Select the correct answer. Which equation matches the function shown in the graph?
A. y = cos(x - π/4)
B. y = cos(x + π/2)
C. y = cos(x - π/2)
D. y = cos(x + π/4)

The distance traveled after 2 hours will be 324 miles.

Average speed is defined as the ratio of the total distance traveled by a body to the total time taken for the body to reach its destination.

The table shows the average speed of the winner of a car race for different

years.

year      average speed

2005     135.17

2010      137.28

2015      161.94

2020     141.11

In order to find out how many miles the winner of the car race in 2015 traveled after 2 hours, we need to know the average speed at which they were traveling, which is given as 161.94 miles per hour. To find out how far they traveled in 2 hours, we can multiply this speed by the time, measured in hours.

So, if the average speed was 161.94 miles per hour, then the distance traveled in 2 hours is:

161.94 miles/hour × 2 hours = 323.88 miles.

Rounding up to the nearest whole number, the distance traveled after 2 hours is 324 miles.

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The question seems to be incomplete the missing table has been attached below

105

x5.6

0630

+5250=

5880

Then add a decimal point

588.0

588

hope it helps!

Answer:

Step-by-step explanation:

First, let's define standard notation. Standard notation is just the normal way to write numbers. So multiply 5.6 x 105 and you get...

Answer:uhhhhhhhhhhhhhhhhhhh 14

Step-by-step explanation:

Answer:

im not good with math sorry :(

Step-by-step explanation:

To factor quadratics with leading coefficients other than 1, you can follow these steps:

Check your factoring by expanding the factored form to see if it simplifies back to the original quadratic equation.

Remember that factoring quadratics with leading coefficients other than 1 may involve more complex algebraic techniques, and in some cases, the quadratic equation may not factor easily. In such cases, you can resort to using the quadratic formula to find the roots of the equation.

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Answer:

6/6 or one foot.

Step-by-step explanation:

If one of the fish tanks is 5/6 of a foot wide, and the other is 1/6, add them together.

5/6+1/6=6/6 or 1 foot wide. 6/6 means a whole number.

The total width of the two fish tanks as per the given relation is equal to 1 foot.

To find the total width of the two fish tanks when placed next to each other, add their widths.

The widths are given as fractions of a foot, so add them directly:

Width of the first fish tank = 1/6 foot

Width of the second fish tank = 5/6 foot

Total width of the two fish tanks = (1/6) + (5/6)

To add fractions, they need to have the same denominator.

Here, both fractions already have the same denominator (6),

So, simply add their numerators:

Total width = (1 + 5)/6

Total width = 6/6

Now, 6/6 is equal to 1.

Therefore, the total width of the two fish tanks is 1 foot.

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Answer:

Rs. 390

Step-by-step explanation:

Question : 30% more than Rs.300.

Answer with explanation

30% of 300 is :

300 × 30 % = Rs. 90

According to the question, they are asking for 30 % more than 300.

For that you have to add  90 ( 30% of 300 ) to 300.

Let us solve now.

Rs. 300 + Rs. 90 0= Rs.390

Therefore , 30% more than Rs.300 is Rs. 390

Hope this helps you :-)

Let me know if you have any other questions :-)

please give me 5 stars

The area enclosed by the ellipse with equation x^2/a^2 + y^2/b^2 = 1 is given by the formula pi * a * b. This formula applies to ellipses with semi-axes a and b. The proof involves solving the equation for y and obtaining the equation of the ellipse in the first quadrant.

To find the area enclosed by the ellipse x²/a² + y²/b² = 1, we begin by solving the equation for y. This gives us y²/b² = 2 - x²/a² or y = ± (b/a)√(a² - x²). Since the ellipse is symmetric with respect to both axes, the total area A is four times the area in the first quadrant.

In the first quadrant, the equation of the ellipse becomes:

y = (b/a)√(a² - x²) for 0 ≤ x ≤ a.

To determine the area, we integrate this equation with respect to x over the interval [0, a]. Substituting x = a sinθ and differentiating, we find dx = a cosθ dθ.

By changing the limits of integration, we note that when x = 0, sinθ = 0, so θ = 0; and when x = a, sinθ = 1, so θ = π/2. Thus, the integral becomes 1/4A = ∫[0,π/2] (b/a)(a cosθ)(a dθ).

Simplifying, we have 1/4A = (b/a) * a² ∫[0,π/2] cosθ dθ. The integral of cosθ over [0,π/2] is sinθ evaluated at the limits, which gives:

sin(π/2) - sin(0) = 1 - 0 = 1.

Therefore, we have 1/4A = (b/a) * a² * 1, which simplifies to 1/4A = a * b. Multiplying both sides by 4, we get A = π * a * b, which proves that the area of an ellipse with semi-axes a and b is given by the formula π * a * b.

In particular, when the ellipse is a circle with radius r, we can substitute a = b = r, yielding A = π * r^2. Thus, we have proven the well-known formula for the area of a circle.

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If z is a standard normal variable, the probability that z is less than 1.13 is given by: A. 0.8708.

In Statistics, the standard normal distribution table is designed and developed to provide only the area to the left of a specified z-score.

Additionally, since z-score (z₁) and z-score (z₂) are generally symmetric about z = 0 and are negatives of one another, then, by symmetry, the area to the right of z-score (z₂) is always equal to the area to the left of z-score (z₁).

This ultimately implies that, the total areas under a standard normal distribution curve in two tails can be determined by calculating the area to the left of z-score (z₁) and multiplying the value by two (2).

From the z-score table, the area to the left of z-score (z₁ = 1.13) is the same as the probability that z is less than 1.13 and this is given by:

Area to the left of z-score (z₁ = 1.13) = 0.8708.

Probability, P(z ≤ 1.13) = 0.8708.

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a) The balloon's height can be determined using the laws of sines and cosines. By measuring the angles of elevation at two points, along with the distance between them, the height of the balloon is found.

b) The angle between the two slanted sections of the shed's roof can be calculated using the laws of sines and cosines. The dimensions of the roof sections are given, and by applying the appropriate formulas, the angle θ can be determined.

a) Let's denote the height of the balloon above the ground as "h" and the distance from point A to the balloon as "x". We can set up two right triangles to solve for "h".

In the first triangle, we have the angle of elevation at point A, which is 32 degrees. The side opposite this angle is "h" and the adjacent side is "x". Using the sine function, we have:

sin(32°) = h / x

Rearranging the equation, we get:

h = x * sin(32°)

In the second triangle, Henry walks 120 feet closer to point B, so the distance from point A to the balloon becomes "x - 120". The angle of elevation at this new position is 54 degrees. The side opposite this angle is still "h", and the adjacent side is now "x - 120". Using the sine function again, we have:

sin(54°) = h / (x - 120)

Rearranging the equation, we get:

h = (x - 120) * sin(54°)

Since the height of the balloon "h" is the same in both equations, we can set the two expressions equal to each other:

x * sin(32°) = (x - 120) * sin(54°)

Now we can solve for "x":

x * sin(32°) = x * sin(54°) - 120 * sin(54°)

x * sin(32°) - x * sin(54°) = -120 * sin(54°)

x * (sin(32°) - sin(54°)) = -120 * sin(54°)

x = (-120 * sin(54°)) / (sin(32°) - sin(54°))

Once we find the value of "x", we can substitute it back into either of the equations to find the height "h" of the balloon above the ground.

b) Let's denote the height of the shed's walls as "h". We can set up a right triangle to solve for the angle between the two slanted sections of the roof.

