With aging, body fat increases and muscle mass declines. The line graphs show the percent body fat in adult women and men as they age from 25 to 75 years. Use this information to complete parts (a) through (c) below.
Answers
The estimate for the percent body fat in 75-year-old men would be 24%.
How do we calculate?with aging, body fat increases and muscle mass declines, and this means that that the percent body fat is likely to increase as the age progresses.
Looking at the given vertical components, we see that the values are decreasing as we move from top to bottom and can be inferred as that the percent body fat decreases as the age increases.
The horizontal component for the age are :
15
25
35
45
55
65
75
The age values are evenly spaced. In this case, the difference between each age value is 10.
The decreasing trend of the vertical components and evenly spaced data, we can estimate the percent body fat in 75-year-old men to be closer to the value of 24.
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Related Questions
Find the missing lengths or missing angles.
Answers
Answer:
M = 70° ( base angles of isosceles triangles are equal)
Answer: M = 70° ( base angles of isosceles triangles are equal)
Step-by-step explanation:
A function and its inverse are shown on the same graph.
f(x)
x
6.
Which statement describes the relationship between the
function and its inverse?
O The slope of f¹(x) is the same as the slope of f(x).
The slope of f¹(x) is the opposite as the slope of f(x).
O The x-intercept of f¹(x) is the same as the y-intercep
of f(x).
The x-intercept of f¹(x) is the opposite as the y-
intercept of f(x).
Answers
Answer:
(c) The x-intercept of f⁻¹(x) is the same as the y-intercept of f(x).
Step-by-step explanation:
You want to know the relationship between the graphs of function f(x) and its inverse f⁻¹(x).
Inverse functionThe inverse of a function maps every y-value of the original function to its corresponding x-value. That is if you have ...
f(a) = b
then the graph of f(x) contains the ordered pair (a, b).
The inverse function will have the ordered pair (b, a). That is,
f⁻¹(b) = a
ApplicationIf an ordered pair (x-intercept) of the inverse function is ...
(P, 0)
Then there will be an ordered pair (0, P) on the graph of the original function. That point is the y-intercept, and its y-coordinate is the same as the x-coordinate of the x-intercept of the inverse function.
The x-intercept of f⁻¹(x) is the same as the y-intercept of f(x).
__
Additional comment
The graphs of the two functions are mirror images of each other across the line y=x.
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10. Higher Order Thinking Each of 5 friends has x action figures in
his or her collection. Each friend buys 11 more action figures. Now
the 5 friends have a total of 120 action figures.
a. Write an equation that models the problem.
b. Solve the equation to find the number of action figures, x, that
each friend had originally.
Answers
Each friend had originally 13 action figures before buying 11 more.
Given that there are 5 friends and each of them has x action figures in his or her collection. When they buy 11 more action figures, the total number of action figures they will have is 120.
a) We need to find an equation that models the problem. Let x be the original number of action figures that each friend had.
Therefore, the total number of action figures that each friend will have after purchasing 11 more is x + 11.
The total number of action figures will be 5(x + 11) = 5x + 55.
Now, according to the problem,5x + 55 = 120
This is our equation that models the problem.
b) We have to solve the equation 5x + 55 = 120 to find the original number of action figures, x, that each friend had before buying 11 more action figures.
5x + 55 = 120
5x = 120 - 55 (subtract 55 from both sides)
5x = 65x = 13
Therefore, each friend had originally 13 action figures before buying 11 more.
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a diver dove to a location 6 3/5 meters below sea level. He then dove to a second location 8 1/5 meters below sea level. How many meters are there between the two locations?
Answers
Answer:
\(1\frac{3}{5}\) meter is the difference in depths of locations diver dove.
Step-by-step explanation:
The distance between a 16 foot tall flagpole and a 40 foot tall tree is equal to the sum of the lengths of their shadows. If the flagpole casts a 18 foot shadow, find the distance from the flagpole to the tree.
Answers
Answer:
The distance from the flagpole to the tree is 27 ft
Step-by-step explanation:
food concession owner in a mall sold 120 beef, vegetable and pork sliders in 7 days. 20% of the sliders sold were beef and 15% were vegetable. How many pork sliders were sold?
Answers
The number of pork sliders sold is given as follows:
24 pork sliders.
How to obtain the number of pork sliders sold?The number of pork sliders sold is obtained applying the proportions in the context of the problem.
