45. Sales The sales S (in thousands of units) of a scasonal product are given by the model S = 74.50 + 43.75 sin πt
where t is the time in months, with t = 1 corresponding to January. Find the average sales for the first quarter (0 ≤ t ≤ 3)
a. 223.5 b. 151.1 c. 74.5 d. 216.7 e. None of the above

The total cost for all the items fish, fish bowl, and aquarium will be $606.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

An audit of the fundamental stock rundown for your pet shop demonstrates you want to reorder the accompanying things: 25 boxes of fish food at $9 every, 12 fish bowls at $13, and 15 aquarium extra starter packs at $15 each.

Then the total cost for all the items will be given as,

Total cost = 25 x $9 + 12 x $13 + 15 x $15

Total cost = $225 + $156 + $225

Total cost = $606

The total cost for all the items fish, fish bowl, and aquarium will be $606.

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In this scenario, the independent variable is the factor that is being manipulated or changed by the researcher. It is what the researcher controls and assigns to different groups in the study.

In this case, the independent variable is whether the participants were told that the house was haunted or not. Shaniqua randomly assigned 14 people to sleep in the house on Friday night and told them that it was haunted. The other 14 people slept in the house on Saturday night and were not told that it was haunted.

So, the independent variable in this study is the information about the house being haunted that was given to the participants. The study aimed to examine how this information affected people's sleep.

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The independent variable in this scenario is whether the participants were told that the house was haunted or not.

In this study, the researcher randomly assigned participants into two groups: the "haunted" group and the "not-haunted" group. The independent variable is the information provided to each group, with the "haunted" group being told that the house was haunted and the "not-haunted" group not being given any information about the haunting.

Thus, the independent variable allows the researcher to investigate the potential causal relationship between being told that the house is haunted and the amount of sleep obtained.

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Answer:

115

Step-by-step explanation:

The probability of the 2nd person will lose after solving the Deathrolling in World of Warcraft using R function is 0.04751.

Probability denotes the likelihood of something happening. It is a mathematical discipline that deals with the occurrence of a random event. The value ranges from zero to one. Probability has been introduced in mathematics to predict the likelihood of occurrences occurring. Probability is defined as the degree to which something is likely to occur. This is the fundamental probability theory, which is also utilised in probability distribution, in which you will learn about the possible results of a random experiment.

By solving the upper problem by using the R function we get,

counter = 0

tries = 100000

for (x in 1:tries) {

x1 <- floor(runif(1,min=1,max=1001))

if (x1 == 1) {next}

x2 <- floor(runif(1, min=1, max=(x1+1)))

if (x2 == 1) {next}

x3 <- floor(runif(1, min=1, max=(x2+1)))

if (x3 == 1) {next}

x4 <- floor(runif(1, min=1, max=(x3+1)))

if (x4 == 1) {counter = counter+1}

}

counter/tries #=0.04751

Therefore, the probability is 0.04751.

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She can select one freshman and one sophomore in 72 ways.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is Phyllis who wants to select one freshman and one sophomore to attend a conference. She teaches 8 freshman and 9 sophomores

Total number of possible combinations are -

C[8,1] x C[9,1]

8!/(7! x 1!) x 9!/(8! x 1!)

8 x 9

72

Therefore, she can select one freshman and one sophomore in 72 ways.

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To find the volume of the solid generated by revolving the region bounded above by y =11 cos x and below by y=4 sec x, -π/4 ≤ x ≤ π/4 about the x-axis, we use the Disk method.

Here are the steps to follow in order to solve the problem:

Step 1: Sketch the region to be rotated. Notice that the region is bound above by `y = 11 cos x` and bound below by `y = 4 sec x`.

Step 2: Compute the interval of rotation. Notice that `-π/4 ≤ x ≤ π/4`.

Step 3: Draw an arbitrary vertical line in the region, then rotate that line around the x-axis.

Step 4: Compute the radius of the disk for a given `x`-value. This is equal to the distance from the axis of rotation to the edge of the solid, or in this case, the distance from the x-axis to the function that is farthest away from the axis of rotation.

