Given that both X and Y are independent normal distributionswhere,Prove that Z = X/Y is normally distributed.

Answer:

Step-by-step explanation:

We can start by using the logarithmic rule that states:

log a (mn) = log a (m) + log a (n)

And also the property:

log a (b^c) = c*log a (b)

With these rules, we can simplify the given expression as follows:

log4 n = 1/4 log4 81 + 1/2 log4 25

log4 n = log4 81^(1/4) + log4 25^(1/2) (using the above properties)

log4 n = log4 (3^4)^(1/4) + log4 (5^2)^(1/2) (81 = 3^4 and 25 = 5^2)

log4 n = log4 3 + log4 5 (using the rule log a (b^c) = c*log a (b))

log4 n = log4 (3*5) (using the rule log a (mn) = log a (m) + log a (n))

log4 n = log4 15

Therefore, the solution to the equation log4 n=1/4 log4 81 + 1/2 log4 25 is:

n = 15

Answer:

THE ANSWER IS B

Step-by-step explanation:

Answer:

B : Zero

Step-by-step explanation:

The cost of cleaning up 40% of the stream is amount $7000, and 97.45% of the stream can be cleaned up for $1100. P must be greater than or equal to zero and p must be less than 100.

a. C = 42000/(100-p) => C = 42000/(100-40) = $7000

b. 1100 = 42000/(100-p) => p = (42000-1100)/42000 = 97.45%

c. P must be greater than or equal to zero and p must be less than 100. This is because the cost of cleaning up a stream cannot be negative and the stream cannot be cleaned up more than 100%.

The cost of cleaning up 40% of the stream is amount $7000, and 97.45% of the stream can be cleaned up for $1100. P must be greater than or equal to zero and p must be less than 100.

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Answer:  a + s = 15

               6.00a + 4.00s = 76

If the straightaway on each side measures 1,000 meters, the distance around the entire track is approximately 2,465.09 meters.

To find the distance around the entire track, we need to add the distance of the straightaways on both sides and the distance around the curves. The straightaways measure 1,000 meters on each side, so the total distance covered in straightaways is 2,000 meters.

The curves are semicircles with diameter 74 meters. The circumference of a circle is given by the formula 2πr, where r is the radius. Since the diameter of the semicircle is given as 74 meters, the radius will be half of it, i.e., 37 meters. Hence, the distance around each semicircle will be:

Circumference = 2πr = 2π(37) = 74π

Since there are two semicircles in the track, the total distance around the curves is 2(74π) = 148π meters.

Therefore, the total distance around the entire track is:

Total distance = Straightaways + Curves

= 2,000 + 148π

= 2,000 + 465.09 (approximating π as 3.14)

= 2,465.09 meters (rounded to the nearest hundredth)

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The two numbers are 5 and 10 and the working equation for this problem is:x + 2x = 15

The sum of the two numbers is 15. If the second number is twice the other, then the working equation for this problem as well as the values of the two numbers according to the given question is the second number y is twice the first number x.

Therefore,y = 2x

Also, the sum of these two numbers is given as 15.

Therefore,x + y = 15

Substituting the value of y in terms of x, we get x + 2x = 15

Simplifying the above equation, we get:3x = 15x = 5

Substituting this value of x in the equation y = 2x, we get:y = 2(5)y = 10

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Answer:

1 lb expensive chocolate

2 lbs other chocolate

Step-by-step explanation:

let x = number of pounds of the expensive candy bars

let y = number of pounds of the other candy bars

here is the first equation:

(the expensive lbs + other lbs comes to a total of 3 lbs altogether)

x + y = 3

here is the second equation:

($6 per pound + $4.5 per pound = $15)

6x + 4.5y = 15

we can do substitution, elimination, or graph.

let's do elimination with these two equations:

x + y = 3  AND 6x + 4.5y = 15

Let's eliminate the variable x to find variable y, and then use what we found for variable y to find variable x.

Multiply (x + y = 3) with 6

Which looks like this: 6(x+y = 3)

And the above becomes 6x + 6y = 18

the equation x + y = 3 becomes 6x + 6y = 18

the equation 6x + 4.5y = 15 stays the same

Subtract to eliminate x.

