The expression d/t can be used to find the average speed of an object that travels a distance d in time t.

What is a car's average speed if it travels 147 miles in 3 hours?

The value of the double integral is  \(I = \int\limits^{\pi/2}_{\pi/4} \int\limits^{3/sin0}_{r=0} r^{2}cos0drd0\).

Let z* be the common (finite) optimal value of P and D.

Given integral is

\(I = \int\limits^3_{y = 0} \int\limits^y_{x=0} {x} \, dxdy\)

The region of integration lies between

y = 0, y = 3, x = 0 & x = y

Let x = rcosθ, y = rsinθ,

\(x^{2} +y^{2}= r^{2}\)

At y = 3, rsinθ = 3

Thus r varies from 0 to 3/sinθ

θ varies from π/4 to π/2

Now, dxdy ----> rdrdθ

Therefore,

\(I = \int\limits^{\pi/2}_{\pi/4} \int\limits^{3/sin0}_{r=0} r^{2}cos0drd0\)

Hence the answer is The value of the double integral is  \(I = \int\limits^{\pi/2}_{\pi/4} \int\limits^{3/sin0}_{r=0} r^{2}cos0drd0\).

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A simple difference is also called a marginal means difference. Option B

In experimental design and statistical analysis, a simple difference refers to the comparison of means between two groups or conditions. It represents the difference in average scores or values between the groups being compared. It is often used to assess the impact of an independent variable on a dependent variable by examining the variation in means between different levels of the independent variable.

The term "marginal means difference" emphasizes that the comparison is based on the average or marginal means of the groups being compared. It helps to distinguish it from other types of differences, such as interaction effects or main effects, which involve more complex comparisons or analyses in factorial designs.

Overall, a simple difference or marginal means difference is a straightforward way to evaluate the effect of an independent variable on a dependent variable by comparing the average values between different groups or conditions.

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Answer:

(0,6)

Step-by-step explanation:

The y intercept is where the line crosses the y axis or the coordinate where x = 0.

Here, when x is equal to 0, y is equal to 6 meaning that the y intercept is at (0,6)

Reflection across the x-axis.

To understand the answer, ignore the shape on the bottom.

Now, imagine a mirror on the x-axis.

It would mirror the image on the top, and it would look exactly like the shape on the bottom.

Hope this helps :))

Therefore, the area of the trapezoid is 6 square inches.

Area is a measure of the size of a two-dimensional surface or shape, such as a square, rectangle, circle, triangle, or any other polygon. It is usually measured in square units, such as square inches, square feet, square meters, or square centimeters. The area of a shape is calculated by multiplying the length of one side of the shape by the length of an adjacent side.

Here,

The formula for the area of a trapezoid is:

Area = (1/2) x (sum of parallel sides) x height

In this case, the parallel sides are 1.1 inches and 2.9 inches, and the height is 3 inches. So we can substitute these values into the formula and calculate the area:

Area = (1/2) x (1.1 + 2.9) x 3

Area = (1/2) x 4 x 3

Area = 6 square inches

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Answer:

x = -3

Step-by-step explanation:

To find and solve the value for x

1.2x + 3.4= -0.2

Transpose

1.2x = -0.2 - 3.4

1.2x = -3.6

x = -3.6/1.2

x = -3.0

x = -3

Answer:

x=-3

Step-by-step explanation:

Based on the given information, we know that x must be 2 since it is the only even prime number. We also know that y must be either 11, 13, 17, or 19 since those are the only prime numbers between 10 and 20.

So, the sum of x and y can be 2 + 11 = 13, 2 + 13 = 15, 2 + 17 = 19, or 2 + 19 = 21.

Out of these four possible sums, only 13, 17, and 19 are prime numbers. Therefore, we can say that the sum of x and y may or may not be a prime number, depending on the specific values of x and y.

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Answer:

a) 24 degrees

b) 50 degrees

Step-by-step explanation:

part a : use sine-1

sine-1 = \(\frac{opposite}{hypotenuse}\)

sine-1 = \(\frac{17}{42}\)

sine-1 = 0.405

missing angle = 23.89

round to the nearest degree = 23.89 = 24

part b : use cosine-1

cos-1 = \(\frac{adjacent}{hypotenuse}\)

cos-1 = \(\frac{16}{25}\)

cos-1 = 0.64

missing angle = 50.208

round to the nearest degree = 50.208 = 50

The sample standard deviation is approximately 2.73.The 95% confidence interval for the population mean heart rate is approximately (73.833, 76.087).

a. To calculate the sample standard deviation, we first need to find the sample mean. The sample mean is the sum of all observations divided by the sample size:

X = (70 + 74 + 75 + 78 + 74 + 64 + 70 + 78 + 81 + 73 + 82 + 75 + 71 + 79 + 73 + 79 + 85 + 79 + 71 + 65 + 70 + 69 + 76 + 77 + 66) / 25

X= 74.96

Next, we calculate the sum of the squared differences between each observation and the sample mean:

Σ(xᵢ - X)² = (70 - 74.96)² + (74 - 74.96)² + ... + (66 - 74.96)²

Σ(xᵢ - X)² = 407.04

Finally, the sample standard deviation is the square root of the sum of squared differences divided by (n-1), where n is the sample size:

s = √(Σ(xᵢ - X)² / (n-1))

s = √(407.04 / 24)

s ≈ 2.73

Therefore, the sample standard deviation is approximately 2.73.

b. The variance is the square of the standard deviation:

σ² = s² ≈ 2.73²

σ² ≈ 7.46

Therefore, the sample variance is approximately 7.46.

c. To calculate the 95% confidence interval (CI) for the population mean heart rate, we can use the formula:

CI = X ± (tα/2 * (s / √n))

where X is the sample mean, tα/2 is the critical value from the t-distribution for a 95% confidence level with (n-1) degrees of freedom, s is the sample standard deviation, and n is the sample size.

For the given sample, n = 25. The critical value tα/2 can be obtained from the t-distribution table or using a statistical software. For a 95% confidence level with 24 degrees of freedom, tα/2 is approximately 2.064.

Plugging in the values, we have:

CI = 74.96 (2.064 * (2.73 / √25))

CI = 74.96  (2.064 * 0.546)

CI ≈ 74.96  1.127

Therefore, the 95% confidence interval for the population mean heart rate is approximately (73.833, 76.087).

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In the event that linear regression is required, we have two options: (1) change the delay column 2) ignore them.

A variable's value can be predicted using linear regression analysis based on the value of another variable. The dependent variable is the one you want to be able to forecast. The independent variable is the one you're using to make a prediction about the value of the other variable.

Given,

You want to run a regression to predict the probability of a flight delay, but there are flights with delays of up to 12 hours that are really messing up your model.

I immediately think of grouping delays into ranges such as those under 40 minutes, those between 40 minutes and 2 hours, those between 2 hours and 10 hours, and those above 10 hours. But doing so requires the use of a classification model, such as logistic regression. We frequently consider whether there will be a delay rather than how long it might last when thinking about delays. In the event that linear regression is required, we have two options: (1) change the delay column 2) ignore them.

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Answer:

G(x) = (1 - x)/4

is the inverse function required.

Step-by-step explanation:

Given F(x) = -4x + 1

Let y = F(x)

Then y = -4x + 1

=> y - 1 = -4x

4x = 1 - y

x = (1 - y)/4

That is, the inverse is (1 - x)/4

Therefore, G(x) has to be (1 - x)/4

The two salesperson will both charge the same amount after 5 hours

Setting up the equation for the problem thus:

Salesperson A :

50 + 5h ___(1)

Salesperson B :

15h ____(2)

Equating (1) and (2)

50 + 5h = 15h

collect like terms

50 = 15h - 5h

50 = 10h

divide both sides by 10 to isolate h

h = 5

Hence, they will both charge the same amount after 5 hours .

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\( \huge \purple {\tt {x + \frac{7}{6} = 2x - \frac{7}{6}}} \)

\( \large {\tt {The \: answer \: in \: reduced}} \)

\( \large {\tt { improper \: fraction \: form.}} \)

\( \huge \pink {\tt {x + \frac{7}{6} = 2x - \frac{7}{6}}} \)

\( \huge \blue {\tt {or, \: x - 2x = - \frac{7}{6} - \frac{7}{6}}} \)

\( \huge \red {\tt {or, \: - x = \frac{ - 14}{6} = \frac{ - 7}{3}}} \)

\( \huge \green {\tt {or, \: x = \frac{7}{3}}} \)

\( \huge \orange {\tt {x = \frac{7}{3}}} \)

Answer:

Answer would be 12

Step-by-step explanation:

i'm not always accurate but your welcome!

Answer:

26 roses

Step-by-step explanation:

89-11 = 78

78/3 = 26

Answer:

Step-by-step explanation:

An arrow has one line of symmetry going through it vertically

A dodecagon has six lines of symmetry going through its points.

Answer: The arrow has 1 line and the dodecagon has 4 lines of symmetry.

Step-by-step explanation:

I just did it.

Answer:

None

Step-by-step explanation:

-18-2 would be equal to -20

-12+(-3) would be equal to -15

-10-5 would be equal to -15

0-8(-4) would be equal to 32

Is that the letter "O" or the number "0"?

Is all of this information given to you for this question here?

Answer:

A. Parallelogram

Step-by-step explanation:

The given points are;

(-10, -4), (-7, -8), (-5, -4), (-2, -8)

Let 'A' represent the point (-10, -4), let 'B' represent the point (-7, -8), let 'C' represent the point (-5, -4), and let 'D' represent the point (-2, -8), we have;

The (horizontal) distance between points A and C = -5 - (-10) = 5

The (horizontal) distance between points B and D = -2 - (-7) = 5

Therefore;

The length of \(\overline {AC}\) = The length of \(\overline {BD}\)

The length of \(\overline {AB}\) = √((-10 - (-7))² + (-4 - (-8))²)) = 5

The length of \(\overline {CD}\) = √((-5 - (-2))² + (-4 - (-8))²)) = 5

∴ The length of \(\overline {AB}\) = The length of \(\overline {CD}\)

\(\overline {AC}\) is parallel to the horizontal axis

\(\overline {BD}\) is parallel to the horizontal axis

∴ \(\overline {AC}\) ║ \(\overline {BD}\)

Given that \(\overline {AB}\) = \(\overline {CD}\), then \(\overline {AB}\) ║ \(\overline {CD}\)

Therefore, the quadrilateral ABCD is a parallelogram

(The angle ∠ABD = 180 - arctan (4/3) ≈ 126.9 > 90, therefore, the parallelogram ABCD is not a rectangle.)

To sketch the region enclosed by the curves y = sin(x) and y = 5x, we plot the curves and find the bounds of the region. We integrate with respect to x to find the area of the region.

To sketch the region enclosed by the given curves, we first plot the curves y = sin(x) and y = 5x on a coordinate plane.

The curves intersect at two points: (0,0) and (π/6,π/3). The x-coordinates of the bounds of the region are x = 0 and x = π/6. The y-coordinate of the lower bound of the region is y = 0, and the upper bound of the region is y = 5x.

Since the region is bounded by the curves y = sin(x) and y = 5x, we can integrate with respect to x or y. However, since the region is easier to describe in terms of x, we will integrate with respect to x.

A typical approximating rectangle for the region is shown below:

To set up the integral for finding the area of the region, we need to determine the limits of integration. We integrate from x = 0 to x = π/6, and the integrand is given by the difference between the upper and lower bounds of the region:

Area = ∫₀^π/6 (5x - sin(x)) dx

We can evaluate this integral using integration techniques such as integration by parts or numerical methods such as Simpson's rule.

Overall, the region enclosed by the given curves is a triangular region, and we can integrate with respect to x to find its area.

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The estimated height of the tree in this question is 17.9 metres which is 30 metres away from the man having 2 m height

The height of man = 2 m

Angle of elevation of the top of the tree =28 deg

Horizontal distance between the man and the tree is 30 m.

we need to calculate the height of the tree.Let us Assume that the height of the tree be x metres. so the vertical height of tree above man's height will be x-2 units.

The height of the tree can be found by using formula

\( \tan(28) =( x - 2) \div 30 \\ 30 \tan(28) = x - 2 \\ x = 2 + 30\tan(28) \\ x = 17.9 \: metres\)

In this problem we have used the trigonometric ratio tany = perpendicular / base

here in this right angle triangle the perpendicular is x-2

while base is 30 metres.

so by putting the values in the above equation we will get the answer.

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Answer:

a) It is not possible to find the mean because these are words, not numbers.

b) If we put these words in alphabetical order, we have:

blue, blue, green, purple, purple, purple, red, red

The median word here is purple.

c) It is possible to find the mode, which in this case is the word that appears the most times in this list. That word is purple, which appears three times.

Answer:

7

Step-by-step explanation:

6m = 3m + 21

6m - 3m = 21

3m = 21

m = 21 / 3

m = 7

Answer:

The answer is Find the equation of a line that passes through the point (-5,-1) and has a gradient of −1/2. Leave your answer in the form y=mx+c​

Step-by-step explanation:

The equation of a line that passes through the point (-5,-1) and has a gradient of −1/2. Leave your answer in the form y=mx+c​

The number of advance tickets sold was 52.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 8 is an equation.

We have,

Advance tickets x = $5.00

Tickets purchased the night of the concert cost y = $10.50

Total number of tickets = 78

The total cost of the tickets = $533

Now,

x + y = 78

x = 78 - y

Substituting

5x + 10.50y = 533

5 (78 - y) + 10.50y = 533

390 - 5y + 10.50y = 533

5.50y = 533 - 390

5.50y = 143

y = 26

Now,

x = 78 - y

x = 78 - 26

x = 52

Thus,

52 advance tickets were sold.

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To determine the complex exponential Fourier series representation for each of the given signals, we can use the formula:

X(t) = ∑[n=-∞ to ∞] Cn * e^(jnω0*t)

where Cn represents the complex Fourier coefficients and ω0 is the fundamental frequency.

X(t) = cos(ωt):

The complex exponential Fourier series representation for X(t) = cos(ωt) is:

X(t) = C0 * e^(j0ω0t) + C1 * e^(j1ω0t) + C(-1) * e^(j*(-1)ω0t)

= C0 + C1 * e^(jω0t) + C(-1) * e^(-jω0t)

x(t) = -cos(0.5 * ωt):

The complex exponential Fourier series representation for x(t) = -cos(0.5 * ωt) is:

x(t) = C0 * e^(j0ω0t) + C0 * e^(j0ω0t) + C1 * e^(j1ω0t) + C(-1) * e^(j(-1)ω0t)

= C0 + C0 + C1 * e^(j0.5ω0t) + C(-1) * e^(-j0.5ω0t)

x(t) = cos(2t + 1):

The complex exponential Fourier series representation for x(t) = cos(2t + 1) is:

x(t) = C0 * e^(j0ω0t) + C2 * e^(j2ω0t) + C(-2) * e^(j*(-2)ω0t)

= C0 + C2 * e^(j2ω0t) + C(-2) * e^(-j2ω0t)

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