The α = 0.01 level of significance, we can conclude that the average alcohol consumption of college students is significantly higher than that of the average American population.
To determine if the average alcohol consumption of college students is significantly different from the average consumption of the average American, we can conduct a hypothesis test.
Let's set up the hypotheses:
Null hypothesis (H0): The average alcohol consumption of college students is equal to the average American consumption. (μ = 81)
Alternative hypothesis (H1): The average alcohol consumption of college students is greater than the average American consumption. (μ > 81)
We can use a one-sample t-test to analyze the data. Since we don't have information about the population standard deviation, we'll use the t-distribution and the sample standard deviation instead.
Given that the sample mean (x) of the 10 randomly selected college students is 97.7 liters and the sample standard deviation (s) is 23 liters, we can calculate the t-statistic using the following formula:
t = (x - μ) / (s / √n)
Where:
x = sample mean
μ = population mean
s = sample standard deviation
n = sample size
Plugging in the values, we get:
t = (97.7 - 81) / (23 / √10)
Calculating this expression gives us the t-value.
However, we also need to determine the critical value for the test based on the significance level (α = 0.01) and the degrees of freedom = n - 1.
Since we have 10 randomly selected college students = 10 - 1 = 9.
To find the critical value, we can consult the t-distribution table. With α = 0.01 and df = 9, the critical t-value is approximately 2.821.
Comparing the calculated t-value to the critical t-value, we can draw a conclusion. If the calculated t-value is greater than the critical t-value, we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.
Now let's calculate the t-value:
t = (97.7 - 81) / (23 / √10)
≈ 16.700
Since the calculated t-value (16.700) is much greater than the critical t-value (2.821), we can reject the null hypothesis.
Therefore, based on the given data and the α = 0.01 level of significance, we can conclude that the average alcohol consumption of college students is significantly higher than that of the average American population.
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HHEEEEEELLLLPPPPPP ANSWER THIS QUICKLYYYYY
Answer: 27
Step-by-step explanation:
[tex]a_{1}=6\\a_{2}=a_{n-1}+7=a_{2-1} +7=a_{1} +7=6+7=13\\a_{3}=a_{n-1}+7=a_{3-1} +7=a_{2} +7=13+7=20\\a_{4}=a_{n-1}+7=a_{4-1} +7=a_{3} +7=20+7=27[/tex]
If A, B and M are three collinear points, such that M divides AB internally in the ratio of 7:5 and P is any point not on the line AB, show that PM = PA + PB (4 marks] = 12 12
Given collinear points A, B, and M, with M dividing AB internally in the ratio of 7:5, and a point P not on the line AB, it can be shown that PM is equal to the sum of PA and PB.
Let's consider the line segment AB, where M is a point that divides it internally in the ratio of 7:5. This means that the ratio of AM to MB is 7:5.
Now, let's consider the triangle PAB, where P is a point not on the line AB. We want to show that PM is equal to the sum of PA and PB.
Since M divides AB internally in the ratio of 7:5, we can express AM and MB in terms of their lengths. Let's assume the length of AM is 7x and the length of MB is 5x.
Using this information, we can express the lengths of PA and PB in terms of x as well. Let's denote the length of PA as y and the length of PB as z.
Since M divides AB internally in the ratio of 7:5, we can write:
AM/MB = 7x/5x = 7/5
Similarly, we can express the ratios of PM to PA and PM to PB:
PM/PA = 7x/y
PM/PB = 5x/z
We need to show that PM is equal to PA + PB:
PM = PA + PB
Substituting the ratios we derived earlier:
(7x/y) = (5x/z) + 1
To simplify the equation, we can multiply both sides by yz:
7xz = 5xy + yz
Next, we can factor out the common factor of y:
7xz = y(5x + z)
Now, we can divide both sides by (5x + z):
PM = y
Therefore, we have shown that PM is equal to PA + PB.
