Determine the exact surface area of the cylinder in terms of π.

The distance from A to B to the nearest tenth of a foot for the ski lift is 1580.34 feet.

Function of Sine: The ratio of the opposing side's length to the hypotenuse is known as an angle's sine function.

Sin a = Opposing or Hypothetical

Cos Feature: The cosine of an angle is the ratio of the neighbouring side's length to the hypotenuse's length.

Adjacent/Hypotenuse = Cos a

Functional Tan: The ratio of the lengths of the adjacent and opposing sides is known as the tangent function. It should be noted that the ratio of sine and cosine to the tan may also be used to express the tan.

Tan a = Adjacent/Opposite

Given that, the distance from A to C is 1500 feet and they measure angle DAC to be 37°.

Using the trigonometric functions, we have:

cos (37) = DA / 1500

(0.79)(1500) = DA

DA = 1197.95 feet.

Using the sine function we have:

sin (37) = DC / 1500

(0.601)(1500) = DC

DC = 902.722

Now, the using the larger triangle:

tan (18) = DC/DB

tan (18) = 902.722 / DB

DB = 2778.29

The value of AB can be calculated as:

AB = DB - DA

AB = 2778.29 - 1197.95

AB = 1580.34

Hence, the distance from A to B to the nearest tenth of a foot for the ski lift is 1580.34 feet.

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The complete question is:

Answer:

The correct graph is shown below.

Hope this helps!

Answer:

Smallest to largest:

1 out of 10, 2/5, 2 out of 3, .75, 7/8

Step-by-step explanation:

An easy way to do this is to write each in decimal form

2/3 = .666666......

2/5 = .4

7/8 = .875

.75

1/10 = .10

Smallest to largest:

1 out of 10, 2/5, 2 out of 3, .75, 7/8

Answer:

it’s B

Step-by-step explanation:

Answer: The answer to the question is option A

Step-by-step explanation:

Answer:

Its Function, but not One-to-one

Answer:

-7/6

Step-by-step explanation:

Answer:

b = ft

Perimeter = 42.6 ft

Step-by-step explanation:

We know that the area is equal to length times width, so in our case

Area = b x a

Since we know the value of the area and the width we can find the length by doing the following...

Area = b x a

b = Area / a

b = 111.6 / 9.3

b = 12 ft

Perimeter = 2b + 2a

Perimeter = 2(12) + 2(9.3)

Perimeter = 42.6 ft

Answer:

Y=4x-2

Step-by-step explanation:

You have to try it (x,y) (2,6)

y=4x-2

6=4(2)-2

6=8-2

Answer:

its 2/3 i think

Step-by-step explanation:

Answer:

B.   3,158

Step-by-step explanation:

h(x) = -49x − 125

Let x = -67

h(-67) = -49(-67) − 125

          =3283-125

          = 3158

Answer:

Answer B

Step-by-step explanation:

To find the value of h(-67) for the function h(x) = -49x - 125,

we substitute -67 for x in the function and evaluate it.

h ( - 67 ) = - 49 ( - 67 ) - 125

Now we can simplify the expression:

h ( -67 ) = 3283 - 125

h ( -67 ) = 3158

the polynomial expression that represents the area of the soccer field is

5x^2 -16xy +3y^2

given length of a rectangular soccer is 5x -y

and width of a rectangular soccer is x- 3y

find the polynomial expression that represents the area of the soccer field.

we know that the formula for the area of a rectangle is

area= length * width

       =( 5x-y)*( x-3y)

       = 5x^2 -15xy-xy +3y^2

        = 5x^2 -16xy +3y^2

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Answer:

17.5 hours

I hope this helps and you can give a brainliest!

Step-by-step explanation:

Given: time spent per day follows the arithmetic sequence 1,1.5,2... (for 7 terms) with first term 1 and common difference 0.5 (in hours)

Concept used: the total study time is the partial sum S7of the given arithmetic series.

Calculation: As the number of terms is small, it can be calculated by hand.

S7 = 1+1.5+2+2.5+3+3.5+4

S7= 17.5 hours

Conclusion: Total time spent after one week is 17.5 hours

Answer:

17 and 1/2 hours.

Step-by-step explanation:

this is an arithmetic series  with common difference 0.5 hours.

Number of hours after 7 days

= (n/2)[2a + (n -1)d]

= (7/2)(2*1 + (7-1)0.5)

= 3.5 * 5

= 17.5 hours

Answer:

y = -5/4x - 7

Step-by-step explanation:

First, find the slope:

3 - -7 / -8 - 0 = -5/4

Put it in point slope form:

y + 7 = -5/4(x-0)

y + 7 = -5/4x

y = -5/4x - 7

The graph have the solution is (0, 8) and (-3, 2).

The graph is simply a structured representation of the data. It aids in our comprehension of the data. The numerical information gathered through observation is referred to as data.

In a line graph, the information or data is represented as a series of markers, or dots, and is then connected to one another by a straight line.

Given:

We have the Equation as f(x) = 2|x + 3| +2.

Usually the mode value shows the absolute value.

If we plot the equation on the graph have the solution is (0, 8) and (-3, 2).

