Use the Three-point midpoint formula to approximate f' (2.2) for the following data
x f(x)
2 0.6931
2.2 0.7885
2.4 0.8755

The answer is 8 just divide 6 and 52 but take 4 away from 52 so 48 divided by 6

Answer:

14, 18, 20

Step-by-step explanation:

You have to replace the number in the "s" column with the "s" in the problem. For example the first number in the table is 2 so you have to put 2 into the problem then add it with 12 and you get 14.

The x-intercept of the equation 4p + 5x = 20 is 4. The equation can be rearranged to solve for p in terms of x, which is p = (20 - 5x)/4. When graphed with x on the horizontal axis, the slope of the equation is -4/5. Similarly, we can solve for x in terms of p, which is x = (20 - 4p)/5.

1) To find the x-intercepts of the equation 4p + 5x = 20, we set p to 0 and solve for x.

By substituting p = 0 into the equation, we get 5x = 20, which simplifies to x = 4.

Therefore, the x-intercept is 4.

2) To solve for p in terms of x, we rearrange the equation 4p + 5x = 20.

Subtracting 5x from both sides gives 4p = 20 - 5x.

Dividing both sides by 4, we obtain p = (20 - 5x)/4.

3) If we were to graph the equation 4p + 5x = 20 with x on the horizontal axis, the slope would be -4/5.

The slope of a linear equation represents the ratio of the vertical change (change in p) to the horizontal change (change in x).

In this case, the coefficient of x is 5, so the ratio is -4/5.

4) To solve for x in terms of p, we rearrange the equation 4p + 5x = 20.

Subtracting 4p from both sides gives 5x = 20 - 4p.

Dividing both sides by 5, we get x = (20 - 4p)/5.

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Answer:

1. y=-2x+5

2. y=1/2x-7.5

Step-by-step explanation:

you plug in the cordinates for the y intercept and you already have the slope.

y=mx+b

m= slope which is -2

Answer:

5.) Associative Law

6.) Commutative Law

7.) Distributive Law

8.) Associative Law

9.) Distributive Law

10.)

Step-by-step explanation:

The associative law means that if all the arithmetic operations in an equation are the same, the position of the brackets do not matter and no matter which variables are associated, the result would still be the same.

The commutative law means that if all the arithmetic operations in an equation are the same, the position of the variables do not matter and no matter what order the variables are placed, the result would still be the same.

The distributive law means that whatever is outside of the bracket has to be multiplied into the variables in the bracket evenly. E.g. 1/4 (8x - 20) involves multiplying both 8x by 1/4 and 20 by 1/4.

Answer:

4 students

Step-by-step explanation:

Although I am not sure if I am completely correct. I’ll try my best.

We know:

The numbers 0-12 on the frequency table is the number of windows.

The numbers on the bottom is the amount of students.

-

What we can see:

As we can see..

-

Calculations:

Since the number of students that have the amount of windows less than 10 is 4 (0-4 section) and 0 (10-14 section)

Add.

4+0

= 4

Therefore, 4 students have less than 10 windows.

To prove that f is one-to-one function, it must be proven that f(x1)=f(x2) and x1=x2.

What is a one to one function?

The mapping of two sets is essentially what a one to one function refers to. When every element in a function's range and domain match exactly one another, the function is said to be one-to-one.

The one-to-one function, also known as an injective function, is one of the many different types of functions.

A function that transfers different components of its domain to different elements of its codomain is known as a one-to-one function.

For example, a function  f:A→B  is said to be one-to-one if -

f(x1)=f(x2)⇒x1=x2

for all elements x1,x2∈A.

To prove  f:A→B  is one-to-one -

Consider the fact that f(x1)=f(x2).  

Then it must be true that x1=x2.

Therefore, it is now understood that f is one-to-one by definition if f(x1)=f(x2) and x1=x2.

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Answer:

1/√2

Approximate numerical value

1/√2 = 0.707106781186548

---------------------------

Rationalize the denominator

(1/√2) * (√2 / √2) = √2 / 2

The Kruskal-Wallis test is a non-parametric test used to compare three or more independent groups to determine if there is a significant difference between the medians of the groups. The test statistic used in this test is denoted by the letter "H," which is calculated based on the ranks of the data.

True. The test statistic calculated in the Kruskal-Wallis test is denoted by the symbol H, not to be confused with the Shapiro-Wilk test statistic denoted by W. The Kruskal-Wallis test is a non-parametric test used to compare the median ranks of three or more independent groups. The test statistic H is calculated by comparing the between-group sum of squares to the total sum of squares. H follows a chi-squared distribution with degrees of freedom equal to the number of groups minus one. The p-value obtained from the chi-squared distribution is used to determine whether to reject or fail to reject the null hypothesis that there is no significant difference between the groups.

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Answer:

A) True

B) False

C) True

Step-by-step explanation:

Answer:

In algebra, like terms are terms that have the same variables and powers. The coefficients do not need to match.

