The average American consumes 81 liters of alcohol per year. Does the average college student consume more alcohol per year? A researcher surveyed 10 randomly selected college students and found that they averaged 97.7 liters of alcohol consumed per year with a standard deviation of 23 liters. What can be concluded at the the α = 0.01 level of significance?

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

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.

To know more about normal matrices, refer here:

https://brainly.com/question/29102682#

#SPJ11

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....

(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.

To know more about the Central Limit Theorem refer here:

https://brainly.com/question/898534#

#SPJ11

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]

Answer:

Your answers are correct

Step-by-step explanation:

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

Answer:

£1.95

Step-by-step explanation:

£41.01 + £49.54 + £12.50 = £103.05

£105 - £103.05 = £1.95

Answer:

Here's a calculator that should help

Step-by-step explanation:

https://www.calculatorsoup.com/calculators/algebra/completing-the-square-calculator.php

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°

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.

Learn more about compund interest:

https://brainly.com/question/3989769

#SPJ11

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.

Learn more about the Extended Euclidean Algorithm for finding modular inverses here:

https://brainly.com/question/32575384

#SPJ4

Answer:

12

Step-by-step explanation:

your welcome :)

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.

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!

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      

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

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)

Answer:

here, i can help you out!

Step-by-step explanation:

Answer:

For 1. 2/5 is less full then 1/2

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

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

Answer:

sin(4x) = sin(2x) is unsolvable.

Step-by-step explanation:

The two sides are not equal.

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.

Learn more about approximately here:

https://brainly.com/question/31695967

#SPJ11

Answer: 0,2

Step-by-step explanation:

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.

To know more about dilated triangle, click here: brainly.com/question/4248623

#SPJ11

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.

To know more about ratio, refer here:

https://brainly.com/question/13419413#

#SPJ11

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

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

Read more about Arithmetic

https://brainly.com/question/22568180

The inverse of the given function is represented by Data Table B.

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.

To know more about Function

https://brainly.com/question/12431044

#SPJ5

Answer:

(2,6)

Step-by-step explanation:

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