A researcher interested in the age at which women have their first child surveyed a simple random sample of 250 women who have one child and found an approximately normal distribution with a mean age of 27.3 and a standard deviation of 5.4. According to the Empirical rule, approximately 95% of women had their first child between the ages of a. 11.1 years and 43.5 years b. 16.5 years and 38.1 years C. 21.9 years and 32.7 years d. 25.0 years and 29.6 years
Answers
According to the Empirical rule, approximately 95% of women had their first child between the ages of 16.5 years and 38.1 years. The correct option is b. 16.5 years and 38.1 years.
The given question states that a researcher interested in the age at which women have their first child surveyed a simple random sample of 250 women who have one child and found an approximately normal distribution with a mean age of 27.3 and a standard deviation of 5.4. We are to find the range of age at which approximately 95% of women had their first child, according to the empirical rule.
There are three ranges for the empirical rule as follows:
Approximately 68% of the observations fall within the first standard deviation from the mean.
Approximately 95% of the observations fall within the first two standard deviations from the mean.
Approximately 99.7% of the observations fall within the first three standard deviations from the mean.
Now, we will apply the empirical rule to find the age range at which approximately 95% of women had their first child. The mean age is 27.3 years and the standard deviation is 5.4 years, hence:
First, find the age at which 2.5% of women had their first child:
µ - 2σ = 27.3 - (2 × 5.4) = 16.5
Then, find the age at which 97.5% of women had their first child:
µ + 2σ = 27.3 + (2 × 5.4) = 38.1
Therefore, approximately 95% of women had their first child between the ages of 16.5 years and 38.1 years. Hence, the correct answer is option b. 16.5 years and 38.1 years.
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Related Questions
\(\frac{4}{\sqrt{13}}\)
Answers
Answer:
\( \frac{4}{ \sqrt{13} } \times \frac{ \sqrt{13} }{ \sqrt{13} } = \frac{4 \sqrt{13} }{13} \)
I hope I helped you^_^
As an estimation we are told £3 is €4.
Convert £27 to euros.
Answers
Answer:
The answer is 38 euros.
Step-by-step explanation:
Determine P(c) using the remainder theorem.. (look at image)
Answers
Answer:
P(-5) = 109
Step-by-step explanation:
Remainder theorem:If the polynomial p(x) is divided by the linear polynomial (x-a), the remainder is p(a).
Dividend = divisor * quotient + remainder.
p(x) = (x-a) * q(x) + p(a)
Here, q(x) is the quotient and p(a) is the remainder.
P(x) = 4x² - x + 4
P(-5) = 4*(-5)² - 1*(-5) + 4
= 4*25 + 5 + 4
= 100 + 5 + 4
= 109
Consider the following data drawn independently from normally distributed populations: (You may find it useful to appropriate table: z table or t table)
xˉ1 = −17.1
s1^2 = 8.4
n1=22
xˉ2 = −16.0
s2^2 = 8.7
n2 = 24
a. Construct the 90% confidence interval for the difference between the population means. Assume the population va unknown but equal. (Round final answers to 2 decimal places.)
confidence interval is __ to __
Answers
The 90% confidence interval for the difference in the population means is -2.51 to 0.31
Calculating the 90% confidence interval for the population mean differenceFrom the question, we have the following parameters that can be used in our computation:
xˉ₁ = −17.1
s₁² = 8.4
n₁ = 22
xˉ₂ = −16.0
s₂² = 8.7
n₂ = 24
Calculate the pooled variance using
P = (df₁ * s₁² + df₂ * s₂²)/df
Where
df₁ = 22 - 1 = 21
df₂ = 24 - 1 = 23
df = 22 + 24 - 2 = 44
So, we have
P = (21 * 8.4 + 23 * 8.7)/44
P = 8.56
Also, we have the standard error to be
SE = √(P/n₁ + P/n₂)
So, we have
SE = √(8.56/22 + 8.56/24)
SE = 0.86
The z score at 90% CI is 1.645, and the CI is calculated as
CI = (x₁ - x₂) ± z * SE
So, we have
CI = (-17.1 + 16.0) ± 1.645 * 0.86
This gives
CI = -1.1 ± 1.41
Expand and evaluate
CI = (-2.51, 0.31)
Hence, the confidence interval is -2.51 to 0.31
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Given the cross section notes of an earthwork between station 10+100 to 10+200. Assume both stations to have the same side slope and width of the base. STA 10+100 ∼Ω
6.45 L
⋯
0
⋯
4.50R
a) Compute the side slope of both sections. b) Compute the value of X at station 10+200 if it has a cross sectional area of 14.64 m 2
. c) Compute the volume between stations 10+100 and 10+200 using end area with prismoidal correction.
