What is the surface area of the cube.
A. 409 cm²
B. 2400 cm²
C. 2004 cm²
D. 40 cm²​

Answer: 2.5, 5.3

Step-by-step explanation:

\(-16t^2 +126t=217\\ \\ 16t^2 -126t+217=0\\\\t=\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(217)}}{2(16)}\\\\t \approx 2.5, 5.3\)

The function f satisfying the given conditions is

f(x) = (1/2) sin(x) cos(0) + 10 = (1/2) sin(x) + 10

How to determine the function f?

To determine the function f satisfying the given conditions f ' (x) = sin(x) cos(x), f (2p) = 10, and f (x) = A sinB(x) cosC(x) + D, where A > 0, we need to follow these steps:

1. Integrate f ' (x) to find f (x).
∫(sin(x) cos(x)) dx = (1/2) * sin^2(x) + C

2. Apply the given condition f (2p) = 10.
(1/2) * sin^2(2p) + C = 10
Since sin(2p) = 0, the equation becomes:
C = 10

3. Now, we have f(x) = (1/2) * sin^2(x) + 10. We need to express this function in the form of A sinB(x) cosC(x) + D.
We can rewrite the given function as:
f(x) = A sin(2x/2) cos(0) + D
Comparing this with f(x) = (1/2) * sin^2(x) + 10, we get:

A = 1/2
B = 2/2 = 1
C = 0
D = 10

So, the function f satisfying the given conditions is:

f(x) = (1/2) sin(x) cos(0) + 10 = (1/2) sin(x) + 10

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the unit normal vector to the curve with vector equation \vec r \, (t) =<1^t,\ln(4/t^2), \, \ln(e/(t^4)) > r (t)=<1 t ,ln(4/t 2 ),ln(e/(t 4 ))> at the point where t=2t=2 is \vec n = <0,0,-1>

A unit normal vector is a normal vector with magnitude 1, and it points in the direction that is perpendicular to the tangent to the curve at a given point.

To determine the unit normal vector to a curve, it's important to find the tangent first and then find the normal. In this case, we're looking for the unit normal vector to the curve with the vector equation \vec r (t) =<1^t,\ln(4/t^2), \ln(e/(t^4)) > at the point where t = 2.

To find the unit normal vector to the curve with the vector equation \vec r (t) =<1^t,\ln(4/t^2), \ln(e/(t^4)) > at the point where t = 2, it is necessary to find the tangent to the curve and then find the normal. This is a crucial step in understanding the geometry of curves in 3D space.

To find the tangent to the curve, we'll differentiate the vector equation with respect to t and evaluate it at t = 2. The derivative of \vec r (t) is given by:

d\vec r/dt = <1, -2t^-3, -4e^-t^-4>

So the tangent to the curve at t = 2 is:

d\vec r/dt = <1, -2(2)^-3, -4e^-2^-4> = <1, 1.5, -1.648721>

Next, we'll find the normal to the tangent by taking the cross product of the tangent with a fixed vector, for example, the unit vector i = <1,0,0>. The cross product of two vectors results in a vector that is perpendicular to both of them.

The cross product of the tangent and the unit vector i is given by:

\vec T x \vec i = <1, 1.5, -1.648721> x <1,0,0> = <0,0,-1.5>

Since the magnitude of the normal is not 1, we'll normalize it by dividing it by its magnitude:

\vec n = \vec T x \vec i / ||\vec T x \vec i|| = <0,0,-1.5> / ||<0,0,-1.5>|| = <0,0,-1>

So the unit normal vector to the curve with the vector equation \vec r (t) =<1^t,\ln(4/t^2), \ln(e/(t^4)) > at the point where t = 2 is given by:

\vec n = <0,0,-1>

This is the unit normal vector that points in the direction that is perpendicular to the tangent to the curve at t = 2. The magnitude of 1 ensures that it's a unit vector and the direction points towards the normal direction.

