The given table of values shows a linear relationship.
x 1 3 5 7 9
y 8 14 20 26 32
What is the rate of change for this relationship?
A.
3
B.
-3
C.
D.
Answers
The rate of change (slope) for a linear relationship can be found by taking the difference in the y-values divided by the difference in the corresponding x-values.
In this case, the change in y from x=1 to x=9 is 32-8=24, and the change in x is 9-1=8. Therefore, the rate of change is:
rate of change = (change in y) / (change in x) = 24/8 = 3
So the answer is A. 3.
Related Questions
many clothing stores use mannequins to display their goods, with many stores using headless mannequins while some use mannequins with a head. the same dress was presented to 95 women on either a mannequin with or without a head. 18 of the 50 women who saw the dress on a mannequin with a head indicated they would purchase the dress while 12 of the 45 who saw the dress on a headless mannequin said they would purchase the dress. is this evidence that a headed mannequin is more effective in selling clothing? perform a hypothesis test.
Answers
Using the hypothesis test, the p-value is greater than the significance level, we fail to reject the null hypothesis. There is not enough evidence to suggest that a headed mannequin is more effective in selling clothing.
To perform a hypothesis test to determine if a headed mannequin is more effective in selling clothing, we can use a two-sample proportion test.
Let p1 be the proportion of women who would purchase the dress when presented on a mannequin with a head, and p2 be the proportion of women who would purchase the dress when presented on a headless mannequin.
The null hypothesis is that there is no difference between the two proportions, i.e. p1 = p2, and the alternative hypothesis is that p1 > p2 since we want to test if the headed mannequin is more effective.
We can use a significance level of 0.05. Using the given data, we calculate the test statistic as:
z = (p1 - p2) / √(p × (1-p) × (1/n1 + 1/n2))
where p = (x1 + x2) / (n1 + n2), x1 = 18, x2 = 12, n1 = 50, and n2 = 45.
The calculated z-value is approximately 1.02.
Using a standard normal distribution table, we find the p-value to be approximately 0.155.
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Calculator
What is the surface area of this right rectangular prism?
Enter your answer as a mixed number in simplest form by filling
in the boxes.
ft²
113
1 2
3 ft
3
4
5
2½ ft
6
7
8
Answers
Answer:93 1/3 yards or 280ft
Step-by-step explanation:Step-by-step explanation: first I converted it all into feet. Giving me L=9ft H=8ft and W= 4ft
Then inserted the values into the formula for surface area SA=2lw+2lh+2hw. Then solved it all out in a calculator
Line A passes through the points (-1, 5) and (3, 21).
Line B passes through the points (4, -2) and (-3, 19).
Find the point where line A intersects line B.
Answers
Answer:
A line's angle of slope between two points is (5, -4).
Step-by-step explanation:
Explanations are given in attachment!
PLS HELP WILL GIVE BRAINLIEST ALMOST DUE
Which equation could represent the line of best fit for the temperatures based on the altitudes?
Answers
Answer:
[tex]y = - \frac{7}{5} x + 59[/tex]
The value of a collectible coin can be represented by the equation y = 2X+ 9.74, where x represents the number of
vears that Consuello has owned the coin and y represents the total value, in dollars, of the coin. What was the value of the coin when Consuello originally purchased it?
Answers
The value of the coin when Consuello originally purchased it was $9.74.
What is the value of coin?
The given equation is y = 2x + 9.74, where x represents the number of years that Consuello has owned the coin and y represents the total value of the coin in dollars.
To find the value of the coin when Consuello originally purchased it, we need to find the value of y when x = 0.
Substituting x = 0 in the equation, we get:
y = 2(0) + 9.74
y = 0 + 9.74
y = 9.74
Therefore, the value of the coin when Consuello originally purchased it was $9.74.
What is coin?
A coin is a small, flat, round piece of metal or other material used as money to buy goods and services. It is typically issued by a government or other authority as legal tender and has a fixed value that is recognized within a specific country or region. Coins can be made from various metals, such as copper, nickel, silver, and gold, and often feature engravings or other designs that are intended to make them difficult to counterfeit.
