Answer:
The standard error of the difference in the mean number of fish caught before and after the fire is 0.2153.
Step-by-step explanation:
Subtraction of normal variables:
When we subtract two normal variables, the standard deviation is the square root of the sum of variances of each variable.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Sample of 195 fishing reports before the fire, the mean catch was 6.3 fish with a standard deviation of 1.6.
The standard error for this sample is:
[tex]s_b = \frac{1.6}{\sqrt{195}} = 0.1246[/tex]
Sample of 143 reports three years after the fire, the mean catch was 7.1 fish with a standard deviation of 2.1.
The standard deviation for this sample is:
[tex]s_a = \frac{2.1}{\sqrt{143}} = 0.1756[/tex]
What represents the standard error of the difference in the mean number of fish caught before and after the fire?
[tex]s = \sqrt{s_a^2 + s_b^2} = \sqrt{0.1756^2 + 0.1246^2} = 0.2153[/tex]
The standard error of the difference in the mean number of fish caught before and after the fire is 0.2153.
Answer:
sqrt [ (1.6^2)/195 + (2.1^2)/143 ]
Simplify:
a) 3x + 5y - x + 2y
b)
3g + 5h + 4g - 2h
Answer:
[tex]\huge\boxed{a) 2x+7y}[/tex]
[tex]\huge\boxed{b) 7g+3h}[/tex]
Step-by-step explanation:
Part a:
= 3x + 5y - x + 2y
Combining like terms
= 3x - x + 5y + 2y
= 2x + 7y
Part b:
= 3g + 5h + 4g - 2h
Combining like terms
= 3g + 4g + 5h - 2h
= 7g + 3h
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807(8x + 11x) + (-7 - 18)
Answer:
19x - 25
steps:
(8x + 11x) + (-7 - 18)
19x + (-25)
positive x negative = negative
19x - 25
Answer:
19x - 25
Step-by-step explanation:
(8x + 11x) + (-7 - 18) <------- add the bold ones (combine like terms)...
19x + (-7 - 18) <--------------- subtract the bold ones...
(19x) - 25 <-------------------- eliminate parenthases
19x - 25 <--------------------- solution...
All the fourth-graders in a certain elementary school took a standardized test. A total of 82% of the students were found to be proficient in reading, 74% were found to be proficient in mathematics, and 65% were found to be proficient in both reading and mathematics.A student is chosen at random. What is the probability that the student is proficient in neither reading nor mathematics
Answer:
0.09 = 9% probability that the student is proficient in neither reading nor mathematics
Step-by-step explanation:
We solve this question treating the events as Venn probabilities.
I am going to say that:
Event A: A student is proficient in reading.
Event B: A student is proficient in mathematics.
A total of 82% of the students were found to be proficient in reading
This means that [tex]P(A) = 0.82[/tex]
74% were found to be proficient in mathematics
This means that [tex]P(B) = 0.74[/tex]
65% were found to be proficient in both reading and mathematics.
This means that [tex]P(A \cap B) = 0.65[/tex]
What is the probability that the student is proficient in neither reading nor mathematics?
This is:
[tex]P = 1 - P(A \cup B)[/tex]
In which
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]
With the values that we have:
[tex]P(A \cup B) = 0.82 + 0.74 - 0.65 = 0.91[/tex]
Then
[tex]P = 1 - P(A \cup B) = 1 - 0.91 = 0.09[/tex]
0.09 = 9% probability that the student is proficient in neither reading nor mathematics
Helppppppppppppppppp
Answer:
3. y = -⅕x - 5
Step-by-step explanation:
The equation of straight line is given by the formula, y = mx + c
Where;
m is the slope.
x and y are the points.
c is the intercept.
Given the standard form equation;
x + 5y = -25
Rearranging the equation, we have;
5y = -x - 25
Dividing all through by 5, we have;
y = -⅕x - 5
What is the value of x in the equation shown? -4 = 5x + 3 A) -3 4/5.
B) -1 2/5
C) 1/5
D) 1 2/5
Answer:
B
Step-by-step explanation:
Please help me with this
WILL GIVE BRAINLIST PLS HELP Find z. Just write the number. Answer should be a whole number.
Answer:
8
Step by Step Explanation
Answer and Step-by-step explanation:
To find Z, we have to use the trigonometric function of Sine.
The Sine trig function looks like this:
sin(Angle) = [tex]= \frac{opposite.side}{hypotenuse}[/tex]
Plug in the values and solve for z.
[tex]sin(30) = \frac{4}{z} \\\\\\\\\\z = \frac{4}{sin(30)}[/tex]
Plug into a calculator and solve.
We get z to be 8.
