Final answer:
The absolute value equation that represents the minimum and maximum heights of adult women, with heights represented by x, is |x - 58| = 34.
Explanation:
To write an absolute value equation representing the minimum and maximum heights of adult women, where the shortest known adult woman is about 24 inches tall and the tallest known adult woman is about 92 inches tall, we can use the variable x to represent an adult woman's height. The midpoint between the smallest and largest height is (24 + 92) / 2 = 58 inches. The distance from this midpoint to each extreme is 34 inches, because 92 - 58 = 34 and 58 - 24 = 34. So, the absolute value equation would be |x - 58| = 34. This equation represents that the height of an adult woman can deviate from 58 inches by 34 inches to be either at the minimum or maximum height recorded.
Final answer:
The absolute value equation representing the minimum and maximum heights of adult women is |x - 58| = 34, where x is the height in inches.
Explanation:
The objective is to write an absolute value equation to represent the minimum and maximum heights of adults.
Using the heights given for the shortest and tallest known adult women, 24 inches and 92 inches respectively, we set the variable x to represent an unknown height.
To express this as an absolute value equation, we identify the midpoint between these two heights, which is (24 inches + 92 inches) / 2 = 58 inches.
The distance from the midpoint to either extreme is (92 inches - 58 inches) = 34 inches, which is the absolute difference.
Therefore, our absolute value equation is |x - 58| = 34.
This equation tells us that the height x must be either 34 inches above or below 58 inches, which corresponds to the minimum and maximum heights of 24 inches (58 - 34) and 92 inches (58 + 34) respectively.
Steve takes 6 hours to get the yard work done by himself. If Bill works alone, it takes him 10 hours. How long would it take them working together to do all of the yard work?
Answer:
In 3 hour 45 minutes Both working together do all of yard work.
Step-by-step explanation:
Time taken by Steve to do yard work = 6 hours
Work Done by Steve in a hour = [tex]\frac{1}{6}[/tex]
Time taken by Bill to do yard work = 10 hours
Work Done by Steve in a hour = [tex]\frac{1}{10}[/tex]
Work done by both in a hour = [tex]\frac{1}{6}+\frac{1}{10}=\frac{5+3}{30}=\frac{8}{30}=\frac{4}{15}[/tex]
Time taken by by both working together = [tex]\frac{1}{\frac{4}{15}}=\frac{15}{4}=3.75=3\,hour\,45\,minutes[/tex]
Therefore, In 3 hour 45 minutes Both working together do all of yard work.
A function f satisfies the following conditions: f(5)=20, f'(5)=2, and f"(x)<0, for x>=5. Which of the following are possible values for f(7)? possible choices are 28, 20, 26, 24, 22
Given the function's conditions, the value of f(7) must be less than or equal to 24 due to the concave-down nature indicated by the negative second derivative, making 20, 22, or 24 possible values for f(7).
Explanation:The student asked about determining possible values for a function f(x) given a set of conditions: f(5)=20, f'(5)=2, and f"(x)<0 for x>=5. The negative second derivative indicates that the function is concave down for x>=5, meaning the rate of increase of f(x) is decreasing. Starting at x=5 with a value of 20 and a slope of 2, we can deduce that after moving 2 units to x=7, the value of f(7) cannot be greater than what it would be if f(x) were linear, since f"(x)<0 implies the function's rate of growth is decreasing. Therefore, f(7) must be less than or equal to 20 + 2*(7-5), which is 24.
Since the rate of increase is decreasing and the function cannot increase at a rate faster than the initial slope of 2, the possible values for f(7) among the given choices must be less than or equal to 24. Thus, the possible values for f(7) could be 20, 22, or 24.
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The value of f(7) is 24.
Given the function f with conditions f(5)=20, f'(5)=2, and f''(x)<0 for x ≥ 5, we need to find possible values for f(7) from the choices given: 28, 20, 26, 24, and 22.
