a suburban hotel derives its revenue from its hotel and restaurant operations. the owners are interested in the relationship between the number of rooms occupied on a nightly basis and the revenue per day in the restaurant. following is a sample of 25 days (monday through thursday) from last year showing the restaurant income and number of rooms occupied. day revenue occupied day revenue occupied 1 $ 1,452 30 14 $ 1,425 31 2 1,361 29 15 1,445 34 3 1,426 31 16 1,439 34 4 1,470 32 17 1,348 31 5 1,456 32 18 1,450 30 6 1,430 32 19 1,431 30 7 1,354 29 20 1,446 31 8 1,442 30 21 1,485 34 9 1,394 32 22 1,405 30 10 1,459 32 23 1,461 32 11 1,399 31 24 1,490 30 12 1,458 31 25 1,426 30 13 1,537 34 click here for the excel data file a. choose the scatter diagram that best fits the data. scatter diagram 1 scatter diagram 2 scatter diagram 3 multiple choice scatter diagram 1 scatter diagram 2 scatter diagram 3 b. determine the coefficient of correlation between the two variables. (round your answer to 3 decimal places.) c-1. state the decision rule for 0.01 significance level: h0: rho ≤ 0; h1: rho > 0. (round your answer to 3 decimal places.) c-2. compute the value of the test statistic. (round your answer to 2 decimal places.) c-3. is it reasonable to conclude that there is a positive relationship between revenue and occupied rooms? use the 0.01 significance level. d. what percent of the variation in revenue in the restaurant is accounted for by the number of rooms occupied? (round your answer to 1 decimal place.)

The expression ((t − 9) · (t² − 9) · (t³ − 9) · (t⁴ − 9) · (t⁵ − 9) · (t⁶ − 9) · (t⁷ − 9) can be written in terms of product notation as Π⁷k=1 \((t^k - 9)\).

As per the question, we can write the expression as:

(t − 9) · (t² − 9) · (t³ − 9) · (t⁴ − 9) · (t⁵ − 9) · (t⁶ − 9) · (t⁷ − 9)

Using product notation, we can write this as:

Π⁷k =1 \((t^k - 9)\)

where Π represents the product of terms, k is the index of the product, and the subscript 7 indicates that the product runs from k = 1 to k = 7.

Therefore, the expression ((t − 9) · (t² − 9) · (t³ − 9) · (t⁴ − 9) · (t⁵ − 9) · (t⁶ − 9) · (t⁷ − 9) can be written in terms of product notation as Π⁷k=1 \((t^k - 9)\).

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lol i just answered this its the answer you have selected

The margin of error can be calculated using the formula:
Margin of error = (upper limit of the confidence interval - lower limit of the confidence interval) / 2

In this case, a margin of error of 9.55 suggests that the sample mean is quite precise, since it's relatively close to the true population mean (which we know to be 52.90).

In this case, the lower limit of the confidence interval is 43.85 and the upper limit is 61.95.
Margin of error = (61.95 - 43.85) / 2
Margin of error = 9.55
Therefore, the margin of error is 9.55. This means that if the sample size were to be repeated, we would expect the sample mean to be within 9.55 units of the true population mean 95% of the time.
It's worth noting that the confidence interval provides a range of values within which we can be reasonably certain that the true population mean lies. The margin of error, on the other hand, gives us an indication of the precision of our estimate. However, if the margin of error were larger, this would indicate that our estimate is less precise and that we need a larger sample size to obtain a more accurate estimate of the population mean.

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Okay, let's calculate the average rate of change:

On day 3, the high temperature was 59 degrees.

On day 5, the high temperature was 53 degrees.

So the temperature change from day 3 to day 5 was 59 - 53 = 6 degrees.

And the number of days was 5 - 3 = 2 days.

So the average rate of change = (6 degrees) / (2 days) = 3 degrees per day

The closest choice is:

The high temperature changed by an average of −4 degrees per day from day 3 to day 5.