#teamtrees #PAW (Plant And Water)
Find the volumes of the solids generated by revolving the regions bounded by the graphs of the equations about the given lines.
y = root x
y = 0
x = 3
the x-axis
the y-axis
the line x = 3
the line x = 6
Answer:
x-axis = [tex]\frac{9\pi }{2}[/tex]
y-axis = [tex]\frac{4\pi }{5} .3(^{\frac{5}{2} } )[/tex]
Line x =3 : [tex]\frac{44\sqrt{3} }{5} \pi[/tex]
Line x = 6 : [tex]\frac{84\sqrt{3}\pi }{5}[/tex]
Step-by-step explanation:
Given lines : y = √x
y = 0
x = 3
To determine the volumes generated we will use the disk method for each of the lines,
attached below is the detailed solution for line x =3 , same procedure will be repeated for each value of x and y to obtain the given results
The volume generated ( x axis )
= [tex]\frac{9\pi }{2}[/tex]
volume generated ( y _axis )
= [tex]\frac{4\pi }{5} .3(^{\frac{5}{2} } )[/tex]
Volume about x = 3
= [tex]\frac{44\sqrt{3}\pi }{5}[/tex]
Volume about x = 6
= [tex]\frac{84\sqrt{3}\pi }{5}[/tex]
What is m∠1?
There is a horizontal line. Point B and D are lies on the line. There is one point C which is joined with point B and D to form a triangle CBD. The angle BCD is 70 degree. The angle CBD is denoted by 2. The supplementary angle of 2 is denoted by angle 1 which is line formed with segment BC. The line formed obtuse angle with CD is 130 degree.
A. 130°
B. 70°
C. 60°
D. 120°
Answer:
i think b
Step-by-step explanation:
What is the product of (x - 5) and (x - 4)? Use the model to find the result.
Answer:
x2 - 9x +20
Step-by-step explanation:
Please help me with this
73
Step-by-step explanation:
I think that this is an isosceles triangle, and like since ST=SR
Therefore, m(<T) = m(<R)= 73
I’ve been at these questions all day. Please help
Answer:
தமிழ்நாட்டில் உள்ள நெல் வகைகளை குறிப்பிட்டு எழுதுக
Answer:
How does the novel "In Cold Blood" address the question of responsibility regarding the Clutter murders?
PLEASE HELP ASAP!!!!
60 divided by 4 - 3^2 + 2 (5)
Answer:
16
Step-by-step explanation:
Answer:
16
Step-by-step explanation:
First Step: Solve the exponent 3^2=9
Then, you get 60 divided by 4-9+2(5)
Then, you do Multiplication and Division from left to right, so 60/4=15, 2(5)=10
Then, you get 15-9+10
Then, you do addition and subtraction from left to right.
15-9=6, then 6+10=16
If a pizza pie had
a diameter of 12
inches, what
would be its
circumference?
Answer:
37.7 inches
Step-by-step explanation:
Formula of circumference:
[tex]2\pi r[/tex]
r = radius
In the current case,
radius is 6 inches
Hence,
circumference=
[tex]2*\pi *6\\= 12\pi\\= 37.6991118431[/tex]
≅ 37.7 inches
Feel free to mark it as brainliest
I NEED HELP ASAP!!!!!!!!!
Answer:
a=81.0
there ya go
giving brainliest *easy*
WHAT'S 675 DIVIDED BY 8 HELPPPP PLEASE TELL ME THE NUMBERS TO SHOW MY WORK
Answer:
85.625 is the answer
Step-by-step explanation:
or, 85 whole 5/675
Yoonie is a personnel manager in a large corporation. Each month she must review 16 of the employees. From past experience, she has found that the reviews take her approximately four hours each to do with a population standard deviation of 1.2 hours. Let X be the random variable representing the time it takes her to complete one review. Assume X is normally distributed. Let X be the random variable representing the mean time to complete the 16 reviews. Assume that the 16 reviews represent a random set of reviews. Complete the distributions.
A. Find the probability that the mean of a month’s reviews will take Yoonie from 3.5 to 4.25 hrs.
B. P(_____) = _______.
C. Find the 95th percentile for the mean time to complete one month's reviews.
D.The 95th Percentile =________.
Answer:
a) [tex]P(3.5 \leq X \leq 4.25) = 0.7492[/tex]
b) The 95th percentile is 4.4935 hours.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score 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. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
The reviews take her approximately four hours each to do with a population standard deviation of 1.2 hours.
This means that [tex]\mu = 4, \sigma = 1.2[/tex]
16 reviews.