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can I have the answer? It’s for completing the square
Answers
So, the equation of the given curve is a circle centered at (-13, 13) with a radius of 3. Therefore, the correct option is:
[tex](x + 13) ^ 2 + (y - 13) ^ 2 = 9[/tex].
What is equation?An equation is a mathematical statement that shows the equality between two expressions, typically separated by an equal's sign (=). Equations are used to represent a wide range of mathematical and scientific relationships, such as physical laws, chemical reactions, and statistical models. The expressions on either side of the equals sign can contain variables, constants, and mathematical operations, and solving the equation involves finding the value or values of the variables that make the equation true. Equations can take many forms, including linear equations, quadratic equations, trigonometric equations, and differential equations, among others.
To determine which option is correct, we can try to convert the given equation to the standard form of the equation of a circle, which is:
[tex](x - h)^2 + (y - k)^2 = r^2[/tex]
where (h, k) is the center of the circle and r is the radius.
We can complete the square for the given equation by adding and subtracting appropriate constants:
[tex]x^2 + 26x + y^2 - 26y + 329 = 0[/tex]
[tex](x^2 + 26x + 169) + (y^2 - 26y + 169) = -329 + 2(169)[/tex]
[tex](x + 13)^2 + (y - 13)^2 = 9[/tex]
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Solve the system of equations.
6x – y = 6
6x2 – y = 6
(0, 6) and (0, –6)
(1, 0) and (0, –6)
(2, 6) and (1, –11)
Answers
Solve by Graphing shown
a good hypothesis group of answer choices does not need a control. can be accepted or rejected. does not require repeated experimentation. all of the above none of the above
Answers
The hypothesis can be accepted or rejected based on the results of the experiment.
A good hypothesis from the given group of answer choices can be accepted or rejected. It is important for a hypothesis to be testable and falsifiable, which means that it should be possible to support or disprove it through experimentation or observation.
A control is necessary in experiments to compare the results and determine if the independent variable has an effect on the dependent variable.
Repeated experimentation is essential to ensure the validity and reliability of the results obtained.
Therefore, the correct answer is none of the above.
A hypothesis is an educated guess or a proposed explanation for an observation or a scientific problem.
In order to be considered a good hypothesis, it should have the following characteristics:
1. Testable and falsifiable: A good hypothesis should be possible to test through experimentation, observation, or other scientific methods. This means that it should be possible to gather evidence that either supports or disproves the hypothesis.
2. Clearly stated: A good hypothesis should be stated clearly and concisely, so that it is easy to understand what is being proposed and what the expected outcome is.
3. Based on existing knowledge: A good hypothesis should be based on existing knowledge and previous research. This means that it should be grounded in known facts, theories, or observations.
4. Specific: A good hypothesis should be specific in its predictions, making it easier to test and providing clearer results.
In conclusion, a good hypothesis can be accepted or rejected, should be testable and falsifiable, requires a control, and requires repeated experimentation to ensure the reliability and validity of the results.
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Rewrite as a logarithmic equation : e^2 =x
Answers
Answer:
e^2 = x, so ln(e^2) = ln x
ln x = 2
how do you solve 2×(6÷2+8)- 4? please help I need a answer and explanation.
Answers
Answer:
18
Step-by-step explanation:
remember parenthesis, always first then left to right so 6/2 is 3 +8 is 11 the x 22 is 22 then - 4 is 18 so your answer is 18
Mrs. Tinney’s class has the following scores on their most recent test:
100
98 95 88 72 16 0 78 80
85
Calculate the five number summary and use it to draw (and label) your box and whisker plot on a number line. Show your work for all calculations.
If Mrs. Aguiar’s class has a five number summary of: 30, 50, 80, 90, 95, which class’ scores are more consistent? How do you know?
The mean for Mrs. Tinney’s class is 71.2 and the mean for Mrs. Aguiar’s class is 79. What conjecture could we make about symmetry? Explain.