    6x + 6y = 18

-    6x +4.5y = 15

-------------------------

    0 + 1.5y = 3

1.5y = 3, divide both sides by 1.5 to get y

1.5y    3

----- = -----

1.5       1.5

y = 2

Therefore, there are 2 pounds of "other" chocolate in the gift bag. Let's use that to find the  pounds of the "expensive" chocolate.

Take one of the original equations and plug in "2" for the variable y.

x + y = 3    OR      6x + 4.5y = 15

Lets use x + y = 3, which becomes   x + 2 = 3. Solve that, and you will get:

x = 1

Therefore, there is 1 pound of "expensive" chocolate in the gift bag.

(after you are done solving, plug in the numbers you found to one of the  equations...ps i checked already so those are correct.

e.g 1 + 2 = 3 )

:))

Answer:

20

Step-by-step explanation:

[tex]55% of a number = 11[/tex]% of a number = 11

[tex]\frac{55}{100} * x = 11[/tex]

solve for x

[tex]55x = 1100[/tex]

[tex]x = 20[/tex]

Hope this helps!

Answer:20

Step-by-step explanation:

55%---------11

100%------x

x=100*11/55=20

Answer:5 3/8

Step-by-step explanation:

[tex]3\frac{1}{8} =\frac{25}{8}\\4\frac{7}{28} =4\frac{1}{4}=\frac{17}{4}\\1\frac{5}{6} =\frac{11}{6}=\frac{33}{18}\\\frac{\frac{25}{8}}{x-\frac{17}{4}}=\frac{17}{18}+\frac{33}{18}=\frac{50}{18}=\frac{25}{9}\\\frac{\frac{25}{8}}{x-\frac{17}{4}}=\frac{\frac{25}{9}}{1}\\\frac{25}{8}=\frac{25}{9}*(x-\frac{17}{4})\\(x-\frac{17}{4})=\frac{25}{8}:\frac{25}{9}=\frac{25}{8}*\frac{9}{25}=\frac{9}{8}\\x=\frac{9}{8}+\frac{17}{4}=\frac{9}{8}+\frac{34}{8}=\frac{43}{8}=5\frac{3}{8}[/tex]

Mila has a DRF of 1. 15 and a 6-month basic rate of $650. Her annual premium is $1,495.

Mila has a 6-month basic cost of $650 and a DRF of 1.15.

We have to determine her annual premium.

As we know that in a year have 12 months and 6 months basic cost is $650. So the time period is 2.

Annual premium is the total amount of money paid in one year for an insurance policy. It is usually paid in one lump sum or in installments throughout the year.

Since we know the cost of premium of 6 months. So

Mila annual premium = 650 x 2 x 1.15

Mila annual premium = $1,495

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The interval of times that represent the middle 99.7% of Aaron's finishing times in the 400 m race is [72.5, 87.5].

Using the empirical rule or the elliptical rule, we know that in a normal distribution:

In this case, we want to find the interval of times that represents the middle 99.7% of Aaron's finishing times, which means we need to find the range of values that fall within three standard deviations of the mean.

So, using the formula for finding the interval of values within k standard deviations of the mean:

lower bound = mean - k * standard deviation

upper bound = mean + k * standard deviation

where k = 3 for this problem, we get:

lower bound = 80 - 3 * 2.5 = 72.5

upper bound = 80 + 3 * 2.5 = 87.5

Therefore, the interval of times that represents the middle 99.7% of Aaron's finishing times in the 400 m race is [72.5, 87.5].

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Akio is a public communication specialist with skill sets to influence and raise awareness for public.

What do you mean by public communication specialist?

Specialists in public-relations develop and uphold a positive public image for the people, groups, or organisations they represent. To influence how the public perceives their clients and to raise awareness of each client's efforts and objectives, they prepare press releases and create social media strategies.

Public relations, information output, and media requests are handled by communications specialists. They can also plan an organization's social media or advertising campaigns.

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Answer:

1

Step-by-step explanation:

Both of those numbers are prime, so their GCF's are 1

Answer:

The value of x in the given figure is 36

What is a line?

