Answer:
[tex]\sin(\theta_1) =\frac{\sqrt{55} }{8}[/tex]
Step-by-step explanation:
The angle [tex]\theta_1[/tex] is located in Quadrant I and [tex]\cos(\theta_1)=\frac{3}{8}[/tex]
From Trigonometric ratio, In the First Quadrant
[tex]\cos \theta=\frac{Adjacent}{hypotenuse}[/tex]
Adjacent =3, Hypotenuse =8
Using Pythagoras Theorem
[tex]Hypotenuse^2=Opposite^2+Adjacent^2\\8^2=Opposite^2+3^2\\Opposite^2=64-9=55\\Opposite=\sqrt{55}[/tex]
Therefore:
[tex]\sin(\theta_1)=\frac{Opposite}{Hypotenuse}\\\sin(\theta_1) =\frac{\sqrt{55} }{8}[/tex]
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)))
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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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
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.
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.
A smartphone costs $280. sales tax is 5%. What is the total cost,including tax?
Answer:
$294
Step-by-step explanation:
1 is equivalent to 100% which would mean .05 is equivalent to 5%.
Therefore, multiply the base cost by 1.05 to find the total cost.
$280 x 1.05 = $294
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]30% of 750 using an table
Answer:
225
Step-by-step explanation:
30%×750 = 30×750/100 = 3×75 = 225
Answer:
525
Step-by-step explanation:
10%= 75 (750 divided by 10)
30%= 225 (75 x 3)
750-225= 525
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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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.
carmen weight 96 pound. Her sister weighs 29 pounds less than carmen.together they weigh 33 pounds less than their dad. how much does carmen sister weight
Answer:
Their dads weight is not important don't body shame him peeps. 96-29=67, therefore that is how much she weighs, leaving out the unnecessary info.
Step-by-step explanation:
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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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.
. You and your friend are playing the following game: two dice are rolled; if the total showing is
divisible by 3, you pay your friend $6. How much should he pay you when the total is not divisible
by 3 if you want to make the game fair? A fair game is one in which your expected winnings are
$0.
Answer:
3$
Step-by-step explanation:
Because every 3 numbers are divisble by 3 and the other 2 are not. Then the chance of you winning is 66%, therefore he should pay you half of what he would make. If this makes sense.
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:
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.
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.
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
The data obtained from a random sample of track athletes showed that as the foot size of the athlete decreased, the average running speed decreased. Which statement is best supported by the data?Immersive Reader
Answer:
The correct option is;
(3) The sample of track athletes show that there is a correlation between foot size and running speed
Step-by-step explanation:
The statements are analysed as follows;
(1) Smaller foot sizes cause track athletes to run slower.
The above statement is a conclusion and it infers more information than is contained in the question statement because there are other factors such as taller athletes run faster than average sized athletes
(2) The sample of track athletes shows a causal relationship between
foot size and running speed.
The above statement is similar to the one above as it is a milder conclusion and it infers more information than is contained in the question statement
(3) The sample of track athletes shows a correlation between foot size
and running speed.
The above statement is correct as is directly supported by the data as it is a statement made based directly the data
(4) There is no correlation between foot size and running speed in
track athletes.
The above statement is not supported by the available data.
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
Which table of ordered pairs represents a proportinal relationship
Answer:
where are the tables lol
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.
What is the measure of
Answer:
A: 28
Explanation:
Vertical angles are congruent.
Answer:
The answer would be 28% because the angles are vertical, which also makes them congruent. Congruent angles have the same angle measure.
A phone company offers two monthly plans. Plan A costs $9 plus an additional $0.17 for each minute of calls. Plan B costs$25 plus an additional $0.15 for each minute of calls. For what amount of calling do the two plans cost the same?
Answer:
800 minutes
Step-by-step explanation:
Make 2 expressions, one for Plan A, and one for Plan B
Plan A:
$9, and 0.17 per minute
9+0.17x
Plan B:
$25, and 0.15 per minute
25+0.15x
We want to find when they are the same, so we can set them equal to each other
9+0.17x=25+0.15x
Solve by isolating the variable, x
Subtract 9 from both sides
0.17x=16+0.15x
Subtract 0.15x from both sides
0.02x=16
Divide both sides by 0.02
x=800
At 800 minutes they will cost the same
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.Calculate the area of this triangle.
13 cm
5 cm
-12 cm-
Answer:
30 cm^2.
Step-by-step explanation:
This is a right angled triangle because it fits the Pythagoras theorem ( 13^2 = 12^2 + 5^2).
The area = 1/2 * 12 * 5
= 30 cm^2.
Find the solution
2cos2x-2cosx=0
Answer:
x = 0, 2π/3, 4π/3
Step-by-step explanation:
2 cos(2x) − 2 cos x = 0
Use double angle formula.
2 (2 cos²x − 1) − 2 cos x = 0
Simplify.
4 cos²x − 2 − 2 cos x = 0
2 cos²x − 1 − cos x = 0
2 cos²x − cos x − 1 = 0
Factor.
(cos x − 1) (2 cos x + 1) = 0
Solve.
cos x = 1 or -½
x = 0, 2π/3, 4π/3
To solve this problem, we have to use trigonometric function in which we can use some trigonometric equations on this. The solutions to this equation is
[tex]\pi , \frac{\pi}{3}, \frac{5\pi}{3}[/tex]
Trigonometric FunctionsWe would apply a simple mathematical rule here;
[tex]a(b+c)=ab+ac[/tex]
Let's substitute our functions and solve
[tex]2cos(2x)+2cosx=0\\2(2cos^2x-1)+2cosx=0\\4cos^2x-2+2cosx=0\\2cos^2x+cosx-1=0\\2cos^2x=2cosx-cosx-1=0\\2cos^2x+cosx-1=0\\[/tex]
We can solve the quadratic equation and get a solution to this problem.
[tex](cosx+1)(2cosx-1)=0[/tex]
Using factorization method,
[tex]cosx+1 = 0\\cosx = -1\\x = cos^-^1(-1)\\x = \pi[/tex]
The second solution is
[tex]2cosx-1=0\\2cosx=1\\cosx=\frac{1}{2} \\x = cos^-^1(\frac{1}{2} \\x = \frac{\pi}{3}, \frac{5\pi}{3}[/tex]
From the above calculations, the solutions to this equation is
[tex]\pi , \frac{\pi}{3}, \frac{5\pi}{3}[/tex]
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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.
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.
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]