Graph they given functions FNG in the same rectangular coordinate system describe the graph of G is related to the graph of F

m∠C = (16x - 7 )° because ∠A ≅ ∠C

When two angles add up to 180 degrees, they are referred to as supplementary angles because they combine to make a linear angle. The opposite is true if the total of two angles is 90 degrees; in this case, they are considered to be complementary angles and together they create a right angle.

When two angles sum up to 180 degrees, they are referred to as supplementary angles in geometry. A and B are referred to as supplementary angles, for instance, if A + B = 180°. When supplementary angles are combined, they always create a straight angle (180 degrees).

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Answer: $25.44

Step-by-step explanation:

Multiply 24 by 0.06.

You get 1.44

Add 1.44 + 24 = 25.44

Given the equation of the function:

The graph of the function will be as shown in the following picture:

As shown in the figure:

The amplitude = 1

The period = 2π

The phase shift = π/4

Answer:

volume=27 multiply 3 =81

Answer:

13x - 2

Step-by-step explanation:

First Were going to do the distributive property:

So, 4(3x) + 4(-6) = 12x + -24

Now we have :

12x - 24 + x + 22

Now we have to add like terms together:

So, 12x + x = 13x

and 22-24 = -2

So in the end we have 13x -2

The equation of a direct proportion is A. y=8x.

It should be noted that a direct proportion is also a direct variation. It is one when the relation between the two quantities have a value that's constant.

In this case, it's illustrated as y = 8x.

Let's say x = 1 y will be = (8 × 1) = 8

When x = 2, y = (8 × 2) = 16

In this case, it should be noted that the constant of 8 is illustrated.

In conclusion, the correct option is A.

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From the given inequality graph

6. The solution shown by the graph is

7. The solution shown by the graph is

8.

The graph of k ≤ -1 is

The graph of k > 4 is

The graph of k ≤ -1, or, k > 4 is

1) Given that rule, we can write out the following for this case:

2) So let's plug into that the data:

Note that we have cross multiplied and then divided both sides by 8. So the dosage of an adult, according to this rule would be 15 ml

In this case, x represents the amount that has increased year after year.

The monetary value of an asset or service is the amount that would be paid in cash if it were sold to a third party. Tangible property, intangible property, labor, and commodities, for example, are priced at their monetary value.

Given,

Belinda wishes to invest $1,000. The table below shows the value of her investment for three different years under two different scenarios:

The number of years is 1 2 3

Option 1 (dollar amount) 1100 1200 1300

Option 2 (dollar amount) 1100 1210 1331

Part A: Using options 1 and 2, linear and exponential functions can be used to describe the value of an investment after a set number of years.

In the case of Option 1, the linear function can be used to describe the investment's value after a set number of years. This is due to the fact that in Option One, the amount increases by a fixed amount each year.

In the case of option 2, the exponential function can be used to calculate the value of the investment after a specified number of years. This is because the amount increase in Option 2 is greater than last year.

Part B: (n=n+100) and (n=n+100x) are functions for each option that describe the monetary value of the investment f(n) after n years.

Option 1's function is n = n + 100.

Option 2's function is n = n + 100 x.

In this case, x represents the amount that has increased year after year.

Part C: Yes, the value of Belinda's investment after 20 years will differ by 1900 if she chooses Option 2 over Option 1.

After 20 years, the option 1 amount would be 3000, and the option 2 amount would be 4900. As a result, there is a difference of 1900.

The complete question is:

Belinda wants to invest $1,000. The table below shows the value of her investment under two different options for three different years:

Number of years 1 2 3

Option 1 (amount in dollars) 1100 1200 1300

Option 2 (amount in dollars) 1100 1210 1331

Part A: What type of function, linear or exponential, can be used to describe the value of the investment after a fixed number of years using option 1 and option 2? Explain your answer. (2 points)

Part B: Write one function for each option to describe the value of the investment f(n), in dollars, after n years. (4 points)

Part C: Belinda wants to invest in an option that would help to increase her investment value by the greatest amount in 20 years. Will there be any significant difference in the value of Belinda's investment after 20 years if she uses option 2 over option 1? Explain your answer, and show the investment value after 20 years for each option. (4 points)

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The inequality is c-7≥-30. The c value we get has inequality c≥-23.

Given that,

The inequality is c-7≥-30.

We have to solve the inequality c.

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. When two values are not equal, we typically use the "not equal symbol (≠)". However, a number of inequalities are used to compare the numbers and determine whether one is greater than the other.

When the symbols  “>”, “<”, “≥”, “≤” are used to connect two real numbers or algebraic expressions, the relationship is referred to as an inequality.

Take the inequality,

c-7≥-30

c≥-30+7

c≥-23

Therefore, The c value we get has c≥-23.

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The binary connective of implication ⇒ is defined as (A ⇒ B) ⇔ ((¬ A) ∨ B). It can be read « A implies B », « A is a sufficient condition for B », or « B is a necessary condition for A ».

What is connective?

Connective is function, or the symbol representing a function, which corresponds to English conjunctions such as "and," "or," "not," etc. that takes one or more truth values as input and returns a single truth value as output.

What is logical connective?

A Logical Connective is a symbol which is used to connect two or more propositional or predicate logics in such a manner that resultant logic depends only on the input logics and the meaning of the connective used.

Generally there are five connectives which are −

OR (∨)

AND (∧)

Negation/ NOT (¬)

Implication / if-then (→)

If and only if (⇔).

connective of implication ⇒ is defined as (A ⇒ B) ⇔ ((¬ A) ∨ B).

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Answer:

students that are in middle school

Step-by-step explanation:

i took the test and got it correct.

The category with the greatest marginal frequency is students who chose playing sports. The correct option is C.

There are 16 students who chose playing sports in middle school and 11 students who chose playing sports in high school, for a total of 27 students who chose playing sports. This is the greatest marginal frequency of all the categories.

The marginal frequency for high school students who chose playing sports is 11.

The marginal frequency for middle school students who chose watching movies/TV is 21.

The marginal frequency for students who chose playing sports is 27.

The marginal frequency for students that are in middle school is 21.

Therefore, the answer is (C) Students who chose playing sports.

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As given by the question

There are given that the graph of line.

Now,

For find the slope, first select point from the graph of line.

So,

The point is:

Then,

From the formula of slope:

Then,

Hence, the slope of the line is 1.

The recursive formula of the arithmetic sequence is

Where d is the common difference between each 2 consecutive terms

The explicit form of the arithmetic sequence is

a is the first term

d is the common difference

Since the given explicit form of the sequence is

Then

a = 13

d = 6

The recursive form of the sequence should be

The missing number is 6

The answer is D

The parent function is given to be:

The new function is given to be:

Therefore, the function will be:

The y-intercept is the value of y when x = 0. Therefore, we have:

Therefore, the y-intercept is:

RANGE

The range of a given data is the difference between the largest and smallest numbers.

Steps for solving range:

Step 1: Arrange the data values in ascending order

Step 2: Identify the largest and smallest numbers

Step 3: Calculate the difference between the numbers.

The range is 70.

MIDRANGE

The midrange of a given set of data is the average of the largest and smallest number.

Steps for solving midrange:

Step 1: Arrange the data values in ascending order

Step 2: Identify the largest and smallest numbers

Step 3: Calculate the average of the numbers.

The midrange is 35.

ANSWER:

The correct option is OPTION B.

Answer:Display data graphically and interpret graphs: stemplots, histograms, and box plots.

Recognize, describe, and calculate the measures of location of data: quartiles and percentiles.

Box plots (also called box-and-whisker plots or box-whisker plots) give a good graphical image of the concentration of the data. They also show how far the extreme values are from most of the data. A box plot is constructed from five values: the minimum value, the first quartile, the median, the third quartile, and the maximum value. We use these values to compare how close other data values are to them.

To construct a box plot, use a horizontal or vertical number line and a rectangular box. The smallest and largest data values label the endpoints of the axis. The first quartile marks one end of the box and the third quartile marks the other end of the box. Approximately the middle

50

percent of the data fall inside the box. The “whiskers” extend from the ends of the box to the smallest and largest data values. The median or second quartile can be between the first and third quartiles, or it can be one, or the other, or both. The box plot gives a good, quick picture of the data.

NOTE

You may encounter box-and-whisker plots that have dots marking outlier values. In those cases, the whiskers are not extending to the minimum and maximum values.

Consider, again, this dataset.

1

,

1

,

2

,

2

,

4

,

6

,

6.8

,

7.2

,

8

,

8.3

,

9

,

10

,

10

,

11.5

The first quartile is two, the median is seven, and the third quartile is nine. The smallest value is one, and the largest value is

11.5

. The following image shows the constructed box plot.

NOTE

See the calculator instructions on the TI web site.

Horizontal boxplot's first whisker extends from the smallest value, 1, to the first quartile, 2, the box begins at the first quartile and extends to the third quartile, 9, a vertical dashed line is drawn at the median, 7, and the second whisker extends from the third quartile to the largest value of 11.5.

The two whiskers extend from the first quartile to the smallest value and from the third quartile to the largest value. The median is shown with a dashed line.

NOTE

It is important to start a box plot with a scaled number line. Otherwise the box plot may not be useful.

EXAMPLE

The following data are the heights of

40

students in a statistics class.

59

;

60

;

61

;

62

;

62

;

63

;

63

;

64

;

64

;

64

;

65

;

65

;

65

;

65

;

65

;

65

;

65

;

65

;

65

;

66

;

66

;

67

;

67

;

68

;

68

;

69

;

70

;

70

;

70

;

70

;

70

;

71

;

71

;

72

;

72

;

73

;

74

;

74

;

75

;

77

Construct a box plot with the following properties; the calculator instructions for the minimum and maximum values as well as the quartiles follow the example.

Minimum value =

59

Maximum value =

77

Q1: First quartile =

64.5

Q2: Second quartile or median=

66

Q3: Third quartile =

70

Horizontal boxplot with first whisker extending from smallest value, 59, to Q1, 64.5, box beginning from Q1 to Q3, 70, median dashed line at Q2, 66, and second whisker extending from Q3 to largest value, 77.

Each quarter has approximately

25

% of the data.

The spreads of the four quarters are

64.5

–

59

=

5.5

(first quarter),

66

–

64.5

=

1.5

(second quarter),

70

–

66

=

4

(third quarter), and

77

–

70

=

7

(fourth quarter). So, the second quarter has the smallest spread and the fourth quarter has the largest spread.

Range = maximum value – the minimum value = 77 – 59 = 18

Interquartile Range:

I

Q

R

=

Q

3

–

Q

1

=

70

–

64.5

=

5.5

.

The interval

59

–

65

has more than

25

% of the data so it has more data in it than the interval

66

through

70

which has

25

% of the data.

The middle

50

% (middle half) of the data has a range of

5.5

inches.

USING THE TI-83, 83+, 84, 84+ CALCULATOR

To find the minimum, maximum, and quartiles:

Enter data into the list editor (Pres STAT 1:EDIT). If you need to clear the list, arrow up to the name L1, press CLEAR, and then arrow down.

Put the data values into the list L1.

Press STAT and arrow to CALC. Press 1:1-VarStats. Enter L1.

Press ENTER.

Use the down and up arrow keys to scroll.

Smallest value =

59

.

Largest value =

77

.

Q

1

: First quartile =

64.5

.

Q

2

: Second quartile or median =

66

.

Q

3

: Third quartile =

70

.

To construct the box plot:

Press 4:Plotsoff. Press ENTER.

Arrow down and then use the right arrow key to go to the fifth picture, which is the box plot. Press ENTER.

Arrow down to Xlist: Press 2nd 1 for L1

Arrow down to Freq: Press ALPHA. Press 1.

Press Zoom. Press 9: ZoomStat.

Press TRACE, and use the arrow keys to examine the box plot.

Step-by-step explanation:

The speed of the car associated with a braking distance of 12 feet is approximately equal to 14.697 miles per hour.

