We can simplify the given expression first and then write it in standard form.
8 × 10 = 80
1 × 1/10 = 1/10
6 × 1/1000 = 6/1000 = 3/500
Adding these three values, we get:
80 + 1/10 + 3/500
To write this in standard form, we need to express it as a single number multiplied by a power of 10. We can do this by finding a common denominator for the fractions and adding them:
80 + 50/500 + 3/500 = 80 + 53/500
Now, we can write this as:
80.106
To express this in standard form, we move the decimal point to the left until there is only one non-zero digit to the left of the decimal point. We moved the decimal point 3 places to the left to get:
8.0106 × 10^1
Therefore, the number in standard form is 8.0106 × 10^1.
Mrs. Rambo got a YMCA membership for her family. The pass has a onetime fee of $30 and then $5 for every visit to the YMCA. Her bill the first month was $150. How many times did her family visit the YMCA?
They visited ------------- times last month. Way to go Rambo family!
Answer:
Step-by-step explanation: Solution:
Total cost: 150
150-30=120
120 divided by 5 = 24
They visited 24 times in a month.
Question 2(Multiple Choice Worth 4 points) (05.03 MC) Solve the system of equations using elimination. 2x + 3y = -8 3x+y=2 O(-4,0) (2,-4) (5.-6) (8-8)
Answer:
(2,-4)
Step-by-step explanation:
In order to solve by elimination, coefficients of one of the variables must be the same in both equations so that the variable will cancel out when one equation is subtracted from the other.
2x+3y=−8,3x+y=2
To make 2x and 3x equal, multiply all terms on each side of the first equation by 3 and all terms on each side of the second by 2. Then simplify
6x+9y=−24,6x+2y=4
Add 6x to −6x. Terms 6x and −6x cancel out, leaving an equation with only one variable that can be solved, add 9y to −2y, add −24 to −4, and divide both sides by 7.
y=−4
Substitute −4 for y in 3x+y=2. Because the resulting equation contains only one variable, you can solve for x directly. Add 4 to both sides of the equation and divide both sides by 3.
x=2
The letters of the word "MOBILE" are arranged at random. Find
the probability that the word so formed i) starts with M ii) starts
with M and ends with E.
The probability that the word so formed starts with M is 1/6, and the probability that it starts with M and ends with E is 1/30.
i) To find the probability that the word starts with M, we need to consider the total number of possible arrangements of the letters and the number of arrangements that start with M. The word "MOBILE" has 6 letters, so there are 6! = 720 possible arrangements of the letters. To find the number of arrangements that start with M, we can fix the M in the first position and arrange the remaining 5 letters in the remaining positions, which gives us 5! = 120 arrangements. Therefore, the probability that the word starts with M is:
P(starts with M) = number of arrangements that start with M / total number of arrangements
= 120 / 720
= 1/6
ii) To find the probability that the word starts with M and ends with E, we can fix the M in the first position and the E in the last position, and then arrange the remaining 4 letters in the remaining positions. This gives us 4! = 24 arrangements. Therefore, the probability that the word starts with M and ends with E is:
P(starts with M and ends with E) = number of arrangements that start with M and end with E / total number of arrangements
= 24 / 720
= 1/30
Thus, the probability that the word so formed starts with M is 1/6, and the probability that it starts with M and ends with E is 1/30.
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Based on the experiment if the spinner is spun 150 times how many times would you expect to get an even number?
Answer:
60
Step-by-step explanation:
((sum of frequency of even numbers)/(total number of tries))(150)
Find the measure of each labeled angles in the rhombus below:
The measure of each labeled angles in the rhombus are ∠1 = 49°, ∠2 = 90°, ∠3 = 49° and ∠4 = 41°
Finding the measure of each labeled angles in the rhombusFrom the question, we have the following parameters that can be used in our computation:
The rhombus
By corresponding angles, we have
∠3 = 49°
∠1 = 49°
The diagonals of a rhombus bisect each other at right angles
So, we have
∠2 = 90°
Ths sum fo angles in a triangle is 180
So, we have
∠4 = 180 - 90 - 49°
Evaluate
∠4 = 41°
Hence, the measure of the angles in the rhombus are ∠1 = 49°, ∠2 = 90°, ∠3 = 49° and ∠4 = 41°
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HELP ASAP!!!!!!!!!!!
Answer:
25%
Step-by-step explanation:
The total number of 7th grade students = 9 + 11 + 11 + 13 = 44
Out of the 44 students 11 play bass
Probability that a seventh grader chosen at random will play the base is:
11/44 = 1/4 = 0.25
As a percentage, this would be 0.25 x 100 = 25%
A can is to be made to hold a litre of oil. Find the radius of the can that will minimize the cost of the metal to make the can. (1L = 1000 cm)
The problem involves finding the radius of a cylindrical can that will minimize the cost of the metal to make the can, given that the can must hold one liter of oil.
Specifically, we need to find the radius of the can that will minimize the surface area, and hence the cost, of the metal required to make the can.
To solve the problem, we need to first write an expression for the surface area of the can in terms of its radius, and then differentiate this expression with respect to the radius to find the critical point. We then need to check that the critical point corresponds to a minimum value of the surface area, which will give us the optimal radius for the can. Optimization problems like this one are used in many fields, including engineering, economics, and physics, to find the best course of action given certain constraints and objectives.
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1) Amy deposits $2,300 in an account that pays 8.5% interest. How much money will Amy have after 4 years?
2)Andres deposits $10,000 in an account that pays 8% interest. How much money will Andres have after 4 years?
a
$ 13,604.89
b
$ 604.90
c
$ 20,004.98
3) Kara deposits $500 in an account that pays 5% interest. How much money will Kara have after 2 years?
a
$ 1,009.34
b
$ 13.97
c
$ 551.25
1) If Amy deposits $2,300 in an account that pays 8.5% interest, after 4 years, the future value will be $3,187.48.
2) If Andres deposits $10,000 in an account that pays 8% interest, after 4 years, the future value will be A. $13,604.89.
3) If Kara deposits $500 in an account that pays 5% interest, after 2 years, the future value will be C. $551.25.
How the future values are determined:The future values represent the present investment compounded at an interest rate.
The future values can be determined using an online finance calculator as follows:
1) N (# of periods) = 4 years
I/Y (Interest per year) = =8.5%
PV (Present Value) = $2,300
PMT (Periodic Payment) = $0
Results:
Future Value (FV) = $3,187.48
Total Interest = $887.48
2) N (# of periods) = 4 years
I/Y (Interest per year) = =8%
PV (Present Value) = $10,000
PMT (Periodic Payment) = $0
Results:
Future Value (FV) = $13,604.89
Total Interest = $3,604.89
3) N (# of periods) = 2 years
I/Y (Interest per year) = 5%
PV (Present Value) = $500
PMT (Periodic Payment) = $0
Results:
Future Value (FV) = $551.25
Total Interest = $51.25
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The radius of a circle measures 7 inches. A central angle of the circle measuring 4π15 radians cuts off a sector.
What is the area of the sector?
Enter your answer, as a simplified fraction
The area of sector is 14π/3 square inches for a circle having a radius of 7 inches and measures an angle of 4π/15 radians.
Radius of circle = 7 inches
Angle of circle = 4π/15 radians
The area of a sector of a circle can be calculated by using the formula:
A = (θ/2) × [tex]r^2[/tex]
A = The area of the sector
θ = central angle in radians
r = radius of the circle.
Substituting the given values in the formula:
Area = (θ/2) × [tex]r^2[/tex]
Area = (4π/15 × 1/2) × [tex]7^2[/tex]
Area= (2π/15) × 49
Area = 14π/3
Therefore, we can conclude that the area of the sector is 14π/3 square inches.
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the life of light bulbs is distributed normally. the standard deviation of the lifetime is 20 hours and the mean lifetime of a bulb is 580 hours. find the probability of a bulb lasting for at most 624 hours. round your answer to four decimal places.
The probability of a bulb lasting for at most 624 hours is 0.9861, rounded to four decimal places.
The standard deviation of the lifetime is a measure of how spread out the lifetimes are. In other words, it tells us how much the lifetimes of bulbs vary from the mean. In this case, the standard deviation of the lifetime is 20 hours.
Now, let's get to the question at hand. We want to find the probability of a bulb lasting for at most 624 hours. To do this, we need to use the properties of the normal distribution.
First, we need to calculate the z-score, which tells us how many standard deviations a value is from the mean. We can use the formula z = (x - mu) / sigma, where x is the value we are interested in, mu is the mean, and sigma is the standard deviation. In this case, x = 624, mu = 580, and sigma = 20.
Plugging these values into the formula, we get z = (624 - 580) / 20 = 2.2.
Next, we need to find the probability of a bulb lasting for at most 624 hours, which is the same as finding the area under the normal curve to the left of z = 2.2. We can use a standard normal distribution table or a calculator to find this probability.
Using a calculator, we can use the normal cdf function with the values -9999 (a very large negative number) and 2.2 to find the probability. This gives us a probability of 0.9861.
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How can you find the value of x in the expression 5x = 20?
Answer:
x = 4
Step-by-step explanation:
5x = 20 Divide both sides by 5
[tex]\frac{5x}{5}[/tex] = [tex]\frac{20}{5}[/tex]
x = 4
Helping in the name of Jesus.
In two or more complete sentences, describe the steps a consumer can take to become more knowledgeable.
uploa
There are several steps a consumer market can take to become more knowledgeable like research and asking questions.
Research The first step is to probe the product or service that you're interested in. This involves looking at reviews, product descriptions, and comparing prices. You can also look for information from dependable sources similar as consumer reports or government websites. Ask questions If you have any dubieties or enterprises, don't vacillate to ask the dealer or service provider.
Ask them about their experience and qualifications, and make sure to clarify any terms or conditions that are unclear. Get a alternate opinion If you're doubtful about a product or service, seek the advice of someone you trust or who has moxie in that area. They can help you make an informed decision grounded on their knowledge and experience.
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7. kayla uses her credit card to purchase a new television for $487.89. she can pay off up to $175 per month. the card has an annual rate of 23.5% compounded monthly. how
much will she pay in interest? (2 points)
o $22.78
$156.76
o $8.95
$18.87
save & exit
submit all answers
o
7:42
hp
o
الا : 2
96
5
4
8
backspace
If Kayla can pay off up to $175 monthly for the purchase of a new television for $487.89, the interest she will pay at 23.5% compounded monthly is D. $18.87.
How the compound interest is computed?The compound interest payable on the credit card for the purchase of a new television can be computed using an online finance calculator as follows:
N (# of periods) = 3 months
I/Y (Interest per year) = 23.5%
PV (Present Value) = $487.89
PMT (Periodic Payment) = $-175
Results:
FV = $18.23
Sum of all periodic payments = $525.00
Total Interest = $18.87
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what is the product of -5 and -10 sign and result
Answer:
50, positive
Step-by-step explanation:
(-5) * (-10) = 50
When a negative multiplies by another negative, the answer is positive
So, the answer is 50 and the sign is positive
which angle is adjacent to TOU
A store has 25 VCRs in stock, but 2 of these are defective. What is the probability
that the second person to buy a VCR gets a defective one and the first
customer's VCR was not defective? Round your answer to the nearest
thousandth. *
. 083
. 0736
. 077
. 08
A store has 25 VCRs in stock, but 2 of these are defective he answer is the probability that the second person to buy a VCR gets a defective one and the first customer's VCR was not defective is .077.
The probability that the first customer's VCR is not defective is 23/25, as there are 23 working VCRs out of the total 25.
Since one VCR has already been sold, there are 24 VCRs left and 1 defective VCR. Thus, the probability that the second customer gets a defective VCR is 1/24.
To find the probability that both events occur, we multiply the individual probabilities:
P = (23/25) x (1/24)
P = 0.077 or 0.0778 when rounded to the nearest thousandth.
Therefore, A store has 25 VCRs in stock, but 2 of these are defective he answer is the probability that the second person to buy a VCR gets a defective one and the first customer's VCR was not defective is .077.
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KLM has vertices K 4,-5 L 2,2 and M 7,3 which translation move the triangle so that point K lies on the Y axis
To move triangle KLM so that point K lies on the Y-axis, you need to apply a translation that shifts the entire triangle horizontally. By translating triangle KLM using the vector (-4, 0), point K now lies on the Y-axis.
To move the triangle so that point K lies on the Y axis, we need to perform a translation. First, we need to determine how far point K is from the Y axis. We can do this by finding the x-coordinate of point K, which is 4. This means that point K is 4 units away from the Y axis.
Next, we need to determine the direction of the translation. Since we want to move point K onto the Y axis, we need to move the triangle in the negative x direction. Therefore, the translation that will move the triangle so that point K lies on the Y axis is a horizontal translation of -4 units. We can express this translation as follows:
T(-4, 0)
This means that we need to move each point of the triangle 4 units to the left (negative x direction) to achieve the desired position of point K on the Y axis.
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Suppose a bus arrives at a bus stop every 26 minutes. If you arrive at the bus stop at a random time, what is the probability that you will have to wait at least 4 minutes for the bus?
The time between buses arriving at the stop follows an exponential distribution with a mean of 26 minutes.
To find the probability of waiting at least 4 minutes for the bus, we can use the cumulative distribution function (CDF) of the exponential distribution:
P(waiting at least 4 minutes) = 1 - P(waiting less than 4 minutes)
The probability of waiting less than 4 minutes can be calculated using the CDF:
P(waiting less than 4 minutes) = 1 - e^(-4/26) ≈ 0.146
Therefore, the probability of waiting at least 4 minutes for the bus is:
P(waiting at least 4 minutes) = 1 - 0.146 ≈ 0.854
So the probability of having to wait at least 4 minutes for the bus is about 85.4%.
Find the equation of the line that
is perpendicular to y = -8x + 2
and contains the point (-4,1).
Help
=
y = (?)X +
X
8
Enter the correct symbol, + or -, that
belongs in the green box
The equation of the line that is perpendicular to y = -8x + 2 and contains the point (-4, 1) is y = (1/8)x + (3/2).
To find the equation of the line that is perpendicular to y = -8x + 2 and contains the point (-4, 1), first, determine the slope of the given line. The slope is -8. Perpendicular lines have slopes that are negative reciprocals of each other, so the slope of the new line will be 1/8.
Now, use the point-slope form of a linear equation, y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point (-4, 1). Plug in the values: y - 1 = (1/8)(x - (-4)).
Simplify the equation: y - 1 = (1/8)(x + 4). Distribute the 1/8: y - 1 = (1/8)x + (1/2). Finally, add 1 to both sides: y = (1/8)x + (1/2) + 1.
So, the equation of the line that is perpendicular to y = -8x + 2 and contains the point (-4, 1) is y = (1/8)x + (3/2).
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pls some help with this question!
Sam needs 2/5 pound of turkey to make one sandwich he is going to make 7 sandwiches how many pounds of turkey does he need
If Sam needs 2/5 pound turkey to make one sandwich, then to make 7 sandwiches, he will need:
(2/5) x 7 = (2 x 7)/5 = 14/5 = 2.8 pounds of turkey
Therefore, Sam needs 2.8 pounds of turkey to make 7 sandwiches.
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The function f (x) = 15(0.85)^x
models the height, in feet, of a bouncing ball after x seconds.
What is the initial height of the bouncing ball?
What is the percent rate of change?
What is the height of the bouncing ball after 5 seconds? Express your answers as a decimal rounded to the nearest hundredth.
a. The initial height of the bouncing ball is 15 feet.
b. The percent rate of change is 85%.
c. The height of the bouncing ball after 5 seconds is approximately 6.79 feet (rounded to the nearest hundredth).
What is Function ?In mathematics, a function is a rule that assigns each element in a set (the domain) to a unique element in another set (the range). The domain and range can be any sets, but they are typically sets of real numbers.
The function f(x) = 15 (0.85)ˣ models the height, in feet, of a bouncing ball after x seconds.
a. The initial height of the bouncing ball is given by f(0). Plugging in x = 0, we get:
f(0) = 15*1
f(0) = 15(1)
f(0) = 15
Therefore, the initial height of the bouncing ball is 15 feet.
b. The percent rate of change is given by the coefficient of the base, which is 0.85 in this case. To convert this decimal to a percentage, we can multiply by 100:
0.85 × 100 = 85
Therefore, the percent rate of change is 85%.
c. The height of the bouncing ball after 5 seconds is given by f(5). Plugging in x = 5, we get:
f(5) = 15
f(5) ≈ 6.79
Therefore, the height of the bouncing ball after 5 seconds is approximately 6.79 feet (rounded to the nearest hundredth).
