Tina won a prize of £1000 000 She spent £40 000 on a new car Then she spent half the money left on a house How much did Tina spend on the house?

To estimate the frequency spectrum of the signal {1, 9, 0, 1, 4, 9} using the FFT, we apply the FFT algorithm to the signal. The FFT decomposes the signal into its constituent frequencies and provides the corresponding magnitude and phase responses.

(a) By applying the FFT to the given signal, we obtain the frequency spectrum. The magnitude spectrum represents the amplitudes of different frequency components in the signal, while the phase spectrum represents the phase shifts of those components.

(b) To plot the magnitude and phase response of the calculated spectrum, we would need to compute the magnitude and phase values for each frequency component obtained from the FFT.

The magnitude values can be plotted on a graph as a function of frequency, representing the strength of each frequency component. Similarly, the phase values can be plotted as a function of frequency, showing the phase shifts at different frequencies.

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Answer:

(x + 6)(x + 7)

Step-by-step explanation:

To factor the trinomial x^2 + 13x + 42, we need to find two numbers that multiply to 42 and add up to 13.

One way to do this is to list all the pairs of factors of 42 and see which pair adds up to 13:

1, 42 -> 1 + 42 = 43

2, 21 -> 2 + 21 = 23

3, 14 -> 3 + 14 = 17

6, 7 -> 6 + 7 = 13

So the pair of factors that we want is 6 and 7. We can use these numbers to rewrite the middle term of the trinomial:

x^2 + 13x + 42 = x^2 + 6x + 7x + 42

Next, we can group the first two terms and the last two terms:

x^2 + 6x + 7x + 42 = (x^2 + 6x) + (7x + 42)

Now, we can factor out the greatest common factor from each group:

x(x + 6) + 7(x + 6)

Notice that we have a common factor of (x + 6) in both terms. We can factor this out:

(x + 6)(x + 7)

Answer:

  about -0.79 mg/hour

Step-by-step explanation:

You want the rate of change of the amount of medication in a patient after 4 hours if the amount after t hours is modeled by y=88/(1+e^(t+0.7)).

The rate of change is found by taking the derivative of the function with respect to time. Let u = 1+e^(t+0.7). Then du/dt = e^(t +0.7).

The function can be written ...

  y = 88/u = 88·u^-1

so its derivative is ...

  dy/dt = (-88·u^-2)·du/dt

  dy/dt = -88(e^(t +0.7))/(1 +e^(t +0.7))^2

The value of the rate of change at t=4 is ...

  dy/dt = -88(e^(4 +0.7))/(1 +e^(4 +0.7))^2 ≈ -88(109.95)/(1 +109.95)^2

  dy/dt ≈ -0.78602 ≈ -0.79 . . . . . . mg/h

The rate of change in the amount of medication is about -0.79 mg/h.

rAnswer:

Step-by-step explanation:

20$

Given the inverse demand function p = 100 - 20q for toasters and a price of $35, we can find the consumer surplus.

First, we'll find the quantity demanded at the given price:

35 = 100 - 20q
20q = 100 - 35
q = (100 - 35) / 20
q = 65 / 20
q = 3.25

Now, to find the consumer surplus, we'll use the formula:

Consumer Surplus = (1/2) × Base × Height

The base represents the quantity (q = 3.25) and the height is the difference between the maximum willingness to pay (p = 100) and the actual price (p = 35).

Consumer Surplus = (1/2) × 3.25 × (100 - 35)
Consumer Surplus = 0.5 × 3.25 × 65
Consumer Surplus = 105.625

So, the consumer surplus is $105.63 when rounded to two decimal places.

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Yes, the data provides convincing statistical evidence that the proportion who would be classified as normal after one month of taking cinnamon is greater than the proportion who would be classified as normal after one month of not taking cinnamon.

To test this hypothesis, a two-proportion z-test can be used to compare the proportions of individuals with normal blood glucose levels in the cinnamon group and placebo group. Using the given data, the test statistic is calculated to be 1.78 with a p-value of 0.038.

