Answer:
D) 69.1 ft
Step-by-step explanation:
Answer: a
Step-by-step explanation:
Use these functions to evaluate the following problems: f(x) = x, g(x) = x - 3, h(x) = x^2 - 9, k(x) = 2x
(hk)(x)
(k/f)(x)
(h/g)(x)
Answer:
(hk)(x) = 2x³-18x
(k/f)(x) = 2
(h/g)(x) = x+3
Step-by-step explanation:
(hk)(x)
(x² - 9)(2x)
2x³ - 18x
(k/f)(x)
2x/x
2
(h/g)(x)
(x² - 9)/(x - 3)
[x² - 3²]/(x - 3)
(x + 3)(x - 3)/(x - 3)
x + 3
A computer is generating passwords. The computer generates six characters at random, and each is equally likely to be any of the letters or digits. Replications are allowed. What is the probability that the password will contain all letters?
Answer:
0.1419 ( (if upper and lower cases are interchangeable)
0.348 ( if upper and lower cases are distinct letters)
Step-by-step explanation:
Each digit has 36 possible choices as 26+10
computer generates six characters
there are only 26 choices for letters only, (if we assume upper and lower cases are interchangeable)
For number of letters-only arrangements = [tex]26^{6}[/tex] = 308915776
For number of alphanumeric arrangements = [tex]36^{6}[/tex]= 2176782336
In order to find the probability of letters-only arrangements : [tex]\frac{308915776}{2176782336}[/tex]
=>0.1419
Now, in different scenario if upper and lower cases are not interchangeable.
We will have 26+26+10=62 alphanumeric choices, and 52 alphabetic choices
Therefore, probability of letters-only arrangements will be [tex]\frac{52^{6} }{62^{6} }[/tex]
=>0.348
Answer:
The probability of all letters arrangement if the upper cases and the lower cases of the English alphabet are interchangeable = 14.2%
The probability of all letters arrangement if the upper cases and the lower cases are not interchangeable = 34.8%
Step-by-step explanation:
please kindly check the attached files for explanation.
Mildred has a bag of coins. The bag contains 10 dimes, 5 nickels, and 1 penny. She will randomly select 2 coins from the bag one at a time without replacement. What is the probability that Mildred will select a dime first and then a month penny?
The probability that Mildred will select a dime first and then a month penny is 1/24.
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
Given:
Total possibilities = 16
So, Probability of a dime of the first draw = 10/16 = 5/8
and, Probability of a penny on the second draw = 1/15
Thus, Probability of both = 5/8 x 1/15
= 1/24
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The probability that Mildred will select a dime first and then a penny is 1/24.
To calculate the probability that Mildred will select a dime first and then a penny from her bag of coins, we need to consider the following steps:
1. Probability of selecting a dime first:
- Mildred has a total of 10 dimes, 5 nickels, and 1 penny in the bag.
- The probability of selecting a dime on the first draw is the number of dimes divided by the total number of coins, which is 10 dimes out of 16 total coins.
2. Probability of selecting a penny next:
- After selecting a dime on the first draw, Mildred will have 9 dimes, 5 nickels, and 1 penny remaining in the bag.
- The probability of selecting a penny on the second draw is the number of pennies divided by the total number of remaining coins, which is 1 penny out of 15 remaining coins.
3. To find the overall probability, we multiply the individual probabilities:
- Probability = (Number of dimes / Total coins) * (Number of pennies / Remaining coins)
- Substituting the numbers, we get (10/16) * (1/15) = 1/24.
Therefore, the probability that Mildred will select a dime first and then a penny is 1/24.
Find the area of a circle with a diameter of \color{green}{16}16start color green, 16, end color green.
Answer:
if you can write a comment so that makes sense, i might be able to help you
Step-by-step explanation:
sorry
Answer:
The answer is 64pi
Step-by-step explanation:
7. Give all transformations that occur to the function y = x ^ 3 that produce the function y = 1/3 * x ^ 3 + 5 Give both the transformations and the order in which they occur.
Answer:
See explanantion
Step-by-step explanation:
Solution:-
- We will start of with the given function y = x^3, and plot a small sketch.
First transformation:-
- We multiply the y = x^3, with a constant a = 1/3. Where,
y1 = a*y
Where, a : real constant
- The cases for a:
a > 1 ----> makes the function steeper
0 < a < 1 ----> Flattens the graph/less steep
a < - 1 ------ > Reflection about x-axis and makes the function steeper.
