approximate the area under the curve y = x 3 y=x3 from x = 1 x=1 to x = 4 x=4 using a right endpoint approximation with 6 subdivisions.
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The slope of the equation P = 0.04x + 95 is 0.04. In the context of the problem, the slope represents the commission rate Joshua receives for his sales.

The equation P = 0.04x + 95 is in slope-intercept form, where P represents Joshua's total pay and x represents the total dollar amount of computers he sells. The coefficient of x, which is 0.04, represents the slope of the equation.

Since the slope is 0.04, it means that for every dollar worth of computers Joshua sells, he receives a commission of 0.04 dollars or 4% of the total sales. In other words, for every increase of $1 in sales, Joshua's pay increases by $0.04.

The slope is a measure of the rate of change in Joshua's pay with respect to the dollar amount of computers he sells. It indicates how Joshua's pay increases as his sales increase. A higher slope would imply a higher commission rate, meaning Joshua would earn more commission for each sale.

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Answer: See explanation

Step-by-step explanation:

Since the number of tickets is represented by t and we're told that the committee earns $4 per ticket and also earned $72 from bake sale, then the inequality will be given as:

= 72+4t>400

The solution if the inequality will then be:

72 + 4t > 400

4t > 400 - 72

4t > 328

t > 328/4

t > 82

Answer:

72+4t>400

t > 82

Step-by-step explanation:

top one is for the inequality

bottom is the solution

Answer:

5+2=7-7+4=4 =4 the answer is 4

Step-by-step explanation:

do not cheat 1st grader

Answer:

4

Step-by-step explanation:

The value of Absolute maximum are (a) 8, (b) -30.36, (c) -10 and the Absolute minimum are (a) -10, (b) -362.39, (c) -362.39.

We are given a function:f(x) = x³ - 12x² - 27x + 8We need to find the absolute maximum and absolute minimum values of the function f(x) over each of the indicated intervals. The intervals are:

a) Interval = [-2, 0]

b) Interval = [1, 10]

c) Interval = [-2, 10]

Let's begin:

(a) Interval = [-2, 0]

To find the absolute max/min, we need to find the critical points in the interval and then plug them in the function to see which one produces the highest or lowest value.

To find the critical points, we need to differentiate the function:f'(x) = 3x² - 24x - 27

Now, we need to solve the equation:f'(x) = 0Using the quadratic formula, we get: x = (-b ± √(b² - 4ac)) / 2a

Substituting the values of a, b, and c, we get:

x = (-(-24) ± √((-24)² - 4(3)(-27))) / 2(3)x = (24 ± √(888)) / 6x = (24 ± 6√37) / 6x = 4 ± √37

We need to check which critical point lies in the interval [-2, 0].

Checking for x = 4 + √37:f(-2) = -10f(0) = 8

Checking for x = 4 - √37:f(-2) = -10f(0) = 8

Therefore, the absolute max is 8 and the absolute min is -10.(b) Interval = [1, 10]

We will follow the same method as above to find the absolute max/min.

We differentiate the function:f'(x) = 3x² - 24x - 27

Now, we need to solve the equation:f'(x) = 0Using the quadratic formula, we get: x = (-b ± √(b² - 4ac)) / 2a

Substituting the values of a, b, and c, we get:

x = (-(-24) ± √((-24)² - 4(3)(-27))) / 2(3)

x = (24 ± √(888)) / 6

x = (24 ± 6√37) / 6

x = 4 ± √37

We need to check which critical point lies in the interval [1, 10].

Checking for x = 4 + √37:f(1) = -30.36f(10) = -362.39

Checking for x = 4 - √37:f(1) = -30.36f(10) = -362.39

Therefore, the absolute max is -30.36 and the absolute min is -362.39.

(c) Interval = [-2, 10]

We will follow the same method as above to find the absolute max/min. We differentiate the function:

f'(x) = 3x² - 24x - 27

Now, we need to solve the equation:

f'(x) = 0

Using the quadratic formula, we get: x = (-b ± √(b² - 4ac)) / 2a

Substituting the values of a, b, and c, we get:

x = (-(-24) ± √((-24)² - 4(3)(-27))) / 2(3)x = (24 ± √(888)) / 6x = (24 ± 6√37) / 6x = 4 ± √37

We need to check which critical point lies in the interval [-2, 10].

Checking for x = 4 + √37:f(-2) = -10f(10) = -362.39

Checking for x = 4 - √37:f(-2) = -10f(10) = -362.39

Therefore, the absolute max is -10 and the absolute min is -362.39.

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Answer:

$6.99

Step-by-step explanation:

4.3+1.7 pounds is 6 pounds. The price per pound would be $41.94 divided by 6. Therefore, $6.99

To determine the number of subsets of $\{1, 2, 3, \dots, 12\}$ that are spacy, we can use a recursive approach. the number of spacy subsets of $\{1, 2, 3, \dots, 12\}$.

