(a) Given that f(x) = 2x + 1, find the nearest whole number of f(2.99), f(2.999) f(3.01), f(3.001). What conclusion can you draw from these results?​

Answer:

What is scenario 6-9?

Step-by-step explanation:

The rate of change of the plot is 2

The initial value the line joining points is 3

The rate of change between 2 points is defined as the change of y cordinate with respect to change of x cordinate

rate of change = slope of line =  Δy/ Δx =[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

point a(0,3) is the initial point and point b(2,7) is the 2nd point

so [tex](x_1,y_1)[/tex] = (0,3) and [tex](x_2, y_2)[/tex] = (2,7)

rate of change  = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

=> (7-3)/(2-0)

=>4/2

so rate of change = 2

Initial value is the y intercept of the line i.e is we write an equation of the line the value of y when x=0 is the inital value

so at point a (0,3)  value of x=0 and at that time value of y=3

and hence initial value = 3

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If MX, MY, sX, and sY are known, the additional number that would be the most helpful to know for calculating the regression line for X and Y is r.

In the context of simple linear regression, r means the correlation between the predictor variable, x, and the response variable, y. And r² means the proportion of the variance in the response variable which can be explained by the predictor variable in the regression model.

It is also considered as denotation of the Pearson correlation coefficient, that is a measure of any linear trend between two variables. The value of r ranges between −1 and 1. When r = zero, it means that there is no linear association between the variables.

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This article would be best suited to a text structure of Problem and Solution.

Research on the development of literacy during the previous two decades has revealed:

A literary device that introduces a problem in the first paragraph and section before moving on to how to solve it in the following paragraph or section.

Example:

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Answer:

£9.40

Step-by-step explanation:

Given variables:

Defined variables:

1 pound = 100 pence  ⇒  1 pence = 0.01 pounds

Therefore, the equation that models the given scenario is:

[tex]y = 0.01px +f[/tex]

Given:

Substitute the given information into the equation to create two equations:

[tex]\implies f+0.01(4)p=5.40[/tex]

[tex]\implies f+0.01(7)p=7.80[/tex]

Therefore:

[tex]\implies f+0.04p=5.40[/tex]

[tex]\implies f+0.07p=7.80[/tex]

Subtract the first equation from the second to eliminate f:

[tex]\implies 0.03p=2.40[/tex]

Solve for p:

[tex]\implies \dfrac{0.03p}{0.03}=\dfrac{2.40}{0.03}[/tex]

[tex]\implies p=80[/tex]

Substitute the found value of p into one of the equations and solve for f:

[tex]\implies f+0.04(80)=5.40[/tex]

[tex]\implies f+3.20=5.40[/tex]

[tex]\implies f=2.20[/tex]

Substitute the found values of p and f into the equation to create an equation for the cost of x miles:

[tex]\implies y=0.8x+2.2[/tex]

To find the cost of a 9-mile journey, substitute x = 9 into the found equation:

[tex]\implies 0.8(9)+2.2=9.40[/tex]

Therefore, the cost of a 9-mile journey is £9.40.

The average rate of change of the number of chevy car sales from 1990 to 1992 is 1

What is the average change rate?

The average rate of change is the rate at which one value in a function changes in relation to another. Usually, the average rate of change is used to calculate the slope of a graphed function.

The average rate of change of a function is determined by the slope of the line connecting the two endpoints of a specific interval (known as the secant line).

According to the given question:

The average rate of change of the number of chevy car sales from 1990 to 1992 is (total chevy car sold in 1992- total chevy car sold in 1990)/ Total difference in no. of years

That gives (156-154)/2

So, the average rate of change of the number of chevy car sales from 1990 to 1992 is 1

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Answer: 300 miles

Step-by-step explanation:

Let x be the number of miles

We have the equation below

20 + 0.35x = 35 + 0.30x

Subtract 20 from both sides

0.35x = 15 + 0.30x

Then subtract 0.30x from both sides

0.05x = 15

Then divide by 0.05 from both sides

x = 300 miles

Answer:

The relationship between the number of gems and the number of chests can be represented by an equation in the form of g = kc, where g is the number of gems, c is the number of chests, and k is a constant.

To find the value of the constant k, we can substitute the values from one of the adventures into the equation and solve for k. For example, using the values from Adventure A:

g = 600

c = 2

Substituting these values into the equation, we get:

600 = k * 2

Solving for k, we get:

k = 600 / 2 = 300

Therefore, the equation that describes the relationship between the number of gems and the number of chests is:

g = 300c

Using the information provided in the table, we know that for Adventure B, Lulu received 1500 gems and needed 5 chests to hold them. Substituting these values into the equation, we get:

g = 1500

c = 5

Substituting these values into the equation g = 300c, we get:

1500 = 300 * 5

This equation can be used to determine the number of chests needed to hold a given number of gems, or vice versa. For example, to find the number of chests needed to hold 1200 gems, we can substitute 1200 for g and solve for c:

g = 1200

c = 1200 / 300 = 4

Thus, 4 chests would be needed to hold 1200 gems.

