Problem 2 Lanny got a short term job selling computers. He is paid on
commission. In order to impress customers, he bought a few nice suits. If he has
$20 000 in sales, he will lose $140. If he has$30 000 in sales, he will make a $90
profit. Determine the:
a. rate of change and initial value
b. the amount he needs to sell to break even
c. The amount he needs to sell in order to make $1000 profit

The answer will be as follows after answering the supplied question It is equation worth noting that this equation is a cubic polynomial.

A math equation is a process that relates two statements by using the equals sign (=) to indicate equivalence. In algebra, an equation is a mathematical statement that shows the equivalence of two mathematical expressions. In the equation 3x + 5 = 14, for example, the equal sign separates the numbers 3x + 5 and 14. A mathematical formula may be used to understand the link between the two phrases written on opposite sides of a letter. Frequently, the logo and the software are the same. For example, 2x - 4 = 2.

The degree n Lagrange polynomial that passes through n+1 unique points (x0,y0), (x1,y1),..., (xn,yn) is given by:

[j=0 to n] L(x) [i=0 to n, ij] * yj (x - xi)/(xj - xi) (xj - xi)

We have 5 points in our situation, thus n = 4. We get the following results by plugging the provided points into the Lagrange polynomial formula:

[tex]L(x) = 1*(x-2)(x-3)(x-4)(x-5)/(-1123) + 2(x-1)(x-3)(x-4)(x-5)/(1123) + 4(x-1)(x-2)(x-4)(x-5)/(1123) + 4(x-1)(x-2)(x-4)(x-5)/(1123) (2123)+ 12(x-1)(x-2)(x-3)(x-4)/(432*1)[/tex]

When we simplify this expression, we get:

[tex]L(x) = x^3/3 - 3x^2/2 + 11x/6 - 1[/tex]

As a result, the equation of the curve passing through the given locations is:

[tex]y = x^3/3 - 3x^2/2 + 11x/6 - 1[/tex]

It is worth noting that this equation is a cubic polynomial.

To know more about equation visit:

https://brainly.com/question/649785

#SPJ1

a) We need to add 2.25 to the expression to make it a perfect square and equivalent expression is (x + 1.5)^2.

b) We need to add 0.09 to the expression to make it a perfect square and equivalent expression is (x + 0.3)^2.

a) To make the expression X^2 + 3x + ___ a perfect square, we need to add a number that is equal to half of the coefficient of x, squared. In this case, half of 3 is 1.5, and 1.5 squared is 2.25.

X^2 + 3x + 2.25 = (x + 1.5)^2

The equivalent expression in factored form is (x + 1.5)^2, which represents a perfect square trinomial.

b) Similarly, to make the expression X^2 + 0.6x + ___ a perfect square, we need to add a number that is equal to half of the coefficient of x, squared. In this case, half of 0.6 is 0.3, and 0.3 squared is 0.09. Therefore, we need to add 0.09 to the expression to make it a perfect square:

X^2 + 0.6x + 0.09 = (x + 0.3)^2

The equivalent expression in factored form is (x + 0.3)^2, which represents a perfect square trinomial.

To learn more about expressions click on,

https://brainly.com/question/30037125

#SPJ4

Here is the probability table to be completed:   A B P(A∩B) P(A∣B) 0.54 0.47 0.38 0.70 0.46 0.32 0.30 x 0.28 0.27 0.42 0.20 0.15 0.35 0.45

42. Let P(A) = 0.70, P(B∣A) = 0.55, and P(B∣AC) = 0.10. The following probabilities are found: a. P(AC) = 0.30 b. P(A∩B) = P(B∣A) × P(A) = 0.55 × 0.70 = 0.385 P(AC∩B) = P(B∣AC) × P(AC) = 0.10 × 0.30 = 0.03 c. P(B) = P(B∣A) × P(A) + P(B∣AC) × P(AC) = 0.55 × 0.70 + 0.10 × 0.30 = 0.415 d. P(A∣B) = P(B∣A) × P(A) / P(B) = 0.55 × 0.70 / 0.415 = 0.9289 43. Here is the probability table to be completed:   A B P(A∩B) P(A∣B) 0.54 0.47 0.38 0.70 0.46 0.32 0.30 x 0.28 0.27 0.42 0.20 0.15 0.35 0.45

Learn more about Probability table

brainly.com/question/29255332

#SPJ11

As per the given temperature, the new reading is  0°F

The formula for converting Fahrenheit to Celsius is (°F - 32) x 5/9 = °C. We can use this formula to determine the new temperature in Celsius and then convert it back to Fahrenheit.