Here is a step-by-step solution:
f(5)=20 indicates that at x=5, the value of the function is 20.f'(5)=2 tells us that the slope or the derivative at x=5 is 2, which implies the function is increasing at this point.f''(x)<0 for x ≥ 5 indicates that the function is concave down, meaning its slope is decreasing as x increases.Since the function is concave down, the rate of increase of the function will decrease as x moves from 5 to 7:
f(x) initially increases from 5 to 7 with a slope of 2, so f(7) cannot be lower than f(5): 7 − 5 = 2 * 2 = 4, thus the function increases by at most 4 from 5 to 7.So the maximum possible value considering the concavity is 20 + 4 = 24.Therefore, among the choices 28, 20, 26, 24, and 22, the possible value for f(7) given the conditions is 24.
What is the greatest common factor of 15t and 21?
If the public debt of a country in 2009 was $12,752,000,000,000 and the budget for 2010 was in deficit by $201,645,000,000, what was the public debt in 2007?
Answer:
$ 12953645000000
Step-by-step explanation:
To find the public debt in 2007, subtract the deficit for 2008 from the public debt in 2007.
Explanation:To calculate the public debt in 2007, we need to work backwards from the given information. We know that the public debt in 2009 was $12,752,000,000,000 and the budget for 2010 was in deficit by $201,645,000,000. We can assume that the deficit for each year is equal to the change in the public debt from the previous year. So, we subtract the deficit for 2010 from the public debt in 2009 to find the public debt in 2010. Then, we subtract the deficit for 2009 from the public debt in 2010 to find the public debt in 2008. Continuing this process, we can subtract the deficit for 2008 from the public debt in 2007 to find the answer.
To summarize, we can find the public debt in 2007 by subtracting the deficit for 2008 from the public debt in 2007.
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If f(x) = x3 – 2x2, which expression is equivalent to f(i)?
–2 + i
–2 – i
2 + i
2 – I
Answer:
It's D
2-i
Step-by-step explanation:
Factorise this
72-6x
-8 ( 3-s) = 32 what is s
A SOCCER TEAM IS LIKELY TO SCORE A GOAL AT ANY TIME DURING A GAME . WHAT IS THE PROBABILITY IT SCORES DURING THE FIRST HALF ?
Which statement can be used to prove that a given parallelogram is a rectangle?
The diagonals of the parallelogram are congruent.
The opposite angles of the parallelogram are congruent.
The consecutive sides of the parallelogram are congruent.
The diagonals of the parallelogram bisect each other.
Just took the test, hope the picture helps! :)))
What is a equalateral triangle?
Step-by-step explanation:
An equalateral triangle is a triangle that has all congruent sides, just like a square. To tell a triangle can be labeled on there sides, if the numbers are the same that means they are all equal, which is why it is called an equalateral triangle, to represent that it has equal sides!
Cheers!
the number of roses was 15 greater than twice the number of prunes. if the roses and prunes totaled 255, how many roses were there?
The problem is a simple algebraic equation that, when solved, shows there were 175 roses.
To solve the problem given by the student, we need to set up an equation based on the information provided. We are told that the number of roses was 15 greater than twice the number of prunes, and together they totaled 255.
Let the number of prunes be p. Then the number of roses can be represented as 2p + 15. Adding these amounts must total 255, so we can write the following equation:
2p + 15 + p = 255
Combining like terms:
3p + 15 = 255
Subtracting 15 from both sides of the equation:
3p = 240
Dividing both sides by 3:
p = 80
Now that we have the number of prunes, we can find out the number of roses:
Roses = 2p + 15 = 2(80) + 15 = 160 + 15 = 175
Therefore, the student had 175 roses.
The triangles are similar. Find the value of a. Picture shown below.
The graph of f(x) = x2 has been shifted into the form f(x) = (x − h)2 + k.
What is the value of K?
A car salesman sells cars with prices ranging from $5,000 to $45,000. The histogram shows the distribution of the numbers of cars he expects to sell over the next 10 years. What is the median of the car price range?
The correct answer is: C. The median will shift to the right.
Adding 200 cars with prices less than $5,000 will increase the number of cars being sold overall but will not significantly affect the upper end of the price range. Since the added cars are all below $5,000, they will contribute to the left side of the distribution.