Answers
The five number summary for Mrs. Tinney's class is: 0, 72, 85, 96.5, 100. Tinney's class has a smaller IQR. We would need to look at a histogram or box and whisker plot to confirm these conjectures.
Describe Median?The median is a statistical measure that represents the middle value of a dataset. It is the value that separates the lower half of the dataset from the upper half. To find the median, the data must be arranged in order from smallest to largest, and then the middle value is identified.
If the dataset contains an odd number of values, then the median is the middle value. For example, if the dataset is {2, 4, 6, 7, 9}, then the median is 6, which is the middle value.
If the dataset contains an even number of values, then the median is the average of the two middle values. For example, if the dataset is {2, 4, 6, 7, 9, 10}, then the median is (6+7)/2 = 6.5, which is the average of the two middle values, 6 and 7.
To find the five number summary for Mrs. Tinney's class, we first need to order the scores from least to greatest:
0, 16, 72, 78, 80, 85, 88, 95, 98, 100
The minimum score is 0 and the maximum score is 100.
The median is the middle score, which is 85.
To find the first quartile, we split the scores into two halves at the median and find the median of the lower half:
0, 16, 72, 78, 80
The median of the lower half is 72.
To find the third quartile, we find the median of the upper half:
88, 95, 98, 100
The median of the upper half is 96.5.
Therefore, the five number summary for Mrs. Tinney's class is: 0, 72, 85, 96.5, 100.
To compare the consistency of the two classes, we can look at the interquartile ranges (IQRs), which give the range of scores that contain the middle 50% of the data. The IQR for Mrs. Tinney's class is 96.5 - 72 = 24.5, while the IQR for Mrs. Aguiar's class is 90 - 50 = 40. Mrs. Tinney's class has a smaller IQR, which means that their scores are more consistent.
The means for the two classes suggest that the data may not be symmetric. If the data were symmetric, we would expect the means to be roughly in the middle of the data set. However, the mean for Mrs. Aguiar's class is closer to the upper end of the data set, which suggests that the data may be skewed to the right. The mean for Mrs. Tinney's class is closer to the lower end of the data set, which suggests that the data may be skewed to the left. However, we would need to look at a histogram or box and whisker plot to confirm these conjectures.
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6. Maximizing Profits - You want to sell a certain number n of items in order to
maximize your profit. Market research tells you that if you set the price at $1.50, you
will be able to sell 5000 items, and for every 10 cents you lower the price below $1.50
you will be able to sell another 1000 items. Suppose that your fixed costs ("start-up
costs") total $2000, and the per item cost of production ("marginal cost") is $0.50.
Find the price to set per item and the number of items sold in order to maximize
profit, and also determine the maximum profit you can get.
Answers
With a price of $1.25, 7,500 goods would be sold and a profit of $3,635 would be made. This price would maximize profit.
What do we mean by profits?Profit in economics is the difference between an economic entity's revenue from outputs and all of its input costs.
It is equivalent to total income less total expenses, which includes both direct and indirect expenses.
Establishing sales methods and capturing your clients' interest requires first analyzing how profitable your goods and services are.
So, since you need to sell a certain number of items to maximize your profit, setting the price at $ 1.50 will enable you to sell 5000 items, and lowering the price by $10 will enable you to sell an additional 1000 items.
Assuming your fixed costs total $ 2000 and the cost of production per item is $ 0.50, you must determine the price to set per item, the number of items sold, and the maximum profit.
(5000 x 1.50) - (5000 x 0.50) - 2000 = 3000
(6000 x 1.40) - (6000 x 0.50) - 2000 = 3400
(7000 x 1.30) - (7000 x 0.50) - 2000 = 3600
(8000 x 1.20) - (8000 x 0.50) - 2000 = 3600
(7500 x 1.25) - (7500 x 0.50) - 2000 = 3625
Therefore, with a price of $1.25, 7,500 goods would be sold and a profit of $3,635 would be made. This price would maximize profit.
