Using the normal distribution and the central limit theorem, it is found that the sample of 36 Great Basin rattlesnakes is more likely to be shorter than 29.65 inches.
Normal Probability DistributionIn a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For the Sample of 36 Great Basin rattlesnakes:
The mean is [tex]\mu = 32.3[/tex].The standard deviation is [tex]\sigma = 5.3[/tex].Sample of 36, hence [tex]n = 36, s = \frac{5.3}{\sqrt{36}} = 0.88[/tex]We are interested in the percentile of 29.65 inches, hence [tex]X = 29.65[/tex].Then:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{29.65 - 32.3}{0.88}[/tex]
[tex]Z = -3.01[/tex]
For the Sample of 100 Southern Pacific rattlesnakes:
The mean is [tex]\mu = 32.3[/tex].The standard deviation is [tex]\sigma = 7.95[/tex].Sample of 100, hence [tex]n = 100, s = \frac{7.95}{\sqrt{100}} = 0.795[/tex]We are interested in the percentile of 29.65 inches, hence [tex]X = 29.65[/tex].Then:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{29.65 - 32.2}{0.795}[/tex]
[tex]Z = -3.33[/tex]
Due to the higher z-score, the random sample of 36 Great Basin rattlesnakes is at a higher percentile, hence it is more likely to be shorter than 29.65 inches,
To learn more about the normal distribution and the central limit theorem, you can take a look at https://brainly.com/question/24663213
simplify 4x-7y-5n+6 .
Answer:
The answer is -5n + 4x - 7y + 6
Step-by-step explanation:
Simplify the expression.
Hoped this helped!
Brainly, Please?
write the equation of the line that is parallel to y=4x-1 and passes through the point (4.9)
9514 1404 393
Answer:
y = 4x -7
Step-by-step explanation:
Rearranging the slope-intercept for equation, we can find the intercept:
y = mx +b
y -mx = b . . . . . subtract mx
We know the slope of the parallel line is the same as that of the given line (m=4), so we only need to find 'b'.
b = 9 -4(4) = -7
The desired equation is ...
y = mx +b
y = 4x -7
find the value of each variable in the parallelogram
Answer:
1. x = 15°
2. y = 12
Step-by-step explanation:
1. Determination of the value of x.
(5x – 5) + 110 = 180 (Adjacent angles add up to 180)
5x – 5 + 110 = 180
5x + 105 = 180
Collect like terms
5x = 180 – 105
5x = 75
Divide both side by 5
x = 75/5
x = 15°
2. Determination of the value of y.
3y – 4 = 2y + 8 (opposite sides are equal)
3y – 4 = 2y + 8
Collect like terms
3y – 2y = 8 + 4
y = 12
convert 135 degrees into radians
Answer:
135° = 2.355 radStep-by-step explanation:
π rad = 180°1° = π/180 rad135° = 135π/180° rad135° = 135*3.14/180 rad135° = 2.355 radWhich of the following is the smallest element in the set of natural numbers?
-1
O 1
There is no smallest element; the set is infinite.
