A salesperson earns $200 a week plus a 4% commission on her sales. Which equation models the relationship between her sales in a given week, s, and her weekly earnings, e?
e = 200s + 4
e = 4s + 200

Answer:

sorry I also dont understand

The jar of glitter was used for each poster is 4/3

Given,

In the question:

Brad used 1/3 jar of glitter evenly among 4 posters.

To find the  how much of the jar of glitter was used for each poster?

Now, According to the question;

Based on the given conditions:

Formulate;

Brad used 1/3 jar of glitter

and, evenly among 4 posters.

= \(\frac{1}{\frac{3}{4} }\)

Calculate:

Divide a fraction by multiplying its reciprocal

= 4/3

Hence, The jar of glitter was used for each poster is 4/3

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The solution of the system of equations is (x, y) = (1/3, 1/3).

To solve the given system of equations, we can use any of the following three methods; the substitution method, the elimination method (also known as the addition/subtraction method), and the graphical method. Below, we will solve it using each of these methods.

1. Substitution method:

We will use the substitution method to solve the system of equations. Step-by-step solution is shown below; Given equations are

Y = 3y - 2x ...(1)2y = 3x - 2 ...(2) From equation (1), we have

Y + 2x = 3y ...(3)Now substitute equation (3) into equation

(2)2y = 3x - 2 ...(2)Y + 2x = 3y ...(3)2(3y - 2x) = 3x - 2

Multiplying both sides by 2:

6y - 4x = 3x - 2 Grouping like terms:

6y - 3x = 2 Adding 3x to both sides:

6y = 3x + 2Dividing both sides by 6:

y = (3/6)x + 2/6y = (1/2)x + 1/3

Therefore, the solution of the system of equations is (x, y) = (1/3, 1/3).

2. Elimination method:

We will use the elimination method to solve the system of equations. Step-by-step solution is shown below; Given equations are

Y = 3y - 2x ...(1)2y = 3x - 2 ...(2)Multiplying equation (1) by 2,

we get;2Y = 6y - 4x ...(3)Multiplying equation (2)

by -3, we get;-6y = -9x + 6 ...(4) Adding equations (3) and (4),

we get;-4x = -9x + 8

Simplifying;-4x + 9x = 8x = -8x = -2

Therefore, we found the value of x, which is -2.

Substitute the value of x in either equation (1) or (2);

If we substitute x = -2 in equation (1), we get;

Y = 3y - 2(-2)Y = 3y + 4Y - 3y = 4Y = 4/2Y = 2Substitute the value of y in equation (1)

;Y = 3y - 2xY = 3(2) - 2(-2)Y = 6 + 4Y = 10

Therefore, the solution of the system of equations is (x, y) = (-2, 10/2).3.

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Answer:

x = 6

Step-by-step explanation:

Okay 16x - 6 is alternate interior to the 90 degrees angle.  Alternate interior is like if you make a slanted line \ like that those endpoints will be congruent.

So you would write the equation like this.

16x - 6 = 90 (add 6 on both sides)

16x = 96 (divide both sides by 16)

x = 6

I hope this helps ya!!

Answer:

y = -5x + 7

Step-by-step explanation:

Segment bisector of the segments AB and CD will pass through the midpoint of these segments.

Midpoint of a segment is given by the coordinates = \((\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})\)

where, \((x_1,y_1)\) and \((x_2,y_2)\) are the coordinates of the extreme ends of the segments.

Coordinates of the midpoint of AB = \((\frac{6-4}{2},\frac{3+1}{2})\)

                                                          = (1, 2)

Coordinates of the midpoint of CD = \((\frac{5-1}{2},\frac{-5-1}{2})\)

                                                          = (2, -3)

Let the equation of the line will be,

\(y-y_1=m(x-x_1)\)

Slope of the line passing through two points \((x_1,y_1)\) and \((x_2,y_2)\) is,

m = \(\frac{y_2-y_1}{x_2-x_1}\)

   = \(\frac{2+3}{1-2}\)

   = -5

Therefore, equation of the line will be passing through (1, 2) and slope (-5),

y - 2 = (-5)(x - 1)

y = -5x + 5 + 2

y = -5x + 7

Answer:

-0.71414

Step-by-step explanation:

using the calculator insert X as A and solve for x.