Answer: P(WY)=1/10*2/9=1/45

P(YW)=2/10*1/9=1/45

P(WY or YW)=2/45

Also 2C1*1C1/10C2=2×1/45=2/45

2/5

Step-by-step explanation:

Answer:

7.5 joules

Step-by-step explanation:

The amount of work done on an object is equal to the force applied to the object times the distance over which the force is applied. In this case, the force applied to the box is 5 newtons and the distance over which the force is applied is 1.5 meters.

The amount of work done on the box is therefore 5 newtons * 1.5 meters = 7.5 joules. This is the amount of energy that has been transferred to or from the box as a result of the force applied to it.

Answer:

A. Eight-four percent of 6th grade girls surveyed prefer cereal A

Step-by-step explanation:

Out of 100 6th grade students, 50 were girls and 50 were boys.

42% of the 100 students i. e. 42 were girls who preferred cereal A

Percentage of girls who liked cereal A = (42/50)x100%

= 84%

Answer:

A

Step-by-step explanation:

42% of entire 6th grade girls were surveyed

it means that 84% of ONLY the 6th grade girls liked Cereal A

Answer:

63

Step-by-step explanation:

using the ratio

[tex] \frac{4}{1} = \frac{252}{x} [/tex]

cross multiply

[tex]4x = 252[/tex]

divide both sides by (4)

[tex] \frac{4x}{4} = \frac{252}{4} [/tex]

x = 63

i hope this helps

The correct answer is x = 63

[tex]\boxed{\frac{4}{1}=\frac{252}{x}4x=252\frac{4x}{4} =\frac{252}{4}x=63 }\\\huge\boxed{\underline_ So, \frac{4}{1}=\frac{252}{\bold{63}} }[/tex]

Therefore, the correct answer is x = 63

Answer:

130 ft

Step-by-step explanation:

The distance across the canyon is 130 feet.

When Christian moved 100 feet from the tree on his side, the angle formed by the tree on his side and the tree on the other side was 70°. This means that the distance across the canyon is the length of the opposite side of the right triangle formed by Christian's position, the tree on his side, and the tree on the other side.

To find the length of the opposite side of the triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In this case, the hypotenuse is the distance across the canyon, and the other two sides are 100 feet and the length of the opposite side of the triangle.

We can write this as an equation: (distance across the canyon)^2 = (100 feet)^2 + (opposite side of the triangle)^2.

To solve for the distance across the canyon, we can take the square root of both sides of the equation: distance across the canyon = √((100 feet)^2 + (opposite side of the triangle)^2).

Since the length of the opposite side of the triangle is equal to the length of the adjacent side (100 feet) divided by the tangent of the angle formed by the tree on his side and the tree on the other side, we can substitute this value into the equation above: distance across the canyon = √((100 feet)^2 + (100 feet / tan 70°)^2).

To calculate the value of tan 70°, we can use a calculator or look up the value in a table of trigonometric functions. The value of tan 70° is approximately 1.73. We can substitute this value into the equation above to get: distance across the canyon = √((100 feet)^2 + (100 feet / 1.73)^2).

We can now use a calculator to evaluate this expression and find the distance across the canyon. When we do this, we get: distance across the canyon = √((100 feet)^2 + (100 feet / 1.73)^2) ≈ 130 feet.

Therefore, the distance across the canyon is approximately 130 feet.

The exact value of the minimum of function  f(x) = x^2 e^−x for x ≥ 0 is f(x) = 0

In this question we have been given a function  f(x) = x^2 e^−x

We need to find the exact value of the minimum of function for x ≥ 0.

Consider the first derivative of the function

f'(x) = x^2 f/dx(e^−x) + e^−xd/dx(x^2)

f'(x) = -x^2 e^(-x) + e^-x (2x)

f'(x) = xe^-x (2 - x)

To find the critical points., consider f'(x) = 0

xe^-x (2 - x) = 0

xe^-x = 0,   (2 - x) = 0

x = 0, x = 2

Substitute the value of critical point into the function.

f(0) =  0^2 e^(0)

f(0) = 0

and f(2) =  2^2 e^-2

f(2) = 0.5413

This means, the minimum of the function occurs at x = 0

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Yes, the instructor should use linear regression to predict exam scores for a student who studied 10 hours for the final.

A variable's value can be predicted using linear regression analysis based on the value of another variable. The dependent variable is the one you want to be able to forecast. The independent variable is the one you're using to make a prediction about the value of the other variable.

Nonlinear regression uses a curve to associate the variables, whereas linear regression uses a straight line.