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The area of a parallelogram can be found by using the formula A = |u × v|, where u and v are two vectors spanning the parallelogram. In this case, the vectors u and v are u=<1,1,-2> and v=<1,0,2>, respectively.

First, let's calculate the cross product of u and v. To do this, we use the formula u × v = (uyvz - uzvy)i + (uzvx - uxvz)j + (uxvy - uyvx)k.

We substitute the components of u and v into the formula and simplify, to get the following: u × v = (1 * 2 - (-2) * 0)i + (-2 * 1 - 1 * 2)j + (1 * 0 - 1 * 1)k. After simplifying, we get u × v = 4i + (-3)j - k.

Now that we have the cross product, we can use it to calculate the area of the parallelogram. We use the formula A = |u × v|, where u × v is the cross product of u and v. Substituting in the cross product we calculated, we get A = |4i + (-3)j - k|. After taking the absolute value, the area of the parallelogram is A = √14 units2.

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Answer:

1/24

Step-by-step explanation:

if there if multiple different color balls the odds of getting a red ball is very small

the answer

1/24 as a fraction

The answer to this question is c.The use of a correlation coefficient.

The use of a correlation coefficient would tell you that an association claim is being made in a research study. A correlation coefficient is a statistical measure that shows the strength and direction of a relationship between two variables. It ranges from -1 to 1, with 0 indicating no relationship and -1 or 1 indicating a perfect negative or positive relationship, respectively.

A scatterplot or bar graph may be used to visually display the relationship between two variables, but they do not necessarily indicate that an association claim is being made. The measurement of two variables is necessary for any type of research study, but it does not inherently imply that an association claim is being made.

Interrogation of internal validity is a process used to ensure that the study's results accurately reflect the relationship between the variables being studied. It is important for any research study but does not specifically indicate that an association claim is being made.

Therefore,the answer to this question is c.The use of a correlation coefficient.

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Answer:

The total cost is:$400

Step-by-step explanation:

Given

\(x \to units\)

\(y \to cost\)

\((x,y) = (0,200)\) --- when the graph intersects the y-axis

\(m = 10\) -- the rate

Required

y when x = 20

First, we determine the equation of the plot using:

\(y = mx + c\)

Substitute 10 for m

\(y = 10x + c\)

Next, solve for c.

Substitute \((x,y) = (0,200)\)

\(200 = 10*0+c\)

\(200 = 0+c\)

\(c = 200\)

So:

\(y = 10x + c\)

\(y =10x + 200\)

When x = 20

\(y =10*20 + 200\)

\(y =200 + 200\)

\(y = 400\)

The distance traveled by the object can be calculated by finding the product of the velocity and the time interval.

To calculate the distance traveled, the formula distance = velocity × time is utilized. With a given velocity of 3 m/s and a time interval of 5 seconds, we can determine the distance. By multiplying the velocity by the time, (3 m/s * 5 s), we obtain 15 meters.

It is important to note that the negative sign in the given velocity of 3+ – 12 m/s indicates a change in direction. However, since we are concerned with distance, the negative sign is disregarded when multiplying velocity and time.

Hence, the object has traveled a distance of 15 meters without considering the direction.

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The expected profit in 2010 is 50,000 dollars. This means that the company's annual profits are projected to decrease further due to the economic slump. It is important to note that this calculation assumes that the exponential decline will continue at the same rate in the future.

The expected profit in 2010 can be calculated using exponential decay. By using the given information, we can find the decay factor. We can then apply the decay factor to the 2009 profit to find the expected profit in 2010.

1. To calculate the expected profit in 2010, we need to determine the decay factor. The decay factor can be found by dividing the profit in 2009 by the profit in 2006.

Decay factor = 200,000 / 800,000 = 0.25

2. Now, we can use the decay factor to calculate the expected profit in 2010. We multiply the 2009 profit by the decay factor.

Expected profit in 2010 = 200,000 * 0.25 = 50,000 dollars

Therefore, the expected profit in 2010 is 50,000 dollars. This means that the company's annual profits are projected to decrease further due to the economic slump. It is important to note that this calculation assumes that the exponential decline will continue at the same rate in the future.

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Answer:

C

Step-by-step explanation:

-18x + 21 > -15  ///  x = 2

20x – 13 >27  ///  x = 2

The solution of inequality -18x + 21 > -15 OR 20x – 13 > 27 is x ∈ (- ∞, ∞), so option E is correct.

An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. It is most frequently used to compare the sizes of two numbers on the number line.

Given:

-18x + 21 > -15 or  20x – 13 >27

Solve the first inequality as shown below,

-18x + 21 > -15

-18x + 21 - 21 > -15 - 21       (Subtract 21 from both sides)

-18x > -36

-18x / -18 > -36 / -18      (Divide by -18 into both sides, the inequality sign changes as the value will become positive)

x < 2

Similarly, solve the second inequality,

20x – 13 > 27

20x > 40

x > 2

Thus, the solution will be x < 2 ∪ x > 2 or x ∈ (- ∞, ∞)

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The digit on the right side of each equation so that each equation has an integer solution are 2.74, 3.78 and 1986.5 respectively.

35x - 11 = 107

35x = 107 - 11

35x = 96

x = 96/35

x = 2.74

9m + 34 = 68

9m = 68 - 34

9m = 34

m = 34/9

m = 3.78

7965 - 4m = 19

-4m = 19 - 7965

-4m = -7946

m = -7946/-4

m = 1986.5

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The mean of the random variable, number of birds that survive migration, if 280 birds were randomly selected, is 238.

To compute the mean of the random variable, we need to multiply the probability of survival (85% or 0.85) by the total number of birds (280). By doing this, we can determine the expected number of birds that will survive the migration trip.

The probability of survival for each bird is independent of the others, so we can treat each bird's survival as a separate Bernoulli trial. In this case, the probability of success (survival) is 0.85, and the probability of failure (not surviving) is 0.15.

We can use the formula for the mean of a binomial distribution to calculate the expected number of successes. The formula is:

mean = \(n * p\)

Where:

- mean is the expected number of successes,

- n is the total number of trials (birds in this case), and

- p is the probability of success (probability of surviving the migration trip).

Plugging in the values, we have:

mean =\(280 * 0.85\) = 238

Therefore, the mean of the random variable, number of birds that survive migration, if 280 birds were randomly selected, is 238.

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Answer:

Step-by-step explanation:

The question lacks appropriate diagram. Find the diagram in the attachment.

From the diagram, it can be seen that the triangle is an isosceles triangle because two of its sides are parallel (i.e the same). Since two of the sides are the same, hence the two base angles will be the same.

From the diagram, <EFG = <EGF

Since  <EFG  = 55° hence  <EGF = y = 55°

Hence the va;ue of y is 55°

Laila's score on the last test could be any number between 83 and 94, inclusive, resulting in a total of 12 possible values.

Let's denote Laila's score on the first four tests as x. Since her average score on the five tests is 82, the sum of her scores on all five tests is 82 * 5 = 410. We can express this as x + x + x + x + y = 410, where y represents her score on the last test.

Simplifying the equation, we have 4x + y = 410. Since x and y must be integers, we need to find all possible integer solutions for this equation. Rearranging the equation, we have y = 410 - 4x.

To determine the possible values of y, we need to find the range of values for x. Since Laila's score on each test is an integer between 0 and 100, the value of x must be between 0 and 100. Substituting these limits into the equation, we get 410 - 4(100) ≤ y ≤ 410 - 4(0), which simplifies to 10 ≤ y ≤ 410.

However, we need to consider that Laila's score on the last test must be higher than her score on the previous four tests. This means that y must be greater than x. Considering this constraint, the possible values for y range from x + 1 to 410.

