16x³ +16x² + 3x=0
&
4x^2-9=0

(a) The work done by gravity is: -1177 J.

(b) The watermelon's kinetic energy is 1177 J and the speed of the is approximately 12.1 m/s.

(c) The answer to part (b) would be different if there were appreciable air resistance.

(a) The work done by gravity on the watermelon as it falls from the roof to the ground is equal to the change in the potential energy of the watermelon. The potential energy of the watermelon when it is at rest on the roof is:

U = mgh = (4.21 kg)(9.81 m/s^2)(27.8 m) = 1177 J

The potential energy of the watermelon when it hits the ground is:

U' = mgh = (4.21 kg)(9.81 m/s^2)(0 m) = 0 J

Therefore, the work done by gravity is:

W = U' - U = -1177 J

The negative sign indicates that the work done by gravity is done on the watermelon, decreasing its potential energy.

(b) (i) Just before it strikes the ground, the watermelon's kinetic energy is equal to the amount of potential energy it had when it was on the roof, since all of its potential energy has been converted to kinetic energy during the fall:

K = U = 1177 J

(ii) The kinetic energy can be expressed in terms of the velocity of the watermelon just before it hits the ground:

K = (1/2)mv^2

Solving for v, we get:

v = sqrt(2K/m) = sqrt(2(1177 J)/(4.21 kg)) = 12.1 m/s

Therefore, the speed of the watermelon just before it hits the ground is approximately 12.1 m/s.

(c) The answer to part (b) would be different if there were appreciable air resistance. Air resistance would cause the watermelon to experience a force opposite to its direction of motion, which would cause a loss of kinetic energy and a decrease in speed.

It would also cause the work done by gravity to be less than the change in potential energy, since some of the potential energy would be converted to heat due to air resistance.

The exact values of the work done and the final kinetic energy and speed would depend on the amount of air resistance and the exact nature of its effects.

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True. The hypothesis being tested is whether Glendale students spend more than 145 minutes per day studying, which is a national average.

True. The students should use a t-test to analyze the significance of the data they collected. The sample size of 25 is large enough to assume normality and the dot plot suggests that the data is approximately normally distributed. Therefore, a t-test can be used to analyze the significance of the data collected.

To test the hypothesis that Glendale students spend more than 145 minutes per day studying, they should conduct a one-sample t-test. This test compares the mean of the sample (in this case, the average study time of Glendale students) to the national mean of 145 minutes. Since the sample size is small (25 students) and the population standard deviation is unknown, the t-test is the appropriate choice for this analysis.

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The length of the other ribbon is 10 1/2 yards.

What is a fraction?

A fraction is a mathematical expression that represents a part of a whole or a division of one quantity by another. It consists of two numbers separated by a horizontal line called a fraction bar or a vinculum.

The length of each of Victoria's blue ribbons is 1 3/4 yd. We can represent this length in terms of yards as:

1 3/4 = 7/4 yards

If another ribbon is 6 times as long as one of Victoria's ribbons, then its length would be:

6 * (7/4) yards = 42/4 yards = 10 1/2 yards

Therefore, the length of the other ribbon is 10 1/2 yards.

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If t is the expected completion time for a given activity, then the correct formula for calculating the early finish time (EF) is EF = ES + t.

This formula adds the expected completion time to the early start time (ES) to determine when the activity is expected to finish.

The other options listed, LF = LS - t and EF = LS - t, involve subtracting the expected completion time from the late start or late finish times, which would not accurately reflect the expected completion time of the activity.

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Sure! Since x is rational and x = -33 + 234, we can write x as a fraction in simplest form:

x = (201)/1

To find the minimum value of x, we want to make the denominator as small as possible. One way to do this is to repeatedly subtract 33 from the numerator until we get to a multiple of 33.

(201)/1 = (168 + 33)/1 = (135 + 33 + 33)/1 = (102 + 33 + 33 + 33)/1 = ...

Continuing this pattern, we see that x can be written as:

x = (33n + 201)/1

where n is a non-negative integer. To minimize x, we want to choose the smallest possible value of n, which is 6.

