The velocity function is v(t) = t^2 + 4t -32, and so the distance traveled in the time interval 0 ≤ t ≤ 6 is given by
∫ (t^2+4t-32 dt)
Remembering that lzl { z ≥ 0
z<0
we must determine where v(t) = t^2+ 4t -32 is positive or negative

Answer:

They ate a total of 7.5 apples.

Step-by-step explanation:

The total number of apples that these 4 students ate is:

2 + 2.5 + 1.25 + 1.75 = 7.5

Therefore, they ate a total of 7.5 apples.

Answer: 7.5

Step-by-step explanation: 2 + 2.5 = 4.5

4.5 + 1.25 = 5.75

5.75 + 1.75 = 7.5

Answer:

f^-1(x)=\(\frac{x}{2}\)+\(\frac{3}{2}\)

Step-by-step explanation:

Using the information, combine the individual probabilities to compute the probability that Peter will pass the quiz is (c) 0.0035.

To compute the probability that Peter will pass the quiz (i.e., get at least 7 questions correct), we need to sum the probabilities of getting exactly 7, exactly 8, exactly 9, and exactly 10 questions correct.

So, the probability of passing the quiz is:

P (getting at least 7 correct) = P (getting exactly 7 correct) + P (getting exactly 8 correct) + P (getting exactly 9 correct) + P (getting exactly 10 correct)

= 0.0031 + 0.000386 + 2.86 × 10⁻⁵ + 9.54 × 10⁻⁷

= 0.0035

Therefore, the result is c. 0.0035.

The binomial formula can be used to solve a wide range of problems in probability and statistics. The binomial formula is used to calculate the probability of getting a specific number of successes in a fixed number of independent trials, where each trial has only two possible outcomes (success or failure).

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Answer:

3.9375oz

i think this is right

Answer:

2.66666666667

Step-by-step explanation:

Answer:

.00231481

Step-by-step explanation:

\(\frac{1}{12}\) * \(\frac{1}{36}\) = \(\frac{1}{432}\) = .00231481

Answer:

108°

Step-by-step explanation:

Answer:

multiply 2 * 5 add 4 +6 multiply both of your answers and you get the answer to 45% of 62

Answer:

45℅of 62is27.9

hope I it helps.

Answer:

2.3a + 0.8a =

2.3

+ 0.8

________

3.1

________

So therefore, 2.3a + 0.8a = 3.1a

Answer: -90

Step-by-step explanation: To solve this equation for y, we need to isolate the variable y on one side of the equation. To do this, we can multiply both sides of the equation by -5 to get rid of the fraction on the right side:

18 = y / -5

18 * -5 = y / -5 * -5

-90 = y

Therefore, the value of y that satisfies the equation is -90.

Answer:

2

Step-by-step explanation:

4/2 = 2

2/1 = 2

4/2=2/1

EZ

The given question can be verified by first substituting the value of x into both the given functions and simplify them separately. Then we can subtract the second function from the first function to get the resulting function h(x).

To solve this problem, we need to first find the value of q by plugging in the value of x in the equation \(FX = 1/2 x^3 - 3/4 x^2 + 2/5 x - 1/6q.\) So, when x = 1/4, we get:

\(FX = 1/2(1/4)^3 - 3/4(1/4)^2 + 2/5(1/4) - 1/6q\)

\(FX = 1/32 - 3/64 + 1/10 - 1/6q\)

\(FX = 5/64 - 1/6q\)

Next, we need to find the value of   \(FX - qX\) by plugging in the values of FX and X:

\(FX - qX = (5/64 - 1/6q) - q(1/4)^3 - 5/4(1/4)^2 + 16/15(1/4) - 5(1/4)\)

\(FX - qX = 5/64 - 1/6q - q/64 - 5/64 + 16/60 - 5/4\)

\(FX - qX = -1/6q - 79/60\)

Finally, we need to find the value of hX by plugging in the value of X = 1/4 in the equation  \(hX = 1/4 x^3 + 1/2 x^2 - 2/3 x + 2/3:\)

\(hX = 1/4(1/4)^3 + 1/2(1/4)^2 - 2/3(1/4) + 2/3\)

\(hX = 1/256 + 1/32 - 2/12 + 2/3\)

