Eli and Samantha work at a dry cleaners ironing shirts. Eli can iron 20 shirts per hour, and Samantha can iron 35 shirts per hour. Samantha worked 2 more hours than Eli and they ironed 400 shirts between them. Write a system of equations that could be used to determine the number of hours Eli worked and the number of hours Samantha worked. Define the variables that you use to write the system.

Answer:

60 degree

Step-by-step explanation:

E,A,D is a straight line .

Straight line=180 degree

100+20=120 -180=60

therefore X=60

After one decade, the car will be worth approximately 4.7% of its original MSRP. To calculate the value of the car after one decade, we need to use the formula for compound interest: A = P(1 + r/n)^(nt)

To calculate the value of the car after one decade, we need to use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where A is the final amount, P is the initial amount, r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time in years.

In this case, P = $18,000, r = -0.18 (since it's a depreciation rate), n = 1 (since the rate is annual), and t = 10. Plugging these values into the formula, we get:

A = $18,000(1 - 0.18)^10

A = $18,000(0.82)^10

A = $2,918.84

So after one decade, the car will be worth $2,918.84. To find the percentage of the original MSRP that this represents, we divide this amount by the original MSRP and multiply by 100:

($2,918.84 / $18,000) x 100 = 16.2168%

Therefore, after one decade, the car will be worth approximately 16.22% of its original MSRP, which is about 4.7% of the original MSRP lost due to depreciation.

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Answer:

\(y = - \frac{3}{20} x + 900 \\ \\ y = - \frac{20}{3} x + 6000\)

Step-by-step explanation:

\( \\ part \: a. \:( food \: expenses) \\ to \: solve \: these \: problems \: we \: surmone \\ \: the \: following \: laws : \to \\m = \frac{ y_{2} -y_{1} }{x_{2} - x_{1}} = \frac{815 - 812}{390 - 410} = - \frac{3}{20} = - 0.15 \\ the \: general \: slope \:i ntercept \: form \: is : \\ y = mx + c \\ to \: find \: c \: lets\: insert \: any \: two \: pairs \: for \: x \: and \: y \to \\ 812 = - \frac{3}{20} (410) + c \\ 16,240 = - 3(410) + 20c \\ c = \frac{1747}{2} \\ c = 873.5 \\ \\ therefore \: y = - \frac{3}{20} x + 900 \: (i.e \: to \: he \: nearest \: thousand). \\ \\ \\ part \: b. \: (medical \: expenses) \\ to \: be \: able \: to \: solve \: these \: problems \: we \: surmone \\ \: the \: following \: laws : \to \\m = \frac{ y_{2} -y_{1} }{x_{2} - x_{1}} = \frac{390 - 410}{815 - 812} = - \frac{20}{3} = - 6.667 \\ the \: general \: slope \:i ntercept \: form \: is : \\ y = mx + c \\ lets \: find \: c \: by \: insert \: any \: two \: pairs \: for \: x \: and \: y \to \\ 410 = - \frac{20}{3} (812) + c \\ 1230 = - 20(812) + 3c \\ c = \frac{17470}{3} \\ c = 5823.3333 \\ \\ therefore \: y = - \frac{20}{3} x + 6000 \: (i.e \: to \: he \: nearest \: thousand). \\ \\ \)

Answer:

y= -3/20x+90

y= -20/3x+6000

Step-by-step explanation:

Answer:

irrational numbers are numbers that can't be written as a fraction

the number 3 is rational because it is an integer

Answer:

Step-by-step explanation:

 *   *    *

let the middle digit is a letter.

as first and second letters are same so consider them as one letter.

It can be filled in 26 ways.

third place is filled in 10 ways (0,1,2,3,4,5,6,7,8,9)

total number of ways=26×10=260 ways

again consider second place is a digit.

so consider second and third place as one digit.

it can be filled in ways=10

first place can be filled in ways=26

Hence number of ways=26×10=260

so total number of ways=260+260=520

The factοred expressiοn is οbtained as m + 8. The sοlutiοn has been οbtained by using the Greatest Cοmmοn Factοr.

The sum οf twο οr mοre numbers is the biggest cοmmοn factοr, οr largest number (GCF). A natural number is prοduced by taking the largest number (factοr) between them.

We are given an expressiοn as 4m + 32.

We knοw that the greatest cοmmοn factοr οf an expressiοn is the largest number which can cοmpletely divide the full expressiοn.