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Luis tiene una mochila de ruedas
que mide 3.5 pies de alto cuando se extiende el mango.Al hacer rodar
su mochila, la mano de Luis se
encuentra a 3 pies del suelo. ?Que ángulo forma su mochila con el suelo? Aproxima al grado más cercano
As a result, the angle formed by Luis's backpack and the ground is roughly 53 degrees (rounded to the nearest degree).
what is function ?A function in mathematics is a relationship between a set of potential outputs and a number of potential inputs, with the feature that each input is associated to only one possible output. It is a principle or set of guidelines that allots a different output value towards each input value. Equations, graphs, and tables are frequently used to depict functions in order to explain how the output changes as the input does. They are employed to express relationships between various quantities, such as the length of time it takes for an automobile to drive a certain distance or the height of an object in relation to its weight. The concept of a function is crucial to many departments of science and math, and it is widely applied in areas like engineering,
given
We can use trigonometry to determine the angle that Luis's backpack creates with the ground.
Consider the backpack's handle to represent the hypotenuse of a right triangle, with the vertical leg being Luis's hand's distance from the ground (3 feet) and the horizontal leg being the backpack's height (3.5 feet).
The angle can be determined using the inverse tangent function (tan-1):
53.13 degrees at tan-1(3.5/3)
As a result, the angle formed by Luis's backpack and the ground is roughly 53 degrees (rounded to the nearest degree).
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11. April shoots an arrow upward at a speed
of 80 feet per second from a platform 25
feet high. The pathway of the arrow can
be represented by the equation h =-
16t2 + 80t + 25, where h is the height
and t is the time in seconds. What is the
maximum height of the arrow? [3]
The maximum height of the arrow is 105 feet. To find the maximum height of the arrow, we need to determine the vertex of the quadratic function h = -16[tex]t^{2}[/tex] + 80t + 25.
The vertex is the highest point on the graph of the function, which represents the maximum height of the arrow.
To find the t-value at the vertex, we use the formula t = -b/2a, where a = -16 and b = 80. Plugging these values into the formula gives us t = -80/(2(-16)) = 2.5 seconds.
To find the maximum height, we plug t = 2.5 into the equation to get h = -16[tex](2.5)^{2}[/tex] + 80(2.5) + 25 = 105 feet. Therefore, the maximum height of the arrow is 105 feet.
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The original selling price of a jacket was
s
s dollars. The selling price was then changed on two occasions by the store owner. Its price is now represented by
0. 85
(
1. 4
s
)
0. 85(1. 4s). Which expression could explain what happened to the price of the jacket?
The expression 0.85(1.4s) represents the final selling price of the jacket after two price changes: an initial 15% decrease in price, followed by another 15% decrease in price.
Find out which expression could explain the happened price of the jacket?The expression 0.85(1.4s) represents the final selling price of the jacket after two price changes. We can break it down into its constituent parts to understand what happened to the price.
Factor 1.4s represents the original selling price of the jacket. This means that the store owner started with a price of 1.4s dollars.
The factor 0.85 represents the first price change. When the store owner lowered the price by 15%, the new price became 0.85 times the original price.
The second factor of 0.85 represents the second price change. After the first price change, the new price was 0.85(1.4s) dollars. When the store owner lowered the price again by 15%, the final selling price became 0.85 times the price after the first price change.
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A watch designer claims that men have wrist breadths with a mean equal to 9 cm. A simple random sample of wrist breadths
of 72 men has a mean of 8.91 cm. The population standard deviation is 0.36 cm.
Assume a confidence level of a = 0.01. Find the value of the test statistic z using
formula below
Z=
X-H
σ
O2.12
O-1.27
O 0.06
O-2.12
The value of the test statistic z is approximately -2.12. The Option D is correct.
What is the value of the test statistic z?To test the hypothesis that the mean wrist breadth of men is equal to 9 cm, we will use a one-sample z-test.