0
Answer:
your answer would be 0 mark as brainliest
The functions f(x) and m(x) are graphed below. If m(x) = f(x) + k, what is the value of k
Answer:
k = m(x) - f(x)
Step-by-step explanation:
m(x) = f(x) +k
m(x) - f(x) = k
In a statistics class, 10 scores were randomly selected with the following results: 74, 73, 77, 77, 71, 68, 65, 77, 67, 66. What are the lower and upper limits of a box-and-whiskers display of this data
Answer:
[tex]L =52[/tex] --- Lower Limit
[tex]U =82[/tex] --- Upper Limit
Step-by-step explanation:
Given
[tex]N = 10[/tex]
[tex]Data: 74, 73, 77, 77, 71, 68, 65, 77, 67, 66[/tex]
Required
Determine the lower and upper limits of box and whisker display
First, arrange the data in ascending order
The sorted data is:
[tex]Data: 65, 66, 67, 68, 71, 73, 74, 77, 77, 77[/tex]
The lower limit (L) is calculated using:
[tex]L = Q_1 - 1.5 * (Q_3-Q_1)[/tex]
The upper limit (U) is calculated using:
[tex]U =Q_3 + 1.5 * (Q_3-Q_1)[/tex]
Q1 is calculated using:
[tex]Q_1 = \frac{1}{4}(N+1)[/tex]
[tex]Q_1 = \frac{1}{4}(10+1) = 2.75 = 3rd\ data[/tex]
[tex]Q_1 = 67[/tex]
Q3 is calculated using:
[tex]Q_3 = \frac{3}{4}(N+1)[/tex]
[tex]Q_3 = \frac{3}{4}(10+1) = 8.25= 8th\ data[/tex]
[tex]Q_3 = 77[/tex]
So:
[tex]L = Q_1 - 1.5 * (Q_3-Q_1)[/tex]
[tex]L =67 - 1.5*(77-67)[/tex]
[tex]L =67 - 1.5*10[/tex]
[tex]L =67 - 15[/tex]
[tex]L =52[/tex]
[tex]U =Q_3 + 1.5 * (Q_3-Q_1)[/tex]
[tex]U =67 + 1.5*(77-67)[/tex]
[tex]U =67 + 1.5*10[/tex]
[tex]U =67 + 15[/tex]
[tex]U =82[/tex]
Pls HELP I BEG YOUUUU
Answer:
x = 60
Step-by-step explanation:
(x+22) + (x+6) + (x-28) = 180
x + 22 + x + 6 + x - 28 = 180
x + x + x + 22 + 6 - 28 = 180
3x = 180
x = 180/3
x = 60
Marilyn buys pens that cost $12 per dozen. What is the cost of one pen?
$12.00
$24.00
$1.00
$1.20
Find the slope of the line below. Help please!
Answer:
-3/2
Step-by-step explanation:
go up 3 and left 2
In the pet show, 3/8 of the pets are dogs. Of the dogs, 2/3 have long hair. What fraction of the pets are dogs with long hair?
NEED NOW I WILL GIVE YOU BRAINLISET
The perimeter of the square is 36. What is the length of the diagonal, x? HELPNPLZ FOR THE LOVE OF GOD
Answer:
D. [tex] 9 \sqrt{2} [/tex]
Step-by-step explanation:
Side length of square = Perimeter/4 = 36/4 = 9
Length of diagonal (x)
[tex] = length \: of \: side \sqrt{2} \\ \\ = 9 \sqrt{2} [/tex]
Here is a rectangle
7 cm
3 cm
Nor drawn
accurately
A square has the same perimeter as the rectangle.
What is the side length of this square?
Answer:
a square and rectangle have the same perimeter. the length of the rectangle is 4 cm less than twice the side of the square, and the width of the rectangle is 6 cm less than the side of the square.
Step-by-step explanation:
jayfeather friend me
The required side length of the square is 5 cm.
What is rectangle?A rectangle is a part of a quadrilateral, whose sides are parallel to each other and equal.
Given that,
Length of rectangle = 7 cm,
Width of rectangle = 3 cm.
The perimeter of rectangle = 2(length + width)
= 2(7 + 3)
= 2 x 10
= 20
Also, given that the perimeter of the rectangle is equal to the perimeter of a square,
Let side of square is a then perimeter = 4a
⇒ 4a = 20
⇒ a = 5
The side length of the square is 5 cm.
To know more about Rectangle on:
https://brainly.com/question/15019502
#SPJ2
Solve for x
-14 + 6b + 7 - 2b = 1 + 5b
b = -8
Hope I helped!!!!!!
A college admits a freshman class of 330 students at the beginning of each academic year and graduates 145 students twice a year. What will be the net change in student population after 5 years?
Answer:
200 studentsStep-by-step explanation:
Change in one year:
330 - 2(145) = 330 - 290 = 40Change after 5 years:
40*5 = 200 studentsWhat is 674.649 rounded to the nearest tenth
Answer:
674.6
Step-by-step explanation:
If the hundreths place is 4 or less, then you stay the same in the tenths place, if it is 5 or more, you go up 1 in the tenths place
Can you help if your are eligible to?
