find a direct relationship between x and y.
x=t-5 and y=t^2-6t

The Sample of student at random from a large statistics class.

a) Sample space for Record the student's letter grade at the end of the course is , S = {A, B, C, D, F }. So, Correct option is option D.

b) Sample space for the student did or did not take a math class in each of the two previous years of school is S = {1st Year - Yes and 2nd Year - Yes, 1st Year - No and 2nd Year - Yes, 1st Year - Yes and 2nd Year - No, 1st Year - No and 2nd Year - No}. So, correct option is option C.

Sample Space: It is defined as the list of all possible outcome for given experiment.

a) record of Students grade are A, B, C, D, F.

These are all possible outcome for Student's letter grade at the end of course.

S= {A, B, C, D, F }

b) Possible outcome for whether student did or

did not take math class in each of the previous year of school is,

1st - Yes & 2nd - yes , 1st-yes & 2nd no

1st- NO & 2nd yes, 1st-NO & 2nd_NO

Hence, S = { 1st year - Yes & 2nd year - Yes,

1st year-NO & 2nd year- Yes, 1st year- yes & 2nd year - NO, 1st year - No & 2nd year - No}

Hence 3rd option is correct option.

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Complete question :

choose a student at random from a large statistics class. describe a sample space s for each of the following. (in some cases you may have some freedom in specifying s.)

a) Record the student's letter grade at the end of the course.

A) S = {0,10,20,30,...,100}

B) S = {0,1,2,...,100}

C) S = {Fail, Passed, Good, Very Good, Excellent}

D) S = {A, B, C, D, F}

b) Ask whether the student did or did not take a math class in each of the two previous years of school.

A) S = {Yes, No}

B)S = {Yes for each of the two years, No for each of the two years}

C) S = {1st Year - Yes and 2nd Year - Yes, 1st Year - No and 2nd Year - Yes, 1st Year - Yes and 2nd Year - No, 1st Year - No and 2nd Year - No}

D) S = {1st Year - Yes, 1st Year - No, 2nd Year Yes, 2nd Year - No}

Answer:

Step-by-step explanation:

To solve this inequality graphically, we need to find the values of x that make the inequality true. We can start by looking at the absolute value expression on its own.

The absolute value of a number is always non-negative, so we can split the inequality into two cases: when the expression inside the absolute value is positive, and when it is negative.

For the first case, we have:

3|2x - 4| > 6

2x - 4 > 0

x > 2

For the second case, we have:

3|2x - 4| > 6

2x - 4 < 0

x < 2

So, the solution to the inequality is the union of these two cases: x > 2 or x < 2. In interval notation, this is written as (-infinity, 2) U (2, infinity).

Answer:

  (-∞, 1) ∪ (3, ∞)

Step-by-step explanation:

You want a graphical solution to 3|2x -4| > 6.

The attached graph is of the expression ...

  3|2x -4| -6

This is greater than 0 where x is a solution to the given inequality. It is greater than 0 for x < 1 or for 3 < x. In interval notation, the solution is ...

  (-∞, 1) ∪ (3, ∞)

Answer:

Option A is the correct answer

Step-by-step explanation:

(3 × 8) + (6 × 8)

24 + 48 = 72

Thus, 9 x 8 = 72

The least total amount Lewis spends to buy 34 cartons of juice is £12.84 for Alternative B instead of £15.30 for Alternative A.

We can determine the total amount for each alternative and compare the two using two mathematical operations of multiplication and division.

We can also compare the alternatives by determining their unit cost per carton using division.

The number of cartons of juice required = 34

The unit cost of a carton = £0.45 or 45p

The total cost of 4 cartons = £1.80 (£0.45 x 4)

The total amount Lewis would spend for Alternative A = £15.30 (£0.45 x 34)

Cost of a pack of 4 cartons = £1.51

Unit cost per carton of the 4-carton pack = £0.3775 (£1.51/4)

The total amount Lewis spends for Alternative B = £12.835 (34/4 x £1.51)

Thus, mathematically Alternative B presents a lower cost than Alternative A, Lewis would choose to spend £12.84.

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The equivalent fraction for the given fraction is 1/5.

Equivalent fractions are two or more fractions that are all equal even though they different numerators and denominators.

The given fraction is 3/15.

The equivalent fraction is 3/15 =1/5

Therefore, the equivalent fraction for the given fraction is 1/5.

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The smallest leg of the triangular garden is 5 feet while the biggest leg is 12 feet.

The three-sided shape known as a triangle is sometimes used to allude to it.

The area of a triangle is defined as (1/2) base height, and the sum of all three angles within a triangle will be 180°.