The null hypothesis is: H0: µ = 9 cm
The alternative hypothesis is: Ha: µ ≠ 9 cm
We are given a sample of n = 72 men with a sample mean of x = 8.91 cm and a population standard deviation = 0.36 cm.
The test statistic for a one-sample z-test is given by: z = (x - µ) / (o / sqrt(n))
Substituting the given values, we get:
= (8.91 - 9) / (0.36 / sqrt(72))
z = -2.119
At a significance level of a = 0.01, the critical values for a two-tailed test are ±2.576.
Since our test statistic (-2.119) falls outside of this range, we reject the null hypothesis and conclude that there is sufficient evidence to suggest that the mean wrist breadth of men is not equal to 9 cm.
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Question 3 of 10
What property does the equation show?
32 19
14
56
1 3
+
=
A. The associative property
B. The commutative property
OC. The distributive property
32 19
14 56
D. The identity property of multiplication
5 8
1 3
+
32
14
19
56
4
7
Answer:
C. The distributive property
You sold a total of 320 student and adult tickets for a total of $1200. Student
tickets cost $3 and adult tickets cost $8. How many adult tickets were sold?
Answer:
48 adult tickets were sold.
Step-by-step explanation:
Let's use algebra to solve this problem:
Let's define:
x: the number of student tickets soldy: the number of adult tickets soldFrom the problem statement, we know:
x + y = 320 (the total number of tickets sold is 320)3x + 8y = 1200 (the total revenue from ticket sales is $1200)We can use the first equation to solve for x in terms of y:
x = 320 - y
Substituting this expression for x into the second equation, we get:
3(320 - y) + 8y = 1200
Expanding the left side, we get:
960 - 3y + 8y = 1200
Simplifying, we get:
5y = 240
Solving for y, we get:
y = 48
Therefore, 48 adult tickets were sold.
Additional:
To find the number of student tickets sold, we can substitute y=48 into the first equation:
x + 48 = 320
x = 272
Therefore, 272 student tickets were sold.
Item #1 - Which set of data points could be modeled by a
decreasing linear function?
A. {(0, 0), (1, 8), (2, 15), (3, 22), (4, 30)}
B. {(0, 5), (1, 6), (2, 10), (3, 16), (4, 28)}
C. {(0, 50), (1, 42), (2, 33), (3, 25), (4, 16)}
D. {(0, 64), (1, 60), (2, 52), (3, 39), (4, 22)}
A set of data points could be modeled by a decreasing linear function include the following: C. {(0, 50), (1, 42), (2, 33), (3, 25), (4, 16)}.
What is a linear function?In Mathematics, a linear function is a type of function whose equation is graphically represented by a straight line on the cartesian coordinate.
For any given function, y = f(x), if the output value (range or y-value) is decreasing when the input value (domain or x-value) is increased, then, the function is generally referred to as a decreasing function.
By critically observing the set of data points, we can reasonably infer and logically deduce that it set C is decreasing as follows 50, 42, 33, 25, 16.
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Rachel and nicole are training to run a half marathon. rachel begins by running 30 minutes on the
tirst day of training. each day she increases the time she runs by 3 minutes. nicole's training follows the
function f(x) = 5x + 30, where x is the number of days since the training began, and f(x) is the time in
minutes she runs each day. what is the rate of change in minutes per day for the training program that
has the least rate of change?
rachel:
starting minutes:
increase in rate:
equation:
nicole:
starting minutes:
increase in rate:
equation:
The training program with the least rate of change is Rachel's, with an increase of 3 minutes per day.
Rachel:
Starting minutes: 30
Increase in rate: 3 minutes per day
Equation: f(x) = 3x + 30
Nicole:
Starting minutes: 30 (since f(0) = 5(0) + 30 = 30)
Increase in rate: 5 minutes per day
Equation: f(x) = 5x + 30
To find the training program with the least rate of change, we need to find the derivative of each equation and set it equal to zero:
f'(x) = 3 for Rachel's equation
f'(x) = 5 for Nicole's equation
Since 3 is less than 5, Rachel's training program has the least rate of change. Therefore, the rate of change in minutes per day for Rachel's training program that has the least rate of change is 3 minutes per day.
More on change rates: https://brainly.com/question/13740952
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