During strenuous exercise, an athlete can burn 12 calories per minute on a treadmill and 8.5 calories per minute on an elliptical machine. If an athlete uses both machines and burns 325 calories In a 30- minute workout, how many minutes does the athlete spend on each machine?
Answers
The athlete spends 20 minutes on the treadmill and 10 minutes on the elliptical machine. This is determined by setting up and solving a system of linear equations based on the calorie burn rate of each machine and the total calories burned during the workout.
To solve the problem of how many minutes an athlete spends on each machine during their workout, we must set up a system of linear equations. The athlete burns 12 calories per minute on a treadmill and 8.5 calories per minute on an elliptical machine. In a 30-minute workout, the athlete burns a total of 325 calories. Let's denote the time spent on the treadmill as t minutes and the time spent on the elliptical machine as e minutes.
The total time spent on both machines is 30 minutes: t + e = 30The total calories burned is 325: 12t + 8.5e = 325We now have two equations and two unknowns, which can be solved simultaneously.
Subtract the second equation from 12 times the first equation to eliminate eSolve the resulting equation for t to find the number of minutes on the treadmillSubstitute the value of t in the first equation to find the number of minutes on the elliptical machineUsing these steps, we find that:
12t + 12e = 360 (by multiplying the first equation by 12)12t + 8.5e = 325 (second equation as is)Subtracting these equations, we get 3.5e = 35Solving for e, we find that e = 10 (the athlete spends 10 minutes on the elliptical machine)Plugging e = 10 into the first equation, we find that t = 20 (the athlete spends 20 minutes on the treadmill)Therefore, the athlete spends 20 minutes on the treadmill and 10 minutes on the elliptical machine during their 30-minute workout.
Related Questions
evaluate the expression h-6 when h=15
Answers
h - 6
When h = 15
All we have to do is replace h by 15
h - 6
15 - 6
= 9
Good luck!
First write the expression:
h - 6
Plug in 15 into h in the expression (since h = 15)
15 - 6
Solve
15 - 6 = 9
your answer is 9
hope this helps
In , is a right angle. find the remaining sides and angles. round your answers to the nearest tenth . show your work. a = 3, c = 1 9
Answers
Y=(2x-3)^5(2-x^4)^3 differentiate the function please
Answers
If an amount of money, called principle, p, is deposited into an account that earns interest at a rate r, compound annually, then in two years that investment will grow to an amount A, given by the formula A=P(1+r)^2. If a principle amount of $5000 grows to $5940.50 in two years, what is the interest rate?
Answers
A = P(1+r)^t
A = $5940.50
P = $5000
r = ?
t = 2yrs
$5940.50 = $5000(1+r)^t
-------------- --------------------
$5000 $5000
1.1881 = (1+r)^2
sqrt(1.1881) = 1+r
1.09 = 1+r
-1 -1
------- ----
0.09 = r
r = 0.09
Final answer:
By using the compound interest formula A=P(1+r)² and the given values, we find the interest rate to be approximately 0.09, or 9% annually.
Explanation:
To find the interest rate r that grew the principal P from $5000 to $5940.50 over two years with compound interest, we use the formula A=P(1+r)². Here, A is the amount of money accumulated after n years, including interest. We are given that A is $5940.50 and P is $5000.
Let's plug in the values and solve for r:
5940.50 = 5000(1+r)²
1.1881 = (1+r)²
To find r, we take the square root of 1.1881:
Subtracting 1 from both sides to isolate r, we get:
r = 1.09 - 1
r = 0.09
The approximate interest rate is 0.09, which means the annual interest rate is 9%.
What is 2/3 times 3/4
Answers
1/2 is your answer
hope this helps
[tex] \frac{2}{3} [/tex] × [tex] \frac{3}{4} [/tex]
First, you would cross simplify the equation... But, you don't have to do it now, you can do it at the end (I think this was is easiest).
[tex] \frac{1}{1} [/tex] × [tex] \frac{1}{2} [/tex]
Finally, you would answer the equation.
[tex] \frac{1}{1} [/tex] × [tex] \frac{1}{2} [/tex] = [tex] \frac{1}{2} [/tex]
Your answer would be [tex] \frac{1}{2} [/tex].
I hope this helps!
Kellogg's produced 715000 boxes of cornflakes this year. This was 110% of annual production last year. What was last year's annual production?
Answers
110% of x means [tex]\displaystyle{ \frac{110}{100}\cdot x [/tex].
