The amount of weight that Sam loses is directly proportional to the number of hours he spends exercising. If Sam loses a pound of weight for each 3 hrs of exercise, how many hours must he spend exercising to lose 25 lbs?
A) 25 hrs
B) 50 hrs
C) 75 hrs
D) 80 hrs
Answers
Answer:
The answer is C. 75 hours.
Step-by-step explanation:
In order to determine the hours, we have to know about direct proportionality.
The direct proportionality happens when two variables increase at the same time and their rate is a constant. It means that if one variable is increased, so the other variable will be increased too.
I have attached an image that shows a graph of two variables with direct proportionality.
In this case, we can get the constant of both variables: losing weight and the spending time.
[tex]k=\frac{Weight}{Time}=\frac{1}{3} =0.33[/tex]
Then we need to know how many hours Sam will spend to lose 25 lbs:
[tex]\frac{25}{T}=k=0.33\\ T=\frac{25}{0.33}\\ T=75.76[/tex] hours.
Finally, Sam needs to spend 75 hours to lose 25 lbs.
Related Questions
What is the sum of the arithmetic sequence 151, 137, 123,..if there are 26 terms?
A. -676
B.-650
C.-624
D.-598
Answers
common difference: d = -14 (we decrease by 14 each time, eg, 151-14 = 137)
nth term of this arithmetic sequence is...
an = a1+d(n-1)
an = 151+(-14)(n-1)
an = 151-14n+14
an = -14n+165
This will be used in the formula below
Sn = n*(a1+an)/2
Sn = n*(151+(-14n+165))/2
S26 = 26*(151+(-14*26+165))/2 ... replace every n with 26
S26 = -624
The final answer here is choice C) -624
Answer:
option C -624
Step-by-step explanation:
Amy earned $25 after babysitting for 3 hours.if she always charges the same rate ,how much will she make after working for 7 hours ?
Answers
A hummingbird beats its wings about 75 times in one second. Based on this rate, what is the number of times a hummingbird beats its wings one minute?
Answers
75 × 60 seconds = 4,500 beats a minute
Two numbers differ by 13 and the sum of their squares is 125 find the numbers
Answers
By substituting the value of one number in terms of the other from the difference equation into the sum of squares equation, we find the two numbers to be 10 and -3.
Explanation:Let's solve the problem step-by-step. Given that two numbers differ by 13 and the sum of their squares is 125, we can set up the following equations where x and y are the two numbers:
Equation 1: x - y = 13 or y = x - 13 (1)Equation 2: x^2 + y^2 = 125 (2)Substitute the value of y from equation (1) into equation (2), giving us:
x^2 + (x - 13)^2 = 125
Solving this, we find that x = 10 and hence y = -3, which means the two numbers are 10 and -3.
You drop a rock off a bridge. The rock’s height, h (in feet above the water), after t seconds is modeled by h = -16t2 + 541. What is the height of the rock after 2 seconds?
Answers
h = - 16(2)² + 541
= - 16(4) + 541
= - 64 + 541
h = 477 feet
Solve:
3/5 − 6/11
A:3/55
B:3/6
C:3/11
Answers
__________________________________
Explanation:
__________________________________
(3/5) - (6/11) = [(3*11) / (5*11) ] - [(6*5) / (11*5)] = (33/55) - (30/55) = 3/ 55.
____________________________________________________
Calculate the length of the circumference of a circle with a diameter of 4cm
Answers
2 π r and r is equal to 2 cm
I.e 12.5 cm
Find the equation of a line with the gradient 5 passing through the point (2,-5)
Answers
Equation of a line is y = mx + b
You have m, which is the gradient so all you need is b. To do this, sub in the point (2,-5) as x and y to get:
-5 = (5)(2) + b
and you get b equaling to -15
so your equation is y = 5x - 15
you can check this by subbing back in your x value and you should get the same y.
One angle has 10 degrees more than another angle. The sum of the angles us 90 degrees . How many degrees are in each angle? Please Explain.
Answers
50 + 40 = 90.
The smaller angle is 40 degrees and the larger angle is 50 degrees.
Explanation:Let's represent the smaller angle by x degrees. According to the problem, the larger angle is 10 degrees more than the smaller angle, so it can be represented by x + 10 degrees. The sum of these two angles is 90 degrees, so we can set up the equation:
x + (x + 10) = 90
Simplifying the equation, we get:
2x + 10 = 90
Subtracting 10 from both sides, we have:
2x = 80
Finally, dividing both sides by 2, we find:
x = 40
So, the smaller angle is 40 degrees and the larger angle is 40 + 10 = 50 degrees.
