For the function f ( x ) = 3x² + 3x , evaluate and simplify. f ( x + h ) − f ( x )/ h

Answer:

FH = 35.64

Step-by-step explanation:

(∠A = 360 so the other angle is 40)

By law of cosines,

FH² = AH² + FA² - 2(AH)(FA) * cos(A)

= 30² + 25² - 2(30)(25) * cos(80)

= 900 + 625 - 1500 * 0.17

= 1525 - 255

FH²  = 1270

FH = √1270

FH = 35.64

Answer:

events at A and B are independent because P(A)(B)≠P(A)

Answer:

The final amount they will pay is $74.49

Step-by-step explanation:

59.36(Check)*0.19(19% tip rate)=11.27

59.36+11.27=70.62 Check+Tip

70.62(Check total)*0.055(5.5% tax)=3.87

70.62+3.87=74.49 Total check, tip & tax

Where the above relations are given, note that Options A,  D, and E are the relations that represents a function. The others are just relations.

To distinguish a function from a relation, look to see if any of the x values are repeated; if not, the relationship is a function. If some x values are repeated but the accompanying y values differ, we have a relation rather than a function.

Note that where you are given domain and range, only the range is represented on the x-axis.

Some of the x values may be seen repeated in B, and C.

How is this so?

B) In a coordinate system, values are represented as (x, y). so

In relations, B 2 is repeated twice to in connection with -5, and -6. That is:

(2, -5) , (2, -6)

Since two is x, then its repetition nullified the relation as a function.

C) On table indicated on C, it is much easier to identify the x and y values. As is seen, -3 is repeated twice in connection with 4 and 2. Thus, its repetition nullified the relation as a function.

As a result, Options A,  D, and E are the relations that represent a function.

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Answer:

1584

Step-by-step explanation:

1.584 x 1000 = 1584

Both Arthur and DW will have the same amount of money saved after 8 weeks. Option D is the correct answer.

A function is a mathematical rule that gives each input value a distinct output value. A function may be used to simulate a wide range of phenomena in many different domains, including science, engineering, economics, and social sciences. A function can be represented by an equation, a graph, or a table.

Mathematicians use functions to describe how variables relate to one another, to solve problems, to make predictions, and to evaluate data. They may be used to examine the qualities and behaviour of several quantities, including distance, time, speed, temperature, and cost.

Given that the equations of Aurthur and DW is:

f(x) = 10x + 5

g(x) = 7.5x + 25

For the same amount of money saved we can equate the two functions:

10x + 5 = 7.5x + 25

2.5x = 20

x = 8

Therefore, both Arthur and DW will have the same amount of money saved after 8 weeks.

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After 8 weeks, both Arthur and DW will have the same amount of money saved.

What is a function?

In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range. In simpler terms, a function is a set of rules that takes an input value and produces a corresponding output value.

To find the week when Arthur and DW have the same amount of money saved, we need to solve the equation 10x+5=7.5x+25, where x is the number of weeks. Simplifying the equation, we get 2.5x=20, which gives x=8. Therefore, after 8 weeks, both Arthur and DW will have the same amount of money saved.

So the answer is (D) 8 weeks.

To determine the rate of increase for each of the savings accounts, we look at the coefficients of x in each function. The rate of increase for Arthur's savings is 10, and the rate of increase for DW's savings is 7.5.

So the correct answers are (B) 10 and (C) 7.5.

The rate of change of Arthur and DW's functions refers to how much the savings increase or decrease concerning the number of weeks.

So the correct answer is (D) the amount of money saved per week.

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The correct two - way frequency table for the data on High School Students, and the kind of band they want to play at the school dance, is:

                                                     Rap          Rock           Country      Total

Grades 9 - 10                                40              30                55              125

Grades 11 - 12                                60              25                35              120

Total                                              100              55                90             245

Option A is therefore correct.

In a two-way frequency table, there will be totals for both the rows and the columns.