Let $S(n)$ represent the number of spacy subsets of $\{1, 2, 3, \dots, n\}$.

For any subset to be spacy, it can either include the element $n$ or not include the element $n$.

If the subset includes $n$, then it cannot include the two previous consecutive integers $(n-1)$ and $(n-2)$. So the number of spacy subsets including $n$ is equal to $S(n-3)$.

If the subset does not include $n$, then it can be any spacy subset of\($\{1, 2, 3, \dots, n-1\}$,\)which is equal to $S(n-1)$.

Therefore, we can define the recursive formula as:

\(\[S(n) = S(n-1) + S(n-3)\]\)

Using this formula, we can calculate $S(0)$, $S(1)$, $S(2)$, $S(3)$, and so on up to $S(12)$ to determine the number of spacy subsets of $\{1, 2, 3, \dots, 12\}$.

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Answer:

Your answer is 30 sq. yd

Step-by-step explanation:

To find the area of the rectangle:

l x w

6 x 4 = 24

To find area of triangle:

1/2(bh)

to find the base of the triangle you subtract 6 from 9:

9 - 6 = 3

So 1/2 (3 x 4)

1/2 (3 x 4)

1/2 (12)

12 / 2 = 6

Area of whole figure:

You will now add 6 + 24 = 30

Answer:

Thus the domain is the real numbers and the range is y>3.

Answer: Option C)

Step-by-step explanation:

Domain and Range of Functions

To determine the domain and range of a function given on a graph, we use the vertical and horizontal line methods respectively.

The domain consists of all the values of x for which the function exists. We are told that the function is an exponential decay. Exponential functions without specified restrictions have a domain of all the real numbers.

Imagine a vertical line moving from minus infinite x to plus infinite. The line would always cross the graph at one point, thus the domain is all the real numbers.

Now for the range, imagine a horizontal line coming from y minus infinite. It won't get in contact with the graph until it approaches y=3. Once it goes up y=3, the line touches the graph in one point up to infinity y. The range is y>3.

Thus the domain is the real numbers and the range is y>3.

Answer: Option C)

Answer:

the equation is 45 + 20x= 225 and her son had a total of nine (9) classes.

Step-by-step explanation:

45 + 20x = 225 is the equation.

to solve it, we do 225-45=180

then, 180/20= 9

so x = 9

4 ounces to pounds

1 ounce = 0.0625 pounds

4 ounces * 0.625 pounds = \(\fbox{2.5 pounds}\)

This question is mid term factorisation

The box plot for the given dataset shows that the third quartile (Q3) is equal to 143.75.

Box plots are a graphical representation of a set of data that shows the distribution of the data and its various quartiles. The box plot displays the minimum value, first quartile (Q1), median (Q2), third quartile (Q3), and maximum value of a dataset.

Now, let's take a look at the box plot for the given data: 0 12.5 20 65 143.75. The box plot consists of a box that represents the middle 50% of the data (i.e., from Q1 to Q3). The line inside the box represents the median (Q2). The lower whisker represents the minimum value, and the upper whisker represents the maximum value.

To find the third quartile (Q3) from the box plot, we need to look at the right-hand side of the box. We can see that the box ends at approximately 143.75, which is also the maximum value of the dataset. Therefore, Q3 is equal to 143.75.

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The error made by Kaitlyn when solving the system of equations is in step 2. Her solution will be incorrect.

The right option will be: No, she made an error in step 2. She should have found y = 0. 5.

Given the system of linear equations:

-3x + 2y = 8 ---> eqn. 1

3x + 2y = -6 ---> eqn. 1

First add both equations together:

Step 1: 4y = 2

Next, divide both sides by 4:

Step 2: y = 2/4

y = 0.5

Therefore, the error made by Kaitlyn when solving the system of equations is in step 2. Her solution will be incorrect.

The right option will be: No, she made an error in step 2. She should have found y = 0. 5.

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Answer:

See answer is Explanation

Step-by-step explanation:

4 divided by 25 is 0.16

6 divided by 25 is 0.24

6 x 4 = 24

4 x 25 = 100

6 x 25 = 150

Answer:

\(\boxed{\sf \ \ \ x=\dfrac{3}{4} \ \ \ }\)

Step-by-step explanation:

hello,

f(x)=x-1

\(g(x)=2x^2+3\)

so

\(fog(x)=f(g(x))=f(2x^2+3)=2x^2+3-1=2x^2+2 \ and \\gof(x)=g(f(x))=g(x-1)=2(x-1)^2+3=2x^2-4x+2+3=2x^2-4x+5 \ \ So\\\fog(x)=gof(x) <=>2x^2+2=2x^2-4x+5\\<=>4x=5-2=3\\<=>x=\dfrac{3}{4}\)

hope this helps

\(\frac{3}{4}\)

The composition of a function is a process in which two functions \(f,g\), are combined to produce a new function, \(h\), with the formula \(h(x)=g(f(x))\). It means that the \(g\) function is being applied to the \(x\) function.