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One side of a triangle is 15 inches, and the area of the triangle is 90 sq. inches. Find the area of a similar triangle in which the corresponding side is 9 inches.
Answers
x=(90×81)/225
x=32.4
What is a theorem called before it is proven?
postulate
proposition
contradiction
tautology
Answers
Before a theorem is proven, it is known as a proposition. This term indicates that the statement is proposed to be true and is pending proof.
Explanation:A theorem called before it is proven is known as a proposition. A proposition is a statement that is proposed to be true and is awaiting proof or disproof. In contrast, a postulate is a statement that is assumed to be true without proof for the purposes of reasoning in mathematics or science, whereas a contradiction refers to a statement that is always false. A tautology is a statement that is true by necessity or by virtue of its logical form.
Final answer:
A theorem before it is proven is known as a proposition. Propositions are statements considered in mathematics and philosophy for investigation and proof. Other terms like postulate, contradiction, and tautology have different distinct meanings in logic.
Explanation:
Before a theorem is proven, it is known as a proposition. A proposition is a statement that proposes an idea, which can be either true or false, but has not yet been proven to be true. In mathematics and philosophy, this term is used to describe concepts that are considered and investigated for proof. Once a proposition is proven conclusively, it becomes a theorem. Other options like postulate, contradiction, and tautology have different meanings within mathematical logic and reasoning.
Divide the complex number: 7i/8+i
(i= imaginary #)
show step-by-step solution
Answers
Prove triangle dih is congruent to triangle egh
Answers
Four of 12 people choose milk what fractional part of the group chose other drinks
Answers
Fraction = Chosen Drinks/Total people = 8/12 = 2/3
If four out of 12 people chose milk, then 8 did not choose milk, resulting in a fractional part of 2/3 representing those who chose other drinks.
Explanation:If four of 12 people chose milk, we can calculate the fractional part of the group that chose other drinks. We subtract the number of people who chose milk from the total number of people surveyed:
12 (total people) - 4 (people who chose milk) = 8 (people who chose other drinks).
The fractional part of the group that chose other drinks is therefore the number of people who chose other drinks divided by the total number of people:
8 (people who chose other drinks) / 12 (total people) = 2/3.
Two-thirds of the group chose drinks other than milk.
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The perimeter of an equilateral triangle is 27 centimeters. Find the altitude of the triangle
Answers
The altitude of the equilateral triangle is [tex]\( \frac{9\sqrt{3}}{2} \)[/tex] centimeters.
In an equilateral triangle, all three sides are equal in length. Let's denote the length of each side of the equilateral triangle as s centimeters.
The perimeter of an equilateral triangle is given as the sum of the lengths of all three sides:
Perimeter = 3s
Given that the perimeter is 27 centimeters, we can set up the equation:
27 = 3s
Now, we can solve for the length of each side s:
[tex]\[ s = \frac{27}{3} = 9 \][/tex]
So, each side of the equilateral triangle is 9 centimeters long.
Now, to find the altitude of the equilateral triangle, we can use the formula for the altitude of an equilateral triangle, which is:
[tex]\[ \text{Altitude} = \frac{\sqrt{3}}{2} \times \text{Length of a side} \][/tex]
Substituting the length of a side s = 9 into the formula, we get:
[tex]\[ \text{Altitude} = \frac{\sqrt{3}}{2} \times 9 \\\[ \text{Altitude} = \frac{9\sqrt{3}}{2} \][/tex]
So, the altitude of the equilateral triangle is [tex]\( \frac{9\sqrt{3}}{2} \)[/tex] centimeters.
Which is longer 1/4 foot or 1/4 yard?
Answers
Final answer:
1/4 yard is longer than 1/4 foot because 1/4 yard is equivalent to 3/4 foot, and 3/4 is greater than 1/4.
Explanation:
The question is asking to compare the lengths of 1/4 foot and 1/4 yard. To make this comparison, it is crucial to understand the relationship between feet and yards. From the reference information, we know that 1 yard is equal to 3 feet. Thus, to find how long 1/4 yard is in feet, we use the conversion ratio:
1/4 yd = (1/4) × 3 ft = 3/4 ft.
Now, we compare 1/4 foot with 3/4 foot. Since 3/4 is greater than 1/4, it is clear that 1/4 yard is longer than 1/4 foot.