First we have to convert the initial temperature to Celsius

(-20°F - 32) x 5/9 = -28.89°C

Now we have to add 20 degrees Fahrenheit to the initial temperature

-20°F + 20°F = 0°F

And then we have to convert the new temperature to Celsius

(0°F - 32) x 5/9 = -17.78°C

When we convert the new temperature from Celsius back to Fahrenheit

-17.78°C x 9/5 + 32 = 0°F

Therefore, the new reading on the thermometer will be 0 degrees Fahrenheit, which indicates that the temperature has risen by 20 units on the Fahrenheit scale.

To know more about temperature here

https://brainly.com/question/11464844

#SPJ4

Answer:

∠ ABC = 38°

Step-by-step explanation:

given AB = DB then Δ ABD is isosceles with base angles congruent, that is

∠ BDA = ∠ BAD = 71°

the sum of the 3 angles in Δ ABD = 180° , so

∠ ABC + 71° + 71° = 180°

∠ ABC + 142° = 180° ( subtract 142° from both sides )

∠ ABC = 38°

Answer:

number 2 is 4

Step-by-step explanation:

Based on the given question, Molly needs a loan of $1,000

A loan occurs when one or more people, businesses, or other entities lend money to other people, businesses, or other entities.

The recipient incurs a debt and is often responsible for both the principal amount borrowed as well as interest payments until the debt is repaid.

How to calculate the amount of loan that Molly needs?

Molly has a $2500 down payment saved for a purchase

The dealer's cash allowance is $1500, this will be deducted from her total

The amount of loan that Molly needs can be calculated by subtracting the dealer's cash allowance from Molly's down payment

Loan= Down payment-cash allowance= 2500 - 1500= 1000

Hence Moly needs a loan of $1,000

Read more on loans here

https://brainly.com/question/16539246

#SPJ1

Answer:

A

because it is a negative number and because it is less than -1/2

Answer:

Step-by-step explanation:

the answer is -1 as negative integers become smaller as they go to the left.

no problem

Answer: p+3

Step-by-step explanation:

if p=12 and you need the answer to be 15, all you need to do is find 12+_= 15. Since 12+3=15 your answer would be p+3.

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 10891.31\\ P=\textit{original amount deposited}\\ r=rate\to 2.9\%\to \frac{2.9}{100}\dotfill &0.029\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &12 \end{cases}[/tex]

[tex]10891.31 = P\left(1+\frac{0.029}{4}\right)^{4\cdot 12} \implies 10891.31=P(1.00725)^{48} \\\\\\ \cfrac{10891.31}{1.00725^{48}}=P\implies 7700\approx P[/tex]

To minimize the distance walked, and the minimum distance is 31.8% of the total circumference of the circle.

If we draw a line segment from A to B, it will intersect the circle at two points, C and D. We can find the distance AC and the distance BD by using the Pythagorean theorem.

Let r be the radius of the circle, and let x be the distance we walk in and then out of the circle.

Then, we have:

AC = √(r^2 - (x/2)^2)

BD = √(r^2 - (x/2)^2)

The total distance we walk is AC + BD + AB. Since AB is fixed, we want to minimize AC + BD.

AC + BD = 2√(r^2 - (x/2)^2)

To minimize this expression, we need to maximize the value inside the square root. That means, we need to set (x/2)^2 to be as small as possible.

In other words, we want x to be as large as possible.

The maximum value of x is the diameter of the circle, which is 2r.

If we walk in and out of the circle along the diameter, then AC and BD are both equal to r, and the total distance we walk is 2r + AB.

Therefore, the percentage of the total circumference that we walk in and out of the circle is:

2r / (2πr) * 100% = 100/π ≈ 31.8%

So, we need to walk in and out of the circle at two points that are opposite to each other, along a diameter, to minimize the distance walked, and the minimum distance is approximately 31.8% of the total circumference of the circle.

Learn more about minimizing distance here: https://brainly.com/question/27349289
#SPJ1

35 1 + 2 = 17. To remember the mathematical operations in the correct order, people frequently use the abbreviation PEMDAS.

You must follow the order of operations, often known as PEMDAS, to evaluate this equation. Parentheses, exponents, multiplication and division (left to right), addition, and subtraction are all referred to as PEMDAS (from left to right).