The distance from the x-axis to `y = 11 cos x` is `11 cos x`, while the distance from the x-axis to `y = 4 sec x` is `4 sec x`. Since we are rotating around the x-axis, we use the formula `r = y`. Thus, the radius of the disk is `r = max(11 cos x, 4 sec x)`.

Step 5: Compute the volume of each disk. The volume of a disk is given by `V = πr²Δx`.

Step 6: Integrate to find the total volume of the solid. Thus, the volume of the solid is given by:

\($$\begin{aligned}V &= \int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} π(11\cos x)^2 - π(4\sec x)^2 dx \\ &= π\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} (121 \cos^2 x - 16 \sec^2 x) dx\\ &= π\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} \frac{121}{2}\cos 2x - \frac{16}{\cos^2 x} dx\\ &= π\left[\frac{121}{4} \sin 2x + 16 \tan x\right]_{-\frac{\pi}{4}}^{\frac{\pi}{4}}\\ &= π\left[\frac{121}{2} + 32\sqrt{2}\right]\end{aligned}$$\)

Thus, the volume of the solid generated by revolving the region bounded above by y =11 cos x and below by y=4 sec x, -π/4 ≤ x ≤ π/4 about the x-axis is `V = π(121/2 + 32√2)`.

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Given the region bounded above by y = 11cos x and below by y = 4sec x, -π/4 ≤ x ≤ π/4. Find the volume of the solid generated by revolving this region about the x-axis.

To find the volume of the solid generated by revolving the given region about the x-axis, we can use the formula:V = π∫ab(R(x))^2 dxwhere R(x) is the radius of the shell at x and a and b are the limits of integration.Here, the region is bounded above by y = 11cos x and below by y = 4sec x, -π/4 ≤ x ≤ π/4.At x = -π/4, the value of cos x is minimum and the value of sec x is maximum.

At x = π/4, the value of cos x is maximum and the value of sec x is minimum.Thus, we take a = -π/4 and b = π/4.Let us sketch the given region:We need to revolve the region about the x-axis. Hence, the radius of each shell is the distance from the x-axis to the curve at a given value of x.The equation of the curve above is y = 11cos x. Thus, the radius of the shell is given by:R(x) = 11cos x

The equation of the curve below is y = 4sec x. Thus, the radius of the shell is given by:R(x) = 4sec x

Using the formula: V = π∫ab(R(x))^2 dx The volume of the solid generated by revolving the region about the x-axis is given by:V = π∫(-π/4)^(π/4)(11cos x)^2 dx + π∫(-π/4)^(π/4)(4sec x)^2 dx= π∫(-π/4)^(π/4)121cos^2 x dx + π∫(-π/4)^(π/4)16sec^2 x dx= π∫(-π/4)^(π/4)121/2[1 + cos(2x)] dx + π∫(-π/4)^(π/4)16[1 + tan^2 x] dx= π[121/2(x + 1/4sin(2x))](-π/4)^(π/4) + π[16(x + tan x)](-π/4)^(π/4)= π[121/2(π/4 + 1/4sin(π/2))] + π[16(π/4 + tan(π/4/2))] - π[121/2(-π/4 + 1/4sin(-π/2))] - π[16(-π/4 + tan(-π/4/2))]= π(363/4 + 16π/3)The volume of the solid generated by revolving the region about the x-axis is π(363/4 + 16π/3) cubic units.

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Answer:

if you meant x times y...

15 x 20 is 300.

if you meant x + y...

15 + 20 is 35.

if you meant anything else, please let me know

the way it was written confused me but I tried.

It's important to choose the right type of graph and axis labeling to present the information accurately and effectively.

It may be possible to draw multiple scatter plots on a single graph to investigate the relationships between the quantitative variables a, b, and c.

Option B suggests drawing two scatter plots, one for the relationship between a and b and another for the relationship between a and c. This could help identify any patterns or correlations between these variables and potentially reveal any potential causation or association.

However, it is important to note that drawing multiple scatter plots on a single graph can sometimes lead to clutter and confusion, so it's important to choose the right type of graph and axis labeling to present the information accurately and effectively.

