dean halverson recently read that full-time college students study 20 hours each week. she decides to do a study at her university to see if there is evidence that students study an average of more than 20 hours each week. a random sample of 33 students were asked to keep a diary of their activities over a period of several weeks. it was found that the average number of hours that the 33 students studied each week was 22.2 hours. the sample standard deviation of 3.9 hours. find the p -value. the p -value should be rounded to 4-decimal places.

The Laplace transform of a cos(ωt) b sin(ωt) is [(a + ib)s]/[(s^2) + ω^2].

We can use the identity cos(a)sin(b) = (1/2)(sin(a+b) - sin(a-b)) to write:

a cos(ωt) b sin(ωt) = (a/2)(e^(iωt) + e^(-iωt)) + (b/2i)(e^(iωt) - e^(-iωt))

Taking the Laplace transform of both sides, we get:

L{a cos(ωt) b sin(ωt)} = (a/2)L{e^(iωt)} + (a/2)L{e^(-iωt)} + (b/2i)L{e^(iωt)} - (b/2i)L{e^(-iωt)}

Using the fact that L{e^(at)} = 1/(s-a), we can evaluate each term:

L{a cos(ωt) b sin(ωt)} = (a/2)((1)/(s-iω)) + (a/2)((1)/(s+iω)) + (b/2i)((1)/(s-iω)) - (b/2i)((1)/(s+iω))

Combining like terms, we get:

L{a cos(ωt) b sin(ωt)} = [(a + ib)/(2i)][(1)/(s-iω)] + [(a - ib)/(2i)][(1)/(s+iω)]

Simplifying the expression, we obtain:

L{a cos(ωt) b sin(ωt)} = [(a + ib)s]/[(s^2) + ω^2]

Therefore, the Laplace transform of a cos(ωt) b sin(ωt) is [(a + ib)s]/[(s^2) + ω^2].

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The Laplace transform of acos(ωt) + bsin(ωt) is (as + bω) / (s^2 + ω^2).

To find the Laplace transform of a function, we can use the standard formulas and properties of Laplace transforms.

Let's start with the Laplace transform of a cosine function:

L{cos(ωt)} = s / (s^2 + ω^2)

Next, we'll find the Laplace transform of a sine function:

L{sin(ωt)} = ω / (s^2 + ω^2)

Using these formulas, we can find the Laplace transform of the given function acos(ωt) + bsin(ωt) as follows:

L{acos(ωt) + bsin(ωt)} = a * L{cos(ωt)} + b * L{sin(ωt)}

= a * (s / (s^2 + ω^2)) + b * (ω / (s^2 + ω^2))

= (as + bω) / (s^2 + ω^2)

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Answer:

Q1: 1:725

Q2: D

Q3: A

Q4: A=400:21 B=580:21

The final temperature of the iron-water mixture is approximately 1.112°C. To find the final temperature of the iron-water mixture, we can use the principle of heat transfer.

The heat gained by the water should be equal to the heat lost by the iron, assuming no heat is lost to the surroundings.

The equation for heat transfer is:

Q = m * c * ΔT

where Q is the heat transfer, m is the mass, c is the specific heat, and ΔT is the change in temperature.

Let's calculate the heat gained by the water and the heat lost by the iron separately.

Heat gained by water:

Q_water = m_water * c_water * ΔT_water

where m_water is the mass of water, c_water is the specific heat of water, and ΔT_water is the change in temperature of water.

Given:

m_water = 88.6 g

c_water = 4.184 J/g°C (specific heat of water)

ΔT_water = final temperature - initial temperature = T f - 12.4°C

Heat lost by iron:

Q _iron = m_ iron * c _iron * ΔT_iron

where m _iron is the mass of iron, c _iron is the specific heat of iron, and ΔT_iron is the change in temperature of iron.