The total number of pork sliders is given as follows:
120 pork sliders.
The percentage of pork sliders sold is given as follows:
20%. (proportion of 0.2).
Hence the amount sold is given as follows:
0.2 x 120 = 24 pork sliders.
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what is = x
help please
Answers
Answer:
about x=38.1
Step-by-step explanation:
9x38.1=342.9
3.) A box in the shape of a rectangular prism has a volume of 180 cm". The length is x cm, the
width is (x + 9) cm, and the height is (x – 4) cm. Find the dimensions of the box.
Answers
Answer:
48
Step-by-step explanation:
i am a smart
The dimensions of the box are;
Length = 2.44 cm
Width = 11.44 cm
Height = 1.56 cm
How to find the volume of a right rectangular prism?Suppose that the right rectangular prism in consideration be having its dimensions as 'a' units, 'b' units, and 'c' units, then its volume is given as:
\(V = a\times b \times c \: \: unit^3\)
Given box in the shape of a rectangular prism has a volume of 180 cm".
The length is x cm, the width is (x + 9) cm, and the height is (x – 4) cm.
Volume = (x + 9) (x – 4) (x)
180 = (x + 9) (x – 4) (x)
180 = (x²+ 9x) (x² – 4x)
x³ + 13x² + 36x - 180 = 0
x = 2.44
Thus, width is (x + 9) cm = 2.44 + 9 = 11.44 cm
The height is (x – 4) cm = 2.44 - 4 = 1.56 cm
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Mr. Hooper has a tree in his front yard that grows every year. If the tree was 3 feet tall when he planted it 6 years ago , what is the current height of the tree in terms of f?
A. 3f + 6 feet
B. 6f + 3 feet
C. 3f + 18 feet
D. 6f + 18 feet
Answers
The height of the tree after 6 years can be expressed as "3 feet + 6f feet."
The correct answer is A. 3f + 6 feet.
To determine the current height of the tree in terms of "f,"
let's analyze the given information.
We know that the tree was initially 3 feet tall when it was planted 6 years ago.
Since the tree grows every year, we can assume that its growth rate is consistent.
Let's denote the current height of the tree as "h" (in feet).
After 6 years, the tree has grown by a certain amount, which we'll represent as "6f" (6 years multiplied by the growth rate "f").
Therefore, the height of the tree after 6 years can be expressed as "3 feet + 6f feet."
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Supóngase que el 2% de la población en promedio son zurdos. La probabilidad que en 100 personas haya 3 o más zurdos es
Answers
The probability of 3 or more deaf people in a sample of 100 is given as follows:
0.3633 = 36.33%.
What is the binomial distribution formula?The mass probability formula, giving the probability of x successes, is of:
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
\(C_{n,x} = \frac{n!}{x!(n-x)!}\)
The parameters are given by:
n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.The values of the parameters for this problem are given as follows:
p = 0.02, n = 100.
The probability of 3 or more deaf people are given as follows:
P(X >= 3) = 1 - P(X < 3).
In which:
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2).
Hence:
P(X = 0) = 0.98^100 = 0.1326.P(X = 1) = 100 x 0.02 x 0.98^99 = 0.2707.P(X = 2) = 99 x 50 x 0.02² x 0.98^98 = 0.2334.Thus:
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)
P(X < 3) = 0.1326 + 0.2707 + 0.2334
P(X < 3) = 0.6367.
P(X >= 3) = 1 - P(X < 3).
P(X >= 3) = 1 - 0.6367.
P(X >= 3) = 0.3633.
TranslationWe suppose that 2% of the population is deaf, and want to find the probability of 3 or more deaf people in a sample of 100.
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Suppose that (1)=−2 , f(4)=5, f'(1)=4 , f'(4)=-7 and f'' is continuous.
Find the value of ∫41″().
Answers
Answer:
integrates by parts:
U = x dV = f''
dU = dx V = f'
The integral becomes:
x f' - integral f' dx
= x f' - f
limit as x->4 : 4 * f'(4) - f(4) = 4 * -3 - 7
= -12-7 = -19
limit as x->1 : 1 * f'(1) - f(1) = 1 * 9 - 8 = 1
subtracting: -19-1 = -20
Step-by-step explanation:
If the function y = sinx is transformed to v= 3.sin(x), how do the amplitude and period change?