When using PEMDAS, you would first calculate the output of the parenthesized expression—which is 3 times 5—and then add 2.

Thus, 35 1+2 reduces to:

3*5 1 + 2 = (3*5) + 2 (first calculate within the parentheses) = 15 + 2 (conduct multiplication) = 17 (perform addition)

Hence, 35 1 + 2 = 17.

Learn more about PEMDAS here:

https://brainly.com/question/27678413

#SPJ4

Step-by-step explanation:

6x6x10 FT = 1 sq cube foot

According to the graph, the true statement is the population will increase more each year than the previous year. The Option B is correct.

in geography context, a population growth means the increase in the number of humans on Earth. In human history, the population size was relatively stable. But with innovation and industrialization, energy, food, water, and medical care became more available and reliable.

On this graph, we can observed how the population increases from 80,000 to 100,000, 120,000, 140,000, 160,000, 180,000, 200,000,  220,000. 240,000, 260,000 and 280,000 on the Y-Axis. Therefore, the statement that population will increase more each year than the previous year is true.

Read more about population increase

brainly.com/question/1437549

#SPJ1

Answer:

Mr Drake is right.

Step-by-step explanation:

Because you first decreased it by 10% of the ORIGINAL value.

You then increased it by 10% of the DECREASED value.

The percentages are the same percentages, but on different base amounts.

Simple example:

$100 decreased by 10% of $100 ($10) is $90.

$90 increased by 10% of $90 ($9) is $99.

Answer:

Mr Drake Is correct

Step-by-step explanation:

When you increase something by 10%, you multiply the original value by 1.1. When you decrease it by 10%, you multiply the increased value by 0.9. So the final amount is:

original value x 1.1 x 0.9 = 0.99 x original value

Therefore, the new amount will be slightly smaller than the original amount, and Mr. Drake is correct.

For the given dilation of the polygons the correct answer are The length AB is 2. The length A'B' is 3. The scale factor is Three-halves.

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is a picture with the same shape as the original. Yet, there is a variation in the shape's size. The initial form should be stretched or contracted during a dilatation. The phrase "scale factor" describes this transition.

The distance formula for the coordinates is given as:

d(A, B) = |x1 - x2|

From the figure we observe that,

d(A, B) = |2 - 4|

d(A, B) = |-2|

d(A, B) = 2 units.

Hence, option A is correct.

Also, the length of A'B' is:

d(A', B') = |3 - 6| = |-3| = 3 units.

Hence, option B is correct.

The original shape is called the pre-image in a transformation (in this example, a dilation), and the transformed shape is called the image.

The third response is untrue since the picture is larger than the pre-image.

The scale factor of the images is:

2k = 3

k = 3/2.

Hence, option 4 is correct.

The last option is also false, as the scale factor is already determined.

Hence, for the given dilation of the polygons the correct answer are The length AB is 2. The length A'B' is 3. The scale factor is Three-halves.

Learn more about dilation here:

https://brainly.com/question/29138420

#SPJ9

The complete question is:

Accοrding tο given proportional data when d = 25, the value οf W is 95.

Relatiοnships between the twο variables that are prοpοrtiοnal οccur when their ratiοs are equal. Anοther apprοach tο cοnsider is that in a prοpοrtiοnal relatiοnship, οne variable is cοnsistently equal tο the οther's cοnstant value. This parameter is referred tο as the "cοnstant οf prοpοrtiοnality".

Accοrding tο the given infοrmatiοn:

Using the prοpοrtiοnality relatiοn W ∝ d, we can set up the fοllοwing prοpοrtiοn:

W/d = k, where k is the cοnstant οf prοpοrtiοnality.

Tο sοlve fοr k, we can use the values given in the prοblem:

133/35 = k

Simplifying, we get:

k = 3.8

Nοw, we can use this value οf k tο find the value οf W when d = 25:

W/25 = 3.8

Simplifying, we get:

W = 95

Therefοre, accοrding tο given infοrmatiοn when d = 25, the value οf W is 95.

To know more about proportional visit:

brainly.com/question/26617614

#SPJ1

To make things easier, consider the residue when each integer between equation 1 and 60 is divided by 5. The remainders might be one, two, three, or four.

A math equation is a process that relates two statements by using the equals sign (=) to indicate equivalence. In algebra, an equation is a mathematical statement that proves the equality of two mathematical expressions. In the equation 3x + 5 = 14, for example, the equal sign separates the numbers 3x + 5 and 14. A mathematical formula may be used to understand the link between the two phrases written on opposite sides of a letter. Frequently, the logo and the software are the same. For example, 2x - 4 = 2.