Given:

m_ iron = 44.1 g

c_ iron = 0.444 J/g° C (specific heat of iron)

ΔT_iron = final temperature - initial temperature = T f - 95.4°C

According to the principle of heat transfer, the heat gained by the water should be equal to the heat lost by the iron:

Q _water = Q _iron

m_ water * c_ water * ΔT_water = m_ iron * c _iron * ΔT_iron

Substituting the given values, we have:

88.6 * 4.184 * (T f - 12.4) = 44.1 * 0.444 * (T f - 95.4)

Simplifying the equation:

370.1384 * T f - 4600.62 = 19.5644 * T f - 4209.4464

Collecting like terms:

370.1384 * T f - 19.5644 * T f = 4600.62 - 4209.4464

350.574 * T f = 390.1736

Dividing both sides by 350.574:

T f = 390.1736 / 350.574

T f ≈ 1.112°C

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A 60 purchases in a single day would represent the 92.7th percentile.

To answer this question, we need to calculate the average number of purchases per day and the standard deviation of the number of purchases per day. Then, we can use the normal distribution to determine the percentile that represents 60 purchases in a single day.

1. Average number of purchases per day:
Since 10% of potential customers buy a product, out of 500 visitors, 10% will be 500 * 0.10 = 50 purchases.

2. Standard deviation of the number of purchases per day:
To calculate the standard deviation, we need to find the variance first. The variance is equal to the average number of purchases per day, which is 50. So, the standard deviation is the square root of the variance, which is sqrt(50) = 7.07.

3. Percentile of 60 purchases in a single day:
We can use the normal distribution to calculate the percentile. We'll use the Z-score formula, which is (X - mean) / standard deviation, where X is the number of purchases in a single day. In this case, X = 60.

Z-score = (60 - 50) / 7.07 = 1.41

Using a Z-score table or calculator, we can find that the percentile associated with a Z-score of 1.41 is approximately 92.7%. Therefore, 60 purchases in a single day would represent the 92.7th percentile.

In conclusion, 60 purchases in a single day would represent the 92.7th percentile.

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We have the point A(6,7), and we need to find the point A' which is the reflection of point A across the x-axis.

the point A is represented in the following image:

And the reflection across the x-axis is like if we reflected the point in a mirror:

As we can see the point A' has the coordinates:

As a general rule, when we make a reflection of a point

the reflection across the x-axis gives the point:

We change the sign of the y-coordinate.

Like in this case (6,7) became (6,-7).

Answer: (6,-7)

Answer:

y=14x−3 .

Step-by-step explanation:

We know that the equation of a line is y=mx+b with m being the slope and b being the y-intercept. We can plug in your slope ( 14 ) and your y-intercept ( −3 ). This simplifies to y=14x−3 .

Mr. Kinders will have $83,858.77 in the RRSP after 20 years. The interest earned over this period will amount to $43,858.77.

To calculate the future value of Mr. Kinders' RRSP, we can use the formula for compound interest:

Future Value (FV) = P * (1 + r/n)^(nt)

Where:

P = Monthly contribution = $200.00

r = Annual interest rate = 3% = 0.03 (expressed as a decimal)

n = Number of compounding periods per year = 4 (quarterly compounding)

t = Number of years = 20

Substituting these values into the formula, we can calculate the future value:

FV = $200 * (1 + 0.03/4)^(4*20)

FV ≈ $83,858.77

Therefore, Mr. Kinders will have approximately $83,858.77 in the RRSP after 20 years.

To calculate the amount of interest earned, we can subtract the total contributions made from the future value:

Interest = FV - Total Contributions

The total contributions can be calculated by multiplying the monthly contribution by the number of months (20 years * 12 months/year = 240 months):

Total Contributions = $200 * 240

Total Contributions = $48,000

Substituting the values into the formula, we can calculate the interest:

Interest = $83,858.77 - $48,000

Interest ≈ $35,858.77

Therefore, the amount of interest earned in the RRSP over 20 years is approximately $43,858.77.

After 20 years of contributing $200 per month to his RRSP, compounded quarterly at an interest rate of 3% per annum, Mr. Kinders will have approximately $83,858.77 in his RRSP.

The interest earned during this period will amount to approximately $43,858.77. Compound interest calculations allow individuals to estimate the growth of their investments over time and make informed financial decisions.

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Answer:A student pays for 8.9 pounds of apples with a $10 bills. How much change does the student receive?