To find the number of possible values, we calculate the number of integers in this range. Since x can take values from 0 to 100, there are 100 possible values for x. Therefore, the number of possible values for y is the sum of integers from 1 to 100, which is given by the formula (100 * (100 + 1)) / 2 = 5050.

However, we need to exclude the cases where x = y, as Laila's score on the last test should be higher than the previous tests. Therefore, the final number of possible values for y is 5050 - 100 = 4950.

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Using rates and ratio concept, Martine received €175.44 after converting 200 Swiss francs (CHF)

A rate is a ratio that compares two different quantities which have different units. The unit rate is different from that of a rate, in which a certain number of units of the first quantity is compared to one unit of the second quantity. In other words, we can say that the second quantity in the comparison is always 1.

To calculate the amount Martine received, we have to use the rate given in the question.

€1 = 1.14 CHF

x € = 200

Cross multiply both sides and solve for x

1 * 200 = 1.14 * x

200 = 1.14x

Divide both sides by the coefficient of x

200 / 1.14 = 1.14x / 1.14

x = 175.44

Martine received €175.44

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Answer:

19 is the area for the problem

To determine whether the rectangles are proportional, Mackenzie could use several processes. First, she could compare the ratios of the sides of the pre-image to the corresponding sides of the image and check if they are equal, such as the proportion 3/1.5 = 4/2.

She could also verify that multiplying each side in the pre-image by one-half results in the length of the corresponding side in the image. Additionally, she could notice that all the sides in the pre-image are whole numbers and conclude that all the sides in the image should also be whole numbers.

One way to determine if two rectangles are proportional is by comparing the ratios of their corresponding sides. In this case, Mackenzie can compare the ratios of the length and width of the pre-image rectangle to the corresponding sides of the image rectangle. If the ratios are equal, such as 3/1.5 = 4/2, then the rectangles are proportional.

Another process Mackenzie could use is verifying if multiplying each side in the pre-image rectangle by a constant, in this case, one-half, results in the corresponding sides of the image rectangle. If the resulting lengths are equal, it indicates proportionality.

Additionally, Mackenzie could notice that all the sides in the pre-image rectangle are whole numbers. If she expects the image rectangle to be proportional, she can conclude that the corresponding sides in the image should also be whole numbers.

It's important to consider multiple processes to confirm the proportionality of the rectangles and avoid making conclusions based on a single observation.

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The equation arccos(cos(5π/6)) = 5π/6 is true.

The arccosine function (arccos) is the inverse of the cosine function. It returns the angle whose cosine is a given value. In this equation, we are calculating arccos(cos(5π/6)).

The cosine of an angle is a periodic function with a period of 2π. That means if we add or subtract any multiple of 2π to an angle, the cosine value remains the same. In this case, 5π/6 is within the range of the principal branch of arccosine (between 0 and π), so we don't need to consider any additional multiples of 2π.

When we evaluate cos(5π/6), we get -√3/2. Now, the arccosine of -√3/2 is 5π/6. This is because the cosine of 5π/6 is -√3/2, and the arccosine function "undoes" the cosine function, giving us back the original angle.

Therefore, arccos(cos(5π/6)) is indeed equal to 5π/6, making the equation true.

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Answer: 15%

Step-by-step explanation:

The Percentage decrease will be:

= Decrease in weight / Old weight × 100

= (200 - 170) / 200 × 100

= 30/200 × 100

= 15%

The Percentage decrease is 15%

Answer:

b =3...................

Step-by-step explanation:

ﹰ

A=4B+3

or, 15 = 4B +3

or, 12 = 4B

or, B = 12/4

:. B = 3

Option D: The number of patrons who prefer roller coasters will be 2 times the number of patrons who prefer food.​

The activities are given as follows:

The number of patrons for each activity is given as follows:

Hence the proportions are:

For the next 300 patrons, the estimates are given as follows:

Hence option d is correct.