If a clear linear relationship can be shown on the scatterplot, linear regression may be useful. The use of linear regression is appropriate because there is a high correlation. So, it is concluded that it is beneficial for instructor to use linear regression.

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The solution to the system of equation is x = -12 and y = 3.

System of equation can be solved using different method such as elimination method, graphical method and substitution method,

Therefore, let's solve the system of equation by using substitution method.

1 / 2 x + 6y = 12

y = x + 15

substitute the value of y in equation(i)

1 / 2 x + 6(x + 15) = 12

1 / 2 x + 6x + 90 = 12

6 1 / 2 x = 12 - 90

13 / 2 x  = - 78

cross multiply

13x = -78 × 2

13x = -156

divide both sides by 13

x = -156 / 13

x = - 12

Let's find the value of y.

y = -12 + 15

y = 3

Therefore,

x = -12

y = 3

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Answer:

360 cm³

Step-by-step explanation:

height of bottom layer = 7 - 2 = 5cm

Volume = 9 · 8 · 5 = 360 cm³

The parameters for the exponential function are given as follows:

Hence the exponential function that gives the value of the book in t years after 2010 is of:

V(t) = 500(1.18)^t.

2017 is 7 years after 2010, hence the value is calculated as follows:

V(7) = 500 x (1.18)^7 = $1,592.74.

First we obtain the rate of change, dividing consecutive entries of the table, as follows:

b = 62.99/34.99 = 1.8.

Thus the function is defined as follows:

f(x) = a(1.8)^x.

When x = 3, f(x) = 34.99, hence the intercept a is calculated as follows:

34.99 = a(1.8)³

a = 34.99/(1.8)³

a = 6.

Then the function is:

f(x) = 6(1.8)^x.

Taking 2016 as the reference year, the initial value is of:

a = 80.

Then the growth rate is of:

b = 132/80.

b = 1.65.

Then the function for the amount in x years after 2016 is of:

f(x) = 80(1.65)^x.

2023 is 7 years after 2016, hence the estimate is given as follows:

f(7) = 80 x (1.65)^7 = 2664 people.

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It is proved that the difference between squares of consecutive even numbers is always a multiple of 4.

Let's consider two consecutive even numbers.

If n = a positive integer

Then the 1st even number would be = 2n

Let the next consecutive even number = 2(n+1)

The consecutive even numbers would be:

2n, 2(n+1)

The square of each consecutive even number is given by -

(2n)² = 2n ×2n = 4n²

[2(n+1)]² = (2n+2)² =(2n+2)(2n+2)

Expanding, we get,

= 4n² +4n +4n+4

[2(n+1)]² = 4n²+8n+4

To determine if the difference between squares of consecutive even numbers is always a multiple of 4, we would substitute values for ' n ' to find the differences between the squares of each consecutive even number.

Let n = 1, 2, 3

For n= 1,

4n² = 4(1)² = 4×1 = 4

4n²+8n+4 = 4(1)² + 8(1) + 4

= 4+8+4 = 16

Thus, the difference between the squares of consecutive even numbers = 16-4 = 12

For n= 2,

4n² = 4(2)² = 4×4 = 16

4n²+8n+4 = 4(2)² + 8(2) + 4

= 16+16+4 = 36

Thus, the difference between the squares of consecutive even numbers = 36-16 = 20

For n= 3

4n² = 4(3)² = 4×9 = 36

4n²+8n+4 = 4(3)² + 8(3) + 4

= 36+24+4 = 64

Thus, the difference between the squares of consecutive even numbers = 64-36 = 28

Clearly, we can see that 12, 20, and 28 are multiples of 4.

Therefore, the difference between squares of consecutive even numbers is always a multiple of 4.

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The angle of elevation of the sun to the nearest hundredth of a degree is 66.83°.

Since we are giving with the height of the building which is 34.98 feet and the length of the shadow which is 38.85 feet long. , so we can use the trigonometric ratios, where we  know that about tan, that is:

angle = arctan (length of the shadow/height of the building )

=>angle = arctan (38.85/34.98)

=> angle = arctan (1.1056)  

=> angle = 66.83°

so,it is the angle of elevation of the sun.

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Answer:

B.  X = 8 degree

Step-by-step explanation:

8x - 4 = 60 degree

8x = 64 degree

x = 8 degree

So, the answer is B

Answer:

x = 8°

Step-by-step explanation:

The angle that say 60° and the angle that says 8x -4 ARE BOTH EQUAL.

They are called Alternate Interior Angles

Let's write an equation to represent this relationship, then we solve it to find x

8x - 4 = 60

SOLVE

8x = 60 + 4

8x = 64

x = 64 / 8

x = 8 °

940 is the initial value, to the closest hundredth, after 30 minutes when amount that starts out at 800 increases exponentially at a rate of 5.5% every 10 minutes.

