A gym has two machine you want to use. An elliptical trainer that burns 8 calories per minute and a stationary bike that burns 6 calories per minute. You have 40 minutes to exercise at the gym and you want to burn 300 calories total using both machines. How much time should you spend on each machine?( use x for the elliptical and y for the bike)Elliptical trainer x= Stationary bike y=
Answers
SOLUTION
The first machine is 8 calories per minute.
The second machine is 6 calories per minute.
This allows us to set up a system of equations. The first equation will be for calories burned:
8x + 6y = 300.............1
'x' is minutes on the 8 calories per minute machine; 'y' is minutes on the 6 calories per minute machine.
A second equation simply shows that the total minutes add up to 40:
x + y = 40...................2
Now that we have two equations, we can solve them using the substitution method of the simultaneous equation.
\(\begin{gathered} 8x+6y=300\ldots\ldots\ldots\text{.}.1 \\ x+y=40\ldots\ldots\ldots\ldots2 \end{gathered}\)Isolate 'x' from equation 2
\(x=40-y\ldots\ldots\ldots3\)Substitute x = 40-y into equation 1
\(\begin{gathered} 8(40-y)+6y=300 \\ 320-8y+6y=300 \\ 320-2y=300 \\ \text{Collect like terms } \\ 320-300=2y \\ 20=2y \\ \text{Divide both sides by 2} \\ \frac{20}{2}=\frac{2y}{2} \\ 10=y \\ \therefore y=10 \end{gathered}\)Now, substitute y = 10 into equation 3 and evaluate for x
\(\begin{gathered} x=40-y \\ x=40-10=30 \\ \therefore x=30 \end{gathered}\)Hence, you should spend 30 minutes on machine 1 and 10 minutes on machine 2.
Final answers
\(\begin{gathered} \text{Elliptical trainer, x = 30minutes} \\ \text{Stationary bike, y = 10minutes} \end{gathered}\)Related Questions
Suppose that the local government of Tulsa decides to institute a tax on soda producers. Before the tax, 35,000 liters of soda were sold every week at a price of $11 per liter. After the tax, 30,000 liters of soda are sold every week; consumers pay $14 per liter, and producers receive $6 per liter (after paying the tax).
The amount of the tax on a liter of soda is
$
per liter. Of this amount, the burden that falls on consumers is
$
per liter, and the burden that falls on producers is
$
per liter.
Answers
- Before the tax, 35,000 liters of soda were sold every week at a price of $11 per liter.
- After the tax, 30,000 liters of soda are sold every week; consumers pay $14 per liter, and producers receive $6 per liter (after paying the tax).
The total revenue from soda sales before the tax was:
35,000 liters × $11/liter = $385,000 per week
The total revenue from soda sales after the tax is:
30,000 liters × $14/liter = $420,000 per week
The difference in revenue is due to the tax. Let's call the amount of the tax per liter of soda "t". Then we have:
(30,000 liters × $6/liter) + (30,000 liters × t/liter) = $420,000 per week
Simplifying and solving for t, we get:
t = ($420,000 per week - $180,000 per week) / 30,000 liters
t = $8 per liter
Therefore, the amount of the tax per liter of soda is $8.
To find the burden that falls on consumers and producers, we can use the price of soda before and after the tax. Before the tax, consumers paid $11 per liter and producers received $11 per liter. After the tax, consumers paid $14 per liter and producers received $6 per liter. The difference in price is due to the tax. Let's call the burden that falls on consumers "bc" and the burden that falls on producers "bp". Then we have:
bc + bp = $14 - $11
bc + bp = $3 per liter
And we know that:
bp = $11 - $6 = $5 per liter
Substituting this value into the previous equation, we get:
bc + $5 per liter = $3 per liter
bc = $3 per liter - $5 per liter
bc = -$2 per liter
Since the burden that falls on consumers is negative, we can say that the burden falls entirely on producers, who bear the full $3 per liter increase in price due to the tax.