Since the p-value is less than the significance level of 0.05, we can reject the null hypothesis and conclude that there is a significant difference between the proportions of individuals with normal blood glucose levels in the cinnamon and placebo groups. Therefore, the data provides convincing evidence that cinnamon can reduce blood glucose levels and increase the proportion of individuals with normal blood glucose levels.

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2 hours will pass before they meet.

"Information available from the question"

In the question:

Aaron starts riding a bike at a rate of 3 mi/h on a road toward a store 20 mi away.

Zhang leaves the store when Aaron starts riding his bike, and he rides his bike toward Aaron along the same road at 2 mi/h.

Now, According to the question:

Total distance = 20mi

Aaron starts riding a bike at a rate of  = 3mi/h

Zhang rides his bike toward Aaron along the same road at  = 2mi/h

Let y be the number of hours for them to meet.

The expression is given as

3y + 2y = 20

solving for y, we have

5y = 20

y = 20/5

y = 4hrs

Therefore, 2 hours will pass before they meet.

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Answer:

I think B.

Step-by-step explanation:

the number of different ways that six customers can line up at these stands: there are 84 different ways that six customers can line up at the four open checkout stands.

We have four open checkout stands and six customers. We need to find the number of different ways these customers can line up at the stands.

We will use the formula for combinations with repetition, which is:

C(n + r - 1, r) = C(n + r - 1)! / (r! * (n - 1)!)

where C represents the number of combinations, n is the number of stands (4), and r is the number of customers (6).

Step 1: Calculate n + r - 1.
4 + 6 - 1 = 9

Step 2: Calculate C(9, 6).
C(9, 6) = 9! / (6! * (9 - 6)!)

Step 3: Calculate the factorials.
9! = 362,880
6! = 720
(9 - 6)! = 3! = 6

Step 4: Plug the factorials into the formula.
C(9, 6) = 362,880 / (720 * 6)

Step 5: Calculate the result.
C(9, 6) = 362,880 / 4,320 = 84

So, there are 84 different ways that six customers can line up at the four open checkout stands.

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1. The official lines of authority. 2. The formal lines of communication. 3. The base level of the organization.

Organizational structure box-and-lines diagrams show at least three things:

1. The official lines of authority: These diagrams illustrate the formal hierarchy within an organization, indicating the chain of command and reporting relationships. The lines represent the flow of authority and communication, highlighting who reports to whom. For example, a manager may have multiple employees reporting to them, and those employees may further have their own subordinates.

2. The formal lines of communication: These diagrams also depict the formal channels through which information flows within the organization. They show how information is passed between different levels and departments. For instance, a diagram may show that information flows vertically from top management to lower-level employees or horizontally between departments.

3. The base level of the organization: These diagrams display the entry-level positions within the organizational structure. This helps to understand the foundational roles that exist and how they fit into the larger structure. For instance, the diagram may indicate positions such as interns, junior associates, or entry-level staff.

In summary, organizational structure box-and-lines diagrams provide a visual representation of the official lines of authority, the formal lines of communication, and the base level of the organization. These diagrams help individuals understand the hierarchy, communication flow, and entry-level positions within an organization.

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Step-by-step explanation:

explain what 7 c is please and I'll write the answer in the comments:))

Answer:

(3,2)

Step-by-step explanation:

-5+8=3

6-4=2

(3,2)

Answer:

21 Dimes and 16 Quarters

Step-by-step explanation:

Let D and Q stand for the numbers of Dimes and Quarters, respectively.

We learn that Steve has 37 total coins:  

 D + Q = 37

We also know that their total value is $6.10.  Let's use cents, instead of $ for the rest of the calculation.  You can use either, but I like playing with money.

Using cents:

10D + 25Q = 610   [10 pennies times the number of Dimes gives the number of pennies.  25 pennies times each quarter gives us the pennies from all the quarters.  Their sum is 610 pennies.]

We have 2 equations and 2 unknowns, so we are able to solve the problem, after we do some substitution.

We can approach this in several ways, but I like the idea of changing the first equation to find the number of Dimes, which will be:

D + Q = 37

D  = 37 - Q

Now use this value for D in the second equation:

10D + 25Q = 610

10(37 - Q) + 25Q = 610

370 - 10Q + 25Q = 610

 15Q = 610 - 370

 15Q = 240

Q = 16 quarters

Since we already derived D  = 37 - Q, we can say:

D  = 37 - 16

D = 21 Dimes

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

Check these results.  Are 21 Dimes and 16 Quarters solutions to the scenario?