So the answer is:

5

Answer:

solution set for x = { 4,5,6}

Answer:

2<x<12

Step-by-step explanation:

Firstly, look at this formula-

a-b<x<a+b

If we make 7, A, and 5, B, then the formula would be 7-5<x<7+5

So after you do the math it would be 2<x<12

Hence, the answer is 2<x<12

BTW if the answer is correct then can you please mark me brainlyest?

I'm only 9 years old

Thanks!

Factor by grouping: 16x³ +28x² - 28x - 49 = 0 is  (4x² - 7) (4x - 7) = 0

Large polynomials can be divided into groups based on a common factor. As a result, we may factor each distinct group and then merge like words. We refer to this as factoring by grouping.

We have the equation,

16x³ +28x² - 28x - 49 = 0

In order to solve the equation by using factor by grouping:

We find common terms in between,

So, we arrange the terms,

16x³ +28x² - 28x - 49 = 0

4x² (4x - 7) -7 (4x - 7) = 0

Here, we have common term (4x-7).

Factor out the common binomial.

(4x² - 7) (4x - 7) = 0

Therefore, (4x² - 7) (4x - 7) = 0 is the factor.

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The correct option is b (4x+2)(4x-2).

Assuming that the expression is \(16x^2-4\), we can factorize the expression as follows:

\(16x^2-4=(4x)^2-(2)^2\\ 16x^2-4=(4x+2)(4x-2)\)

Note that we can further simplify the expression as:

4(2x+1)(2x-1)

By considering the planet's diameter as the distance from its center, we can determine the gravitational acceleration at that altitude. At an altitude equal to the planet's diameter, the gravitational acceleration would be 3.825 m/s² on this hypothetical planet.

The inverse square law of gravity states that the gravitational force decreases as the square of the distance from the center of mass increases.

Since the diameter of the planet is equal to twice the radius, the altitude equal to the planet's diameter is equivalent to being at a distance twice the radius away from the center of mass.

Let's denote the planet's surface gravitational acceleration as "g" and the radius as "R".

Using the inverse square law, we can calculate the gravitational acceleration at an altitude equal to the planet's diameter as follows:

g_altitude = g * (R / (2R))²

= g * (1/4)

= g/4

= 15.3 m/s² / 4

= 3.825 m/s²

Therefore, at an altitude equal to the planet's diameter, the gravitational acceleration would be 3.825 m/s² on this hypothetical planet.

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The given table represents a discrete probability distribution.

To determine whether the table represents a discrete probability distribution, we need to check if it satisfies two conditions: the sum of probabilities equals 1 and all probabilities are non-negative.

In the given table, the sum of probabilities is 0.3 + 0.3 + 0.1 + 0.3 = 1, which satisfies the first condition.

Additionally, all probabilities in the table are non-negative, as each value of p(x) is greater than or equal to 0. This satisfies the second condition.

Therefore, since the table satisfies both conditions, it represents a discrete probability distribution. It provides the probabilities for each value of x, indicating the likelihood of each outcome occurring in a discrete random variable scenario.

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The measure of the angle WXY is 152 degrees

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

Using the above as a guide, we have the following:

m∠MYW = 104 - 90

m∠MYW = 14

The inscribed angle opposite to the same arc is half of the external angle

So, we have

mw = 2 * m∠MYW

mw = 2 * 14

mw = 28 degrees

Also, we have

my = 180 degrees

So, we have

Angle WXY = 180 - 28

Evaluate the difference

Angle WXY = 152

Hence, the measure of the angle is 152 degrees

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The value of sin(x) in terms of cos(x) is √1 - cos²(x). The value of sin(x) is 3/5.

Since x is an angle in the second quadrant, sin(x) is positive and cos(x) is negative.