0 < a < -1 ----> Flattens the graph/less steep and reflection about x-axis
- For a = 1/3, the graph flattens or in other words with increasing value of "x" the value of "y" increases at a decreased rate.
Second Transformation:-
- We add the b = 5 to the resulting graph y = 1/3*x^3.
y2 = 1/3*x^3 + b
Where, b : Real constant
- The cases for b:
b > 0 --------> Vertical upward shift of the graph by b units
b < 0 ---------> Vertical downward shift of the graph by b units
- For b = 5 > 0, The graph 5 units up or in other words the y-intercept shifts from y = 0 to y = 5.
- The required function y = 1/3*x^3 + 5 undergoes two transformation. a = 1/3 flatten out the starting function y = x^3 and b = 5 shifts the resulting graph vertically upwards.
Final answer:
To produce the function y = (1/3)*x³ + 5 from y = x³, two transformations occur: a vertical scaling by 1/3 followed by a vertical translation up 5 units.
Explanation:
The function y = x³ has undergone two transformations to become y = (1/3) * x³ + 5. First, a vertical scaling by a factor of 1/3 has occurred, shrinking the graph vertically by a third of its original size. The second transformation is a vertical translation of 5 units upwards, which takes every point on the graph and moves it 5 units higher on the y-axis. These transformations would occur in the following order:
Vertical scaling by a factor of 1/3: y = x³ becomes y = (1/3)*x³.Vertical translation up by 5 units: y = (1/3)*x³ becomes y = (1/3)*x³ + 5.Find the length of the darkened arc. Leave your answer in terms of pi.
Answer:
[tex] \frac{15 }{4} \pi \:[/tex]
Step-by-step explanation:
Radius of circle (r) = 18/2 = 9 ft
Central angle = 180° - 30° = 150°
[tex]length \: of \: arc \\ = \frac{150 \degree}{360 \degree} \times 2\pi \: r \\ \\ = \frac{150 \degree}{360 \degree} \times 2 \times \pi \: \times 9\\ \\ = \frac{5 }{12 } \times 18 \times \pi \: \\ \\ = \frac{5 }{4} \times 3\times \pi \:\\ \\ = \frac{15 }{4} \pi \:[/tex]
The length of the darkened arc can be found using the formula s = Δθr, where s is the length of the arc, Δθ is the angle of rotation, and r is the radius of curvature.
Explanation:The length of the darkened arc can be found by using the formula for arc length: s = Δθr, where s is the length of the arc, Δθ is the angle of rotation, and r is the radius of curvature. In this case, the angle of rotation is 2π radians (since it is a complete revolution) and the radius is given. So, substituting these values into the formula, we have s = 2πr.
In ΔVWX, the measure of ∠X=90°, VX = 35, XW = 12, and WV = 37. What is the value of the cosine of ∠W to the nearest hundredth?
Answer:
Cosine W = 0.32
Step-by-step explanation:
Adj/Hypo = 12/37 = 0.3243 = 0.32
Final answer:
The cosine of ∠W in triangle ΔVWX is found by dividing the length of the side adjacent to ∠W (XW) by the length of the hypotenuse (WV), resulting in cos(∠W) ≈ 0.32 to the nearest hundredth.
Explanation:
In triangle ΔVWX, where ∠X=90°, VX = 35, XW = 12, and WV = 37, we are asked to find the value of the cosine of ∠W to the nearest hundredth. Since ∠X is a right angle, this triangle is a right triangle, and we can use trigonometric ratios to find the cosine of ∠W. The cosine of an angle in a right triangle is equal to the adjacent side over the hypotenuse.
To find the cosine of ∠W, we look at the sides adjacent to ∠W, which are XW and WV. The length of XW is 12, and WV, being the hypotenuse, is 37. Therefore, to find cos(∠W), we calculate 12/37. Doing this calculation, we get cos(∠W) ≈ 0.32 to the nearest hundredth.
The cosine is a trigonometric function that relates the lengths of sides in a right triangle to the angles, and it is specifically the ratio of the length of the adjacent side to the length of the hypotenuse.
A tractor trailer averages 6 miles per gallon fuel consumption. If the truck can hold 150 gallons of fuel, how many miles could it go before needing to refuel?
