how long does it take a 30.0 mci sample of gold-198 to decay so that only 15.0 mci remains?
Answers
It will take 2.7 days for a 30.0 mCi sample of gold-198 to decay so that only 15.0 mCi remains.
The decay of a radioactive substance is modeled by the exponential decay law, which states that the amount of the substance remaining after a certain amount of time t is given by:
N(t) = N0 * e^(-λt)
where N0 is the initial amount of the substance, λ is the decay constant, and e is the mathematical constant approximately equal to 2.71828.
To solve this problem, we can use the following steps:
Determine the decay constant λ for gold-198. The half-life of gold-198 is 2.7 days, which means that the amount of gold-198 is halved every 2.7 days. The decay constant can be calculated using the formula:
λ = ln(2) / t1/2
where ln is the natural logarithm function and t1/2 is the half-life. Substituting the values for gold-198, we get:
λ = ln(2) / 2.7 days
λ = 0.2571 per day
Use the exponential decay law to solve for the time t when only 15.0 mCi remains. Substituting the initial amount N0 = 30.0 mCi, the remaining amount N(t) = 15.0 mCi, and the decay constant λ = 0.2571 per day, we get:
15.0 mCi = 30.0 mCi * e^(-0.2571 t)
Dividing both sides by 30.0 mCi, we get:
0.5 = e^(-0.2571 t)Taking the natural logarithm of both sides, we get:
ln(0.5) = -0.2571 t
Solving for t, we get:
t = ln(0.5) / (-0.2571)
t = 2.7 days
Therefore, it will take 2.7 days for a 30.0 mCi sample of gold-198 to decay so that only 15.0 mCi remains.
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Related Questions
What’s an equivalent fraction to 5/6 that has a denominator of 12
Answers
Answer:
An equivalant faction would be 10/12
Step-by-step explanation:
Answer:
10/12
Step-by-step explanation:
12/6 = 2
5/6 * 2/2 = 10/12
Answer: 10/12
*HELP I WILL MARK BRAINLIST*
Answers
The volume of plaster Darla needs for the miniature stairs is 418³.
What is the volume?The volume is the space occupied by a three-dimensional object.
Volume is the product of the multiplication of length, width, and height.
We first calculate the total volume for this situation, assuming that the stairs have not cut portions.
Secondly, calculate the volume of the cut portions and subtract the result from the total volume to get the volume of the stairs, which represents the quantity of plaster required by Darla.
Length of the miniature stairs = 12 cm
Width of the miniature stairs = 11 cm
Height of the miniature stairs = 4 cm
The volume of the stairs with the cut portion = 528 cm³ (12 x 11 x 4)
The length of the cut portion of the stairs = 12 cm
The width of the cut portion of the stairs = 11 cm
The height of the cut portion of the stairs = 2 cm (4 - 2)
The volume of the cut portion of the stairs = 110 cm³ (11 x 5 x 2)
The volume of the stairs without the cut portion = 418 cm³ (528 - 120)
The total volume of plaster can also be computed separately as the volume of the larger object plus the volume of the smaller object.
418 cm³= (7 cm x 4 cm x 11 cm) + (5 cm x 2 cm x 11 cm)
= (308 cm³ + 110 cm³)
Thus, the quantity (volume) of plaster Darla needs is 418 cm³.
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1. Of the three measures, which tends to reflect skewing the most, the mean, the mode, or the median? Why?
2. Which is the least, the mean, the mode, and the median of the data set? 56; 56; 56; 58; 59; 60; 62; 64; 64; 65; 67
3. The mean and median for the data are the same. 3; 4; 5; 5; 6; 6; 6; 6; 7; 7; 7; 7; 7; 7; 7 Is the data perfectly symmetrical? Why or why not?
Answers
The data is not perfectly symmetrical, since the mean and median are the same but the mode is different, and there are more values above the mean/median than below it.
The measure that tends to reflect skewing the most, is the mean. This is due to the fact that it is heavily affected by outliers, which are values that are very different from the rest of the dataset. The mean is calculated by summing up all the values and dividing by the number of values, therefore, the larger the outlier, the more the mean will be skewed.