Answers
Answer:
The amplitude changes from 1 to 3
The period is unchanged
Explanation:
Given that the function
\(y=\sin x\)is transformed to
\(v=3\sin x\)We want to know how the amplitude and period change.
Consider the transformation:
\(y=a\sin \mleft(bx+c\mright)+d\)Where a is the amplitude
Period is:
\(\frac{2\pi}{b}\)The amplitude changes from 1 to 3
The period is unchanged
Number graph ranging from negative four to four on the x and y axes. A line with a positive slope is drawn on the graph, passing through the labeled point A at (zero, two) and the labeled point B at three, three). What is the slope of the line passing through points A and B? Responses −3 − 3 , −15 − 1 5 14 1 4 13
Answers
The slope of the line passing through points A and B is 1/3.
The formula for the slope of a line to find the slope passing through points A and B. The formula is:
slope = (change in y) / (change in x)
Let's label the coordinates of point A as (x₁, y₁) and the coordinates of point B as (x₂, y₂).
Then, substitute the values and calculate the slope:
slope = (y₂ - y₁) / (x₂ - x₁)
slope = (3 - 2) / (3 - 0)
slope = 1 / 3
Therefore, the slope of the line passing through points A and B is 1/3.
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what is the initial value of y = 2/3x - 5
Answers
Answer:
solve for y:
\(y=-5+\frac{2}{3x} ,x\neq 0\\\)
solve for x:
\(x=\frac{2}{3(y+5)} ,y\neq -5\)
Step-by-step explanation:
pls tell me if wrong have a good night/day
) 65 people were asked on the activities they engage in during their free time. The results showed that 23 visit national parks, 26 engage in cycling while 22 engage in swimming. Furthermore 9 engage in swimming and visit national parks, 9 engage in swimming only while 11 visit national parks only. How many engage in
i. Swimming and cycling
Answers
Answer:
Step-by-step explanation:
i am working on the assumption that nobody does all three of them
i got 4 because including the people that do swimming and park, the total number of people that do swimming is 22.
the same logic goes for cycling: including the people that do swimming and visit the national park, the total is 23.
so that means that find how many people do swimming and cycling, we have to add the people doing only swimming, with the people doing both swimming and park and then subtract that answer from 22 which gives you 4
Solve the following equation for X, if Y = 3 and Z = -1. 3XY- 5XZ^2+Y=19
Answers
5) Abhasra invests $7,053 in a savings
account with a fixed annual interest rate of
3% compounded quarterly. What
will the account balance be after 4 years?
Answers
Answer:
After 4 years the account balance will be $ 7,948.67.
Step-by-step explanation:
Given that Abhasra invests $ 7,053 in a savings account with a fixed annual interest rate of 3% compounded quarterly, to determine what the account balance will be after 4 years, the following calculation must be performed:
7.053 x (1 + 0.03 / 4) ^ 4x4 = X
7,053 x 1.0075 ^ 16 = X
7.053 x 1.12699211 = X
7,948.67 = X
Therefore, after 4 years the account balance will be $ 7,948.67.
The following table shows the numbers that were rolled with adie during a game.
Answers
Part a.
The mean is the average of all numbers. From the given table, we can see that the number 1 ocurrs 42 times, the number 2 ocurrs 60 times and so on. Then, the mean of the given numbers is
\(\operatorname{mean}=\frac{1\times42+2\times60+3\times64+4\times89+5\times11+6\times31}{42+60+67+89+11+31}\)which gives
\(\begin{gathered} \operatorname{mean}=\frac{960}{300} \\ \operatorname{mean}=3.2 \end{gathered}\)so the mean is 3.2
Part b.
The sample variance formula is given by:
\(S^2=\frac{\sum ^{\infty}_{n\mathop=0}f\cdot(x-\operatorname{mean})^2}{n-1}\)where f is the frequency and n-1=299
So, by substituting the given values, we have
\(\begin{gathered} S=\frac{628}{299} \\ S\questeq2.1003 \end{gathered}\)then, the variance is 2.1003
An automobile manufacturer claims that its jeep has a 59.8 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the MPG for this jeep since it is believed that the jeep has an incorrect manufacturer's MPG rating. After testing 160 jeeps, they found a mean MPG of 59.7. Assume the standard deviation is known to be 1.3. A level of significance of 0.02 will be used. Find the value of the test statistic. Round your answer to 2 decimal places. Enter the value of the test statistic.