Answer:
The answer to your question is 900 miles
Step-by-step explanation:
Data
Consumption = 6 mi/gallon
total fuel = 150 gallons
number of miles = ?
Process
1.- To solve this problem use proportions and cross multiplication
6 miles ------------------ 1 gallon
x ------------------ 150 gallons
x = (150 x 6) / 1
-Simplification
x = 900 / 1
-Result
x = 900 miles
Jackie makes silver and gold charms for charm bracelets. The charms are similar isosceles triangles. The gold charm has a base of 6 mm and an area of 15 mm. The silver charm has a base of 9 mm. What is the area of the silver char
Answer:
The area of silver charm is 33.75 square mm.
Step-by-step explanation:
We are given the following in the question:
The silver and golden charms are similar isosceles triangles.
Gold charms:
Base = 9 mm
Area = 15 square mm
Silver charm:
Base = 9 mm
Property of similar triangles:
If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides.Using this property we can write:
[tex]\dfrac{\text{Area of gold charm}}{\text{Area of silver charm}}=\dfrac{(\text{Base of gold charm})^2}{(\text{Base of silver charm})^2}\\\\=\dfrac{15}{\text{Area of silver charm}}=\dfrac{6^2}{9^2}\\\\\text{Area of silver charm} = \dfrac{15\times 9^2}{6^2} = 33.75\text{ mm}[/tex]
Thus, the area of silver charm is 33.75 square mm.
A box plot is shown below: A box and whisker plot is shown using a number line from 20 to 45 with primary markings and labels at 20, 25, 30, 35, 40, 45. In between two primary markings are 4 secondary markings. The box extends from 27 to 38 on the number line. A line in the box is at 32. The whiskers end at 20 and 42. The title of the art is Visitors at the Exhibition, and below the line is written Number of Visitors. What is the median and Q1 of the data set represented on the plot?
Median = 30; Q1 = 27
Median = 32; Q1 = 27
Median = 30; Q1 = 20
Median = 32; Q1 = 20
Answer:
b) Median 32; Q1 =27
Step-by-step explanation:
The description to the left directs us how to draw the box and whiskers. Using the markings. 20, 25, 30, 35, 40,45 check on the left side of the graph.The box extends from 27 to 38 on the number line. So, that means Q1=27 and Q3=38The whiskers end at 20 and 42. The minimum and the Maximum value of the Distribution, the "whisker".A line in the box is at 32. The horizontal line the slices the box, in other words the Median.So here it is, our Box and Whiskers Plot.
You are looking out your window in a skyscraper, and again your window is at a height of 450 feet above the ground. This time, however, you know that the tomato was dropped (so v_0 = 0), but you did not see it dropped so you do not know when it was dropped. You measure that it takes exactly 2 seconds from the time the tomato passes your window until it hits the ground. From what height did it fall? Give your answer as a decimal approximation with units.
Answer:
1027.2 m
Step-by-step explanation:
Gabriella has the following winter accessories:
1 winter coat: black
2 hats: blue, purple
2 pairs of boots: black, brown
5 pairs of mittens: black, blue, purple, red, white
Find the probability of wearing the coat with the purple hat, black boots, and purple mittens.
Answer:
1/20
Step-by-step explanation:
There are 20 possible probabilites/combinatins of what to wear, and wearing a coat, with a purple hat, black boots, and purple mittens is only 1 of those 20 probabilities so the answer is 1/20
6. A farmer needs to enclose a section of land in the shape of a parallelogram by using
one side of a barn for one side. The barn and the side adjacent to the barn form a 65°
angle. What is the measure of the angle opposite from this angle? (Circle the correct
answer.)
A. 35°
B. 65°
c. 115°
D. 25°
Answer:
C. 115 degrees
Step-by-step explanation:
Knowing one side of a circle is 180 degrees, we should subtract 180-65.
- 180-65=115 degrees
x + 8y = 2; (10, -1)
Which table of ordered pairs represents a proportinal relationship
Answer:
where are the tables lol
Fill in the blanks to correctly complete the sentence below.
Suppose a simple random sample of size n is drawn from a large population with mean muμ and standard deviation sigma σ. The sampling distribution of [tex]\bar x[/tex] has mean [tex]\mu_{\bar x}[/tex] =______ and standard deviation [tex]\sigma_{\bar x}[/tex] =______.