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Answer:

I think The Options Are Wrong

Step-by-step explanation:

3 + (9-5)^2 × 8

3 + 4^2 × 8

3 + 16 × 8

3 + 128

131 ans

Answer:

11

Step-by-step explanation:

6 2/8 = 6 1/4

6 1/4 + 4 3/4 = 10 4/4

11

Answer:

11

Step-by-step explanation:

add the whole numbers and fractional parts of the mixed numbers separately

(6+4) +(2/8+3/4)

10+(2/8+3/4)

10+1

11 is the answer

the commission rate is 752.

Answer:

For instance, if the point (1, 3) is on the graph of the function, then the point (3, 1) is on the graph of the inverse. That is, if you start with x = 1, you will go to y = 3; then you plug this into the inverse, and you'll go right back to x = 1, where you started from.

Answer:

hiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii

Step-by-step explanation:

.

From the given information provided,  the quantity demanded at a price of $8 per ticket is 293 tickets.

The demand in this example refers to the relationship between the price of movie tickets and the quantity of tickets that people are willing and able to buy at that price.

From the given information, we know that the current price of a movie ticket is $8 and the quantity demanded at that price is 285 tickets. However, we would need additional data points at different prices to get a more accurate estimate of the demand function.

Assuming that the demand for movie tickets is downward sloping (i.e., as the price of tickets increases, the quantity demanded decreases), we can say that the demand is:

Inverse: The price and quantity demanded move in opposite directions. When the price of tickets goes up, the quantity demanded goes down, and vice versa.

Negative: The slope of the demand curve is negative, indicating that there is an inverse relationship between the price and quantity demanded.

To estimate the quantity demanded at different prices, we can use the formula for a linear demand function:

Q = a - bP

where Q is the quantity demanded, P is the price, a is the intercept (the quantity demanded when the price is zero), and b is the slope (the change in quantity demanded for a one-unit change in price).

Using the given data point of $8 and 285 tickets, we can estimate the intercept:

285 = a - 8b

Assuming a relatively elastic demand, we can use a slope of -2:

Q = a - 2P

Substituting the intercept value we solved for earlier, we get:

Q = 309 - 2P

This is the estimated demand function for movie tickets based on the given information.

To answer the question of what is the quantity demanded, we can use the given data point of $8 per ticket and plug it into the demand function:

Q = 309 - 2(8)

Q = 293

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We can fill in the boxes to make each equation complete as follows:

1. x³x⁹ = x¹²

2. x⁷/x³ = x⁴

3. 1/x⁻⁵ = x⁵

4. (7b³c⁵)³ = 343b⁹c¹⁵

To solve the exponents as provided above, the rules have to be factored in. One of the rules is that when multiplying exponents of the same base, we simply add their powers together. So, we have the powers of 3 and 9 for the first expression and they add up to 12.

1. x³x⁹ = x³ ⁺ ⁹ = x¹²

For the second expression, the rule of exponents says that when dividing, we will subtract the powers. This gives us x⁴ for the second expression.

2. x⁷/x³ = x⁷ ⁻ ³ = x⁴

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The value of the give expression is  \(\frac{313}{748845}\) OR 4.18 × 10⁻⁴

From the question, we are to determine the value of

2(5+34-67/45*43)^2

This can be written as

\(2 (\frac{5+34-67}{45 \times 43 })^{2}\)

First, we will simplify the bracket

\(2 (\frac{-28}{1935 })^{2}\)

Then, we get

\(2 \times \frac{-28}{1935 }\times \frac{-28}{1935 }\)

= \(\frac{1568}{3744225}\)

= \(\frac{313}{748845}\) OR 4.18 × 10⁻⁴

Hence, the value of the give expression is  \(\frac{313}{748845}\) OR 4.18 × 10⁻⁴

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Answer:

n = 24

Step-by-step explanation:

(4/12)*72 = n

24 = n