A line is a straight arrangement of points that extends in opposite directions. It has no beginning and no end in any way (infinite). It has only one dimension.

What are Parallel lines?

Parallel lines are two lines in the same plane that are equal distances apart and never intersect. They can be both horizontal and vertical in orientation.

According to the given information:

By the Triangle proportionality theorem, If a line parallel to one side of a triangle contacts the other two sides of the triangle, the line proportionally separates these two sides.

Then we have

[tex]\frac{x-16}{16} =\frac{25}{20}[/tex]

On simplifying,

[tex]x-16=\frac{25}{20}*16[/tex]

x-16 = 20

x = 36

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A graph with the x-axis labelled number of side dishes and the y-axis equation labelled cost in dollars, as well as a line connecting the points 0, 7.25 and 3, 11.75.

An equation is a mathematical statement that validates the equivalent of two expressions joined by the equal symbol '='. For instance, 2x - 5 = 13. 2x-5 and 13 are two examples of expressions. The character '=' connects the two expressions. An equation is a mathematical formula that has two algebras on each side of an assignment operator (=). It demonstrates the equivalency link between the left and middle formulas. L.H.S. = R.H.S. (left side = right side) in any formula.

The table depicts the link between the quantity of side dishes and the overall cost of a restaurant's lunch special. We need to plot the data points on the graph and see which graph matches the pattern to identify which graph exhibits the relationship given in the table.

Number of Side Dishes                     Total Cost

2                                                         $10.25

4                                                              $13.25

5                                                         $14.75

8                                                         $19.25

The first choice has a shorter slope than the second, and the data points are perfectly aligned with the line. As a result, the first graph depicts the link described in the table. The solution is:

A graph with the x-axis labelled number of side dishes and the y-axis labelled cost in dollars, as well as a line connecting the points 0, 7.25 and 3, 11.75.

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Therefore, the ratio of red tiles in the first mosaic to red tiles in the second mosaic is 33:34 in its simplest form.

A ratio is a way of comparing two or more quantities that are of the same type. It is a mathematical expression that compares the size or amount of one quantity relative to another. Ratios are expressed as a pair of numbers separated by a colon (:) or as a fraction. For example, the ratio of apples to oranges in a basket might be 3:2 or 3/2, which means there are three apples for every two oranges in the basket. Ratios are used in many different areas of mathematics and in real-world applications such as cooking, finance, and engineering.

Here,

17x tiles used in the first mosaic, and 13x tiles used in the second mosaic.

If we want to use the same number of blue tiles in each mosaic, we need to make sure that the total number of tiles used in each mosaic is the same. This means we need to find a common multiple of 17 and 13 that we can use as the total number of tiles in each mosaic. The smallest such multiple is:

17 * 13 = 221

So, we'll assume that Oliver used 221 tiles in each mosaic (even though we don't know the actual number of tiles he used).

For the first mosaic, the ratio of red to blue to purple tiles is 12:3:2. This means that for every 17 tiles used, we have:

12/17 (red tiles), 3/17 (blue tiles), and 2/17 (purple tiles)

Multiplying each of these fractions by 221 (the total number of tiles), we get:

132 (red tiles), 33 (blue tiles), and 44 (purple tiles)

For the second mosaic, the ratio of red to blue tiles is 8:5. This means that for every 13 tiles used, we have:

8/13 (red tiles) and 5/13 (blue tiles)

Multiplying each of these fractions by 221 (the total number of tiles), we get:

136 (red tiles) and 85 (blue tiles)

So, the ratio of red tiles in the first mosaic to red tiles in the second mosaic is:

132/136 = 33/34

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By following the steps mentioned we can create unique kite design and enjoy flying it with your friends and family using mathematics concepts.

Steps:

Designing the kite:

Designing a kite can be a fun and creative process. First, you need to determine the shape and size of your kite. You can choose from different shapes such as diamond, triangle, hexagon, or even a custom design. Once you have determined the shape, you can start working on the materials. For instance, you may choose to use plastic, paper, or cloth. After that, you need to consider the frame of the kite. You may use bamboo sticks or other lightweight materials. Lastly, you can decorate your kite with colors, patterns, and designs.

