Answer:
a) 0.0038 = 0.38% probability that the mean weight of the sample is less than 5.97 ounces.
b) Given a mean of 6.05 ounces, it is very unlikely that a sample mean of less than 5.97 ounces, which means that the true mean must be recalculated.
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 z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes 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.
Mean of 6.05 ounces and a standard deviation of .18 ounces.
This means that [tex]\mu = 6.05, \sigma = 0.18[/tex]
Sample of 36:
This means that [tex]n = 36, s = \frac{0.18}{\sqrt{36}} = 0.03[/tex]
a. Find the probability that the mean weight of the sample is less than 5.97 ounces.
This is the p-value of z when X = 5.97. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{5.97 - 6.05}{0.03}[/tex]
[tex]Z = -2.67[/tex]
[tex]Z = -2.67[/tex] has a p-value of 0.0038.
0.0038 = 0.38% probability that the mean weight of the sample is less than 5.97 ounces.
b. Suppose your random sample of 36 cans of salmon produced a mean weight that is less than 5.97 ounces. Comment on the statement made by the manufacturer.
Given a mean of 6.05 ounces, it is very unlikely that a sample mean of less than 5.97 ounces, which means that the true mean must be recalculated.
What is the ratio of the area of the inner square to the area of the outer square?
Answer:
Step-by-step explanation:
If we are looking for the ratio of the area of the inner square to the area of the outer square, that means that we need the areas of each of these squares, and we need to find the areas without any numbers. But that's ok; the answer they want is not a number answer. The answer will have a's and b's in it instead of numbers.
First the area of the inner square. Here we go:
Look at the triangle in the lower left corner of this coordinate plane. It is a right triangle. The height of it is b. That's because the height is a "y" thing and the y-coordinates of each of those sets of coordinates is b and 0. The height is then b - 0 = b.
The length of the base is a - b. That's because the length is an "x" thing and the x-coordinates of each of those sets of coordinates is (a - b) and 0. The length is then a - b - 0 = a - b.
Now we need the length of the hypotenuse which also serves as one of the sides of the inner square. Using Pythagorean's Theorem, we can find the length of the hypotenuse, which I will label as "?":
[tex]?^2=b^2+(a-b)^2[/tex] and
[tex]?^2=b^2+a^2-2ab+b^2[/tex] and
[tex]?^2=a^2-2ab+2b^2[/tex] so
?, the length of the hypotenuse, is
[tex]?=\sqrt{a^2-2ab+2b^2}[/tex] and now we can use that to find the area of the inner square. The formula for a square's area is
[tex]A=s^2[/tex] so
[tex]A=(\sqrt{a^_2}-2ab+2b^2})^2[/tex] which gives us finally:
[tex]A=a^2-2ab+2b^2[/tex] **
Now for the outer square. Those blue triangles you see are all congruent. We can use the side lengths for the triangles we found above to find the length of a side of the outer square. One side of the outer square is made up of one base length of these triangles and one height. We found the base length to be (a - b) and the height to be b; therefore, the length of one side of the outer square is b + (a - b) which is just "a". That's is, just a length of "a". The area is found by multiplying this side length by itself, so the area of the outer square is
A = a²
The ratio of the area of the inner to the outer is:
[tex]\frac{A_i}{A_o}:\frac{a^2-2ab+2b^2}{a^2}[/tex] and that does not reduce.
Answer:
A
Step-by-step explanation:
Edmentum
Please I need a step by step explanation ASAP.
Calculate the perimeter and area of the shape below:
Answer:
38.6 cm
Step-by-step explanation:
add all of the sides up to get your perimeter
In the picture the exponent says 5/3
Answer:
the answer is B
Step-by-step explanation:
[tex] {{ (- 2)}^{3}}^{5 \div 3} = { ( - 2)}^{5} = - 32[/tex]
write -8 form of 2 on up and complete other steps
Find x on this triangle
Answer:
3 sqrt(3) =x
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos theta = adj / hyp
cos 30 = x/6
6 cos 30 = x
6 ( sqrt(3)/2) = x
3 sqrt(3) =x
If you have two six sided die each labelled one throgh six. Which set of independent events has a higher probability?