The totals for the rows in this instance are:

Grade 9 - 10 totals :

= 40 + 30 + 55

= 125

Grade 11 - 12 :

= 60 + 25 + 35

= 120

The totals for the columns are:

Rap totals :

= 40 + 60

= 100

Rock :

= 30 + 25

= 55

Country :
= 55 + 35

= 90

Two-way frequency tables allow for us to be able to conclude on the event described by looking at totals from both the columns and the rows. This gives a clearly understanding on preferences and categories.

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We need to know about percentage to solve the given problem. The amount of money that Kelly has in dollars is approximately $24.

Percentage is a number or ratio expressed as a ratio or fraction of 100. If for example we have to find out one-fourth of a quantity then we can say that we need to find 25% of the quantity. In the given question we know that Maria has $40 which is 170% of the money that Kelly has, we need to find out the amount of money that Kelly has.

170/100x a=40

a=40x100/170=23.5

Therefore the amount that Kelly has in dollars is $23.5 approximately $24.

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9514 1404 393

Answer:

  270 miles

Step-by-step explanation:

For h hours of driving the distance d is covered:

  h = 2 +d/54

Solving for d, we find the distance covered in h hours is ...

  d = 54(h -2)

In 7 hours, the distance they traveled is ...

  d = 54(7 -2) = 270 . . . miles

They traveled 270 miles on the first day.

Based on the standard deviation, the region with more consistent rainfall totals over the course of a year is the eastern region, the correct choice is A.

To calculate the standard deviation, we need to find the average of each region's rainfall totals and then find the difference between each individual rainfall total and the mean, square those differences, add them up, divide by the number of data points, and then take the square root.

The average monthly rainfall for the eastern region is (0.1+1.6+1.6+3.8+4.1+4.2+9.2+6.8+6.1+6.1+5.6+4.8) ÷ 12 = 4.25 inches.

The standard deviation for the eastern region is 2.405 inches.

The average monthly rainfall for the western region is (0.9+1.2+2.6+4.2+4.6+6.0+9.4+9.4+8.1+7.5+7.1+6.7) ÷ 12 = 5.6167 inches.

The standard deviation for the western region is 2.4044 inches.

Since the standard deviation for the eastern region is smaller than the standard deviation for the western region, the eastern region has more consistent rainfall totals over the course of a year.

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*check attachment for the correct figure given in this question with the right labelled angles

Answer:

\( x = 86, y = 67, z = 94 \)

Step-by-step explanation:

From the given figure attached below, values of x, y, and z can be found as follow:

Value of x:

\( x = 180 - (38 + 56) \) => sum of angles in a triangle

\( x = 180 - 94 \)

\(x = 86\)

Value of z:

\( z = 180 - 86 \) => angles on a straight line

\(z = 94\)

Value of y:

\( y = 180 - (19 + 94) \) => sum of angles in a triangle.

\( y = 180 - 113 \)

\(y = 67\)

\( x = 86, y = 67, z = 94 \)

Answer:

3(n-9)-2(n+4)=6n

3n-27-2n-8=6n

n-35=6n

-35=5n

n= -7

Step-by-step explanation:

3(n-9)-2(n+4)=6n

open the brackets by multiplication

3n-27-2n-8= 6n

n-35=6n

n=-7

so when we add to the function outside of the parentheses of (x)^3, we are moving the graph in the up down direction so it would look like x^3 but shifted up 2 units. the way to easily know which one it is, plug in zero for x in the original and 0^3 is zero so we know the original fuction will go through the origin so the function who's center is is only shifted up (because it's positive 2) two units so graph 1

note: the reason i know that what looks like a center point is actually at the origin is because f(x)= x^3 is a very famous graph that you should know the shape of :)

Answer:

See attached image

Step-by-step explanation:

Attached

Use the chain rule to compute the second derivative:

\(f(x)=\ln(\sin(2x))\)

The first derivative is

\(f'(x)=(\ln(\sin(2x)))'=\dfrac{(\sin(2x))'}{\sin(2x)}=\dfrac{\cos(2x)(2x)'}{\sin(2x)}=\dfrac{2\cos(2x)}{\sin(2x)}\)