Step-by-step explanation:

Domain of the function (-8, positive infinity)

All of the graphs are correct.

A = 2, B = (2, 1)

The vertical asymptote is x = 3.

It would be more appropriate to multiply the rate of 4 apples per minute by the given time of 8 minutes. This would result in 32 apples, as Dennis correctly stated, but his reasoning behind this calculation was flawed.

Dennis' reasoning is incorrect.

To determine the rate of picking apples per minute, Dennis correctly divided the total number of apples (24) by the time it took (6 minutes), resulting in 4 apples per minute. However, his approach to calculating the number of apples that could be picked in 8 minutes is flawed.

Dennis multiplied the rate of picking apples per minute (4 apples) by the given time (8 minutes), assuming that the rate remains constant. This approach would be valid if the rate of picking apples per minute were constant, but in this scenario, it is not necessarily the case.

The rate of picking apples could vary depending on factors such as fatigue, efficiency, or other variables. Therefore, it is not accurate to assume that the rate of picking apples per minute remains the same over a longer duration of time.

To determine the number of apples that could be picked in 8 minutes, it would be more appropriate to multiply the rate of 4 apples per minute by the given time of 8 minutes. This would result in 32 apples, as Dennis correctly stated, but his reasoning behind this calculation was flawed.

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Every quadratic nonresidue of p is a primitive root of p, when p = 2^k + 1 is primeIf p = 2^k + 1 is a prime number, we want to show that every quadratic nonresidue of p is a primitive root of p.

In other words, we aim to prove that if an element x is a quadratic nonresidue modulo p, then it is also a primitive root of p.

Let's assume p = 2^k + 1 is a prime number. To prove that every quadratic nonresidue of p is a primitive root of p, we can use the properties of quadratic residues and quadratic nonresidues.

A quadratic residue modulo p is an element y such that y^((p-1)/2) ≡ 1 (mod p), while a quadratic nonresidue is an element x such that x^((p-1)/2) ≡ -1 (mod p).

Now, let's consider an element x that is a quadratic nonresidue modulo p. We want to show that x is a primitive root of p.

Since x is a quadratic nonresidue, we know that x^((p-1)/2) ≡ -1 (mod p). By Euler's criterion, this implies that x^((p-1)/2) ≡ -1^((p-1)/2) ≡ -1^2 ≡ 1 (mod p).

Since x^((p-1)/2) ≡ 1 (mod p), we can conclude that the order of x modulo p is at least (p-1)/2. However, since p = 2^k + 1 is a prime, the order of x modulo p must be equal to (p-1)/2.

By definition, a primitive root of p has an order of (p-1). Since the order of x modulo p is (p-1)/2, it follows that x is a primitive root of p.

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a is the correct answer I Hope it help

Answer:

A and B

Step-by-step explanation:

AE ≅ CE  and ∠BAE ≅ ∠DCE  are true based on CPCTC.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

CPCTC stands for "corresponding parts of congruent triangles are congruent" and tells us if two or more triangles are congruent, then their corresponding angles and sides are congruent as well.

Because the triangles  are congruent their corresponding sides and angles are congruent.

These are right triangles, so

AE ≅ CE - true, because AE and CE are hypotenuses,

∠BAE ≅ ∠DCE -true,  as corresponding angles.

Hence, AE ≅ CE  and ∠BAE ≅ ∠DCE  are true based on CPCTC.

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1) The event is considered as rare.

2) It is called a rare event event because the probability is less than 5% and is well below threshold.

1) The probability of winning the grand prize is 0.005, which means there is a 0.5% chance of winning the prize.

Since this probability is low, Michele winning the grand prize is considered a rare event.

The term "rare event" is often used to describe an event with a low probability of occurrence.