The graph is attached below.

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A) The exponential function that models the mass show many grams remain from a 480-gram sample after t minutes is G(t) = 22(1/2)^(t/5.5)

B) The grams that remain after 2 hours is 51.42 grams.

A substance's half-life is the amount of time needed for half of a radioactive substance to decay. It is a word that is used in nuclear chemistry to describe how quickly unstable atoms undergo radioactive decay into other nuclear species by emitting particles or the amount of time needed for the rate of disintegrations per second of radioactive material in order to reduce by half of its initial value.

Given:

The half-life of goo is 22 minutes/4 = 33.75 minutes

b) A formula for the amount remaining could be ...

G(t) = 22(1/2)^(t/5.5)

c) After 2 hours, the amount remaining is ...

G(120) = 135(1/2)^(47/33.75) ≈ 51.42 . . . grams

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A). After t minutes, the exponential function used to describe the mass remaining from a 480-gram sample is \(G(t) = 22(\frac{1}{2} )^{(t/5.5)}\)

B). 51.42 grammes are still there after two hours.

The amount of time required for a radioactive substance to decay by half is known as its half-life. It is a term used in nuclear chemistry to describe how quickly unstable atoms transform into different nuclear species by emitting particles or how long it takes for the rate of radioactive material's disintegrations per second to fall by half of its initial value.

Given:

The half-life of goo is 22 minutes/4 = 33.75 minutes

b) The amount left could be calculated using the method...

\(G(t) = 22(\frac{1}{2} )^{(t/5.5)}\)

c) The amount left after two hours is...

\(G(120)=135(\frac{1}{2} )^{(\frac{47}{33.5} )}\) ≈ 51.42 . . . grams

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Answer:

\(0.0000000642 = 6.42 \times {10}^{ - 8} \)

I hope I helped you^_^

Answer:

6.42 x 10^-8

Answer:

x = 0 hopefully this helps

The  length of each congruent side of the isosceles triangle is given to be equal 2.75 inches while the base calculated to be equal to 23.5 inches

We first have to define x as the length of the congruent side. The question tells us that the base is 7 inches longer than 3x the length of 2 sides

This would be represented as:

= 3(2x) + 7

= 6x + 7

The perimeter of the shape is said to be 29, hence we would have

x + x + (6x + 7) = 29

= 2x + 6x + 7 = 29

= 8x = 29 - 7

8x = 22

x = 22 / 8

= 2.75

Given the value of x we would have to put it in

6x + 7

= 6 x 2.75 + 7

= 23.5

Therefore the  length of each congruent side of the isosceles triangle is given to be equal 2.75 inches while the base calculated to be equal to 23.5 inches

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Answer:

To find -134 + 53, add the ones place (4+3=7) and the tens place (5+3=8), giving you -81.

Answer: -81.

Answer:

-81

Step-by-step explanation:

You subtract the absolute values and take the sign of the larger absolute value.

Absolute value is the distance from zero.  This will be a positive number

134 - 53 = 81

The sign will be negative because the sign of the higher absolute value number is negative.  134 has a larger absolute value than 53 and it is negative, so our answer is negative.

Helping in the name of Jesus.

Answer:

You have a 50% chance of picking a multiple of 3.

Step-by-step explanation:

If we include 1 and 24 as factors of 24, then the possible choices would be:

1, 2, 3, 4, 6, 8, 12, 24

Of those, the only ones that are multiples of 3 are 3, 6, 12 and 24.  Meaning that the chance of getting a multiple of 3 is 4/8, or 1/2, i.e. 50%

If we don't include 1 and 23, then we have:

2, 3, 4, 6, 8, 12

and 3, 6 and 12 are divisible by 3.

Which again gives 1/2, or 50%

So regardless of whether 1 and 24 are included, the chance of picking a multiple of three from the factors of 24 is 50%.

For a large enough n (i.e., N≥n), any subset of [1, n] containing at least n/c elements must have three equally spaced numbers.

This is a classic problem in combinatorics known as the van der Waerden's theorem. The theorem states that for any positive integers k and c, there exists a positive integer N such that any subset of {1, 2, ..., N} with cardinality at least N/k contains an arithmetic progression of length k.

In the specific case you mentioned, we have k=3 and the set S has at least n/c elements. So, according to the van der Waerden's theorem, there exists a positive integer N such that any subset of {1, 2, ..., N} with cardinality at least N/3 contains a 3-term arithmetic progression.

Therefore, for a large enough n (i.e., N≥n), any subset of [1, n] containing at least n/c elements must have three equally spaced numbers.

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Answer:

\( \frac{11}{7} \)

Step-by-step explanation:

\(2 \frac{3}{4} \div 1\frac{4}{7} \)

\( = 2 \frac{3}{4} \times \frac{4}{7} \)

\( = \frac{11}{4} \times \frac{4}{7} \)

\( = 11 \times \frac{1}{7} \)

\( = \frac{11}{1} \times \frac{1}{7} \)

\( = \frac{11 \times 7}{1 \times 7} \)

\( = \frac{11}{1 \times 7} \)

\( = \frac{11}{7} \)

If A is invertible and AB = AC, then B = C is true. Also we can find two different matrices such that AB = AC.