Step-by-step explanation:

Answer:the answer is 2 dollar

Step-by-step explanation:

We know that,

\( \qquad{ \pmb{ \bf{{Total \: surface \: area}_{(cylinder)} = 2πr(h + r) }}}\)

Now, Substituting the given values in the formula :

\(\qquad \sf \: { \dashrightarrow 2 × π × 2 (9 + 2) }\)

\(\qquad \sf \: { \dashrightarrow 2 × π × 2 (11) }\)

\(\qquad \sf \: { \dashrightarrow 2 × π × 22 }\)

\(\qquad \sf \: { \dashrightarrow 44 π }\)

\(\qquad \sf \: { \dashrightarrow 44 π } \: \)

Since, value of pi is 3.14 approximately, therefore here we will take the value of pi as 3.14

\(\qquad \sf \: { \dashrightarrow 44 \times 3.14 } \: \)

\(\qquad \sf \bf { \dashrightarrow 138.16 } \:\)

Therefore,

The surface area of the cylinder with the given values of base radius and height is approximately 138.16 units².

A cylinder is simply a 3-dimensional shape having two parallel circular bases joined by a curved surface.

The surface area of a cylinder is expressed as;

A = 2πrh + 2πr²

Where r is radius of the circular base, h is height and π is constant pi ( π = 3.14 )

Given the data in the question;

We substitute our values into the expression above.

A = 2πrh + 2πr²

A = ( 2 × 3.14 × 2 units × 9 units ) + ( 2 × 3.14 × (2 unit)² )

A = ( 2 × 3.14 × 2 units × 9 units ) + ( 2 × 3.14 × 4 unit² )

A = 113.04 units² + 25.12 units²

A = 138.16 units²

Therefore, the surface area of the cylinder with the given values of base radius and height is approximately 138.16 units².

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Answer:

40

Step-by-step explanation:

because 180- 140 = 40

a linear pair means they equal 180

The measure of angle ACD (∠ACD) is 40 degrees.

Given that angles ACD and DCB forms a linear pair, also m ∠DCB = 140°,

We are asked to find the measure of ∠ACD,

So,

If angles ACD and DCB form a linear pair, it means that their sum is equal to 180 degrees.

Let's denote the measure of angle ACD as x.

So, we have the equation:

m∠ACD + m∠DCB = 180°

Substituting the given value for m∠DCB:

x + 140° = 180°

To solve for x, we can subtract 140° from both sides of the equation:

x = 180° - 140°

x = 40°

Therefore, the measure of angle ACD (∠ACD) is 40 degrees.

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Please post your question fully !!

Answer:

huh?.............

Step-by-step explanation:

im not smart

To determine if there has been a change in the distribution of motivations for using a credit card among college students, a survey of 425 students was conducted.

The alternate hypothesis states that the distribution of motivations differs from the old survey. The critical value and rejection region need to be determined to test this hypothesis.

To test if there has been a change in the distribution of motivations, the null hypothesis assumes that the distribution remains the same as in the old survey, while the alternate hypothesis suggests a difference. In this case, the alternate hypothesis is that the distribution of motivations differs from the old survey.

To determine the critical value and rejection region, the significance level (α) needs to be specified. In this case, α is given as -0.005. However, it seems there may be some confusion in the provided information, as a negative significance level is not possible. The significance level should typically be a positive value between 0 and 1.

Without a valid significance level, it is not possible to determine the critical value and rejection region for hypothesis testing. The critical value is typically obtained from a statistical table or calculated based on the significance level and the degrees of freedom.

In conclusion, without a valid significance level, it is not possible to determine the critical value and rejection region to test the hypothesis regarding the change in the distribution of motivations for credit card usage among college students.

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Answer:

-2 = -6

Step-by-step explanation:

first, you type -2 in the left box and -6 in the middle box

given a finite alphabet Σ, the set PΣ can be recursively defined

as: ϵ ∈ PΣ. a ∈ PΣ for all a ∈ Σ. if u ∈ PΣ, then a u a ∈ PΣ for

all a ∈ Σ.