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Answer:

3x + 4 -7x - 6

3x -7x -6 +4

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

Answer:

nvm my answer was wrong ignore this lol

Rashid spent a total of 1 hour and 30 minutes on homework for these three subjects.

If Rashid spent 30 minutes on each piece of homework for three subjects, we can calculate the total time he spent by multiplying the time spent per subject (30 minutes) by the number of subjects (3).

30 minutes * 3 = 90 minutes.

To convert this into hours and minutes, we divide 90 minutes by 60 since there are 60 minutes in an hour.

90 minutes ÷ 60 = 1 hour and 30 minutes.

Therefore, Rashid spent a total of 1 hour and 30 minutes on homework for these three subjects.

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Answer:

-(x^2 + 10x^2 - 2x - 4)

Step-by-step explanation:

Answer:

coxkyxkyxoydoyd

Step-by-step explanation:

kysoydoyxlhxlhxohxoudyodgufudytdxgchjvgufychvjugfychgifuyfchuguffychjbohihfydtxgbjjbhcvjgujfjfjf

Answer:

15%

Step-by-step explanation:

0.15 x 100 = 15%

The correct formula that defines an arithmetic sequence is option d) tn = 5n + 14.

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms remains constant. In other words, each term can be obtained by adding a fixed value (the common difference) to the previous term.

In option a) tn = 5 + 14, the term does not depend on the value of n and does not exhibit a constant difference between terms. Therefore, it does not represent an arithmetic sequence.

Option b) tn = 5n² + 14 represents a quadratic sequence, where the difference between consecutive terms increases with each term. It does not represent an arithmetic sequence.

Option c) tn = 5n(n+14) represents a sequence with a varying difference, as it depends on the value of n. It does not represent an arithmetic sequence.

Option d) tn = 5n + 14 represents an arithmetic sequence, where each term is obtained by adding a constant value of 5 to the previous term. The common difference between consecutive terms is 5, making it the correct formula for an arithmetic sequence.

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Answer:

0.21ft/min

Step-by-step explanation:

   \(\sf Volume \ at \ given \ time = \dfrac{dV}{dt}= 20 \ cubic \ feet /min\)

             h = d

             h = 2r

             \(\sf r = \dfrac{h}{2}\)

            Volume of heap = (1/3) πr²h

                     \(\sf V =\dfrac{1}{3}\pi r^2h\\\\V =\dfrac{1}{3}\pi (\frac{h}{2})^2h\\\\V =\dfrac{1}{3}\pi \dfrac{h^2}{4}*h\\\\V=\dfrac{1}{12}\pi h^3\)

Take derivative w.r.t time,

                     \(\sf \dfrac{dV}{dt}=\dfrac{1}{12}\pi * 3h^2 \dfrac{dh}{dt}\)

                     h = 11 ft

                     \(\sf 20 = \dfrac{1}{12}\pi *3*11*11*\dfrac{dh}{dt}\\\\20=\dfrac{121}{4}\pi \dfrac{dh}{dt}\\\\\)

               \(\sf \dfrac{20*4}{121*\pi }=\dfrac{dh}{dt}\\\\ \dfrac{80}{120*3.14}=\dfrac{dh}{dt}\)

                        \(\sf \dfrac{dh}{dt}=0.21\)

             The height is increasing at the rate of 0.21 ft/min

Answer:

$15

Step-by-step explanation:

Sonia will take $57, and his grandparents will give another $78. 57 + 78 = 135. Sonia will have 135 dollars, but it is a 9 day vacation, so 135/9 = 15

Sonia will spend 15 dollars a day.

Answer: 14% of 600 is 84

Step-by-step explanation:

Write 14% as 14/100

Since finding the fraction of a number is the same as multiplying the fraction with the number, we have

14/ 100 of 600 =

14/ 100  × 600

therefore the answer is 84

Answer:2.33333334

Step-by-step explanation:

it could be 84

Yes, it is possible to have negative probabilities in some cases.

It is possible to have a negative probability?