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Correct question:
You want to sell a certain number n of items in order to maximize your profit. Market research tells you that if you set the price at $1.50, you will be able to sell 5000 items, and for every 10 cents you lower the price below $1.50 you will be able to sell another 1000 items. Suppose that your fixed costs (“start-up costs”) total $2000, and the per item cost of production (“marginal cost”) is $0.50.
Solve the above engineering problem using calculus.
Hints: Find the price to set per item and the number of items sold in order to maximize profit, and also determine the maximum profit you can get.
To achieve M3, you must present your work using coherent, logical development of principles/concepts in determining the maximum profit and use technical language accurately.
To achieve D1, you must evaluate the validity of your answer using the given data.
Cuanto es ¿2x-3=6+x?????????
Answers
Answer: x=9
Step-by-step explanation:
2x-3=6+x
Add similar variables.
2x-3=6+x
+3 +3
2x=9+x
-x -x
x=9
Hope this helped!
Answer:
x=9
Step-by-step explanation:
primero, tomas y restas x de ambos lados.
2x-3=6+x
-x. - x
eso te deja con x-3=6. luego sumas 3 a ambos lados
x-3=6
+3. +3
eso te deja con x=9
HELP!!!!! Please. I really need it.
Answers
Let's call the price of the motorcycle "x".
We know that Lenny paid 12.5% in tax, which is the same as 0.125 as a decimal.
To find out how much tax Lenny paid, we can multiply the price of the motorcycle by 0.125:
0.125x = $1437.50
Now we can solve for x by dividing both sides by 0.125:
x = $11,500
Therefore, the price of the motorcycle, not including tax, was $11,500.
Answer:
Your question is:
1437.5 is 12.5% of what number?
1437.5 = 0.125x
x = 1437.5/.125 = $11,500
Therefore, the answer is $11,500!
Step-by-step explanation:
Please brainliest if the helped you a lot! And tell me if I am wrong! I would be so sorry if it was wrong! :D
This shows the net of a triangular prism.
What is the surface area of the prism?
3,900 m2
4,200 m2
4,800 m2
12,000 m2
Answers
Step-by-step explanation:
Two rectangles 2 x 25 x 40
one rectangle 40 x 40
two triangles (Area = 1/2 * base * height)
2 x 1/2 * 40 * 15
Total = 4200 m^2
5 yards of shirt fabric cost nine dollars how much does 12 yards of the same fabric cost? Please help me understand if you could!!!
Answers
Addition and Subtraction of polynomials
PLEASE SOLVE THIS I NEED THIS ASAP
Answers
The polynomial that represents the profit is P(x) = 6x^2z + 8x^2 + 18xz + 24x + 12z + 16.To find the polynomial that represents the profit P(x), we need to multiply the revenue polynomial R(x) by the cost polynomial C(z). We can set up the multiplication as:
P(x) = R(x) * C(z)
P(x) = (2x^2 + 6x + 4) * (3z + 4)
Using the distributive property, we can multiply each term of the first polynomial by each term of the second polynomial:
P(x) = (2x^2 * 3z) + (2x^2 * 4) + (6x * 3z) + (6x * 4) + (4 * 3z) + (4 * 4)
Simplifying each term, we get:
P(x) = 6x^2z + 8x^2 + 18xz + 24x + 12z + 16
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The perimeter of the shape below is 84 feet. What is the area (in square feet)?
The dimensions are as follows for a rectangle:
6x and 4x+2
Answers
Answer:
432 square feet
Step-by-step explanation:
12x+8x+4=84
20x=80
x=4
6(4)=24
4(4)+2=18
24 x 18 = 432
Find the volume of the cylinder rounded to the nearest tenth.
PLSSSSSSS HELP!!
Answers
To calculate the volume, you'll need to use the formula V = πr²h, where V represents the volume, r is the radius of the circular base, h is the height of the cylinder,
and π (pi) is a mathematical constant approximately equal to 3.14159.