A rare event typically has a probability of less than 5%, and in this case, the probability is well below that threshold. A probability of less than 0.05 is generally considered a rare event.

The fact that Michele won the grand prize means that she defied the odds, which makes the event rare.

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APR is obtained by dividing the finance charge for the loan by the total amount borrowed, given by this formula APR = ((F / P) x 12) x 100

The formula for APR (annual percentage rate) is given as;

APR = ((F / P) x 12) x 100

Where;

The annual percentage rate (APR) of a loan if you know the number of monthly payments and the finance charge per $100, is calculated as follows;

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There are no more common factors or like terms that can be further simplified, the expression 3x - 12 is already in its completely factored form.

Therefore, the answer is:c) 3(x - 4)

To factor completely the expression 3x - 12, we can first look for a common factor among the terms. In this case, both 3x and 12 have a common factor of 3.

We can factor out the common factor of 3 from both terms:

3x - 12 = 3(x) - 3(4)

Now, we can simplify the expression:

3x - 12 = 3x - 12

Since there are no more common factors or like terms that can be further simplified, the expression 3x - 12 is already in its completely factored form.

Therefore, the answer is:c) 3(x - 4).

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Expression for the Area of a circle is A = πr²

Hence the radius of the circle is given by r = 7x³y⁴

hence the area of the given circle = πr²

                                                        = π(7x³y⁴) ²

                                                        = π(49x⁶y⁸)

                                                        = 49πx⁶y⁸

Therefore, the area of the given circle is 49πx⁶y⁸.

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The value of a is 0.14, b is 0.2 and c is 0.33.

The horizontal straight lines in mathematics known as number lines are where integers are arranged in equal intervals. A number line can be used to represent every number in a sequence. The endpoints of this line go on forever.

Given:

The number a and b lies between 0/4 and 1/4. (0 and 0.25).

We have the numbers is 0.2, 0.333 (3/9) and 0.14 (1/7).

So, the value of a can be 0.14

and, value of b is 0.2.

and, the value of c is 0.33.

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(a) The firm is operating in the long run, and its supply function is determined by the profit maximization condition.

(b) The firm's input demand functions can be derived from the profit function, and their degree of homogeneity is 1/2. Changes in input prices will impact the firm's input demand.

(c) The market supply function can be derived by aggregating the supply functions of all 40 firms operating in the market.

(d) Given the market conditions and demand function, the total market supply can be calculated.

(a) The firm is operating in the long run because it has the flexibility to adjust its inputs and make decisions based on market conditions. The firm's supply function is determined by maximizing its profit, which is achieved by setting the marginal cost equal to the market price. In this case, the supply function for each firm can be derived by taking the derivative of the profit function with respect to the price of output (p).

(b) The input demand functions for the firm can be derived by maximizing the profit function with respect to each input price. The degree of homogeneity of the input demand functions can be determined by examining the exponents of the input prices. In this case, the degree of homogeneity is 1/2. Changes in the input prices will affect the firm's input demand as it adjusts its input quantities to maximize profit.

(c) The market supply function can be derived by aggregating the individual supply functions of all firms in the market. Since there are 40 identical firms, the market supply function can be obtained by multiplying the supply function of a single firm by the total number of firms (40).

(d) To determine the total market supply, we substitute the given market conditions and demand function into the market supply function. By solving for the market quantity at a given market price, we can calculate the total market supply.

In conclusion, the firm is operating in the long run, and its supply function is determined by profit maximization. The input demand functions have a degree of homogeneity of 1/2, and changes in input prices impact the firm's input demand. The market supply function is derived by aggregating the individual firm supply functions, and the total market supply can be calculated using the given market conditions and demand function.

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Answer:

MK = 80

M= 10

K= 8                  

By using probability, it can be calculated that-

the optimal number of cookies to make is 2400 dozens

What is probability?

Probability gives us the information about how likely an event is going to occur

Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.

Probability of any event is greater than or equal to zero and less than or equal to 1.

Probability of sure event is 1 and probability of unsure event is 0.