The least of the data set is the mode since it is the value that appears most frequently.
In this case, since the numbers 56, 64, and 7 all appear the same number of times, the data set has three modes.
No, the data is not perfectly symmetrical. In a perfectly symmetrical distribution, the mean, median, and mode are all the same.
In this case, the mean and median are the same, but the mode is different.
The mode is 7, but since it occurs multiple times, it cannot be used to determine symmetry.
If we look at the values, we can see that there are more values above the mean/median (which is 6) than there are below it. This creates a slightly skewed distribution, which is not perfectly symmetrical.
Therefore, we can conclude that the data is not perfectly symmetrical.
The measure that tends to reflect skewing the most is the mean. The least of the data set is the mode. The data is not perfectly symmetrical, since the mean and median are the same but the mode is different, and there are more values above the mean/median than below it.
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Excel wants to increase the productivity of its line workers. four different programs have been suggested to help increase productivity. twenty employees, making up a sample, have been randomly assigned to one of the four programs and their output for a day's work has been recorded. you are given the results in the file name ahmadi. State the null and alternative hypotheses.
Answers
The null hypothesis would be that there is no significant difference in productivity between the four programs. The alternative hypothesis would be that there is a significant difference in productivity between at least two of the programs.
In this scenario, Excel is trying to increase the productivity of its line workers and is testing four different programs. A sample of twenty employees has been randomly assigned to one of the programs, and their daily output has been recorded in the file named "ahmadi." We will use these data to determine if any of the programs are effective in increasing productivity. The null and alternative hypotheses can be stated as follows:
Null Hypothesis (H0): There is no significant difference in productivity between the four programs. In other words, none of the programs have a meaningful impact on the productivity of the line workers.
Alternative Hypothesis (H1): At least one of the four programs has a significant impact on the productivity of the line workers, leading to increased output compared to the other programs.
To test these hypotheses, you would typically perform an analysis of variance (ANOVA) on the data provided in the "ahmadi" file. If the ANOVA result is significant, you would reject the null hypothesis and accept the alternative hypothesis, indicating that at least one program effectively increases productivity.
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in the data set shown, calculate the Mean and median absolute deviation 0,2,4,6, 8,12,8,4
Answers
Answer:
the mean is 44 but i don't know the MAD
Step-by-step explanation:
To find the mean absolute deviation of the data, start by finding the mean of the data set.
0 , 2 , 4 , 4 , 6 , 8 , 8 , 12The mean is 44The only thing i could tell you is the mean
Consider △XYZ in the figure below.
The perpendicular bisectors of its sides are XG, YG, and ZG. They meet at a single point G . (In other words, G is the incenter of △XYZ.)
Suppose EG = 20, ZG = 25, and m
Find the following measures.
Note that the figure is not drawn to scale.
Answers
Answer:
m<DXF=52°
m<DXF=52°m<DYG=94°
m<DXF=52°m<DYG=94m<DG=20°
Step-by-step explanation:
hope it helps...
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In the U.S., shoe sizes are defined differently for men and women, but in Europe, both genders use the same shoe size scale. The accompanying histograrn shows the European shoe sizes of 269 male and female college students, converted from their reported U.S. shoe sizes. a) Describe the shape. b) How many modes does the histogram have? What might explain that? Click the icon to view the histogram of shoe sizes. a) The distribution is roughly symmetric and bimodal. b) Choose the correct answer below.
Answers
a) The distribution is roughly symmetric and bimodal. b) The histogram has two modes, which may be due to the different shoe size scales used for men and women in the U.S. but not in Europe.
The histogram of European shoe sizes of 269 male and female college students converted from their reported US shoe sizes is not visible based on the information provided, but the questions are clear.
a) The shape of the distribution is not visible, but it is mentioned that it is "roughly symmetric and bimodal".
b) There are two modes in the histogram. This could be because shoe sizes in the United States are defined differently for men and women, but not in Europe. As a result, the histogram of the distribution of European shoe sizes for both men and women may show two distinct peaks.