0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 = 0 (if all answers are wrong or not attempted) (if all answers are incorrect or not attempted)

5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 = 60 (assuming all answers are accurate) (if all answers are correct)

10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 = 120 (assuming all answers are accurate and attempted twice) (if all answers are correct and attempted twice)

. The impossible scores may be obtained by locating all the numbers between 1 and 60 that cannot be stated as a sum of 0, 5, or 10.

To make things easier, consider the residue when each integer between 1 and 60 is divided by 5. The remainders might be one, two, three, or four.

To know more about equation visit:

https://brainly.com/question/649785

#SPJ1

Answer:

3/4

Step-by-step explanation:

Hope this helps! Pls give brainliest!

By writting all the numbers as decimals we can see that the lake that lost the least amount of water is the last one.

The first lake lost a fraction of 5/6 of its total water.

The second lake lost the 85% of its water.

The last lake lost a fraction of 246/300 of its water.

We want to see which of these 3 numbers is the smaller one, we can write all of them as decimals ot get:

5/6 = 0.833

85% = 0.85

246/300 = 0.82

With this we conclude that the lake that lost the least amount of water is the last one.

Learn more about fractions at:

https://brainly.com/question/11562149

#SPJ1

The value of x is 0. This means that [tex]8/10 = 16/20 = 4x+6/4x+11[/tex], so the corresponding sides of triangles abc and def have the same ratio.

The similarity of two triangles can be determined by the ratio of their corresponding sides. In the case of triangles abc and def, the ratio of corresponding sides is [tex]8/10 = 16/20 = 4x+6/4x+11[/tex].

To calculate the value of x, we can use the first two ratios and cross-multiply. With 8/10 = 16/20, we get 8*20=16*10, which simplifies to 160=160. Therefore, the first two ratios are equal.

To calculate the value of x using the third ratio, we can use the same method. With 4x+6/4x+11, we get ([tex]4x+6)*(4x+11)=4x^2+44x+66[/tex]. This simplifies to [tex]4x^2+44x+66=4x^2+44x+66[/tex], so the third ratio is also equal.

Learn more about triangles here:

https://brainly.com/question/2773823

#SPJ4

Complete question:

What is the value of x in the ratio 8/10 = 16/20 = 4x+6/4x+11?

Answer:

x-3

Step-by-step explanation:

martin =  x

jennifer = x-3

connor = 2x

what is jennifer's age?

According to the figure and using the corresponding angle theorem we have that

Corresponding angles are pairs of angles that are formed when a straight line intersects two parallel lines.

They are located on opposite sides of the transversal (the line that intersects the parallel lines) and in corresponding positions. Corresponding angles have the same degree measurement as each other.

angle 1 = 82 degrees corresponding angles are equal

angle a = 58 degrees corresponding angles are equal

angle a and angle 2 are linear pair hence angle a and angle 2 are supplementary angles

hence we have that

angle a + angle 2 = 180 degrees

58 + angle 2 = 180

angle 2 = 180 -58

angle 2 = 122 degrees

Learn more about corresponding angles at:

https://brainly.com/question/28769265

#SPJ1

The length of the base is 1/64 and can be simplified to the fraction 1/64 = 1/64 in simplest form.

A fraction is a mathematical expression which represents a part of a whole. It is written as a ratio that compares two numbers, the numerator and denominator. The numerator indicates the number of parts, the denominator indicates the total number of parts that make up the whole. Fractions can be expressed as decimals, percentages, and other forms of representation.

To solve this problem, we must use the formula for area of a triangle. This formula states that the area of a triangle is equal to one-half the product of the base and the height. In this problem, the area of the triangle is given as 1/16 square centimeters. This means that the base times the height must equal 1/8.

To find the length of the base, we must isolate the base from the equation. To do this, we must divide both sides of the equation by the height. This will leave us with the equation base = 1/8/height. Since the height is unknown, we can solve for it by taking the reciprocal of the base. This will give us the equation height = 1/8/base.

Combining both equations, we can solve for the base by multiplying both sides of the equation by 1/8. This will give us the equation base = (1/8)(1/8) = 1/64. The length of the base is 1/64 and can be simplified to the fraction 1/64 = 1/64 in simplest form.