Expert Answer
Answers
Summary: To compute the side slope of the given cross sections, determine the value of X at station 10+200, and calculate the volume between stations 10+100 and 10+200 using end area with prismoidal correction.
a) To compute the side slope of both sections, the given cross section notes provide the information "6.45 L" and "4.50 R." The "L" and "R" represent the left and right slopes, respectively. The side slope is expressed as a ratio of vertical to horizontal distance. For example, a 6.45:1 side slope means that for every 6.45 units of vertical rise or fall, there is 1 unit of horizontal distance.
b) To determine the value of X at station 10+200, additional information is needed. X represents the distance from the station to a specific point on the cross section. Without more details, it is not possible to calculate the specific value of X at station 10+200.
c) To compute the volume between stations 10+100 and 10+200 using end area with prismoidal correction, you need the cross-sectional areas at both stations. Given the cross-sectional area of 14.64 m^2 at station 10+200, you would also require the cross-sectional area at station 10+100. With these areas, the distance between the stations, and the appropriate formulas, you can calculate the volume of earthwork between the two stations, accounting for the prismoidal correction.
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HELP HELP HELP HELP
Answers
Answer:
24
Step-by-step explanation:
help me just
plz
hmmm
or let me die
i neeeeeeed help :)))))
Answers
So area of base = 3 x volume / height = 3 x 15pi / 5 = 9pi m^2
The radius of the base will be 3 m but this was not asked for.
For every 0.3048 meters, there is one foot. Determine the number of feet in 7.9248 meters. Use paper to support your answer.
Answers
Answer:
26 feet
Step-by-step explanation:
7.9248 divided by 0.348
Sierra drove five miles to stevens house at thirty six mph. she then drove seventeen miles to amanda's house. for the entire trip, sierra averaged a speed of 42 18/31 mph. what was her average speed driving from stevens to amanda's house?
Answers
The average speed of Sierra for driving from Steven's house to Amanda's house is 45mph.
We are given that the distance from Sierra's house to Steven's house is 5 miles and Sierra drove at the speed of 36mph.
Also the distance from Steven's house to Amanda's house is 17 miles.
The average speed of Sierra for the whole journey is \(42\frac{18}{31} mph\).
We know that,
\(Speed =\frac{Distance}{Time} \\\\Hence,\\\\Time=\frac{Distance}{Speed} \\\\Time =\frac{5}{36}hours\)
Hence, time taken by Sierra to reach Steven's house is \(\frac{5}{36} hours\).
Now,
Overall distance travelled By Sierra = 5 + 17 = 22 miles
Average speed for the journey = \(42\frac{18}{31} mph=\frac{1320}{31}mph\)
Hence,
Time taken for the whole journey = \(\frac{22}{\frac{1320}{31} } =\frac{31}{60} hours\)
Hence,
Total time taken = \(\frac{5}{36}\)+ Time taken to drive to Amanda's house from Steven's house
Hence,
\(\frac{31}{60}=\frac{5}{36}\)+ Time taken to drive to Amanda's house from Steven's house
Time taken to drive to Amanda's house from Steven's house=
\(\frac{31}{60}-\frac{5}{36}=\frac{93-25}{180}=\frac{68}{180}=\frac{17}{45} hours\)
Hence,
Speed when Sierra is driving from Steven's house to Amanda's house =
\(\frac{17}{\frac{17}{45} }=\frac{17}{1}*\frac{45}{17}= 45mph\)
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Find the rule. Solve for n. Х 12 15 20 Y 7 10 15 17 n Rule:
Answers
Answer:
n =22
Step-by-step explanation:
12-5=7
15-5=10
20-5=15
n-5=17
collect like terms
n=17+5
n=22
Answer:
Looking at the rule we can see that our x value is always 5 more than our y value. So to get our n we just take the y value of 17 and add 5 and we get 22. So our n is equal to 22.
