to get:

height + 5 = 66 / height

We can then subtract 5 from both sides of the equation to get:

height = 66 / height - 5

We can then multiply both sides of the equation by the height to get:

height^2 = 66 - 5 * height

We can then use the quadratic formula to solve for the height of the piece of cardboard:

height = (-5 +/- sqrt(5^2 - 4 * 1 * -66)) / (2 * 1)

The value of the square root in the quadratic formula must be positive, so we take the positive value for the height:

height = (-5 + sqrt(5^2 + 4 * 1 * 66)) / (2 * 1)

This simplifies to:

height = (5 + sqrt(61)) / 2

The height of the piece of cardboard is approximately 7.244 centimeters. Since the piece of cardboard is 5 centimeters longer than it is tall, it must be 5 + 7.244 = 12.244 centimeters long.

Therefore, the piece of cardboard is approximately 12.244 centimeters long.

(a) At 95% confidence interval z- value is 1.96 and t-value is 2.447.

(b) At 80% confidence interval z- value is 1.282 and t-value is 1.440.

(c) At 90% confidence interval z- value is 1.645 and t-value is 1.943.

Given that,

Let's say you randomly choose n=7 measurements from a normal distribution. If you were constructing the following confidence intervals, compare the standard normal z values with the appropriate t values.

We have to find

(a) At 95% confidence interval what is z- value and t-value.

(b) At 80% confidence interval what is z- value and t-value.

(c) At 90% confidence interval what is z- value and t-value.

We know that,

Sample size = n = 7

Degrees of freedom = df = n - 1 = 7 - 1 = 6

(a)  At 95% confidence level

α = 1 - 95%  

α = 1 - 0.95 =0.05

α/2 = 0.025

Zα/2 = Z0.025  = 1.96

z = 1.96

At 95% confidence level

α= 1 - 95%

α =1 - 0.95 =0.05

α/2 = 0.025

tα/2,df = t0.025,6 = 2.447

t = 2.447

(b)  At 80% confidence level

α = 1 - 80%  

α = 1 - 0.80 =0.20

α /2 = 0.10

Zα /2 = Z0.10  = 1.282

z = 1.282

At 80% confidence level

α = 1 - 80%

α =1 - 0.80 =0.20

α /2 = 0.10

tα /2,df = t0.10,6 = 1.440

t = 1.440

(c) At 90% confidence level

α = 1 - 90%  

α = 1 - 0.90 =0.10

α /2 = 0.05

Zα /2 = Z0.05  = 1.645

z = 1.645

At 90% confidence level

α = 1 - 90%

α =1 - 0.90 =0.10

α /2 = 0.05

tα /2,df = t0.05,6 = 1.943

t = 1.943

Therefore,

(a) At 95% confidence interval z- value is 1.96 and t-value is 2.447.

(b) At 80% confidence interval z- value is 1.282 and t-value is 1.440.

(c) At 90% confidence interval z- value is 1.645 and t-value is 1.943.

To learn more about interval visit: https://brainly.com/question/29197921

#SPJ4

The slope of a line that is perpendicular to it Undefined.

What is slope?

A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).

That is the only slope which cannot be defined by a number.

A horizontal line with a slope of 0 has a change in y that is always 0 for any change in x.
As long as x is not 0, m=03, 08, 0x.

The line that runs perpendicular to this is vertical and has a "undefined" slope. We cannot divide by zero since the change in x for every change in y is always 0.
m=60,−50,y0 etc.
The slope remains undefined.

To know more about Slope visit,

https://brainly.com/question/4184986

#SPJ1

For the best cases there will be 6+operations, The number of operations are best cases 6 and the worst cases are 10.

Given that,

The following pseudocode snippet performs the maximum number of + operations. Assume that the probability of each potential piece of data is equal. Preconditions: X = {x₁, x₂, x₃, x₄, x₅} ⊆ {10, 20, 30, 40, 50, 60, 70, 80}, where x1 < x2 < x3 < x4 < x5. t ← 0 i ← 1 while t < 101 do t ← t + xi i ← i + 1

We know that,

Here,

X = {x₁, x₂, x₃, x₄, x₅} ⊆ {10, 20, 30, 40, 50, 60, 70, 80}

By doing the iteration method

Iteration process till 4th iteration we get 6

Therefore, For the best cases there will be 6+operations, The number of operations are best cases 6 and the worst cases are 10.