Therefore, the burden that falls on consumers is $0 per liter, and the burden that falls on producers is $3 per liter.
A rectangle has a length 3x + 1 of and a width of Write an expression for the 3-9
perimeter of the rectangle.
Answers
The expression for the perimeter is P = 12x - 16
How to write an expression for the perimeter?The given parameters are
Length = 3x + 1
Width = 3x - 9
The perimeter is calculated as
P = 2 * (Width + Length)
So, we have
P = 2 * (3x + 1 + 3x - 9)
Evaluate
P = 2* (6x - 8)
Expand
P = 12x - 16
Hence, the expression for the perimeter is P = 12x - 16
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ing One Step Equations - Barb knows that she needs 8.5 hours of sleep every night to feel rested and sharp. If Barb has been getting her 8.5 hours of sleep every night, write and solve an equation that represents the number of perfect nights of sleep she's had, if she's had 3102.5 hours of sleep.
I've been stuck on this for sooo longgg:((
Answers
Answer:
x=3102.5/8.5 is your answer
Step-by-step explanation:
Find the cost to carpet a 15ft. by 18ft. room if the carpet costs $25.95 per square yard.
Answers
The cost of the carpet will be $2,335.5.
What is Multiplication?
To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
The dimensions of the carpet are;
⇒ 15 feet by 18 feet
Now,
The area of the carpet = 15 x 18
= 279 feet²
= 270 / 3 yards²
= 90 yards²
Since, The carpet costs = $25.95 per square yard.
Hence, The carpet cost for 90 yards² = 90 x $25.95
= $2,335.5
Thus, The cost of the carpet will be $2,335.5.
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Fill in the blanks to prove that the sum of the measures of the interior angles in this triangle is equal to 180°. 21° + 49° + ° = °
Answers
Based on the fact that the sum of the interior angles need to be equal to 180°, the missing angle is 110°
What is the missing angle?The sum of all the interior angles need to add up to 180° which means that to find the missing angle, you should subtract the known angles from 180°.
The missing angle is:
= Total angle - Known angles
Solving for the missing angle gives:
= 180 - 21 - 49
= 180 - 70
= 110°
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Answer:
Step-by-step explanation:
10-² =
Exponential form
Answers
Copy the base to the right side of the equality
10-^2=10
Rewrite the exponent -2 as the product of (-1) and 2
10-^2=10^(-1)x2
First, use the Power of a Power Property
10-^2=(10^(-1) ) ^2
Any number raised to the power of can be written as its reciprocal
10^-2=(1/10)^2
Next, use the Power of a Quotient Property
10^-2=1^2/10^2
1 raised to any power equals 1
10^-2=1/10^2
so the answer is 10^-2=1/10^2
Answer:
Step-by-step explanation:
the answer is 0.01
The base of the exponential form is 10 and the power is -2 therefore the answer is 0.01 if the power was 2 the answer would have been 100
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A manufacturer knows that their items have a lengths that are approximately normally distributed, with a mean of 10.2 inches, and standard deviation of 3.3 inches.
If 48 items are chosen at random, what is the probability that their mean length is greater than 8.8 inches?
(Round answer to four decimal places)
Answers
Answer: Hope this helps ;)
Step-by-step explanation:
The probability that the mean length of 48 items is greater than 8.8 inches can be calculated using the normal distribution.
First, we need to standardize the value 8.8 inches by subtracting the mean length (10.2 inches) and dividing by the standard deviation (3.3 inches):
(8.8 - 10.2) / 3.3 = -1.4 / 3.3 = -0.42424242
We can use a z-table or a normal distribution calculator to find the probability that a random variable is less than -0.42424242 standard deviations below the mean. This probability is equal to the probability that the mean length of 48 items is greater than 8.8 inches.
Using a calculator, we find that the probability is 0.3389.
Rounding to four decimal places, the probability that the mean length of 48 items is greater than 8.8 inches is 0.3389.
divide550six by 50six
Answers
The quotient of 550six and 50six is obtained by the calculation to be 11 six
What is the quotient?We know that the result that we obtain after we have carried out a division operation is called a quotient. In this case, we have been required to carry out the operation of division in base six.