A number is les than or equal to -11
Answers
Answer:
-12 is the answer for this question
Step-by-step explanation:
make me as brainlist
Answer:
\(x\leq-11\)
Step-by-step explanation:
01. Which of the choices below constitutes a simultaneous solution to these equations? ( 2 pts.) (1) 4X+3Y=12 and (2) 2X+4Y=8? 02. What combination of X and Y will yield the optimum for this problem? ( 3 pts.) Maximize Z=$10X+$50Y subject to: (1)3X+4Y≤12 and (2)2X+5Y≤10 03. What combination of X and Y will provide a minimum for this problem? (3pts.) Minimize Z=X+5Y subject to: (1) 4X+3Y≥12 and (2) 2X+5Y≥10
Answers
1. The simultaneous solution of the given equations is X=12/5 and Y=4/5
2.1)The combination of X and Y that will yield the optimum for this problem is X=0 and Y=3.3.
2)The combination of X and Y that will provide a minimum for this problem is X=3 and Y=0.
To find the simultaneous solution of the given equations 4X+3Y=12 and 2X+4Y=8, we can use the method of elimination, also known as the addition method. Multiplying the second equation by 2, we get 4X+8Y=16.
Now, we can subtract the first equation from the second equation: 4X+8Y - (4X+3Y) = 8Y - 3Y = 5Y and 16 - 12 = 4. Thus, 5Y=4 or Y = 4/5.
Substituting this value of Y in any of the two equations, we can find the value of X. Let's substitute this value of Y in the first equation: 4X+3(4/5)=12 or 4X
= 12 - (12/5)
= (60-12)/5
= 48/5.
Thus, X = 12/5. Hence, the simultaneous solution of the given equations is X=12/5 and Y=4/5.2. To find the optimal values of X and Y that will maximize the objective function Z=$10X+$50Y, we need to use the method of linear programming.
First, let's plot the feasible region defined by the given constraints:We can see that the feasible region is bounded by the lines 3X+4Y=12, 2X+5Y=10, X=0, and Y=0.
To find the optimal solution, we need to evaluate the objective function at each of the corner points of the feasible region, and choose the one that gives the maximum value.
Let's denote the corner points as A, B, C, and D, as shown above. The coordinates of these points are: A=(0,3), B=(2,1), C=(5/2,0), and D=(0,0). Now, let's evaluate the objective function Z=$10X+$50Y at each of these points:
Z(A)=$10(0)+$50(3)
=$150, Z(B)
=$10(2)+$50(1)
=$70, Z(C)
=$10(5/2)+$50(0)
=$25, Z(D)
=$10(0)+$50(0)=0.
Thus, we can see that the maximum value of Z is obtained at point A, where X=0 and Y=3. Therefore, the combination of X and Y that will yield the optimum for this problem is X=0 and Y=3.3.
To find the combination of X and Y that will provide a minimum for the problem Minimize Z=X+5Y subject to: 4X+3Y≥12 and 2X+5Y≥10, we need to use the same method of linear programming as above.
First, let's plot the feasible region defined by the given constraints:We can see that the feasible region is bounded by the lines 4X+3Y=12, 2X+5Y=10, X=0, and Y=0.
To find the optimal solution, we need to evaluate the objective function Z=X+5Y at each of the corner points of the feasible region, and choose the one that gives the minimum value.
Let's denote the corner points as A, B, C, and D, as shown above.
The coordinates of these points are: A=(3,0), B=(5,1), C=(0,4), and D=(0,0).
Now, let's evaluate the objective function Z=X+5Y at each of these points:
Z(A)=3+5(0)=3,
Z(B)=5+5(1)=10,
Z(C)=0+5(4)=20,
Z(D)=0+5(0)=0.
Thus, we can see that the minimum value of Z is obtained at point A, where X=3 and Y=0. Therefore, the combination of X and Y that will provide a minimum for this problem is X=3 and Y=0.
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Please help.............
Answers
Answer:
...........
2(x + 2) + 2x = 20
Answer:
x(x+2) = 20
Step-by-step explanation:
Perimeter Formulas of rectangle is: Perimeter = 2 × (a + b)
Cube a and cube b are similar solids. the volume of cube a is 27 cubic inches, and the volume of cube b is 125 cubic inches. how many times larger is the base area of cube b than the base area of cube a?
Answers
The base area of cube B is 25/9 times larger than the base area of cube A.
What is area cubic?
Surface area of cube is the sum of areas of all the faces of cube, that covers it. The formula for surface area is equal to six times of square of length of the sides of cube. It is represented by 6a2, where a is the side length of cube. It is basically the total surface area.We know that volume of cube with each side of units is equal to .