Sample kite design:

Parts of the kite:

Mathematics concepts involved:

Designing a kite involves several mathematical concepts, such as:

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1) The ball bounced 0.125 feet high on its 10th bounce.

2) The total distance traveled by the ball by the time it reached its peak after its 10th bounce is 255.75 feet.

3) If Bobo drops his magic ball from the top of the Empire State Building, the ball will have traveled 382 feet by the time it hits the pavement for the 7th time.

1) To find out how high the ball bounced on its 10th bounce, we can use the fact that the ball always bounces to half its previous height. We can start by finding the height of the first bounce, which we know is 64 feet since that's the height of the building. Then, we can keep dividing by 2 to find the height of each subsequent bounce. So, the height of the 2nd bounce is 32 feet, the height of the 3rd bounce is 16 feet, and so on. Continuing this pattern, we can find that the height of the 10th bounce is:

64 feet / 2^(10-1) = 64 feet / 512 = 0.125 feet

2) To find out how far the ball had traveled altogether by the time it reached its peak after its 10th bounce, we can use the fact that the distance traveled is equal to the sum of the distances of each bounce. The distance of each bounce is equal to twice the height of the bounce (since the ball travels up and then back down). So, the distance of the first bounce is 264 = 128 feet. The distance of the second bounce is 232 = 64 feet, and so on. Continuing this pattern, we can find that the distance of the 10th bounce is:

2×0.125 = 0.25 feet

So the total distance traveled by the ball by the time it reached its peak after its 10th bounce is:

128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 + 0.5 + 0.25 = 255.75 feet

3) We know that the height of each bounce is half the height of the previous bounce, so we can use this to find the height of the 7th bounce. Starting with the height of the first bounce (which is the height of the Empire State Building), we can keep dividing by 2 to find the height of each subsequent bounce. So, the height of the 2nd bounce is 64/2 = 32 feet, the height of the 3rd bounce is 32/2 = 16 feet, and so on. Continuing this pattern, we can find that the height of the 7th bounce is:

64/2^(7-1) = 1 foot

Since the ball bounces up and down, it travels twice the height of each bounce. So, the distance traveled by the ball on each bounce is 2 feet. To find out how far the ball will have traveled by the time it hits the pavement for the 7th time, we can add up the distances traveled on the first 7 bounces:

2×(64 + 32 + 16 + 8 + 4 + 2 + 1) = 382 feet

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Answer:

A

Step-by-step explanation:

[tex](2x-5)^{(x-1)}[/tex] ← substitute x = 5

[tex](2(5)-5)^{(5-1)}[/tex]

= [tex](10-5)^{4}[/tex]

= [tex]5^{4}[/tex]

= 625

The lower bound of the mass at the end of the experiment is 65.25 g and the upper bound is 64.25 g.

To calculate the lower and upper bounds of the mass of the chemicals at the end of the experiment, we need to take into account the uncertainty in the initial mass and the change in mass.

The initial mass of the chemicals is given as 73 g, rounded to 2 significant figures. This means that the actual value of the initial mass could lie anywhere between 72.5 g and 73.4 g, since the last significant digit (the 3) is uncertain.

Similarly, the change in mass during the experiment is given as 8.2 g, rounded to 2 significant figures. This means that the actual value of the change in mass could lie anywhere between 8.15 g and 8.25 g.

To find the lower bound of the mass at the end of the experiment, we assume that the initial mass was at its upper bound (73.4 g) and the change in mass was at its lower bound (8.15 g):

Lower bound = 73.4 g - 8.15 g = 65.25 g

To find the upper bound of the mass at the end of the experiment, we assume that the initial mass was at its lower bound (72.5 g) and the change in mass was at its upper bound (8.25 g):

Upper bound = 72.5 g - 8.25 g = 64.25 g

Therefore, the lower bound of the mass at the end of the experiment is 65.25 g and the upper bound is 64.25 g.

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Ruth will need 30 lemons to make lemonade with 10 cups of water.

Ruth is making Lemonade. For 1 cup of water she uses 3 lemins, for 2 cups 6 lemons, ect. The formula to calculate the number of lemons needed for a given cups of water is:

Lemons = 3 × Cups of Water

Therefore, the number of lemons needed for 10 cups of water is:

Lemons = 3 × 10

Lemons = 30

Hence, Ruth will need 30 lemons to make lemonade with 10 cups of water.