To learn more about number visit: https://brainly.com/question/17429689

#SPJ4

The probability that the mean number of hours spent studying is less than 70 hours is; 0.023

We are given that:

Population mean; μ = 75

Population Standard deviation; σ = 25

Sample size; n = 100

The formula for the z-score is;

z = (x' - μ)/(σ/√n)

We want to find P(x < 70). Thus;

z = (70 - 75)/(25/√100)

z = -5/2.5

z = -2

From online p-value from z-score calculator, we have;

P(Z < -2) = 0.023

Read more about p-value from z-score at; https://brainly.com/question/25638875

#SPJ1

Answer:

see explanation

Step-by-step explanation:

given Δ ABD is isosceles with AB = AD then base angles are congruent, so

∠ ADB = ∠ ABD = 72°

then

∠ BAD = 180° - (72 + 72)° = 180° - 144° = 36° ( sum of angles in a triangle )

given Δ ABC is isosceles , then

∠ BCD = ∠ BAD = 36°

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠ ADB is an exterior angle of Δ BCD , then

∠ BCD + ∠ DBC = ∠ ADB

36° + ∠ DBC = 72° ( subtract 36° from both sides )

∠ DBC = 36°

So ∠ BCD = ∠ DBC = 36°

Thus the base angles of Δ BCD are congruent , then

Δ BCD is isosceles with BD = CD

The distribution is not normal. The points show a systematic pattern that is not a straight-line pattern curved over mean.

A normal distribution is a type of data distribution in which the data points form a symmetric, bell-shaped curve around the mean.

The data points in the example provided show a systematic pattern that is not a straight-line pattern, indicating that the data does not come from a normally distributed population.

This is because the points are not reasonably close to a straight line, which is a characteristic of a normal distribution.

Learn more about mean here

https://brainly.com/question/15323584

#SPJ4

In the two period consumer model , the net effect from a decrease in the interest rate for a net borrower is increase in present consumption (C1 increases) , future consumption decreases (C2 decreases) and savings decreases.

What is two period consumer model?

Hence, the net effect from a decrease in the interest rate for a net borrower is increase in present consumption (C1 increases) , future consumption decreases (C2 decreases) and savings decreases.

To know more about income check the below link:

https://brainly.com/question/28735352

#SPJ4

Answer:

sqrt2

Step-by-step explanation:

csc (x)= 1/sin(x)

sin(x)= (sqrt22)/(sqrt22*sqrt2)= 1/sqrt2

1/(1/sqrt2)=sqrt2/1=sqrt2

a) The maximum mean weight of the passengers is 187.5 lb.,b) The probability that the mean weight exceeds 187.5 lb is 0.0062.

The mean weight of each passenger is 198 lb and the standard deviation is 42 lb. The water taxi has a stated capacity of 25 passengers and a load limit of 3750 lb. The maximum mean weight of the passengers is 187.5 lb, which is determined by the load limit of 3750 lb divided by the stated capacity of 25 passengers. The probability that the mean weight exceeds 187.5 lb is 0.0062, which is calculated using the normal distribution table. If the capacity is revised to 20 passengers, the maximum mean weight is still 187.5 lb. The probability of the mean weight exceeding 187.5 lb is still 0.0062. The probability that an individual passenger exceeds the maximum load limit of 3750 lb is 0.0228, which is calculated using the normal distribution table.

Learn more about probability here

https://brainly.com/question/11234923

#SPJ4

Answer:

20(3-2y)

Step-by-step explanation:

60−40y =

10(6-4y) =   ==> both 60 and 40 are multiples of 10

2(10(3-2y)) =  ==> both 6 and 4 are factors of 2

2*10(3-2y) = ==> simplify

20(3-2y)

Answer:

El ecuación es y = 3x + 2

Step-by-step explanation:

Lo primero que tienes que hacer es poner 3x - y = 8 en la forma y = mx + b para para saber que 'm'. Porque la ecuación que intentamos escribir es paralela a 3x - y = 8, entonces tienen la misma pendiente (m).