Let's break down the given problem step by step and provide a direct answer, followed by an explanation and calculation, and conclude our findings.

The set PΣ is recursively defined as follows:

The empty string ϵ (epsilon) belongs to PΣ.

Each individual letter a in the alphabet Σ belongs to PΣ.

If a word u belongs to PΣ, then the word a u a also belongs to PΣ for all letters a in Σ.

To understand the set PΣ, let's consider an example where the alphabet Σ is {a, b, c}. We'll calculate the elements of PΣ step by step.

According to the definition, ϵ (epsilon) belongs to PΣ. So, ϵ is an element of PΣ.

Each individual letter a, b, and c in the alphabet Σ also belongs to PΣ. Therefore, a, b, and c are elements of PΣ.

Now, let's apply the recursive rule to generate more elements of PΣ. We'll use the word u = a, which belongs to PΣ as per the previous step.

Applying the rule for a = a, we have:

a u a = a a a

Therefore, a a a is an element of PΣ.

We can repeat this process for b and c as well. Let's calculate a u a for b and c.

For b:

b u b = b a b

Therefore, b a b is an element of PΣ.

For c:

c u c = c a c

Therefore, c a c is an element of PΣ.

To summarize, the elements we have calculated so far are:

ϵ, a, b, c, a a a, b a b, c a c.

We can continue applying the recursive rule to generate more elements. Let's calculate a u a for a a a, b a b, and c a c.

For a a a:

a a a u a a a = a a a a a a a a a

Therefore, a a a a a a a a a is an element of PΣ.

For b a b:

b a b u b a b = b a b a b a b

Therefore, b a b a b a b is an element of PΣ.

For c a c:

c a c u c a c = c a c a c a c

Therefore, c a c a c a c is an element of PΣ.

So far, the elements we have calculated are:

ϵ, a, b, c, a a a, b a b, c a c, a a a a a a a a a, b a b a b a b, c a c a c a c.

We can continue applying the recursive rule to generate more elements of PΣ. The set PΣ can potentially have infinitely many elements, depending on the alphabet Σ and the number of applications of the recursive rule.

The set PΣ is recursively defined as a set that includes the empty string ϵ, each individual letter in the alphabet Σ, and new words generated by sandwiching existing words in PΣ between two letters from Σ. The size of the set PΣ can vary depending on the finite alphabet Σ and the number of applications of the recursive rule.

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Answer:

So I don't think an 11 year old like me can solve this question because I don't even know the concept used for this but from what I can see, this is somewhat easy.

y = 6.5

Step-by-step explanation:

If 3x = 5.5 on the table, then

y = 3x + 1   turns into   y = 5.5 +1

5.5 + 1 = 6.5

So    y = 6.5

Answer: 14.99

Step-by-step explanation:

Each pound of bark is 2.10 so 1/2 of a pound of bark is 2.10/2 or 1.05

Same goes with mulch. 2.6*2/5=1.04

2.58*5=12.9 pounds of sand and a Suna Suna no mi

Total is 1.04+1.05+12.9 or 14.99 or approx 15 dollars

Answer:

$13.41

Step-by-step explanation:

Multiply the number of drinks (3) by the cost of one drink ($4.47).

4.47 times 3 (if you do the math) is equal to 13.41

have a good day :)

Answer:

$13.41

Step-by-step explanation:

just add it all up $4.47 + $4.47 + $4.47=$13.41

Answer:

Step-by-step explanation:

(1/5)(x)+3=(1/2)(x)

3=(1/2)x-(1/5)x

3=(5/10)x-(2/10)x

3=(3/10)x

3=0.3x

30=3x

x=30/3

x=10

Answer:

Step-by-step explanation:

U have to show the sentence before the question so the reader will understand

Answer:

122.5 People

Step-by-step explanation:

4500-90 = 4410

4410 divided by 36 equals 122.5

==========================================================

Explanation:

n = number of people invited

n+2 = total number of people after adding Oscar and Julie

36(n+2) = total cost before the $90 fee

36(n+2)+90 = total cost after the $90 fee

Set that equal to the budget of 4500 and isolate n

36(n+2)+90 = 4500

36n+72+90 = 4500

36n+162 = 4500

36n = 4500-162

36n = 4338

n = 120.5

n = 120

We round down so that we don't go over budget

Oscar and Julie can invite 120 people.