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a) Monthly payment = $489.77

b) John will paying $163.69 less per month

c) John will end up saving $3,943.28

d) John's car will be worth approximately $23,142.58

e) John actually lost $8,182.86 at the end of the 4-year loan.

The interest rate is the percentage of the amount of money borrowed, lent or invested that is charged or earned as a fee or return over a certain period of time. It is usually expressed as an annual percentage rate (APR) and can be fixed or variable depending on the type of loan or investment.

a) To calculate John's monthly payments, we need to use the formula for the present value of an annuity, which is:

PMT = P*(r/12)/(1-(1+r/12)^(-n*12))

Where PMT is the monthly payment, P is the principal amount (the amount financed after the down payment), r is the monthly interest rate, and n is the number of years.

So, we have:

P = 32,451 - 3,500 = 28,951

r = 0.055/12

n = 6

PMT = 28,951*(0.055/12)/(1-(1+0.055/12)^(-6*12)) = $489.77

Therefore, John's monthly payments would be $489.77.

b) Using the same formula, we can calculate John's monthly payments with the special financing:

P = 28,951

r = 0.0475/12

n = 4

PMT = 28,951*(0.0475/12)/(1-(1+0.0475/12)^(-4*12)) = $653.46

So, John's monthly payments with the special financing would be $653.46.

Difference in monthly payments between the above options is:

$653.46 - $489.77 = $163.69

Therefore, John would have to pay $163.69 more per month with the special financing.

c) To calculate how much John will save by going with the special financing, we need to calculate the total cost of each option.

For the original financing, the total cost can be found by multiplying the monthly payment by the number of payments:

Total cost = $489.77 * (6 * 12) = $35,268.72

For the special financing, the total cost is:

Total cost = $653.46 * (4 * 12) = $31,325.44

Therefore, John will save:

$35,268.72 - $31,325.44 = $3,943.28

So, John will end up saving $3,943.28 by going with the special financing.

d) To calculate the value of John's car when he finishes paying off his loan, we need to use the formula for continuous compounding:

A = P*e^(rt)

Where A is the final amount, P is the initial amount (the purchase price of the car), e is the mathematical constant e (approximately 2.71828), r is the annual interest rate, and t is the time in years.

The car depreciates at a continuous rate of 6%, which means that the value of the car decreases by 6% every year. So, the effective annual rate of depreciation is:

r = e^(-0.06) - 1 = -0.0589

Note that we use a negative value for r, since the value of the car is decreasing.

John will finish paying off his loan in 4 years. So, the time t is 4 years.

Therefore, the value of John's car when he finishes paying off his loan is:

A = 32,451e^(-0.05894) = $23,142.58

So, John's car will be worth $23,142.58 when he finishes paying off his loan.

e) To calculate how much John actually lost at the end of the 4-year loan, we need to subtract the value of his car at the end of the loan from the total amount he paid:

Total amount paid = $653.46 * (4 * 12) = $31,325.44

Value of car at end of loan = $23,142.58

Amount lost = Total amount paid - Value of car at end of loan

= $31,325.44 - $23,142.58  =  $8,182.86

Therefore, John actually lost $8,182.86 at the end of the 4-year loan.

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The turtle and snail are apprοaching each οther at a rate οf 6 feet per minute.

Let's use the cοncept οf relative speed tο sοlve this prοblem. The relative speed οf twο οbjects mοving tοwards each οther is the sum οf their individual speeds.

Relative speed is the speed οf an οbject οr persοn in relatiοn tο anοther οbject οr persοn. It is the difference between the velοcities οf twο οbjects mοving relative tο each οther. The relative speed can be calculated by subtracting the velοcity οf οne οbject frοm the velοcity οf the οther οbject.

Let's call the rate at which the turtle and snail are apprοaching each οther "r".

Relative speed = turtle's speed + snail's speed

r = 5 + 1

r = 6 feet per minute

Sο the turtle and snail are apprοaching each οther at a rate οf 6 feet per minute.

