9 Real / Modelling Naomi rents a room to teach yoga to x people.
She uses this equation to work out her profit, y, in pounds:
y = 10x - 50
a Draw the graph of the line y = 10x - 50.
b i What is her profit when 0 people attend the class?
ii What does the y-intercept represent?
c How much does each person pay for the class?
Answers
Her profit when 0 people attend is -$50 and each person pays 10
Drawing the graph of the lineFrom the question, we have the following parameters that can be used in our computation:
y = 10x - 50.
The graph is added as an attachment
Her profit when 0 people attendThis means that
x = 0
So, we have
y = 10(0) - 50.
y = -50
She made a loss of 5-
What the y-intercept representsThis represents her profit when 0 people attend
How much each person pays per classThis represents the slope of the function
The slope of the function is 10
So, each person pays 10
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Related Questions
Angad adds 20 to it, then doubles it and gets an answer of 53. what was the original number?
Answers
The original number was 17 to which when Angad adds 20, then doubles it and gets an answer of 53.
To solve this problem, we need to work backwards from the final answer. If Angad added 20 to the original number, we can subtract 20 from 53 to get 33. This means that after Angad doubled the number, he had 33.
To find the original number, we need to undo the doubling process. If Angad had 33 after doubling the number, we can divide 33 by 2 to get the original number.
33 divided by 2 equals 16.5. However, we know that the original number must be a whole number since we cannot add 20 to a decimal. Therefore, we can round up to the nearest whole number to get 17.
So, the original number was 17.
In summary, to find the original number, we worked backwards from the final answer and undid the steps that Angad took. We subtracted 20 to undo the addition, then divided by 2 to undo the doubling. We rounded up to the nearest whole number since the original number must be a whole number.
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Jesse can mow 3 yards in 8 hours. Jackson can mow twice as many yards per hour. What is the constant of proportionality between the number of yards Jackson can mow and the number of hours?
Answers
If Jesse can mow 3 yards in 8 hours. Jackson can mow twice as many yards per hour the constant of proportionality between the number of yards Jackson can mow and the number of hours is 3/4.
To find the constant of proportionality between the number of yards Jackson can mow and the number of hours, we can use the formula:
k = y/x
where k is the constant of proportionality, y is the number of yards, and x is the number of hours.
We know that Jesse can mow 3 yards in 8 hours, which means his rate of mowing is: 3 yards/8 hours = 3/8 yards per hour
We also know that Jackson can mow twice as many yards per hour as Jesse, which means his rate of mowing is:
2 * (3/8) yards per hour = 3/4 yards per hour
Now we can use the formula to find the constant of proportionality for Jackson:
k = y/x = (3/4) yards per hour / 1 hour = 3/4
Therefore, the constant of proportionality between the number of yards Jackson can mow and the number of hours is 3/4.
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Q 28 : A new school has built lockers for its students. All the digits from 0 to 9, together with
the letters A to Y, have been used to identify the lockers. Only 4 digits have been used to
identify the lockers with the letter Z. How many lockers have been built in this school, if each
locker is identified by one letter and one digit?
Answers
If each locker is identified by one letter and one digit, the total number of lockers built in the school is 229.
There are 26 letters in the alphabet (A to Z), and if each locker is identified by one letter and one digit, then there are a total of 26 × 10 = 260 possible locker identifications using the letters A to Y and digits 0 to 9.
Out of these, there are 4 digits used to identify the lockers with the letter Z. So, there are 10 − 1 = 9 digits left to use for the remaining lockers, as we cannot use the digit already used for the lockers with the letter Z.
Similarly, there are 25 letters left to use for the remaining lockers, as we cannot use the letter Z.
Therefore, the number of remaining lockers is 9 × 25 = 225. Adding the 4 lockers with the letter Z, the total number of lockers built in the school is 225 + 4 = 229.
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A 3-inch candle burns down in 3 hours. At what rate does the candle burn, in inches per hour?