\(hX = 1/256 + 8/256 - 32/256 + 128/256\)

\(hX = 105/256\)

Now, we need to verify that  \(FX - qX = hX\) . Let's substitute the values we have found:

\(-1/6q - 79/60 = 105/256\)

Multiplying both sides by -6 gives:

\(q/10 + 79/320 = -35/128\)

Subtracting  \(79/320\) from both sides gives:

\(q/10 = -35/128 - 79/320\)

\(q/10 = -819/2560\)

Multiplying both sides by 10 gives:

\(q/10 = -819/2560\)

Therefore, we have verified that \(FX - qX = hX when X = 1/4 and q = -819/256.\)

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Answer:

A is 1

B is 5

Step-by-step explanation:

0 times 2 is 0 plus 1 is 1 that gives the answer to A

2 times 2 is 4 plus 1 is 5 which gives you B

Mean = 157.8

Test statistic = z = 0.14

p-value = 0.4463

There is no significant trend in the data.

To analyze the data and determine if there is a trend in law enforcement fatalities over the 20-year period, we will follow these steps:

Step 1: Calculate the mean

To find the mean, we sum up all the values and divide by the total number of values (20):

183 + 141 + 173 + 170 + 145 + 162 + 241 + 158 + 149 + 164 + 164 + 156 + 192 + 149 + 125 + 160 + 172 + 127 + 108 + 117 = 3149

Mean = 3149 / 20 = 157.8

Step 2: Identify values above and below the mean

Comparing each value to the mean, we can determine if it is above (A) or below (B) the mean:

183(A), 141(B), 173(A), 170(A), 145(B), 162(B), 241(A), 158(B), 149(B), 164(A),

164(A), 156(B), 192(A), 149(B), 125(B), 160(B), 172(A), 127(B), 108(B), 117(B)

Step 3: Test for randomness using alpha = 0.05

To test for randomness, we can perform a runs test. A run is defined as a sequence of consecutive values above or below the mean. We count the number of runs (N) and calculate the expected number of runs (E) under the assumption of randomness:

N = 10 (observed number of runs)

E = (2 * N1 * N2) / (N1 + N2) + 1

 = (2 * 8 * 11) / (8 + 11) + 1

 ≈ 9.63 (expected number of runs)

Next, we calculate the standard deviation of the number of runs (SD):

SD = sqrt((2 * N1 * N2 * (2 * N1 * N2 - N)) / ((N - 1) * (N + 1)))

  = sqrt((2 * 8 * 11 * (2 * 8 * 11 - 10)) / ((10 - 1) * (10 + 1)))

  ≈ 2.68

Finally, we calculate the Z-test statistic:

Z = (N - E) / SD

 = (10 - 9.63) / 2.68

 ≈ 0.14

Step 4: Hypotheses test, p-value, and conclusion

Null hypothesis (H0): The distribution of values above and below the mean is random.

Alternative hypothesis (H1): The distribution of values above and below the mean is not random.

Since we are testing for randomness, we will perform a two-tailed test. Looking up the Z-value of 0.14 in a standard normal distribution table, we find that the p-value is approximately 0.4463.

The p-value (0.4463) is greater than the significance level (0.05), so we fail to reject the null hypothesis. Therefore, we do not have sufficient evidence to conclude that there is a non-random trend in law enforcement fatalities over the 20-year period.

Now we need to find the range of values that will include the values around the mean with 95% confidence interval. Therefore, the critical values for the given α value can be calculated as follows:

Lower Limit = μ - z(σ/√n)

Upper Limit = μ + z(σ/√n)

We do not know the population standard deviation, therefore we use the sample standard deviation in its place. To get that, let us calculate the sum of the squared deviations from the mean:

(104 - 157.8)² + (167 - 157.8)² + (143 - 157.8)² + (134 - 157.8)² + (148 - 157.8)² + (156 - 157.8)² = 3152.8

To get the sample variance, divide the sum by (n - 1): 3152.8 / (6 - 1) = 630.56

Then take the square root to get the sample standard deviation: σ = √630.56 = 25.1

Now we can substitute these values in the critical value formula:

Lower Limit = 157.8 - 1.96(25.1/√6) = 138.18

Upper Limit = 157.8 + 1.96(25.1/√6) = 177.42

Thus, the range of values that will include the values around the mean with 95% confidence interval is (138.18, 177.42).From the given data, we can see that there are 3 values below the mean and 3 values above the mean. Thus, there is no significant trend in the data.