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Answer:

heeeeeeeee

Step-by-step explanation:

heeeeeeeeee bad

In conclusion for part A  it would take T - 32.5 minutes to cook a 1.5 kg joint. For part B w is given by the formula w = (T - 25) / (-35). For part C 6.6 kg of beef needs to be cooked for 207 minutes. For part D  5.91 kg of beef needs to be cooked for 3 hours and 48 minutes.

How to solve?

a) To find how long it would take to cook a 1.5 kg joint, we can substitute w = 1.5 into the formula:

T - 35w + 25 = T - 35(1.5) + 25 = T - 32.5

So, it would take T - 32.5 minutes to cook a 1.5 kg joint.

b) To make w the subject of the formula, we need to isolate w on one side of the equation. We can start by subtracting 25 from both sides:

T - 35w = T - 25

Next, we can divide both sides by -35:

w = (T - 25) / (-35)

Therefore, w is given by the formula w = (T - 25) / (-35).

c) To find the weight of beef that needs to be cooked for 207 minutes, we can substitute T = 207 into the original formula:

T - 35w + 25 = 207

Simplifying this equation, we get:

-35w = -232

Dividing both sides by -35, we get:

w = 6.6 kg

Therefore, 6.6 kg of beef needs to be cooked for 207 minutes.

d) To find the weight of beef that needs to be cooked for 3 hours and 48 minutes (which is equivalent to 3 × 60 + 48 = 228 minutes), we can substitute T = 228 into the original formula:

T - 35w + 25 = 228

Simplifying this equation, we get:

-35w = -207

Dividing both sides by -35, we get:

w = 5.91 kg

Therefore, 5.91 kg of beef needs to be cooked for 3 hours and 48 minutes.

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Answer:

b d

Step-by-step explanation:

The arc measure of AE A, E, start superscript, frown, finish superscript in degrees cannot be determined without more information. To make this conclusion, additional information .

Such as the locations of points A and E and/or the degree measures of other angles in the same circle would be required.  An arc is a piece of a circle's circumference, and its degree measure is equal to the degree measure of the central angle that subtends the arc. To compute the arc measure of AE A, E, start superscript, frown, end superscript in degrees, we would need to know the degree measure of the central angle that subtends this arc or the degree measure of the central angle that subtends this arc.

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The mean of the sampling distribution of X turns out as 11 and the standard deviation is identified as 3.13. By using concepts of standard deviation, the sample deviation can be calculated.

The mean and standard deviation of the sampling distribution of X can be calculated using the formulas for the mean and standard deviation of a binomial distribution. The mean is given by: [tex]μ = np[/tex]

Where n is the sample size and p is the proportion of left-handed students in the population. In this case, n = 100 and p = 0.11, so:
[tex]μ = (100)(0.11) = 11[/tex]
The standard deviation is given by:
[tex]σ = √(np(1-p))σ = √((100)(0.11)(1-0.11)) = √(9.79) = 3.13[/tex]
So the mean of the sampling distribution of X is 11 and the standard deviation is 3.13.

The standard deviation of the sampling distribution of X tells us how much variability we can expect in the number of left-handed students in a random sample of 100 students from the population.

In this case, the standard deviation of 3.13 tells us that there is a moderate amount of variability in the number of left-handed students in different samples of 100 students from the population.

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Answer:

b.0.45

Step-by-step explanation:

Answer: B 0.45  

0.42 < 0.45  

Step-by-step explanation:

The vectors 4 1 and 16 are linearly dependent because they can be expressed as multiples of each other. This means that there are scalars that are not all zero that will make the equation below true:

4a + 16b = 0

To find the scalars, we can set one of them to any non-zero value and solve for the other. For example, if we set a = 1, then we can solve for b:

4(1) + 16b = 0
16b = -4
b = -4/16
b = -1/4

So the scalars that will make the equation true are a = 1 and b = -1/4. These are not all zero, which confirms that the vectors are linearly dependent.

If the vectors were linearly independent, then the only scalars that would make the equation true would be all zero. In other words, a = 0 and b = 0 would be the only solution. However, since we found scalars that are not all zero that make the equation true, we know that the vectors are not linearly independent.

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