In the given expressiοn, the greatest cοmmοn factοr is the number 4.

Sο, by dividing the expressiοn by 4, we get

⇒ (4m + 32) ÷ 4

⇒ m + 8

Hence, the factοred expressiοn is οbtained as m + 8.

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Complete question;

Factor the expression using the GCF,

4m+32

Factored expression: __________

Answer:

5^3 = 1 2^3

One and two thirds.

Answer:

the answer is C

Step-by-step explanation:

The negative graph has

So the equetion for the negative slop is y= -m + b

from the given 3 equetion C fulfill all the requirment .

So the answer is C

Base-case analysis, worst-case analysis, and best-case analysis are techniques used in business and project management to assess the potential outcomes of a given situation. These analyses help in making informed decisions and managing risks.

In a base-case analysis, the most likely scenario is considered. It assumes that all factors will perform as expected and there are no major deviations or unforeseen events. The base case provides a baseline for comparison with other scenarios.

Worst-case analysis, on the other hand, examines the scenario with the most negative outcome. It takes into account all possible risks and assumes that everything that can go wrong will go wrong. It helps identify potential vulnerabilities and plan for contingencies.

Best-case analysis evaluates the scenario with the most positive outcome. It assumes that everything will work perfectly and all favorable conditions will be met. This analysis is useful for setting performance targets and assessing the potential benefits of a project or decision.

To perform these analyses, specific variables and factors are identified, and their impact on the outcome is assessed. This includes considering financial data, market conditions, competition, technological factors, and other relevant aspects.

It is important to note that the base-case, worst-case, and best-case analyses are not definitive predictions but rather tools to assess different scenarios and their potential outcomes. They help in understanding the range of possibilities and making informed decisions based on risk tolerance and objectives.

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3. The test result provides significant evidence that the company is under-filling their containers.

4. Based on the hypothesis test, it can be concluded that the grip adjustment had a significant impact on Marco's throwing distance.

3. Null hypothesis (H0): μ = 12 (the true mean filling volume is equal to 12 oz)

Alternative hypothesis (H1): μ < 12 (the true mean filling volume is less than 12 oz)

We'll use a one-sample t-test since we have the sample mean, the population standard deviation, and a sample size less than 30.

The test statistic can be calculated as:

Plugging in the values:

sample mean (X) = 11.85

population mean (μ) = 12

population standard deviation (σ) = 0.45

sample size (n) = 36

t = (11.85 - 12) / (0.45 / √36)

t = -0.15 / (0.45 / 6)

t = -0.15 / 0.075

t = -2 (rounded to two decimal places)

To find the p-value associated with this test statistic, we'll use a t-distribution table or statistical software.

With a sample size of 36 and a significance level of 5%, the degrees of freedom are 35.

Looking up the p-value for a t-score of -2 with 35 degrees of freedom, we find that it is approximately 0.026.

Since the p-value (0.026) is less than the significance level of 0.05, we reject the null hypothesis.

There is significant evidence to suggest that the company is under-filling their soda cans.

4.

Null hypothesis (H0): μ = 42 (the true mean throwing distance is equal to 42 yards)

Alternative hypothesis (H1): μ > 42 (the true mean throwing distance is greater than 42 yards)

We'll use a one-sample t-test since we have the sample mean, the population standard deviation, and a sample size of 50.

The test statistic can be calculated as:

Plugging in the values:

sample mean (X) = 44

population mean (μ) = 42

population standard deviation (σ) = 4

sample size (n) = 50

t = (44 - 42) / (4 / √50)

t = 3.53

To find the p-value associated with this test statistic, we'll use a t-distribution table.

With a sample size of 50 and a significance level of 0.01, the degrees of freedom are 49.

Looking up the p-value for a t-score of 3.53 with 49 degrees of freedom, we find that it is very close to 0 (essentially 0).

Since the p-value is less than the significance level of 0.01, we reject the null hypothesis.

There is significant evidence to suggest that Marco's grip adjustment helped him throw the football farther than 42 yards.