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divide 54 books between A and B in the ratio 13:14
Answer:
hi
Step-by-step explanation:
i think,
13:14=54
13k+14k=54
27k=54
k=54/27
k=2
13×2=26 and 14×2=28
to verify the correctness of the answer-26+28=56
have a nice day
hope it helps
The ratio of the divide is mathematically given as
26:28
What is the ratio of the divide?Question Parameters:
divide 54 books between A and B in the ratio 13:14
Generally, ratios are mathematically given as
X=13/27*54
X=26
Y=14/27*54
Y=28
In conclusion, the ratio of the divide would be
26:28
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Solve -72 = 8 (y - 3) pls
Step-by-step explanation:
Given
- 72 = 8 ( y - 3 )
or - 72 / 8 = y - 3
or, - 9 = y - 3
y = - 9 + 3
Therefore X = - 6
Hope it will help :)❤
Answer:
Step-by-step explanation:
-72=8y-24
-72+24=8y
-48=8y
-48/8=y
-6=y
What is the solution to the following graph? Write it as an ordered pair to get credit.
Answer:
(2,6)
Step-by-step explanation:
2( 5/3 + 3/4 ) − 4/3
Answer: = 42/12 Or simply = 7/2
Step-by-step explanation:
2(5/3 + 3/4 ) − 4/3
= 2(5/3) + 2(3/4) − 4/3
= 10/3 + 6/4 - 4/3
= 6/3 + 6/4
= 24/12 + 18/12
= 42/12
Or simply = 7/2
Given the coordinates for the function below, which of the following are coordinates for its inverse?
The inverse of the given function is represented by Data Table B.
What is a Function?A function is a law that relates a dependent and an independent variable.
The Inverse of the function is determined by interchanging the values of a and y in an f(x,y) function and then express the equation of y in terms of x.
Th table of the function is
Miles to go Miles Travelled
0 0
100 310
200 450
340 550
650 650
The inverse of this data table will be
Miles Travelled Miles to go
650 650
340 550
200 450
100 310
0 0
This is represented by Data Table B.
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find the value of X such that the data set has a mean of 118. 101, 119, 104, 115, 109, x
Answer:
160
Step-by-step explanation:
101+119+104+115+109+x=548+x
there are 6 terms including x so divide the sum by 6
(548+x)/6=118
multiply both sides by 6
548+x=708
subtract 548
x=160
hope that helps :)
Answer:
160
Step-by-step explanation:
There are 6 numbers in the set
101 + 119 + 104 + 115 + 109 + x = 6(118)
101 + 119 + 104 + 115 + 109 + x = 708
548 + x = 708
-548 -548
x = 160
EASY POINTS!!
INCLUDE A DISC
Answer:
I don't know what you mean by disc but the answer is 80 degrees.
Step by Step explanation:
A triangle is made up of 180 deg
65+35=100
180-100=80
Answer:
F. 80°
Step-by-step explanation:
Because a triangle measues 180°
35+65= 100
180-100=80
So the remaining angle must measure an exact 80°
OMG HELP PLS IM PANICKING OMG OMG I GOT A F IN MATH AND I ONLY HAVE 1 DAY TO CHANGE MY GRADE BECAUSE TOMORROW IS THE FINAL REPORT CARD RESULTS AND I DONT WANNA FAIL PLS HELP-
AND CAN ANYONE PLS DRAW ME THE ANSWERS I CANT UNDERSTAND ANYTHING PLS I BEG U ILL GIVE U BRAINLEST
Answer:
here, i can help you out!
Step-by-step explanation:
Answer:
For 1. 2/5 is less full then 1/2
Use completing the square to find the equation of the following circle in standard form.
x2 + y2 - 4x + 12y - 16 = 0
Answer:
Here's a calculator that should help
Step-by-step explanation:
https://www.calculatorsoup.com/calculators/algebra/completing-the-square-calculator.php
Please help me out you can just give me the answer! PLEASE AND THANK YOU!
Answer:
(Disclaimer: all digits in the answers are in the measuring unit degrees)
1) 15
2) 16
3) 46
4) 59.
Step-by-step explanation:
The first one is said to add up to 89, so you have to do 89 subtract 44 and 30 as they are told. That = 15
The second one is a right angle, meaning it adds up to 90. You do 90 - 74 as that is the value told. That = 16
Angles on a straight line = 180 so you have to do 180 - 134 as that is the value told. This = 46
This is 54 as opposing angles on two lines are =. That means this = 59 too.
the top of a swimming pool is at ground level. if the pool is 2.50 m deep, how far below ground level does the bottom of the pool appear to be located for the following conditions?
Given a swimming pool that is 2.50 m deep, we need to determine how far below ground level the bottom of the pool appears to be located.