As a result, the median, which represents the middle value of the distribution, will shift to the right, reflecting the increase in the number of lower-priced cars being sold.
The mean may or may not be affected, depending on the relative prices of the additional cars compared to the existing distribution, but it's not guaranteed to shift in any particular direction.
Similarly, the median and mean do not necessarily have to be the same, so option B is not accurate. Thus, option C is the most appropriate choice.
Complete question:
Car salesman sells cars with prices ranging from $5,000 to $45,000. The histogram shows the distribution of the numbers of cars he expects to sell over the next 10 years. The salesman has observed that many students are looking for cars that cost less than $5,000. If he decides to also deal in cars that cost less than $5,000 and projects selling 200 of them over the next 10 years, how will the distribution be affected?
A. The mean will shift to the right.
B The mean and the median will be the same.
C The median will shift to the right.
D The mean will shift to the left.
What is the elasped time for 9:30p.m to8:30a.m?
Two rooms in a house are similar rectangles. Room A is 12 ft by 16 ft. The longer side of Room B is 4 ft shorter than twice the length of the shorter side of Room A. What are the dimensions of Room B?
How do I factorise 5a2 + 6ab
2 is squared
what is the angular velocity of a 6-foot pendulum that takes 3 seconds to complete an arc of 14.13 feet?
At wild thing zoo, you can rent a motorized cart to tour grounds for a $3 initial charge and $7 per hour. at safari zoo, you can rent the same cart for a $7 initial charge and $6 per hour. for how many hours is the total charge the same?
Which equation translates to the sentence "the sum of fifty-three and x, minus ten, is y."
a. 53 y ��� 10 = x
b. 53y x = 10
c. 53x ��� y = 10
d. 53 x ��� 10 = y?
The sentence translates to the algebraic equation '53 + x - 10 = y,' which simplifies to 'x + 43 = y.' The closest matching option provided is d. 53 + x - 10 = y.
Explanation:The sentence "the sum of fifty-three and x, minus ten, is y" translates to an algebraic equation that adds 53 to x and then subtracts 10 to equal y. This can be expressed mathematically as 53 + x - 10 = y. When simplified, this equation becomes x + 43 = y, which is not one of the provided options. Therefore, the correct option that most closely matches the sentence, after considering simplification, is d. 53 + x - 10 = y.
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A country's population in 1991 was 114 million. In 1997 it was 120 million. Estimate the population in 2014 using exponential growth. ...?
Car A began a journey from a point at 9 am, traveling at 30 mph. At 10 am car B started traveling from the same point at 40 mph in the same direction as car A. At what time will car B pass car A?
solve 7n 6 4n-2=2n 2(4n 6)
Yolanda is finding 23,567-12,458. She added 2 to 12,458 before subtracting. Then she added it in again after she subtracted. Is her method correct? Explain.
Yolanda's method is incorrect because she should have subtracted the 2 she added before subtracting, not added it. Adding it before and after the subtraction alters the original values and results in an inaccurate subtraction.
Explanation:No, Yolanda's method is not correct. If you add a value to a number before subtracting, you have to subtract that same value after the subtraction, not add it again. This is because the addition of 2 alters the original value of 12,458, making it 12,460, and thus changes the result of the subtraction. However, by adding 2 again after subtracting, Yolanda incorrectly compensates for the initial addition. The correct approach would have been to subtract 2 after the subtraction, returning 12,458 to its original value and ensuring the accuracy of the subtraction.
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Mike has $126 to spend at the amusement park he spends about 25% of the money on his tickets into the park how much does my cat have left to spend
Which of the following is an equivalent representation of 3Which of the following is an equivalent representation of 3^-4 ?
A. 1/9
B. 1/81
C. 1/27
D. 1/256
Answer:
B
Step-by-step explanation:
edge
Silver scooter finds that it costs $300 to produce each scooter and the fixed costs are $750. The price is given by p=900-x, where p is the price in dollars at which exactly x scooters will be sold. Find the quantity of scooters that the company should produce and the price it should charge to maximize profit. Find the maximum profit. ...?