Answer : Four sides (1, 2, 3, 4) are less than 5. The probability is 4 out of 6, or 2/3 or 0.6667.
The solution is, the correct answer is B. comparing all the probabilities, the set of independent events with the highest probability is the event of You land on an odd number or you roll a 6.
What is probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
here, we have,
We will consider all the sets of probabilities, the one with the highest probability is the right answer.
a) You roll an odd number and roll a 5: the probability is calculated thus:
1/6 * 3/6
=0.0833
b) You land on an odd number or you roll a 6: the probability is calculated thus:
3/6 +1/6
= 0.6667
c) You roll a six and roll a 4: the probability is calculated thus:
1/6 * 1/4
= 0.0417
d) You roll a 3 and roll an old number: the probability is calculated thus:
1/6 * 3/6
=0.0833
Now, comparing all the probabilities, the set of independent events with the highest probability is the event of You land on an odd number or you roll a 6.
Therefore the correct answer is B.
To learn more on probability click:
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If there is a 65% chance you will make a free throw, what percent of the
time you will miss? *
Given:
There is a 65% chance you will make a free throw.
To find:
The percent of the time you will miss.
Solution:
If p is the percent of success and q is the percent of failure, then
[tex]p+q=100\%[/tex]
[tex]q=100\%-p[/tex] ...(i)
It is given that there is a 65% chance you will make a free throw. It means the percent of success is 65%. We need to find the percent of the time you will miss. It means we have to find the percent of failure.
Substituting p=65% in (i), we get
[tex]q=100\%-65\%[/tex]
[tex]q=35\%[/tex]
Therefore, there is a 35% chance you will miss the free throw.
(a+b)^2 hihhhhhhhhhhhhhhhhhhhh
Answer:
a^2 + 2ab + b^2
Answered by Gauthmath
Select the correct answer.
Simplify the following expression. Classify the resulting polynomial.
3x(x − 3) + (2x + 6)(-x − 3)
quadratic monomial
quadratic binomial
quadratic trinomial
linear binomial
Answer:
quadratic trinomial
Step-by-step explanation:
3x(x − 3) + (2x + 6)(-x − 3)
Distribute
3x^2 -9x + (2x + 6)(-x − 3)
FOIL
3x^2 -9x + -2x^2 -6x -6x -18
Combine like terms
x^2-21x-18
This has 3 terms so it is a trinomial
The highest power of x is 2 so it is quadratic
9514 1404 393
Answer:
x² -21x -18quadratic trinomialStep-by-step explanation:
Eliminating parentheses, we get ...
= (3x)(x) -(3x)(3) +(2x)(-x -3) +6(-x -3)
= 3x² -9x +(2x)(-x) +(2x)(-3) +(6)(-x) +(6)(-3)
= 3x² -9x -2x² -6x -6x -18
= x²(3 -2) +x(-9-6-6) -18
= x² -21x -18
The highest power is 2, so this is a quadratic.
There are 3 terms, so this is a trinomial.
HELP PLZ<3
An international company has 28,300 employees in one country. If this represents 34.1% of the company's employees, how many employees does it have in
total?
Round your answer to the nearest whole number.
Answer:
82991 employees
Step-by-step explanation:
One way to solve this would be to solve for 1% of the company's employees and use that value to solve for 100% (100%=the whole part, or the total). We know that
28300 = 34.1%
If we divide a number by itself, it turns into 1. Dividing both sides by 34.1, we get
829.912 = 1%
Then, we know that anything multiplied by 1 is equal to itself. We want to figure out 100%, or the whole part, so we can multiply both sides by 100 to get
100% = 82991
Use the sum of the first 10 terms to estimate the sum of the series summation n=1 to infinity 1/n^2.How good is this estimate?
Answer:
its perfectly correct you did good
can someone help me out with this question???
Answer:
a
Step-by-step explanation:
y _minus 7 equal 10.find y
Answer:
y=17
Step-by-step explanation:
y-7=10
transpose 7
y=10+7
y=17
Mikita is painting a spherical model of a human cell for a science fair. She uses 452.16 square inches of paint to evenly cover the outside of the cell with one coat of paint. What is the diameter of the cell model? (Use 3.14 for the value of π.)
6 in.
12 in.
24 in.
36 in.
