2. (a. Two power functions are given. Simplify both functions.
f(x) = 5x³.x²
g(x) = (2x)S
(b) Which function grows faster? Explain how you know.
11/1
Both power functions from part a are graphed to the right. Label
each function on the graph. Explain how you know which is which.
19

Step-by-step explanation:

No of people likes tea = 4000

No of people like coffee = 4500

Total = 8500

No of people don't like tea and coffee = 2500

No of people like tea and coffee = 8500 - 2500 = 6000

Answer:

500

Step-by-step explanation:

n(t)=4000

n(c)=4500

n(tea only )= 4000-x

n(coffee only )= 4500-x

n(coffee and tea )= x

note...using Venn diagram ..all together must add up to 9000

(4000-x)+(4500-x) +x = 9000

..............

...........collect like terms

9500-9000 = x

x = 500

Answer:

Step-by-step explanation:

Thde y-intercept is the value oy y when x = 0.  The data table tells us the value of y when x=0 is 4.  The ordered pair is (0,4)

The next step in the series will be a circle divided into five shapes.

option D.

A series is a sequence of numbers or events that are arranged or added in a particular pattern.

From the given diagrams, the next step in the series is calculated as follows;

the first diagram is a circle divided into two shapes,

the second diagram is a circle divided into three shapes

the third diagram is a circle divided into four shapes

the fourth diagram will be a circle divided into five shapes

So the next step in the series will be a circle divided into five shapes or pentagon.

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The equation h(t) = -16t² + 24t is an illustration of a quadratic model

The equation that represents the path of the kick ball is given as

h(t) = -16t² + 24t

The fielder catches the ball at a height of 3 ft above the ground.

This means that:

h(t) = 3

So, we have:

-16t² + 24t = 3

Hence, the equation when the fielder catches the ball is -16t² + 24t = 3

In (a), we have:

-16t² + 24t = 3

Rewrite as:

-16t² + 24t - 3 = 0

Next, we determine the solutions of -16t² + 24t - 3 = 0 using a graphing technology

From the graph (see attachment), we have the following solutions

t = 0.14 and t = 1.36

Hence, the fielder will catch the ball after 0.14 seconds or 1.36 seconds

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Answer:

third option; 70 cm²

Step-by-step explanation:

Rectangle:

5 x 10 = 50

Triangle:

1/2bh

18 - 10 = 8

1/2 5(8)

1/2 40

20

Total area:

50 + 20 = 70 cm²

Answer:

3.25

Step-by-step explanation:

Public opinion polls use sample sizes of more than 1000 people because it helps to ensure that the results are statistically significant. This means that the results are likely to be accurate and representative of the population as a whole.

The margin of error for a poll is the amount by which the results of the poll could be off from the actual results. The margin of error is calculated using the sample size, the confidence level, and the standard deviation of the population.

The confidence level is the probability that the results of the poll are within the margin of error. The standard deviation of the population is a measure of how spread out the opinions of the population are.

The larger the sample size, the smaller the margin of error will be. This is because the larger the sample size, the more likely it is that the sample will be representative of the population as a whole.

For example, if a poll has a sample size of 1000 people and a confidence level of 95%, the margin of error will be +/- 3%. This means that there is a 95% chance that the results of the poll are within 3% of the actual results.

If a poll has a sample size of 500 people and a confidence level of 95%, the margin of error will be +/- 4.4%. This means that there is a 95% chance that the results of the poll are within 4.4% of the actual results.

As you can see, the larger the sample size, the smaller the margin of error will be. This is why public opinion polls use sample sizes of more than 1000 people. It helps to ensure that the results are statistically significant and that they are likely to be accurate and representative of the population as a whole.

The probability of having 7 boys in a family with 7 children is 1 out of 128, as there is only one favorable outcome out of 128 total possible outcomes.

To find the probability, we need to calculate n(E) and n(S).

In this case, event E represents the scenario where all 7 children are boys. The sample space S consists of all possible permutations of boys and girls for the 7 children, which is 2^7 = 128.

