What is the surface area of the cylinder in terms of pi? The diagram is not drawn to scale.A) 288B) 360C) 72D) 162thank you ! :)

The piecewise function f(x) is composed bt two lines: 3/2x + 1 and x - 5. To graph a line, we need to connect two points that lie on the line. In the case of the first line, we can use its endpoints x = -4 and x = 0.

Substituting x = -4 into the equation of the first line, we get:

Then, the point (-4, -5) lies on the first line.

Substituting x = 0 into the equation of the first line, we get:

Then, the point (0,1) lies on the first line.

In the case of the second line, the endpoints x = 1 and x = 3.

Substituting x = 1 into the equation of the second line, we get:

Then, the point (1,-4) lies on the second line.

Substituting x = 3 into the equation of the second line, we get:

Then, the point (3,-2) lies on the second line.

Connecting these points with two different lines as stated before, we get the graph of f(x) as follows:

1) Given that t =-12 let's plug into that expression the value for t

2) Now let's plug into that and solve it.

-3|t-8| +1.5 Applying the absolute value property

-3|t -8| +1.5 Plug into that t=-12

-3|-12 -8| +1.5

-3|-20| +1.5

-3*20 +1.5

-60 +1.5

-58.5

Input data

The vertex and axis of symmetry are to the left of the vertex

The volume of a sphere can be calculated using this formula:

Where "r" is the radius of the sphere and "V" is the volume of the sphere.

If you solve for "r", you get this new formula:

In this case you know that:

Therefore, you can substitute this value into the second formula and then evaluate, in order to find the radius of this sphere:

The answer is:

Remember that

The speed is equal to divide the distance by the time

speed=d/t

Let

t ----> time spend to go to the conference in hours

s ----> speed trip going

Conference trip

s=360/t ------> equation 1

Return trip

speed=360/(t+3)

speed=s-30

s-30=360/(t+3) ------> equation 2

substitute equation 1 in equation 2

(360/t)-30=360/(t+3)

Multiply both sides by t(t+3) to remove fractions

360(t+3)-30t(t+3)=360t

360t+1,080-30t^2-90t=360t

simplify

30t^2+90t-1,080=0

Solve the quadratic equation

The solutions for t are

t=-7.7 h -----> is not a solution, because is a negative number

t=4.69 hours

Find out the average speed on the return trip

speed=360/(t+3)

speed=360/(4.69+3)

GIVEN:

We are given the set of data as indicated below;

Required;

To find the variance of the data set.

Step-by-step solution;

We begin by calculating the mean of the data set as follows;

We now round the mean to two decimal places and we have;

Next we subtract the mean from EACH value in the data set. the individual results are the "deviation from the mean."

After that we square each deviation from the mean, and then add them all up.

This is effectively explained by the formula for the variance which is;

We now have;

Now we can refine the formula as shown below;

We can round this to 2 decimal places and the variance therefore is;

ANSWER:

a)

b)

c)

d)

e)

f)

g)

h)

We know that the four side of a square are congruent, this means that

every side have the same length. Then, the perimeter (P) is given by

From the given information, we know that P= 292 yards. So we have

Then, by dividing both sides by 4, we get

Therefore, each side measures 73 yards

Answer:

73 yards

Step-by-step explanation:

292 divided by 4= 73

Please mark brainliest have a nice day

For the sinusoidal function:

we have that:

A represents the amplitude

2pi/B represents the Period

C is the phase shift

D is the vertical shift.

In this case, we have the following equation:

then, the amplitude is A = 1.

For the period, we have the following:

thus, the period is pi.

Finally, notice that C = -pi/2, thus, the phase shift is -pi/2

Given the equation:

Applying the exponent laws:

Simplify:

Applying the exponent laws:

Answer: x = 4

Percentage decrease in price

Original price = $60

Find 15% of 60

Then

10% of 60 is $6

5% of 60 is $6/2 = $3

In consecuence 15% of $60 is 6+3 = $9

Then precent decrease in price is $9

And New price is 60-9 = $51

To solve this problem you have to subtract the remaining pretzels from the initial number of bags of pretzels.

Computing the subtraction, you get:

Simplifying the above result, you get:

True

1) Let's evaluate that, using one identity for that:

2) Since the cosine of the arc cosine (theta) is equal to theta, we can state that this trigonometric equation is true.

3) Hence, that's true.

SOLUTION:

Step 1:

In this question, we are given the following:

Step 2:

Using the data in the table to find the rate of change in the length of the baby girl:

Choosing any two consecutive points, we have that the:

CONCLUSION:

The final answer = 0. 75 inch per month

Given data:

27 quarters (25¢)

18 dimes (10¢)

11 nickels (5¢)

124 pennies (1¢)

Total coins: 180

Coins that are less than 25¢: 27+18+11=56

Probability that the coin that falls out worths less than 25¢:

To fill the values, we are given a list of the percentage of customers that spend a specific amount of money.