Hi there! I understand you need help finding the volume of a cylinder
To apply this formula, you'll first need to know the values of the radius and the height of the cylinder. Once you have these values, follow these steps:
1. Square the radius (r²).
2. Multiply the squared radius by the height (r²h).
3. Multiply the result by π (V = πr²h).
Lastly, round the calculated volume to the nearest tenth as requested. Remember that I cannot provide you with the exact volume without the radius and height of the cylinder. Please provide the values, and I'll be glad to assist you with the calculation.
Keep in mind that the answer should be concise, so providing an answer in 180 words is not necessary. The information above should be sufficient to help you understand how to calculate the volume of a cylinder.
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3. Sarah is ready to buy her first car and will need to finance $32,000. She is currently considering two different loan options through Capital One Auto and Chase Auto. Each of the loan options is for a 72 month term.
Capital One Auto is offering a 6.9% interest rate compounded annually
Chase Auto is offering a 7.8% simple interest rate
Using a full sentence, explain which of the two loans you believe
Sarah should choose and why.
Answers
Answer:
Capital One Auto
Step-by-step explanation:
Based on the provided information, Sarah should go for the loan option offered by Capital One Auto with a 6.9% interest rate compounded annually because it is a lower interest rate than that of Chase Auto and compounded annually is more beneficial in the long term as opposed to simple interest rate offered by Chase Auto.
find the probability of tossing two dice and showing at least a 4 or the sum of dice is precisely 7
Answers
The probability of tossing two dice and showing at least a 4 or the sum of dice is precisely 7 is 5/12 or approximately 0.417.
To find the probability of tossing two dice and showing at least a 4 or the sum of dice is precisely 7, we need to add the probabilities of these two events happening.
The probability of rolling at least a 4 on one die is 3/6, or 1/2 because there are three ways to roll a number greater than or equal to 4 (4, 5, or 6) out of six possible outcomes. The probability of rolling at least a 4 on both dice is the product of the probabilities of rolling at least a 4 on each die, which is (1/2) x (1/2) = 1/4.
The probability of rolling a sum of 7 on two dice is 6/36, or 1/6 because there are six possible ways to roll a sum of 7 (1+6, 2+5, 3+4, 4+3, 5+2, or 6+1) out of 36 possible outcomes.
To find the probability of rolling at least a 4 or a sum of 7, we need to subtract the probability of rolling both from the total probability of rolling either. The total probability of rolling at least a 4 or a sum of 7 is the sum of their probabilities minus the probability of rolling both, which is:
(1/2) + (1/6) - (1/4) = 5/12
Therefore, the probability of tossing two dice and showing at least a 4 or the sum of dice is precisely 7 is 5/12 or approximately 0.417.
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Find the x- and y-intercepts of the graph of x+7y=12. State each answer as an integer or an improper fraction in simplest form
Answers
The x-intercept is (12, 0) and the y-intercept is (0, 12/7) or (0, 1 5/7) in mixed number form.
What are the intercepts?
Intercepts are the points where the graph intersects either the x-axis or the y-axis. The x-intercept is the point where the graph intersects the x-axis, which means the y-coordinate of the point is 0. The y-intercept is the point where the graph intersects the y-axis, which means the x-coordinate of the point is 0. To find the intercepts of a function, you can set one of the variables (x or y) to 0 and solve for the other variable. The resulting point will be the intercept.
To find the x-intercept, we set y to zero and solve for x:
x + 7(0) = 12
x = 12
So the x-intercept is (12, 0).
To find the y-intercept, we set x to zero and solve for y:
0 + 7y = 12
y = 12/7
So the y-intercept is (0, 12/7) or (0, 1 5/7) in mixed number form.
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pls help me, I have to give it in, pls help!!