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Complete question:

Listed below, from left to right and then top to bottom, are numbers of law enforcement fatalities for 20 recent and consecutive years. First find the mean, identify each value as being above the mean (A) or below the mean (B), then test for randomness above and below the mean using α=0.05. Is there a trend?

183 , 141 , 173 , 170 , 145 , 162 , 241 , 158 , 149 , 164

164 , 156 , 192 , 149 , 125 , 160 , 172 , 127 , 108 , 117

Answer:

\(\huge\boxed{\sf t = 0.6}\)

Step-by-step explanation:

\(\sf 0.15(10t-9) = 0.75(4t-3)\\\\Resolving \ Parenthesis\\\\1.5t-1.35 = 3t - 2.25\\\\Combining \ like \ terms\\\\-1.35 + 2.25 = 3t-1.5t\\\\0.9 = 1.5t\\\\Dividing \ both \ sides \ by \ 1.5\\\\0.9/1.5 = t\\\\0.6 = t\\\\OR\\\\\bold{t = 0.6}\)

Hope this helped!

Answer:

Step-by-step explanation:

Okay, so first, let's get our data out.

DAY                    SPEED

  1         8 min per mile / 6 miles an hour

  2        Under 8 min per mile / 7 miles per hour

  3        More than 8 min per mile / 6 miles per hour

  4        7 min per mile / 8 miles per hour

Yes

Yes

No

Hope this helps :)

Stay Cold,

Brook

Answer:

\(Density = 1.1546\ kg/pint\)

Step-by-step explanation:

Given

\(Mass = 7\ lb\)

\(Cups = 5.5\)

Required

Determine the density in Kg/Pint

Density is calculated as thus:

\(Density = \frac{Mass}{Volume}\)

\(Density = \frac{7\ lb}{5.5\ cups}\)

Convert pound to kg

\(Density = \frac{7/ 2.205\ kg}{5.5\ cups}\)

\(Density = \frac{3.17515\ kg}{5.5\ cups}\)

Convert cups to pint

\(Density = \frac{3.17515\ kg}{5.5/2\ pint}\)

\(Density = \frac{3.17515\ kg}{2.75\ pint}\)

\(Density = 1.1546\ kg/pint\)

Answer:

There are three terms in the expression.

Step-by-step explanation:

Some background knowledge:

Algebraic expressions do not include equal signs.

Terms are generally values that are added or subtracted.

For example,

2x+6 has two terms which are 2x and 6.

Here:

The term 2x has a coefficient (the number next to a variable) of 2 and the term '6' is a constant.

Please note that a constant is a number that does not include a variable.

LET US SOLVE OUR CASE:

Given the expression

15.5 - (6 x 2) - (16 ÷ 4)

Please note that:

Therefore, there are three terms in the expression.

Step-by-step explanation:

A higher confidence interval means less power which in turns means a smaller rejection religion.So our confidence interval would become wider.

The maximum earning is v(r,b)

Let v(r,b) be the expected value of the game for the player, assuming optimal play, if the remaining deck has r red cards and b black cards.

Then v(r,b) satisfies the recursion

and

The stopping rule is simple: Stop when v(r,b)=0.

To explain the recursion . . .

If r,b>0, and the player elects to play a card, then:

Thus, if r,b>0, electing to play a card yields the value f(r,b).

But the player always has the option to quit, hence, if r,b>0, we get v(r,b)=max(0,f(r,b)).

Implementing the recursion in Maple, the value of the game is

v(26,26)=41984711742427/15997372030584

v(26,26)  ≈2.624475549

and the optimal stopping strategy is as follows . . .

So, The maximum earning is v(r,b)

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Answer:

1. 330,400

2. 0.000084

3. 2,100

4. 7.823 x 10^9

Answer:1. 330,400

2. 0.000084

3. 2,100

4. 7.823 x 10^9

Step-by-step explanation:hope this helps

The final coordinates of the figure are: A" (30, 6), B" (46, 6) and C" (2x + 4, 2y + 6).