(a) To prove that if A is invertible and AB = AC, then B = C, we can multiply both sides of the equation by the inverse of A.

Given AB = AC and A is invertible, we can multiply both sides by \(A^{-1}\):

\(A^{-1}\)(AB) = \(A^{-1}\)(AC)

Using the associative property of matrix multiplication, we have:

\(A^{-1}\)A)B = \(A^{-1}\)A)C

Since \(A^{-1}\)A is the identity matrix I, we have:

IB = IC

And since multiplying any matrix by the identity matrix gives the same matrix, we have:

B = C

Therefore, we have proved that if A is invertible and AB = AC, then B = C.

(b) If A = [1 1], we can find two different matrices B and C such that AB = AC.

Let's consider:

B = \(\left[\begin{array}{ccc}1&0\\0&0\\\end{array}\right]\)

C = \(\left[\begin{array}{ccc}0&0\\0&1\end{array}\right]\)

Now, we can calculate AB and AC:

AB = [1 1] [1 0] = [1 1]

[1 0]

AC = [1 1] [0 0] = [0 0]

[1 1]

As we can see, AB is equal to AC. Therefore, we have found two different matrices B and C such that AB = AC.

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The most appropriate technique for the researcher to make this prediction would be multiple regression analysis, which would allow her to examine the relationship between the two predictor variables (high school grade-point averages and SAT scores) and the outcome variable (first semester college grade-point averages) while controlling for their effects on each other. This technique would help the researcher to determine the most accurate way to combine these two predictors in order to make the most accurate prediction possible.

A researcher aiming to predict first semester college grade-point averages (GPAs) using high school GPAs and SAT scores as predictor variables should use the Multiple Linear Regression technique. This technique allows the researcher to analyze the relationship between multiple predictor variables (high school GPAs and SAT scores) and a single continuous outcome variable (college GPAs), which can lead to more accurate predictions.

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The correct values to fill in the point-slope formula are y1 = 3 and m = -2. The answer is option D (-1). To find the equation of the line that is parallel to y = -2x - 5 and intersects the point (-1, 3), we need to use the point-slope formula.

The point-slope form of a linear equation is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Since the line is parallel to y = -2x - 5, it has the same slope, which is -2. Now, we can substitute the given point (-1, 3) and the slope -2 into the point-slope formula:
y - 3 = -2(x - (-1))
y - 3 = -2(x + 1)
y - 3 = -2x - 2
y = -2x + 1

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Answer:

\(x = - 16\)

Step-by-step explanation:

Let's solve:

\( \frac{3}{4} x = - 12\)

Step 1: Multiply both sides by 4/3.

\(( \frac{4}{3} )*( \frac{3}{4} x)=( \frac{4}{3} )*(−12)\)

\(x = - 16\)

\( \frac{3}{4} x = - 12 \\ \\ = > 3x = - 12 \times 4 \\ \\ = > x = \frac{ \cancel{- 12} \times 4}{ \cancel3} \\ \\ = > x = - 4 \times 4 \\ \\ = > x = 16\)

(a) The expected length of the queue, not including the vehicle being served, is 0.625 vehicles.

(b) The probability that there are no more than 5 cars at the gate, including the vehicle being served, is approximately 0.0176.

(c) The average waiting time of a vehicle at the ticket gate is 1.5 minutes or 0.025 hours.

(a) To find the expected length of the queue at the ticket gate, we need to calculate the expected number of vehicles waiting in the queue at any given time. This can be found by using the Little's Law, which states that the expected number of customers in a stable system is equal to the arrival rate multiplied by the average time spent in the system.

In this case, the arrival rate is 25 vehicles per hour, and the average time spent in the system is the time it takes to buy the tickets, which is 1.5 minutes or 0.025 hours. Therefore, the expected number of vehicles waiting in the queue is

E[N] = λW = 25 x 0.025 = 0.625 vehicles

So the expected length of the queue, not including the vehicle being served, is 0.625 vehicles.

(b) To find the probability that there are no more than 5 cars at the gate, including the vehicle being served, we need to use the Poisson distribution with a mean of 25 vehicles per hour. Let X be the number of vehicles arriving in an hour, then X Poisson(25).

P(X ≤ 5) = ∑ P(X = k) for k = 0 to 5

= ∑ (e^(-λ) × λ^k / k!) for k = 0 to 5

= e^(-25) × (25^0 / 0!) + e^(-25) × (25^1 / 1!) + ... + e^(-25) × (25^5 / 5!)

Using a calculator or software, this probability is found to be approximately 0.0176.

(c) The average waiting time of a vehicle can be found by dividing the expected number of vehicles waiting in the queue by the arrival rate. From part (a), we know that the expected number of vehicles waiting in the queue is 0.625 vehicles. The arrival rate is 25 vehicles per hour. Therefore, the average waiting time of a vehicle is

W = E[N] / λ = 0.625 / 25 = 0.025 hours or 1.5 minutes

So the average waiting time for a vehicle at the ticket gate is 1.5 minutes.

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