The x1, x2, x3, and x4 are the money spent, and the P(x1), P(x2),... are the proportion of customers that spend that amount, in decimal

Then, we can complete:

Answer: Volume of a cylinder = 3, 077.20 cubic centimeter

Given data

Diameter of the cylinder = 14cm

Height of the cylinder = 20cm

Radius = diameter / 2

radius = 14/2

radius = 7 cm

We have the next functions

For f(g(x))

For g(f(x))

ANSWER

We have the general rule for a rotation of 90° counterclockwise:

and the general rule for a y=-x reflection is:

In this case, we have the points R=(2,-2), S=(5,-1) and T=(3,-5).

Then, we first have to use the 90° rotation on all points:

Now we use the y=-x reflection on our new points:

therefore, the final points after the transformations are:

R''=(2,2)

S''=(5,1)

T''=(3,5)

From the model, we notice that for three hours Jonathan earns $105. This means that he earns $35 (105 divided by 3) per hour.

Now, we have in total 10 hours in the model, hence he will earn a total of $350 (35 times 10).

First pattern

The number of squares in the first term is 3

The second term is 5

The third term is 7

So this pattern increased by 2

The rule of any pattern increased by a constant number is

y = a + (x-1)d, where

a is the first term

d is the constant difference

x is the position of the term

So a = 3

and d = 2

The equation is

y = 3 + (x - 1)2

Multiply 2 by the bracket

y = 3 + 2x - 2

Add the like terms

y = 2x + 1

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Let us find the slope first

The equation can be found as follows using the points (0 ,1)

To add 2 algebraic fractions we must make their denominators the same

Then we must have the LCM of both denominators

Since the denominators area (x + 2) and (3x + 6), then

We can take 3 as a common factor from the 2nd denominator

Then the LCM of the 2 denominators is 3(x + 2)

Now we can change the first denominator to 3(x + 2) by multiplying up and down by 3

Given that -50=3(15)+b

expand

-50=45+b

collect like terms

-50 - 45 = 45 - 45 + b

-95 = b

b = -95

15 can vary by 2%, this means that the range of values you can observe are 2% below 15 and 2% above 15.

First, you have to determine how much does the percentage represents with regards to the value of reference. To do so, you have to calculate the 2% of 15:

-Multiply 2 by 15 and divide the result by 100

The 2% of 15 is 3, which means that the range of values you are looking for is 3 units below 15 and 3 units above.

The minimum value of the range: subtract 3 to 15

The maximum value of the range: add 3 to 15

The range of allowable values is [12;18]

To factor the given equation, rewrite the middle terms as binomials.

Group the terms and then factor out the common monomial from each group.

Factor the common binomial factor.

Since the factored form of the expression at the left is

we may obtain the values inside the squares by multiplying the factors. We may use the FOIL method to obtain each term.

Thus, we get the following.

Product of the first terms:

Product of the Outer Terms:

Product of the Inner Terms:

Product of the Last Terms:

Thus, the terms inside the first figures should be -x and -24x, respectively.

The formula that the physicists told was

We know that

v₀ = 400 ft/s

h₀ = 2400 ft

Then let's put it into the formula

We want to know then it will land on the desert, in other words, when the height is equal to zero, then

Then we must solve that quadratic equation, to solve it let's first divide all by 16

Because it's an easier equation to solve and the solution is the same. Now we can apply the quadratic formula

Plug the values

We can ignore the other solution because it's negative and negative time is not a valid solution. Therefore, 30 seconds after its launch, the rocket will land in the desert

Since m is the number of miles driven and company A charges a base price of $56 plus a charge of $0.25 per mile, we can write the following equation:

Again, since m is the number of miles driven and company B charges a base price of $45 plus a charge of $0.58 per mile, we can write the following equation:

The cost of renting a car from both companies will be the same when:

Then, we solve the following equation for m:

Therefore, the cost of renting a car from both companies will be the same at 33.33 miles.

Answer:

Explanation:

• Parallel lines ,are lines that ,do not intersect ,no matter how long the line is drawn.

• Perpendicular lines, are lines that ,form an angle of 90 degrees, with one another.

From the given options, the following options apply:

• Graph 1: Parallel

• Graph 2: Neither

• Graph 3: Perpendicular

• Graph 4: Neither

Consider the given equation,

Apply the method of completing square as follows,

Thus, the solutions of the quadratic equation are -2 and -8.