If C = 6 2 - 2 2 3 1 2 2 2 B And B is the basis (b1,b2,63 }, where , b2 = 21, 63 11:11 62-63 = ) Find the matrix of the transformation Cx in the basis B.

The product of the expression 3/(x+7) and 4/x is equivalent to the expression 12/(x²+7x) option 12/(x²+7x) is correct.

Since, Polynomial is the combination of variables and constants in a systematic manner with "n" number of power in ascending or descending order.

We have polynomial:

⇒ 3/(x + 7) × 4/x

⇒ 12 / (x (x + 7))

⇒ 12 / (x² + 7x)

Thus, the product of the expression 3/(x+7) and 4/x is equivalent to the expression 12/(x²+7x).

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Answer:

x = 3

Step-by-step explanation:

29 - 3x = 5x + 5

You want to have the variable of x on one side of the equation, so add 3x to both sides.

29 = 8x + 5

You want to isolate the variable of x, so subtract 5 from both sides.

24 = 8x

You want the variable x on its own, so divide both sides by 8.

3 = x

Check your answer by plugging x back into the original equation.

29 - 3(3) = 5(3) + 5

Solve.

29 - 9 = 15 + 5

20 = 20

Your answer is correct!

Answer:

D- 5hrs

Step-by-step explanation:

If the family can hike 3 miles per hour,
for 15 miles: 15/3 = 5 hours.

Every hour they cover 3 miles per hour, so to cover 15 miles, they will take 5 hours

Answer:

D. 5 hours

Step-by-step explanation:

3 miles per 1 hour so 3/1

15 miles per x hours so 15/x

3/1 = 15/x or 3 = 15/x

get x by itself so

3 divided by 3 and 15 divided by 3

x = 5 hours

Answer:

Liquid nitrogen is 1. Liquid and 2. 90°C and dry ice is, well, ice. So dry ice is obviously colder.

Step-by-step explanation:

The solutions are given below,

(a) f(g(x)) = 2x² - 4x + 2

(b) g(f(x)) = 2x² - 1

(c) f(f(x)) = 8x⁴

To find f(g(x)), we substitute g(x) into the function f(x):

f(g(x)) = 2(g(x))²

f(g(x)) = 2(x-1)²

f(g(x)) = 2(x² - 2x + 1)

f(g(x)) = 2x² - 4x + 2

Therefore, f(g(x)) = 2x² - 4x + 2.

b. To find g(f(x)), we substitute f(x) into the function g(x):

g(f(x)) = f(x) - 1

g(f(x)) = 2x² - 1

Therefore, g(f(x)) = 2x² - 1.

c. To find f(f(x)), we substitute f(x) into the function f(x):

f(f(x)) = 2(f(x))²

f(f(x)) = 2(2x²)²

f(f(x)) = 2(4x⁴)

f(f(x)) = 8x⁴

Therefore, f(f(x)) = 8x⁴.

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There is a significant difference between the average numbers of traffic accident related emergency room admissions between Friday the 6th and Friday the 13th.

To conduct a hypothesis test to evaluate if there is a difference between the average numbers of traffic accident related emergency room admissions between Friday the 6th and Friday the 13th, we can use a paired t-test. The null hypothesis would be that there is no difference between the means of the two populations, while the alternative hypothesis would be that there is a difference.

We can calculate the paired differences by subtracting the number of admissions on Friday the 6th from the number of admissions on Friday the 13th. Then we can calculate the mean and standard deviation of these differences. Using the given data, the mean of the differences is 10.83 - 7.5 = 3.33 and the standard deviation of the differences is 3.6.

Next, we can calculate the t-statistic by dividing the mean difference by the standard deviation of the differences and multiplying by the square root of the sample size. Using the given data, the t-statistic is (3.33 - 0) / (3.6 / sqrt(6)) = 3.07.

We can look up the critical value for a two-tailed test with 5 degrees of freedom (n-1) at a significance level of 0.05. The critical value is 2.571.

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The population of Melonville follows a population growth, and the population of Melonville in 1993 is 201

Let the population in 1991 be x².

The 1992 population is

P₂ = y² + 1 = x² + 100

This means that:

x² + 100 = y² + 1

Rewrite as:

y² - x² = 100 - 1

y² - x² = 99

Express as difference of two squares

(y - x)(y + x) = 99

Express 99 as 9 * 11

(y - x)(y + x) = 9 * 11

Rewrite as:

(y - x)(y + x) = (10 - 1) * (10 + 1)

By comparison, we have:

y = 10 and x = 1

So, the populations are:

P₁ = x² --- 1991

P₂ = x² + 100 --- 1992

P₃ = x² +100 +100 --- 1993

Substitute 1 for x

P₃ = 1² +100 +100

Evaluate

P₃ = 201

Hence, the population of Melonville in 1993 is 201

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There are 336 different 5-digit telephone numbers that can be constructed using the digits 0 to 9, starting with "67" and with no repeated digits.

To answer your question, we need to find the number of ways to arrange the remaining three digits after "67" is fixed.

Since we cannot repeat any digit, the first digit has 8 possibilities (0 to 9 except for 6 and 7).

the second digit has 7 possibilities, and the third digit has 6 possibilities.
To find the total number of arrangements, we multiply the number of possibilities for each digit together:

8 × 7 × 6 = 336.
Therefore, there are 336 different 5-digit telephone numbers that can be constructed using the digits 0 to 9, starting with "67" and with no repeated digits.
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Answer/Step-by-step explanation:

What do you mean by property?

I will guess for now, but if it is not right I will update it.

It would be the associative property since you are flipping the equation around.

Hope this helps :)

The total surface area of the triangular prism is: 111 ft²

To find the total surface area of the given triangular prism, we will find the area of all the surfaces and add it up.

Formula for the area of a rectangle is:

Area = Length * Width

Area of a triangle is:

Area = ¹/₂ * base * height

Thus:

Total Surface area = 2(¹/₂ * 3 * 7) + (7 * 5) + (8 * 5) + (3 * 5)

Total Surface area = 21 + 35 + 40 + 15

Total Surface area = 111 ft²

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In the event that linear regression is required, we have two options: (1) change the delay column 2) ignore them.

A variable's value can be predicted using linear regression analysis based on the value of another variable. The dependent variable is the one you want to be able to forecast. The independent variable is the one you're using to make a prediction about the value of the other variable.

Given,

You want to run a regression to predict the probability of a flight delay, but there are flights with delays of up to 12 hours that are really messing up your model.

I immediately think of grouping delays into ranges such as those under 40 minutes, those between 40 minutes and 2 hours, those between 2 hours and 10 hours, and those above 10 hours. But doing so requires the use of a classification model, such as logistic regression. We frequently consider whether there will be a delay rather than how long it might last when thinking about delays. In the event that linear regression is required, we have two options: (1) change the delay column 2) ignore them.

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The sale price of the backpack is $25.5, the sale price of the soccer ball is $13.005, and the sale price of one jacket is 17.918.

Given:

The sale price of every item in a store is 85 percent of its regular price.

1. The regular price of a backpack is $30.

Then, the sale price = 85% of (the regular price of a backpack )

= 0.85  x ($30)

= $25.5

Hence, the sales price of the backpack = $25.5

2. The regular price of a soccer ball is = $15.30

The sale price of the soccer ball is 85% of its regular price.

Therefore, the sale price = 85% of $15.30

= $13.005

So, the sale price of the soccer ball is $13.005.

3. The regular price of a jacket is $21. 08

The sale price of a jacket is 85% of its regular price.

Therefore, the sale price = 85% of $21. 08

= $17.918

So, the sale price of a jacket is $17.918.

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Answer:

Yes. it takes 57 seconds.

Step-by-step explanation:

We first need to calculate the volume of the when it is full of air

volume = 4/3πr³

= 4/3π X 15³

= 14137.17 cm³

we then subtract the amount of air it had before pumping began

that is, 14 137.17 - 5000

= 9137.17 cm³

we need to calculate the time it will take to pump 9137.17 cm³ of air at the rate of 160cm³ per second

1 second = 160 cm³

? = 9137.17 cm³

9137.17/160 = 57.11 seconds

this approximately 57 seconds.

given the fact that 1 minute = 60 seconds, 57 seconds was less than a minute.

Answer:

\(choice \: c. \: - 77 < f(x) < - 2\)

Step-by-step explanation:

\(f( - 4) = - 5 ({ - 4}^{2}) + 3 = - 77\)

\(f( - 1) = - 5( { - 1}^{2}) + 3 = - 2\)

Thus finding the range of F(x).

The range of the given function is - 77 < f(x) < - 2.

"The range of a function is a set of all the images of elements in the domain."

The given function is:

f(x) = - 5x² + 3

It is defined over the domain - 4 < x < - 1.

For x = - 4, f(x) = - 5(- 4)² + 3 = - 80 + 3 = - 77

For x = - 1, f(x) = - 5(- 1)² + 3 = - 5 + 3 = - 2

Therefore, the range of the given function f(x) is:

- 77 < f(x) < - 2.

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F(3) is equal to 9, based on the given table and the corresponding values of x and f(x). Option D.

To find the value of F(3) based on the given table, we look at the corresponding x-value of 3 and find its corresponding f(x) value.

From the table, we see that when x = 3, f(x) = 9. Therefore, F(3) = 9.

The table shows the values of x and their corresponding f(x) values. We can see that when x increases by 1, f(x) also increases by 3. This indicates that the function has a constant rate of change, where the change in f(x) is always 3 units for every 1 unit change in x.

Given that F(3) represents the value of the function when x = 3, we look at the x-values in the table and find the corresponding f(x) value. In this case, when x = 3, f(x) = 9.

Therefore, the value of F(3) is 9. Option D is correct.

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Answer:

Elena's move will lead to the solution of the problem

Step-by-step explanation:

To solve the equation 7.5d=2.5d, Lin divides each side by 2.5d, and Elena subtracts 2.5d from each side. Will both moves lead to the solution? Explain your reasoning

Given:

7.5d = 2.5d

Lin divides each side by 2.5d, Lin:

7.5d / 2.5d = 2.5d / 2.5d

3 = 1

This can not be the solution to the problem because 3 can not be Equal to 1

Elena subtracts 2.5d from each side

7.5d = 2.5d

7.5d - 2.5d = 2.5d - 2.5d

5d = 0

This can lead to the solution of the problem

Elena's move will lead to the solution of the problem

Answer:

T=PV/nR

Step-by-step explanation:

Use the division property of equality to solve the ideal gas equation for T. Divide both sides of the equation by nR, then simplify.

PV=nPT

PV/RT=nRT/nR

PV/nR=T  

Therefore, the equation below is equivalent to the ideal gas equation.

T= PV/nR

The solution to the inequality are the region in the shaded area and the graph is attached

From the question, we have the following parameters that can be used in our computation:

y ≥3(0.8)^x

y ≥ x² - 5

Represent properly

y ≥ 3(0.8)^x

y ≥ x² - 5

Next, we make a plot of the system to determine the solution

The shaded area in the plot represent the solution to the inequality

In this case, one of the coordinates in the shaded area has a coordinate of (0, 5)

None of the options represent the shaded area (see attachment)

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Answer:

Step-by-step explanation:

\(V = ?\\r = 8\\h =5 \\\pi = 3.14\\\\V = \pi r^2 h\\\\V = 3.14 \times 8^2 \times 5\\V = 1004.8 cubic units\)

Answer:

C. 1004.8  cubic units

Step-by-step explanation:

Lets analyze the problem given, we have to find the volume of cylinder and use 3.14 as pi.

We can use the formula V=(3.14)r^2h to find the volume of the cylinder.

Below is the work to solve the formula:

8^2= 64

64(5)=320

320(3.14)=

1004.8  cubic units is our answer.

The horizontal distance of the boat from the sailor will be 196.26 meters.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

From a coastal lookout P,100 m above sea level, a sailor sights a boat at an angle of depression of 27 degrees.

Then the horizontal distance of the boat from the sailor is given as,

tan 27° = 100 / d

d = 100 / tan 27°

d = 196.26 m

The horizontal distance of the boat from the sailor will be 196.26 meters.

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The equation of the inequality graph with dashed line

The equation of the inequality graph with solid line

Using the slope intercept form of the straight line which is of the form

y = mx + c

The slope, m is the ratio of the change in the output to the change in the input. This is given by the formula

m = (y₀ - y₁) / (x₀ - x₁)

Slope calculation using the points (0, -4) and  (2, 0)

m = (-4 - 0) / (0 - 2)

m = 2

y intercept, c from the graph

c = -4

applying inequality representations

shading above the line is greater than and dotted lines means it does not have equal to

hence y > 2x - 4

for the solid line graph

the slope, m calculating using the points on the graph (0, 4) and  (4, 0)

m = (4 - 0) / (0 - 4)

m = (4) / (-4)

m = -1

y intercept, c from the graph

c = 4

The equation of the line is y = -x + 4

Solid lines indicate an equality in the inequality, while shading over the line indicates a greater than

hence y ≥ -x + 4

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The function h(x,y,z) is continuous at certain points in space. We will determine the points of continuity for the given functions.


a. To determine the points of continuity for h(x,y,z) = ln(3z³ - x - 5y - 3), we need to consider the domain of the natural logarithm function. The function is continuous when the argument inside the logarithm is positive, i.e., when 3z³ - x - 5y - 3 > 0.