Here

Each dozen of cookies is sold for $1.99 and cost $0.99

Shortage = $(1.99 - 0.99) = $1

Cookies that are not sold at the end of the day are reduced to $0.49

Overage = $(0.99 - 0.49) = $0.5

Service = \(\frac{1}{1 + 0.5}\\\)

              \(=\frac{1}{1.5}\\\\=\frac{2}{3}\\\\=0.67\)

Now the table is

Demand               Probability of demand             Cumulative probability  

(Dozen)

1800                          0.05                                             0.05

2000                         0.15                                              0.2

2200                         0.2                                               0.4

2400                         0.3                                                0.7

2600                         0.2                                               0.9

2800                         0.1                                                 1

Here the closest to service is 0.7

So the optimal number of cookies to make is 2400 dozens

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Complete Question

Famous Albert prides himself on being the Cookie King of the West. Small, freshly baked cookies are specialty of his shop. Each dozen sells for $1.99 and costs $0.99, which includes handling and transportation. Cookies that are not sold at the end of the day are reduced to $0.49 and sold the following day as day-old merchandise. Famous Albert has asked for help to determine the number of cookies he should make each day. From an analysis of past demand he estimates demand for cookies as

Demand                Probability of demand            Cumulative probability    

(Dozen)

1800                          0.05                                          

2000                         0.15                                            

2200                         0.2                                              

2400                         0.3                                              

2600                         0.2                                            

2800                         0.1                                                

Using the information in q8, what is the optimal number of cookies to make? 2,600 dozen 2,400 dozen 2,200 dozen 2,000 dozen 2,800 dozen

2,600 dozen 2,400 dozen 2,200 dozen 2,000 dozen 2,800 dozen

Answer:

N/A

Step-by-step explanation:

the question is not in depth could you add a photo

Answer:

14

Step-by-step explanation:

5x = 70

x = 14

Answer:

The answer is option 1.

Step-by-step explanation:

Given that total angles in a quadrilateral is 360°. So in order to find x, you have to substract the remaining angles from 360° :

\(5x + 110 + 110 + 70 = 360\)

\(5x + 290 = 360\)

\(5x = 360 - 290\)

\(5x = 70\)

\(x = 70 \div 5\)

\(x = 14\)

Answer:

(13mn² - 2nm² + 5n²) - (11mn² - 2n²) = 2mn² - 7n².

Step-by-step explanation:

(13mn² - 2nm² + 5n²) - (11mn² - 2n²) can be simplified by removing the parentheses and distributing the negative sign to all the terms inside the second set of parentheses.

This gives:

13mn² - 2nm² + 5n² - 11mn² + 2n²

Simplifying further, we can combine like terms:

(13mn² - 11mn²) + (-2nm²) + (5n² + 2n²)

This gives:

2mn² - 7n²

Therefore, the simplified expression is 2mn² - 7n².

Answer:

k = 4, t = 2

Step-by-step explanation:

Express 2025 as a product of its prime factors

2025 = \(3^{4}\) × 5², that is

\(3^{4}\) × 5² = \(3^{k}\) × \(5^{t}\)

Comparing exponents of same bases on both sides, gives

k = 4 and t = 2

Answer:

arcola spent 916 dollars

Answer:

the answer is 916

Step-by-step explanation:

The weight of the liquid can be calculated as follows:

Weight = Volume x Density

The volume is given as 182.8 milliliters.

The density is given as 0.135 grams over milliliter.

Weight = 182.8 x 0.135 = 24.67 grams

Therefore, the weight of the liquid that exactly fills a 182.8 milliliter container if the density of the liquid is 0.135 grams over milliliter is 24.67 grams.

Probably this

Answer:

congruent SAS

Step-by-step explanation:

We know two sides of the triangles are congruent to each other

MD = MT

and MA = MU

We also know that <DMA = < TMU

Two sides and the included angle

We can use SAS to show that the triangles are congruent

Answer

DM = MT (sides)

AM =MU ( sides)

<DMA = < TMU ( Angles)

So, DMA triangle is congruent to TMU triangle

According to SAS