Therefore, the minimum value of x is:

x = (33(6) + 201)/1 = 399

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Answer:

Arc length = The measure of the arc's angle in radians * The radius of the circle where the arc is in

Otherwise known as

Arc length = theta * radius = Θ * r

The value of b include the following: C. 2√21.

In order to determine the value of b, we would apply Cathetus theorem (leg rule), which states that each leg of a right-angled triangle is the geometric mean that's directly proportional between the hypotenuse and the part of the hypotenuse that's directly below the leg.

By applying Cathetus theorem (leg rule) to this right-angled triangle, we have the following:

b² = m × a

b² = (8 + 6) × 6

b² = 14 × 6

b² = 84

b = √84

b = 2√21 units.

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3375 is the volume of the solid created upon dilation.

What is the volume of a cube

The formula for the volume of a cube is given as a³

That is all of the sides are equal

Here the cube is dilated by the scale factor of 3

Then we have 5 x 3 = 15

Then the sides would be 15 each

the the volume = 15³

= 3375

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The mean of monthly cell phone bills today is different from $48.41. (2) his would be a false positive result,(3) having a large sample size, or having high variability in the data.

A null hypothesis is a type of hypothesis which explains the population parameter whose purpose is to test the validity of the given experimental data.

(a) The null hypothesis for the researcher's test could be:

H0: The mean of monthly cell phone bills today is equal to $48.41.

The alternative hypothesis could be:

Ha: The mean of monthly cell phone bills today is different from $48.41.

(b) A Type I error occurs when the null hypothesis is rejected, even though it is actually true. In this case, it would mean that the researcher concludes that the mean of monthly cell phone bills today is different from $48.41, when in reality it is not. This would be a false positive result, and it could happen due to various factors such as using a significance level that is too high, having a small sample size, or experiencing random sampling error.

(c) A Type II error occurs when the null hypothesis is not rejected, even though it is actually false. In this case, it would mean that the researcher concludes that the mean of monthly cell phone bills today is equal to $48.41, when in reality it is different. This would be a false negative result, and it could happen due to various factors such as using a significance level that is too low, having a large sample size, or having high variability in the data.

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The probability of between (and inclusive) 2 and 5 non-conforming basketballs being produced in a given hour is approximately 0.667 or 66.7%.

Using the Poisson distribution with λ=3.6 (from the previous question), the probability of between 2 and 5 non-conforming basketballs being produced in a given hour is:

P(2 ≤ X ≤ 5) = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

where X is the number of non-conforming basketballs produced in a given hour.

Using the Poisson probability mass function:

P(X = k) = (e^(-λ) * λ^k) / k!

we have:

P(X = 2) = (e^(-3.6) * 3.6^2) / 2! ≈ 0.129

P(X = 3) = (e^(-3.6) * 3.6^3) / 3! ≈ 0.195

P(X = 4) = (e^(-3.6) * 3.6^4) / 4! ≈ 0.195

P(X = 5) = (e^(-3.6) * 3.6^5) / 5! ≈ 0.148

Therefore,

P(2 ≤ X ≤ 5) = 0.129 + 0.195 + 0.195 + 0.148 ≈ 0.667

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We used was t = sin(θ), which will be helpful when converting back to the original variable t after evaluating the integral.

To evaluate the integral ∫(2√(1-2t²) dt), we will use a suitable trigonometric substitution. In this case, we'll use the substitution t = sin(θ), where θ is an angle.

Here's the step-by-step explanation:

1. Make the substitution: Replace t with sin(θ) in the integral, so we have ∫(2√[tex](1-2sin²(θ)) d(sin(θ))).[/tex]

2. Differentiate t with respect to θ: Since t = sin(θ), dt/dθ = cos(θ), or dt = cos(θ) dθ.

3. Update the integral: Replace dt with cos(θ) dθ, resulting in ∫(2√(1-2sin²(θ)) cos(θ) dθ).

4. Simplify the integrand: Use the trigonometric identity 1-2sin²(θ) = cos²(θ), so the integral becomes ∫(2√(cos²(θ)) cos(θ) dθ).