What is the distance between the two points? Use
the distance formula:
d= V(x2 – «1)? + (y2 – yı)?
Answer:
[tex]d= 3.61\ units[/tex]
Step-by-step explanation:
The points (missing) from the question are:
-2,1 and -5,3
Required
Evaluate [tex]d= \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2[/tex]
In the points given:
[tex](x_1,y_1) = (-2,1)[/tex] and [tex](x_2,y_2) = (-5,3)[/tex]
Substitute these values in [tex]d= \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2[/tex]
[tex]d= \sqrt{(-5 - (-2))^2 + (3 - 1)^2[/tex]
[tex]d= \sqrt{(-3)^2 + (2)^2[/tex]
[tex]d= \sqrt{9 + 4[/tex]
[tex]d= \sqrt{13[/tex]
[tex]d= 3.61\ units[/tex] -- approximated
A student has to buy graph paper and printer paper. The graph paper, x, costs $2, while the printer paper, y, costs $3. She wants to buy at least 8 packs of paper but wants to spend at most $23.
Enter a system of inequalities for the given situation and select the graph of the system. Then determine if the point (3, 6) is a solution to the system.
The system of inequalities is _______ and ______
The point (3, 6)____ a solution because it _______lie in the region shared by the two inequalities, and it ______ satisfies both inequalities.
Answer:
8+3+23
Step-by-step explanation:
How do I do problems like this????
Answer:
m<1 = 62°
m<2 = 45°
m<3 = 24°
Step-by-step explanation:
Hi!
Let me walk you through it!
The first step is to find angle 1.
Angle 1 is supplementary with the angle 118°
So we do 180° - 118° = 62°
m<1 = 62°
Then we find angle 2.
There are two ways to do this
The sum of interior angles in a triangle is 180°
So we do 180° - (73 + 62°)
Open parenthesis:
180° - 73° - 62° = 45°
You can also use the exterior angle theorem
118° = 73° + m<2
Same to both sides:
45° = m<2
So
m<2 = 45°
Now, using this information, we can find angle measure 3.
Now we look at the big triangle. Again, there are two ways to do this.
First way:
m<1 + 49° + m<2 + m<3 = 180°
Plug in known-values
62° + 49° + 45° + m<3 = 180°
Combine like terms:
156° + m<3 = 180°
Same to both sides:
m<3 = 24°
Second way:
Exterior angle theorem.
118° = m<2 + m<3 + 49°
Plug in known-values:
118° = 45° + m<3 +49°
Combine like terms:
118° = 94° + m<3
Same to both sides:
24° = m<3
So m<3 = 24°
There you go! You just need to take it step-by-step and you can get the answer. Be open-minded, don't just try to go for a certain angle, see what you can do, and work from there. It all comes together at the end.
Let me know if you have any questions, have a good day!
Please help!!!!
If f(1) = 2 and f(n+1) = f(n)^2 – 3 then find the value of f(3).
Answer:
The value of f(3) is -2.
Step-by-step explanation:
This is a recursive function. So
[tex]f(1) = 2[/tex]
Now, we find f(2) in function of f(1). So
[tex]f(1+1) = f(1)^2 - 3[/tex]
[tex]f(2) = f(1)^2 - 3 = 2^2 - 3 = 1[/tex]
Now, with f(2), we can find the value of f(3).
[tex]f(2+1) = f(2)^2 - 3[/tex]
[tex]f(3) = f(2)^2 - 3 = 1^2 - 3 = -2[/tex]
The value of f(3) is -2.
The price of lunch in the school cafeteria was 2.50$ last year this year the price is 2.70$. What is the percent increase
Answer:
8 percent
Step-by-step explanation:
There is an 8 percent increase, because if you do 20 cents divided by 250 cents, you get 0.08, which is 8 percent. Also to double check, you can do 250 * 1.08. By the way, that is some rip off lunch.