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Consider a beam loaded as shown. Let w=6kN/m,P=12kN, a =5 m, and b=3 m. The beam is made of four planks with widths of d=125 mm and h=270 mm
Answers
The beam is made of four planks with widths of d = 125 mm and h = 270 mm. The load on the beam is w = 6 kN/m and P = 12 kN, with a = 5 m and b = 3 m.The distance x from the left end of the beam to the point of maximum bending can be determined using the formula below.
Let the bending moment at the point of maximum bending be Mmax.
Mmax = P(a-b) + w((a^2)/2 - ab).
First, calculate the maximum bending moment:
Mmax = 12(5-3) + 6((5^2)/2 - 5*3) = 3 kN.m.
Now we can calculate the distance x from the left end of the beam to the point of maximum bending.
x = (Mmax * (h/2)) / (w * d^2) = (3 * 0.135) / (6 * (0.125^2)) = 3.24 m
In this case, the beam is made of four planks with widths of d = 125 mm and h = 270 mm. The load on the beam is w = 6 kN/m and P = 12 kN, with a = 5 m and b = 3 m. The maximum bending moment can be found using the formula
Mmax = P(a-b) + w((a^2)/2 - ab).
When we plug in the values for P, w, a, and b,
we get
Mmax = 12(5-3) + 6((5^2)/2 - 5*3) = 3 kN.m.
The distance x from the left end of the beam to the point of maximum bending can be determined using the formula
x = (Mmax * (h/2)) / (w * d^2).
Plugging in the values for Mmax, h, w, and d, we get x = (3 * 0.135) / (6 * (0.125^2)) = 3.24 m.
Therefore, the distance from the left end of the beam to the point of maximum bending is 3.24 m.
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need help ASAP midterm
- 40 points .
Answers
Answer:
how do you want me to help you with
Step-by-step explanation:
Which equation is correct?
which equation is correct? a. tanx=1/secx b.sinx=1/cosx c.cscx=1/sinx d.cosx=1/cotx
Answers
Answer:
Step-by-step explanation:
csc and sin are inverses of one another, therefore, c is the correct statement.
On a farm there are dogs and chickens. There are a total of 17 animals and 48 legs. How many chickens and dogs are on the farm
Answers
Answer:
7 dogs and 10 chickens
Step-by-step explanation:
dogs have 4 legs, chickens have 2 legs. 7 dogs which would be 28 legs and 10 chickens which would be 20 legs adds up to 48 legs
Find the volume of a right circular cone that has a height of 17.7 m and a base with a diameter of 18.2 m. Round your answer to the nearest tenth of a cubic meter.
Answers
9514 1404 393
Answer:
1534.9 m³
Step-by-step explanation:
The volume formula is ...
V = (1/3)πr²h
The radius (r) is 1/2 the diameter, so is 9.1 m. Then the volume is ...
V = (1/3)π(9.1 m)²(17.7 m) = 1534.9 m³
_____
Using 3.14 for π, you get 1534.1 m³.
Answer:
1534.9 m³
Step-by-step explanation:
2.2.115
The per capita (per person) income from 1980 to 2010 can be modeled by
f(x) = 2000(X – 1980) + 10,000
where x is the year. Determine the year when the per capita income was $18,000.
The per capita income was $18,000 in the year N.
Answers
Answer:
X= 1984
Step-by-step explanation:
f(x) = 2000(X – 1980) + 10,000
Where,
f(x)= per capita income
x= year
Find x when f(x)= $18,000
f(x) = 2000(X – 1980) + 10,000
18,000 = 2000(X - 1980) + 10,000
18,000 = 2000X - 3,960,000 + 10,000
18,000 = 2000X - 3,950,000
Add 3,950,000 to both sides
18,000 + 3,950,000 = 2000X
3,968,000 = 2000X
Divide both sides by 2000
X= 3,968,000 / 2000
= 1984
X= 1984
Therefore, the per capita income was $18,000 in the year 1984
Ms. Sung budgets a maximum of $320 per month for groceries. She grocery shops 4 times a month. Which inequality can be used to find the possible values of x, the amount she can spend at the grocery store during each shopping trip
A. 4+x<320
B.4x < 320 (btw they have like a dark line under the < yk)
C.4x > 320 (they have a dark line in the bottom of >)
D. 4+ x > 320
Answers
If 7 people share 17 muffins, how many does each person get? O 1023/7O 7/17O 1/2
Answers
Answer:
2 3/7
Explanation:
Given that 7 people share 17 muffins.