Thus, we solve the equation:
[tex]\displaystyle{ \frac{110}{100}\cdot x=715,000[/tex].
Multiplying both sides by [tex]\displaystyle{ \frac{100}{110}[/tex], we have:
[tex]\displaystyle{ x=715,000 \cdot \frac{100}{110}=650,000[/tex].
Answer: Last year's annual production was 650,000 boxes.
The submarine is traveling at a depth of 152 feet below sea level. The submarine was given instructions to rise 63 feet and then drop 84 feet. Write an expression that describes this situation
Answers
What is the equation with the difference of 54.57
Answers
100.00-45.43 is NOT an equation, however. Please ensure that you have copied down the original problem exactly as presented.
Write a rule for the linear function in the table.
x; f(x)
2 8
5 17
5 11
11 23
A; f(x) = x + 5
B;f(x) = x + 1
C;f(x) = 2x + 1
D;f(x) = –2x – 1
Answers
the correct answer is A. [tex]\( f(x) = 2x + 1 \).[/tex]
To find the rule for the linear function represented in the table, we can use the formula for a linear function, which is:
[tex]\[ f(x) = mx + b \][/tex]
Where:
- m is the slope of the line
- b is the y-intercept
Given the table:
[tex]\[ \x & : 2, 5, 8, 11 \\f(x) & : 5, 11, 17, 23\end{align}\][/tex]
We can start by finding the slope (m) using the formula:
[tex]\[ m = \frac{{f(x_2) - f(x_1)}}{{x_2 - x_1}} \][/tex]
Let's choose two points from the table, for example, (2, 5) and (5, 11):
[tex]\[ m = \frac{{11 - 5}}{{5 - 2}} \]\[ m = \frac{{6}}{{3}} \]\[ m = 2 \][/tex]
So, we have found that the slope m is 2.
Now, we can use the slope-intercept form of a line to find the y-intercept (b). We can pick any point from the table to do this. Let's use the point (2, 5):
f(x) = mx + b
5 = 2(2) + b
5 = 4 + b
b = 5 - 4
b = 1
So, we have found that the y-intercept b is 1.
Now, we can write the rule for the linear function:
[tex]\[ f(x) = 2x + 1 \][/tex]
Therefore, the correct answer is A. [tex]\( f(x) = 2x + 1 \).[/tex]
The complete question is:
Write a rule for the linear function in the table.
x = 2,5,8,11
f(x) = 5,11,17,23
A. f(x) = 2x + 1
B. f(x) = x + 5
C. f(x) = –2x – 1
D. f(x) = 1/2x+1
Josiah invests $360 into an account that accrues 3% interest annually. Assuming no deposits or withdrawals are made, which equation represents the amount of money in Josiah’s account, y, after x years?
Answers
Y=360*(1+0.03)^x
Answer:
D
Step-by-step explanation:
Beverly made a deposit of $375 into her checking account. Then she withdrew $ 65. The next day, she wrote a check for $ 135. She had $475 before any of these transactions. How much money is in her account now?
Answers
add 375(since made deposit)
475+375=850
850-65=785
785+135=$920
Write an equation in point-slope form of the line through point p(9, -1) with slope -5.
Answers
The problem is
2n>14
n=?
Answers
n>14/2
n>7
=n>7
so, n can be any number which is greater than 7.
what is a fixed charge for borrowing money; usually a percentage of the amount borrowed?
Answers
that simply means, you have to return it in a year, and it has to be that amount PLUS 11.75% of whatever that amount was. the extra amount is the interest.
It is found that 5 out of every 8 college students like algebra. If a certain college has 4,000 students, how many of them like algebra?
Answers
Hope this helped.
the number of students that like it will go on top and the total college students will be on bottom
5/8
if a college has a total of 4000 students, that will go on bottom and x will be on top
x/4000
to solve for x you would multiply 5 by 4000, and then divide by 8
this would give you x=2500
I Need to identify the property that justifies each step to simplify the expression
Answers
1) equality of addition , subtraction , multiplication, and division
This graph models the number of teachers assigned to a school, as determined by the number of students. What is the constant of proportionality?
1/25
1/20
1/15
1/10
Answers
slope = (8 - 4) / (120 - 60) = 4/60 = 1/15 <== the constant of proportionality is the slope
Answer:
The correct option is 3.
Step-by-step explanation:
Form the given figure it is noticed that the line is passing through the points (60,4) and (120,8).