Answer:
12
Step-by-step explanation:
Basically you have to divide 3.14 by 452.16 (the formula for area of circle is pi times r squared) and that will get you 144. The square root of 144 is 12 :)
WILL MAKE BRAINLIEST
Answer:
x=3
Step-by-step explanation:
The ratios need to be the same
AB CB
---------- = ----------
AD ED
3 x
----- = ---------
3+9 12
3 x
----- = ---------
12 12
X must equal 3
Find the area of the irregular figure. Round to the nearest hundredth.
Answer:
44.5 units squared
Step-by-step explanation:
First, separate the figure into two different shapes. You should get a rectangle and a triangle after doing this. Next, we'll work on the rectangle. Multiply 2 by 10, and you'll get the area of the rectangle, which would be 20 units squared. We can't multiply 3 by 2, as that would cause the triangle to have 4 sides rather than 3. A triangle can ONLY have 3 sides anyway, so always remember that. Next, we'll work on the triangle. Subtract 10 by 3, and you'll get 7. This will be the triangle's height, so the equation would be 7 X 7 divided by 2, which would be 24.5 units squared. Finally, add 24.5 and 20. You should get 44.5 units squared as your final answer.
So, the final answer for this problem would be 44.5 units squared.
Hope this helped!
Not sure how to do this
Assume that in the absence of immigration and emigration, the growth of a country's population P(t) satisfies dP/dt = kP for some constant k > 0.
a. Determine a differential equation governing the growing population P(t) of the country when individuals are allowed to immigrate into the country at a constant rate r > 0.
b. What is the differential equation for the population P(t) of the country when individuals are allowed to emigrate at a constant rate r > 0?
Answer:
[tex](a)\ \frac{dP}{dt} = kP + r[/tex]
[tex](b)\ \frac{dP}{dt} = kP - r[/tex]
Step-by-step explanation:
Given
[tex]\frac{dP}{dt} = kP[/tex]
Solving (a): Differential equation for immigration where [tex]r > 0[/tex]
We have:
[tex]\frac{dP}{dt} = kP[/tex]
Make dP the subject
[tex]dP =kP \cdot dt[/tex]
From the question, we understand that: [tex]r > 0[/tex]. This means that
[tex]dP =kP \cdot dt + r \cdot dt[/tex] --- i.e. the population will increase with time
Divide both sides by dt
[tex]\frac{dP}{dt} = kP + r[/tex]
Solving (b): Differential equation for emigration where [tex]r > 0[/tex]
We have:
[tex]\frac{dP}{dt} = kP[/tex]
Make dP the subject
[tex]dP =kP \cdot dt[/tex]
From the question, we understand that: [tex]r > 0[/tex]. This means that
[tex]dP =kP \cdot dt - r \cdot dt[/tex] --- i.e. the population will decrease with time
Divide both sides by dt
[tex]\frac{dP}{dt} = kP - r[/tex]
Purpose: The purpose of this learning activity is to demonstrate the understanding of correlation and regression and how they could be important in your future practice. Instructions: Submit 1 paragraph answering the following questions: • What are the differences between results that demonstrate a correlation between two variables and results where a regression is run using two variables? • Think about your future clinical role and provide a clinical example of variables that you may want a correlation analysis run and explain. • Think about your future clinical role and provide a clinical example of variables that you may want a regression analysis run and explain.
Answer:
A correlation shows strength and regression tells the pattern.
Step-by-step explanation:
• The differences between the results that demonstrate a correlation between two variables and results where a regression is run using two variables are as follows
1) the correlation is the measure of degree to which any two variables may vary together.
2) if both variables tend to increase or decrease together the correlation is said to be direct or positive.
3) the correlation gives the strength of relationship between two quantities
4) The regression gives the relationship in the form of an equation.
5) The regression investigates the dependence of the dependent variable on the independent variable.
6) it shows the relationship whether it is linear or curved or parabolic etc.
• I may record the ages and the blood pressure of the patients and run a correlation analysis which may not be positive as blood pressure does not always increase with age
• I may record the ages and the blood pressure of the patients and may want to run a regression analysis which will show the relationship of the patients suffering from high blood pressure and their ages whether it follows a similar pattern or not.