In the triangle, the height of the shed's walls "h" is the opposite side of the angle θ, and the difference in lengths between the two slanted sections (12 ft - 5 ft = 7 ft) is the adjacent side. We can use the tangent function to find the angle:

tan(θ) = h / 7

To find θ, we can take the inverse tangent (arctan) of both sides:

θ = arctan(h / 7)

To find the value of θ, we need to know the value of "h." If the height of the shed's walls is not given, we cannot determine the exact value of θ.

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Answer:

it would be C≈13.19cm

hope this helps :)

Answer:

Step-by-step explanation:

The lateral surface area is:

\(\\ \tt\longmapsto SA=2\pi rh[[/te]

\(\\ \tt\longmapsto SA=2\times 22}{7}\times (2.5)(9.25)\)

\(\\ \tt\longmapsto SA=145.23in^2\)

The initial amount A is 1 and the growth factor B is 1.4 in the Exponential function f(t)=14^x.

Given,

f(x) = 1.4^x

It is an exponential function.

y = a.b^x

where a is the initial quantity and b is the growth/ decay component.

Now we are able to examine the given feature with

A = 1

B = 1.4

An exponential function is a mathematical function that has the form f(x) = a^x, where a is a constant greater than zero and not equal to one, and x is a variable. This function is widely used in a variety of fields, such as finance, physics, and biology, due to its ability to model growth, decay, and change over time.

Exponential functions are essential in understanding various natural phenomena, from population growth to radioactive decay, and they play a crucial role in the advancement of scientific research.The exponential function has several unique properties, such as exponential growth, where the function grows at an increasing rate as x increases. Additionally, the function has an asymptotic relationship with the x-axis, meaning it never actually touches the x-axis but gets infinitely close to it.

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Answer:

48 cups

Step-by-step explanation:

There are 16 cups in a gallon.

16 x 3 = 48

Using a linear function, it is found that the costs are given as follows:

A linear function is modeled by:

y = mx + b

In which:

Considering the price of admission and the price per ride, the y-intercept is of 20 and the slope is of 4, the cost for r rides is given by:

C(r) = 20 + 4r.

Hence, for 6 rides, the cost is given by:

C(6) = 20 + 4 x 6 = $44.

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The equation for the balance of the savings account after Y months can be expressed as B = 500(1 + 0.005)^Y. After 15 months, the account balance would be approximately $525.31.

The equation B = 500(1 + 0.005)^Y represents the balance of the savings account after Y months.

The initial deposit of $500 is multiplied by (1 + 0.005) raised to the power of Y, which represents the monthly interest rate. The interest rate is expressed as a decimal by dividing the percentage value by 100.

To find the account balance after 15 months, we substitute Y = 15 into the equation. B = 500(1 + 0.005)^15 ≈ $525.31.

Therefore, the account balance after 15 months would be approximately $525.31. This calculation takes into account the monthly interest of 0.5% on the initial deposit of $500 over the given period.

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Based on the original image, if this figure is reflected across the x-axis the orientation of the new or reflected figure should be the one shown in A or the first image.

In geometry and related fields, a reflection is equivalent to a mirror image. Due to this, the reflection of an image is the same size as the original image, it has the same sides and also the same dimensions. However, the orientation is going to be inverted, this means the right side is going to show on the left side and vice versa.

Based on this, the image that correctly shows the reflection of the figure is the first image or A.

Note: This question is incomplete; below I attach the missing images:

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Answer:

25  i used g00gle trans

Step-by-step explanation:

The given statement "A successful proof can indeed turn a conditional statement into a theorem.'' is true because a successful proof can transform a conditional statement into a theorem by providing a logical and rigorous demonstration of its truth based on the given hypothesis.

In mathematics, a conditional statement is a proposition that asserts a relationship between two or more mathematical objects or concepts. It consists of a hypothesis and a conclusion.

A conditional statement is typically expressed in the form "If A, then B," where A represents the hypothesis and B represents the conclusion.

To establish a conditional statement as a theorem, one needs to provide a valid proof that demonstrates the truth of the statement. A proof is a logical argument that follows a series of logical deductions from axioms, definitions, and previously established theorems.

