ACTIVITY 3: Given the following functions, find the following:

Answer: your answer would be A.

The percent of Container B that is empty after the pumping is complete, to the nearest tenth, is [tex]23.2[/tex]%.

[tex]V = r^2h[/tex] , where r is the radius of the cylinder's base, h is its height, and (pi) is a mathematical constant corresponding roughly to 3.14159, gives the volume of a cylinder.

To solve this problem, we need to calculate the volumes of the two containers and then determine how much of Container B is empty after the water from Container A is transferred to it.

The volume of a cylinder is given by the formula  [tex]V = \pi r^2h[/tex] , where r is the radius of the base and h is the height of the cylinder.

Container A has a radius of  [tex]4[/tex] feet and a height of 18 feet, so its volume is:

[tex]V(A) = \pi (4^{2} )(18) = 288\pi[/tex] cubic feet

Container B has a radius of 5 feet and a height of 15 feet, so its volume is:

[tex]V(B) = \pi (5)^2(15) = 375\pi[/tex]  cubic feet

When the water from Container A is transferred to Container B, the volume of water in Container B will be:

V(water in [tex]B) = V(A) = 288\pi[/tex] cubic feet

The total volume of Container B is 375π cubic feet, so the volume that is empty after the transfer is:

V(empty in  [tex]B) = V(B) - V(water in B) = 375\pi - 288\pi = 87\pi[/tex] cubic feet

To find the percentage of Container B that is empty, we need to divide the volume that is empty by the total volume of Container B and then multiply by 100:

Percent empty [tex]= (V(empty in B) / V(B)) \times 100[/tex]

[tex]= (87\pi / 375\pi) \times 100[/tex]

[tex]= 23.2[/tex]%

Therefore, the percent of Container B that is empty after the pumping is complete, to the nearest tenth, is [tex]23.2[/tex]%.

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Answer: 44%, 26%, less likely

Step-by-step explanation:

just do the math!!

Answer: y = 3/5x - 2/5

Step-by-step explanation: The slope-intercept form is y = mx+b. Hence, solve for y. 3x - 5y = 2.

Move 5y to the right side and move 2 to the left. 3x - 2 = 5y. Divided 5 for all sides: 3/5x - 2/5 = y. Hence, writing in slope-intercept form is y= mx + b, y = 3/5x - 2/5.

The evaluations are:

i. 11!  = 39916800

ii. 24! = 2.045 x 10^37

Expansion by factorial is a method of expanding a given number from 1 to the number given. An example is given thus;

5! = 5 x 4 x 3 x 2 x 1!

   = 120

To evaluate the given expressions;

a. 11! = 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1!

       = 39916800

Also,

b. 24! = 24 x 23 x 22 x 20 x ........ x 5 x 4 x 3 x 2 x 1!

          = 204484017332398 x 10 ^23

          = 2.045 x 10^37

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The unit rate that relates the two quantities of distance and volume of gas is:

U = 30 miles per gallon.

To do so, we can find the unit rate.

This would say how many gallons are consumed to drive a unit of distance, or which distance can you drive with one gallon.

Here we have the values:

10 gallons and 300 miles.

Then the unit rate is the quotient between these:

300miles/10 gallons = 30 miles per gallon

This says that with one gallon of gas you can travel 30 miles.

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Stan used 19/40 of a gallon of gasoline.

Given that;

At first, Stan's lawn mower had 1/8 of a gallon of gasoline in the tank. When it got finished, he put 6/10 of a gallon of gasoline in the tank.

Hence, It means that the number of gallons of gasoline that he has already put in the tank is

1/8 + 6/10 = 29/40 of a gallon.

Now, After he mowed, 1/4 of a gallon was left in the tank.

Therefore, the total amount of gasoline Stan used is

29/40 - 1/4 = 19/40 of a gallon

Thus, the total amount of gasoline Stan used is, 19/40 of a gallon

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The bank should invest $38,750 in bonds to earn an annual income of $14,650 from the investments.

(162,000 - 2x) is invested in mortgages.

The annual income earned from the bond investment is:

0.09x

The annual income earned from the CD investment is:

0.07x

The annual income earned from the mortgage investment is:

0.10(162,000 - 2x) = 16,200 - 0.20x

The total annual income earned from the investments is:

0.09x + 0.07x + 16,200 - 0.20x = 14,650

Simplifying and solving for x, we get:

-0.04x + 16,200 = 14,650

-0.04x = -1,550

x = 38,750

Therefore, the bank should invest $38,750 in bonds to earn an annual income of $14,650 from the investments.

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The ramp has a volume capacity of around 37.5 cubic feet.

Calculating the volume of a triangular prism shaped ramp follows a specific formula. First, identify the shape and refer to the equation:

Volume = (1/2) * Base Area * Height

To begin, the base is always in a right-angled triangle form, where its area depends on its width denoted as W, and height noted specifically as H.

Based on these computations, knowing that its triangular base measures 5 feet at its length while taking its height equates 3 feet therefore assessing how much it covers can be found using:

Triangle Area = (1/2) * Base * Height

Substituting values into solving areas leads us to have an answer of over 7 square feet.

Next is computing the volume of the said triangular prism. Placing all given data results in the same formula:

Volume = (1/2) * Base Area * Height

With one-half of the product of both areas which resulted in 7.5 square feet and then multiplying the figure by 10 ft, this yields us an approximate volume of 37.5 cubic feet.

In conclusion, we have determined that the ramp has a volume capacity of around 37.5 cubic feet.

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Length (L) = 10 feet

Width (W) = 5 feet

Height (H) = 3 feet

Mr. González designed a ramp for his car with a length of 10 feet, a width of 5 feet, and a height of 3 feet. What is the volume of the ramp in cubic feet?

Answer:

I can tell

Step-by-step explanation:

Ok so to help you understand it do you see the button that says video? Yeah, click it. A video will pop up and explain it to you! :)

Answer:

Step-by-step explanation:

f(x)=2x

note: putting anything in the f(x) parentheses replaces x in the function with that value

so,

f(-3) = 2(-3) = -6

f(0) = 2*0 = 0

f(2) = 2(2) = 4

for the first question  answer is 35 , which we can clearly see its pointing 35 degree in the protractor  .second question is incomplete

what is protractor ?

To measure an angle using a protractor instrument, follow these steps:

Place the protractor on the angle: Place the flat side of the protractor on one of the angle's sides, making sure that the vertex (the point where the two sides of the angle meet) is at the center of the protractor.Align the protractor with the angle: Make sure the protractor is aligned with the angle you want to measure. The zero-degree mark on

In the given question,

for the first question  answer is 35 , which we can clearly see in the protractor  

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Answer:

a) (1/2)(5)(CD) = 20 cm^2

5CD = 40, so CD = 8 cm

b) (1/2)(12)(8) = 48 cm^2

The equation that represent the number of bracelets b and the number of rings r is 6b + 8r > 600 and 2b + 4r < 275, hence, option A is correct.

Let b represent the number of bracelets and r represent the number of rings that Marisol makes. Marisol plans to sell each bracelet for $6 and each ring for $8. So the amount she earns from selling bracelets is 6b and the amount she earns from selling rings is 8r.

The craft fair committee charges a $25 fee to sell at the fair. So Marisol's total earnings after paying the fee is 6b + 8r - 25. It costs Marisol $2 to make a bracelet and $4 to make a ring. So the total cost of making b bracelets and r rings is 2b + 4r. To make a profit, Marisol's earnings must be greater than her costs,

6b + 8r - 25 > 2b + 4r

Simplifying this inequality, we get,

4b + 4r > 25

We also know that Marisol wants to sell at least $600 in jewelry. This can be expressed as,

6b + 8r > 600

Finally, Marisol wants to spend less than $300 for supplies and the fee. This can be expressed as,

2b + 4r + 25 < 300

Simplifying this inequality, we get,

2b + 4r < 275

Therefore, the system of inequalities that represents the situation is,

6b + 8r > 600

4b + 4r > 25

2b + 4r < 275

where b represents the number of bracelets and r represents the number of rings that Marisol makes.

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The probability of drawing a pink case on the first draw is 30/80.

Probability is a branch of mathematics that deals with the measurement and analysis of random phenomena. It is the study of the likelihood or chance of an event occurring. It involves analyzing and predicting the likelihood of certain outcomes based on the available information and the rules of probability theory. Probability is used extensively in various fields, including statistics, physics, finance, engineering, and computer science, among others.

In the given question,

The probability of drawing a pink case on the first draw is 30/80. Since the cases are not replaced, the probability of drawing a pink case on the second draw is 29/79 (there are now 29 pink cases left out of 79 total cases). Similarly, the probability of drawing a pink case on the third draw is 28/78. Therefore, the probability of drawing three pink cases in a row is:

(30/80) * (29/79) * (28/78) = 0.0412 or about 4.12%.

So, the probability that the first three cases are all pink is 0.0412 or about 4.12%.

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The total carbon dioxide emission over a period of 7 years will be 5,13,183 kilotons.

Considering the carbon emissions follow an exponential rate then

A(t)=A₀(1-r)^t

where A₀ is the initial value, and r is the decay rate as a decimal.