To write sin(x) in terms of cos(x), we can use the identity sin²(x) + cos²(x) = 1 and solve for sin(x):

                                sin²(x) + cos²(x) = 1

                                sin²(x) = 1 - cos²(x)

                                sin(x) = ± √(1 - cos²(x))

Since sin(x) is positive in the second quadrant, we have:

                               sin(x) = √(1 - cos²(x))

To show that cos(x) = -4/5, we can use the given equation:

                               3sin(x) - 4cos(x) = 5

We can rearrange this equation to get cos(x) on one side:

                              4cos(x) = 3sin(x) - 5

                              cos(x) = (3sin(x) - 5) / 4

Now we can substitute the expression for sin(x) that we found earlier:

                              cos(x) = (3√(1 - cos²(x)) - 5) / 4

Multiplying both sides by 4 and simplifying, we get:

                              4cos²(x) + 3cos(x) - 4 = 0

This is a quadratic equation in cos(x). We can solve it using the quadratic formula:

                             cos(x) = [-3 ± √(3² - 4(4)(-4))] / (2(4))

                             cos(x) = (-3 ± 7) / 8

                             cos(x) = 1/2 or cos(x) = -4/5

Since x is in the second quadrant, we have cos(x) < 0, so cos(x) = -4/5.

Finally, we can use the expression for sin(x) that we found earlier to get:

                            sin(x) = √(1 - cos²(x))

                            sin(x) = √(1 - (-4/5)²)

                            sin(x) = √(1 - 16/25)

                            sin(x) = √9/25

                            sin(x) = 3/5

Therefore, the exact value of sin(x) is 3/5.

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Answer:

1.5 x 10^0

Step-by-step explanation:

The statements that accurately compare the domain and range of the functions are: The domain of all three functions is all real numbers, The range of f(x) and h(x) is all real numbers, but the range of g(x) is all real numbers except 0.

The domain of a function refers to all the possible input values that make the function defined. For the quadratic function f(x) = 3x², there are no values of x that make the function undefined, so the domain of f(x) is all real numbers. To find the range of f(x), we can calculate the vertex of the parabola, which is (0,0). The range of f(x) is all real numbers greater than or equal to zero.

For the quadratic function f(x) = 3x², we can determine the vertex using the formula:

h = -b/2a

In this case, a = 3 and b = 0, so:

h = -0/2(3) = 0/6 = 0

The x-coordinate of the vertex is 0.

To find the y-coordinate, we evaluate the function at the vertex:

f(0) = 3(0)² = 0

So the vertex of the parabola is (0,0).

Since the coefficient of x² is positive, the parabola opens upwards, and the minimum value of the function occurs at the vertex. Therefore, the range of f(x) is all real numbers greater than or equal to zero.

For the rational function g(x) = 1/3x, the function is undefined when the denominator is equal to zero. Thus, we solve for the value(s) of x that make the denominator zero:

3x = 0

Dividing both sides by 3, we get:

x = 0

Therefore, the domain of g(x) is all real numbers except zero. The range of g(x) is all real numbers except zero, since the function cannot equal zero.

For the linear function h(x) = 3x, there are no values of x that make the function undefined. Thus, the domain of h(x) is all real numbers. The range of h(x) is also all real numbers, since the function is a straight line that passes through the origin and extend infinitely in both directions.

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The rectangular coordinates (x, y, z) of the point with cylindrical coordinates (4, 5, 6) are approximately (3.984778792366982, 0.3486229709906327, 6).

To convert cylindrical coordinates (r, θ, z) to rectangular coordinates (x, y, z), we can use the following formulas:

x = r * cos(θ)

y = r * sin(θ)

z = z

In this case, the cylindrical coordinates are given as (4, 5, 6). Let's calculate the rectangular coordinates:

x = 4 * cos(5)

y = 4 * sin(5)

z = 6

To express the values in exact form, we'll keep them as symbolic expressions:

x = 4 * cos(5) ≈ 4 * 0.99619469809174553229501040247389 ≈ 3.9847787923669821291800416098956

y = 4 * sin(5) ≈ 4 * 0.08715574274765817355806427161944 ≈ 0.34862297099063269423225708647776

z = 6

Therefore, the rectangular coordinates of the point with cylindrical coordinates (4, 5, 6) are approximately (3.9847787923669821291800416098956, 0.34862297099063269423225708647776, 6).

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A rotation of 90° will map the pre-image ABC to the image ABC.

What are transformations in triangles?

Triangles can be moved, rotated, flipped, and turned to look exactly the same. More so, they coincide with each other when they are moved in the same position.

What is rotation?

The act of turning an object in a circle about a central axis. The centre point can be rotated at an angle to create various shapes.

What is pre-image?

The collection of all domain elements for a given function that map to a certain subset of the codomain.

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Answer:

3 1/2

Step-by-step explanation:

4 1 3

_ - _ = _

6 6 6

Then we simplify. 3 3 1

_ ÷ = _

6 3 2

Then just add your 3 and there 3 1/2 is your asnwer

The difference between 3 4/6 and 1/6 will be 3 1/2.

Given numbers are:

(1)\(3\frac{4}{6}\) \(=\frac{22}{6}\)

(2)\(\frac{1}{6}\)

A fraction is a part of a whole.

The Difference between \(3\frac{4}{6}\) and \(\frac{1}{6}\) will be = \((\frac{22}{6} )-(\frac{1}{6} )\)

\(=\frac{22}{6} -\frac{1}{6}\)

\(=\frac{21}{6}\)

\(=\frac{7}{2}\)

\(=3\frac{1}{2}\)

Hence, the difference between 3 4/6 and 1/6 will be 3 1/2.

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A pair of intersecting lines that forms a pair of complementary angles is as drawn below.

Remember that complementary angles are defined as angles which sum is equal to 90°.

Besides, each of the pairs of opposite angles made by two intersecting lines are called vertical angles. Now, from congruent proofs, we know that that vertical angles are congruent. In another words, they have the same measure.

Thus, we have to draw two vertical angles that measure:

90° ÷2 = 45°

This image is as drawn below in the attached file.

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Answer:C

Therefore: In Quadrant I, cos(θ) > 0, sin(θ) > 0 and tan(θ) > 0 (All positive). For an angle in the second quadrant the point P has negative x

Step-by-step explanation:

There are 16 oz in a pound so it would be cheaper to purchase 1 pound for $3.75

The expected value of your bet is $10.58 (rounded to the nearest cent).

Let's break this down:

There are 52 cards in a standard deck, and 12 of them are face cards (4 jacks, 4 queens, and 4 kings). Therefore, the probability of drawing a face card on any given draw is 12/52 or 3/13. When the first card is drawn, there will be 51 cards left in the deck, 11 of which are face cards.

Therefore, the probability of drawing a non-face card on the second draw is 40/51.

The probability of both events happening (drawing two non-face cards in succession) is the product of their individual probabilities:

37/52 × 40/51 ≈ 0.5646.

The probability of the opposite event (drawing at least one face card) is therefore 1 − 0.5646 ≈ 0.4354.

If your friend draws two non-face cards in succession, you pay him $30.

The expected value of that outcome is −$16.94 (the probability of the event multiplied by the amount you pay:

0.5646 × −$30).

If your friend doesn't draw two non-face cards in succession, he pays you $50.

The expected value of that outcome is $21.77 (the probability of the event multiplied by the amount you receive: 0.4354 × $50).

The expected value of the entire bet is the sum of these two expected values: −$16.94 + $21.77 = $4.83. Therefore, your expected profit is $4.83 per bet. Since you're making one bet, your expected value is $4.83. However, this answer isn't quite correct because it doesn't account for the initial $50 you pay to enter the bet. Therefore, you need to subtract that $50 from the expected value to get the net expected value of the bet:

$4.83 − $50 = −$45.17.

This means that, on average, you lose $45.17 per bet. However, the question asks for the expected value of your bet, not the expected value of your profit or loss.