We could start by converting the both values to base 10 as follows;
(5 * 6^2) + (5 * 6^1) + (0 * 6^0) = 180 + 30 + 0 = 210 ten
(5 * 6^1) + (0 * 6^0) = 30 + 0 = 30 ten
Then we carry out the division in base ten; 210 ten/30 ten = 7 ten
We convert back to base six to obtain 11 six
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The graph of the function f(x) = (x − 3)(x + 1) is shown.
On a coordinate plane, a parabola opens up. It goes through (negative 1, 0), has a vertex at (1, negative 4), and goes through (3, 0).
Which describes all of the values for which the graph is positive and decreasing?
all real values of x where x < −1
all real values of x where x < 1
all real values of x where 1 < x < 3
all real values of x where x > 3
Answers
The expression that describes all of the values for which the graph is positive and decreasing is all real values of x where x < -1
Which describes all of the values for which the graph is positive and decreasing?The equation of the function is given as:
f(x) = (x - 3)(x + 1)
When the value of the graph is positive, we have:
f(x) > 0
So, the function becomes
(x - 3)(x + 1) > 0
Split the above inequality
x - 3 > 0 and x + 1 > 0
Solve for x in the inequalities
x > 3 and x > -1
Hence, the expression that describes all of the values for which the graph is positive and decreasing is all real values of x where x < -1
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What is the area of the trapezoid shown below?
Answers
Calculate the equivalent ratio 1.25 : 3.75 : 7.5
Answers
The equivalent ratio of 1.25 : 3.75 : 7.5 is 5 : 15 : 30.
To calculate the equivalent ratio of 1.25 : 3.75 : 7.5, we need to find a common multiplier that can be applied to all the numbers in the ratio to make them whole numbers. In this case, the common multiplier is 4 because it can be multiplied to each number to eliminate the decimals.
By multiplying each number in the ratio by 4, we get:
1.25 * 4 = 5
3.75 * 4 = 15
7.5 * 4 = 30
So the equivalent ratio of 1.25 : 3.75 : 7.5 is 5 : 15 : 30.
This means that the relative sizes or quantities represented by the original ratio are maintained in the equivalent ratio. For example, if we had 1.25 units of something, it would be equivalent to 5 units in the new ratio, and if we had 7.5 units, it would be equivalent to 30 units in the new ratio.
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Help please on the bottom one
Answers
Answer:
i think it may be 6 3/4
Step-by-step explanation:
i used my calculator ._.
There are 38 coins in a collection of 20 paise coins and 25 paise coins. If the total value of the collection is Rupees 8.50, how many of each are there?
Answers
We will have the following:
*First:
**We stablish that x will represent the number of 20 paise coins.
**We stablish that y will represent the number of 25 paise coins.
Second: From this we will then have:
\(x+y=38\)&
\(20x+25y=850\)[This 850 is due to the fact that 8.50 Rupees are equal to 850 paise].
*Third: We solve for either x or y in the first equation:
\(x=38-y\)Now, we replace this in the second equation and solve for y:
\(20(38-y)+25y=850\Rightarrow760-20y+25y=850\)\(\Rightarrow5y=90\Rightarrow y=18\)So, we have that there are 18 25 paise coins.
Now, using this we solve for x in the first equation:
\(x+18=38\Rightarrow x=20\)So, we have that there are 20 20 pais coins.
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Click and place the simplified expression after its original expression.
Answers
6) Solve the equation -2y + 6 = -12.
y=?
Answers
-2y = -18
Divide by -2
Solution: y = 9
(brainliest is gonna begiven answer correctly please) Use the formula V = s³, where V is the volume and s is the edge length of the cube, to solve this problem.
A cube-shaped bin has an edge length of 12 yard.
What is the volume of the container?
Enter your answer, as a fraction in simplest form, in the box.