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To assist Roman in dealing with his frustration and politely interrupt Mr. Adamson to focus on the main business, Roman can try the following steps:

1. Find a polite opening: Roman can wait for a pause in the conversation or a natural transition to interject and bring up the main business.
2. Use a transition statement: Roman can politely transition the conversation by saying something like, "I appreciate the opportunity for small talk, Mr. Adamson. However, I believe it's important for us to discuss the confidential matters we planned to address in this meeting."
3. Remind of the purpose: Roman can then remind Mr. Adamson of the purpose of their meeting and express the urgency by saying something like, "We have some pressing matters to discuss that require our immediate attention. It would be greatly appreciated if we could shift our focus to those topics."
4. Maintain a professional tone: Throughout the conversation, Roman should maintain a professional and respectful tone to ensure a constructive discussion.


1. Find a polite opening: It is important for Roman to find an appropriate moment to interject and redirect the conversation towards the main business. This could be when Mr. Adamson takes a pause or when there is a natural transition point in the conversation.

2. Use a transition statement: Roman can use a polite transition statement to acknowledge the small talk and then redirect the conversation towards the main business. By appreciating the small talk and politely mentioning the need to discuss the confidential matters, Roman sets the stage for the transition.

3. Remind of the purpose: After the transition statement, Roman should remind Mr. Adamson of the purpose of their meeting. This helps bring the focus back to the main business and emphasizes the importance of addressing the pressing matters they had planned to discuss.

4. Maintain a professional tone: Throughout the conversation, Roman should maintain a professional and respectful tone. This helps ensure that the conversation remains constructive and that the main business is addressed without offending Mr. Adamson or the other individuals present in the room. It is essential to be assertive but not aggressive in the approach to maintain a positive working relationship.

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Answer:

see explanation

Step-by-step explanation:

The perimeter is the sum of the 3 sides , then

2x - 6 + x + 4 + 10 > 50

3x + 8 > 50 ( subtract 8 from both sides )

3x > 42 ( divide both sides by 3 )

x > 14

(4)

The area is calculated by multiplying length and breadth , then

3(4x - 2) < 138 ( divide both sides by 3 )

4x - 2 < 46 ( add 2 to both sides )

4x < 48 ( divide both sides by 4 )

x < 12

Answer:

98

Step-by-step explanation:

Let b = the total number of boxes

b * 4/7 = 56

Multiply each side by 7/4

7/4 * b* 4/7 = 7/4 *56

b =98

The store had 98 boxes

Answer:

the second one, 98

Step-by-step explanation:

56/4=14

14*7=98

hi;augh4 vhaugawhfdb

Step-by-step explanation:

Answer:-46

Step-by-step explanation: just took test

The remainder when f(x) is divided by (x - 3) is 8 and this can be determined by using the factorization method.

Given :

\(\rm f(x) = x^4-5x^2-6x-10\)

The following steps can be used in order to determine the remainder if f(x) is divided by (x - 3):

Step 1 - Write the mathematical expression of the statement "f(x) is divided by (x - 3)".

\(=\dfrac{x^4-5x^2-6x-10}{x-3}\)

Step 2 - Now, try to factorize the numerator in the above expression.

\(=\dfrac{x^4-3x^3+3x^3-9x^2+4x^2-12x+6x-18+18-10}{x-3}\)

Step 3 - Further simplify the above expression.

\(=\dfrac{x^3(x-3)+3x^2(x-3)+4x(x-3)+6(x-3)+8}{x-3}\)

\(=(x^3+3x^2+4x+6) +\dfrac{8}{x-3}\)

So, the remainder when f(x) is divided by (x - 3) is 8.

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The volume of the solid is (2048π/15) - (572π/3) cubic units, which simplifies to approximately 146.66 cubic units.

To solve for the volume of the described solid, we need to integrate the area of each cross-section perpendicular to the y-axis over the range of y values.

The base is given by the two curves:

x = -y^2 + 16y - 36 ...(1)

x = y^2 - 26y + 172 ...(2)

We need to find the limits of integration for y. To do this, we set the two equations equal to each other and solve for y:

-y^2 + 16y - 36 = y^2 - 26y + 172

2y^2 - 10y - 136 = 0

y^2 - 5y - 68 = 0

Solving for y using the quadratic formula, we get:

y = (5 ± sqrt(309)) / 2

Therefore, the limits of integration for y are (5 - sqrt(309)) / 2 and (5 + sqrt(309)) / 2.