For the given problem A₀ =80000 kilotons and emissions will decrease at the rate of 2.5% per year therefore, r=0.025

The general equation for emission becomes

[tex]A(t)=80000(1-0.025)^t[/tex]

[tex]A(t)=80000(0.975)^t[/tex]

To calculate total emissions for 7 years it is calculated as follows

[tex]I=\int\limits^{7}_0 {A(t)} .dt=\int\limits^{7}_0 {80000(0.975)^tdt}[/tex]

[tex]I=80000(0.975)^t/ln (0.975)\left \{ {{t=7} \atop {t=0}} \right.[/tex]

I=5,13,183Kilotonnes

Hence, the total emission of 5,13,183 kilotons of carbon dioxide would be emitted over the course of the 7-year period.

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There is higher variability of y with large values of x.

There is a non linear relation between x and y.

We observe from figure b that for lower values of x the residuals are negative and as the values of x increases the residuals become positive but are distributed very close to the zero line.

Again for the extremely high values of x the residuals become negative following a decreasing non linear trend. Hence, from the residual plot we can conclude that the relation between x and y is a non linear one. Hence, the correct option is fourth option i.e, There is a non linear relation between x and y.

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1. If the expression is set equal to 10x + 5, the expression will have infinitely many solutions. 2. If the expression is set equal to 10x + 7, there would be no solution. 3. One solution.

In algebra, like terms are those in which the same variables are raised to the same powers. For instance, the fact that the variable x has been raised to the first power makes the expressions 3x, 2x, and -5x similar. Related expressions include 4y², -y², and 7y², all of which have the variable y increased to the second power. By maintaining the variable and its exponent the same, like terms can be joined by adding or removing the coefficients (the numbers placed in front of the variables).

The given expression is given as 12x - 6x + 4x + 5 = 10x + 5.

Simplifying the expression we het 10 x + 5.

1. If the expression is set equal to 10x + 5, the expression will have infinitely many solutions as it will always be true.

2. If the expression is set equal to 10x + 7, there would be no solution, as the variable is eliminated.

3. If the expression is set equal to -10x + 5, there would be only one solution.

10x + 5 = -10x + 5

20x = 0

x = 0

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she needs to clean 15 uniforms to break even

Answer:

D

Step-by-step explanation:

- 4( [tex]\frac{3}{2}[/tex] x - [tex]\frac{1}{2}[/tex] ) = - 15 ← distribute parenthesis by - 4

- 6x + 2 = - 15 ( subtract 2 from both sides )

- 6x = - 17 ( divide both sides by - 6 )

x = [tex]\frac{-17}{6}[/tex] , that is

x = [tex]\frac{17}{6}[/tex]

The team can sell 50 half dozen boxes and 50 full dozen boxes to raise at least $1000.

We can derive an inequality from the problem statement which is:

8X + 12Y >= 1000

This inequality represents the amount of money the basketball team needs to raise by selling donuts.

X is the number of half dozen boxes sold

Y is the number of full dozen boxes sold.

To find a solution in terms of the given context, we can plug in different values for X and Y that satisfy the inequality. For example:

If the team sells 50 half dozen boxes and 50 full dozen boxes, they will make:

8(50) + 12(50) = $400 + $600 = $1000

So this is a valid solution that meets the fundraising goal.

If the team sells 100 half dozen boxes and 0 full dozen boxes, they will make:

8(100) + 12(0) = $800

This is not enough to meet the fundraising goal, so it is not a valid solution.

If the team sells 0 half dozen boxes and 100 full dozen boxes, they will make:

8(0) + 12(100) = $1200

This is more than the fundraising goal, so it is a valid solution, but the team may not want to sell so many full dozen boxes.

Therefore, one solution in terms of the given context is that the team can sell 50 half dozen boxes and 50 full dozen boxes to raise at least $1000.

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Based on the data given in the table, B. Median for both coffee shops because the data distribution is not symmetric

It is better to describe the centers of distribution in terms of the median rather than the mean for both coffee shops because the data distribution is not symmetric.

The median is a better measure of central tendency in this case because it is not influenced by outliers or extreme values, which may exist in the data.

The mean, on the other hand, is sensitive to outliers and may not provide an accurate representation of the data distribution.

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To find the probability of winning the lottery game, we can use the formula for combinations:

nCk = n! / (k! * (n - k)!)

where n is the total number of choices (22 in this case) and k is the number of choices we make (6 in this case).

So, the number of possible combinations of six numbers from 22 is:

22C6 = 22! / (6! * 16!) = 13,983,816

Therefore, the probability of winning the lottery game is 1 in 13,983,816.

The expected value of playing the lottery game can be calculated as follows:

Expected value = (Probability of winning * Amount won) - (Probability of losing * Amount lost)

Expected value = (1/13,983,816 * $40,000) - (13,983,815/13,983,816 * $1)

Expected value = $0.5709

This means that on average, the player can expect to win about 57 cents per game played. However, it is important to note that this is just an average and the actual outcome of any single game can vary widely.