To get the expected value of the bet, you need to add back in the initial $50 that you paid to enter the bet. Therefore, the expected value of your bet is −$45.17 + $50 = $4.83 (rounded to the nearest cent).

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Answer:

4x4, 2x8

Step-by-step explanation:

Factor means numbers u multiply to give u the required number and can go without any remainder.

Answer:

15

Step-by-step explanation:

Answer:

176 !

Step-by-step explanation:

Answer:

a. 2/3 = 0.67

b. 8/5 = 1.6

c. -5/2 = -2.5

d. 7/4 = 1.75

e. 9/2 = 4.5

f. -11/3 = -3.67

g. 13/5 = 2.6

h. -7/4 = -1.75

Step-by-step explanation:

Convirtiendo las fracciones dadas a decimales, tenemos:

a. 2/3 = 0.67

b. 8/5 = 1.6

c. -5/2 = -2.5

d. 7/4 = 1.75

e. 9/2 = 4.5

f. -11/3 = -3.67

g. 13/5 = 2.6

h. -7/4 = -1.75

The amount anna would make in a week if she made x dollars in sales is $450 + 0.15x

We are given that;

Salary per week= $450

Now,

To find her total earnings in a week in which she made $2400 in sales, you need to add her base salary and her commission. To find her commission, you need to multiply $2400 by 15%:

Commission = Sales * Commission Rate Commission = $2400 * 15% Commission = $2400 * 0.15 Commission = $360

To find her total earnings, you need to add her base salary and her commission:

Total Earnings = Base Salary + Commission Total Earnings = $450 + $360 Total Earnings = $810

Therefore, Anna would make $810 in a week in which she made $2400 in sales.

To find her total earnings in a week in which she made x dollars in sales, you need to follow the same steps but use x instead of $2400:

Commission = Sales * Commission Rate Commission = x * 15% Commission = x * 0.15 Commission = 0.15x

Total Earnings = Base Salary + Commission Total Earnings = $450 + 0.15x

Therefore, by algebra the answer will be $450 + 0.15x.

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Answer:

$70

Step-by-step explanation:

700*0.05=35

35*2=70

The initial amount and rate of change given a table for a linear function are $5 and $48, respectively

The table of linear function represents the given parameter

On the table, we have the following points

(x, y) = (10, 98) and (15, 123)

The rate of change is calculated as

Rate = (y2 - y1)/(x2 - x1)

So, we have

Rate = (123 - 98)/(15 - 10)

Evaluate

Rate = 5

This means that the rate of change is $5

The initial amount is calculated as

y = m(x - x1) + y1

Where

m = 5

So, we have

y = 5(x - x1) + y1

Using one of the points, we have

y = 5(x - 10) + 98

Set x = 0

So, we have

y = 5(0 - 10) + 98

Evaluate

y =  48

Hence, the initial amount and rate of change given a table for a linear function are $5 and $48, respectively

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The least number of seats the manger could order to 270 seats

The information that the the seats are sold only in groups of 10 will help to know that the order will be in a multiple of 10.

The manager wants to order 267 seats and this is not a multiple of 10 the nearest multiple of 10 is 270.

This is because, 260 will be short of want the manager want however ordering for 270 will be in excess with three seats.

Hence the manager will order 270 and heave 3 extra seats

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Answer:

Below

Step-by-step explanation:

x^2 -4    =  (x+2)(x-2)

x^2 -5x+6 = (x -2)(x-3)            See the common factor ?

The correct answer is (B) 14 inches.

To determine the rise of the ramp, we can use the trigonometric relationship between the angle and the rise. The rise of the ramp is given by the formula:

Rise = Run × tan(angle)

In this case, the angle is given as 4.5°, and the run is given as 180 inches. Substituting these values into the formula, we can calculate the rise:

Rise = 180 × tan(4.5°)

Using a calculator, we find that the rise is approximately 14.017 inches.

Rounded to the nearest inch, the rise of the ramp is 14 inches.

The correct answer is (B) 14 inches.

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