Now, let's consider a cross-section at a fixed value of y. Since each cross-section is a semi-circle, its area is given by:

A(y) = πr^2 / 2

where r is the radius of the semi-circle. To find r, we need to find the value of x at the given value of y by substituting y into equations (1) and (2) and subtracting the resulting values:

r = (y^2 - 26y + 172) - (-y^2 + 16y - 36) / 2

r = y^2 - 21y + 104

Now, we can find the volume of the solid by integrating the area of each cross-section over the range of y:

V = ∫[(π/2)(y^2 - 21y + 104)^2]dy (from y = (5 - sqrt(309)) / 2 to y = (5 + sqrt(309)) / 2)

This integral can be evaluated using standard calculus techniques such as u-substitution or integration by parts. After performing the integration, we get:

V = 2048π/15 - 572π/3

Therefore, the volume of the solid is (2048π/15) - (572π/3) cubic units, which simplifies to approximately 146.66 cubic units.

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When three standard six-faced dice are rolled, the probability that the sum of the three numbers rolled is 9 is equal to 10/216 or 5/108.

Total number of ways three dice can be rolled = 6 × 6 × 6 = 216.

Each dice can have any number from 1 to 6. The probability of rolling a particular number on a dice = 1/6.

The probability of rolling a particular number on three dice = (1/6) × (1/6) × (1/6) = 1/216.

In order to get a sum of 9, there are four combinations that can be rolled:

3 + 3 + 3 = 9

3 + 4 + 2 = 9

3 + 5 + 1 = 9

4 + 3 + 2 = 9

The probability of rolling any of these combinations = probability of rolling 3-3-3 + probability of rolling 3-4-2 + probability of rolling 3-5-1 + probability of rolling 4-3-2

= (1/216) + (3/216) + (3/216) + (3/216)

= 10/216 or 5/108.

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Answer:

x = 8

Step-by-step explanation:

Hello!

The missing angle in the triangle can be found by subtracting 90° and 45° from 180°. The missing angle is 45°.

This means that the triangle is isosceles, as there are two congruent base angles, 45° and 45°.

The side lengths opposite these two angles are congruent.

We can see that 8 is opposite 45°, and x is opposite 45°. Therefore, x must be equal to 8.

The value of x is 8.

Answer:

x = 8

Step-by-step explanation:

The interior angles of a triangle sum to 180°.

The given triangle is a right triangle, so the missing angle is 45°

⇒ 180° - 90° - 45° = 45°

As the triangle has 2 equal angles, this means it is an isosceles triangle (with its vertex at the right angle).  An isosceles triangle has legs of equal measure, therefore \(x=8\).

Proof

This can be proven by using the tan trigonometric ratio to calculate the value of x.

Tan trig ratio

\(\sf tan(\theta)=\dfrac{O}{A}\)

where:

Given:

Substituting the given values into the equation and solving for x:

\(\implies \tan (45^{\circ})=\dfrac{8}{x}\)

\(\implies x=\dfrac{8}{\tan (45^{\circ})}\)

\(\implies x=\dfrac{8}{1}\)

\(\implies x=8\)

Answer:

Step-by-step explanation:

Answer:

0 (none).  Just bc their is no exact value therefore when u compare them all they equal 0 equivalents

The m and b into slope-intercept form results in the equation y = 3x + 70

You need the y-intercept and the rate of change in order to write the equation of a line (slope). You can create your equation by substituting these values into the slope-intercept form of a line (y = mx + b).

You already know b because there are initially 70 gallons of water in the tank on Saturday. You must write two data points using the information provided in the question in order to determine m.

The number of gallons is the dependent variable, and time is the independent variable because the amount of water in the tank is dependent on how long Lena has been filling it. This indicates that the information should be presented in the form (time, gallons).

On Saturday at time = 0, there are 70 gallons, hence the data point is (0, 70). The tank is full (400 gallons) after 1 hour and 50 minutes, which is 60 + 50 = 110 minutes, so another data point is (110, 400). Using the slope formula, determine the rate of change as follows:

(400-70)/(110-0)

= 330/110

=3 gallons per minute. Substituting m and b into slope-intercept form results in the equation y = 3x + 70

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Answer:

Step-by-step explanation:

This description applies to both X and Z.

Answer:

7

Step-by-step explanation:

Distribute where we can

24m - 18 + 6 = 16m +44

24m - 16m = 44 + 12

8m = 56

m = 7

The value of m that satisfies the equation 6(4m-3)+6=4(4m +11) is 7.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

To know the value of m that will satisfy this equation we need to solve the equation for m,

6(4m-3) +6 = 4(4m +11)

24m - 18 + 6 = 16m + 44

Bring like terms on the same side of the equation,

24m - 16m = 18 - 6 + 44

8m = 56

m = 56/8

m = 7

Hence, the value of m that satisfies the equation 6(4m-3)+6=4(4m +11) is 7.

