The quantity of paper that needed to wrap 6 mini muffins is 84.857 inches^2
The surface area of a cylinder can be calculated using the formula:
Surface Area = 2πr^2 + 2πrh
where r is the radius of the cylinder (which is half of the diameter) and h is the height of the cylinder.
For the mini muffins in question, the diameter is 2 inches, so the radius is 1 inch. The height is 1 and 1/4 inches, or 5/4 inches.
So the surface area of one mini muffin is:
Surface Area = 2π(1)^2 + 2π(1)(5/4)
Surface Area = 2π + 5π/2
Surface Area = 9π/2
To wrap 6 mini muffins, we need to multiply this surface area by 6:
Total Surface Area = 6 x (9π/2)
Total Surface Area = 27π
Approximating π as 22/7, we get:
Total Surface Area ≈ 27 x (22/7)
Total Surface Area ≈ 84.857 inches^2
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Answer:
The quantity of paper that needed to wrap 6 mini muffins is 84.857 inches^2
Step-by-step explanation:
Find the value of x.
The value of the angle subtended by the chord WV is: x° = 79°.
How to find the angle subtended by the chord?The equal angles equal Chords Theorem states that If the angles subtended by the chords of a circle are equal in measure, then it means that the length of the chords is equal.
Now, we are given that the 2 chords are equal and we are given one angle extended by one chord as 79°. Therefore, we can easily say that by using the equal angles equal Chords theorem, that angle x° is equal to 79°.
Thus, we can say that is the value of the angle x°.
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g suppose that you are an elementary school teacher and you are evaluating the reading levels of your students. you find an individual that reads 46.2 word per minute. you do some research and determine that the reading rates for their grade level are normally distributed with a mean of 85 words per minute and a standard deviation of 22 words per minute. a. at what percentile is the child's reading level (round final answer to one decimal place).
This shows that they read less frequently than 95.7% of their classmates in the same grade level.
what is percentile ?In statistics, a percentile is a metric that is used to express where one observation stands in relation to a larger group of data. It displays the proportion of data points that fall under a given value. For instance, if a student achieves a score in the 90th percentile on a standardised test, it signifies that they outperformed 90% of their peers who also took the test. As an alternative, if a child is taller than 25% of children their age and shorter than 75%, their height is in the 25th percentile for their age.
given
We must first compute the z-score using the following formula to determine the percentile of the child's reading proficiency.
z = (x - μ) / σ
where x represents the child's reading rate, represents the grade-level mean reading rate, and represents the standard deviation.
Inputting the values provided yields:
z = (46.2 - 85) / 22
z = -1.727
We can calculate or use a conventional normal distribution table to obtain the value of 0.0428 for the region to the left of z = -1.727. The child's reading rate is at the 4.28th percentile according to this statistic.
As a result, the child's reading proficiency is 4.3 percentile (rounded to one decimal place).
This shows that they read less frequently than 95.7% of their classmates in the same grade level.
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The vertices of a square are located at (0, 2), (2, 0), (0, -2), and (-2, 0).
Select all transformations that will carry this square onto itself.
A reflection across the line y = x
B reflection across the line y = -X
C reflection across the x-axis
D 45° rotation about the origin
E 90° rotation about the origin
Answer:
Step-by-step explanation:
A reflection across the line y = x will not carry the square onto itself, since the vertex (0, 2) would be reflected to (2, 0) which is not a vertex of the original square.
A reflection across the line y = -x would also not carry the square onto itself, since the vertex (0, 2) would be reflected to (−2, 0) which is not a vertex of the original square.
However, a reflection across the x-axis would carry the square onto itself since all of the vertices lie in the same quadrant, and reflecting across the x-axis does not change their signs.
A 45° or 90° rotation about the origin would also carry the square onto itself since the square has rotational symmetry of order 4.
Therefore, the correct answers are C, D, and E.
this is so confusing. i have to round to either 106 or 67 in.
The circumference of a circle with a radius of 15 inches is 30π inches, or 94.25 inches
How to calculate the circumferenceThe circumference of a circle can be calculated using the formula:
C = 2πr
where C is the circumference, r is the radius, and π (pi) is a mathematical constant approximately equal to 3.14159.
In this case, the radius is 15 inches. Substituting this value into the formula, we get:
C = 2π(15) = 30π
So the circumference of a circle with a radius of 15 inches is 30π inches, or approximately 94.2478 inches.
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Wendall and Stacey measured the lengths of several wooden planks. Wendall recorded his measurements in inches, and Stacey recorded her measurements in feet. In order to compare the lengths of the wooden planks, they recorded their measurements in the table below. Find the measurements of the wooden planks Wendall measured in feet, and then find the measurements of the wooden planks Stacey measured in inches.
To convert Wendall's measurements from inches to feet, we need to divide each measurement by 12, since there are 12 inches in a foot. So, the measurements in feet are:Length (in)Length (ft)242363484605To convert Stacey's measurements from feet to inches, we need to multiply each measurement by 12. So, the measurements in inches are:Length (ft)Length (in)6727848969108Therefore, the measurements of the wooden planks Wendall measured in feet are 2, 3, 4, and 5 feet, and the measurements of the wooden planks Stacey measured in inches are 72, 84, 96, and 108 inches.
Question 8 of 10
Floyd's brick house is located in the suburbs. If his building property
insurance is $652.50 per year, how much is his house worth?
Annual Premium per $100 of coverage
Brick
Steel
Area
rating
Building Contents
Building Contents
City
0.39
0 43
Suburb 0.45
0.52
Rural 0.6
0.69
OA. $185,000
OB. $145,000
OC. $125,000
O D. $95,000
05
0.56
0.71
0.54
0.63
0.8
Mixed
Building Contents
0.55
0.72
0.89
0.65
0.74
0.91
Wood
Building Contents
0.66
0.83
1
0.76
0.85
1.02
The right answer is (B), which is $145,000, given that his building property insurance costs $652.50 annually.
what is interest ?In mathematics, interest usually refers to the sum of money that is charged or made over the course of a given period of time on a principal sum of money. In finance and economics, interest—which can be basic or compound—is frequently used to calculate borrowing costs and return on investment. The principal sum, the interest rate, and the duration for which the interest is being charged or earned are the three factors used to compute simple interest.
given
We are informed that Floyd's home is situated in a suburban area, where building property insurance costs $0.45 for every $100 of coverage.
Assume Floyd's home is worth x. Then, the yearly payment for his home's building property insurance is:
0.0045x = $652.50
After finding x, we obtain:
x = $652.50 ÷ 0.0045
x ≈ $145,000
Floyd's home is therefore currently worth about $145,000.
The correct response is (B ) $145,000 as his building property insurance is $652.50 per year.
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Dalton's weekly allowance is $5. He can also earn $1 each time he walks the family dog.
Write an equation that shows how the amount of money Dalton gets in a week, y, depends
on the number of times he walks the dog, x.
Do not include dollar signs in the equation.
y =
The equation that shows how the amount of money Dalton gets in a week, y, depends on the number of times he walks the dog, x is y = 5 + x
Calulating the equation of the number amount of moneyGiven that
Weekly allowance = $5
Amount earned for walking the dog = $1
The above means that
Total money = Weekly allowance + Amount earned for walking the dog * Number of times
So, we have
y = 5 + 1 * x
Evaluate
y = 5 + x
Hence, the equation is y = 5 + x
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Pls help i will give brainiest
Answer:
1. No, the side lengths 3, 5, and 9 cannot make a triangle.
2. If you are scaling an object by ¹/₃, it makes the object smaller.
If the real object is 30 inches long, it is 10 inches once it is scaled.
3. A cube has 6 faces.
To find the volume, cube the side length: 6³ = 216 in³
Step-by-step explanation:
Question 1According to the Triangle Inequality Theorem, the sum of any two sides of a triangle is greater than the length of the third side.
As the sum of the two sides measuring 3 and 5 is 8, and 8 is not greater than 9, the side lengths 3, 5, and 9 cannot make a triangle.
Question 2Scaling an object reduces or enlarges its size. When scaling an object:
If the scale factor is greater than 1, the object becomes larger. If the scale factor is between zero and 1, the object becomes smaller.Therefore, if you are scaling an object by ¹/₃, the object becomes smaller, since ¹/₃ is between zero and 1.
To scale length, simply multiply the length by the scale factor.
Therefore, if a real object is 30 inches long, its length once it is scaled is:
[tex]\implies \sf 30 \times \dfrac{1}{3}=\dfrac{30}{3}=10\;inches[/tex]
Question 3A cube is a three-dimensional solid shape with six square faces.
The volume of a cube is the product of its width, length and height.
If the side of a cube measures 6 inches, its volume is:
[tex]\begin{aligned}\implies \sf Volume &=\sf 6 \times 6 \times 6 \\&= \sf 36 \times 6 \\&= \sf 216\;in^3\end{aligned}[/tex]
Answer:
See below, please.
Step-by-step explanation:
Ans 1.
In order to make a triangle, three line segments are needed, and the sum of the lengths of any two sides must be greater than the length of the remaining side. The side lengths 3, 5, and 9 cannot make a triangle because 3 + 5 is less than 9, which violates the triangle inequality.
Ans 2.
Scaling an object by 3 makes the object larger, as each dimension (length, width, and height) is multiplied by 3. If the real object is 30 inches long and is scaled by 3, it will be 90 inches long.
Ans 3.
A cube has 6 faces. To find the volume of a cube when one side measures 6 inches, we use the formula V = s^3, where s is the length of one side. Plugging in s=6, we get V = 6^3 = 216 cubic inches.
Write the slope-intercept form of the equation of the line described.
through: (-4, -1), parallel to y =
-1/2x-2
Answer:
y = - [tex]\frac{1}{2}[/tex] x - 3
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - [tex]\frac{1}{2}[/tex] x - 2 ← is in slope- intercept form
with slope m = - [tex]\frac{1}{2}[/tex]
• Parallel lines have equal slopes , then
y = - [tex]\frac{1}{2}[/tex] x + c ← is the partial equation
to find c substitute (- 4, - 1 ) into the partial equation
- 1 = - [tex]\frac{1}{2}[/tex] (- 4) + c = 2 + c ( subtract 2 from both sides )
- 3 = c
y = - [tex]\frac{1}{2}[/tex] x - 3 ← equation of parallel line
Which choice would transform the pre-image to the composite image? Make sure the letter for each vertex matches! Select one: a. Reflect across the y-axis and translate 4 down and three left. b. Rotate 180° and reflect across the x-axis. c. Rotate 90° and translate 4 up and 3 right. d. Reflect across the x-axis and translate up 4 and right 3.
d. Reflect across the x-axis and translate up 4 and right 3, this transforms the pre-image to the composite image.
What is composite image?
A composite image is the result of applying multiple transformations to a given pre-image. It is formed by first applying one transformation to the pre-image and then applying another transformation to the resulting image, and so on. The final result is the composite image.
Let's analyze the given options:
a. Reflect across the y-axis and translate 4 down and three left.
This transformation would reflect the pre-image across the y-axis, which would change the signs of the x-coordinates, and then translate it 4 units down and 3 units left. However, this transformation would not result in the composite image provided.
b. Rotate 180° and reflect across the x-axis.
This transformation would rotate the pre-image 180 degrees counterclockwise around the origin, which would change the signs of both the x and y-coordinates, and then reflect it across the x-axis. This transformation would not result in the composite image provided.
c. Rotate 90° and translate 4 up and 3 right.
This transformation would rotate the pre-image 90 degrees counterclockwise around the origin, which would swap the x and y-coordinates and negate the new x-coordinate, and then translate it 4 units up and 3 units right. This transformation would not result in the composite image provided.
d. Reflect across the x-axis and translate up 4 and right 3.
This transformation would reflect the pre-image across the x-axis, which would change the signs of the y-coordinates, and then translate it 4 units up and 3 units right. This transformation would result in the composite image provided.
Therefore, the correct answer is d. Reflect across the x-axis and translate up 4 and right 3.
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A manager orders laptop covers for some employees. Each laptop cover costs $28 . There is a one-time shipping fee of $7 . Which function can be used to find t , the total amount the manager pays, in dollars, when s laptop covers are ordered? Responses
Thus, the function for the total amount paid by the manager is: t = 7 +28s.
Explain about the term function?a mathematical phrase, rule, or legislation that establishes the link between an independent variable and a dependant variable (the dependent variable).
In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.A relation where both x is linked with just one y is called a function. The same y can really be paired with many xs, but not the other way around. Except for both horizontal and vertical lines, all linear equations are functions.Given data:
Cost of each laptop cover = $28.Cost of one-time shipping = $7Let the number of bags ordered be 's'.
The total amount paid 't'.
Thus, the function for the total amount paid by the manager is:
t = 7 + 28s.
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Triangle ABC is congruent to triangle A′′B′′C′′ .
Which sequence of transformations could have been used to transform triangle ABC to produce triangle A′′B′′C′′ ?
Triangle ABC was reflected across the x-axis and then translated 9 units right.
Triangle ABC was translated 7 units down and then 9 units right.
Triangle ABC was translated 10 units right and then reflected across the x-axis.
Triangle ABC was reflected across the y-axis and then translated 7 units down.
Whether the economy is in a recession is illustrated in the AD/AS model by how close the _____ is to the potential GDP line.
a. AD curve
b. AS curve
c. AS and AD curve
d. equilibrium
When the equilibrium point is above the potential GDP line, the economy is experiencing inflationary pressure.
In the AD/AS model, whether the economy is in a recession is illustrated by how close the equilibrium is to the potential GDP line. The potential GDP line represents the maximum level of output that an economy can produce with its existing resources and technology.What is the AD/AS model?The AD/AS model is a graphical representation of the macroeconomic relationship between aggregate demand (AD) and aggregate supply (AS). This model is used to explain the behavior of the economy by demonstrating how changes in the level of aggregate demand and aggregate supply can impact the economy's level of output and prices.
The model's AD curve represents the total demand for all goods and services in an economy at different price levels. The AS curve represents the total supply of all goods and services in the economy at different price levels.
The intersection of the AD and AS curves represents the equilibrium point where the economy's output level and price level are determined. The economy is in a recession when the equilibrium point is below the potential GDP line.
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A farmer wants to fence in a rectangular portion of land along one side of her barn. She uses the side of the barn for one side of the rectangle, and makes the other three sides from a total of 60 feet of fencing. Find the side lengths that give the maximum area she can fence in, as well as the maximum area. Show all of your work.
the answer is 62x IAM take a guess so
a quiz consists of three true or false questions. what is the probability that there are exactly two true answers?
The probability of getting exactly two true answers in a quiz that consists of three true or false questions is 3/8 or 0.375. Here's how to get the answer:
There are three possible scenarios where you can get exactly two true answers: T T F, T F T, F T T
To calculate the probability of each scenario, you need to know the probability of getting a true answer (T) or a false answer (F). Since each question is independent, the probability of getting a true or false answer is 0.5.
Scenario 1: T T F,The probability of getting two true answers and one false answer is: P(T T F) = 0.5 x 0.5 x 0.5 = 0.125
Scenario 2: T F T,The probability of getting one true answer and two false answers is:P(T F T) = 0.5 x 0.5 x 0.5 = 0.125
Scenario 3: F T T,The probability of getting one false answer and two true answers is:P(F T T) = 0.5 x 0.5 x 0.5 = 0.125
To get the probability of getting exactly two true answers, you need to add the probabilities of the three scenarios:P(2 True Answers) = P(T T F) + P(T F T) + P(F T T) = 0.125 + 0.125 + 0.125 = 0.375.Therefore, the probability of getting exactly two true answers in a quiz that consists of three true or false questions is 3/8 or 0.375.
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solve the inequality and please show work !!
The solution to the inequality 2√(x-3) < √(x+3) is x ∈ (3, 7].
What is an inequality?
In mathematics, an inequality is a statement that compares two values or expressions and states that one is greater than, less than, or not equal to the other. An inequality is typically written using inequality symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "!=" (not equal to). Inequalities are used to represent a wide range of mathematical concepts, such as the relationships between two quantities, the constraints on a system, or the conditions for a particular outcome to occur. Solving inequalities involves finding the set of values that satisfy the inequality, which may be a single value, a range of values, or no values at all.
What are the key steps to solve this inequality?
To solve the inequality, we need to isolate the variable x on one side of the inequality and then square both sides to eliminate the square roots. However, we need to be careful when squaring both sides because this may introduce extraneous solutions. To avoid this, we need to check our solutions at the end to make sure they satisfy the original inequality.
Isolate the square root term on one side of the inequality
2√(x-3) < √(x+3)
Square both sides:
4(x-3) < x+3
Simplify and rearrange the inequality to get x on one side
4x - 15 < 0
x < 15/4
Check the solution by plugging it into the original inequality
2√(15/4 - 3) < √(15/4 + 3)
2√(3/4) < √27/4
2(√3/2) < 3/2
√3 < 3/2 (This is true)
Therefore, the solution to the inequality is x ∈ (3, 7].
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A nurse is teaching an older adult client about good bowel habits. Which statement by the client indicates to the nurse that additional teaching is required?
- "I should eat a fiber-rich diet with raw, leafy vegetables, unpeeled fruit, and whole grain bread."
- "I need to use laxatives regularly to prevent constipation."
- "I should exercise four times per week."
- "I need to drink 2 to 3 liters of fluids every day."
In order to ensure the client understands the information being taught, the nurse should ask follow-up questions and provide resources, such as written handouts, for the client to review.
No, drinking 2 to 3 liters of fluids every day would not be an indication that additional teaching is required for good bowel habits. Instead, an indication that more teaching is needed could be the client saying that they are constipated, or that they are not having regular bowel movements.
In order to have healthy bowel habits, an older adult should aim for 3 to 4 bowel movements per week, with the stool being soft and easy to pass. Dietary fiber, drinking plenty of fluids, regular physical activity, and timed trips to the bathroom can help.
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calculate the percent yield of copper (ii) oxide. 4. explain why you obtained a yield different than g
To calculate the percent yield of copper (II) oxide, you need to have the actual yield and the theoretical yield. The percent yield can be calculated using the following formula: Percent Yield = (Actual Yield / Theoretical Yield) * 100
1. Obtain the actual yield: This is the amount of copper (II) oxide produced in your experiment or reaction, typically measured in grams.
2. Calculate the theoretical yield: Use the balanced chemical equation and the stoichiometry of the reaction to determine the maximum amount of copper (II) oxide that could be produced from the given reactants.
3. Plug the values into the formula: Divide the actual yield by the theoretical yield and multiply the result by 100 to get the percent yield.
If you obtained a yield different than the expected or theoretical yield, there could be several reasons, including experimental errors, impure reactants, or side reactions occurring during the process. These factors can cause the actual yield to be higher or lower than the theoretical yield.
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Each of the 17 guinea pigs needs its cage cleaned. If it takes 1 hour to clean 4 cages, how many hours will it take to clean all 17 cages?
It will take
hours to clean all the cages.
Answer:
Step-by-step explanation:
4 hours and 30 minutes
A grocery store manager took inventory of all the fruit to decide what needed to be donated. Of the 8 pieces of fruit deemed "overripe," 5 were apples.
If the manager randomly selected 4 of the overripe pieces for the first donation package, what is the probability that all of them are apples?
Write your answer as a decimal rounded to four decimal places.
Answer:
The probability of selecting an apple from the overripe fruit is 5/8. Since there are no replacement, the probability of selecting another apple from the remaining overripe fruit is 4/7, and the probability of selecting another apple after that is 3/6, and the probability of selecting another apple after that is 2/5. Therefore, the probability of selecting all apples is:
(5/8) × (4/7) × (3/6) × (2/5) = 0.0429
Rounded to four decimal places, the probability is 0.0429.
State the vertex for the quadratic function, and determine if the vertex is the highest or lowest point on the graph. Then state the range of the function. y = - 32 - 2)2 - 1 The vertex, (), is the Select an answer point on the graph. The range is Preview
The vertex for the quadratic function and the range of the function are determined in the following answer.The given quadratic function [tex]isy = -32 - 2(x - 1)²[/tex]
It is noted that the quadratic function is in the vertex form, i.e.,[tex]y = a(x - h)² + k[/tex]
where (h, k) is the vertex of the parabola. Comparing the given function with the vertex form of the quadratic equation, we get the value of the vertex, i.e.,(h, k) = (1, -32).This implies that the vertex of the given quadratic function is located at (1, -32).Since the coefficient of the quadratic term is negative in the given function, the parabola opens downwards, and the vertex is the highest point on the graph.Therefore, the vertex (-32, 1) is the highest point on the graph of the given quadratic function. The range of a function is the set of all possible values that the function can attain. The given quadratic function is in the form y = a(x - h)² + k where a, h, and k are constants.
Since the coefficient of the quadratic term is negative in the given function, the parabola opens downwards. Therefore, the range of the given function is (-∞, -32].Hence, the range of the given quadratic function is[tex](-∞, -32].[/tex]
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Todd is training for a marathon. The following histogram summarizes the number of kilometers that he ran each day.
The probability that Todd runs more than 15kms tomorrow is 38.46%.
Define probability?By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula.
Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.
Moreover, the proportion of positive outcomes cannot be negative.
Here in the question,
Probability = No.of days with more than 15kms run/total no.of days.
= 5/2+3+3+5
= 5/13
= 0.3846
= 38.46%
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The complete question is:
Todd is training for a marathon. The following histogram summarizes the number of kilometers that he ran each day.
the park service is considering offering a discount for the 5% of their patrons who spend the least time at the hot springs. what is the longest amount of time a patron can spend at the hot springs and still receive the discount? minutes.
The longest amount of time a patron can spend at the hot springs and still receive the discount is approximately 43.55 minutes.
To determine the longest amount of time a patron can spend at the hot springs and still receive the discount, we need to find the 5th percentile of the time spent by all patrons.
Let's say we have a sample of 1000 patrons and their time spent at the hot springs is normally distributed with a mean of 60 minutes and a standard deviation of 10 minutes. We can use the z-score formula to find the value corresponding to the 5th percentile:
[tex]$z = \frac{x - \mu}{\sigma}$[/tex]
where x is the value at the 5th percentile, [tex]$\mu$[/tex] is the mean, [tex]$\sigma$[/tex] is the standard deviation, and z is the z-score corresponding to the 5th percentile.
Since we want to find the value of x, we can rearrange the formula as:
[tex]$x = z\sigma + \mu$[/tex]
To find the z-score, we can use a standard normal distribution table or a calculator. For the 5th percentile, the z-score is approximately -1.645.
Plugging in the values, we get:
[tex]$x = -1.645 \times 10 + 60 \approx 43.55$[/tex]
Therefore, the longest amount of time a patron can spend at the hot springs and still receive the discount is approximately 43.55 minutes.
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william can mulch a garden in 20 minutes. together, william and tina can mulch the same garden in 11 minutes. how long will it take tina to mulch the garden when working alone?
Tina can mulch the garden alone in 25 minutes.
Let's use the formula for the work rate to solve the problem. If William can mulch the garden alone in 20 minutes, his work rate is 1/20. Similarly, let's assume that Tina can mulch the garden alone in x minutes, so her work rate is 1/x.
When they work together, their work rates add up, so we have:
1/20 + 1/x = 1/11
Now we can solve for x:
1/x = 1/11 - 1/20
1/x = (20 - 11) / (11 x 20)
1/x = 9 / 220
x = 220 / 9
x ≈ 24.4
So it would take Tina 24.4 minutes to mulch the garden alone.
However, we need to round this up to the nearest minute because you can't have a fraction of a minute. Therefore, Tina can mulch the garden alone in 25 minutes.
Alternatively, we can use the inverse formula for the work rate to solve for Tina's time alone:
1/20 + 1/t = 1/11
1/t = 1/11 - 1/20
1/t = (20 - 11) / (11 x 20)
1/t = 9 / 220
t = 220 / 9
t ≈ 24.4
So Tina can mulch the garden alone in 24.4 minutes, which rounds up to 25 minutes.
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Find the missing dimension of the triangle.
Area = 14 ft²
6 ft
b
b = ? ft
help pls I'll mark brainlisest
the smith family has $4$ cats and $3$ dogs. in how many ways can these $7$ pets be placed in a row of $7$ chairs such that at least $2$ cats are next to each other?
There are 4896 ways of arranging 7 pets in a row of 7 chairs such that at least 2 cats are next to each other.
Arrangement of entities can be done using permutation and combination in mathematics.
Consider the distributions where 2 cats are not next to each other as
C D C D C D C.
There are 4! ways to seat the cats, and 3! ways to seat the dogs that gets us N=4! 3! = 144
There are a total of 7!=5040 possible ways to seat both cats and dogs.
At least 2 cats seat together= All possible arrangements- None of the cat seat together.
Thus the number of seatings where at least 2 cats are adjacent is
5040-144 = 4896
So, there are 4896 arrangements can be made so that at least 2 of the cats seat together.
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if x and y are positive integers, find the domain and the range of 2y = 30 - 3x
The domain of the equation is {1, 3, 5, 7, 9}. and the range of the equation is {6, 8, 10, 12, 14}.
What is range and domain of a function?