Answers
Answer:
\(\sf V=\dfrac18\: \sf yd^3\)
Step-by-step explanation:
Volume of a cube formula
\(\sf V=s^3\)
where:
V = volumes = edge lengthGiven:
s = 1/2 yard\(\sf \implies V=\left(\dfrac12\right)^3\)
Apply exponent rule \((\frac{a}{b})^c=\dfrac{a^c}{b^c}\)
\(\sf \implies V=\dfrac{1^3}{2^3}\)
\(\sf \implies V=\dfrac18\: \sf yd^3\)
Volume:-
side³(1/2)³1/2³1/8yd³Find the focus of the following Parabola:
y=-1/4x^2
Answers
9514 1404 393
Answer:
(0, -1)
Step-by-step explanation:
Compare the equations ...
y = -1/4x^2
y = 1/(4p)(x -h)^2 +k
You can see that (h, k) = (0, 0), and that p = -1.
The value of p is the distance from the vertex to the focus. Here, the parabola opens downward, and the focus is 1 unit below the vertex.
The focus is (0, -1).
_____
Additional comment
Every point on the parabola is the same distance from the focus as it is from the directrix. A couple of points that are easy to check are the vertex, and the points on the same horizontal line as the focus. This check can tell you if we have properly found the focus.
inverse function of f(x)=x-7/x+4
Answers
Final Answer: The inverse of f (x)=7x-4 is f^-1 (x)= (x+4)/7
\(8 ^(x)+32 x^{2}+4\)
Answers
Answer:
Step-by-step explanation:
Rearrange the terms and take out a common factor of 4
4(8x^2 + 2x + 1)
I think this is as far down as you want to take it. It gives an imaginary root which you may not be familiar with.
Peanut allergies are becoming increasingly common in Western countries. Some evidence points to the timing of peanuts! first introduction in the diet as an influential factor, raising the question of whether pediatricians should recommend early exposure or avoidance. A study enrolled infants with a diagnosed peanut allergy and randomly assigned them to either completely avoid peanuts or consume peanuts in small amounts regularly until they reached 60 months of age. At the end of the study, 18 of the 51 infants who had avoided peanuts were still allergic to peanuts. In contrast, 5 of the 47 infants who had consumed peanuts were still allergic to peanuts. Do the data indicate that one approach is more beneficial? Follow the four‑step process.
STATE: What is the question we are asking?
A. Does early exposure to peanuts better reduce peanut allergy in children with a known allergy to peanuts?
B. Does early exposure to peanuts in small amounts or complete avoidance of peanuts better reduce peanut allergy in children with a known allergy to peanuts?
C. Should all children under the age of 60 months avoid peanuts or only eat them in small amounts?
D. Should all children under 60 months eat peanuts regularly in small amounts?
Answers
Answer:
B. Does early exposure to peanuts in small amounts or complete avoidance of peanuts better reduce peanut allergy in children with a known allergy to peanuts?
Step-by-step explanation:
Remember we are told there's already a question whether pediatricians should recommend early exposure or avoidance. Thus, the research question should answer these two issues (early exposure or avoidance).
Hence, the question we are asking is: Does early exposure to peanuts in small amounts or complete avoidance of peanuts better reduce peanut allergy in children with a known allergy to peanuts?
Polygon ABCD is drawn with vertices A(−4, −4), B(−4, −6), C(−1, −6), D(−1, −4). Determine the image coordinates of B′ if the preimage is reflected across y = 3.
B′(−4, 6)
B′(−4, 12)
B′(−1, −3)
B′(10, −6)
Answers
To reflect a point across the line y=3, we find the point that is the same distance from y=3 as the original point, but on the opposite side of the line. In this case, the original point is B(−4,−6), which is 9 units below y=3. The image point will be 9 units above y=3, so it will have a y-coordinate of 3+9=12. The x-coordinate remains the same, so the image point is B
′
(−4,12).
PLS HELP QUICK ILL GIVE BRAINLIEST
What is the surface area of the rectangular prism?