First, for classical experiments, the probability for a given outcome on an experiment is always a number between 0 and 1, so it is defined as positive.

In some cases, we can have probability distributions with negative values, which are associated to unobservable events.

For example, negative probabilities are used in mathematical finance, where instead of probability they use "pseudo probability" or "risk-neutral probability"

Concluding, yes, is possible to have a negative probability.

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The x value would be 3.

Answer:

416.7pounds

Step-by-step explanation:

Given parameters:

         Weight of the small box  = 125pounds

Unknown:

Weight of the larger box = ?

Solution:

The large box weighs \(3\frac{1}{3}\) times as the small box:

               So;

                =   125pounds x \(\frac{10}{3}\)

                = 416.7pounds

The number of constraints required at each cut-point for a cubic spline is two, and the total degrees-of-freedom for the curve can be calculated using the formula:

degrees-of-freedom = (number of cubic polynomials) x 4 - (number of cut-points) x 2

When fitting a piecewise polynomial for a regression, the number of constraints required at each cut-point to obtain a cubic spline is two. These two constraints are known as continuity constraints. The first continuity constraint is that the two adjacent cubic polynomials must have the same function value at the cut-point. The second continuity constraint is that the two adjacent cubic polynomials must have the same derivative value at the cut-point. These constraints ensure that the cubic spline is smooth and continuous at each cut-point.
The total degrees-of-freedom for the curve can be calculated by subtracting the total number of constraints from the total number of parameters in the model. For a cubic spline, there are four parameters for each cubic polynomial and two constraints at each cut-point. Therefore, the total degrees-of-freedom for the curve can be calculated using the formula:
degrees-of-freedom = (number of cubic polynomials) x 4 - (number of cut-points) x 2
It is important to note that the number of cut-points is equal to the number of pieces minus one, where a piece refers to a continuous interval in the data that is fitted with a single cubic polynomial.

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Answer:

(3, 8)

Step-by-step explanation:

Coordinate (-3, -8)

Reflect across the y-axis. The x will change to the opposite, and the y will remain the same. So, the coordinate is (3, -8)

Then reflect the result across the x-axis. The y will change to the opposite, and the x will remain the same. So, the coordinate is (3, 8)

So, the coordinate of the final point is (3, 8)

Answer:

abc + bca + cab

abc(1+1+1)

3×18

54

Answer:

54

Step-by-step explanation:

a + b + c = 18

abc + bca + cab = ???

18 / 3 = 6

a = ? = 6

b = ? = 6

c = ? = 6

(6 + 6 + 6) + (6 + 6 + 6) + (6 + 6 + 6)

(18) + (18) + (18)

abc + bca + cab = 54

Answer: $20

Step-by-step explanation:

20% of 25 is 5

You can figure that out by writing 20/100 (percents are out of 100)

Simplified 20/100 would be 1/5

so we are finding 1/5 of 25

1/5 x 25/1 = 25/5 or 5

So the discount is $5

$25 - $5 is $20

Answer:

-6r+5 by combining like terms

According to the question, the study is based on the organic pesticide for a particular plant. The pesticide manufacturer is developing a new type of organic pesticide for the particular plants. To understand the application of a new organic pesticide, then perform one experiment where the members of plants have controlled the environment for the testing purpose. In this way, plants can be protected from pest attack. These types of experiments fall under matched pair experiments.

In the matched pair experiments, the samples are divided into two parts. The first part should be based on some controlled characteristics, whereas the other one should be based on randomly assigned characteristics.

What are matched pair experiments.?

Matched pair designs are experimental based designs. In this, one group is protected in a controlled environment whereas the other one is in a random environment.

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\(32^5\) - \(16^5\) + \(2^{19}\) is divisible by 63.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

\(32^5\) - \(16^5\) + \(2^{19}\)

= 33554432 - 1048576 + 524288

= 33030144

Now,

33030144 ÷ 63

= 524288

Thus,

It is divisible by 63.

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Answer:

Step-by-step explanation:

A credit score is a number that helps lenders assess how well you manage your financial obligations in the past.

I hope this helps.