\(f'(x)=2\cot(2x)\)

Then the second derivative is

\(f''(x)=(2\cot(2x))'=-2\csc^2(2x)(2x)'\)

\(f''(x)=-4\csc^2(2x)\)

Then plug in π/4 for x :

\(f''\left(\dfrac\pi4\right)=-4\csc^2\left(\dfrac{2\pi}4\right)=-4\)

Answer:

rectangle- 2 lines of reflection

trapezoid- 0 lines of reflection

regular pentagon- 5 lines of reflection

square- 4 lines of reflection

Step-by-step explanation:

Answer:

  1/60 gallon

Step-by-step explanation:

You want to know what is left of 4/5 gallon of paint if 3/4 gallon was used to paint a doghouse, and 2/3 of the remaining amount was used to paint a door.

To find the amount remaining we subtract the amount used for the doghouse from the original amount:

  4/5 -3/4 = (16 -15)/20 = 1/20 . . . . . gallon

2/3 of that was used, so 1/3 of it remains:

  (1/3)(1/20 gallon) = 1/60 gallon

There is 1/60 of a gallon of paint left in the can.

__

Additional comment

In a standard size gallon paint can, that's about 0.11 inches of paint in the bottom.

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The distance to second base is approximately 127.28 feet. Round to the nearest hundredth

Since the angle is 45 degrees, the other side of the right triangle are equal, hence we have two sides of 90 ft to be used to find the hypotenuse

Using Pythagoras theorem given by the  the formula

hypotenuse² = opposite² + adjacent²

plugging the values as in the problem

let x be the required distance

x² = 90² + 90²

x² = 16200

x = √16200

x = 90√2

x = 127.28 ft (to the nearest hundredth)

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Answer:

if 8 equal parts then we have 16 parts

O is at zero

16 as at 2

and

29 is away from 2 between 3 and 4

We know this as 16 + 16 is 32 which is 4

count 3/8 between 4 and 3  and when counting 3/8 back we get 29.

Step-by-step explanation:

If 29 meant to be 2/9 then we are still at 2/8 and show the second part 0-1

if 16 was meant to be 1/6 then we know 1/6 is still closer to 1/8 and we show the first divided equal part 1/8

Zero stays 0

Answer: 39.7

Step-by-step explanation:18/55 = 13/x you can get x by solving for it.

Answer:

3 1/4 hours = 3 + 1/4 = 3 + 0.25 = 3.25. 2 1/2 hours = 2 + 1/2 = 2.5. To find out how much travel time can be saved by taking the express, simply subtract its travel time (which is shorter) from the regular's one. So 3.25 - 2.5 = 0.75 or 3/4.

so the answer is a

Answer:

The 80% confidence interval for the mean number of seeds for the species is of 50.848 seeds.

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

T interval

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 18 - 1 = 17

80% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 17 degrees of freedom(y-axis) and a confidence level(as we want the one-sided upper-bound confidence interval) of \(1 - \frac{1 - 0.8} = 0.8\). So we have T = 0.863

The margin of error is:

\(M = T\frac{s}{\sqrt{n}} = 0.863\frac{14}{\sqrt{18}} = 2.848\)

In which s is the standard deviation of the sample and n is the size of the sample.

The upper end of the interval is the sample mean added to M. So it is 48 + 2.848 = 50.848 seeds.

The 80% confidence interval for the mean number of seeds for the species is of 50.848 seeds.

When the former image is rotated, the dots will be located at section 2 and 7.

When an image is rotated, the constituents within it also changes its position as the object is moves from a point to another about a pivot junction.

From the given image above, after the rotation of the initial image, the dot should be located at number 2 and 7 of the new image.

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Answer:

C=20

Step-by-step explanation:

1. 25÷5=5

2. 5×4=20

I hope this helped☺

Using an algebraic equation to represent the word problem, the smallest integer is 1

This is a way of representing mathematical problems with words. To solve this, we have to use algebraic equations or expressions.