The apparent depth of an object submerged in a medium, such as water, can be calculated using the concept of refraction. Refraction occurs when light travels from one medium to another, and its speed changes. According to Snell's law, the apparent depth (d') of an object in a medium is related to its actual depth (d) and the refractive index (n) of the medium.
The formula for calculating the apparent depth is:
d' = d / n.
In this case, the actual depth of the pool is 2.50 m, and the pool is filled with water, which has a refractive index of approximately 1.33.
Substituting the values into the formula, we have:
d' = 2.50 m / 1.33 ≈ 1.88 m.
Therefore, the bottom of the pool appears to be located approximately 1.88 meters below ground level. This means that when observing the pool from above, it would appear as if the bottom of the pool is situated 1.88 meters below the surface of the ground.
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What is the surface area 3yd 3yd 3yd
Answer:
12
Step-by-step explanation:
your welcome :)
Use the Extended Euclidean Algorithm to show that the inverse of 177 in mod 901 is 56 by hand calculations ?
The inverse of 177 in mod 901 is indeed 56, as determined through the Extended Euclidean Algorithm by hand calculations.
Given that the inverse of 177 in mod 901 is 56.
To find the inverse of 177 modulo 901 using the Extended Euclidean Algorithm, perform the calculations step by step.
Step 1: Initialize the algorithm with the given values:
a = 901 (modulus)
b = 177 (number for which to find the inverse)
Introduce two variables:
[tex]x_0 = 1, y_0 = 0[/tex]
[tex]x_1 = 0, y_1 = 1[/tex]
Step 2: Perform the iterations of the Extended Euclidean Algorithm:
While b is not zero, repeat the following steps:
Calculate the quotient and remainder of a divided by b:
q = a / b
r = a % b (modulus operator)
Update the values of a and b:
[tex]a = b[/tex]
[tex]b = r[/tex]
Update the values of x and y:
[tex]x = x_0 - q * x_1[/tex]
[tex]y = y_0 - q * y_1[/tex]
Update the values of [tex]x_0, y_0, x_1, y_1[/tex]:
[tex]x_0 = x_1[/tex]
[tex]y_0 = y_1[/tex]
[tex]x_1 = x[/tex]
[tex]y_1 = y[/tex]
Step 3: Once the loop ends and b becomes zero, and obtain the [tex]gcd(a, b) = gcd(901, 177) = 1[/tex], indicating that 177 has an inverse modulo 901.
Step 4: The inverse of 177 modulo 901 is given by [tex]y_0[/tex], which is 56.
Therefore, the inverse of 177 in mod 901 is indeed 56, as determined through the Extended Euclidean Algorithm by hand calculations.
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Expert Help me plssss. I dont understand how to do it
Answer:
V=301.44ft^3
Step-by-step explanation:
l^2°r^2r^2+h^2
10^2=6^2+h^2
100=36+h^2
100-36=h^3
h^2=64
h=8
Volume of cone:
1/3πr^2h
1/3(π)(6)^2(8)
301.44ft^3
Hope it helps....
x is 40% of 60
x=?
please help!!
Answer:
x = 24
Step-by-step explanation:
x = .4(60)
x = 24
40% of 60 can be found by converting 40% to a decimal and multiplying it by 60.
40% = 0.4
60x0.4=2.4
Now move the decimal point right one.
So x is 24.
---
hope it helps
Prove that for a normal matrix A, eigenvectors corresponding to different eigenvalues are necessarily orthogonal.
Eigenvalues and eigenvectors play a crucial role in the study of linear transformations and matrices. For a normal matrix A, it can be proven that eigenvectors corresponding to different eigenvalues are necessarily orthogonal.
To understand why eigenvectors corresponding to different eigenvalues are orthogonal for a normal matrix, we need to consider the properties of normal matrices. A matrix A is normal if it commutes with its conjugate transpose A* (i.e., A * A* = A* A).
Now, let's consider two eigenvectors v₁ and v₂ corresponding to different eigenvalues λ₁ and λ₂, respectively. We want to show that v₁ and v₂ are orthogonal, meaning their dot product is zero (v₁ · v₂ = 0).