You are painting a room that is 16 feet long, 10 feet wide, and 8 feet high. On the walls of the room, there are two windows that are each 2 feet wide and 5 feet tall, and a door that is 4 feet wide and 7 feet tall. A gallon of paint covers 350 square feet. How many gallons of paint do you need to cover the 4 walls with one coat of paint, not including the windows and the door
You will need approximately 1.33 gallons of paint to cover the four walls with one coat, not including the windows and the door.
Given that,
Room dimensions:
Length: 16 feet
Width: 10 feet
Height: 8 feet
Features on the walls:
Two windows:
Width: 2 feet
Height: 5 feet
One door:
Width: 4 feet
Height: 7 feet
Paint coverage:
1 gallon of paint covers 350 square feet
Calculate the area of the walls first:
Subtract the area of the windows and door area from the total wall area.
The total wall area is the sum of the areas of all four walls.
The area of each wall is calculated by multiplying the height of the room by its length.
So, the area of each wall = 8 feet (height) x16 feet (length)
The area of each wall = 128 square feet.
Calculate the area of the windows and the door.
The area of each window is calculated by multiplying its width by its height.
So, the area of each window = 2 feet (width) x 5 feet (height)
The area of each window = 10 square feet.
The area of the door is calculated by multiplying its width by its height. So,
The area of the door = 4 feet (width) x 7 feet (height)
The area of the door = 28 square feet.
Now, subtract the total area of the windows and the door from the total wall area.
Total wall area = 4 walls x 128 square feet
Total wall area = 512 square feet
The total area of the windows = 2 windows x 10 square feet
The total area of the windows = 20 square feet
The total area of the door = 1 door x 28 square feet
The total area of the door = 28 square feet
Area to be painted = Total wall area - Total area of the windows - Total area of the door
Area to be painted = 512 square feet - 20 square feet - 28 square feet
Area to be painted = 464 square feet.
Now, we can determine the number of gallons of paint needed.
Since 1 gallon of paint covers 350 square feet,
Divide the area to be painted by 350.
The number of gallons of paint needed = Area to be painted / Coverage per gallon
The number of gallons of paint needed = 464 square feet / 350 square feet/gallon
The number of gallons of paint needed ≈ 1.33 gallons.
Hence, you will need approximately 1.33 gallons of paint to cover the four walls with one coat, not including the windows and the door.
To learn more about rectangles visit:
https://brainly.com/question/15019502
#SPJ4
Jeff invests $1000 in an account that pays 4.25% interest compounded monthly. How much will Jeff have in his account at the end of 4 years?
$1184.95
$1014.24
$5315.29
$1181.15
Answer:
1181.15
Step-by-step explanation:
i need help due tonight
Answer:
Y=6
Step-by-step explanation:
5(6)+1=31
30+1=31
Answer:
y=6
Step-by-step explanation:
5y+1=31
simplify
5y=30
divide both sides by 5
y=6
In XYZ right angled at Y. find the length of the hypotenuse if the length of the other two sides is 1.6 cm and 6.3 cm.
9514 1404 393
Answer:
6.5 cm
Step-by-step explanation:
The Pythagorean theorem applies. You want c for a=1.6, b=6.3.
c² = a² +b²
c² = 1.6² +6.3² = 2.56 +36.69 = 42.25
c = √42.25 = 6.5
The length of the hypotenuse is 6.5 cm.
The coordinate plane shows the graphs of two exponen functions which equation is true?
Answer:
A
Step-by-step explanation:
What operation should be done first to solve 6x + 5 = 35?
Answer:
Subtract 5
Step-by-step explanation:
Pemdas is done backwards in algebra
A cylinder has a base diameter of 6 centimeters and a height of 15 centimeters. What is its volume in cubic centimeters, to the nearest tenths place?
Please help
Step-by-step explanation:
V
≈
424.12
cm³
d
Diameter
cm
h
Height
cm
What is the formula you would use to find the area of a triangle? Explain how that formula is related to the area formula for a rectangle.
Answer:
1/2 b*h
Step-by-step explanation:
for rectangle it is b*h means double of that traingle