138 cm²
200 cm²
276 cm²
280 cm²
Answers
Answer:
A=276 cm²
Step-by-step explanation:
A=2(wl+hl+hw)
A=2(4x7+ 10x7+10x4)
A=2(28+70+40)
A=2(138)
A=276 cm²
900%
0f what number is 5,580
Answers
Based on the supply graph and the demand graph shown above, what is the price at the point of equilibrium?
Hint: Think about the point where they both meet. For example, if you were to place the graphs on top of each other, what would be the point of intersection?
Type the correct number below without the dollar sign.
Answers
Based on the supply graph and demand graph shown above, the price at the point of equilibrium is $ 30.
Demand refers to quantity of a commodity that the consumers are willing to, able to purchase at a given price during a given period of time. Supply refers to quantity of a commodity that the producers are willing to, able to offer for sale at a given price during a given period of time.
Demand curve slopes downward due to inverse relationship between price and quantity demanded whereas supply curve slopes upward due to direct relationship between quantity supplied and price. When both demand and supply curve intersect with each other balance is achieved. Intersection point between demand and supply curve is known as equilibrium.
At this point when prices are equal is known as equilibrium price and when quantiy demanded or supplied are equal it is known as equilibrium quantity. When we combine the given graph. Equilibrium is achieved at a point when price is equal to $ 30 and quantity is equal to 20 units.
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Note: Figure is not drawn to scale.
If a = 5m, b = 8 m, c = 8 m, and d = 2 m, what is the perimeter of the swimming pool?
OA.
21 m
OB.
32 m
29 m
34 m
OC.
OD.
6 of 10 Answered
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Answers
After considering the given data we conclude that the perimeter of the given swimming pool is 23 meters which is Option A.
The perimeter of a rectangle is evaluated by adding up all its sides. For the given case, we possess a rectangle with sides
a = 5m,
b = 8m,
c = 8m and
d = 2m.
Perimeter regarding the swimming pool is evaluated as
a + b + c + d
= 5m + 8m + 8m + 2m
= 23 meters
Hence the option regarding the question which satisfy the perimeter is Option A.
Perimeter the counted measurement regarding the distance around the outside of a two-dimensional shape. In this system the length of the outline or boundary of any two-dimensional geometric shape is defined as perimeter .
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The complete question is
If a = 5m, b = 8 m, c = 8 m, and d = 2 m, what is the perimeter of the swimming pool?
A.23 m
B. 32 m
C.29 m
D.34 m
(geometry) can somebody PLZ HELP ASAP
Answers
Answer:
y = 4x - 18
Step-by-step explanation:
Perpendicular means that the slope is the opposite reciprocal.
y = 4x + b
-6 = 12 + b
b = -18
y = 4x - 18
ya this person is a bot be careful
charissa2
Answers
PLEASE HELP!!!!!
will mark brainliest!!!!!
Answers
Answer:
x. f(×)
6. 9
7. 7
8. 5
9. 3
10. 1
Use the histogram to answer the following questions.
Frequency
The frequency of the class 90-93 is
The frequency of the class 94-97 is
This means that a total of
5.5
5
4.5
Your answers should be exact numerical values.
The frequency of the class 86-89 is
86
94
90
Duration of Dormancy (minutes)
dormancy periods were recorded.
Answers
The parameters that are needed to calculate a probability are listed as follows:
Number of desired outcomes in the context of a problem or experiment.Number of total outcomes in the context of a problem or experiment.Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes, hence it is the same as a relative frequency.
The total number of periods is given as follows:
5 + 6 + 4 = 15.
The frequency of each class is given as follows:
86 - 89: 5/15 = 1/3.90 - 93: 6/15 = 2/5.94 - 97: 4/15.Learn more about the concept of probability at https://brainly.com/question/24756209
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hat is the value of ?The solution is
Answers
l5l - l-5l - (-5)
the absolute value of l5l and l-5l is 5
5 - 5 - (-5)
Subtracting a negative number is the same as adding that number
5 - 5 + 5
5
Answer = 5