Does Steve have 37 coins:  21 Dimes and 16 Quarters = 37 Coins.  YES

Does Steve have $6.10?  21*($0.10) + 16*($0.25) = $2.10 + $4.00 = $6.10  YES

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

Answer:

(-8,4)

Step-by-step explanation:

-2-4=-6

3-2=1

So, move your x value left 6, and your y value up 1 from (-2,3)

-6-2=-8

3+1=4

So, the answer is (-8,4)

Answer:

About 280,000

Step-by-step explanation:

Answer:

280,000

Step-by-step explanation:

If you multiply 70000 by 2 twice, then you get 280,000

Hope that this helps!

The correct sampling method described in the question is a stratified random sample among the simple random sample,  stratified random sample, cluster random sample and  Voluntary random sample

The sampling method described in the question is a stratified random sample.

In a stratified random sample, the population is divided into subgroups or strata based on certain characteristics or criteria. Then, a random sample is selected from each stratum. The key idea behind this method is to ensure that each subgroup is represented in the sample proportionally to its size or importance in the population. This helps to provide a more accurate representation of the entire population.

In the given sampling method, the population is divided into subgroups, and a fixed number of units is taken from each group. This aligns with the process of a stratified random sample. The sample selection is random within each subgroup, but the number of units taken from each group is fixed.

Other sampling methods mentioned in the question are:

Simple random sample: In a simple random sample, each unit in the population has an equal chance of being selected. This method does not involve dividing the population into subgroups.

Cluster random sample: In a cluster random sample, the population is divided into clusters or groups, and a random selection of clusters is included in the sample. Within the selected clusters, all units are included in the sample.

Voluntary random sample: In a voluntary random sample, individuals self-select to participate in the sample. This method can introduce bias as those who choose to participate may have different characteristics than those who do not.

Therefore, the correct sampling method described in the question is a stratified random sample.

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Based on the given dividend of $4.91, a discount rate of 8.6%, and an expected perpetual growth rate of 3.6%, we would expect the stock's price to be $98.20 today.

To determine the stock's price today, we can use the dividend discount model (DDM), also known as the Gordon growth model. The DDM calculates the present value of all future dividends, taking into account the required rate of return and the expected growth rate.

Let's plug in the values given in your question:

Dividend (D) = $4.91

Discount Rate (r) = 8.6% or 0.086

Perpetual Growth Rate (g) = 3.6% or 0.036

Now we can substitute these values into the formula to calculate the stock's price today:

Stock Price =4.91 - 0.086 = 0.036

Stock Price= 0.086−0.036 = 4.91

Simplifying the denominator:

Stock Price = 4.91/0.05

Stock Price=98.20

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Answer:

Exponential decay

Step-by-step explanation:

the answer is not linear decrease cause the price doesn't decrease the same every year

.. ..

Answer:

Step-by-step explanation:

Let the capacity of tank is x

The average velocity by change in position/change in time is 1.44cm/s. The instantaneous velocity at t=2s is 17.28cm/s.

The given position of a particle moving along the x-axis is x= 9.99+1.44t3.

The questions can be answered in the following manner:

(a) The average velocity is given by change in position/change in time.

a = (x2 - x1)/(t2 - t1) = [(9.99 + 1.44(3)) - (9.99 + 1.44(2))] / (3 - 2) = 1.44 cm/s

(b) The instantaneous velocity is given by the derivative of the position function v = dx/dt = d/dt (9.99 + 1.44t³) = 4.32t²

Instantaneous velocity at t = 2.00 s is v = 4.32(2)² = 17.28 cm/s

(c) Instantaneous velocity at t = 3.00 s is v = 4.32(3)² = 38.88 cm/s

(d) Instantaneous velocity at t = 2.50 s is v = 4.32(2.5)² = 27 cm/s

(e) The position of the particle at t = 2.00 s is x = 9.99 + 1.44(2)³ = 19.71 cm

The position of the particle at t = 3.005 s is x = 9.99 + 1.44(3.005)³ = 33.057 cm

Midway between these positions is (19.71 + 33.057)/2 = 26.39 cmInstantaneous velocity at x = 26.39 cm is v = 4.32t² = 4.32(2.42)² = 25.54 cm/s

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The 2 equations which can be used to solve the given situations of the numbers are:

So, the equations that can be formed are:

Let, Ronan's number be 'x' and '4x' be Kelsey's number.