What is the center of the circle that you can circumscribe about a triangle with vertices A(2, 6), B(2, 0), and C(10, 0)?
Answers
Each point is then equal distance from the center, that distance being the radius of the circle.
Using the distance formula, we can find the center of the circle (x,y):
[tex]d^2 = (x-x_0)^2 + (y-y_0)^2[/tex]
Plugging in points A and B into distance formula, then setting them equal to each other gives:
[tex](x-2)^2+(y-6)^2 = (x-2)^2 + y^2[/tex]
Right away we can cancel out the x terms leaving:
[tex](y-6)^2 = y^2[/tex]
Expand Left side and Solve for y:
[tex]y^2 -12y +36 = y^2[/tex]
[tex]y = 3[/tex]
Plug in points B and C as before:
[tex](x-2)^2 + y^2 = (x-10)^2 + y^2[/tex]
Here we can cancel the y-terms.
Expand and solve for x:
[tex]x^2 -4x+4 = x^2 -20x+100[/tex]
[tex]16x = 96[/tex]
[tex]x = 6[/tex]
Therefore the center of the circle is the point (6,3)
The center of the circle that can be circumscribed about a triangle with vertices A(2, 6), B(2, 0), and C(10, 0) is calculated by finding the intersection of the perpendicular bisectors of the sides of the triangle. In this case, the center of the circle is at (6,3).
Explanation:For the triangle with vertices A(2, 6), B(2, 0), and C(10, 0), the circle that you can circumscribe about it is known as the circumcircle. The center of this circle is the circumcenter which is obtained by the intersection of the perpendicular bisectors of the sides of the triangle.
Since points A and B lie along the same vertical line, the perpendicular bisector of line AB is a horizontal line halfway between them at y=3. The bisector of line BC is a vertical line halfway between points B and C at x=6.
The intersection of these two bisectors (x=6, y=3) is the circumcenter. So, the center of the circumcircle is at (6,3).
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which ordered pairs are a solution to the equation? y=3x Select all that apply (-1,3) (2,5) (1,3) (-2,-6)
Answers
(-1,3)
3=3(-1)
3=-3
it is not true,so not a solution.
(2,5)
5=3×1
5=3
it is not true so not asolution.
(1,3)
3=3×1
3=3
it is true so (1,3)is a solution.
(-2,-6)
-6=3×(-2)
-6=-6
which is true.
Hence (-2,-6) is also a solution.
Find the key number to the equation, the intervals into which the key numbers divide the number line, and the sign of y over each of these intervals. y=x+1/(x-1)^2
Answers
1) key number
The key number (also called critical values) is where the denominator equals zero.
(x -1)^2 = 0 => x = 1
2) intervals: (-∞,1) ,(1,∞)
3) Sign of the function
The sign of the denominator is always positive, then the sign of the function is the same sign of the numerator
x +1 > 0 => x > - 1
x+ 1 < 0 => x < -1
Then in the interval (-∞,1) the function is negative for (-∞,-1) and positive for (-1,1).
The function is positive for all the values in the interval (1,∞)
Briefle, the functionis negative in (-∞,-1) and positive in (-1,∞).
what are the coordinates of the x and y intercepts of the equation 3x+2y=12
Answers
3x+2y=12 - substitute 0 for y
3x+2(0)=12 - multiply 2 and 0
3x+0=12 - add zero
3x=12 - divide by 3
x=4
To find the y-intercept you must make x=0
3x+2y=12 - substitute 0 for x
3(0)+2y=12 - multiply 3 and 0
0+2y=12 - add 0 and 2y
2y=12 - divide by 2
y=6
you randomly draw a marble from a bag of marbles that contains 7 blue marbles, 2 green marbles, and 1 red marble. what is the probability not draw a blue marble
Answers
Answer:
0.3
Step-by-step explanation:
It is given that,
Number of blue marbles = 7
Number of green marbles = 2
Number of red marbles = 1
Total number of marbles = 7+2+1=10
We need to find the probability that we do not draw a blue marble.
[tex]P=\dfrac{\text{Number of non-blue marbles}}{\text{Total number of marbles}}[/tex]
[tex]P=\dfrac{2+1}{10}[/tex]
[tex]P=\dfrac{3}{10}[/tex]
[tex]P=0.3[/tex]
Therefore, the required probability is 0.3.
P= $975, r=5.5%, t=60 days
Answers
The typical exponential function, y = ax, has asymptote ________ and y-intercept ________.