Answers
Answer 1 inch per hour
Step-by-step explanation:
Answer:
1 inch per hour
Step-by-step explanation:
Let x represent inches burned per hour
The equation to finding the rate of the candle burning:
3x=3
For those who dont know, whenever you have a variable with a term, its basically multiplying, and we want to do the opposite to get x by itself, so we divide
x=3/3
Which can be simplified as:
x=1
Where x is the inches burned per hour, which equal 1
Joyner Company’s income statement for Year 2 follows:
Sales $ 703,000
Cost of goods sold 109,000
Gross margin 594,000
Selling and administrative expenses 151,700
Net operating income 442,300
Nonoperating items:
Gain on sale of equipment 9,000
Income before taxes 451,300
Income taxes 135,390
Net income $ 315,910
Its balance sheet amounts at the end of Years 1 and 2 are as follows:
Year 2 Year 1
Assets
Cash and cash equivalents $ 294,410 $ 55,900
Accounts receivable 228,000 141,000
Inventory 318,000 289,000
Prepaid expenses 10,000 20,000
Total current assets 850,410 505,900
Property, plant, and equipment 639,000 508,000
Less accumulated depreciation 165,300 130,200
Net property, plant, and equipment 473,700 377,800
Loan to Hymans Company 46,000 0
Total assets $ 1,370,110 $ 883,700
Liabilities and Stockholders' Equity
Accounts payable $ 311,000 $ 262,000
Accrued liabilities 49,000 57,000
Income taxes payable 84,200 80,700
Total current liabilities 444,200 399,700
Bonds payable 209,000 105,000
Total liabilities 653,200 504,700
Common stock 340,000 287,000
Retained earnings 376,910 92,000
Total stockholders' equity 716,910 379,000
Total liabilities and stockholders' equity $ 1,370,110 $ 883,700
Equipment that had cost $31,500 and on which there was accumulated depreciation of $10,400 was sold during Year 2 for $30,100. The company declared and paid a cash dividend during Year 2. It did not retire any bonds or repurchase any of its own stock.
Required:
1. Using the indirect method, compute the net cash provided by/used in operating activities for Year 2.
2. Prepare a statement of cash flows for Year 2.
3. Compute the free cash flow for Year 2
Answers
the free cash flow for Joyner Company in Year 2, we need to follow these steps:
Step 1: Calculate operating cash flow (OCF).
Operating cash flow is calculated by taking the company's net income, adding back non-cash expenses (depreciation and amortization), and adjusting for changes in working capital.
Step 2: Calculate capital expenditures (CapEx).
Capital expenditures are the funds used by the company to acquire, upgrade, and maintain physical assets, such as equipment or buildings. In this case, we need to find the net change in equipment and accumulated depreciation.
Step 3: Subtract the cash dividend.
The cash dividend paid by the company during Year 2 should be subtracted from the operating cash flow.
Step 4: Calculate the free cash flow.
Free cash flow is the remaining cash after deducting capital expenditures and cash dividends. It represents the cash available for the company to repay debt, reinvest in the business, or distribute to shareholders.
Unfortunately, the provided information is not sufficient to compute the free cash flow for Year 2. Specifically, the net income, changes in working capital, and complete equipment transactions are needed to perform these calculations. Please provide the missing information so that a detailed step-by-step explanation can be given to compute the free cash flow for Joyner Company in Year 2.
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7. 7 puzzle time when do you put the cart before the horse
Answers
The phrase "putting the cart before the horse" refers to doing things in the wrong order or prioritizing less important tasks over more crucial ones.
In the context of the puzzle time question, the answer is: You should never put the cart before the horse, as it is essential to follow the proper sequence of actions to achieve the desired outcome effectively.
In the context of the puzzle time question, the phrase "putting the cart before the horse" implies that it is crucial to follow the proper sequence of actions or steps to solve the puzzle correctly.
By prioritizing less important tasks or skipping essential steps, the desired outcome may not be achieved, and the solution may be flawed.
To effectively solve the puzzle, it is essential to understand and follow the rules, guidelines, and necessary steps in the correct order. This ensures that each action builds upon the previous one and leads to a coherent solution.
By doing so, you avoid the mistake of putting the cart (less important tasks) before the horse (more crucial steps), leading to a successful and accurate solution.
In summary, the phrase "putting the cart before the horse" emphasizes the importance of following the correct sequence of actions or steps in any given task, including solving puzzles. It serves as a reminder to prioritize tasks appropriately to achieve the desired outcome effectively.
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You are throwing a birthday party and are ordering pizza for your guests! You are guessing there will be about 30 people in attendance. You have two options for pizzas! You have budgeted $215 for food so you want to go with the option that will give you the better deal. This means the option that gives you a cheaper price per square inch of pizza
Answers
Based on these calculations, option 1 gives you the cheaper price per square inch of pizza.
To determine which option will give you a cheaper price per square inch of pizza, you will need to compare the prices of the two options and calculate their respective prices per square inch.
Let's say option 1 is a large pizza with a diameter of 18 inches and costs $20, while option 2 is a medium pizza with a diameter of 14 inches and costs $15.
To calculate the area of each pizza, you need to use the formula for the area of a circle:
A = πr^2
For option 1, the radius is 9 inches (half of the diameter), so the area is:
A = π(9)^2 = 81π square inches
For option 2, the radius is 7 inches (half of the diameter), so the area is:
A = π(7)^2 = 49π square inches
Now you can calculate the price per square inch for each option by dividing the cost by the area:
Option 1:
Price per square inch = $20 / (81π) = $0.078/square inch
Option 2:
Price per square inch = $15 / (49π) = $0.098/square inch
Based on these calculations, option 1 gives you the cheaper price per square inch of pizza.
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C = 172. 7 cm
Use the formula, c = πd, and π = 3. 14, to find the diameter of this circle whose circumference equals 172. 7 cm.
O A. 55 cm
O B. 27. 5 cm
O C. 542. 278 cm
O D. 5. 5 cm
O E. 86. 35 cm
Answers
The diameter of the circle whose circumference equals 172.7 cm is approximately 55 cm, as found using the formula c = πd with the given value of π as 3.14. The answer is option A.
The formula for the circumference of a circle is c = πd, where c is the circumference and d is the diameter. We are given that the circumference of the circle is 172.7 cm, and π is approximately 3.14. So we can solve for the diameter as
d = c/π = 172.7/3.14 ≈ 55
Therefore, the diameter of the circle is approximately 55 cm.
The correct answer is option A: 55 cm.
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What is the volume of the following rectangular prism?
2 units and 7 1/3 units
Answers
The volume of a rectangular prism is calculated by multiplying the length, width, and height. In this case, we are given the length and width, but not the height. So, we cannot calculate the exact volume without knowing the height.
To find the volume of a rectangular prism, we need to multiply its length, width, and height.
Given:
Length = 2 units
Width = 7 1/3 units
To calculate the volume, we first need to convert the mixed fraction to an improper fraction.
7 1/3 = (7 * 3 + 1) / 3 = 22/3 units.
Now, we can calculate the volume:
Volume = Length * Width * Height
= 2 units * (22/3 units) * Height.
Since the height is not provided, we cannot calculate the exact volume without that information. However, if you provide the height of the rectangular prism, I can help you find the volume by substituting the value into the formula.
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A Texas House representative proposed placing solar panels on all public schools to increase green energy and reduce energy costs for districts. Suppose a manufacturer’s panels will be purchased only if real world results of the proposed panels show that more than 18% of the panels produce an efficiency rating greater than 20%. Of a random selection of 140 panels, 32 of the panels result in an efficiency rating greater than 20%. Is there sufficient evidence at the 5% significance level to purchase the proposed panels?
Answers
By null hypothesis there is sufficient evidence at the 5% significance level to purchase the proposed panels.
To determine if there is sufficient evidence to purchase the proposed panels, we can perform a hypothesis test. Let's define the following:
- p: the proportion of all panels that produce an efficiency rating greater than 20%
- p0: the proportion specified in the proposal, which is p0 = 0.18
- n: the sample size, which is n = 140
- x: the number of panels in the sample that produce an efficiency rating greater than 20%, which is x = 32
We want to test the null hypothesis H0: p <= p0 against the alternative hypothesis Ha: p > p0. The significance level is alpha = 0.05.
We can use the normal approximation to the binomial distribution since both np0 and n(1-p0) are greater than 10, where np0 is the expected number of panels that produce an efficiency rating greater than 20% under the null hypothesis.
Under the null hypothesis, the test statistic z is approximately:
z = (x - np0) / sqrt(np0(1-p0))
Plugging in the values, we get:
z = (32 - 140*0.18) / sqrt(140*0.18*0.82) ≈ 1.96
The critical value of z at alpha = 0.05 with a one-tailed test is 1.645. Since our calculated z value is greater than the critical value, we reject the null hypothesis.
Therefore, there is sufficient evidence at the 5% significance level to purchase the proposed panels.
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Please help asap I need this until tmr
Answers
The finished table contains the following amount of cans per day:
- 4 1 - 5 2/5- 6 1 ¹/₂- 7 1 ³/₄- 8 2- 9 2¹/₄- 10 2¹/₂- 11 2³/₄- 12 3- 13 3¹/₈- 14 3³/₁₀- 15 3³/₄How to determine fractions?To find out how many cans of food per day to give a cat, divide the cat's weight by 4. If the weight is not a multiple of 4, the result will be a fraction, which represents a fraction of a can of food.
A 5-pound cat needs 5/4 or 1.25 cans of food per day. Simplify this fraction to 1 ¹/₄ or 1.25.
Others include:
6/4 = 1.5
7/4 = 1.75
8/4 = 2
9/4 = 2.25
10/4 = 2.5
11/4 = 2.75
12/4 = 3
13/4 = 3.25
14/4 = 3.5
15/4 = 3.75
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The table shows the number of cups of flour, f, that a bakery needs for the number of pound cakes that they make, p.
Pound Cakes, p 3 6 9 14
Cups of Flour, f 8. 25 16. 5 24. 75 ?
Part A
Which equation relates the number of cups of flour to the number of pound cakes that the bakery makes?
f = 2. 75p
f = 0. 343p
f = 2. 75p + 8. 25
f = 0. 343p + 16. 5
Part B
How many cups of flour are needed for 14 cakes?
4. 802
21. 302
38. 5
46. 75
Answers
A) The equation relates the number of cups of flour to the number of pound cakes that the bakery makes is f = 2.75p
B) Cups of flour are needed for 14 cakes is 38.5
A) The number of cups of flour, f, that a bakery needs for the number of pound cakes that they make, p is directly proportional to each other which can be written in form ,
f/p = 8.25/3
f = (8.25/3)×p
f = 2.75 p
The equation forms is f = 2.75p
B) Cups of flour are needed for 14 cakes
Here p = 14
by putting the value in the equation we get ,
f = 2.75(14)
f = 38.5
hence , cups of flour are needed for 14 cakes is 38.5
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Describe the specific sequence of transformations that would map triangle abc to triangle a'b'c'.
Answers
Translation, rotation, and reflection, By following these transformations in sequence, you can map triangle ABC to triangle A'B'C'.
To map triangle ABC to triangle A'B'C', you would need to follow a specific sequence of transformations, which may include translation, rotation, and reflection. Here's a step-by-step explanation:
Step 1: Translation
Translate triangle ABC by a specific vector (x, y) so that point A moves to point A'. The same vector will also move points B and C to their corresponding new positions.
Step 2: Rotation
If triangle A'B'C' is rotated compared to the translated triangle, rotate the translated triangle around point A' by a specific angle, either clockwise or counterclockwise, until point B aligns with point B'.
Step 3: Reflection
If triangle A'B'C' is a mirror image of the rotated triangle, reflect the rotated triangle across a line of symmetry (usually a line passing through A'). This will change the orientation of the triangle and align point C with point C'.
By following these transformations in sequence, you can map triangle ABC to triangle A'B'C'. Keep in mind that the specific details of translation, rotation, and reflection will depend on the coordinates and orientation of the given triangles.
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Please hurry I need it ASAP
Answers
Answer:
20
Step-by-step explanation:
(x-3)+(8x+3)=180
9x=180
x=20
Solve for x. −43x 16<79 drag and drop a number or symbol into each box to correctly complete the solution.
Answers
-43x < 79 - 16
How can the inequality −43x + 16 < 79 be solved?To solve the inequality −43x + 16 < 79, we need to isolate the variable x.
Let's begin by subtracting 16 from both sides of the inequality:
−43x + 16 - 16 < 79 - 16
Simplifying the equation, we have:
−43x < 63
Next, we divide both sides of the inequality by -43. However, when we divide by a negative number, the direction of the inequality sign will be flipped:
x > 63 / -43
Simplifying further, we have:
x > -1.465
Therefore, the solution to the inequality is x > -1.465.
In interval notation, we can represent the solution as (-1.465, ∞), indicating that x is greater than -1.465 and extends indefinitely towards positive infinity.
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A spinner is divided into 15 identical sectors and labeled 1 through 15.
how many spins are expected for a multiple of 4 to be spun 7 times?
select from the drop-down menu to correctly complete the sentence.
the spinner is expected to have to spin approximately times for a multiple of 4 to be spun 7 times.
Answers
Answer: 35
Step-by-step explanation: The other person is wrong
Hope this helped :)
A restaurant needs a block of ice that is exactly 480 cubic inches in volume
The height of the ice block must be 10 inches. Pls help is this right ????
Answers
The height of the ice block must be 10 inches, the length and width could be any combination of dimensions that multiply together to equal 48 square inches.
Explain volume?The overall number of cube units that the cube totally occupies is the definition of a cube's volume. Volume is simply the total amount of space an object takes up. The cube's volume can be calculated using the formula a3 where an is the cube's edge.
given,
To check if the height of the ice block must be 10 inches to have a volume of 480 cubic inches, we can use the formula for the volume of a rectangular solid:
V = l * w * h
where l represents the length, w represents the measurement of width, while h is the peak, and V is the volume.
Since the volume is given as 480 cubic inches, and the height is specified as 10 inches, we can write:
480 = l * w * 10
Dividing both sides by 10, we get:
48 = l * w
This means that the product of the length and width must be equal to 48 square inches in order for the block of ice to have a volume of 480 cubic inches with a height of 10 inches.
There are many possible dimensions that satisfy this condition. For example, the block of ice could have dimensions of 8 inches by 6 inches by 10 inches, or 12 inches by 4 inches by 10 inches, or 16 inches by 3 inches by 10 inches, and so on.
Therefore, while the height of the ice block must be 10 inches, the length and width could be any combination of dimensions that multiply together to equal 48 square inches.
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A rectangle city park measures 7/10 mile by 2/6 mile. what is the area of the park?
Answers
The area of the rectangular park is equal to 0.233 sq miles.
The measurements of the park that are given in the question are given as 7/10 mile by 2/6 mile.
The length of the rectangle park is 7/10 and the width of the park is 2/6 mile. We know that the area of the rectangle park is given as the:
= length * width of the park.
= L * W
= (7/10) * (2/6)
we can reduce the fraction even further to make the calculation easy
= (7/10) * (1/3)
Multiplying the denominators we get
= 7/30
To make the answer even simpler it can be converted into a decimal form which will be:
= 0.233 sq miles.
Therefore, The area of the rectangular park is equal to 0.233 sq miles.
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23. A triangular earring has side lengths of 1. 5 centimeters, 2 centimeters, and 3
centimeters. What is the approximate measure, in degrees, of the largest angle of the
triangular earring?
А
36. 3°
B.
45. 8°
C. 117. 3°
D.
134. 2°
Answers
Using cosine rule, the largest angle In the triangle is
C. 117. 3°How to find the measure of the largest angleThe angle is found first using cosine rule by the formula
cos A = (b² + c² - a²) ÷ 2bc
Solving for the largest angle
substituting the values
cos γ = (2² + 1.5² - 3²) ÷ 2 * 1.5 * 2
< γ = arc cos ( -0.4583 )
< γ = 117.28 degrees
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The demand function for an exclusive wool blanket is given byp=D(x)=33-2√x dollars, where x is in thousands of blankets. Findthe level of production for which the demand is elastic
Answers
To maximize the company's profit, we need to find the profit function and then differentiate it with respect to the quantities produced by each plant to find the optimal values.
The profit function is given by:
π = TR - TC
where TR is the total revenue and TC is the total cost.
Using the demand function p = 40 - 0.04q, we can express the total revenue as:
TR = p * q = (40 - 0.04q) * q = 40q - 0.04q²
The total cost is the sum of the costs of each plant, so we have:
TC = C1 + C2 = 6.7 + 0.03q1² + 7.9 + 0.04q2² = 14.6 + 0.03q1² + 0.04q2²
Substituting these expressions into the profit function, we get:
π = 40q - 0.04q² - 14.6 - 0.03q1² - 0.04q2²
To find the optimal values of q1 and q2, we differentiate the profit function with respect to each quantity and set the derivatives equal to zero:
∂π/∂q1 = 40 - 0.06q1 - 0.04q2 = 0
∂π/∂q2 = 40 - 0.03q2 - 0.04q1 = 0
Solving these equations, we get:
q1 = 357.14
q2 = 285.71
So each plant should produce 357.14 and 285.71 units of the item, respectively, in order to maximize the company's profit.
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Select all of the statements that are true
The [9.7] = -9.7 because the distance from -9.7 to 0 on the number line is 9.7 units.
Numbers with the same absolute value are opposites because they are the same distance from each other.
The [7.1] = 7.1 because the distance from 7.1 to 0 on the number line is 7.1 units.
The [-8.4] = 8.4 because the distance from -8.4 to 8.4 on the number line is 0 units.
Numbers with the same absolute value are opposites because they are the same distance from 0 on the number line.
The [-12.5] = 12.5 because the distance from 12.5 to 0 on the number line is -12.5 units.
Answers
The true statements are Numbers with same absolute value are opposites because they are same distance from each other and from 0 on the number line. The |7.1| = 7.1. So, correct options are B, C and E.
b) Numbers with the same absolute value are opposites because they are the same distance from each other. This is true because absolute value is the distance from a number to zero on the number line, and if two numbers have the same distance from zero, then they must be equidistant from zero and therefore, they are opposite in sign.
c) The |7.1| = 7.1 because the distance from 7.1 to 0 on the number line is 7.1 units. This is true because the absolute value of a number is always positive, and it represents the distance of that number from zero on the number line.
d) The |-8.4| = 8.4 because the distance from -8.4 to 8.4 on the number line is 0 units. This is false, as the distance between -8.4 and 8.4 on the number line is 16.8 units. The correct value of the absolute value of -8.4 is 8.4.
e) Numbers with the same absolute value are opposites because they are the same distance from 0 on the number line. This is true because 0 is the midpoint of the number line, and if two numbers have the same distance from 0, then they must be equidistant from zero and therefore, they are opposite in sign.
Therefore, the correct statements are b, c, and e.
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A national grocery chain is considering expanding their selection of prepared meals available for purchase. They believe that nationwide, 67 percent of households purchase at least one prepared meal per week from the grocery store. The results of a survey given to a random sample of Maryland households found that 641 out of 1,035 households purchase at least one meal per week at the store
Answers
61.93% of the surveyed Maryland households purchase at least one prepared meal per week from the grocery store.
A national grocery chain is considering expanding their selection of prepared meals, and they believe that 67 percent of households purchase at least one meal per week from the grocery store. In a survey conducted in Maryland, 641 out of 1,035 households purchase at least one meal per week at the store.
To determine the percentage of Maryland households purchasing at least one prepared meal per week, follow these steps:
Divide the number of households purchasing at least one meal per week (641) by the total number of households surveyed (1,035).
Multiply the result by 100 to get the percentage.
Here's the calculation: (641 / 1,035) x 100 = 61.93%
So, 61.93% of the surveyed Maryland households purchase at least one prepared meal per week from the grocery store.
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The antiderivative ofeᵏˣ, where k is any constant, is... ½ eᵏˣ + c keᵏˣ + c eᵏˣ + c In(kx)+C
Answers
The antiderivative of e^(kx), where k is any constant, is (1/k)e^(kx) + C, where C is the constant of integration.
1. As we can see, you are asked to find the antiderivative of the function e^(kx).
2. Recall that the antiderivative of a function is the function that, when differentiated, gives you the original function.
3. The derivative of the function (1/k)e^(kx) is e^(kx), as the constant k in the exponent gets multiplied by the (1/k) factor, canceling each other out.
4. So, the antiderivative of e^(kx) is (1/k)e^(kx) + C, where C is the constant of integration.
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In a nuclear disaster, there are multiple dangerous radioactive isotopes that can be detected. If 91.9% of a particular isotope emitted during a disaster was still present 6 years after the disaster, find the continuous compound rate of decay of this isotope. The continuous compound rate of decay of this isotope is
Answers
The first derivative of the implicit function given by x^(2/3) + y^(2/3) = 14 can be found using implicit differentiation. We take the derivative of both sides with respect to x and use the chain rule to differentiate the terms involving y:(2/3)x^(-1/3) + (2/3)y^(-1/3) * dy/dx = 0Then, we solve for dy/dx:dy/dx = -(x/y)^(1/3)This is the first derivative of the implicit function. To evaluate it at a specific point, we need to substitute the coordinates of that point into the equation above.
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The continuous compound rate of decay of this isotope is approximately 1.41%.
In order to find the continuous compound rate of decay of the radioactive isotope, we can use the formula:
N(t) = N0 * e^(-λt)
Where N(t) is the amount of the isotope present at time t, N0 is the initial amount of the isotope, λ is the continuous decay constant, and t is the time elapsed (in this case, 6 years).
We are given that 91.9% of the isotope is still present after 6 years, so:
0.919 = e^(-λ * 6)
To solve for λ, we can take the natural logarithm of both sides:
ln(0.919) = -6λ
Now, we can solve for the decay constant:
λ = -ln(0.919) / 6 ≈ 0.0141
So, the continuous compound rate of decay of this isotope is approximately 1.41%.
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Use any method to determine whether the series converges а. น k2 sk (5 pts) b 6. Ex 2+(-1){ 5k (5 pts)"
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To determine whether the series น k2 sk converges, we can use the Integral Test. Let f(x) = x2, then f'(x) = 2x. Since 2x is continuous, positive, and decreasing on [1,∞), In summary, the series Σ (1/k^2) converges, while the series Σ (2 + (-1)^{5k}) does not converge.
∫1∞ f(x) dx = ∫1∞ x2 dx = lim (t → ∞) [1/3 x3]1t = ∞
Since the integral diverges, the series น k2 sk also diverges.
b. To determine whether the series 2+(-1){ 5k converges, we can use the Alternating Series Test. The series has alternating signs and the absolute value of each term decreases as k increases. Let ak = 2+(-1){ 5k, then:
|ak| = 2+1/32k ≤ 2
Also, lim (k → ∞) ak = 0. Therefore, by the Alternating Series Test, the series 2+(-1){ 5k converges.
a. For the series Σ (1/k^2) (denoted as น k2 sk), we can use the p-series test. A p-series is a series of the form Σ (1/k^p), where p is a constant. If p > 1, the series converges, and if p ≤ 1, the series diverges. In this case, p = 2, which is greater than 1. Therefore, the series Σ (1/k^2) converges.
b. For the series Σ (2 + (-1)^{5k}), we can use the alternating series test. An alternating series is a series that alternates between positive and negative terms. In this case, the series alternates because of the (-1)^{5k} term. However, the series does not converge to zero as k goes to infinity, since there is a constant term 2. Therefore, the series Σ (2 + (-1)^{5k}) does not converge.
In summary, the series Σ (1/k^2) converges, while the series Σ (2 + (-1)^{5k}) does not converge.
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A man sets out to travel from A to C via B. From A he travels a distance of 8km on a bearing N30degreesE to B. From B he travels further 6km due east. Calculate how far is north of A, east of A
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The displacement of the man from Noth east of A from C is 12.2 km.
What is the displacement of the man?
The displacement of the man is the distance between his initial position at A and final position at C.
The angle formed at position B is calculated as follows;
θ = 30⁰ + 90⁰
θ = 120⁰
The displacement of the man is calculated by applying cosine rule as follows;
d² = 8² + 6² - 2(8 x 6) cos (120)
d² = 148
d = √148
d = 12.2 km
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Find the magnitude and direction of the vector u = <-4, 7>
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The magnitude and direction of the vector u = <-4, 7> are |u| ≈ √65 and θ ≈ 119.74°.
To find the magnitude and direction of the vector u = <-4, 7>, we will use the following steps:
1. Calculate the magnitude using the Pythagorean theorem.
2. Calculate the direction using the arctangent function.
Step 1: Calculate the magnitude.
Magnitude (|u|) = √((-4)^2 + (7)^2) = √(16 + 49) = √65
Step 2: Calculate the direction (angle θ).
θ = arctan(opposite/adjacent) = arctan(7/-4) ≈ -60.26° (in degrees)
Since the vector is in the second quadrant, we need to add 180°.
θ = -60.26° + 180° ≈ 119.74°
So, the magnitude and direction of the vector u = <-4, 7> are |u| ≈ √65 and θ ≈ 119.74°.
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tommy solved the equation x ^²-x-12=0 select the factores of x^-x-12
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——
First, find the 2 numbers that add to -1 and multiply to -12. The numbers are -4 and +3.
Split x^2 - x - 12 using these factors;
(x^2 + 3x)(-4x - 12)
Factor out x from terms in the first parentheses and factor out -4 from terms in the second set of parentheses.
x(x + 3) + -4(x + 3).
Take out the common term (x+3) and we are left with:
(x + 3)(x - 4).
x^2 - x - 12 factored = (x+3)(x-4)
Part D
The rectangular bases of the treasure box will be cut from wooden planks
4 1/8 feet long and 4 1/8 feet wide. How many planks will Mr. Penny need for his
18 students to each
make one treasure box?
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Answer:
Step-by-step explanation:
Annmarie can plow a field in 240 minutes. Gladys can plow a field 80 minutes faster. If they work together, how many minutes does it take them to plow the field?
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It would take Annmarie and Gladys 96 minutes to plow the field together.
How long to plow field together?
Annmarie can plow a field in 240 minutes. Gladys can plow the same field 80 minutes faster than Annmarie.
So Gladys can plow the field in 240 - 80 = 160 minutes.
Let x be the time it takes for both of them to plow the field together.
The combined rate of Annmarie and Gladys is the sum of their individual rates.
Annmarie's rate is 1 field per 240 minutes, which is 1/240 field per minute.
Gladys's rate is 1 field per 160 minutes, which is 1/160 field per minute.
Their combined rate is:
1/240 + 1/160 = 1/x
Simplifying this equation:
1/x = (4/960) + (6/960) = 10/960
1/x = 1/96
Multiplying both sides by 96, we get:
x = 96 minutes
Therefore, it would take Annmarie and Gladys 96 minutes to plow the field together.
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