Let's denote the conjugate transpose of A as A*, and the eigenvalues and eigenvectors as follows:
A * A = A * A* (1)
Multiplying both sides of equation (1) by v₂* (the conjugate transpose of v₂) from the left gives:
v₂* A * A = v₂* A * A* (2)
Since v₂ is an eigenvector of A, we can express it as:
A * v₂ = λ₂ v₂ (3)
Substituting equation (3) into equation (2) gives:
v₂* λ₂ A = v₂* A * A* (4)
Now, let's multiply equation (4) by v₁ from the right:
v₂* λ₂ A v₁ = v₂* A * A* v₁ (5)
Since v₁ is an eigenvector of A, we can express it as:
A * v₁ = λ₁ v₁ (6)
Substituting equation (6) into equation (5) gives:
v₂* λ₂ λ₁ v₁ = v₂* λ₁ A* v₁ (7)
Notice that λ₁ and λ₂ are scalars, so we can move them around. Taking the conjugate transpose of equation (7), we get:
(λ₂ λ₁) v₁* v₂ = (λ₁ v₁)* A v₂ (8)
Now, we have v₁* v₂ on the left-hand side and (λ₁ v₁)* A v₂ on the right-hand side. If v₁ and v₂ are not orthogonal (v₁ · v₂ ≠ 0), then v₁* v₂ ≠ 0. However, the right-hand side of equation (8) is proportional to (λ₁ v₁)* A v₂, which is proportional to A v₂. This implies that A v₂ is a scalar multiple of v₁, which contradicts the assumption that v₁ and v₂ correspond to different eigenvalues.
Therefore, we conclude that eigenvectors corresponding to different eigenvalues for a normal matrix are necessarily orthogonal.
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Assume that women's heights are normally distributed with a mean given by = 62.5 in, and a standard deviation given by a = 2.1 in. (a) If 1 woman is randomly selected, find the probability that her height is less than 63 in. (b) If 33 women are randomly selected, find the probability that they have a mean height less than 63 in.
(a) The probability is approximately __________ (Round to four decimal places as needed.)
(b) The probability is approximately_______________
(a) The probability is approximately 0.6915. (Round to four decimal places as needed.)
(b) The probability is approximately 0.9999.
(a) The probability that a randomly selected woman's height is less than 63 inches is approximately 0.6915.
To find this probability, we can use the standard normal distribution and z-scores. The z-score is calculated using the formula z = (x - μ) / σ, where x is the value we are interested in, μ is the mean, and σ is the standard deviation. In this case, x = 63 inches, μ = 62.5 inches, and σ = 2.1 inches.
Substituting these values into the formula, we get z = (63 - 62.5) / 2.1 = 0.2381. To find the probability corresponding to this z-score, we can look it up in the standard normal distribution table or use a statistical calculator. The probability associated with a z-score of 0.2381 is approximately 0.5915.
However, since we want to find the probability that the height is less than 63 inches, we need to find the area to the left of the z-score. Since the standard normal distribution is symmetrical, the area to the left of a positive z-score is equal to 1 minus the area to the right. Therefore, the probability that a randomly selected woman's height is less than 63 inches is approximately 1 - 0.5915 = 0.6915.
(b) The probability that a sample of 33 randomly selected women has a mean height less than 63 inches is approximately 0.9999.
When we have a sample of multiple individuals, the distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution. This phenomenon is known as the Central Limit Theorem.
For this problem, we can assume that the mean height of the sample of 33 women follows a normal distribution with the same mean as the population (62.5 inches) but with a standard deviation equal to the population standard deviation divided by the square root of the sample size. In this case, the sample standard deviation would be 2.1 inches divided by the square root of 33, which is approximately 0.3669 inches.
To find the probability that the sample mean height is less than 63 inches, we can again use z-scores. The z-score is calculated using the formula z = (x - μ) / (σ / √n), where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.
Substituting the values into the formula, we get z = (63 - 62.5) / (0.3669) = 1.3662. The probability corresponding to this z-score can be found using a standard normal distribution table or a statistical calculator. The probability associated with a z-score of 1.3662 is approximately 0.9082.
However, since we want to find the probability that the sample mean height is less than 63 inches, we need to find the area to the left of the z-score. Thus, the probability that a sample of 33 randomly selected women has a mean height less than 63 inches is approximately 0.9999.
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Show your work please
Answer:
B 2208cm squared
you follow this formula
A=2(wl+hl+hw)
w means width
l means length
h means height
input the numbers and you got your answer.