Unlike terms are two or more terms that are not like terms, i.e. they do not have the same variables or powers. The order of the variables does not matter unless there is a power. For example, 8xyz2 and −5xyz2 are like terms because they have the same variables and power while 3abc and 3ghi are unlike terms because they have different variables. Since the coefficient doesn't affect likeness, all

Answer:

unlike terms

Step-by-step explanation:

are more than two hope this helps I just answer quickly

Answer:

Area of a circle= 1/4*π d^2

A=1/4*π*12^2=

A=1/4*π*144=113.1

Step-by-step explanation:

Hope this helps!! :)). Mark me brainliest! :))

Answer:

5 Hours

Step-by-step explanation:

The required regression equation is y=−15.9x+1081.6 and new cases for 2008 is 950.

To find the linear regression equation that represents the given set of data, we need to find the slope and y-intercept of the line of best fit.

We can use the following formulas to find the slope and y-intercept:

\($\begin{align*}\text{slope } b &= \frac{\sum_{i=1}^{n}(x_i - \overline{x})(y_i - \overline{y})}{\sum_{i=1}^{n}(x_i - \overline{x})^2} \\text{y-intercept } a &= \overline{y} - b\overline{x}\end{align*}\)

where n is the number of data points, \($x_i$\) and \($y_i$\) are the i th values of x and y, respectively, \($\overline{x}$\) and\($\overline{y}$\) are the means of x and y, respectively.

Using the given data, we can calculate:

\(\overline{x} &= \frac{0+1+2+3}{4} = 1.5 \\overline{y} &= \frac{998+1047+1106+1084}{4} = 1058.75\)

\(\sum_{i=1}^{n}(x_i - \overline{x})(y_i - \overline{y}) &= (0-1.5)(998-1058.75) + (1-1.5)(1047-1058.75) \&\quad+ (2-1.5)(1106-1058.75) + (3-1.5)(1084-1058.75) \&= -79.5 \\sum_{i=1}^{n}(x_i - \overline{x})^2 &= (0-1.5)^2 + (1-1.5)^2 + (2-1.5)^2 + (3-1.5)^2 \&= 5 \\end{align*}\)

Therefore, the slope is:

\($\begin{align*}b &= \frac{-79.5}{5} \&= -15.9 \\end{align*}\)

The y-intercept is:

\(\begin{align*}a &= 1058.75 - (-15.9)(1.5) \&= 1081.55 \\end{align*}\)\($\begin{align*}a &= 1058.75 - (-15.9)(1.5) \&= 1081.55 \\end{align*}\)

So the linear regression equation is:

y=−15.9x+1081.6

To find the projected number of new cases for 2008 (which is 8 years after 2000), we substitute x=8 into the equation and round to the nearest whole number:

\($\begin{align*}y &= -15.9(8) + 1081.6 \&= 949.8 \&\approx \boxed{950}\end{align*}\)

Therefore, the projected number of new cases for 2008 is 950.

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Answer:

42 cm²

Explanation:

cut into 2 rectangles

area of rectangle: Length * Width

Answer:

i didnt get it

Step-by-step explanation:

can you explain

Answer:

true

Step-by-step explanation:

if you rewrite \(sec\left(\frac{\pi }{2}\:-x\right)\) with trigonometric identities:

\(sec\left(\frac{\pi }{2}\:-x\right)\)    \(=\frac{1}{\sin \left(x\right)}\)

\(\frac{1}{\sin \left(x\right)}\)  \(=\csc \left(x\right)\)

so, yes,  \(sec\left(\frac{\pi }{2}\:-x\right)\)  \(=\csc \left(x\right)\)

hope this helps!!

Answer:

Step-by-step explanation:

Yes, because the sample is random. If she had chosen the participants in any way other than randomly, it would not be representative of her entire school.

By solving the quadratic equations,

It will take the ball 1 second to reach 18 feet

It will take the ball 1.71 seconds to be at 10 feet

It will take the ball 2.06 seconds to hit the ground

From the question, we are to determine how long it would take the ball to reach 18 feet

To determine how long it would take the ball to reach 18 feet, we will set h = 18 in the equation

The given equation is

h = -16t² + 32t + 2

Put h = 18

18 = -16t² + 32t + 2

Rearrange

16t² - 32t - 2 + 18 = 0

16t² - 32t + 16 = 0

16t² - 16t - 16t + 16 = 0

16t(t - 1) -16(t - 1) = 0

(16t - 16)(t - 1) = 0

16t - 16 = 0 OR t - 1 = 0

16t = 16 OR t = 1

t = 16/16 OR t = 1

t = 1 OR t = 1

Hence,

t = 1 second

Hence, it will take the ball 1 second to reach 18 feet

To determine how long it will take the ball to reach 10 feet, we will set h = 10

h = -16t² + 32t + 2

Put h = 10

10 = -16t² + 32t + 2

Rearrange

16t² - 32t - 2 + 10 = 0

16t² - 32t + 8 = 0

Using the quadratic formula,

t = 0.29 second OR t = 1.71 seconds

The ball will hit the ground when h = 0

Set h = 0 in the equation

h = -16t² + 32t + 2

0 = -16t² + 32t + 2

16t² - 32t - 2 = 0

Using the quadratic formula,

t = -0.06 OR t = 2.06

Since t cannot be negative,

t = 2.06 seconds

Hence, it will take 2.06 seconds for the ball to hit the ground

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Answer:

-81i

Step-by-step explanation:

(-3i)^3(-3)=-81i

Step-by-step explanation:

Larval mosquitoes breath through trachea in their siphons. This is a structure analogous to the snorkel on a diesel electric submarine. It allows for gas exchange with the atmosphere while the remainder of the insect is submerged. The opening of the siphon is hydrophobic so it won’t get wet and blocked by water. This works well to keep the siphon and the trachea open under normal conditions. Oil when poured on water forms a thin film. When there are mosquitos in that water, when their siphons contact the oil layer, the oil wets and blocks their siphons and suffocates the mosquitoes. This works against most, but not all mossies, as evolution is an amazing process. Some mosquitoes (Mansonia, Coquilletidia) have a siphon designed to penetrate the air vessels in aquatic plants and they don’t need to come to the surface to breath like other mossies. So oil won’t work on these genera.

Answer:

6 games on each of the three shelves

Step-by-step explanation:

The total of  22 books minus the 4 books on the top shelf leaves 18 remaining books. You take that 18 and divide by 3 since there are three more shelves. This will leave you with a total of 6 books on each of the other shelves

22 - 4 = 18

18 / 3 = 6

The law firm must carefully consider the potential for both Type I and Type II errors when deciding whether to handle the lawsuit based on the results of their sample.

In the context of this situation, a Type I error would occur if the law firm incorrectly decides to handle the lawsuit based on the sample results, even though the defect rate in the overall population is actually 5 percent or less. This would result in the firm incurring expenses and taking on the case, but ultimately not recovering their costs if the lawsuit is unsuccessful.

A Type II error would occur if the law firm decides not to handle the lawsuit based on the sample results, even though the defect rate in the overall population is actually more than 5 percent. This would result in the firm missing out on potential profits from a successful lawsuit.

A Type I error is also known as a false positive, where the null hypothesis is rejected even though it is actually true. In this case, the null hypothesis would be that the defect rate is 5 percent or less. If the law firm decides to handle the lawsuit based on the sample results and the defect rate in the overall population is actually 5 percent or less, the firm would incur expenses but ultimately not recover their costs if the lawsuit is unsuccessful. Therefore, the consequences of a Type I error for the law firm would be financial loss.

A Type II error is also known as a false negative, where the null hypothesis is accepted even though it is actually false. In this case, the null hypothesis would be that the defect rate is more than 5 percent. If the law firm decides not to handle the lawsuit based on the sample results and the defect rate in the overall population is actually more than 5 percent, the firm would miss out on potential profits from a successful lawsuit. Therefore, the consequences of a Type II error for the law firm would be a missed opportunity to recover potential profits.

Therefore, the law firm must carefully consider the potential for both Type I and Type II errors when deciding whether to handle the lawsuit based on the results of their sample

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Answer:

400 miles

Step-by-step explanation:

Let m be the number of miles.

\(85(2) + .30m = 290\)

\(170 + .30m = 290\)

\(.30m = 120\)

\( m = 400\)

The rate of change of demand with respect to price, D'(p), can be found by taking the derivative of the demand function D(p) = -3p² + 3p + 4.

To find the rate of change of demand with respect to price, we need to take the derivative of the demand function, D(p), with respect to the price variable, p. In this case, the demand function is given as D(p) = -3p² + 3p + 4.

To take the derivative of D(p), we apply the power rule and the sum rule of differentiation. The power rule states that the derivative of pⁿ, where n is a constant, is equal to n*pⁿ⁻¹. Applying the power rule, the derivative of -3p² is -6p, and the derivative of 3p is 3.

Therefore, the derivative of the demand function D(p) is D'(p) = -6p + 3.

D'(p) represents the rate of change of demand with respect to price. It indicates how the demand for the item changes as the price of the item varies. In this case, the derivative -6p + 3 tells us that for each unit increase in price, the demand decreases by 6 units, with an initial increase of 3 units.

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Answer:

= 2.9/ 5.72

= 0.50

Round off to one significant figure.

= 1

Step-by-step explanation:

=2.9/5.72

=0.50

Therefore significant figure = 1

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Answer:

10/21

Step-by-step explanation:

\((-\frac{2}{3})\)\((-\frac{5}{7} )\)

-2·-5=10

3·7=21

10/21

Answer:

10/21

Step-by-step explanation:

hope it helps!

Legend

The term that refers to the labels at the right of the graph indicating how each subcategory is represented is the Legend.

The Legend is a key that indicates what the different colors, lines, or other symbols in a graph represent. It is usually located at the right or bottom of the graph and provides a clear explanation of the different subcategories.

The Legend is an essential component of a graph, as it helps the viewer understand the information presented in the graph. Without the Legend, the graph can be confusing and difficult to interpret. It is important to ensure that the Legend is clear and easy to understand so that the viewer can quickly identify the different subcategories represented in the graph.

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