This is because each child has 2 possibilities (boy or girl), and we multiply these possibilities for all 7 children.

Since event E includes only one specific outcome (all boys), n(E) is equal to 1. Therefore, both n(E) and n(S) are 1 and 128, respectively. The probability of having 7 boys is given by n(E)/n(S) = 1/128.

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The expression in standard form for the volume V of the box is: \(V = 6n^3 + 5n^2 + 2n\)

How do you measure the volume of a box?

You must take measurements of a box's length, breadth, and height in order to determine its size. To get the box's volume in cubic units, multiply all three measurements together.

The volume V of the box can be expressed as:

V = (depth) x (height) x (width)

Substituting the given values, we get:

V = n x (2n+1) x (3n+2)

Expanding the expression, we get:

V =\(6n^3 + 5n^2 + 2n\)

Therefore, the expression in standard form for the volume V of the box is: \(V = 6n^3 + 5n^2 + 2n\)

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False. the denominator in the formula for calculating the return on investment includes operating and nonoperating assets.

The denominator in the formula for calculating the return on investment (ROI) typically includes only operating assets, not non-operating assets. Operating assets are those that are necessary to generate revenue and include items such as inventory, equipment, and property. Non-operating assets, on the other hand, are not directly related to revenue generation and include items such as investments, patents, and trademarks. In order to calculate ROI, the numerator is the profit or gain from the investment, while the denominator is typically the total amount of operating assets used to generate that profit. By dividing the profit by the investment, ROI provides a measure of how much profit was generated relative to the amount of resources invested.

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Therefore, visually interpreting histograms can be a powerful tool for data analysis, but it is important to be aware of their strengths and limitations.

Histograms are an effective way to display data graphically. They are used to show how often certain values or ranges of values appear in a data set. Visual interpretation of histograms has many strengths and limitations. Some of the strengths of visually interpreting histograms are that they are easy to read and understand, they provide a clear picture of how the data is distributed, and they can help identify outliers or gaps in the data. However, some of the limitations of visually interpreting histograms are that they can be influenced by the number of bins chosen, the way the data is grouped, and the choice of the scale used. Therefore, it is important to carefully consider these factors when interpreting a histogram. In conclusion, visually interpreting histograms can be a powerful tool for data analysis, but it is important to be aware of their strengths and limitations.

Therefore, visually interpreting histograms can be a powerful tool for data analysis, but it is important to be aware of their strengths and limitations.

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Answer:

is there an example? or picture?

Any two points can be at most 1 unit far from each other. As, any two points can lie at maximum distance from each other when they both lie on the boundary of the triangle.

Given, an equilateral triangle of side length 1 unit.

Five points are inside the triangle.

we have to show that there are 2 points at distance of at most 1 unit.

As, Five points lie inside the triangle.

So, any two points can lie at maximum distance from each other when they both lie on the boundary of the triangle.

As, it is given that the side length of the triangle is 1 unit so, the two points can be at most 1 unit far from each other.

Hence, it is shown that any two points can be at most 1 unit far from each other. As, any two points can lie at maximum distance from each other when they both lie on the boundary of the triangle.

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The value of the expression "true && !false" can be determined by evaluating each part separately and then combining the results.

1. The "!" symbol represents the logical NOT operator, which negates the value of the following expression. In this case, "false" is negated to "true".

2. The "&&" symbol represents the logical AND operator, which returns true only if both operands are true. Since the first operand is "true" and the second operand is "true" (as a result of the negation), the overall expression evaluates to "true".

Therefore, the value of the expression "true && !false" is "true".

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Answer:

9\(\pi\)\(x^{4}\)

Step-by-step explanation:

A monomial is an algebraic expression with one term.

So that,

area of a circle = \(\pi\)\(r^{2}\)

if r = 3\(x^{2}\), then;

area of the circle = \(\pi\) x \((3x^{2} )^{2}\)

                            = \(\pi\) x 9\(x^{4}\)

                            = 9\(\pi\)\(x^{4}\)

The area of the circle is 9\(\pi\)\(x^{4}\) square units.