To get how many muffins each person gets, divide the total number of muffins by the number of people.
\(\begin{gathered} \text{ The number of muffins each person gets}=\frac{17}{7} \\ =2\frac{3}{7} \end{gathered}\)Each person gets 2 3/7 muffins.
The second option is correct.
Please someone help me!!!
It’s solving for x
(Due at 3:00 pm)
Answers
|
|
|
24x-8
\
______ Simplify again
/
/
________________
-192
HELP PLEASE! FOR EACH RELATION, DECIDE WHETHER OR NOT IT IS A FUNCTION.
Answers
Answer:
relation 1: function
Relation 2: function
relation 3: not a function
relation 4: not a function
Explanation:
There should be no repeating values in the domain for the relation to qualify for a function.
find the area of the trapezoid. if the answer is not an integer, leave it in simplest radical form. the figure is not to scale. PLEASE HELP
Answers
I'm sorry this question is not clear and I am not really able to answer it.
Find the product.
0.3(12)
Answers
Answer:3.6
Step-by-step explanation:
Answer:
3.6
Step-by-step explanation:
A kangaroo hops 2 kilometers in 3 minutes. At this rate, how far does the kangaroo travel in 2 minutes? Round to the nearest tenth.
Answers
2kilometers........3 minutes
xkilometers..........2 minutes
x=2*2/3=4/3=1.33km
Answer:
1.3 kilometers
Step-by-step explanation:
The first ratio of minutes to kilometers is 3:2
The second ratio of minutes to kilometers is 2:x
x is what you are trying to find (how far the kangaroo travels in 2 minutes)
Solve for x:
Change the ratios into fractions:
\(\frac{3}{2}\) \(\frac{2}{x}\)Cross multiply:
3x = 4
x = 4/3 = 1.33333333333…
and if you round that to the nearest tenth, you get 1.3.
Hope this helped!
What is the value of t?
Answers
Your friend is celebrating her 25 th birthday today and wants to start saving for her anticipated retirement at age 65 . She wants to be able to withdraw $250,000 from her saving account on each birthday for 20 years following her retirement; the first withdrawal will be on her 66th birthday. Your friend intends to invest her money in a retirement account, which earns 8 percent return per year. She wants to make an equal annual deposit on each birthday into the account for her retirement fund. Assume that the annual return on the retirement account is 8 percent before retirement and 5 percent after retirement. If she starts making these deposits on her 26 th birthday and continue to make deposits until she is 65 (the last deposit will be on her 65 th birthday and the total number of annual deposits is 40), what amount must she deposit annually to be able to make the desired withdrawals at retirement? (Hint: One way to solve for this problem is to first find the value on your friend's 65 th birthday of the $250,000 withdrawal per year for 20 years after her retirement using the annual return after retirement and then find the equal annual deposit that she needs to make from her 26th birthday to 65 th birthday using the annual return before retirement.) Ignore taxes and transaction costs for the problem.
Answers
The correct answer is your friend needs to deposit approximately $13,334.45 annually from her 26th birthday to her 65th birthday to be able to make the desired withdrawals at retirement.
To determine the annual deposit your friend needs to make for her retirement fund, we'll calculate the present value of the desired withdrawals during retirement and then solve for the equal annual deposit.
Step 1: Calculate the present value of the withdrawals during retirement
Using the formula for the present value of an annuity, we'll calculate the present value of the $250,000 withdrawals per year for 20 years after retirement.
\(PV = CF * [1 - (1 + r)^(-n)] / r\)
Where:
PV = Present value
CF = Cash flow per period ($250,000)
r = Rate of return after retirement (5%)
n = Number of periods (20)
Plugging in the values, we get:
PV = $250,000 * \([1 - (1 + 0.05)^(-20)] / 0.05\)
PV ≈ $2,791,209.96
Step 2: Calculate the equal annual deposit before retirement
Using the formula for the future value of an ordinary annuity, we'll calculate the equal annual deposit your friend needs to make from her 26th birthday to her 65th birthday.