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The correct values for a, b, c, d, and e are a = 16, b = 29, c = 24, d = 22, and e = 30 for group of 75 students on asking whether they like Algebra or Geometry.

For the values of a, b, c, d, and e, we can use the information provided in the table. Let's break it down step-by-step:

We are given that a total of 75 math students were surveyed. Therefore, the total number of students should be equal to the sum of the students who like algebra, the students who like geometry, and the students who do not like either subject.

75 = 45 (Likes Algebra) + 53 (Likes Geometry) + 6 (Does Not Like Either)

Simplifying this equation, we have:

75 = 98 + 6

75 = 104

This equation is incorrect, so we can eliminate options c and d.

Now, let's look at the information given for the students who do not like geometry. We know that a + b = 6, where a represents the number of students who like algebra and do not like geometry, and b represents the number of students who do not like algebra and do not like geometry.

Using the correct values for a and b, we have:

16 + b = 6

b = 6 - 16

b = -10

Since we can't have a negative value for the number of students, option a is also incorrect.

The remaining option is option e, where a = 29, b = 16, c = 24, d = 22, and e = 30. Let's verify if these values satisfy all the given conditions.

Likes Algebra: a + c = 29 + 24 = 53 (Matches the given value)

Does Not Like Algebra: b + d = 16 + 22 = 38 (Matches the given value)

Likes Geometry: c + d = 24 + 22 = 46 (Matches the given value)

Does Not Like Geometry: b + e = 16 + 30 = 46 (Matches the given value)

All the values satisfy the given conditions, confirming that option e (a = 29, b = 16, c = 24, d = 22, and e = 30) is the correct answer.

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Answer:

b= 11

c= 121

Step-by-step explanation:

equation for b-

48 = 4x + 4

48-4 = 44

44 / 4 = 11

11 = b

and then for c

48 + 11 = 59

180 - 59 = 121

you use 180 as the number to subtract from because thats how many degrees are in a triangle

The composite function g(f(x)) is |x| - 4.

In mathematics, a function is a relationship between two sets of numbers, known as the domain and the range, that assigns each element of the domain a unique element in the range. A function can be thought of as a machine that takes input from the domain and produces output in the range.

More formally, a function f from a set X to a set Y is denoted as f: X → Y

For example, the function f(x) = 2x assigns to each real number x a unique real number 2x. When x = 1, f(1) = 2; when x = -3, f(-3) = -6.

Functions can be represented in a variety of ways, including algebraic expressions, tables of values, and graphs. The graph of a function is a visual representation of the relationship between the input and output values and can be used to analyze the behavior of the function.

Functions are important in many areas of mathematics, science, and engineering, and are used to model relationships between quantities, solve problems, and make predictions. They are also used in computer programming, where they are used to encapsulate behavior and modularize code.

I assume you want to find the composite function g(f(x)).

To find g(f(x)), we first need to find f(x) and then substitute it into g(x).

We have f(x) = |x|.

Substituting f(x) into g(x), we get:

g(f(x)) = g(|x|) = |x| - 4

So the composite function g(f(x)) is |x| - 4.

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Answer:

33 shirts

Step-by-step explanation:

100% of 20 = 20

65% of 20 = 13

total = 33

Step-by-step explanation:

-2,10 is the answer according to my working

The product of the expression is 2x⁶ + 23x³ + 63

First, we should note that algebraic expressions are described as expressions that are composed of coefficients, terms, constants, variables and factors.

These algebraic expressions are also made up of mathematical operations, such as;

From the information given, we have that;

2x3 +9 and x3 +7?

Then,

(2x³ + 9)(x³ + 7)

expand the bracket

2x⁶ + 14x³ + 9x³ + 63

add like terms

2x⁶ + 23x³ + 63

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Answer:

It is NOT c

Step-by-step explanation:

I clicked c and it was wrong lol.

Answer:

its D

Hope this helps ⊂◉‿◉つ

Answer:

Have you tried to do x+6+4x-21=180

combine the like terms and then solve for 180 so (x+4x)(6-21)=180

5x-15=180

    +15  +15

5x=195

5x/5=195/5

x=39

Step-by-step explanation: