Evaluate the limit { lim_(x rarr 6) } 7(7 x+7)^ 3 Question 13 Evaluate the limit: lim−(x−>9)(7x−63)/(x^2−2x−63)=

Answer:-12&-8

Step-by-step explanation:

since 3x is negative the -12 and -8 become positive to combine with 5 to either become 41 or 37

Answer below

Step-by-step explanation:

For the first 3x+7=-x-3 you will get 4x=-10 and the final answer is x=-5/2

The second is 3(x+7)=-x-3 which is different since it will equal 3x+21=-x-3 then 4x=-24 and you get x=-6

{18, 36, 24, 48, 39, 72}

In Exercises 1-6, the subgroup generated by the given subset is a set of elements that are all powers of the same element.

1. The subset {2,3} of Z12 generates the subgroup {2, 4, 8, 3, 9, 6, 12}.
2. The subset {4,6} of Z12 generates the subgroup {4, 8, 6, 12}.
3. The subset {8,10} of Z18 generates the subgroup {8, 16, 10, 18}.
4. The subset {12,30} of Z36 generates the subgroup {12, 24, 30, 36}.
5. The subset {12,42} of Z6 generates the subgroup {12, 6}.
6. The subset {18,24,39} of Z generates the subgroup {18, 36, 24, 48, 39, 72}.

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The length of 2W in inches can be calculated by using the measurements of the parallelogram. Wxx is 2x+15, and xY is x+27. Since the length of W xx and xY is referring to the same line, x+27=2x+15. Solving for x, x=12. Knowing the value of x, Wxx=2(12)+15=39 inches and xY=12+27=39 inches. Therefore, 2W=2(39)=78 inches.

The length of a line in a parallelogram can be calculated by adding the two measurements of the two lines containing the same point. Since the line containing point W is the same line containing point x, the two measurements can be solved for the same variable, x. Once the variable is determined, the value of the two lines containing the same point can be determined. The value of the two lines can then be multiplied by 2 to determine the length of the line in the parallelogram.

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Null hypothesis (H0): The population median price of single-family homes in the town has not changed since 2018.

H0: μ = $250,000

Alternative hypothesis (Ha): The population median price of single-family homes in the town has increased since 2018.

Ha: μ > $250,000

The null hypothesis assumes that there has been no change in the median price since 2018, while the alternative hypothesis assumes that the median price has increased. The alternative hypothesis is one-sided, as the broker is interested in testing whether the price has increased, rather than testing whether there has been any change (i.e., a two-sided test).

The null and alternative hypotheses for the scenario can be stated as follows:

Null hypothesis (H0): The population median price of single-family homes in the town has not changed since 2018.

H0: μ = $250,000

Alternative hypothesis (Ha): The population median price of single-family homes in the town has increased since 2018.

Ha: μ > $250,000

In the above hypotheses, μ represents the population median price of single-family homes in the town.

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Answer: 29%

Step-by-step explanation:

109/360=.294 Then move the decimal to make it a percent

Let A, B, and C be 3x3 matrices such that det(A) =2, det(C) = 4, and 2A^TB^-1 = C the determinant of matrix B is 4.

To find the determinant of matrix B, we can use the property of determinants that states that det(AB) = det(A)det(B). We can rearrange the given equation 2A^TB^-1 = C to get B = 2A^T C^-1. Then, we can take the determinant of both sides to get det(B) = det(2A^T C^-1).

Using the property of determinants, we can expand the right side of the equation to get det(B) = det(2)det(A^T)det(C^-1). Since the determinant of a scalar multiple of a matrix is the scalar multiple of the determinant, det(2) = 2^3 = 8. Also, the determinant of the transpose of a matrix is the same as the determinant of the original matrix, so det(A^T) = det(A) = 2.

Finally, the determinant of the inverse of a matrix is the reciprocal of the determinant of the original matrix, so det(C^-1) = 1/det(C) = 1/4.

Substituting these values back into the equation, we get det(B) = 8*2*(1/4) = 4. Therefore, the determinant of matrix B is 4.
det(B) = 4.

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a) The average rate of change of f on [−3,1] is 4.

b) The average rate of change of f on [x,x+h] is 3+16/h.

The average rate of change of a function f(x) on an interval [a,b] is given by the formula:

Average rate of change = (f(b)-f(a))/(b-a)

(a) To find the average rate of change of f on [−3,1], we plug in the values of a=-3 and b=1 into the formula:

Average rate of change = (f(1)-f(-3))/(1-(-3))
= (f(1)-f(-3))/4

Now, we need to find the values of f(1) and f(-3) by plugging in the values of x into the given function:

f(1)=1+3(1)-8=-4
f(-3)=-3+3(-3)-8=-20

Plugging these values back into the formula, we get:

Average rate of change = (-4-(-20))/4
= 16/4
= 4

Therefore, the average rate of change of f on [−3,1] is 4.

(b) To find the average rate of change of f on [x,x+h], we plug in the values of a=x and b=x+h into the formula:

Average rate of change = (f(x+h)-f(x))/(x+h-x)
= (f(x+h)-f(x))/h

Now, we need to find the values of f(x+h) and f(x) by plugging in the values of x and x+h into the given function:

f(x+h)=x+h+3(x+h)-8
=4x+3h-8
f(x)=x+3x-8
=4x-8

Plugging these values back into the formula, we get:

Average rate of change = (4x+3h-8-(4x-8))/h
= (3h+16)/h
= 3+16/h

Therefore, the average rate of change of f on [x,x+h] is 3+16/h.

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Answer:777

Step-by-step explanation:888

The equation which we can use to find the length "s" of long piece of string before Diana cuts it is (a) 8s = 1.25.

In order to find the length "s" of the long piece of string, we need to multiply the length of each of the 8 equal pieces of string by 8, because they are all cut from the same long piece of string.

So, the equation we can use to find the length s of the long piece of string before Diana cuts it is:

⇒ 8 × 1.25 = s,

Simplifying the equation:

We get,

⇒ 10 = s

Therefore, the correct equation is option(a) 8s = 1.25.

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The given question is incomplete, the complete question is

Diana is a junior counselor at Cactus Ville craft camp. One day, Diana's campers make lanyard keychains out of plastic string. For each keychain, Diana cuts a long piece of string into 8 equal pieces. Each piece is 1. 25 feet long.

Which equation can you use to find the length s of the long piece of string before Diana cuts it?

(a) 8s = 1.25

(b) s - 8 = 1.52

(c) s + 8 = 1.25

(d) s/8 = 1.25

Step-by-step explanation:

remember,

100% = 1

1% = 100%/100 = 1/100 = 0.01

as decimal

2/5 % = 1% × 2/5 = 0.01 × 0.4 = 0.004

as fraction

1% × 2/5 = 1/100 × 2/5 = 2/500 = 1/250

Answer:

C

Step-by-step explanation:

They are not proportional

If 3 pie cost $12, one pie will be $4

If 10 pie cost $25, then 1 pie is $2.5

$4 is not proportional to $2.5

Hence 12/3 is not proportional to 25/10

Answer:

option (1)

Step-by-step explanation:

rearrange making x the subject, then x is the inverse

y = [tex]\frac{3}{2}[/tex] x ( multiply both sides by 2 to clear the fraction )

2y = 3x ( isolate x by dividing both sides by 3 )

[tex]\frac{2}{3}[/tex] y = x

change y back into terms of x , then inverse is

[tex]f^{-1}[/tex] (x) = [tex]\frac{2}{3}[/tex] x , or

y = [tex]\frac{2}{3}[/tex] x

The simple  interest values are all wrong

Simple Interest (S.I) is a method of charging or yielding a specific percentage on the principal amount borrowed/deposited in a particular period. It is calculated using the formula

SI = (Principal*Rate*Time)/100,

a) SI = (450*25.2*3)/100,

SI = %70.2

2) SI = (Principal*Rate*Time)/100,

SI = (250*3.75*5)/100,

$46.875

(3) SI = (Principal*Rate*Time)/100,

SI = (1800*2.1*2)/100,

SI = $75.6

4) SI = (Principal*Rate*Time)/100,

SI = (1500*2.9*2)/100,

SI = $87

5) SI = (Principal*Rate*Time)/100,

SI = (50*1.9*10)/100,

SI =$9.5

6) SI = (Principal*Rate*Time)/100,

SI = (8*0.7*300)/100,

SI = $16.8

7) SI = (Principal*Rate*Time)/100,

SI = (125*2.03*4)/100,

SI = $10.15

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a) The factor in this experiment would be the use of a parachute during skydiving.

b) The experimental units would be individuals who are participating in skydiving.

c) A placebo for this study would be a dummy or fake parachute that is identical in appearance to a real parachute, but does not actually function as a parachute.

d) The treatments would be the use of a real parachute and the use of the placebo or fake parachute.

e) The response variable would be the incidence of injury or death during the skydiving experience.

f) Some sources of variability that would be controlled include

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Step-by-step explanation:

please answer this question quickly

Answer:

H<5

Step-by-step explanation:

u solve it as a normal equation but with the symbol <.

Answer:

a) (0.333, 13.11)

b)  (1, 9)

Step-by-step explanation:

a)

5x+3y=41

2x+3y=40

[The steps are labelled so they can be referenced in the subsequent problems]

A.  Rearrange one of the two equations so as to isolate the x or y to one side.  I'll use 2x+3y=40:

2x+3y=40

2x = 40-3y

x = (40-3y)/2

B.  Now use that expression of x in the other equation:

5x+3y=41

5((40-3y)/2)+3y=41

(200-15y)/2 +3y = 41

100 - 7.5y + 3y = 41

-4.5y = - 59

 y = 13.11

C.  Now use y=13.11 in either equation to find x:

2x+3y=40

2x+3*(13.11)=40

2x + 39.33 = 40

2x = 0.67

x = 0.333

D.  Answer: The lines intersect at (0.333, 13.11)

b)

x+7y=64

x+3y=28

A.  

x+7y=64

x=64-7y

B.

x+3y=28

(64-7y)+3y=28

64-4y = 28

-4y = -36

  y = 9

C.

x=64-7y

x=64-7*9

x = 1

D.  Answer: The lines intersect at (1, 9)

See the attached graph for proof of the points of intersection.

HELPPP PROVIDED (I hope)

[tex]y =ax+b[/tex]

[tex]x = 0 \iff a(0) + b = 3 \implies b = 3[/tex]

[tex]x = 1 \iff a(1) + 3 = 5 \implies a = 2\\[/tex]

[tex]\implies \bf y = 2x + 3[/tex]

___________

[tex]x = 2 \iff 2(2) + 3 = 4 + 3 = 7[/tex]

[tex]x = 3 \iff 2(3) + 3 = 6 + 3 = 9[/tex]

The equation that quickly reveals the y-intercept is f(x) = 3x²+ 36x + 33 and the y- intercept is 33

The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis.

This shows that the y-intercept is gotten when x is 0

Therefore amongst the equation above equation 1 is the equation that easily shows the y-intercept.

The equation f(x) = 3x²+ 36x + 33 is presented in a standard form of quadratic equation.

when x= 0

f(x) = 3x²+ 36x + 33

f(x) = 3(0)²+ 36(0) + 33

f(x) = 0+ 0+ 33

= 33

therefore the y-intercept is 33

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Answer:

If it costs 5% of $75  it would be $3.75

If it is 5% off $75 it would be $71.25

How we find the answer.

To find 10% of an item you move the decimal point once to the right

If we do this to 75.00 it would be 7.500

We can remove the two 0's

7.5

We are not looking for 10% though we are looking for 5%

Half of 10 = 5 so half 7.5

3.75 is 5% of 75

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

Now if we want to find out 5%  off of 75 we subtract

75.00 - 3.75

71.25

Hope i could help

Answer:

$3.75

Step-by-step explanation:

If the item was on sale and cost 5% of its original price, to find the answer we would have to find 5% of 75 and to do this we have to do 5 ÷ 100 × 75

This means that the price would be $3.75

Hope this helps, have a lovely day! :)

In the following question, among the various parts to solve- a- "x = [[3/2x3-3/2x3x3]]", b- the dimension of the solution set of Ax = 3x is 1.

(a) To find all solutions of the equation system Ax = 3x, we need to solve the following system of linear equations:

(3 4 3) (x1) (3x1)

(2 5 3) (x2) = (3x2)

(0 2 6) (x3) (3x3)

This can be written as (A - 3I)x = 0, where I is the identity matrix. To find the solutions, we need to find the null space of A - 3I.

(A - 3I) = [[0 4 3 2 2 3 0 2 3]]

To find the null space of this matrix, we row-reduce it to obtain:

[[1 0 -3/2 0 1 3/2 0 0 0]]

The last row tells us that x3 is a free variable, while the first two rows give us:

x1 = (3/2)x3

x2 = (-3/2)x3

Therefore, the general solution to Ax = 3x is:

x = [[3/2x3-3/2x3x3]]

where x3 is any real number.

(b) We can speak about the dimension of the solution set of Ax = 3x because it is a linear homogeneous equation. In this case, the solution set is a subspace of the vector space R^3, and the dimension of this subspace is the number of linearly independent solutions. Since we have one free variable in the solution, the set of solutions is a line in R^3, and its dimension is 1. Therefore, the dimension of the solution set of Ax = 3x is 1.

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x and y must have values of 3 and 11, respectively.

What is a Parallelogram?

A parallelogram is a geometric shape with sides that are parallel to one another in two dimensions. It is a form of polygon with four sides (sometimes known as a quadrilateral) in which each parallel pair of sides have the same length. A parallelogram has adjacent angles that add up to 180 degrees.

The angles in a parallelogram are given in the diagram.

As opposite sides are equal and parallel in a parallelogram, the alternate interior angles must also be the same.

This gives:

5y - x = 52 ...(i)

6y - 18 = 48 ...(ii)

Solving (ii)

6y = 66

y = 11

Substituting in (i)

5(11) - x = 52

x = 3

The values of x and y must be 3 and 11 respectively.

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Let ((2) = ve- 4 and g(2) = 12 11r + 30. Then f(1) = i√3, g(1) = 21, Domain of f(x) = [4, ∞) and  Domain of g(x) = (-∞, ∞)

First, let's find f(1) and g(1). To do this, we simply substitute x = 1 into the equations for f(x) and g(x):

f(1) = √(1 - 4) = √(-3) = i√3

g(1) = 2(1) - 11(1) + 30 = 2 - 11 + 30 = 21

Now, let's find the domains of f(x) and g(x). The domain of a function is the set of all values of x for which the function is defined.

For f(x) = √(x - 4), the expression inside the square root must be greater than or equal to 0 in order for the function to be defined. This means that:

x - 4 ≥ 0

x ≥ 4

So the domain of f(x) is [4, ∞).

For g(x) = 2x - 11x + 30, there are no restrictions on the domain, so the domain of g(x) is (-∞, ∞).

So the final answers are:

f(1) = i√3

g(1) = 21

Domain of f(x) = [4, ∞)

Domain of g(x) = (-∞, ∞)

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To show that a pattern repeats indefinitely, a bar is put over it. For example, 2.2616161 in bar notation is: 2.26¯.

The meaningful numbers in a number are known as significant figures, also known as significant digits. They are the digits that indicate the level of measurement uncertainty and add to the precision of a number. In other words, important figures are one digit that is either uncertain or estimated in addition to the digits that are known for sure.

given

Repeating digits are represented using the bar notation.

We must recognise the repetitive pattern in the decimal before we can represent 2.2616161 as a repeating decimal using bar notation.

The repetitive pattern is 6161, as can be seen by looking at the decimal. As a result, we can write 2.2616161 as:

2.26 16161...

To show that a pattern repeats indefinitely, a bar is put over it. For example, 2.2616161 in bar notation is: 2.26¯.

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The coordinates (2,1) will be on graph but (1,3) is not on graph.

What is a coordinate?

A coordinate is a set of two or more numbers or variables that identify the position of a point, line, or plane in a space of a given dimension. Coordinates are used to pinpoint a particular location, such as a specific point on a map or a specific point in a mathematical equation.

This means that for every 1.5 cups of dried fruit, there is 1 pound of granola. The graph of this proportional relationship would be a line that goes through the origin and has a slope of 1.5. For the point (2,1), the x-coordinate (2) is exactly 1.5 times the y-coordinate (1). This means that if you used 2 cups of dried fruit, you would get 1 pound of granola. Therefore, this point would be on the graph of the proportional relationship, so the answer is Yes. However, for the point (1,3), the x-coordinate (1) is not 1.5 times the y-coordinate (3). This means that if you used 1 cup of dried fruit, you would not get 3 pounds of granola.

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The probability that a random sample of 289 students will have a mean score of more than 621 is 0.0869. The probability that a random sample of 289 students will have a mean score of less than 595 is 0.1597.

To answer this question, we need to use the central limit theorem. The central limit theorem states that the distribution of sample means approaches a normal distribution as the sample size increases. In this case, the sample size is 289 students.

First, we need to calculate the standard error of the mean. The standard error of the mean is the standard deviation of the distribution of sample means. It is calculated as:

SE = σ/√n

Where σ is the standard deviation of the population and n is the sample size. In this case, σ = 187 and n = 289. So, the standard error of the mean is:

SE = 187/√289 = 11.04

Next, we need to calculate the z-score for each of the two scenarios. The z-score is a measure of how many standard deviations away from the mean a data point is. It is calculated as:

z = (x - μ)/SE

Where x is the data point, μ is the population mean, and SE is the standard error of the mean. In the first scenario, x = 621, μ = 606, and SE = 11.04. So, the z-score is:

z = (621 - 606)/11.04 = 1.36

In the second scenario, x = 595, μ = 606, and SE = 11.04. So, the z-score is:

z = (595 - 606)/11.04 = -0.996

Now, we can use the z-score to find the probability. The probability that a random sample of 289 students will have a mean score of more than 621 is:

P(z > 1.36) = 0.0869

The probability that a random sample of 289 students will have a mean score of less than 595 is:

P(z < -0.996) = 0.1597

So, the probability that a random sample of 289 students will have a mean score of more than 621 is 0.0869 (rounded to four decimal places) and the probability that a random sample of 289 students will have a mean score of less than 595 is 0.1597 (rounded to four decimal places).

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Answer:

think its this not sure : Alternate interior angles theorem

Step-by-step explanation:

Answer:

The two numbers are 90 and 59

Step-by-step explanation:

Let's call the two numbers x and y.

From the problem statement, we know that:

x + y = 149 (the sum of two numbers is 149)

x - y = 31 (the difference of the two numbers is 31)

To solve for x and y, we can use the method of elimination. Adding the two equations together eliminates the y term:

(x + y) + (x - y) = 149 + 31

2x = 180

x = 90

Substituting x = 90 into one of the original equations, we can solve for y:

x + y = 149

90 + y = 149

y = 59

Therefore, the two numbers are 90 and 59.

Answer:Answer:

1) SA = 2(wl + hl + hw) = 2(12*2 + 12*6 + 6*2) = 2(24 + 72 + 12) = 2(108) = 216

2) SA = (6*4)/2 + 6*11 + 2(5*11) = 12 + 66 + 110 = 188

3) SA = 2(6*12 + 14*12 + 6*14) = 648

4) (9*12)/2 + 15*6 + 9*6 + 12*6 = 54 + 90 + 54 + 72 = 270

5) 2(16*9 + 4*9 + 16*4) = 488

6) SA = 2πrh+2πr^2 = 2*3.14*10*16 + 2*3.14*10^2 = 1004.8 + 628 = 1632.8

7) SA = 2(7*7 + 14*7 + 7*14) = 490

8) SA = 2πrh+2πr^2 = 2*3.14*7*11 + 2*3.14*7^2 = 483.56 + 307.72 = 791.28

9) (12*10)/2 + 2(14*13) + 14*10 = 60 + 364 + 140 = 564

Step-by-step explanation:

The mathematical statement οf given statement Sux less than twο times a number is nο mοre than 17 is  2x - 6 ≤ 17.

A mathematical statement is a sentence that can be either true οr false and cοntains mathematical expressiοns οr variables, such as numbers, variables, οperatiοns, relatiοns, οr lοgical cοnnectives.

Mathematical statements can take many fοrms, such as equatiοns, inequalities, geοmetric theοrems, and lοgical prοpοsitiοns. Fοr example, "2 + 2 = 4" is a mathematical statement that is true, while "1 + 1 = 3" is a mathematical statement that is false.

Nοw,

Given statement can be written as

Twο times=2x

six less than 2 times=2x-6

is nο mοre than 17= 2x-6≤17

where x is the number.

Hence,

          The mathematical statement οf given statement Sux less than twο times a number is nο mοre than 17 is  2x - 6 ≤ 17.

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