\(f(x)=x-1\\g(x)=2x^2+3\)

\(f(g(x))=f(2x^2+3)\)

            \(=2x^2+3-1\\=2x^2+2\)

\(g(f(x))=g(x-1)\)

           \(=2(x-1)^2+3\\=2x^2+2-4x+3\\=2x^2-4x+5\)

\(f(g(x))=g(f(x))\)

\(2x^2+2=2x^2-4x+5\)

       \(4x=3\)

        \(x=\frac{3}{4}\)

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Answer: 6.75 cc

Step-by-step explanation:

Answer:  C

Step-by-step explanation:

A. is wrong, only 6 students liked pineapple and 12 bacon, so they did not prefer pineapple to bacon

B. is wrong,  the most students liked was not cheese, it was pepperoni

C. is correct, pineapple is the least liked at 6 student

D. is wrong, not all the students liked pepperoni, some students liked other things

Answer:divideing by the whole number

Step-by-step explanation:

Answer:

\(3.1\)

Step-by-step explanation:

Range = biggest no. - smallest no.

Range = \(6.3-3.2\)

Range = \(3.1\)

Answer:

3.1

Step-by-step explanation:

Range is the difference between the highest and the least number in a set.

Out of all the numbers given, 6.3 is the highest and 3.2 is the least. When, I found the difference of those two numbers, the difference was 3.1. :)

The qualitative change in the shape of a graph is related to changes in the critical points, slope, and curvature of the function.

However, in general, the qualitative change in the shape of a graph occurs when there is a change in the number, location, or type of critical points (e.g., local maximum or minimum) of the function. Additionally, the behavior of the graph may change when there are changes in the slope or curvature of the function at certain points.

A qualitative change in the shape of a graph refers to a change that alters the overall appearance of the graph. This change occurs when there are significant modifications in the function's behavior that affect the number, location, or type of critical points of the function. For example, if the function has a single critical point at x=a, and as x increases, another critical point emerges at x=b, then there is a qualitative change in the shape of the graph.

Additionally, the behavior of the graph may change when there are alterations in the slope or curvature of the function at certain points. For instance, if the function has a point of inflection at x=c, and as x increases, the curvature changes significantly, then there is a qualitative change in the shape of the graph.

In summary, the qualitative change in the shape of a graph is related to changes in the critical points, slope, and curvature of the function.

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When x is correlated with y, it means that there exists a relationship between the two variables, where a change in one variable (x) is associated with a change in the other variable (y).

This relationship can be either positive or negative.

In a positive correlation, as the value of x increases, the value of y also increases, and as the value of x decreases, the value of y decreases as well. This indicates that both variables move in the same direction. On the other hand, in a negative correlation, as the value of x increases, the value of y decreases, and as the value of x decreases, the value of y increases. This shows that the variables move in opposite directions.

It is essential to note that correlation does not imply causation. Just because two variables are correlated does not mean that one variable causes the other to change. There could be other factors or variables that influence the observed relationship between x and y. Additionally, the strength of the correlation can vary, with values close to 1 or -1 representing a strong relationship and values close to 0 representing a weak relationship or no relationship at all.

In conclusion, when x is correlated with y, it means that there is a relationship between the two variables that can be either positive or negative, but this does not necessarily imply causation. The strength of the relationship can also vary, depending on the correlation coefficient value.

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Answer:

20

Step-by-step explanation:

7+4=11

11*5= 55

4*5=20 :)

The number of children and adults will be 35 and 20, respectively.

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.

You go into the store and observe the folks in queue. There are 7 adults and 4 children. If this ratio remains constant and there are 55 people in the store.

7x / 4x = constant

Then the equation is given below.

7x + 4x = 55

11x = 55

x = 11

Then the number of adults is given as,

7x = 7 (5) = 35

Then the number of children is given as,

4x = 4 (5) = 20

The number of children and adults will be 35 and 20, respectively.

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Answer:

4 * 2 = 8 and 10^6 * 10^3 = 10^(6 + 3) = 10^9 so the answer is 8 * 10^9.