As the given triangular garden has been drawn below,

By Pythagoras' theorem,

x² + (x + 7)² = (x + 8)²

x² + x² + 49 + 14x = x² + 64 + 16x

x² - 2x - 15 = 0

x² - 5x + 3x - 15 = 0

x(x - 5) + 3(x - 5) = 0

(x + 3)(x - 5) = 0

x = -3,5

Since length can never be negative thus x = 5.

The smallest leg = 5 feet

Biggest leg = 5 + 7 = 12 feet

Hence "The triangular garden's smallest leg is 5 feet long, while its longest leg is 12 feet".

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Answer:

1 1/6

Step-by-step explanation:

Hope it helps!

Note that to achieve a volume of 64cm³, the height of the cuboidal packet will equal 0.33cm²; If three layers of such are stacked on each other the total volume gained is: 192cm³.

The volume of a cuboid is given as L x B x H.

Where L = Lenght

B = Breath (or Width); and

H = Height.

To solve this problem, we need to first find the height of the box.

Since the volume of a Cuboid is given as L x B X H,

and we have

L = 16 and

B = 12, and

V= 64cm³

Then the expression for getting H will evolve from:

64 = 16 x 12 x H

64 = 192 x H

H = 64/192

H = 0.33cm

If three layers are placed on top of the volume amounts to:

64 x 3 = 192cm³

As a result, it is reasonable to declare that the height of the cuboidal packet will equal 0.33cm² to derive a volume of 64cm³; if three layers of such are piled on top of each other, the total volume acquired is: 192cm³.

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The principal that would need to be invested is  $4202.

We know that the principal has to  do with the amount of money that you have to invest so as to be able to obtain an interest. The interest in this case is a simple interest and it is charged on the principal. The amount is the sum of the principal and the interest.

We now have;

A = I + P

A = amount

I = interest

P = principal

But I = PRT/100

R = rate

T = time

We have;

A = PRT/100 + P

5000 = P * 9.5 * 2/100 + P

5000 = 19P/100 + P

5000 = 19P + 100P/100

5000 * 100 = 119P

P = 500000/119

P = $4202

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Answer:

A.) Yes, because 0.064 is less than 0.4

Step-by-step explanation:

The equation [tex]0.4^3 = 0.064[/tex] is a counterexample to the given conjecture because 0.064 is less than 0.4. This shows that the cube of a number is not always greater than the number.

In general, the cube of a number is the result of multiplying the number by itself three times. For example, the cube of 2 is [tex]2 * 2 * 2 = 8[/tex], and the cube of 5 is [tex]5 * 5 * 5 = 125[/tex]. The cube of a number is always greater than the number when the number is positive, because a positive number multiplied by itself three times is always a larger number. However, when the number is negative or a decimal, this is not always the case.

In the given equation, 0.4 is a decimal number, and [tex]0.4^3[/tex] is the cube of 0.4. The result of this calculation is 0.064, which is less than 0.4. This means that the cube of 0.4 is not greater than 0.4, and therefore the given conjecture is false.

Total 26, 250 passengers are flew in June in an airline flights between Chicago and Denver .

An Equations with roots , such as the square root cannot be solved until its root is eliminated. Once we have isolated the square root on one side, we can eliminate it by raising both sides of the equation to powers equal to the square root. For example, if the square root is only one-sided, we can square both sides. We have , An airline offers daily flights between Chicago and Denver. Cost function of flight is,

C = 0.2x + 1

where x represents the number of passengers (in thousands) in flight.

To calculate how many passengers flew each day in June, we need to set the function to 2.5 (since the cost is in millions of dollars) and solve for the variables. This means taking the square root equal to 2.5. Therefore, to solve for the variables contained in its square root, we need to square both sides. This process and solution are described below,

√(0.2x + 1) = 2.5

Squaring both sides

=> (√(0.2x + 1) )² = ( 2.5 )²

=> 0.2x + 1 = 6.25

=> 0.2 x = 6.25 - 1 = 5.25

=> x = 5.25/0.2

=> x = 26.25

Now, we know that our variable i.e x measures passengers in thousands, so total passenger flew in June are 26.25 × 1000 = 26, 250 .

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Answer:

56 points

Step-by-step explanation:

Let's say that for the next 5 days, you earn x points each day. This means that you will earn 5x more points before the month ends.

Since you already earned 1300 points, you will have earned 1300 + 5x points, which through the question we know is equal to 1580 points. Using this knowledge, we can set up the equation below:

1300 + 5x = 1580

5x = 280

x = 56

Therefore, you will need 56 points each day to reach your goal.

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The quotient will be 102.

What is a quotient?

In arithmetic, a quotient is a quantity produced by the division of two numbers. The quotient has widespread use throughout mathematics and is commonly referred to as the integer part of a division, or as a fraction or a ratio.

The number 8976 is called the numerator or dividend, and the number 88 is called the denominator or divisor.

The quotient of 8976 and 88, the ratio of 8976 and 88, as well as the fraction of 8976 and 88 all, mean (almost) the same:

8976 divided by 88, often written as 8976/88.

= 8976/88

= 102

Hence, the quotient will be 102.

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Answer:

The ladder rests against the wall at 6ft.

The ladder in Figure 2 rests about 3ft higher than the ladder in Figure 1.

Step-by-step explanation:

We can assume both of the figures display the ladder, ground, and wall forming a right triangle because the assignment is titled "apply the Pythagorean theorem", suggesting we should use the Pythagorean theorem and both figures are right triangles.

The Pythagorean theorem states that the sum of each leg squared is equal to the hypotenuse squared, or a^2 + b^2 = c^2, where "a" and "b" are legs and "c" is the hypotenuse.

At what height does the ladder in Figure 1 rest on the wall?

First, identify which sides are the legs and which is the hypotenuse. The hypotenuse is always the longest side and is the side opposite from the right angle. Thus, the hypotenuse in Figure 1 is the ladder length, and the two legs are the distance the ladder is from the wall and the height of the ladder against the wall. In other words, c = 10, a = 8, and b = the missing side length. Now, plug in the values to the Pythagorean theorem:

8^2 + b^2 = 10^2

64 + b^2 = 100

b^2 = 36

b = 6

The height at which the ladder in Figure 1 rests on the wall is 6 ft.

Approximately how much higher up the wall does the ladder in Figure 2 rest compared to the ladder in Figure 1?

We can set up the equation: Figure 2 ladder height - Figure 1 ladder height. We already know how where the ladder height of Figure 1 is, so we only need to solve for the ladder height in Figure 2 to get the result. Applying the same method as in the previous problem, we can input the values of Figure 2 into the Pythagorean theorem:

4^2 + b^2 = 10^2

16 + b^2 = 100

b^2 = 84

b = sqrt84

b ~ 9 ft

Now, we can find the difference between the Figure 2 ladder height and Figure 1 ladder height to get the answer to the question:

9 ft - 6 ft = 3 ft

The graph of the line segment after the translation (x, y) → (x-2, y-3) and (x, y) → (x-4, y + 5) has been drawn.

Transformation is rearranging a graph by a given rule it could be either increment of coordinate or decrement or reflection.

If we reflect any graph about y = x then the coordinate will interchange it that (x,y) → (y,x).

As per the given coordinate,T(1,2) and U(4,6)

Apply the translation (x, y) → (x-2, y-3)

T(1,2) → T'(1 - 2,2 - 3) = T'(-1,-1)

U(4,6) →  U'(4 - 2,6 - 3) = U'(2,3).

Apply the translation (x, y) → (x-4, y + 5)

T(1,2) → T'(1 - 4,2 + 5) = T'(-3,7)

U(4,6) →  U'(4 - 4,6 + 5) = U'(0,11)

All points have been plotted below.

Hence"After the translations (x, y) → (x-2, y-3)  and (x, y) → (x-4, y + 5), the graph of the line segment has been drawn.".

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Answer:

Translation (x, y) → (x - 2, y - 3):

Translation (x, y) → (x - 4, y + 5):

Step-by-step explanation:

Given endpoints of line segment TU:

Translation 1 (blue on attached diagram)

This means to subtract 2 from the x-values of the endpoints, and subtract 3 from the y-values of the endpoints:

Therefore:

Translation 2 (red on attached diagram)

This means to subtract 4 from the x-values of the endpoints, and add 5 to the y-values of the endpoints:

Therefore:

Answer:

Yes, they are equivalent.

Step-by-step explanation:

18 + 3.1m + 4.21m - 2

Combine like terms.

7.31m + 18 - 2

7.31m + 16 = 16 + 7.31m

Answer:

15.

Step-by-step explanation:

The common ratio = 60/120 = 1/2

So the next term is 30 * 1/2 = 15.

The amount Damian earns on Friday if he works for 2.75 hours is $43

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

f(x) = 12x + 10

For working for 2.75 hours, the value of x is

x = 2.75

Substitute x = 2.75 in the equation f(x) = 12x + 10

So, we have the following representation

f(2.75) = 12 x (2.75) + 10

Evaluate the sum of products

f(2.75) = 43

hence, the earnings is $43

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The rule of dilation is (4x, 4y)

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

Scale factor = 4

This means that

Image = point * scale factor

So, we have

Image = (x, y) * 4

Evaluate

Image = (4x, 4y)

Here, we have

Point = (-2, 8)

Scale factor = 1/2

So, we have

Image = (-2, 8) * 1/2

Image = (-1, 4)

Here, we have

Point = (2, 3)

Transformation = reflected across the y-axis.

So, we have

Image = (-x, y)

Image = (-2, 3)

Here, we have

A (4, 3) to point A' (12, 9)

The scale factor is

Scale factor = A'/A

So, we have

Scale factor = (12, 9)/(4, 3)

Evaluate

Scale factor = 3

Hence, the scale factor is 3

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Answer:

[tex]a_8=-\dfrac{729}{15625}[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Geometric sequence}\\\\$a_n=ar^{n-1}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\\phantom{ww}$\bullet$ $r$ is the common ratio.\\\phantom{ww}$\bullet$ $a_n$ is the $n$th term.\\\phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]

Given geometric sequence:

[tex]\dfrac{5}{3},\;-1,\;\dfrac{3}{5},\;...[/tex]

To find the common ratio, divide a term by the previous term:

[tex]\implies r=\dfrac{a_3}{a_2}=\dfrac{\frac{3}{5}}{-1}=-\dfrac{3}{5}[/tex]

Substitute the found common ratio and given first term into the formula to create an equation for the nth term:

[tex]a_n=\dfrac{5}{3}\left(-\dfrac{3}{5}\right)^{n-1}[/tex]

To find the 8th term, substitute n = 8 into the equation:

[tex]\implies a_8=\dfrac{5}{3}\left(-\dfrac{3}{5}\right)^{8-1}[/tex]

[tex]\implies a_8=\dfrac{5}{3}\left(-\dfrac{3}{5}\right)^{7}[/tex]

[tex]\implies a_8=\dfrac{5}{3}\left(-\dfrac{2187}{78125}\right)[/tex]

[tex]\implies a_8=-\dfrac{729}{15625}[/tex]

Answer: Lets do 2 1/7

Step-by-step explanation: first you will start off by turning it to an improper fraction.

you multiply the denominator with the whole number (2x7) which you get 14 then add the numrinator with the number you got from multiplying (14+1= 15 then you get 15/7

Then after that divide the fraction 15/7 and you get 2 with a remander of 1  

Here is a website you can use for fractions into whole numbers-https://www.cuemath.com

Based on the two (2) parallel lines m||n, the value of x is equal to 4.

The vertical angles theorem is also referred to as vertically opposite angles theorem and it states that two (2) opposite vertical angles that are formed whenever two (2) lines intersect each other are always congruent, which simply means being equal to each other.

In Geometry, when two (2) parallel lines are cut by a transversal, the pair of vertically opposite angles that are formed would always be equal to each other. In this context, we have the following;

m∠2 = m∠3

7x - 3 = x + 21

7x - x = 21 + 3

6x = 24

x = 24/6

x = 4.

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Answer:

A. Reflection

The length (in inches) of the second tablecloth is 43.75 inches

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

Width = 48 inches. and Length = 72 inches ⇒ Small tablecloth

Width = 30 inches. and Length = ?? inches ⇒ Large tablecloth

Represent the unknown length with x

So, we have

Width = 48 inches. and Length = 72 inches ⇒ Small tablecloth

Width = 30 inches. and Length = x inches ⇒ Large tablecloth

This shows a direct variation

So, we cross multiply the equation

x * 48 = 70 * 30

So, we have

x = 70 * 30/48

Evaluate

x = 43.75

Hence, the length is 43.75 inches

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The value of ATC, AFC, TVC if TC = 6Q² + 5Q + 10, are 6Q + 5 + 10/Q, 5 + 6Q,  5Q + 6Q² respectively.

Average total cost (ATC) is calculated by dividing the entire cost by the total amount of output produced. The additional cost incurred by creating one more unit of output is known as marginal cost (MC).

Given:

TC = 6Q² + 5Q + 10,

Calculate the value of AFC as shown below,

AFC = 10 / Q

Calculate the value of TVC as shown below,

TVC = TC - TFC

TVC = 5Q + 6Q²

Calculate the value of AFC as shown below,

AFC = TVC / Q

AFC = 5Q + 6Q² / Q

AFC = 5 + 6Q

Calculate the value of ATC as shown below,

ATC = TC / Q

ATC = 6Q² + 5Q + 10 / Q

ATC = 6Q + 5 + 10/Q

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The unit rate at which Darrell walks is 1.5 meters per second.