Given that,

An amount that starts out at 800 increases exponentially at a rate of 5.5% every 10 minutes.

We have to find what is the quantity's value, to the closest hundredth, after 30 minutes.

We know that,

Formula is

S=a(r+1)ⁿ

Here,

S is initial value

a is 800

r is 5.5%

n is time 30/10

800×(5.5%+1[tex])^{30\div10}[/tex]

=939.3931

Therefore, 940 is the quantity's value, to the closest hundredth, after 30 minutes when amount that starts out at 800 increases exponentially at a rate of 5.5% every 10 minutes.

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Answer:

939.39

Step-by-step explanation:

Answer:

3m

Step-by-step explanation:

hope this helps :D

to see the overall long-term tendency of the series, we should set large weight w in exponential smoothing is True statement.

Exponential smoothing is a technique used to smooth out data to uncover trends and make predictions. When setting the weight (w) for exponential smoothing, a large w will result in a longer-term trend being captured by the smoothing. This is because a larger w will give more weight to the older data points, and thus the overall long-term tendency of the series will be more visible. Therefore, it is true that setting a large weight w in exponential smoothing will help to see the overall long-term tendency of the series.

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Answer:

Erik's chips are a better buy by 10 cents per ounce

Step-by-step explanation:

Erik's chips cost by ounce: $0.32

Al's chips cost by ounce: $0.42

This means the Eriks chips are better to buy

Second one:

Answer: 1.26

Step-by-step explanation:

Since he bought a 18 gallon tank of gas with regular fuel for 55.08.

The station across the street sold regular fuel for 2.99 per gallon. A 18 gallon tank will cost:

= 18 × 2.99

= 53.82

The amount that could have been saved would be:

= 55.08 - 53.82

= 1.26

4 quarts in a gallon, 8 quarts in 2 gallons, so 32.40 divided by 8 is $4.05..

each quart cost 4 dollars and 5 cents

Step-by-step explanation:

The price per quart will be $4.05.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

It should be noted that 4 quarts are in a gallon. Therefore, since the 2-gallon container of laundry detergent costs $22.00. The price per quart will be:

= $22.00 / (4 × 2)

= $4.05

The price is $4.05.

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Answer:

Step-by-step explanation:

To write a linear function for a given set of points, we can use the slope-intercept form of the equation, which has the form f(x) = mx + b. The coefficient m is the slope of the line and the constant b is the y-intercept, where the line crosses the y-axis.

To find the slope m of the line, we can use the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are any two points on the line. For example, we can use the points (-2, -6) and (-1, -2.5) to find the slope:

m = (y2 - y1) / (x2 - x1) = (-2.5 - (-6)) / (-1 - (-2)) = 3.5 / 1 = 3.5

Now that we know the slope, we can use any of the given points to find the y-intercept b. For example, we can use the point (0, 1):

f(x) = mx + b

1 = 3.5 * 0 + b

b = 1

Therefore, the linear function that passes through the given points is:
f(x) = 3.5x + 1

Note that we could also have used any of the other points to find the y-intercept, and we would have arrived at the same result.

By using multiplication and division, it can be calculated that-

The multiple according to the number 3 = 162

The submultiple according to the number 7 = 7

What is multiplication and division?

Repeated addition is called multiplication. Multiplication is used to find the product of two or more numbers.

Division is the process in which a value of single unit can be calculated from the value of multiple unit.

The number to be divided is called dividend. The  number by which dividend is divided is the divisor. The result obtained is called quotient and the remaining part is the remainder.

This is a problem of multiplication and division.

One segment measures 161 cm

So, to find the multiple according to the number 3, we have to divide 161 by 3

161 [tex]\div[/tex] 3 = 53.67

Nearest integer of 53.67 is 54

The multiple according to the number 3 = 54 [tex]\times[/tex] 3 = 162

To find the submultiple according to the number 7, we have to divide 161 by 7

161 [tex]\div[/tex] 7 = 23

Nearest integer of 23 is 23

The submultiple according to the number 7 = 161 [tex]\div[/tex] 23 = 7

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Answer:

So the answer is A and D

Step-by-step explanation:

I think it is A and D cause it is 3 and -3 its a bigger number and smaller number

A) The value of h, h = 2r.

The height of the can is two times of the radius.

B) The formula for the Can Area is  4πr².

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

For a can with radius r and height h, this goal is reached when

2 πr³= πr²h

a) 2 πr³= πr²h

Solve for 'h'

h= 2 πr³ / πr²

h = 2r

So, the height of the can is two times of the radius.

b) Now, The area of a label for a can is A=2 πrh.

So, putting h= 2r

Area, A = 2 πrh

            = 2πr(2r)

            = 4πr²

So, the formula for the Can Area is  4πr².

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