First of all, we will find the each side of cube A and B as:
\(A^{3} = 27\)
\(\sqrt[3]{A^{3} } = \sqrt[3]{27}\)
A = 3
\(B^{3} = 125\)
\(\sqrt[3]{B^{3} } = \sqrt[3]{125}\)
B = 5
Now, we will find base area of both cubes as:
\(\frac{Base area of B}{Base area of A} = \frac{B^{2} }{A^{2} }\)
\(\frac{Base area of B}{Base area of A} = \frac{5^{2} }{3^{2} }\)
\(\frac{Base area of B}{Base area of A} = \frac{25}{9}\)
Therefore, the base area of cube B is 25/9 times larger than the base area of cube A.
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Two families have been out on dinner.at the end of the night they pay their 100 pound bill they use a 50 percent of coupon which halves their bill then they split their remaining amount equally between the two families
Answers
The amount that one family paid is 25 pound
Here two families had dinner and bill was 100 pound
They used the coupon on which they got 50% off
To find the percentage we have to use percentage formula:
\(=\frac{Value}{Total \ Value} *100\)
\(=\frac{50}{100} *100\)
\(= 50 \ Pounds\)
The remaining bill was 50 pound
Now this amount is divided between the 2 families
\(=\frac{50}{2}\)
\(= 25 \ pound\)
So one family has to pay 25 pounds
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pls help asap if you can!!!!!
Answers
Answer: A x=11
Step-by-step explanation:
We are assuming the lines are parallel so the angles would be equal from transverse line rules.
7x + 13 = 90 >Subtract 13 from both sides
7x = 77 >divide both sides by 7
x = 11
What is the quotient?
Answers
For the function, find the points on the graph at which the tangent line is horizontal. If none exist, state that fact.
Answers
The points on the graph at which the tangent line is horizontal are:
(-1.414, 4.886) and (1.414, 1.114).
What is the horizontal point on the tangent line?
Since the horizontal tangent is parallel to the x-axis, its slope, or derivative, should also have a value of 0 at the tangent point. This is the key concept for finding the point on the graph where the tangent line is horizontal.
The function is given as:
y = ¹/₃x³ - 2x + 3
The tangents are horizontal where the derivative is zero. The derivative of the given function is:
y' = x² -2
This is zero when:
0 = x² -2
2 = x²
x = ±√2 . . . x-values where the derivative is zero
The corresponding y-values are:
y = (¹/₃x² - 2x + 3)
y = (¹/₃(2) - (2(±√2)) + 3
The turning points are (-1.414, 4.886) and (1.414, 1.114).
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Complete question is:
For the function, find the points on the graph at which the tangent line is horizontal. If none exist, state that fact.
y = ¹/₃x³ - 2x + 3
To find the points on the graph at which the tangent line is horizontal, we need to find the x-values where the derivative of the function is equal to zero.
To find the points on the graph at which the tangent line is horizontal, we need to find the x-values where the derivative of the function is equal to zero. The derivative represents the rate of change or slope of the function at any given point.
Let's say we have a function f(x). To find the derivative of f(x), we differentiate the function with respect to x. The resulting derivative function is denoted as f'(x) or dy/dx.
Next, we set the derivative function f'(x) equal to zero and solve for x. The x-values obtained from this equation represent the points on the graph where the tangent line is horizontal.
If there are no solutions to the equation f'(x) = 0, it means there are no points on the graph where the tangent line is horizontal.
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Eric and Nancy both had a successful year selling fish tanks for theirrespective employers, and so they were both given raises.Eric: Eric's base salary is still $1400, but now he makes a commission of$100 for each fish tank that he sells.Nancy: Nancy now gets a base salary of $500 per month, but her commissionhas stayed the same at $250 per fish tank.Eric and Nancy still want to make sure that they contribute the same amountto their total monthly income, and Nancy proposes using algebra to figureout how many fish tanks that they would each need to sell. She tells Ericthat he can calculate his monthly income by using the formula f(x) = 100x +1400. She says that she can calculate her own salary by using the functiong(x) = 250x + 500.1.How many fish tanks would each person need to sell so that they made the same amount of money
Answers
For this question, since we need to show that Eric and Nancy contributes the same amount to their monthly income, we just need to equate both expressions with each other, and then solve for the value of x.