Therefore, the monomial the represent the number of square units in the area of the circle is 9\(\pi\)\(x^{4}\) square units.

The monomial which represents the number of square units in the area of a circle with radius 3x³ units is; 9πx⁶ square units.

The area of a circle is given in terms of its radius as follows;

However, the radius of the circle, r = 3x³ units.

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since we cannot have a fraction of a serving, we can only make 9 servings of soup with 2 quarts (or 8 cups) of chicken broth.  Therefore, the proportion we should use is 5 cups of chicken broth to 6 servings of soup.

To answer this question, we need to convert 2 quarts to cups. Since there are 4 cups in a quart, 2 quarts would be 8 cups.

Now that we know we have 8 cups of chicken broth, we can set up a proportion to determine how many servings of soup we can make.

5 cups of chicken broth = 6 servings of soup

x cups of chicken broth = y servings of soup

To solve for x and y, we can cross-multiply:

5y = 6x

x = 8 cups of chicken broth

y = (6/5) * 8 = 9.6 servings of soup

However, since we cannot have a fraction of a serving, we can only make 9 servings of soup with 2 quarts (or 8 cups) of chicken broth.

Therefore, the proportion we should use is 5 cups of chicken broth to 6 servings of soup.

 To determine how many servings you can make with 2 quarts of chicken broth, you should set up a proportion using the given information: 6 servings require 5 cups of broth. First, convert 2 quarts to cups (1 quart = 4 cups, so 2 quarts = 8 cups). Now, set up the proportion:

6 servings / 5 cups = x servings / 8 cups

Here, x represents the number of servings you can make with 8 cups (2 quarts) of chicken broth. By cross-multiplying and solving for x, you will find the number of servings possible with the available broth.

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Answer:

4. 30

Step-by-step explanation:

-3(-10)

=3×10

= 30

the present value of the $90,000 balloon payment will be approximately $61,008.09 for annual compounding and $60,732.45 for continuous compounding.

The present value of a $90,000 balloon payment due in 4 years can be calculated using different compounding methods.

For annual compounding at an interest rate of 11%, we can use the present value formula: PV = FV / (1 + r)^n, where PV is the present value, FV is the future value, r is the interest rate, and n is the number of compounding periods. Substituting the given values, PV = 90000 / (1 + 0.11)^4 ≈ $61,008.09.

For continuous compounding at an interest rate of 11%, we can use the continuous compounding formula: PV = FV / e^(r * n), where e is the base of the natural logarithm. Substituting the given values, PV = 90000 / e^(0.11 * 4) ≈ $60,732.45.

Therefore, the present value of the $90,000 balloon payment will be approximately $61,008.09 for annual compounding and $60,732.45 for continuous compounding.

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Answer:

35 square units

Step-by-step explanation:

Area of the parallelogram = 7*5 = 35 square units

To find how much oil the pumping stations will deliver during the 3-hour period from t=0 to t=3, we need to integrate the function D(T) from t=0 to t=3:

∫[0,3] (6t/1+2t) dt

Using substitution, let u = 1+2t, then du/dt = 2 and dt = du/2. The integral becomes:

∫[1,7] (3/u) du

= 3 ln|u| from 1 to 7

= 3 ln(7/1)

= 3 ln(7)

≈ 5.048

Therefore, the pumping stations will deliver approximately 5.048 gallons of oil during the 3-hour period from t=0 to t=3, to 3 decimal places.
Hi! I'd be happy to help you with your question. We need to find the total amount of gasoline delivered during the 3-hour period from t=0 to t=3 using the given function D(t) = 6t / (1 + 2t). We can do this by integrating the rate function with respect to time.

Step 1: Integrate the rate function, D(t), with respect to t:

∫(6t / (1 + 2t)) dt

Step 2: Evaluate the integral between t=0 and t=3:

|∫(6t / (1 + 2t)) dt| from 0 to 3

Step 3: Calculate the definite integral:

Since it's difficult to evaluate this integral directly, we can use a numerical integration method like the trapezoidal rule or Simpson's rule, or a calculator with an integration function. Using a calculator, we find that the integral value is approximately 1.802.