In this problem we find a radical equation that describes the speed (s), in miles per hour, and the braking distance (d), in miles. If we know that d = 12 ft, then the initial speed of the car is:

s = √(18 · d)

s = √[18 · (12)]

s = 6√6 ft

s ≈ 14.697 mi / h

The initial speed of the car is approximately 14.697 miles per hour.

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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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2 orders of bacon and eggs cost: 2*$3.99 = $7.98

an order of pancakes cost: $2.55

3 glasses of milk cost: 3*$0.95 = $2.85

Total bill: $7.98 + $2.55 + $2.85 = $13.38

Each person pays $13.38/3 = $4.46

Step 1

break the parenthesis

Add similar terms

so, the answer is 3a+101

10 m

Explanation:

Data:

Second side : x

Third side : four times the second side : 4*x

The other side : 5 m longer than the second side : 5 + x

Perimeter of the triangle : 65 m

Formula:

Perimeter of a triangle = one side + second side + third side

Solution:

65 = 5 + x + x + 4 * x

65 = 5 + 6 * x

65 - 5 = 5 + 6 * x - 5

60 = 6 * x

60 / 6 = 6 * x / 6

10 = x

In a case whereby Sarah used 3.5 cups of cheese in a dish that serves 10 people the constant of proportionality that  relates the number of servings to cups of cheese is  0.35.

We were told that Sarah used 3.5 cups of cheese with 10 people, this can be written as :

let the c= the cups of cheese which is 3.5 cups of cheese

let n = number of the people that is been served

Then the equation can be written as :

c∝n

then we can bring in the proportionality constant sign as ;

then c=kn

then we can introduce the given figures into the equation as ;

3.5=k *10

the we can determine the value of the constant as :

k=3.5/10 = 0.35

Therefore, option A is correct.

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Winning the jackpot in a certain lottery requires you to pick two correct numbers between 1 and 59, and in a separate drawing, you also have a 7.32397915e-8 chance of winning when you also pick one correct number between 1 and 30.

A number of ways to select r items from n, nCr = n!/(r! x (n - r)!)

Number of possible methods to choose 4 winning numbers from 59 = 59C4

= 59!/(55! x 4!)

= 455,126

The number of possible ways to choose a single accurate number from 30 = 30.

The odds of winning the jackpot are 1/(probability) (Number of ways in which 4 winning numbers can be selected from 59 x Number of ways in which the correct single number can be selected from 30)

= 1/(455,126 x 30)

= 1/13653780

= [tex]7.32397915^{8}[/tex]

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Answer:

15

Step-by-step explanation:

from the equation 50+40h=650

solving for h which is the number of hours worked.

40h=650-50

40h=600

h=600÷40

h=15

Answer:

Any answer greater than 10 seems to work.

Step-by-step explanation:

This question is not that specific, but 5*2 is 10, so anything more than 10 would be more than double the quantity.

From the information provided, we know that Mr Chandler travels at a speed of 40 miles per hour (40mph). He also left 5 hours before Mrs Chandler.

Therefore, we can tell that for 5 hours he has travelled

We shall now label the total distance covered as d, and the number of hours taken (time) as t.

We now have for Mr Chandler;

For Mrs Chandler, we would have;

We would now solve the system of equations as follows;

This result shows that, travelling at the speed given for both Mr and Mrs Chandler, it would take her 5 hours to catch up with him.

ANSWER:

5 hours

PART B

If Mr Reeds leaves 3.5 hours ahead of Mrs Reeds and he travels at the speed of 55 miles per hour (55 mph), then his distance would be;

If the total distance covered is given as d, then for Mr Reeds the total distance would be;

For Mrs Reeds, we would have;

Note that d represents the total distance covered and t represents the time taken (in hours).

We shall now solve the system of equations, as follows;

We shall substitute for the value of d into equation two. Note that d = d, which means equation (1) equals equation (2). We now have;

The calculations here shows that travelling at the speeds given for both of them, it would take Mrs Reeds 5.5 hours to catch up with Mr Reeds.

ANSWER:

5.5 hours

Answer:

200 millimeters

Step-by-step explanation:

The radius is the distance from the center outwards.  The diameter goes straight across the circle through the center, and is therefore twice the radius.