Answer:

x=25

Step-by-step explanation:

(2x-10)=(65-x)

2x +x= 65+10

3x = 75

x=75/3

x =25

I hope I helped you^_^

Answer: 29

Step-by-step explanation: since m is the midpoint, then the two sides are equal

4x + 13 = 3x + 17

4x - 3x = 17 - 13

x = 4

Therefore

BM = 3x + 17

BM = 3(4) + 17

BM = 12 + 17

BM = 29

To assist you in filling in the missing part of the equation, it is crucial to have the full equation provided by the student. Without it, it is not possible to accurately determine the missing part or provide a precise answer.

However, I can provide some general guidance on how to approach measurement conversions. Typically, conversion equations involve multiplying the given measurement by a conversion factor. The conversion factor relates the given unit to the desired unit of measurement. By multiplying the given measurement by the appropriate conversion factor, the student can obtain the equivalent value in the desired unit.

For example, if the equation is related to converting distance from miles to kilometers, the missing part might involve the conversion factor representing the number of kilometers in one mile. The student would need to fill in the missing part with the appropriate value. To ensure accuracy, it is essential to identify the specific units involved in the measurement conversion and find the corresponding conversion factor. Common conversion factors can be found in reference materials or online resources.

Please provide the complete equation or any additional information you have so that I can provide a more specific and accurate answer. With the complete equation, I will be able to guide you step-by-step in filling in the missing part correctly.

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Answer:

if she does so multiply by seven to get final answer

Answer:

56 cups per week

Step-by-step explanation:

there is 16 cups of water in a gallon

.5 gallon x 7days = 3.5 gallons

3.5 gallons  *  16 cups/ gallon = 56 cups per week

Selecting all students with last names beginning with the letter M would not produce a random sample of a school population of 1000 students. Hence the answer is no.

A random sample is obtained by selecting individuals from a population in a way that ensures every member of the population has an equal chance of being included in the sample.

By choosing only students with last names beginning with the letter M, you are introducing a bias and not providing an equal chance for all students to be selected.

To obtain a random sample of 1000 students from a school population, you would need to use a random selection method that ensures each student has an equal probability of being chosen.

This could be achieved through techniques such as random number generators, random sampling software, or random sampling techniques like stratified or cluster sampling.

Selecting all students with last names beginning with the letter M would not meet the requirements of a random sample, as it would not provide an equal chance for all students in the population to be included.

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The inputs or features that are fed into the model and with which the model is expected to make a prediction for the linear regression are x.

Linear regression is a statistical approach to establish a relationship between dependent and independent variables. In linear regression, the model is f_{w,b}(x) = wx + bfw,b​(x)=wx+b. The independent variable (x) is the feature that is fed into the model and with which the model is expected to make a prediction.

In the equation f_{w,b}(x) = wx + bfw,b​(x)=wx+b, w is the weight of the input feature x, and b is the bias term that makes an adjustment in the output. These parameters w and b are learned through training the model with input-output examples.

The purpose of linear regression is to create a mathematical model that defines the relationship between the input feature x and the output y. The model is then used to predict the outcome for new data points or to understand the relationship between the variables.

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Fiona must have bought 3 pairs of socks and 2 belts to spend $27.95 in all.

What is the linear equation?

A linear equation is defined as a function that has either one or two variables without exponents. It is a function that graphs to a straight line.

We can model the scenario with a system of two equations in two variables as follows:

a: number of pairs of socks purchased

b: number of belts purchased

The cost of each pair of socks is $4.95, so the total cost of a pairs of socks is 4.95a.

Similarly, the cost of each belt is $6.55, so the total cost of b belts is 6.55b.

The total amount Fiona spent is $27.95, so we can write:

4.95a + 6.55b = 27.95

This is the first equation in our system.

We also know that a and b are both non-negative integers, since Fiona cannot buy a negative number of socks or belts.

To model this restriction, we can add the following inequalities to the system:

a ≥ 0

b ≥ 0

Now we have a system of two equations and two inequalities:

4.95a + 6.55b = 27.95

a ≥ 0

b ≥ 0

We can use this system to solve for the values of a and b that satisfy all the constraints of the problem. We could use a variety of methods to solve the system, such as substitution, elimination, or graphing.

For example, one way to solve the system is to solve the first equation for b in terms of a:

b = (27.95 - 4.95a) / 6.55

Since b must be a non-negative integer, we can try plugging in different values of a and see which ones yield integer values of b.

For instance, if we let a = 0, then b = (27.95 - 4.950) / 6.55 = 4.27, which is not an integer. Similarly, if we let a = 1, then b = (27.95 - 4.951) / 6.55 = 3.42, which is also not an integer.

However, if we let a = 2, then b = (27.95 - 4.95*2) / 6.55 = 2.57, which is not an integer. Continuing in this way, we find that the first integer value of b occurs when a = 3, which gives:

b = (27.95 - 4.95*3) / 6.55 = 1.71 ≈ 2

Hence, Fiona must have bought 3 pairs of socks and 2 belts to spend $27.95 in all.

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