The logarithm expression can be simplified to:

In(6x^9)-In(x^2) =7·ln(6x)

There are some logarithm properties we can use here.

log(a) - log(b) = log(a/b)

log(a^n) = n*log(a)

(these obviously also apply to the natural logarithm)

Now let's look at our expression, it says that:

In(6x^9)-In(x^2)

Using the first rule, we can rewrite this as.

In(6x^9)-In(x^2) = ln(6x^9/x^2)

Now solving the quotient in the argument:

ln(6x^9/x^2) = ln(6x^7) = 7·ln(6x)

That is the expresison simplified.

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Therefore, there are 3,628,800 different routes possible for the delivery truck to visit all 10 locations only once.

Factorial notation is a mathematical notation used to represent the product of all positive integers up to a given number. It is denoted by an exclamation mark (!) placed after the number. Factorial notation is often used in combinatorics to calculate the number of possible permutations and combinations of a set of objects.

Here,

The number of different routes possible for the delivery truck can be calculated using factorial notation.

10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

This simplifies to:

10! = 3,628,800

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A: The data provides convincing evidence, at α=0.02 level, that the glucose drug is effective in reducing mean glucose level.

B: The 98% confidence interval for the difference in mean reduction of glucose level between placebo and drug groups is 3.5 to 13.7 mg/dL, supporting the effectiveness of the glucose drug

A: To test whether the glucose drug is effective in producing a reduction in mean glucose level, we will use a two-sample t-test with equal variances assuming normality of the differences.

Let μA be the true mean reduction in glucose level for the placebo group and μB be the true mean reduction in glucose level for the glucose drug group. The null hypothesis is H0: μA - μB = 0, and the alternative hypothesis is Ha: μA - μB < 0

Using the given data, the sample mean reduction for the placebo group is 9.7 mg/dL and for the glucose drug group is 18.3 mg/dL. The pooled sample standard deviation is 8.064 mg/dL, and the t-statistic is calculated to be:

t = (xB - xA) / (sP × √(1/nA + 1/nB))

= (18.3 - 9.7) / (8.064 × √(1/10 + 1/10))

= 2.551

where xA and xB are the sample means, sP is the pooled sample standard deviation, and nA and nB are the sample sizes.

B: To create a 98% confidence interval for the difference in the placebo and the new drug, we will use the formula:

CI = (xB - xA) ± tα/2,sP × √(1/nA + 1/nB)

where xA and xB are the sample means, sP is the pooled sample standard deviation, nA and nB are the sample sizes, and tα/2,sP is the t-value corresponding to a 98% confidence level with 18 degrees of freedom.

Using the values from Part A, we have:

CI = (18.3 - 9.7) ± 2.101 × 8.064 × √(1/10 + 1/10)

= 8.6 ± 5.103

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The correct question is:

Twenty middle-aged men with glucose readings between 90 milligrams per deciliter and 120 milligrams per deciliter of blood were selected randomly from the population of similar male patients at a large local hospital. Ten of the 20 men were assigned randomly to group A and received a placebo. The other 10 men were assigned to group B and received a new glucose drug. After two months, posttreatment glucose readings were taken for all 20 men and were compared with pretreatment readings. The reduction in glucose level (Pretreatment reading − Posttreatment reading) for each man in the study is shown here.

Group A (placebo) reduction (in milligrams per deciliter): 12, 8, 17, 7, 20, 2, 5, 9, 12, 6

Group B (glucose drug) reduction (in milligrams per deciliter): 29, 31, 13, 19, 21, 5, 24, 12, 8, 21

Part A: Do the data provide convincing evidence, at the α = 0.02 level, that the glucose drug is effective in producing a reduction in mean glucose level?

Part B: Create and interpret a 98% confidence interval for the difference in the placebo and the new drug.

Answer:

Step-by-step explanation:

I'm sorry, but there isn't enough information to solve for the missing side of a triangle with just the perimeter given as 8x-6. We would need at least one more piece of information, such as the lengths of the other sides or angles of the triangle.

Answer:

Step-by-step explanation:

This is a word problem involving percentages. To solve it, we need to follow these steps:

Identify the given information and the unknown quantity. In this problem, we are given that Natalie has $330 to spend at the amusement park, 5% is spent on games, 5/11 is for food and drinks, and she spends $13 on parking. The unknown quantity is the price of one ticket.

Write an equation that relates the given information and the unknown quantity. We can use the fact that the sum of all parts of the whole is 100%1. Let x be the price of one ticket. Then we have:

games+food and drinks+parking+tickets0.05×330+115​×330+13+2x​=total amount=330​

Solve the equation for the unknown quantity. We can simplify and rearrange the equation to get:

16.5+150+13+2x2x2xxx​=330=330−16.5−150−13=150.5=2150.5​=75.25​

Therefore, the price of one ticket is $75.25.