\(FV = P * [(1 + r)^n - 1] / r\)
Where:
FV = Future value (PV calculated in Step 1)
P = Payment (annual deposit)
r = Rate of return before retirement (8%)
n = Number of periods (40)
Plugging in the values, we get:
$2,791,209.96 = \(P * [(1 + 0.08)^40 - 1] / 0.08\)
Now, we solve for P:P ≈ $13,334.45
Therefore, your friend needs to deposit approximately $13,334.45 annually from her 26th birthday to her 65th birthday to be able to make the desired withdrawals at retirement.
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Complete the table to determine the cost assigned to ending inventory and cost of goods sold using specific identification
Answers
The ending inventory that van be gotten from the table will be $9905 and the cost of goods sold is $5083.
What is ending inventory?It should be noted that the ending inventory simply means the goods that are still available for sale at the end of an accounting period.
From the complete question, the ending inventory will be:
= $3190 + $2295 + $4420
= $9905
Also, the cost of goods sold will be:
= $2465 + $473 + $2145
= $5083
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ANY MATH EXPERTS PLS HELP RN I GOT 30 MIN LEFT I PUT 100 POINTS
Answers
4/5
Explanation:
The slope of a line is defined by change in y/change in x. Notice that when the line’s x value changes from -2 to 3, it’s y value changes from 0 to 4. Therefore, the slope is 4/5
You have $60 and your sister has $120. You are saving $14 per week and your sister is saving $10 per week. How long will it be before you and your sister have thr same amount of money? What amount would you have the same ?
Answers
Answer:
15 weeks
The amount of money is 270
Step-by-step explanation:
You: 60 +14x
Sister: 120+10x
Set them equal to each other
60+14x = 120+10x
Subtract 10x from each side
60+4x= 120
Subtract 60 from each side
4x= 60
Divide by 4
4x/4 = 60/4
x = 15
15 weeks
The amount of money is 120+10*15 = 120+150 = 270
Answer:
15 weeks
$270
Steps:
1: 60+14x=120+10x
2: 4x=60
3: x=15 weeks
4: Amount= 60+14*15= $270
Description:
The first step is to get the money u have that is $60 plus it with the saving u have that is $14 answer will equal as 120+10x as a equation. Now simplify the equation 4x=60. You will get x=15 that will be the weeks. And now get 60+14 times it by 15 answer will equal as $270. So 15 weeks and $270 is the answer.
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Danielle Cecil's driver-rating factor is 1.60 and her car is in age group D and insurance-rating group is 12.
She wants 100/300 bodily injury and $50,000 property damage coverage.
102377
Answers
The value of the annual premium will be $1134.40
How to calculate the premium?From the information given, the annual base premium will be:
= Liability premium + Collision premium + Comprehensive premium
= $383 + $240 + $86
= $709
The annual premium will be:
= Annual base premium × Driver eating factors
= $709 × 1.60
= $1134.40
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Hi, I really need help with this question as fast as possible. *Will give 20 points*
So it's Anaya is preparing for a dance recital during the month of March and April in March she is practicing for 2 weeks and in April she is practicing for 4 weeks the table below shows the numbers of hours she practiced and each type of dance per week. on In Macrh while practicing ballet she practiced for 2 1/2 hours per week and in jazz on March she practice 4 and 3/4 hours and in April for ballet she practice 3 and 1/4 and for jazz in april she practiced 6 1/2 hours ( ANSWER THIS ) what is the difference in the total number of hours practiced in March and April.
Answers
The difference in the total number of hours practiced in March and April is \(24\frac{1}{2}\) hours
To find the difference in the total number of hours practiced in March and April
we need to calculate the total number of hours practiced in each month and then find the difference between the two totals.