\(f(x)=g(x)\)\(100x+1400=250x+500\)\(100x-250x=500-1400\)\(-150x=-900\)\(\frac{-150x}{-150}=\frac{-900}{-150}\)\(x=6\)In order to check if we got the right answer, we just need to substitute the value of x to both equations.
\(100x+1400=250x+500\)\(100(6)+1400=250(6)+500\)\(600+1400=1500+500\)\(2000=2000\)Therefore, we can conclude that Eric and Nancy has to sell 6 fish tanks each.
Please help!!! Its due today
Answers
Answer:
59
Step-by-step explanation:
\(f(x) = 2^{6} - 5\\\ f(x)= 64-5\\f(6)=59\\\)
Answer:
it's 59
you have to plug it in
Step-by-step explanation:
you have to plug in 6 in X so it would be 2^6 -5 and 2^6 it's 64 and minus 5 is 59
Question 3 (4 points)
(04.05)
Which description best describes the graph? (4 points)
10
O a
Linear increasing
Ob
Linear decreasing
OC
Nonlinear increasing
Od
Nonlinear decreasing
Answers
Answer:
Option D
Step-by-step explanation:
Option A and Option B are completely wrong because the word Linear represent a straight line graph and the figure in the question that is given is not a straight line.
Option C is wrong because the graph in the figure is decreasing there is an arrowhead at (3 , -6) it shows the graph is going downwards increasing its negative value hence decreasing
Option D is correct because all the other three options are wrong and hence the arrow the figure is decreasing and non linear.
Answer:
D
Step-by-step explanation:
cuz it going down
p.s. mark other person brainliest cuz my explantion sucks lol
Refer to the figure to complete the following problem.
Given: A RST is circumscribed about circle A. What is the measure of angle S?
0.5 arc XQ minus arc XPQ
0.5 (arc XPQ- arc XQ)
angle R + angle T
Answers
the measured angle S is 1/2((Arc XPQ-Arc XQ)).
What is are of triangle?
The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.
The sum of all angles of the triangle = 180
The circle is within the triangle,
The arc XPQ is the total, arc XQ
So the measured angle S is 1/2((Arc XPQ-Arc XQ)).
0.5 (Arc XPQ-Arc XQ)
Hence the measured angle S is 1/2((Arc XPQ-Arc XQ)).
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I’ll give brainliest
Answers
Answer:
B
Step-by-step explanation:
We know that it costs 37 cents to mail a letter that weighs 1 oz or less. This would mean that for x ≤ 1, P(x) should equal 37. Already, we can eliminate A and D.
We also know that it costs an additional 26 cents for at most another ounce added to the original 1 ounce. This means that for 1 < x ≤ 2, P(x) = 26 + 37 = 63. This is shown by B.
Thus, the answer is B.
~ an aesthetics lover
please solve all of them Elaine bought a total of 15 shirts and pairs of pants She bought 7 more shirts then pants how many of each did she buy?Together Preston and shady Have 49 video games, shady has 11 more games than Preston. How many does each person have?The cost of 8 muffins in 2 quarts of milk is $18. The cost of 3 muffins and 1 quart of milk is 7.50. How much does 1 buffet in 1 quart of milk cost?
Answers
Answer
Question 1
4 pants
11 shirts
Question 2
Shady has 30 video games.
Preston has 19 video games.
Question 3
1 muffin costs $1.5
1 quart of milk costs $3
Explanation
Question 1
Let the number of shirts be s
Let the number of pants be p
She bought a total of 15 shirts and shirts
s + p = 15
She bought 7 more shirts than pants.
s = 7 + p
So, we can solve the simultaneous equation.
s + p = 15
s = 7 + p
Substitute for s in equation 1
s + p = 15
7 + p + p = 15
7 + 2p = 15
2p = 15 - 7
2p = 8
Divide both sides by 2
(2p/2) = (8/2)
p = 4 pants
s = 7 + p = 7 + 4 = 11 shirts
Question 2
Let the number of games Shady has be s
Let the number of games Preston has be p
Together, they have a total of 49 video games
s + p = 49
Shady has 11 more games than Preston.
s = 11 + p
So, we can solve the simultaneous equation.
s + p = 49
s = 11 + p
Substitute for s in equation 1
s + p = 49
11 + p + p = 49
11 + 2p = 49
2p = 49 - 11
2p = 38
Divide both sides by 2
(2p/2) = (38/2)
p = 19 video games
s = 11 + p = 11 + 19 = 30 video games
Question 3
Let the cost of a muffin be m
Let the cost of a quart of milk be q
The cost of 8 muffins and 2 quarts of milk is $18.