Answers
By algebra properties, the values of x for each equation are listed below:
Case A: x = 0
Case B: x = 0
Case C: x = 1.584 or x = 1
Case D: x = 1.262 or x = - 0.631
Case E: x = 0.569
Case F: x = 2 or x = 1.322
How to solve equations involving exponential expressions
In this problem we find six cases of equations containing exponential expressions where the value of x must be found. This can be done by means of algebra properties:
Case A
2²ˣ - 2 ˣ⁺¹ + 1 = 0
(2ˣ)² - 2 · 2ˣ + 1 = 0
u² - 2 · u + 1 = 0
(u - 1)² = 0
u = 1
2ˣ = 1
x · ㏒₂ 2 = ㏒₂ 1
x = ㏒₂ 1
x = 0
Case B
3²ˣ - 3ˣ = 0
(3ˣ)² - 3ˣ = 0
3ˣ · (3ˣ - 1) = 0
3ˣ - 1 = 0
3ˣ = 1
x = 0
Case C
2²ˣ - 5 · 2ˣ + 6 = 0
(2ˣ)² - 5 · 2ˣ + 6 = 0
u² - 5 · u + 6 = 0
(u - 3) · (u - 2) = 0
u = 3 or u = 2
2ˣ = 3 or 2ˣ = 2
x = ㏒₂ 3 or x = 1
x = 1.584 or x = 1
Case D
2 · (3²ˣ) - 9 · 3ˣ + 4 = 0
2 · u² - 9 · u + 4 = 0
2 · [u² - (9 / 2) · u + 2] = 0
2 · (u - 4) · (u - 1 / 2) = 0
u = 4 or u = 1 / 2
3ˣ = 4 or 3ˣ = 1 / 2
x = ㏒₃ 4 or x = ㏒₃ (1 / 2)
x = 1.262 or x = - 0.631
Case E
6 · (5²ˣ) - 11 · 5ˣ - 10 = 0
6 · u² - 11 · u - 10 = 0
6 · [u² - (11 / 6) · u - 5 / 3] = 0
6 · (u - 2.5) · (u + 0.667)
u = 2.5 or u = - 0.667
x = 0.569
Case F
2²ˣ⁺¹ - 13 · 2ˣ + 20 = 0
2 · (2ˣ)² - 13 · 2ˣ + 20 = 0
2 · u² - 13 · u + 20 = 0
2 · [u² - (13 / 2) · u + 10] = 0
2 · (u - 4) · (u - 5 / 2) = 0
u = 4 or u = 5 / 2
2ˣ = 4 or 2ˣ = 5 / 2
x = 2 or x = 1.322
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A researcher estimates that a fossil is 3200 years old.Using carbon-14 dating,a procedure used to determine the age of an object,the researcher discovers that the fossil is 3600 years old.
a.Find the percent error
b.what other estimates gives the same percent error?Explain your reasoning
Answers
The percentage error between the estimated age and the carbon-14 dating age of the fossil is 12.5% and an estimated age of approximately 2978 years would give the same percent error of 12.5%.
What is the definition of percentage?
Percentage is a way of expressing a fraction or proportion as a part of 100. It is denoted by the symbol "%". The term "percent" means "per hundred". For example, if 50% of a group of people are men, it means that 50 out of every 100 people in the group are men.
Now,
a). To find the percent error between the estimated age and the carbon-14 dating age of the fossil, we can use the formula:
percent error = |(estimated age - carbon-14 dating age) / estimated age| x 100%
Substituting the given values, we get:
percent error = |(3200 - 3600) / 3200| x 100%
= |-400 / 3200| x 100%
= 12.5%
Therefore, the percent error between the estimated age and the carbon-14 dating age of the fossil is 12.5%.
b). To find other estimates that give the same percent error, we can use the formula:
percent error = |(estimated age - carbon-14 dating age) / estimated age| x 100%
If we let x be the estimated age that gives the same percent error, then we can write:
12.5% = |(x - 3600) / x| x 100%
Simplifying, we get:
0.125 = |(x - 3600) / x|
Taking the positive square root of both sides (since percent error cannot be negative), we get:
√0.125 = (x - 3600) / x
Simplifying, we get:
x = 3600 / (1 - √0.125)
x ≈ 2978
Therefore, an estimated age of approximately 2978 years would give the same percent error of 12.5% as the original estimated age of 3200 years. This means that if the fossil were actually 2978 years old, the carbon-14 dating would have given an age estimate of approximately 3299 years, which is 12.5% higher than the true age.