Answers
Answer:
The value of the test statistic is -0.97
Step-by-step explanation:
This test is two tailed test.
Null and Alternative hypothesis is as follow
Null Hypothesis is used when it is assumed that there is no significant difference between the values.
Null Hypothesis = \(H_{0}\) = \(\mu =\) 59.8
The Alternative hypothesis is the alternative of the Null Hypothesis. It is an experimental technique that is used when it is assumed that there is some difference
Alternative Hypothesis = \(H_{a}\) = \(\mu \neq\) 59.8
Test statistcs is z
The value of test statistics can be calculated using the following formula
Test Statistics \(= (\bar x - \mu ) / \sigma / \sqrt n\)
Test Statistics \(= (59.7-59.8) / 1.3 / \sqrt 160\)
Test Statistics = -0.97
Suppose you start with one liter of vinegar and repeatedly remove 0.14 L, replace with water, mix, and repeat. a. Find a formula for the concentration after n steps. b. After how many steps does the mixture contain less than 9% vinegar?
Answers
Formula for the concentration after n steps is \(C(n) = C(0) * (0.86)^n\) and
after 11 steps, the mixture contains less than 9% vinegar.
What is concentration?
Concentration in science refers to the amount of a particular substance (the solute) that is dissolved in a given amount of a solution. It is typically expressed in units of moles per liter (M or mol/L) or as a percentage or fraction of the total solution.
a. Let C(n) be the concentration of vinegar after n steps. At each step, we remove 0.14 L of the mixture, which contains C(n) liters of vinegar. So we are left with (1 - C(n)) liters of water. We then add back 0.14 L of water, giving us a total volume of 1 liter. Therefore, the concentration after one step is:
\(C(1) = C(0) * \frac{1 - 0.14}{1}\)
where C(0) is the initial concentration of vinegar, which is 1 liter per liter or 100%. After two steps, we repeat the process:
C(2) = C(1) * \(\frac{1 - 0.14}{1}\)
Substituting the formula for C(1), we get:
C(2) = C(0) * \((\frac{1 - 0.14}{1}) * (\frac{1 - 0.14}{1})\)
or, more generally:
\(C(n) = C(0) * (0.86)^n\)
b. We want to find the smallest integer n such that C(n) < 0.09 or 9%. Substituting the formula from part (a), we get:
\(C(0) * (0.86)^n < 0.09\)
Dividing both sides by C(0), we get:
\((0.86)^n < 0.09\)
Taking the natural logarithm of both sides, we get:
n * ln(0.86) < ln(0.09)
Dividing both sides by ln(0.86), we get:
n > ln(0.09) / ln(0.86)
Using a calculator, we get:
n > 10.7
Since n must be an integer, the smallest possible value of n is 11. Therefore, after 11 steps, the mixture contains less than 9% vinegar.
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Clean Machine is Middletown's premier house cleaning service. The company used 2,920 gallons of soap last year, and 35% less this year. How many gallons of soap did the company use this year?
Answers
Answer:
Step-by-step explanation:)
what equation results from completing the square and then factoring? x^2+24x=33
a.) (x+24)^2=57
b.) (x+12)^2=57
c.) (x+12)^2=177
d.) (x+24)^=177
Answers
The factorisation of the given equation using completing square method is (x+12)²=177. Therefore, option D is correct.
The given equation is x²+24x=33.
We need to factorise the equation using completing the square method.
What is completing the square method?Completing the square means writing a quadratic in the form of a squared bracket and adding a constant if necessary.
Now, x²+24x-33=0
Add and subtract (b/2)²=144 to the equation.
x²+24x-33+144-144=0
⇒x²+24x+144-33-144=0
⇒(x+12)²-177=0
⇒(x+12)²=177
The factorisation of the given equation using completing square method is (x+12)²=177. Therefore, option D is correct.
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The mark scored in a test by ten pupils are as follows: 15, 14, 15, 13, 16, 16, 17, 13, 16, 17. Find the modal mark?
Answers
The modal mark is 16.because as we can see there are two 15, two 13,one 14, two 17 and three 16.
Complete the explanation for how you could find the number of seconds in one full 24-hour day-
Then solve.
You would multiply 24 hours by _____ minutes and then multiply my answer by _____
Seconds.