8m + 2q = 18
The cost of 3 muffins and 1 quart of milk is $7.50
3m + q = 7.5
So, we can solve the simultaneous equation
8m + 2q = 18
3m + q = 7.5
Solving this,
m = 1.5 dollars
q = 3 dollars
Hope this Helps!!!
The ratio 5:11 can also be used to describe a relationship between the beads on each necklace. What relationship could this ratio describe? Show or explain how you got your answer.
Answers
The ratio 5:11 can be used to describe the relationship between the beads on each necklace. In this case, the relationship that the ratio describes is the number of beads on the two necklaces.
The ratio indicates that for every 5 beads on one necklace, there are 11 beads on the other necklace. The ratio can be simplified by dividing both the terms by the greatest common factor of 5 and 11, which is 1, to get 5:11.
Hence, the ratio 5:11 can describe the relationship between the number of beads on two necklaces. In this case, the relationship that the ratio describes is the number of beads on the two necklaces.
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what is 2 + x ≤ 3x – 6 ≤ 12
Answers
Answer:
4≤x≤6
Hope that helps! :)
inclusive or exclusive or? a: you must take chemistry or physics to graduate b: you can have a complimentary coffee or tea question 3 options: a is exclusive, b is inclusive both are exclusive a is inclusive, b is exclusive both are inclusive
Answers
If you have two options, A and B, exclusive means only one option is required (A or B) while inclusive means both options are available (A and B).
To calculate the answer to this question, we need to consider what the words “exclusive” and “inclusive” mean. Exclusive means that one option is required and the other is not, while inclusive means that both options are available. In the case of the question a, the answer is exclusive because you must take either chemistry or physics to graduate. In the case of question b, the answer is inclusive because you can have either a complimentary coffee or tea.
To illustrate the difference between exclusive and inclusive with a formula, we can use the following:
Exclusive: A + B = A
Inclusive: A + B = A + B
This formula demonstrates that if you have two options, A and B, exclusive means only one option is required (A or B) while inclusive means both options are available (A and B).
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Starting at home, Luis traveled uphill to the gift store for 50minutes at just 6 mph. He then traveled back home along the same path downhill at a speed of 12mph.
Answers
Answer:
Average speed for the entire trip, both ways, is
(Total distance) divided by (total time) .
We don't know the distance from his house to the gift store,
and we don't know how long it took him to get back.
We'll need to calculate these.
-- On the trip TO the store, it took him 50 minutes, at 6 mph.
-- 50 minutes is 5/6 of an hour.
-- Traveling at 6 mph for 5/6 of an hour, he covered 5 miles.
-- The gift store is 5 miles from his house.
-- The total trip both ways was 10 miles.
-- On the way BACK home from the store, he moved at 12 mph.
-- Going 5 miles at 12 mph, it takes (5/12 hour) = 25 minutes.
Now we have everything we need.
Distance:
Going: 5 miles
Returning: 5 miles
Total 10 miles
Time:
Going: 50 minutes
Returning: 25 minutes
Total: 75 minutes = 1.25 hours
Average speed for the whole trip =
(total distance) / (total time)
= (10 miles) / (1.25 hours)
= (10 / 1.25) miles/hours
= 8 miles per hour
Step-by-step explanation:
The population of deer on an island is given by P(x)= 100(0. 85)^x, where x represents the number of years. Determine the percent rate of change for the population of deer per year.
A- 85% decrease
B- 15% decrease
C- 85% increase
D- 15% increase
Answers
The correct option is B percent rate of change is - 15% decrease.
To determine the percent rate of change for the population of deer per year, we need to calculate the derivative of the population function P(x) with respect to x, and then evaluate it at x = 1 (since we are interested in the annual rate of change).
Given the population function:\(P(x) = 100(0.85)^x\)
Taking the derivative of P(x) with respect to x:
\(P'(x) = d/dx [100(0.85)^x]\)
= \(100 * ln(0.85) * (0.85)^x\) [Applying the chain rule]
Now, let's evaluate P'(x) at x = 1 to find the annual rate of change:
P'(1) = \(100 * ln(0.85) * (0.85)^1\)
≈ 100 * (-0.1625) * 0.85
≈ -13.8125
The annual rate of change is approximately -13.8125. Since the value is negative, it represents a decrease in the population.
Therefore, the correct option is B- 15% decrease.
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