In March:
Ballet: \(2\frac{1}{2}\) hours per week × 2 weeks = 5 hours
Jazz: \(4\frac{3}{4}\) hours per week × 2 weeks = 9 1/2 hours
Total hours practiced in March = 5 hours (ballet) + \(9\frac{1}{2}\) hours (jazz)
= \(14\frac{1}{2}\) hours
In April:
Ballet: \(3\frac{1}{4}\) hours per week × 4 weeks = 13 hours
Jazz: \(6\frac{1}{2}\) hours per week × 4 weeks = 26 hours
Total hours practiced in April = 13 hours (ballet) + 26 hours (jazz) = 39 hours
To find the difference, we subtract the total hours in March from the total hours in April:
39 hours (April) - \(14\frac{1}{2}\) hours (March) = \(24\frac{1}{2}\) hours
Therefore, the difference in the total number of hours practiced in March and April is \(24\frac{1}{2}\) hours
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what is the surface area of the regular pyramid given below 9 8 8
Answers
The surface area of a regular pyramid can be calculated using the formula: Surface Area = base area + lateral area. To find the base area, we need to determine the shape of the base.
In the given case, the base shape is not specified, so we cannot determine the surface area without additional information. To calculate the surface area of a regular pyramid, we need to consider the base area and the lateral area.
The base area depends on the shape of the base, which is not provided in the given information. Without knowing the shape of the base, we cannot calculate the base area. The lateral area depends on the slant height and perimeter of the base, which are also not provided.
Therefore, without further information, we cannot determine the surface area of the given regular pyramid.
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Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.)
lim x→−2
x + 2x^3 + 8
Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.)
lim h → 0
(−9 + h)^2 − 81h
Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.)
lim x → 4
x^2 − 4x + 3
x − 4
Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.)
lim x → 5
x^2 − 7x + 10
x − 5
Answers
For the first limit lim x→−2 x + 2x^³ + 8, the answer is -2.
For the second limit, the answer is -18.
For the third limit, the answer is does not exist.
For the fourth limit, the answer is 3.
For the first limit:
lim x→−2
x + 2x³ + 8
We can directly substitute x = -2 and get:
(-2) + 2(-2)³ + 8 = -2
Therefore, the limit is -2.
For the second limit:
lim h → 0
(−9 + h)² − 81h
Expanding the square and simplifying, we get:
((h²) - 18h)/h
Factoring out h, we get:
h(h - 18)/h
Canceling the h terms, we get:
h - 18
Substituting h = 0, we get:
-18
Therefore, the limit is -18.
For the third limit:
lim x → 4
x² − 4x + 3
x − 4
We can factor the numerator and cancel common factors with the denominator to get:
lim x → 4
(x - 1)(x - 3)
x - 4
Substituting x = 4 gives an indeterminate form of 0/0. We can factor the numerator further:
(x - 1)(x - 3) = (x - 4 + 3)(x - 4 + 1) = ((x - 4)^2 - 1)
So the limit becomes:
lim x → 4
((x - 4)² - 1)
x - 4
Canceling the (x - 4) terms, we get:
lim x → 4
(x - 4 + 1/x - 4)
Substituting x = 4 gives:
1/0
Therefore, the limit does not exist.
For the fourth limit:
lim x → 5
x² − 7x + 10
x − 5
We can factor the numerator and cancel common factors with the denominator to get:
lim x → 5
(x - 5)(x - 2)
x - 5
Canceling the (x - 5) terms, we get:
lim x → 5
x - 2
Substituting x = 5 gives:
3
Therefore, the limit is 3.
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Please help me pleasse I really need help please help me
Answers
Answer:
A) -25 feet per second
Step-by-step explanation:
The average rate of change [2.5, 4 ]
\(=f(4)-+(2.5)/4-2.5\)
\(f(4)=60 ft\)
\(f(2.5)=97.5 ft\)
\(4-2.5=1.5 sc\)
\(Answer:-\frac{60-97.5}{1.5}\)
\(= -25\)
So option A is your answer
\(--------------\)
hope it helps...
have a great day!!
Answer:
A. -25 feet per secondStep-by-step explanation:
Average rate of change in the interval (2.5, 4) is:
(60 - 97.5)/(4 - 2.5) = -25Correct choice is A