When a proof is successfully constructed for a conditional statement, it provides rigorous justification for the truth of the conclusion based on the given hypothesis.

By demonstrating the logical validity and coherence of the argument, the proof confirms the truth of the conditional statement and establishes it as a theorem.

The process of proving a conditional statement involves carefully reasoning through logical steps, utilizing mathematical principles and logical inference rules.

It requires precise and accurate reasoning, ensuring that each step in the proof is valid and consistent with the underlying mathematical framework.

Once a conditional statement has been proven, it is elevated to the status of a theorem. Theorems are fundamental results in mathematics that have been rigorously proven and hold true within a given mathematical system.

They serve as building blocks for further mathematical investigations and form the foundation of mathematical knowledge.

In summary, a successful proof can transform a conditional statement into a theorem by providing a logical and rigorous demonstration of its truth based on the given hypothesis.

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The expected value of a binomial random variable is the mean number of successes in a given experiment. In this case, the binomial random variable is denoted by x and the probability of success is 0.84. If 67 trials are conducted, where n=67 and p=0.84. Thus, the expected value of x is 56.28.

This means that, on average, 56.28 successes out of 67 trials are expected to occur when the probability of success is 0.84. This can be visualized as rolling a dice with a 4/5 chance of success 67 times. The expected value represents the average number of times the dice will land on 4 or 5, which is 56.28. This is also the same as saying that 56.28 successes, on average, are expected to occur out of every 67 trials.

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The line integral of the vector field F = y^2 dx + x^2 dy over the square C with the given orientation is 5/3.

To compute the line integral of the vector field F = y^2 dx + x^2 dy over the square C with vertices (0,0), (1,0), (1,1), and (0,1) oriented counterclockwise, we can parameterize the boundary of the square and evaluate the line integral using the parameterization.

Let's divide the boundary of the square C into four line segments: AB, BC, CD, and DA.

On the line segment AB, we have x = t, y = 0, where t varies from 0 to 1.

On the line segment BC, we have x = 1, y = t, where t varies from 0 to 1.

On the line segment CD, we have x = t, y = 1, where t varies from 1 to 0.

On the line segment DA, we have x = 0, y = t, where t varies from 1 to 0.

Now, let's evaluate the line integral over each line segment:

∫AB F · dr = ∫[0,1] (0^2 dt) + (t^2 * 0) = ∫[0,1] 0 dt = 0

∫BC F · dr = ∫[0,1] (1^2 * 1) + (1^2 dt) = ∫[0,1] (1 + 1) dt = ∫[0,1] 2 dt = 2t | [0,1] = 2

∫CD F · dr = ∫[1,0] (t^2 * 1) + (0^2 * -1) = ∫[1,0] t^2 dt = (1/3)t^3 | [1,0] = (1/3)(0^3 - 1^3) = -1/3

∫DA F · dr = ∫[1,0] (0^2 * -1) + (t^2 * 0) = ∫[1,0] 0 dt = 0

Adding up the line integrals over each line segment, we get:

∫C F · dr = ∫AB F · dr + ∫BC F · dr + ∫CD F · dr + ∫DA F · dr = 0 + 2 + (-1/3) + 0 = 5/3

Therefore, the line integral of the vector field F = y^2 dx + x^2 dy over the square C with the given orientation is 5/3.

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Answer:

288

Step-by-step explanation:

area of the base times the height. base is 6*6=36. Then 36*8 is 288

The argument that the sun will rise tomorrow morning and set tomorrow evening is based on inductive reasoning, using past observations of consistent sunrise and sunset patterns to predict future occurrences.

1. The observation: Throughout your entire life, you have consistently noticed that the sun rises every morning and sets every evening. This is an observation based on personal experience.

2. Inductive reasoning: Based on this observation, you make an inference or prediction about the future. You reason that since the sun has always risen in the morning and set in the evening in the past, it is likely to continue doing so in the future.