Let the integers be represented as

We can write an equation from the word problem given as

7 × (x + 2) = 15 + [x + (x + 4)]

7x + 14 = 15 + x + x + 4

7x + 14 = 15 + 2x + 4

collect like terms

7x - 2x = 15 - 14 + 4

5x = 5

Divide both sides by coefficient of x

5x / 5  = 5 / 5

x = 1

The smallest integer is 1

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Translation:

Find the smallest of three consecutive odd integers such that 7 times the middle integer is 15 more than the sum of the first and third integers

Answer: y = 4/3x -8

Step-by-step explanation:

(6,0) (0,-8)

0-(-8)/6-0 = 8/6 = 4/3

y intercept is given already

Answer:

7)  Domain:  (-∞, ∞)

    Range:  [-1, ∞)

8)  Domain:  (-∞, ∞)

    Range:  (-∞, ∞)

Step-by-step explanation:

Interval notation

( or ) : Use parentheses to indicate that the endpoint is excluded.

[ or ] : Use square brackets to indicate that the endpoint is included.

Domain & Range

The domain is the set of all possible input values (x-values).

The range is the set of all possible output values (y-values).

From inspection of the graph, the line is continuous.

The arrows either end of the line indicate that the line continues indefinitely in those directions.

Therefore, the domain of the relation is unrestricted:  (-∞, ∞)

From inspection of the graph, the minimum y-value is y = -1.  

The end behavior of the relation is:

\(y \rightarrow + \infty, \textsf{as } x \rightarrow - \infty\)

\(y \rightarrow + \infty, \textsf{as } x \rightarrow +\infty\)

Therefore, the range of the relation is restricted:  [-1, ∞)

From inspection of the graph, the line is continuous.

The arrows either end of the line indicate that the line continues indefinitely in those directions.

Therefore, the domain of the relation is unrestricted:  (-∞, ∞)

The end behavior of the function is:

\(y \rightarrow + \infty, \textsf{as } x \rightarrow - \infty\)

\(y \rightarrow -\infty, \textsf{as } x \rightarrow +\infty\)

Therefore, the domain of the relation is unrestricted:  (-∞, ∞)

The equation of the line that is parallel to the line that passes through the point (7, 6) is y = 8x - 50.

A line is an object in geometry that is indefinitely long and has neither breadth nor depth nor curvature.

Since lines can exist embedded in two, three, or higher dimensions environments, they are one-dimensional objects.

The term "line" can also be used to describe a line segment in daily life that contains two locations that serve as its ends.

So, the lines with the same slope but a different y-intercept are said to be parallel.

Therefore, we must use the same slope to plug in the point (7, 6) and solve for the y-intercept.

We thus have:

y = 8x + b

6 = 8(7) + b

6 = 56 + b

b + 56 = 6

b + 56 - 56 = 6 - 56

b = -50

The equation is: y = 8x - 50

Therefore, the equation of the line that is parallel to the line that passes through the point (7, 6) is y = 8x - 50.

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Correct question:

Consider the line y = 8x - 4. Find the equation of the line that is parallel to this line and passes through the point (7, 6).

The z-score of a person who scored 330 on the exam is approximately 2.7.

To find the z-score of a person who scored 330 on the exam, we can use the formula for calculating the z-score:

z = (x - μ) / σ

where:

z is the z-score

x is the raw score (330 in this case)

μ is the mean (195 in this case)

σ is the standard deviation (50 in this case)

Substituting the values into the formula, we get:

z = (330 - 195) / 50

z = 135 / 50

z = 2.7

The z-score of a person who scored 330 on the exam is 2.7.

The z-score measures the number of standard deviations a particular data point is away from the mean.

In this case, a z-score of 2.7 indicates that the person's score of 330 is 2.7 standard deviations above the mean score of 195.

The z-score is useful for comparing data points across different normal distributions or for determining the relative position of a data point within a distribution.

A positive z-score indicates a value above the mean, while a negative z-score indicates a value below the mean.

In this context, a z-score of 2.7 suggests that the person's score is relatively high compared to the average performance on the exam.

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