Therefore, h(x,y,z) is continuous for all points (x,y,z) in space where 3z³ - x - 5y - 3 > 0.

b. For h(x,y,z) = 1 / (z³ - √(x+y)), we need to consider the domain of the function, which includes avoiding division by zero and square roots of negative numbers.

Thus, h(x,y,z) is continuous for all points (x,y,z) in space where z³ - √(x+y) ≠ 0 and x+y ≥ 0 (to avoid taking the square root of a negative number).

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Evaluating the distribution sample surveyed and comparing the long run state of the market of the three companies

i) The distribution of sample as at the beginning month of August is :

  Benfel limited =  5000 customers

  Cromwell Ltd  =   7167 customers

  Samtec  Ltd   =   4400 customers

ii) In the long run Benfel limited will have more customers than Cromwell and Samtec because they both lose more customers to Benfel limited than Benfel loses to them. also Benfel keeps a higher percentage of its customer

i) At the Beginning of the month of August the sample size for each company respectively will be

X * 70/100 = 3500 ∴ x ( sample size at August ) = 5000  ( Benfel )

y * 60/100 = 4300 ∴ y ( sample size at August ) = 7167   ( Cromwell )

z * 50/100 = 2200 ∴ z ( sample size at August ) = 4,400  ( Samtec )

ii) In the long run Benfel limited will have more customers than Cromwell and Samtec because they both lose more customers to Benfel limited than Benfel loses to them. also Benfel keeps a higher percentage of its customers

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Step-by-step explanation:

Length of the rectangle = 6.5 m

Width of the rectangule = 7.3 m

First case,

Area of the rectangle

= length × width

= 6.5 m × 7.3 m

= 47.45 sq.m (Ans)(i)

Second case,

Perimeter of the rectangle

= 2(length + width)

= 2(6.5 + 7.3)m

= 2 × 13.8 m

= 27.6 m (Ans)(ii)

The coefficient of determination, R^2, is the square of the correlation coefficient (r). Given that r = +0.275, we can calculate R^2 as follows:

R^2 = r^2 = (0.275)^2 = 0.075625

To express R^2 in percentage terms, we multiply it by 100:

R^2 = 0.075625 * 100 ≈ 7.56% (rounded to one decimal place)

Interpreting the coefficient of determination:

- % of the variation in scores on the verbal ability test can be explained by the variation in scores obtained on the mathematical ability test.

- Therefore, only % (7.56%) of the variation observed in scores on the verbal ability test can be explained by the variation in scores obtained on the mathematical ability test.

- The remaining % (92.44%) of the variation in verbal ability scores is explained by other factors.

- Scores on the mathematical ability test are predictors of the scores on the verbal ability test for % (7.56%) of the variation.

- % (7.56%) of the variation in verbal ability scores is explained by other factors.

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To find the vector v with the same direction as u and a length of 3, we can scale the vector u by a factor of 3 divided by its magnitude.

Given vector u = (1, 2, -1, 0) and the desired length of v as 3, we first need to calculate the magnitude (or length) of vector u.

The magnitude of a vector is computed using the formula:

∥u∥ = √(u1² + u2²+ u3² + u4²), where u₁, u₂, u₃, and u₄ are the components of vector u.

In this case, the magnitude of vector u is √(1² + 2² + (-1)² + 0²) = √6. To find vector v with the same direction as u and a length of 3, we scale u by the factor 3/√6.

This can be done by multiplying each component of u by the scaling factor.

Therefore, vector v = (3/√6) * (1, 2, -1, 0) = (√6/2, √6, -√6/2, 0).

Hence, vector v has the same direction as u and a length of 3.

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Answer:

sequence rule is + negative integers. Next 3 terms are -9,-15,-22