To maximize profit, the company should produce 300 scooters and charge a price of $600. The maximum profit is $88,500.
Explanation:The company should produce a quantity of scooters that maximizes profit. To find this quantity, we need to find the point where marginal revenue (MR) equals marginal cost (MC). In this case, MR is given by the derivative of the price equation, which is -1. So, we set -1 equal to the derivative of the cost equation and solve for x:
-1 = 300
This gives us x = 300. So, the company should produce 300 scooters to maximize profit. To find the price, we substitute this value of x into the price equation:
p = 900 - 300 = 600
Therefore, the company should produce 300 scooters and charge a price of $600 to maximize profit. The maximum profit can be calculated by subtracting the total cost from the total revenue. The total revenue is given by the price multiplied by the quantity sold, and the total cost is given by the fixed costs plus the cost per unit multiplied by the quantity sold. Using the given values, we have:
Total revenue = 600 * 300 = $180,000
Total cost = 750 + 300 * 300 = $91,500
Maximum profit = Total revenue - Total cost = $180,000 - $91,500 = $88,500
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The number of people that belong to a certain social website is 412 and growing at a rate of 5% every month. How many members will there be in 9 months? Enter your answer in the box. Round to the nearest whole number.
Answer:639
Step-by-step explanation:
The equation for exponential growth is: initial amount( 1 + rate in decimal form)^time
So we put in our numbers and it is: 412( 1 + 0.5) ^ 9 = 639 (rounded)
I know this is late but I hope I helped anyone who's looking for an explanation now!
To estimate the number of members on a social website after 9 months with a 5% monthly growth rate, use the formula for exponential growth. After calculations, there will be approximately 639 members after 9 months.
Explanation:The question is related to exponential growth, which is a topic in mathematics. To calculate the number of members on a social website after 9 months given a monthly growth rate of 5%, you can use the formula for exponential growth:
Future Value = Present Value * (1 + growth rate)^number of periods
In this case, the Present Value is 412 members, the growth rate is 5%, or 0.05 when expressed as a decimal, and the number of periods is 9 months. Plugging these values into the formula gives:
Future Value = 412 * (1 + 0.05)^9
Calculating this gives:
Future Value ≈ 412 * (1.05)^9 ≈ 412 * 1.55132822 ≈ 639.25
After rounding to the nearest whole number, there will be approximately 639 members on the social website after 9 months.
Which equation represents the line that passes through (–6, 7) and (–3, 6)?
Answer:
Equation of line become [tex]y= \frac{- 1 *x}{3}+ 5[/tex].
Step-by-step explanation:
slope of the line
we know that the formula to calculate the slope between two points is equal to
Slope (m) = [tex]\frac{y_{2}- y_{1} }{x_{2}-x_{1}}[/tex].
substitute the values
(m) = [tex]\frac{6 - 7} }{ -3 - (-6)}[/tex].
(m) = [tex]\frac{-1} }{3}[/tex].
With the slope m and the point (-6, 7) find the equation of the line
we know that
the equation of the line in the point-slope form is equal to
[tex](y - y_{1}) = m ( x - x_{1})[/tex].
substitute the values
[tex](y - 7) = \frac{-1}{3} (x - ( -6))[/tex].
[tex](y - 7) = \frac{-1}{3} (x + 6)[/tex].
[tex](y - 7) = \frac{-x}{3} +2 )[/tex].
On adding both sides by 7.
[tex]y= \frac{-x}{3} - 2 + 7 [/tex].
[tex]y= \frac{-x}{3}+ 5[/tex].
Therefore, equation of line become [tex]y= \frac{-1 *x}{3}+ 5[/tex].
what happens to the graph of a line when the slope is negative? Check all that apply. may choose more then 1.
A. As the absolute value of the negative slope gets bigger, the graph of the line gets steeper.
B. As the absolute value of the negative slope gets smaller, the graph of the line gets steeper.
C. The line goes down from left to right.
D. The line shifts down.
E. The line goes up from left to right