Hope this helped ;)
Answer:5760 cm2
Step-by-step explanation:length times width times height 12 times 12 is 144 and 144 times 40 is 5770 cm2
Interest earned in the first year was $75 . If the total interest for the next 10 years is $750 ,
then the investment must be receiving simple interest .
True
False
Interest earned in the first year was $75. If the total interest for the next 10 years is $750, then the investment must be receiving simple interest. False.
If the total interest for the next 10 years is $750, it indicates that the investment is receiving compound interest, not simple interest. In compound interest, the interest earned in each period is added to the principal, resulting in an increasing base for calculating subsequent interest. Simple interest, on the other hand, is calculated solely based on the initial principal amount and does not incorporate any interest earned over time.
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help pls Evaluate.
169−−−√
Enter your answer in the box.
Answer:
square root is 13
Step-by-step explanation:
Answer:
13!
Step-by-step explanation:
i used my calculator and did the test k-12! its right!
find the range of f(x)=2/5x + 5 for the domain (-4, -2, 0 3)
my answer is 3.4, 4.2, 5, 6.2 but im not fully sure
Answer:
Your answers are correct
Step-by-step explanation:
how do I solve sin(4x)=sin(2x)?
Answer:
sin(4x) = sin(2x) is unsolvable.
Step-by-step explanation:
The two sides are not equal.
PLS HELP ME QUICK I NEED THIS GOOD GRADE PLS HELPPPP! Tell whether each statement is true or false. If false, provide a counterexample. The set of whole numbers contains the set of rational numbers. Every terminating decimal is a rational number. Every square root is a rational number. The integers are closed under addition.
Answer:
1. The set of whole numbers contains the set of rational numbers. FALSE.
The set of integers contains the set of rational numbers
2. Every terminating decimal is a rational number. TRUE
3. Every square root is a rational number. FALSE
Many square roots are irrational numbers, meaning there is no rational number equivalent.
4. The integers are closed under addition. TRUE
Tbh you can guess for the fractions
Answer:
4:1 ratio
Sugar: 1 cup
Butter: 3/4 cups
Eggs: 2
Baking powder: 3/8 tsp
Flour: 5/8 tsp (you need way more flour for cookies)
Salt: 1/8 tsp (original # was hard to make out but I think it was 1/2 tsp)
For the quadratic function show below the coordinates of its vertex are
Answer: 0,2
Step-by-step explanation:
You spend £41.01 on groceries, £49.54 on fuel, and £12.50 on lottery tickets, how much do you have left from £105?
Answer:
£1.95
Step-by-step explanation:
£41.01 + £49.54 + £12.50 = £103.05
£105 - £103.05 = £1.95
a triangle with an area of 23 cm² is dilated by a factor of 6. what is the area of the dilated triangle?
When a triangle is dilated by a scale factor, the area of the dilated triangle is equal to the scale factor squared times the area of the original triangle. The area of the dilated triangle is 828 cm².
In this case, the original triangle has an area of 23 cm². The triangle is dilated by a factor of 6, so the scale factor is 6.
To find the area of the dilated triangle, we use the formula:
Area of Dilated Triangle = (Scale Factor)^2 * Area of Original Triangle
Plugging in the values:
Area of Dilated Triangle = 6^2 * 23 cm²
= 36 * 23 cm²
= 828 cm²
Therefore, the area of the dilated triangle is 828 cm².
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pls pls pls, I beg you to answer this question only if you know the correct answer please please please I beg you
Answer:
Median is the middle line of the box, Lower quartile is the number of the lower end of the box, Upper quartile is the line at the larger end of the box, Maximum is the largest number in the box plot (end of right whisker), Minimum is the lowest number (end of left whisker).
Step-by-step explanation:
32.
Median: 88
Maximum (largest number): 102
Minimum (lowest number): 38
Interquartile range:
96 - 72 = 24
b.
25 % higher
75 % lower?
c.
You can see the range is more towards the right of the box meaning they have higher scores, and that the median or middle is a higher number so it means that most of the students understood and did well on the test.
???.
First quartile: 16
Second: 19
Third: 20
Range: 4
34. Since they are already in least to greatest order, all we have to do is graph it!
85 - 99 is 2
100 - 114 is 1
115 - 129 is 5
130 - 144 is 6