5. Simplify further: The square root of cos²(θ) is cos(θ), so the integral becomes ∫(2cos²(θ) cos(θ) dθ).

Now you have a trigonometric integral, which can be solved using standard integration techniques. Remember that the substitution we used was t = sin(θ), which will be helpful when converting back to the original variable t after evaluating the integral.

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An equation for the translation of y = 6/x that has the asymptotes x =4 and y = 5 is y = 6/(x - 4) + 5.

Given,

Vertical asymptotes x = 4

Horizontal asymptotes y = 5

The graph of y = 6/x has vertical asymptote x = 0 (the y-axis) and horizontal asymptote y = 0 (the x-axis).

An asymptote is a line to which the curve converges.

When the resulting independent variable is zero, the vertical asymptote occurs.

The values of the dependent variable coincide with the horizontal asymptote when the independent variable diverges to plus or minus infinity.

The translation formula is y = 6/(x - 4) + 5

Therefore, the equation is y = 6/(x - 4) + 5.

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Answer:

Mean is the average of all of the numbers. Median is the middle number, when in order.

Answer:

10,000πft³

Step-by-step explanation:

the formula for circumference is 2πr so you put 20π equal to that and when you simplify you get 10 as your radius.  The formula for a cylinder is Volume=πr²h where r is radius and h is height when you plug in your numbers the equation is V=π(10)²(100) simplify that and you get 10,000πft³

Answer: Solve the system of equations using substitution.

3x + 2y = 5

x = 2y + 7

(3, −2)

(5, −5)

(7, 0)

(11, 2)

Step-by-step explanation:

Answer:

Area of large rectangle = 12(8) = 96

Area of triangle = (1/2)(5)(4) = 10

Area of square = 4^2 = 16

(a) 16/96 = 1/6

(b) 1 - (10/96) = 86/96 = 43/48

Step-by-step explanation:

The number of triangles that can be drawn with the given side lengths is equal to three.

In Mathematics, a triangle is a two-dimensional (2D) geometric shape that comprises three (3) sides, three (3) vertices and three (3) angles only.

In order to determine the magnitude of angle A (m∠A), angle B (m∠B), and angle C (m∠C) in this triangle with the adjacent, opposite and hypotenuse side lengths given, we would have to apply the law of cosine:

C² = A² + B² - 2(A)(B)cosθ

Where:

A, B, and C represent the side lengths of a triangle.

In this context, we can reasonably infer and logically deduce that three (3) triangles can be drawn based on the given side lengths because they would each have three different angle measures.

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The graph that  represents the function f(x)  = |x − 1| − 3 is:

Graph B

To find out which graph can represent the given function f(x) = |x − 1| − 3, we need to look at each of the functions individually to deduce that.

The key to this is the point (1,-3) That point must be found first. C is incorrect because you are using 3 not - 3 which does not change (as C has changed it) through out the problem.

A is using (-1,-3) which makes it wrong. Also the equation is y = -abs(x-1) - 3 which is also a mistake. The given graph points upwards not downwards.

D has it's minimum point at (-1,-3) which is not correct.

We are left with b which opens upwards (correct) has it's min at (1,-3) [also correct] so the answer is

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Answer:

35% when awake 65% when asleep

Step-by-step explanation:

Answer:

59%

Step-by-step explanation:

divide sleep hours by total hours

295 ÷ 500= .59 = 59%

Answer: (1/3) π r 2 h

Step-by-step explanation:

The formula for the volume of a cone is V = (1/3)πr^2h, where r is the radius of the base, h is the height of the cone, and π is a constant approximately equal to 3.14.

Substituting the given values, we get:

V = (1/3)π(21)^2(25)

V = (1/3)π(441)(25)

V = (1/3)(3.14)(11025)

V = (1/3) π r 2 h

Therefore, the volume of the cone is approximately (1/3) π r 2 h.

The equation of the tangent plane to the given surface at the point (1,2,-4) is 16x + 3y - z = 27.