How many subsets will the sets have? {sheep that have eight legs }
Answer:
256
Step-by-step explanation:
How to find subsets = 2 raise the power n.
N=number of elements in a set.
=2raise the power 8 which is 256.
If you make $11.25/hour, how many hours will you need to work to earn $416.25? Please explain how you figured this out.
Answer:
37 hours.
Step-by-step explanation:
Since you need $416.25 start with that. Then divide by $11.25 to see how many hours you need to work. 416.25 divided by 11.25 is 37.
Hii guys if you have time plz help me
Answer:
[tex]5 {x}^{2} + 21 + 5x[/tex]
Step-by-step explanation:
TOTAL AMOUNT earned = Tim money + Melina money
[tex]5 {x}^{2} - 4x + 8 + (9x + 13)[/tex]
[tex] = 5 {x}^{2} - 4x + 8 + 9x + 13[/tex]
[tex] = 5 {x}^{2} + 21 + 5x[/tex]
f(x) = 2x2 + 4x - 5
g(x) = 6x3 – 2x2 + 3
Find (f + g)(x).
Answer:
4x-5=4x-5
(f+g) (x)=6x³+3Step-by-step explanation:
For a standard normal distribution, find:
P(z > -1.6)
Express the probability as a decimal rounded to 4 decimal places.
Answer:
P(z > -1.76) = 1 - P(z < -1.76) = 1 - 0.0392 = 0.960
a soft drink vendor at a popular beach analyzes his sales recods and finds that if he sells x cans of soda pop in one day, his profit (in dollars) is given by
Complete Question:
A soft-drink vendor at a popular beach analyzes his sales records, and finds that if he sells x cans of soda pop in one day, his profit (in dollars) is given by P(x) = -0.001x² + 3x - 1800.
a. What is his maximum profit per day?
b. How many cans must be sold in order to obtain the maximum profit?
Answer:
a. $450
b. 1500 cans
Step-by-step explanation:
Given the following quadratic function;
P(x) = -0.001x² + 3x - 1800 ......equation 1
a. To find his maximum profit per day;
Since P(x) is a quadratic equation, P(x) would be maximum when [tex] x = \frac {-b}{2a} [/tex]
Note : the standard form of a quadratic equation is ax² + bx + c = 0 ......equation 2
Comparing eqn 1 and eqn 2, we have;
a = -0.001, b = 3 and c = -1800
Now, we determine the maximum profit;
[tex] x = \frac {-b}{2a} [/tex]
Substituting the values, we have;
[tex] x = \frac {-3}{2*(-0.001)} [/tex]
Cancelling out the negative signs, we have;
[tex] x = \frac {3}{2*0.001} [/tex]
[tex] x = \frac {3}{0.002} [/tex]
x at maximum = 1500
Substituting the value of "x" into equation 1;
P(1500) = -0.001 * 1500² + 3(1500) - 1800
P(1500) = -0.001 * 2250000 + 4500 - 1800
P(1500) = -2250 + 2700
P(1500) = $450
b. Therefore, the soft-drink vendor must sell 1500 cans in order to obtain the maximum profit.
APP
A set of quiz scores has a mean of 78 and a standard
deviation of 9. Using a common grading scale where 60
and above is a passing score, what percentage of the
students passed this test?
Explain your answer in terms of the 68-95-99.7 rule.
Answer:
The answer is "There are [tex]97.5\%[/tex] of the students pass in the test ".
Step-by-step explanation:
Since a normally distributed random variable, the practical rule states:
About 68% of the metrics are in the 1 default deviation
About 95% of metrics correspond to 2 standard deviations from the average.
About 3 standard deviations of the average represent 99.7% of the measurement.
We have the following in this problem:
Average of 78, the average 9 default.
Calculating the percentage of students that passed the test.
[tex]Above 60\\\\60 = 78 - 2\times 9[/tex]
Therefore 60 is under the average for two standard deviations.
Its normality test is symmetric, so 50% of such observations are below mean and 50% below mean.
Everything was cleared of the 50 percent above.
Of the 50% below, 95% (within 2 known mean deviations) succeeded.
therefore
[tex]p=0.5+0.5 \times 0.95=0.975[/tex]
Determine if the triangles are similar. If they are, state the theorem.