-----------

Check:

If n = 120 then 36(n+2)+90 = 36(120+2)+90 = 4482 which is under budget

If n = 121 then 36(n+2)+90 = 36(121+2)+90 = 4518 which is over budget

This confirms that 120 is the answer.

Answer: 1 decameter

Step-by-step explanation:

Answer:

1 decameter

Step-by-step explanation:

1 decameter is 10 meters or 1000 centimeters

The decimal expansion of the given fraction is 0.0208. Therefore, the correct answer is option D.

The given fraction is 13/625.

Decimals are one of the types of numbers, which has a whole number and the fractional part separated by a decimal point.

Here, the decimal expansion is 13/625 = 0.0208

So, the number of places of decimal are 4.

Therefore, the correct answer is option D.

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Answer:

4 ways

Step-by-step explanation:

3+4+5+6+7+8+9+10=52

1/4×52=13

13×3=39

3+10=13

4+9=13

5+8=13

6+7=13

so there are 4 ways to divide in two parts.

1.

A={3,10}

B={4,5,6,7,8,9}

2.

A={4,9}

B={3,5,6,7,8,10}

3.

A={5,8}

B={3,4,6,7,9,10}

4.

A={6,7}

B={3,4,5,8,9,10}

Answer:

the answer is 3 hours because when he paid for the fee he had money leftover for how long he can stay.

Answer:

3 hours

Step-by-step explanation:

Because $35×3=$105+$20 for equipment rental=$125

Answer:

90 diagonais.

Step-by-step explanation:

\(n(n-3)/2=15(15-3)/2=15*6=90\)

Answer:

a) 7/12

b) 5/9

Step-by-step explanation:

a)  

\(\frac{7}{12} = \frac{49}{84}\\\\\frac{4}{7} = \frac{48}{84}\\\\\frac{49}{84} > \frac{48}{84}\\\\\frac{7}{12} > \frac{4}{7}\)

b)

\(\frac{6}{11} = \frac{54}{99}\\\\\frac{5}{9} = \frac{55}{99}\\\\\frac{55}{99} > \frac{54}{99}\\\\\frac{5}{9} > \frac{6}{11}\)

Answer:

y = |x| is a parent function

y = |x| - 7 is a translation of the parent function vertically by 7 points down

The shape is same, just the entire graph has shifted down.

It's translated edition of parent function y=|x|

If we translate it 7units down then the function is

So

Everything is same

Just the graph shifted 7units downwards

The most appropriate model to represent the data in the table is (d)

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

The table of values

In the above table of values, we can see that

To show as the number of miles change by day

A linear or line graph has to be plotted

Hence, the most appropriate model to represent the data is (d)

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The length of XZ is 5.5 m.

The length of side XZ is calculated by applying the following cosine and sine rule.

If the length of WY is 7 m, then ∠WYZ is calculated as follows;

cos Y = (z² + w² - y² ) / (2zw)

where;

cos Y = ( 7² + 5.1² - 3² ) / ( 2 x 7 x 5.1 )

cos Y = 0.9245

Y = cos⁻¹ (0.9245)

Y = 22.4⁰

The value of ∠WYX is calculated as follows;

cos Y = (x² + w² - y² ) / (2xw)

cos Y = ( 7² + 5² - 4.8² ) / ( 2 x 7 x 5)

cos Y = 0.728

Y = cos⁻¹ (0.728)

Y = 43.28⁰

The value of ∠ZYX = 43.28⁰ + 22.4⁰ = 65.68⁰

The length of XZ is calculated by using the following cosine rule.

|XZ|² = |XY|² + |ZY|² - (2 x |XY| x |XY|) cos Y

|XZ|² = 5² + 5.1²  -  (2 x 5 x 5.1 ) x cos (65.68)

|XZ|² = 30

|XZ| = √30

|XZ| = 5.5 m

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