There are ____ seconds in one full day
Answers
Answer:
Step-by-step explanation:
You would multiply 24 hours by 60 minutes and then multiply my answer by
60 Seconds.
There are 86400 seconds in one full day
A map shows the vertices of a campsite are (25,10), (25,-5), (-5,-5), and (-5,10). The vertices of your tent are (0,-3), (0,6), (10,6), and (10,-3). The coordinates are measured in feet. What percent of the campsite is not covered by your tent?
Answers
The percent of the area that is not covered is 80 percent
How to calculate the area that is not coveredIn mathematics area is defined as the absolute or total space that an object or shape occupies. It is usually measured using centimeters, cm ² square or the use of meter square m ².
area of tent
= (10 - 0) * (6 - (-3))
= 90
The area of the campsite would be:
(25 - (-5) x (10 - (-5))
= 450
Then the area would be 450 - 90
= 360
the percentage that is not covered by tent = 360 / 450 x 100
= 80 percent
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Connie can clean her house in 3.5 hours. If Alvaro helps her, together they can clean the house in 1 hour and 40 minutes. How long would it take Alvaro to clean the house by himself?
Answers
Answer:
1 hour and 50 minutes
Step-by-step explanation:
Time Connie takes to clean the house: 210 minutes
Time takes for both of them at the same time: 100 minutes.
210 - 100 = 110 minutes
Therefore, Alvaro takes one hour and 50 minutes to clean the house by himself.
Answer:Alvaro can clean the house alone in approximately 3.89 hours.
Step-by-step explanation:
If Connie can clean her house in 3.5 hours, then her rate of work is 1/3.5 of the house per hour. Together, Connie and Alvaro can clean the house in 1 hour and 40 minutes, or 1.67 hours.
To find how long it would take Alvaro to clean the house alone, we can use the formula:
combined rate of work = sum of individual rates of work
So, (1/3.5 + 1/a) * 5/3 = 1, where "a" is the time it takes Alvaro to clean the house alone.
Simplifying the equation, we get 1/a = 9/35, which means that Alvaro can clean the house alone in approximately 3.89 hours (or 3 hours and 53 minutes).
Question 2(Multiple Choice Worth 2 points)
(Slope-Intercept Form MC)
The table shown represents a linear relationship.
x 0 1 3 4
y −8 −6 −2 0
Based on the table, what is the equation of the linear relationship in slope-intercept form?
y = 2x − 8
y = 2x + 8
y = −2x + 4
y = −2x − 4
Answers
The equation of the linear relationship in slope-intercept form is y = 2x - 8. Option A is the correct answer.
To determine the equation of the linear relationship in slope-intercept form based on the table, we need to find the slope and y-intercept.
By observing the table, we can calculate the slope by selecting any two points. Let's choose the points (0, -8) and (4, 0).
Slope (m) = (change in y) / (change in x)
= (0 - (-8)) / (4 - 0)
= 8 / 4
= 2
Now that we have the slope, we can find the y-intercept by substituting the values of one point and the slope into the equation y = mx + b and solving for b.
Using the point (0, -8):
-8 = 2(0) + b
b = -8
Therefore, the equation of the linear relationship in slope-intercept form is: y = 2x - 8. Option A is the correct answer.
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9) 1 = 0.99 + z? 10
Answers
Answer:
0.99+10=10.99
Step-by-step explanation:
If Anna's test grades are 66, 90, and 99, what is her test average?
Answers
Answer:
90 because it is the mean
Answer: it’s 83%
Step-by-step explanation: you add them up and divide by 3
The wheel on a scooter completes 124 revolutions and travels 22.4 meters. What is the diameter of the wheel in mm? Use 3.14 for pi and round to the nearest whole millimeter.
Answers
If wheel on a scooter completes 124 revolutions and travels 22.4 meters then diameter of the wheel is 57 mm
Each revolution of the wheel covers a distance equal to the circumference of the wheel.
The diameter of the wheel "d".
The distance covered in 124 revolutions is:
distance = 124 x circumference
= 124 x pi x d
= 124 x 3.14 x d
We know that this distance is equal to 22.4 meters, so we can set up an equation:
124 x 3.14 x d = 22.4
Simplifying and solving for d:
d = 22.4 / (124 x 3.14)
d = 0.057 meters
As we know that 1 meter is equal to thousand millimeters so multiply by 1000 to get in millimeters
d = 57 millimeters
Therefore, the diameter of the wheel is approximately 57 mm.
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