3. Pattern and consistency: The assumption is that natural phenomena, such as the rising and setting of the sun, follow a pattern or regularity. This assumption is based on the principle of uniformity of nature, which suggests that the future will resemble the past in terms of natural occurrences.

4. The limitations of inductive reasoning: While inductive reasoning provides a useful way to make predictions based on past observations, it is not foolproof. There is always a small possibility that something unexpected could happen, such as a rare astronomical event or an external factor that alters the pattern. However, based on the available evidence and the consistency of the observed pattern, the prediction that the sun will rise tomorrow morning and set tomorrow evening is highly probable.

In summary, the argument relies on inductive reasoning, using the past consistent observation of the sun's rising and setting to predict that it will continue to do so in the future. While this reasoning is not infallible, it is a reasonable and practical way to make predictions based on observed patterns in nature.

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Answer:

A is correct

Step-by-step explanation:

A has no solution because since the slopes are the same, setting both equations equal to each other will cancel out the slopes and result in 8=16, meaning no solution will make both sides equal to each other.

B does have a solution because of different slopes

C does have a solution because of different slopes

D does have a solution because of different slopes

The first integral, \(\( \int x^{6}\left(1-4 x^{2}+x^{3}\right) d x \)\) is equal to \(\( \frac{1}{7} x^{7} - \frac{4}{9} x^{9} + \frac{1}{10} x^{10} + C \),\)    the second integral, \(\( \int(6-2 u)^{2} d u \)\) is equal to \(\( 36u - 12u^2 + \frac{4}{3}u^3 + C \)\), where \(\( C \)\) is the constant of integration.

For the first integral, \(\( \int x^{6}\left(1-4 x^{2}+x^{3}\right) d x \)\), we can expand the expression inside the integral to get \(\( \int x^{6}-4 x^{8}+x^{9} d x \)\). Now we can integrate each term separately using the power rule of integration. The integral of \(\( x^{6} \)\) is \(\( \frac{1}{7} x^{7} \)\), the integral of \(\( -4 x^{8} \)\) is \(\( -\frac{4}{9} x^{9} \)\), and the integral of \(\( x^{9} \) is \( \frac{1}{10} x^{10} \)\). Applying linearity of integration, we add up these integrals to get the final result: \(\( \frac{1}{7} x^{7} - \frac{4}{9} x^{9} + \frac{1}{10} x^{10} + C \),\) where \(\( C \)\) is the constant of integration.

For the second integral, \(\( \int(6-2 u)^{2} d u \)\), we can expand the square to get\(\( \int (36 - 24u + 4u^2) d u \)\). Now we can integrate each term using the power rule of integration. The integral of 36 is 36u , the integral of  -24u is\(\( -12u^2 \)\), and the integral of \(\( 4u^2 \)\) is \(\( \frac{4}{3}u^3 \)\). Adding up these integrals, we get the final result: \(\( 36u - 12u^2 + \frac{4}{3}u^3 + C \)\), where \(\( C \)\) is the constant of integration.

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Answer:

D

Step-by-step explanation:

Answer:

A and D

Step-by-step explanation:

A and D

Answer:

13 1/3

____

         \(1\:2/3 = 5/3\\1/8 = 1/8\\\\5/3 \div 1/8\\=\frac{5\cdot8}{3\cdot1}\\= \frac{40}{3}\\= 13\:1/3\)

When working with mixed numbers that are being divided, you know where to start. Start by converting mixed numbers to fractions, then multiply the fractions together to divide them. Simplify your improper fraction by counting how many times it surpasses the denominator.

Answer:

20 percent

Step-by-step explanation:

Because there are 160 total people, you would divide 32 by 160 which gives you 0.2 multiply 0.2 by 100 then you get 20 percent

32/160 = 0.2

0.2*100 = 20

Answer:

53.3%

Step-by-step explanation:

(32/63)×100

=53.3%