3x - y = 8

-3x        -3x

-y = -3x + 8

/-1    /-1     /-1                   dividir todo por -1 para hacer 'y' positivo.

y = 3x - 8

Y como sabemos que la ecuación pasa por (7, 2), sabemos que pasa por 2 en el y-axis (vertical). Entonces 2 es el intercepto en y (b).

The Shannon's %Net market contribution = 40%

What is NMC (Net market contribution)?

Net market contribution (NMC) is equal to total sales revenue less total costs (except market costs) minus market costs.

Cost overall (not including market expenses):

150000 packaged (in cans and bottles).

Kegs =80000

WIP Loss/Reduction = 42000

Labor Contracts = 9000

Total Direct Labor: 240000

18000 inbound pounds

180000 in compensation

Total= 719000

Consumer advertising costs 26850 on the market.

Marketing for trade = 31761

Promotional Sales = 18000

Total=76611 Net market contribution=1320271-719000-76611=$ 524660 %NMC=524660/1320271=0.3974=39.74%=40%

To learn more about the Net market contribution from the given link

https://brainly.com/question/16829947

#SPJ1

it is 6.1

Step-by-step explanation:

Answer:

x = 56

Step-by-step explanation:

[tex]\frac{3}{7}[/tex] x + [tex]\frac{1}{4}[/tex] x = 38  The common denominator would be 28

[tex]\frac{12}{28}[/tex] x + [tex]\frac{7}{28}[/tex] x =38                                                                                                                                                

[tex]\frac{19}{28}[/tex] x = 38  Multiply both sides by [tex]\frac{28}{19}[/tex]

[tex](\frac{28}{19})[/tex][tex]\frac{19}{28}[/tex] x = [tex](\frac{28}{19})[/tex][tex]\frac{38}{1}[/tex]  Cross cancel the 19 and 38.  

x = [tex](\frac{28}{1})[/tex][tex]\frac{2}{1}[/tex]

x = 56

The transformed graph is attached

The domain is (-∝, ∝) and the range is (-3, ∝)

From the question, we have the following parameters that can be used in our computation:

y = eˣ

To transform the graph to y = e⁻ˣ - 3, we make use of the following rules:

See attachment for the graph of y = e⁻ˣ - 3

From the attached graph, we have:

The graph extends across the x-axis i.e. domain = (-∝, ∝)

The graph opens upward from y > -3 i.e. range = (-3, ∝)

Read more about domain and range at

https://brainly.com/question/2264373

#SPJ1

The probability distribution for the statistic is ; for m = 0 , P(0) =  0.216  , for m = 5 ,P(5) = 0.296 and for m = 10 , P(10) = 0.488  .

In the question ,

it is given that ,

the box has 10 sealed envelopes , that contains number from 1,2,...,10 .

the first six envelopes has no money .

next two envelopes has $5

and the last two contains $10 bill .

if x₁, x₂, and x₃ denote the amounts in the selected envelopes,

the statistic of interest is m = maximum of X₁ , X₂ and X₃ .

we need to find probability distribution for the statistic m,

So , P(m = 0) = P( all three envelope contains no money) = (6/10)³ = 0.216

and P(m = 5) = P( all from 8 envelope which contains at most $5) - P(all three envelope with 0 money)

= (8/10)³ - 0.216

= 0.296

and P(m = 10) = 1 - (8/10)³ = 0.488

Therefore , the required probability is P(0) = 0.216 ,   P(5) =  0.296 and P(10) = 0.488  .

The given question is incomplete , the complete question is

A box contains ten sealed envelopes numbered 1, . . . , 10. the first six contain no money, the next two each contains $5, and there is a $10 bill in each of the last two. a sample of size 3 is selected with replacement (so we have a random sample), and you get the largest amount in any of the envelopes selected. if x₁, x₂, and x₃ denote the amounts in the selected envelopes, the statistic of interest is M = the maximum of X₁ ; X₂ , and X₃ .  Obtain the probability distribution of this statistic ?

Learn more about Probability here

https://brainly.com/question/11938528

#SPJ4