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Darlene organizes recycling drives for old cellular phones and other electronics. She is paid
$200 per week plus $25 for each event. This month, she will work four weeks and wants to
earn at least $1,200. Darlene decides to organize four recycling events each week this month.
Enter an inequality for the number of events Darlene needs to organize to reach her goal of
at least $1,200. Solve the inequality and explain whether four events each week are enough
to meet her goal.
(Please help)
Answers
If the number of events is taken as x then the inequality is:
[tex](200*4)+(x*25)\geq 1200[/tex] ( as there are only 4 weeks in a month )
If we further solve this inequality we can get the answer:
[tex]800+(x*25)\geq 1200[/tex]
[tex]x*25\geq 400[/tex]
[tex]x\geq \frac{400}{25}[/tex]
[tex]x\geq 16[/tex]
So, as we saw here, the minimum number of events required for Darlene to complete the goal is 16.
But she is planning to organize 4 events which is insufficient. She needs to organize 12 more events in order to satisfy the inequality.
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Let's first calculate how much Darlene will earn in one week by organizing four recycling events:
$200 (base pay) + $25 (per event) x 4 (number of events) = $300
So, if Darlene organizes four recycling events per week, she will earn $300 per week.
To reach her goal of at least $1,200 in four weeks, we can set up the following inequality:
4 x (number of events) x $25 + $200 x 4 ≥ $1,200
100 x (number of events) + $800 ≥ $1,200
100 x (number of events) ≥ $400
(number of events) ≥ 4
Therefore, the number of events Darlene needs to organize to reach her goal of at least $1,200 is at least 4.
Since Darlene plans to organize four recycling events per week, this means she would need to work four weeks to reach her goal. Therefore, organizing four events each week would be enough to meet her goal, as long as she works all four weeks
I need help finding the product to these algebra problems.
Answers
7. The simplified expression is 96[tex]x^{-1}[/tex][tex]y^{-5}[/tex], 8. The simplified expression is 5(m - 2)/(m - 1), 9. The simplified expression is 3/5,
10. The simplified expression is -(p + 10)/(p(9 - p)).
What is an expression?
7. To simplify the expression, we can cancel out common factors in the numerator and denominator:
(32x³ * y)/(5x * y²) * (15y)/(8x² *[tex]y^{4}[/tex] )
= (32/5) * (x³/x²) * (1/y²) * (3/2) * (1/x²) * (1/y³)
= 96[tex]x^{-1}[/tex][tex]y^{-5}[/tex]
Therefore, the simplified expression is 96[tex]x^{-1}[/tex][tex]y^{-5}[/tex].
8. The simplified expression is 5(m - 2)/(m - 1).
To simplify the expression, we can factor the numerator:
(m² - 6m + 8)/(2m - 2) = (m - 4)(m - 2)/(2(m - 1))
We can then cancel out common factors:
(m - 4)(m - 2)/(2(m - 1)) * 10/(m - 4)
= 5(m - 2)/(m - 1)
Therefore, the simplified expression is 5(m - 2)/(m - 1).
9. The simplified expression is 3/5.
To simplify the expression, we can first simplify the fractions within the parentheses:
28n + 40/35n + 50 = (4n + 8)/(5n + 10)
12n + 24/8n + 16 = (3n + 6)/(2n + 4)
We can then simplify the expression by multiplying the two fractions:
(4n + 8)/(5n + 10) * (3n + 6)/(2n + 4)
= 2(2n + 4)/(5n + 10) * 3(n + 2)/(2(n + 2))
= 3/5
Therefore, the simplified expression is 3/5.
10. The simplified expression is -(p + 10)/(p(9 - p)).
To simplify the expression, we can factor the second fraction in the numerator and then cancel out common factors:
(p + 10)/(9 - p) * (p² - 5p - 36)/(4p² + 16p)
= (p + 10)/(9 - p) * ((p - 9)(p + 4))/(4p(p + 4))
= -(p + 10)/(p(9 - p))
Therefore, the simplified expression is -(p + 10)/(p(9 - p)).