To find the equation of the tangent plane to the given surface at the point (1,2,-4), we first need to find the partial derivatives of the surface equation with respect to x and y:
∂z/∂x = 4xy^2
∂z/∂y = 4x^2y - 5

Then, we can evaluate these partial derivatives at the point (1,2,-4):
∂z/∂x(1,2) = 4(1)(2^2) = 16
∂z/∂y(1,2) = 4(1^2)(2) - 5 = 3

Next, we can use these values to find the equation of the tangent plane using the point-normal form:
z - z0 = ∂z/∂x(x0,y0)(x - x0) + ∂z/∂y(x0,y0)(y - y0)

Plugging in the values we found, we get:
z - (-4) = 16(x - 1) + 3(y - 2)

Simplifying, we get the equation of the tangent plane:
16x + 3y - z = 27

Therefore, the equation of the tangent plane to the given surface at the point (1,2,-4) is 16x + 3y - z = 27.

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Decimal numbers : The second number is 10 times the first number, which is 10 * 5.19 = 51.9.

The third number is 10 times the second number, which is 10 * 51.9 = 519.

Therefore, the sum of the three numbers is 5.19 + 51.9 + 519 = 576.09.

The ten multi-digit numbers that make up the decimal system are: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The numbers 10 and 11 come after the number 9, then 12 and so on. When the digit to the right exceeds 9, the number on the left is increased by 1 each time.

Decimals are a form of number in algebra that have a full integer and a fractional portion separated by a decimal point. The decimal point is the dot that separates the full number from the fractional element of the number. A decimal number is, for instance, 34.5.

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Answer: $8.75

Step-by-step explanation:

An 8% increase means that the Lasagne's cost has increased to 108% of the original amount.

We can use the inverse operation.

To work out an increase of 8%, you multiply by 1.08

The inverse of multiplying by 1.08 is dividing by 1.08

Original price = Price after increase ÷ 1.08

                       = $9.45 ÷ 1.08

                       =  $8.75

Therefore, the original price of the Lasagne is $8.75.

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Answer: When graphed, the line will cross through the letter "Y" at the point (−3, 0).

Step-by-step explanation: To graph the equation y = x + 3, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is 1 and the y-intercept is 3.

We can start by plotting the y-intercept at the point (0, 3). Then, since the slope is 1, we can move up 1 unit and to the right 1 unit to find another point on the line. If we repeat this process, we can find more points on the line and connect them to create the graph of the equation.

When graphed, the line will cross through the letter "Y" at the point (−3, 0).

The correct circle graph that represents the data in the table is:

Circle graph titled New York City visitor's transportation, with five sections labeled walk 40 percent, bicycle 8 percent, car service 15 percent, bus 10 percent, and subway 27 percent.

What is percentage?

Percentage is a way of expressing a number or proportion as a fraction of 100. It is represented by the symbol "%".

The table shows the number of visitors who used different types of transportation in New York City, and we need to represent this data in a circle graph.

To create a circle graph, we need to convert the numbers into percentages, and then divide the circle into sections proportional to these percentages.

The total number of visitors is 300 (the sum of all the numbers in the table). To find the percentage for each type of transportation, we divide the number of visitors for each type by 300 and multiply by 100.

For example, the percentage of visitors who walked is (120/300) * 100 = 40%. We can repeat this process for each type of transportation to get the following percentages:

Walk: 40%

Bicycle: 8%

Car Service: 15%

Bus: 10%

Subway: 27%

Next, we can divide the circle into sections proportional to these percentages. The correct circle graph is the one that accurately represents these percentages.

The circle graph that shows "walk" as the largest section (80%) is incorrect because it over-represents the number of visitors who walked. The circle graph that shows "subway" as the largest section (80%) is also incorrect because it under-represents the number of visitors who walked and over-represents the number of visitors who took the subway.

The correct circle graph is the one that shows "walk" as the largest section (40%), followed by "subway" (27%), "car service" (15%), "bus" (10%), and "bicycle" (8%). This accurately represents the percentages of visitors who used each type of transportation in New York City.

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The volume is changing at a rate of 54,000 [tex]cm^{3/s}[/tex].

The edges of a cube increase at a rate of 5 cm per second. How fast is the volume changing when the length of each edge is 60 cm?

Step 1: Write the formula for the volume of a cube.
Volume (V) = s³, where s is the side length of the cube.