[tex]y\propto x[/tex]
[tex]y=kx[/tex]
Where, k is the constant of proportionality or slope.
The slope of a line is defined as
[tex]k=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]k=\frac{8-4}{120-60}[/tex]
[tex]k=\frac{4}{60}[/tex]
[tex]k=\frac{1}{15}[/tex]
Therefore option 3 is correct.
483 is what part of 121?
Answers
483/121 = 3.991, or about 4. "483 is approx. four times 121."
Answer:
yes, since 483 is greater than 121, the correct answer is a whole number with a fraction:
483/121 = 3.991, or about 4. "483 is approx. four times 121."
A scientist has four petri dishes of different sizes. Each dish contains a different number of bacteria. Find each population density, to the nearest hundredth. Which statement is true? Dish A has the lowest population density. Dish C has the greatest population density. Dish A and Dish B have approximately the same population density. Dish C and Dish D have approximately the same population density.
Answers
The statement that is True is Option D which says:
"Dish C and Dish D have approximately the same population density."
What is Population Density?The population density of an area is the Number of Entities in that space/Total Area occupied by the population.
It can also be written as Dp = N/A.
Because the Dp of Dish C and Dish D is approximately 0.68, we can say that they have approximately the same Dp.
Learn more about Population Density at:
https://brainly.com/question/13902749
Find an equation of the tangent line to the bullet-nose curve y=|x|/sqrt(2−x^2) at the point (1,1) I think that square root is what is confusing me on this question
Answers
[tex]\bf \cfrac{dy}{dx}=\cfrac{\frac{x\sqrt{2-x^2}}{\sqrt{x^2}}~~+~~\frac{x\sqrt{x^2}}{\sqrt{2-x^2}}}{2-x^2}\implies \cfrac{dy}{dx}=\cfrac{\frac{x(2-x^2)~~+~~x(x^2)}{\sqrt{x^2}\sqrt{2-x^2}}}{2-x^2}\\\\\\ \cfrac{dy}{dx}=\cfrac{\frac{2x\underline{-x^3+x^3}}{\sqrt{x^2}\sqrt{2-x^2}}}{2-x^2}\implies \cfrac{dy}{dx}=\cfrac{\frac{2x}{\sqrt{x^2}\sqrt{2-x^2}}}{2-x^2}[/tex]
[tex]\bf \cfrac{dy}{dx}=\cfrac{2x}{\sqrt{x^2}\sqrt{2-x^2}(2-x^2)} \implies \boxed{\cfrac{dy}{dx}=\cfrac{2x}{|x|\sqrt{2-x^2}(2-x^2)}} \\\\\\ \left. \cfrac{dy}{dx} \right|_{1,1}\implies \cfrac{2(1)}{|1|\cdot \sqrt{2-1^2}(2-1^2)}\implies 2\\\\ -------------------------------\\\\ \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-1=2(x-1)\implies y-1=2x-2 \\\\\\ y=2x-1[/tex]
Norma and Rene are serving cupcakes at a school party. If they arrange the cupcakes in groups of 2.3.4.5. or 6 they have exactly one cupcake left over. what is the smallest number of cupcakes they could have?
Answers
We are given that there are 5 groups which are:
group of 2
group of 3
group of 4
group of 5
group of 6
and 1 left over
So the smallest number of cupcakes would simply be the sum of all:
smallest number of cupcakes = 2 + 3 + 4 + 5 + 6 + 1
smallest number of cupcakes = 21
Two pools are being filled with water. To start, the first pool contains 890 liters of water and the second pool is empty. Water is being added to the first pool at a rate of 20.5 liters per minute. Water is being added to the second pool at a rate of 42.75 liters per minute.
Answers
First pipe empties at the rate of 540,000/150=3600 liters/min
Second pipe empties at the rate of 540,000/225=2400 liters/min
Together, both pipes empties at the rate of 3600+2400=6000 liters/min, so our equation to solve is:
6000*x=540000
Where are the asymptotes of f(x) = tan(4x − π) from x = 0 to x = pi over 2 ?
Answers
The asymptotes are where the graph is undefined. Since: tan(x) =sin(x)/cos(x)
It is where cos(4x-π) = 0
cos(4x-π) = 0 when the inside is -π/2 , π/2 , 3π/2
4x - π = π/2
4x = π/2 + π
4x = 3π/2
x = 3π/8
4x - π = 3π/2
4x = 3π/2 + π
4x = 5π/2
x = 5π/8
This ones outside the interval (5π/8 > π/2) , try -π/2
4x - π = -π/2
4x = -π/2 + π
4x = π/2
x = π/8
Asymptotes are π/8 and 3π/8
Answer:
D 3pi/8 , 5pi/8
Step-by-step explanation:
find the missing values in the ratio table .then write the equivalent ratios .