So, the pumping stations will deliver approximately 1.802 gallons of gasoline during the 3-hour period from t=0 to t=3.

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We will get that the angle theta is:

θ = β/2

Remember that the sum of the interior angles of any triangle must be equal to 180°.

Now, looking at the triangle in the left, we can see that the top angle is equal to:

180 - 2α

The right angle is equal to:

180 - 2β

And the left angle is α

Then we can write:

α + (180 - 2α) + (180 - 2β) = 180

-α - 2β = -180

α = 180 - 2β

Now we can go to the other triangle, where theta is, and write:

α + β + 2θ = 180

Replacing what we found above, we get:

180 - 2β + β + 2θ = 180

-β + 2θ = 0

θ = β/2

That is the best simplification we can get with the given diagram.

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The independent variable is the variable that is deliberately changed or manipulated by the researcher to see its effect on the dependent variable.

It is the presumed cause of the observed effect on the dependent variable, which is the variable that is being measured or observed in the experiment.

For example, in an experiment to test the effect of caffeine on reaction time, the independent variable is the amount of caffeine given to the participants, while the dependent variable is the reaction time of the participants. By manipulating the amount of caffeine given, the researcher can observe the effect of caffeine on reaction time.

It is important to carefully control and manipulate the independent variable in an experiment to ensure that any observed effect on the dependent variable can be attributed to the independent variable and not to other extraneous variables.

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Answer:

- 11f + 15

Step-by-step explanation:

- f - 5(2f - 3)

= - f - 10f + 15

= - 11f + 15

Answer:

(2,-1)

x=2

y=-1

Step-by-step explanation:

The exact values of the sine, cosine, and tangent of the angle 255° are -1/√2, 1/√2, and -1, respectively.

To find the exact values of the sine, cosine, and tangent of the angle 255°, we can use the identity that relates the trigonometric functions of an angle to the trigonometric functions of its complement.

By expressing 255° as the sum of 300° and -45°, we can determine the exact values of the trigonometric functions for the given angle.

We know that the sine, cosine, and tangent of an angle are periodic functions, repeating every 360 degrees. To find the exact values of the trigonometric functions for 255°, we can express it as the sum of 300° and -45°, where 300° is a multiple of 360°.

Since the sine, cosine, and tangent functions are odd or even functions, we can use the values of the trigonometric functions for 45° to determine the values for -45°.

For 45°:

sin(45°) = cos(45°) = 1/√2

tan(45°) = 1

Since cosine is an even function, cos(-45°) = cos(45°) = 1/√2.

Since sine is an odd function, sin(-45°) = -sin(45°) = -1/√2.

Using the definition of tangent as the ratio of sine to cosine, tan(-45°) = sin(-45°) / cos(-45°) = (-1/√2) / (1/√2) = -1.

Therefore, for the angle 255°:

sin(255°) = -1/√2

cos(255°) = 1/√2

tan(255°) = -1

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╭┄┈┄────────❥

Answer:

↣ A.) Third person limited

Explanation:

A story told from a third person limited point-of-view, or POV, is defined as a narration that describes the thoughts, feelings, and actions of one character.

. . • ☆ . ° . • °: . * ₊ ° . ☆

I hope this helps!

peachtea ^-^

╰┄┈┄──❥

The value of the test statistic is **2.73**.

The test statistic is calculated using the following formula:

z = (sample proportion - population proportion) / standard error of the proportion

In this case, the sample proportion is 0.35, the population proportion is 0.32, and the standard error of the proportion is 0.014. Plugging these values into the formula, we get a test statistic of 2.73.

A z-score of 2.73 is significant at the 0.01 level, which means that there is a 1% chance that we would get a sample proportion of 0.35 or higher if the population proportion is actually 0.32. Therefore, we can reject the null hypothesis and conclude that there is enough evidence to support the claim that the percentage of residents who favor construction is over 32%.

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