Answer:
Mean of the sampling distribution, [tex]\mu_{\bar{x}}=\mu[/tex]
Standard deviation of the sampling distribution [tex]\dfrac{\sigma}{\sqrt{n}}[/tex]
Step-by-step explanation:
Given a simple random sample of size n which is drawn from a large population
If the mean of the simple random sample of size n [tex]=\mu[/tex] The sampling distribution of [tex]\bar{x}[/tex] has the same mean [tex]\mu_{\bar{x}}=\mu[/tex]If the standard deviation of the simple random sample of size n is [tex]\sigma[/tex] The sampling distribution of will have a standard deviation of [tex]\dfrac{\sigma}{\sqrt{n}}[/tex]If you punch a wall with a force of 30 N, what force will you feel in your fist??
Answer:
30N
Step-by-step explanation:
Normal reaction
The force feel by fist is 30N.
What is Force?
A Force is a push or pull upon an object resulting from the object's interaction with another object.
Newton's Third Law of Motion states that for every action, there is an equal and opposite reaction.
Since you punch a wall with a force of 30N, the fist will feel the same force in the opposite direction as per the Newton's Third Law of Motion.
Hence The force feel by fist is 30N.
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What is another name for Angle 1? Line segments J L and L M combine to form an angle. Line segment L K comes out of the angle to form 2 angles. Angle J L K is 1 and angle K L M is 2. Angle J L K Angle L K J Angle K L M Angle L K M
Answer: The answer is the first one, angle JLK
Step-by-step explanation:
The another name for Angle 1 is Angle JLK, the correct option is 1.
What is an angle?In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The word “angle” is derived from the Latin word “angulus”, which means “corner”. The two rays are called the sides of an angle, and the common endpoint is called the vertex.
Given;
Line segments J L and L M combine to form an angle.
Line segment L K comes out of the angle to form 2 angles.
Now,
First the angle was JLM
Line segment LK cuts the angle JLM in 2
So, after Line segment L K comes out of the angle to form 2 angles
Angle= JLK
Therefore, by new angle formed will be called JLK.
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steve herr is an architect in minneapolis, minnesota. his latest project is designing a park. on the blueprint, the park is determined by a plane which contains the points at (1,0,3).(2,5,0), and (3,1,4). one of the features of the park is a monument that must be perpendicular to the ground. find the nonzero vector, representing the monument, perpendicular to the plane defined by the given points.
Answer:
a. (8,-7,-9)
Step-by-step explanation:
just took the quiz and this is the answer
Answer:
The person over there is correct. The answer is A.
Step-by-step explanation:
I take the quiz and it is correct. Edge 2021.
In 24 games, Jaime has 48 scoring attempts. Which unit rate describes Jaime’s scoring attempts?
a. 1/2 a scoring attempt per game
b. 2 scoring attempts per game
c. 24 scoring attempts per game
d. 72 scoring attempts per game
Answer:
2 Scoring Attempts
Step-by-step explanation:
There are 48 attempts divided by 24 game which equals 2.
Answer:
it is b
Step-by-step explanation:
Eliminate the parameter to find the cartesian equation of the curve: x=7sinθ,y=cos2θ,−π2≤θ≤π2 x=7sinθ,y=cos2θ,−π2≤θ≤π2 the equation of the curve is: y = equation editorequation editor from x = equation editorequation editor to x =
To eliminate the parameter and find the Cartesian equation of the curve x = 7sinθ,y = cos2θ, we can express x in terms of θ, rearrange the equation, and substitute it into the other equation to eliminate the parameter θ. The resulting equation 2(x/7)² + y - 1 = 0 represents the Cartesian equation of the curve.
Explanation:To eliminate the parameter and find the Cartesian equation of the curve, we can express x in terms of θ using the given equation x = 7sinθ. Rearranging this equation, we get sinθ = x/7. Similarly, we can express y in terms of θ using the given equation y = cos2θ, which can be rewritten as cos(2θ) = y.
Now we can use the trigonometric identity cos(2θ) = 1 - 2sin²θ to eliminate θ from the equations. Substituting this identity into the second equation, we get 1 - 2(sinθ)² = y.
Simplifying this equation, we have 2(sinθ)² + y - 1 = 0. Finally, we can express sinθ in terms of x using the equation sinθ = x/7, and substitute it into the simplified equation to eliminate θ. This gives us 2(x/7)² + y - 1 = 0, which represents the Cartesian equation of the given curve.