9514 1404 393
Answer:
ΔGHF ~ ΔMLF by AA theorem
Step-by-step explanation:
Solve for f(-2)
PLEASE HELPPPPP
Answer:
5/9
Step-by-step explanation:
f(x) = 5 * 3^x
Let x = -2
f(-2) = 5 * 3^-2
We know a^-b = 1/a^b
= 5 * 1/3^2
= 5/9
F(-2) means the value of x is -2
Replace x with -2 and solve:
3^-2 = 1/9
5 x 1/9 = 5/9
Answer: D.5/9
What is the common difference in this sequence: 3, 11, 19, 27,35?
1
ОА.1/8
O B. 3
O C. 8
O D. 12
Answer:
8
Step-by-step explanation:
To determine the common difference, take the second term and subtract the first term
11-3 = 8
Check with the other terms in the sequence
19-11= 8
27-19 = 8
35-27=8
The common difference is 8
Answer:
C. 8
Step-by-step explanation:
There is a common difference between them and that’s 8.
3 + 8 = 11
11 + 8 = 19
19 + 8 = 27
27 + 8 = 35
Seventy-two percent of all observations fall within one standard deviation of the mean if the data is normally distributed. a. True b. False
Answer:
I think this answer is A.
Find the exact length of the curve. x=et+e−t, y=5−2t, 0≤t≤2 For a curve given by parametric equations x=f(t) and y=g(t), arc length is given by
The length of a curve C parameterized by a vector function r(t) = x(t) i + y(t) j over an interval a ≤ t ≤ b is
[tex]\displaystyle\int_C\mathrm ds = \int_a^b \sqrt{\left(\frac{\mathrm dx}{\mathrm dt}\right)^2+\left(\frac{\mathrm dy}{\mathrm dt}\right)^2} \,\mathrm dt[/tex]
In this case, we have
x(t) = exp(t ) + exp(-t ) ==> dx/dt = exp(t ) - exp(-t )
y(t) = 5 - 2t ==> dy/dt = -2
and [a, b] = [0, 2]. The length of the curve is then
[tex]\displaystyle\int_0^2 \sqrt{\left(e^t-e^{-t}\right)^2+(-2)^2} \,\mathrm dt = \int_0^2 \sqrt{e^{2t}-2+e^{-2t}+4}\,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^2 \sqrt{e^{2t}+2+e^{-2t}} \,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^2\sqrt{\left(e^t+e^{-t}\right)^2} \,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^2\left(e^t+e^{-t}\right)\,\mathrm dt[/tex]
[tex]=\left(e^t-e^{-t}\right)\bigg|_0^2 = \left(e^2-e^{-2}\right)-\left(e^0-e^{-0}\right) = \boxed{e^2-\frac1{e^2}}[/tex]
The exact length of the curve when the parametric equations are x = f(t) and y = g(t) is given below.
[tex]e^2 -\dfrac{1}{e^2 }[/tex]
What is integration?It is the reverse of differentiation.
The parametric equations are given below.
[tex]\rm x=e^t+e^{-t}, \ \ 0\leq t\leq 2\\\\y=5-2t, \ \ \ \ \ 0\leq t\leq 2[/tex]
Then the arc length of the curve will be given as
[tex]\int _0^2 \sqrt{(\dfrac{dx}{dt})^2+(\dfrac{dy}{dx})^2}[/tex]
Then we have
[tex]\rm \dfrac{dx}{dt} = e^t-e^{-t}\\\\ \dfrac{dy}{dt} = -2[/tex]
Then
[tex]\rightarrow \int _0^2 \sqrt{(\dfrac{dx}{dt})^2+(\dfrac{dy}{dx})^2}\ \ dt\\\\\rightarrow \int _0^2 \sqrt{(e^t-e^{-t})^2 + (-2)^2} \ dt\\\\\rightarrow \int _0^2 \sqrt{(e^t+e^{-t})^2} \ dt\\\\\rightarrow \int _0^2 (e^t+e^{-t}) \ dt\\\\\rightarrow (e^2-e^{-2}) \\\\\rightarrow e^2 - \dfrac{1}{e^2}[/tex]
More about the integration link is given below.
https://brainly.com/question/18651211