For more questions related to triangle

https://brainly.com/question/2773823

#SPJ9

if Ivy received two Paychecks during the time period shown on the statement, each paycheck would be $1,784.34.

To find out how much each of Ivy's paychecks is, we need to subtract the amount she withdrew from her account from the overall increase in her account balance.

So, the calculation would be:

Overall increase in account balance - Total amount withdrawn = Total amount deposited

$1,692.45 - $1,876.23 = -$183.78

This means that Ivy actually spent more than she earned during the time period shown on the statement. Therefore, we cannot determine the amount of each of her paychecks with the given information.

However, if we assume that Ivy did not have any other income or expenses during the time period, we can use the following equation:

2x - $1,876.23 = $1,692.45

where x is the amount of each paycheck.

Simplifying the equation, we get:

2x = $3,568.68

x = $1,784.34

Therefore, if Ivy received two paychecks during the time period shown on the statement, each paycheck would be $1,784.34.

To Learn More About Paychecks

https://brainly.com/question/29143273

SPJ11

Beth will need approximately 3365.76 [tex]cm^{2}[/tex] of plastic wrap to cover all 12 jars of jam.

What is a Circle?

A circle is simply a round shape that has no corners or line segments. It is a closed curve shape in geometry. The points of circle are at a fixed distance from the center.

So now, to calculate the surface area of each jar, we need to find the area of the circular top and the area of the rectangular side.

The area of the circular top can be calculated using the formula for the area of a circle:

[tex]A=\pi r^{2}[/tex], where r is the radius of the circle.

The diameter of the jar is given as 7 cm, so the radius is half of that:

r = [tex]\frac{7}{2}[/tex] cm = 3.5 cm

Therefore, the area of the circular top is:

A_top = [tex]\pi r^2[/tex] = π[tex](3.5)^{2}[/tex] = 38.48 [tex]cm^{2}[/tex]

The area of the rectangular side can be calculated using the formula for the area of a rectangle:

A_side = base x height

The base of the rectangle is the circumference of the circular top, which can be calculated using the formula:

C = 2πr

C = 2π(3.5) = 22 cm

So the base of the rectangle is 22 cm, and the height is 11 cm, since that is the height of the jar.

Therefore, the area of the rectangular side is:

A_side = base x height = 22 cm x 11 cm = 242 [tex]cm^{2}[/tex]

To find the total surface area of each jar, we can add the area of the circular top and the area of the rectangular side:

A_total = A_top + A_side = 38.48 [tex]cm^{2}[/tex]+ 242 [tex]cm^{2}[/tex] = 280.48 [tex]cm^{2}[/tex]

For 12 jars, the total surface area of plastic wrap needed would be:

Total area = 12 x A_total = 12 x 280.48 [tex]cm^{2}[/tex] = 3365.76 [tex]cm^{2}[/tex]

Learn more about circles on:

https://brainly.com/question/8553827

#SPJ1

It is untrue to say that the exponential function f(x) has a base of 3.

A mathematical function termed an exponential function has the formula f (x) = axe, where x is a variable and a constant called the base of the function, which must be greater than 0. The most often used exponential function basis is the transcendental number e, or approximately 2.71828.

An exponential function has the form f(x) = bx for b > 0 and b 1. Like in any exponential expression, the base is b and the exponent is x. Bacterial growth serves as an example of an exponential function. Some bacteria grow by two per hour.

To know more about exponential function visit:-

https://brainly.com/question/14355665

#SPJ1

The exponential function passing through the points (1960, 179323175) and (2010, 308745538) is given as follows:

y = 0.1(1.01092581)^x.

The standard definition of an exponential function is given as follows:

y = ab^x.

In which the coefficients a and b are explained as follows:

The points for this problem are given as follows:

(1960, 179323175) and (2010, 308745538).

Considering that between 1960 and 2010 there is an increase of 50 in the input, the parameter b is obtained as follows:

b^50 = 308745538/179323175

b = (308745538/179323175)^(1/50)

b = 1.01092581.

Hence:

y = a(1.01092581)^x.

When x = 1960, y = 179323175, hence the parameter a is obtained as follows:

a = 179323175/[(1.01092581)^1960]

a = 0.1.

Hence the function is:

y = 0.1(1.01092581)^x.

More can be learned about exponential functions at https://brainly.com/question/30374198

#SPJ1

Answer:

9

Step-by-step explanation:

1 dozen -12

there dozen - 36

thus

red blocks -4

36/4

= 9