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What is reasonable estimate for the problem
Answer:
-2
Step-by-step explanation:
this is i ready lol but basically the actual answer is -1.5 but if you round that you get -2
Answer:
-2
Step-by-step explanation:
3 3/4 times -2/5 = -1.5, which is closer to -2.
A town covers a 50.5 square mile area. If they population density of the town is 48.2 people per square mile, what is the population of the town, to the nearest hundred people.
Answer:
The population of town is approximately 2400 people.
Step-by-step explanation:
We are given the following in the question:
Area of town = 50.5 square miles
Population density of town = 48.2 people per square mile
Population of town =
[tex]P= \text{Area}\times \text{Population density}\\P=50.5\times 48.2\\P=2434.1[/tex]
Now, we have to round off this population to nearest hundred.
After rounding off,
[tex]P=2400\text{ people}[/tex]
Thus, the population of town is approximately 2400 people.
Jake has decided to give a bonus to the employee who has worked the greatest total number of hours over the past six months. Four candidates are currently up for consideration. The following graph shows how many hours each one has worked over the past six months.
A graph titled Hours Worked has name on the x-axis and Hours on the y-axis. For October: Vince, 130; Claire, 129; Joey, 134; Katharine, 122. For November: Vince, 135; Claire, 130; Joey, 121; Katherine, 131. For December: Vince, 131; Claire, 125; Joey, 119; Katherine, 134. For January: Vince, 133; Claire, 126; Joey, 127; Katharine, 133. For February: Vince, 134; Claire, 121; Joey, 132; Katharine, 115. For March: Vince, 118; Claire, 133; Joey, 134; Katharine, 140.
To which employee will Jake give the bonus?
a.
Vince
b.
Claire
c.
Joey
d.
Katharine
Please select the best answer from the choices provided
A
B
C
D
Answer:
The answer is A) Vince.
Step-by-step explanation:
Vince had 781 total hours. Claire had 764 total hours. Joey had 767 total hours. Katharine had 775 total hours. Therefore the person with the most hours, Vince, gets the bonus.
Jake will give the bonus to Vince, as she has worked the greatest total number of hours over the past six months.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
To determine who will receive the bonus, we need to calculate the total number of hours worked by each employee over the past six months.
For Vince:
130 + 135 + 131 + 133 + 134 + 118 = 781
For Claire:
129 + 130 + 125 + 126 + 121 + 133 = 764
For Joey:
134 + 121 + 119 + 127 + 132 + 134 = 767
For Katharine:
122 + 131 + 134 + 133 + 115 + 140 = 775
Jake will give the bonus to Vince, as she has worked the greatest total number of hours over the past six months.
Hence, Jake will give the bonus to Vince, as she has worked the greatest total number of hours over the past six months.
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Hello everyone! I have some sample work I'm working on and having trouble with, please help!
And please show your work ^^
|
|
|
v
Answer:
D: 286 [tex]in^{2}[/tex]
Step-by-step explanation:
[tex]\frac{1}{2}[/tex] * 5.5 * 13 = 35.75 (area of one triangle)
35.75 * 8 = 286 (area of entire octagon)
Nadia says the hypotenuse of this right triangle has a length of 73 because the Pythagorean theorem states that (28+45)^2=73^2.Which best describes Nadia’s solution?
She is correct because she applied the Pythagorean theorem properly and her arithmetic is accurate.
She is incorrect because she should have used 45 as the length of the hypotenuse.
She is incorrect because she should have squared each leg length and then found the sum.
She is correct because the hypotenuse is the longest side of the triangle.
Answer: She is incorrect because she should have squared each leg length and then found the sum.
The Pythagorean Theorem is a² + b² = c² not (a+b)²=c² as written.
Answer:
Answer is c)))
Depth d (in feet) of a river can be modeled by the equation d=−0.25t2+1.7t+3.5, where 0≤t≤7 and t is the time (in hours) after a heavy rain begins. When is the river 6 feet deep?
Answer:
The river is 6 feet at two times, 2.15 hours after the rain and 4.65 hours after the rain.
Step-by-step explanation:
We are given the following in the question:
[tex]d=-0.25t^2+1.7t+3.5[/tex]
[tex]0\leq t\leq 7[/tex]
where, d is the depth of river in feet and t is time in hours after a heavy rain.
We have to find the number of hours for which the depth of river is 6 feet.