Step 2: Differentiate both sides with respect to time (t).
dV/dt = 3s² * ds/dt

Step 3: Plug in the given values and solve for dV/dt.
The side length (s) is 60 cm, and the rate of increase of the edges (ds/dt) is 5 cm/s.

dV/dt = 3(60)²  * 5
dV/dt = 3 * 3600 * 5
dV/dt = 54,000 [tex]cm^{3/s}[/tex]

So, when the length of each edge of the cube is 60 cm, the volume is changing at a rate of 54,000 [tex]cm^{3/s}[/tex].

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Answer:

A line graph would best display the data for a student's average grade in math class for each month in a school year. A line graph would show the trend of the student's grades over time and help to identify any patterns or changes in the grades throughout the year.

It is shaped like a U.

It is also called a parabola!

Answer:

A quadratic function is parabolic in shape.

Step-by-step explanation:

A parabola is a cross-section (2D plane) of a cone (3D object). The shape and size of the parabola depend on the angle at which the plane intersects the cone. If the plane is more vertical, the resulting parabola will be narrower, while if it is more horizontal, the parabola will be wider.

a) To find the number of customers who have both checking and money market savings accounts, we need to use the principle of inclusion and exclusion.

Let A be the set of customers with checking accounts, B be the set of customers with money market savings accounts, and C be the set of customers with both checking and money market savings accounts. Then we have:

|A ∪ B| = |A| + |B| - |A ∩ B|

We know that |A| = 168, |B| = 120, and |A ∩ B| = ? (what we need to find)

We can also use the fact that the total number of customers is 250, so:

|A ∪ B| = 250 - |A' ∩ B'|

where A' and B' are the complements of A and B, respectively. Since no customer is allowed to have both regular savings and money market savings accounts, we know that:

|B ∩ C| = 0

So we can use the principle of inclusion and exclusion again to find:

|A ∪ B ∪ C| = |A| + |B| + |C| - |A ∩ B| - |B ∩ C| - |C ∩ A| + |A ∩ B ∩ C|

We know that |A ∪ B ∪ C| = 250 and |A|, |B|, and |C| are given. We also know that |B ∩ C| = 0 and we can use the fact that:

|A' ∩ B' ∩ C'| = |(A ∪ B)' ∩ (B ∪ C)' ∩ (C ∪ A)'|

= |(A' ∩ B') ∪ (B' ∩ C') ∪ (C' ∩ A')|

= |A' ∩ B'| + |B' ∩ C'| + |C' ∩ A'| - |A' ∩ B' ∩ C'|

We know that |A' ∩ B'| = |(A ∪ B)'| = 250 - |A ∪ B| and |C' ∩ A'| = |(C ∪ A)'| = 250 - |C ∪ A|. Since we already know |A ∪ B| and |C ∪ A| from the previous calculations, we can find |A' ∩ B' ∩ C'|. Then we can use the principle of inclusion and exclusion to find |A ∩ B|:

|A ∩ B| = |A| + |B| + |C| - |A ∪ B ∪ C| + |A' ∩ B' ∩ C'|

Substituting the given values, we get:

|A ∩ B| = 168 + 120 + 0 - 250 + (250 - 168 - 75 - 120 + |A ∩ B|)

Solving for |A ∩ B|, we get:

|A ∩ B| = 26

Therefore, there are 26 customers who have both checking and money market savings accounts.

b) To find the number of customers who have a checking account but no savings account, we can use the same principle of inclusion and exclusion. Let D be the set of customers with no savings account. Then we have:

|A ∩ D| = |A| - |A ∩ B ∪ A ∩ C|

We know that |A| = 168 and we just found |A ∩ B| = 26. To find |A ∩ C

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The distance of the diagnoal line connecting the points is 11.4 units

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

(-4,-1) and (5, 6).

The distance is calculated as

Distance = √[(x2 -x1)² + (y2 - y1)²]

substitute the known values in the above equation, so, we have the following representation

Distance = √[(-4 -5)² + (-1 - 6)²]

Evaluate

Distance = 11.4

HEnce, the distance is 11.4

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