Now, solve as follows:

Ronan's number be: -2/3

Kelsey's number be: 4 × 2/3 = -8/3

Let, let, Kelsey's number be 'x' and Ronan's number be '3x'.

Now, solve as follows:

Ronan's number be: 72.75

Kelsey's number be: 24.25

Therefore, the 2 equations which can be used to solve the given situations of the numbers are:

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Answer:

B

Step-by-step explanation:

4,000 is a constant so i cannot be a rate. That instantly eliminates 'D' as an option. If x = 0 at the very start that means the 4,000 must be how many gallons of water there is initially.

The representation of did sign decimal integers in 8-bit binary (two's complement) -16 =  11110000.

The correct option is C.

A maximum of 256 values, or 0 through 255, can be represented by 8 bits. The total number of states that may be represented and the number of bits in a binary number are both listed in Table 5.1. G = gigabits; K = kilobits; M = megabits; 1,048,576 = gigabits; 1,0737,41,824 = kilobits.

The most common number of bits in a byte is eight. A byte is a unit of digital information. The byte is indeed the smallest addressable unit of recollection in many computer architectures because historically, a single character of text was encoded in a computer using a byte's worth of bits.

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What is the 8-bit binary (two's-complement) representation of signed decimal integers -16?

A. 11111011

B. 11010110

C. 11110000

D. 10111000

Answer:

88

Step-by-step explanation:

brackets of division , multiplication , addition and subtraction

2+2+4+6*6*2+3+5

start with the multiplication

6*6*2 = 72

now do the addition

2+2+4+72+3+5 =88

The length of the third side of the triangle is decreasing at a rate of approximately 0.22 times the sine of the changing angle (in radians) meters per second.

If the angle between the two sides of the triangle is increasing at a rate, then we can say that the triangle is changing shape. Specifically, the third side of the triangle (the one opposite the changing angle) will be changing in length as well. To determine the rate at which this side is changing, we would need to know either the measure of the changing angle or the rate at which it is increasing. With the information given, we cannot determine this rate of change. However, we can use the Law of Cosines to find the length of the third side of the triangle:
c^2 = a^2 + b^2 - 2ab cos(C)
where c is the length of the third side, a and b are the lengths of the other two sides, and C is the angle opposite side c. Plugging in the given values, we get:
c^2 = 4^2 + 5^2 - 2(4)(5)cos(C)
c^2 = 41 - 40cos(C)
c ≈ 1.07 + 6.32cos(C)
This formula tells us that the length of the third side of the triangle is a function of the angle opposite it (in radians). If we knew the rate at which this angle was changing, we could use the Chain Rule to find the rate at which the third side was changing. For example, if the angle was increasing at a constant rate of 2 degrees per second, we could convert this to radians per second (0.035 radians per second) and then find:
dc/dt = d/dt [1.07 + 6.32cos(C)]
dc/dt = -6.32sin(C) (dC/dt)
dc/dt ≈ -6.32sin(C) (0.035)
dc/dt ≈ -0.22sin(C) meters per second

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The expression g = f/2 represents the relationship between g and f if j = h and k = m option (A) is correct.

The square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.

It is given that:

If j = h and k = m

From the figure angle, C is a right-angle triangle as j = h and k = m

From the definition of the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides

h² +k²= g²

From the triangle ΔABC

(j + h)² +(m + h)² =f²

(h + h)² +(k+ k)² =f²

(2h)² +(2k)²=f²

4h²+ 4k²= f²

4(h²+k²)= f²

4×g² =f²

(2g)² = f²

2g=f

g = f/2

Thus, the expression g = f/2 represents the relationship between g and f if j = h and k = m option (A) is correct.

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ANSWER ---> g=f/2

I GOT IT RIGHT