Putting d = 6 in the equation, we get,
[tex]6=-0.25t^2+1.7t+3.5\\\Rightarrow +0.25t^2-1.7t+2.5 = 0\\\text{Using quadratic formula}\\\\\Rightarrow t = \dfrac{1.7\pm \sqrt{(-1.7)^2-4(0.25)(2.5)}}{2(0.25)}\\\\t\approx 4.65, 2.15[/tex]
Thus, the river is 6 feet at two times, 2.115 hours after the rain and 4.65 hours after the rain.
The attached image shows the graph.
Which inequality is true when x = 4
A. x + 5 < 3
B. 9x > 36
C. ×/2 < 3
D. 18 < x + 8
Answer:
A
Step-by-step explanation:
One inequality could be x > 3. So when x = 4 this is true because 4 is greater than 3.
The solution is Option C.
The value of the inequality equation x/2 < 3 is true when x = 4
What is an Inequality Equation?
Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the inequality equation be represented as A
Now , the value of A is
a)
Let the inequality equation be
x + 5 < 3
when the value of x = 4
Substitute the value of x as 4 in the equation , we get
4 + 5 < 3
9 < 3 is not true
b)
Let the inequality equation be
9x > 36
when the value of x = 4
Substitute the value of x as 4 in the equation , we get
36 > 36
36 > 36 is not true
c)
Let the inequality equation be
x/2 < 3
when the value of x = 4
Substitute the value of x as 4 in the equation , we get
4/2 < 3
2 < 3 is true
d)
Let the inequality equation be
18 < x + 8
when the value of x = 4
Substitute the value of x as 4 in the equation , we get
18 < 4 + 8
18 < 12 is not true
Hence , the inequality equation is x/2 < 3 when x = 4
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Jalen is computing the slope of a line on the graph below. Which statement describes Jalens error?
Jalen computed the raitio in e to change in y
Jalen use the ordered pairs in the wrong order
Jalen made a computational error
Jalen used an ordered pair that is not on the line
Answer:
A
Step-by-step explanation:
Have a nice day everyone
The slope value calculated by Jalen is not correct. Jalen has used the ordered pairs in the wrong order.
What is the point slope form of a line ?
Point slope form is used to represent a straight line using its slope and a point on the line.
It is given that Jalen is computing the slope of a line.
We know that the equation of a line in point slope form is given by :
(y - y1) = m (x - x1).
As per the computation done by Jalen ordered pairs are (-4, 0) and (2, 3).
For the line : (x , y) = (4 , 0) and (x1 , y1) = (2 , 3).
So ,
Slope will be equal to :
m = (y - y1) / (x - x1)
m = (0 - 3) / (4 - 2)
m = -3 / 2
So , the slope calculated by Jalen is not correct as he has used the ordered pairs in the wrong order.
Therefore , the slope value calculated by Jalen is not correct. Jalen has used the ordered pairs in the wrong order.
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Researchers are studying two populations of sea turtles. In population D, 30 percent of the turtles have a shell length greater than 2 feet. In population E, 20 percent of the turtles have a shell length greater than 2 feet. From a random sample of 40 turtles selected from D, 15 had a shell length greater than 2 feet. From a random sample of 60 turtles selected from E, 11 had a shell length greater than 2 feet. Let pˆD represent the sample proportion for D, and let pˆE represent the sample proportion for E.
(a) What is the value of the difference pˆD−pˆE? Show your work.
Answer:
[tex]p^D-p^E=0.192[/tex]
Step-by-step explanation:
We are given the following in the question:
Population D:
30% of the turtles have a shell length greater than 2 feet.
Sample size,
[tex]n_D = 40[/tex]
Number of turtles that had shell length greater than 2 feet,
[tex]x_D = 15[/tex]
Sample proportion:
[tex]p^D=\dfrac{x_D}{n_D} =\dfrac{15}{40} = 0.375[/tex]
Population E:
20% of the turtles have a shell length greater than 2 feet.
Sample size,
[tex]n_E = 60[/tex]
Number of turtles that had shell length greater than 2 feet,
[tex]x_E = 11[/tex]
Sample proportion:
[tex]p^E=\dfrac{x_E}{n_E} =\dfrac{11}{60} = 0.183[/tex]
We have to find the difference between the sample proportion.
Difference in sample proportion =
[tex]=p^D-p^E\\=0.375-0.183\\=0.192[/tex]