The domain of a function in mathematics is the set of all possible input values (usually denoted by x) for which the function is defined. It is the set of all values of the independent variable (input) for which the function is defined.
A function's range, on the other hand, is the set of all potential output values (typically indicated by y) that the function may generate. It is the set of all values of the dependent variable (output) that the function can take.
Now,
To solve for y:
2y = 30 - 3x
y = (30 - 3x)/2
The domain of the equation is the set of all possible values of x that will make the equation valid. Since x and y are positive integers, we need to find integer solutions for x that will also result in integer values for y.
Let's look at the equation (30 - 3x)/2 = y. For y to be an integer, (30 - 3x) must be even. This means that x can only take on odd integer values between 1 and 9, inclusive. Therefore, the domain of the equation is {1, 3, 5, 7, 9}.
To find the range of the equation, we need to find the possible values of y that correspond to the values of x in the domain. We can substitute each value of x into the equation y = (30 - 3x)/2 and simplify to find the corresponding value of y.
When x = 1, y = 14
When x = 3, y = 12
When x = 5, y = 10
When x = 7, y = 8
When x = 9, y = 6
Therefore, the range of the equation is {6, 8, 10, 12, 14}.
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A certain computer can perform a maximum number of operations per second. If this computer is running at 40%
of the maximum and is performing 30 operations per second, what is the maximum number of operations the
computer can perform per second? Round your answer to the nearest whole number.
1. 70 operations per second
2. 12 operations per second
3. 1,200 operations per second
4. 75 operations per second
Answer:
Step-by-step explanation:
Let's represent the maximum number of operations per second as "x".
If the computer is running at 40% of the maximum, it is performing 0.4x operations per second.
We are given that the computer is performing 30 operations per second, so we can set up an equation:
0.4x = 30
Solving for x:
x = 75
Therefore, the maximum number of operations the computer can perform per second is 75.
So, the correct answer is 4. 75 operations per second.
Help me find the Lateral Area and the Surface Area
Answer:
Step-by-step explanation:
The lateral area consists of 2 trapezia and 2 rectangles.
= 2 * 1/2 * 4 *(4 + 6) + 2 * 9 * length of the sloping line
= 40 + 18 * length of the sloping line.
Find the length of the sloping lines:
Consider the right triangle whose height is 4 ft.
The trapezium is isosceles so the base of this triangle
= (6 - 4)/ 2 = 1 ft.
By Pythagoras:
Sloping line = √(1^2 + 4^2) = √17
So lateral area
= 40 + 18√17.
= 114.22 ft^2 to nearest hundredth
Total area =
40 + 18√17 + 4*9 + 6*9
= 130 + 18√17
= 204.22 ft^2 to nearest hundredth
Good start.
Surface area:
Area of 2 trapezoids: 2 ((4+6)/2*4) = 40
Area of two side rectangles: [tex]2*9*\sqrt{17}=18\sqrt{17}[/tex] (I got root 17 from constructing a right triangle from the altitude just like last time and then finding the missing side using pythag)
Area of top rectangle: 4*9 = 36
Area of bottom rectangle: 6*9 = 54
Summing these up we get [tex]130+18\sqrt{17}[/tex]
Lateral area is the area excluding the bases (correct me if i'm wrong) so it will be [tex]130+18\sqrt{17}-40=90+18\sqrt{17}[/tex] (we need to subtract the areas of the trapezoids).
The Morris family is planning to carpet their entire home. The type of carpet they want is sold at two different stores. The table and graph below show the costs for different amounts of carpet sold by the two stores. Which store sells the carpet for the lesser amount, in cost per square yard? Show work or explain your answer.
By charging $11 per square yard as opposed to $12 per square yard at Shop A, Store B offers the carpet for a lower price per square yard.
What distinguishes a table from a graph?The same data that is displayed in tables is also presented in charts and graphs. Yet, compared to a table, a chart or graph provides less detail or greater imprecision.
We must divide the total cost by the quantity of carpet square yards in order to determine the price per square yard. Seeing from the table that Shop A charges $360 for 30 square yards of carpet, the following information is provided:
Shop A's price per square yard is $360.30 sq yard divided by $12 per sq yd
A similar price of $550 is charged by Store B for 50 square yards of carpet, giving us:
$550 divided by 50 square yards yields $11 per square yard at store B.
The graph also shows that, for all carpet sizes, Shop B consistently charges less per square yard than Store A.
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