This means that [tex]n = 16, s = \frac{1.2}{\sqrt{16}} = 0.3[/tex]
A. Find the probability that the mean of a month’s reviews will take Yoonie from 3.5 to 4.25 hrs.
This is the pvalue of Z when X = 4.25 subtracted by the pvalue of Z when X = 3.5. So
X = 4.25
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{4.25 - 4}{0.3}[/tex]
[tex]Z = 0.83[/tex]
[tex]Z = 0.83[/tex] has a pvalue of 0.7967
X = 3.5
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{3.5 - 4}{0.3}[/tex]
[tex]Z = -1.67[/tex]
[tex]Z = -1.67[/tex] has a pvalue of 0.0475
0.7967 - 0.0475 = 0.7492
So
[tex]P(3.5 \leq X \leq 4.25) = 0.7492[/tex]
C. Find the 95th percentile for the mean time to complete one month's reviews.
This is X when Z has a pvalue of 0.95, so X when Z = 1.645.
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]1.645 = \frac{X - 4}{0.3}[/tex]
[tex]X - 4 = 0.3*1.645[/tex]
[tex]X = 4.4935[/tex]
The 95th percentile is 4.4935 hours.
Enter an algebraic expression that represents the product of r cubed and one hundred seven.
Answer:
107r³
Step-by-step explanation:
Try solving it using
An algebraic expression that represents the product of r cubed and one hundred seven is 107r³.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
We are given that represents the product of r cubed and one hundred seven.
Therefore, an algebraic expression that represents the situation
r cubed = r³
one hundred seven = 107
Thus, it would be;
107r³
Hence, an algebraic expression that represents the product of r cubed and one hundred seven is 107r³.
To know more about an expression follow;
brainly.com/question/19876186
#SPJ5
A football team has 5 freshman, 8 sophomores, 11 juniors, and 16 seniors. If two are chosen at random to participate in the coin toss, what is the probability that both players chosen will be seniors?
Answer:
The probability percentage that both players will be seniors is 15.38%.
Step-by-step explanation:
Given that a football team has 5 freshman, 8 sophomores, 11 juniors, and 16 seniors, if two are chosen at random to participate in the coin toss, to determine what is the probability that both players chosen will be seniors the following calculation must be done:
5 + 8 + 11 + 16 = 40
16/40 = X
4/10 = X
0.4 = X
15/39 = X
5/13 = X
0.38 = X
0.4 x 0.38 = X
0.1538 = X
Thus, the probability percentage that both players will be seniors is 15.38%.
Pete painted 4/5 of a rectangle green. He painted 1/8 of the same rectangle blue. Pete painted the rest the rectangle red. What fraction of the rectangle did Pete paint red? please explain!
Answer:
Step-by-zbastep explanation:
Show that sin( + 180°) + 2 cos( − 360°) − sin( − 180°) = 2x
Answer:
Example 1: Change sin 80° cos 130° + cos 80° sin 130° into a trigonometric function in ... Example 2: Verify that cos (180° − x) = − cos x ... Example 7: Verify that sin (360° − x) = − sin x.
Plzzz someone help me
as a medical technician, Stephanie has been offered a job that pays $53 000.00 per year and another job that pays $25.50 per hour. assuming a 40 hour work week and all other conditions being the same, at which job will she earn more?
Answer:
25.50x40= 1020/ week
times 52 weeks- $53040
can yall help please
Step-by-step explanation:
I think your answer will be 15
What is the distance between (-2, -3) and (-4, 3)? Use the distance formula and show your work.
Answer:
D = 6.32
Step-by-step explanation:
-2 to -4 = 2
-3 to 3 = 6
D² = 2² + 6²
D² = 4 + 36 = 40
D = 6.32
Write each product using an exponent. 9 x 9 x 9 x 9 x9
(Will be giving brainliest)
Answer: 9^ 5
Step-by-step explanation: since there is 5 9’s multiplied by each other, it would be 9 to the 5th power.
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathtt{9\times9\times9\times9\times9}\\\mathtt{= 81\times 81\times9}\\\mathtt{= 6,561\times9}\\\mathtt{= 59,049}\\\mathtt{= 9\times 9\times 9 \times 9 \times 9 \rightarrow 9^5}[/tex]
[tex]\huge\text{Therefore your answer should be:}[/tex]
[tex]\huge\boxed{\mathtt{9^5}}\huge\checkmark[/tex]
[tex]\huge\boxed{\mathtt{Good \ luck \ on \ your \ assignment\ \& \ enjoy}}\\\huge\boxed{\mathtt{your \ day!}}[/tex]
Jordyn is weighing the ingredients on a kitchen scale to make bread. The bowl weighs 1 1/2 pounds. He adds several scoops of flour. the total weight of the bowl and the flour is 2 3/4pounds. If each cup weighs 5/16 pound, how many cups of flour does he add?
Answer: 4 pounds of flour
Step-by-step explanation:
(9z+7) whats the value of z
Answer:
-0.78
Step-by-step explanation:
9z+7
9z = -7
z = -7÷9
z = -0.78