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pat designs a patio with a trapezoid shaped deck consisting of 16 rows of congruent slate tiles. the numbers of tiles in the rows form an arithmetic sequence. the first row contains 15 tiles and the last row contains 30 tiles. how many tiles are used in the deck?
Answers
Let d be the common difference between the rows. We can write the following equation:
15 + 15d = 30
Solving for d:
15d = 30 - 15
15d = 15
d = 1
Now that we know the common difference is 1, we can use the arithmetic series formula to find the total number of tiles used in the deck:
S = n * (a1 + an) / 2
Here,
S = total number of tiles
n = number of rows (16)
a1 = number of tiles in the first row (15)
an = number of tiles in the last row (30)
S = 16 * (15 + 30) / 2
S = 16 * 45 / 2
S = 16 * 22.5
S = 360
So, Pat used a total of 360 tiles for the trapezoid-shaped deck.
Answer:360
The number of tiles used in the deck is 525. This can be answered by the concept of arithmetic sequence.
Let x be the number of tiles in each row in the arithmetic sequence. Then, the sum of the number of tiles in all 16 rows can be expressed as the sum of an arithmetic series:
S = (n/2)(a + l),
where n is the number of terms, a is the first term, and l is the last term. In this case, n = 16, a = 15, l = 30, and x is the common difference, which can be found by using the formula:
x = (l - a) / (n - 1)
Substituting the values given, we get x = 1.25. Therefore,
S = (16/2)(15 + 30) = 525.
Therefore, the total number of tiles used in the deck is 525.
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which of the following is the standard equation of a circle with center (-1,-6) and radius 5?
Answers
Answer:
(x + 1)^2 + (y + 6)^2 = 25.
Step-by-step explanation:
The standard equation of a circle with center (h, k) and radius r is given by:(x - h)^2 + (y - k)^2 = r^2In this case, the center of the circle is (-1, -6) and the radius is 5. Substituting these values into the equation, we get:(x - (-1))^2 + (y - (-6))^2 = 5^2Simplifying and rearranging terms, we get:(x + 1)^2 + (y + 6)^2 = 25Therefore, the standard equation of the circle with center (-1, -6) and radius 5 is (x + 1)^2 + (y + 6)^2 = 25.two forces are acting upon an object F1 is 10N and is being applied at a 270 angle with the positive x-axis...
here's the answers:
Answers
The components of force F1 are F1x = 0N (along the x-axis) and F1y = -10N (along the y-axis).
To determine the components of the two forces acting upon an object with F1 = 10N at a 270° angle with the positive x-axis,
follow these steps:
Step 1: Convert the angle to a standard position
Since the angle is given in degrees and with respect to the positive x-axis, it is already in the standard position.
Step 2: Find the x and y components of F1
To find the components of F1, we'll use trigonometry.
At 270°, the force is pointing straight down along the negative y-axis.
So, the x-component (F1x) is 0, and the y-component (F1y) is -10N.
F1x = F1 * cos(270°) = 10N * 0 = 0N
F1y = F1 * sin(270°) = 10N * (-1) = -10N.
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or
Find WX.
4
W
X
Y
49°
Write your answer as an integer or as a decimal rounded to the nearest tenth.
Answers
The length of side WX is 2.61 units
Trigonometric ratios:
Trigonometric ratios are mathematical relationships that describe the proportions between the sides of a right triangle. There are three main trigonometric ratios: sine, cosine, and tangent.
Cosine (cos) is defined as the ratio of the length of the side adjacent to the angle to the length of the hypotenuse of the right triangle. It is expressed as cosθ = adjacent/hypotenuse.
Here we have
The triangle XYW is right-angled
Where Hypotenues WY = 4
The measure of angle W = 49°
From triangonometric ratios
Cos θ = Adjacent/Hypotenuse.
Cos 49° = WX/4
0.6561 = WX/4 [ Since Cos 49° = 0.6561 ]
=> WX = 4(0.6561)
=> WX = 2.6244
=> WX = 2.61
Therefore,
The length of side WX is 2.61 units
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