To complete the transformations and find the final coordinates of the figure, we'll apply two transformations: a translation and a dilation.

Translation: Given the vector <2,3>, we will translate each point by adding the corresponding components of the vector to their initial coordinates.

Let's assume the initial coordinates of points A, B, and C are:

A (13, 0)

B (21, 0)

C (x, y)

After the translation, the new coordinates will be:

A' (13 + 2, 0 + 3) = (15, 3)

B' (21 + 2, 0 + 3) = (23, 3)

C' (x + 2, y + 3) = (x + 2, y + 3)

Dilation: Given the scale factor K = 2, we will dilate each point by multiplying their coordinates by the scale factor.

After the dilation, the new coordinates will be:

A" (15 * 2, 3 * 2) = (30, 6)

B" (23 * 2, 3 * 2) = (46, 6)

C" ((x + 2) * 2, (y + 3) * 2) = (2x + 4, 2y + 6)

Please note that since the initial coordinates of point C were not provided, we cannot determine its final coordinates precisely without additional information. The coordinates of point C in the final figure depend on the values of x and y.

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Answer:

sure

Step-by-step explanation:

Answer:

4000 meters

Step-by-step explanation:

Shortest run was 5 laps (2000 meters), and longest was 15 (6,000 meters)

Answer:

142.75

Step-by-step explanation:

Answer:

Volume of Cylinder 1 = π×r×r×h

= 22÷7×1×1×8

= 25.13cm

Volume of Cylinder 1 = π×r×r×h

= 22÷7×2×2×8

= 100.53cm

Volume of Cylinder 1 = π×r×r×h

= 22÷7×3×3×8

= 226.19cm

The appropriate regression model depends on the stationarity properties of both the dependent and independent variables, as well as the error term. The researcher can use a standard OLS regression model with first-order differencing of both Y and X.

In the first scenario, both Y and X are I(0), which means they are stationary time series. In this case, the researcher can perform a standard linear regression analysis, as the stationary series would lead to a stable long-run relationship. The answer from this model will be reliable and less likely to suffer from spurious regressions. In the second scenario, Y is I(2) and X is I(0). This implies that Y is integrated of order 2 and X is stationary. In this case, the researcher should first difference Y twice to make it stationary before performing a regression analysis. However, this approach might not be ideal as the integration orders differ, which can lead to biased results.

In the third scenario, Y and X are both I(1) and the error term is I(0). This indicates that both Y and X are non-stationary time series, but their combination might be stationary. The researcher should employ a co-integration analysis, such as the Engle-Granger method or Johansen test, to identify if there is a stable long-run relationship between Y and X. If co-integration is found, then an error correction model can be used for more accurate predictions.

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Answer:

3:50 P.M.

Step-by-step explanation: 3 * 10 = 30 minutes

4:20 - 30 = 3:50

To calculate the frequencies and eigenvectors for the given system, you can use MATLAB's eig function. Here's a MATLAB code snippet that demonstrates how to perform these calculations:

% Define the system matrices

M = [0 1; 2 0];

C = [3 2; -2 2];

K = [3 -2; -2 2];

% Solve the eigenvalue problem

[V, W] = eig(K, M);

% Extract eigenvalues and frequencies

eigenvalues = diag(W);

frequencies = sqrt(abs(eigenvalues)) / (2*pi);

% Display the results

disp("Eigenvalues:");

disp(eigenvalues);

disp("Frequencies:");

disp(frequencies);

% Extract eigenvectors

eigenvectors = V;

disp("Eigenvectors:");

disp(eigenvectors);

In this code, the system matrices `M`, `C`, and `K` represent the mass, damping, and stiffness matrices, respectively. The `eig` function is used to solve the eigenvalue problem, where `K` and `M` are the input matrices. The resulting eigenvectors are stored in the matrix `V`, and the eigenvalues are stored in the matrix `W`. The frequencies are then calculated from the eigenvalues by taking the square root of the absolute values and dividing by `2*pi`.

Finally, the code displays the eigenvalues, frequencies, and eigenvectors using the `disp` function. Note that the code assumes a 2x2 system, as indicated by the provided system equations. You can modify the code accordingly if your system has a different dimension.

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