A)y = 0; (0,a)
B)y = 0; (0,1)
C)y = a; (0,a)
D)y = a; (0,1) ...?
Answers
Answer: B) The typical exponential function, y = ax, has asymptote the x-axis and y-intercept x = 0.
Step-by-step explanation:
For the funcion [tex]y = a^x[/tex], the asymptote is the value that the function would never assum, but gets really close. In this case, there is no value for y = 0, because[tex]y = a^x\\0 = a^x \\ln(0) = x.lna\\ln(0)[/tex]is not defined! This way, asymptote is x-axis (y=0).
y-intercept ⇒ x=0, so
[tex]y=a^x\\y=a^0=1[/tex]
This, way, the point (0,1)
alternative b
The typical exponential function y = ax has a horizontal asymptote y = 0 and a y-intercept at the point (0,1), which makes Option B the correct answer.
In this context, the function will approach an asymptote, which is a line that the graph gets infinitely close to without touching. Specifically, for an exponential function, the horizontal asymptote is y = 0 regardless of the value of a, provided that a is nonzero. As the value of x gets very large or very negative, the value of y will get very close to 0 but will never actually reach it.
Additionally, the y-intercept of the function is the point at which it crosses the y-axis. This occurs when x is 0. Substituting 0 for x in the function, we get y = a0, which simplifies to y = 1 because any nonzero number to the power of 0 is 1. Therefore, the y-intercept of the function is (0,1).
So, for the question asking about the asymptote and y-intercept of the typical exponential function y = ax, the correct answer is Option B: asymptote y = 0; y-intercept (0,1).
The cost to rent a dump truck is $50 per day plus $26 per hour of use. What is the maximum number of hours the truck can be used each day if the rental cost should not exceed $193 per day?
A 2.5
B 8.04
C 5.5
D 3.34
Please explain and show work! ☺☺
Thanks!
Answers
If $7,000 is placed in an account with an annual interest rate of 5.5%, how long will it take the amount to triple if the interest is compounded annually? Round your answer to two decimal places.
...?
Answers
21000=7000(1+0.055/2)^1t
t = 20.52 years
A tortoise is walking in the desert. It walks for 4 minutes at a speed of 10.24 meters per minute. For how many meters does it walk?
Answers
Final answer:
To find the total distance a tortoise walked in the desert, use the formula distance = speed x time. In this case, the tortoise walked 40.96 meters by walking for 4 minutes at a speed of 10.24 meters per minute.
Explanation:
A tortoise is moving laboriously-khwanya-khwanya-khwanya! To calculate the total distance the tortoise walked, we use the formula: distance = speed x time. Given the tortoise walks for 4 minutes at a speed of 10.24 meters per minute, the calculation is 10.24 m/min x 4 min = 40.96 meters. Therefore, the tortoise walked a distance of 40.96 meters.
The tables represent two linear functions in a system.
What is the solution to this system?
(1, 0)
(1, 6)
(8, 26)
(8, –22)
Answers
y = kx + n
Now we need to find k and n for both linear functions. We do that by using table
We need only 2 values of x and 2 coresponding values of y to find k and x for one equation.
Function 1:
10 = k*0 + n which means n1 = 10
2 = k*2 + 10
2k = -8
k1 = -4
Function 2
2 = n2 ( we used values of 3rd row because x = 0 there and we can find n straight away)
-4 = 2k + 2
2k = -6
k2 = -3
Our system is now:
y = -4x + 10
y = -3x + 2
if we subtract second from first we get:
-4x + 3x + 10 - 2 = 0
-x + 8 = 0
x = 8
y = -3*8 + 2 = -22
Answer is (8,-22)
what I'll are the coordinates of point J (-5, -3) if point k (1,2) is the midpoint of JL
a) 4, 1
b) 7, 7
c) 8, 2
d) 6, 5
Answers
0.87 written as a fraction is _____.
Answers
The decimal 0.87 can be written as the fraction 87/100, which cannot be simplified further.
Explanation:The decimal 0.87 can be written as a fraction by placing the decimal over 100 and then simplifying the fraction if possible. In this case, 0.87 can be written as 87/100. However, this fraction can be simplified further. Both 87 and 100 can be divided by 1, making the simplified fraction 87/100.
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What is 15x7 for the real answer?
Answers
7(10). 7(5)
^. ^
70. + 35
70
+ 35
______
105
The answer is 105