Answers
9 shoes to 12 socks
18 shoes to 24 socks
The missing values are 12 and 18.
The ratios are [tex]\dfrac{9}{12}[/tex] and [tex]\dfrac{18}{24}[/tex].
The given table is:
[tex]\begin{center}\begin{tabular}{ c c c c } shoes & 36 & 9 & y \\ socks & 48 & x & 24 \\\end{tabular}\end{center}[/tex]
Since all the columns are pertaining same ratio; thus we have:
[tex]\dfrac{36}{24} = \dfrac{9}{x} = \dfrac{y}{24}\\\\\dfrac{3}{4} = \dfrac{9}{x} = \dfrac{y}{24}\\\\\\or\\\\\dfrac{3}{4} = \dfrac{9}{x}\\\\x = 12\\\\and \\\\\dfrac{3}{4} = \dfrac{y}{24}\\\\y = 18[/tex]
Thus, the missing values x and y are 12 and 18 respectively.
And the are ratios [tex]\dfrac{9}{12}[/tex] and [tex]\dfrac{18}{24}[/tex].
Learn more here:
https://brainly.com/question/1504221
What are the coordinates of the vertices of the triangle under the translation (x, y) mc011-2.jpg (x + 1, y - 4)?
(0, -3), (0, 0), (3, -3)
(-3, 0), (3, -3), (0, -3)
(0, -3), (-3, -3), (-3, 0)
(-3, 0), (0, 0), (-3, -3)
Answers
(-1,1) (-4,1) (-4, 4)
translation (x, y) to (x + 1, y - 4)
(0,-3) (-3,-3) (-3, 0)
answer
(0, -3), (-3, -3), (-3, 0)
it is c :
(0,-3), (-3,-3), (-3,0)
just take the X and Y of the coordinates of the original triangle and substitute it in the given equation (x + 1, y - 4)
try it out yourself it works :)
Let a = {2, 9}, b = {9, 13, 28}, d = {40} and s = sample space = a ∪ b ∪
d. identify bc ∪
a.
Answers
The union of sets a, b, and d (a ∪ b ∪ d) gives you the set {2, 9, 13, 28, 40}. Set 'a' is simply the set containing elements 2 and 9.
Explanation:To resolve the question, we need to analyze what each symbol means. The ∪ symbol in set theory represents union, meaning everything that is in either of the sets or in both. However, it seems there is a typographical error in your question with 'bc'. As 'c' is not defined, we will proceed by ignoring that particular part and focus on 'a' which is defined.
So, if we're looking to identify a = {2,9}, it simply means the set that contains two elements: 2 and 9.
As your question stands, based on the provided sets, s = a ∪ b ∪ d = {2, 9, 9, 13, 28, 40} but when we simplify the set (since a set does not contain duplicate values), we get s = {2, 9, 13, 28, 40}.
Learn more about Set Theory here:https://brainly.com/question/35494444
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The science club raised money to clean the beach. They spent $29 on trash bags and $74 on waterproof boots. They still have $47 left. How much did they raise?
Answers
Answer:
They raised $150
Step-by-step explanation:
In order to solve this you just need to reverse the actions that they took in order to get to 47 dollars left, so the total amount they raised will be represented by letter X, so 47 is what is left after spending 29 on trash bags and 74 on waterproof boots, that means that from the total we are withdrawing those amounts and the result will be 47:
Total-Money spent=47
X-29 - 74= 47
x=47+74+29
x=150
So now we know that they originally had 150 dollars and that would be what they raised.
long division 573÷15=
Answers
15 goes int 57 3 times: 45
57-45=12, bring down the 3
15 goes into 123 8 times
123-120=3
573/15= 38 with a remainder of 3
38R3 is the answer
how many hours would someone who earns 9.75 per hour have to work to earn 351
Answers
351/9.75 = 36
x = 36
Thus, 36 hours must be worked in order to get $351 if you have a salary of $9.75
Determine the number of significant digits in each number and write out the specific significant digits. 405000
Answers
___________________________________________________________
The THREE (3) significant digits are: "4", "0", and "5" —(the first three digits).
___________________________________________________________