What is the unit rate?

A ratio that compares two amounts of DIFFERENT types of UNITS is called a rate. When a rate is expressed as a fraction, the denominator is 1 unit. Divide the numerator and denominator of the rate by the denominator to represent a rate as a unit rate.

Here, we have

Given

Darrell is walking for a distance of 90 meters in time 60 seconds.

We have to find the unit rate at which he walks.

To find out the unit rate we must divide the distance traveled by Darrell by the time taken to travel that distance.

The unit rate is given by :

Unit rate = Distance traveled in meters / Time taken in seconds

Unit rate = 90 meters / 60 seconds

Unit rate = 1.5 meters per second.

Hence, the unit rate at which Darrell walks is 1.5 meters per second.

In 60 seconds, Darrell walks 90 meters. Select the two answers that describe the unit rate at which he walks.

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So in this question, we have to convert the rectangular coordinates to polar coordinates.

Polar coordinates are (r, Q).

To convert rectangular coordinates to polar coordinates we use that x is equal to  rcosQ and y is equal to rsinQ

In this question x is equal to -2 and y is equal to 5.

Hence we have -2 is equal to rcosQ and 5 is equal to rsinQ .

From here, we have tanQ equal to -2.5 . Hence, Q = tan⁻¹ (-2.5)

We have x²+y² =r² and also x²+y² = 5²+2²=29 .

Hence, r=√29 and Q = tan⁻¹ (-2.5) .

Therefore the polar coordinates of (-2,5) are ( √29, tan⁻¹ (-2.5)).

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There is insufficient evidence to conclude that there is a significant linear relationship between

x and y because the correlation coefficient is not significantly different from zero.

The correlation coefficient, r, tells us about the strength and direction of the linear relationship between x and y.

However, the reliability of the linear model also depends on how many observed data points are in the sample.

We need to look at both the value of the correlation coefficient r and the sample size n, together.

We perform a hypothesis test of the “significance of the correlation coefficient” to decide whether the linear relationship in the sample data is strong enough to use to model the relationship in the population.

The sample data are used to compute r, the correlation coefficient for the sample. If we had data for the entire population, we could find the population correlation coefficient. But because we have only have sample data, we cannot calculate the population correlation coefficient. The sample correlation coefficient, r, is our estimate of the unknown population correlation coefficient.

The symbol for the population correlation coefficient is ρ, the Greek letter “rho.”

The hypothesis test lets us decide whether the value of the population correlation coefficient

ρ is “close to zero” or “significantly different from zero”. We decide this based on the sample correlation coefficient r and the sample size n.

If the test concludes that the correlation coefficient is significantly different from zero, we say that the correlation coefficient is “significant.”

There is sufficient evidence to conclude that there is a significant linear relationship between x and y because the correlation coefficient is significantly different from zero. What the conclusion means: There is a significant linear relationship between x and y. We can use the regression line to model the linear relationship between x and y in the population.

If the test concludes that the correlation coefficient is not significantly different from zero (it is close to zero), we say that correlation coefficient is “not significant.”

“There is insufficient evidence to conclude that there is a significant linear relationship between

x and y because the correlation coefficient is not significantly different from zero.” What the conclusion means: There is not a significant linear relationship between x and y. Therefore, we CANNOT use the regression line to model a linear relationship between x and y in the population.

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We must consider the sample size n together with the correlation coefficient r's value.

To determine whether the linear relationship in the sample data is strong enough to utilize to model the relationship in the population, we conduct a hypothesis test of the "significance of the correlation coefficient."

The correlation coefficient for the sample, r, is calculated using the sample data. The population correlation coefficient could be discovered if we had data for the entire population. However, we are unable to determine the population correlation coefficient because we only have sample data. Our best guess for the unknown population correlation coefficient is the sample correlation coefficient, or r.

The Greek letter "rho" serves as the sign for the population correlation coefficient.

is "near zero" or "quite different from zero." Based on the sample correlation coefficient r and the sample size n, we make this determination.

We refer to the correlation coefficient as "significant" if the test results show that it differs considerably from zero.

The fact that the correlation coefficient differs sufficiently from zero is sufficient evidence that x and y are meaningfully related linearly. The result indicates that there is a significant linear relationship between x and y. The regression line can be used to model the population's linear relationship between x and y.

Because the correlation coefficient does not deviate considerably from zero, x and y. What the conclusion says is that x and y do not have a meaningful linear connection.