Select the correct answer.
Consider functions f and g.
f(x)=3 √x + 1
What is the value of f(g(1)) ?
A. 0
B. 3 √2 + 1
C. 1
D. 9

The circumference (c) is the dependent variable.

The radius (r) is the independent variable.

An independent variable is a variable that does not depend on any other variable for its value

A dependent variable is a variable depend on any other variable for its value.

In the rule c = 6.3r, the circumference (c) of a circle depends on the  radius for its value while the radius (r) does not depend on the circumference for its value.

Thus, the circumference (c) is the dependent variable while the radius (r) is the independent variable

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Answer:

13. x=4

14. x=8

Step-by-step explanation:

We know that these are both isosceles triangle because the two base angles are the same on #13, and the two sides are the congruent on #14. So all we need to do is make equations of equivalence. So #13 9x-8=28 and #14 11x-18=70. Look at the work shown in the image and follow those steps.

-Hope this helped & Happy New Year!

First, we can set up the ratio of carrots to potatoes as 3:4. Since there are 12 carrots, we can set up the following proportion:

3/4 = 12/x

To solve for the number of potatoes, we can cross-multiply to get:

4x = 12 * 4

x = 48/4

x = <<48/4=12>>12 potatoes.

Therefore, there are 12 potatoes in the sack.

Answer:

Here's a graph that represents the relationship between the number of carrots and the number of potatoes in the sack:

Carrots (x) Potatoes (y)

0 0

3 4

6 8

9 12

12 16

As you can see from the graph, if there are 12 carrots in the sack, then there are 16 potatoes in the sack.

You can also use this graph to find the number of potatoes if you know the number of carrots, or to find the number of carrots if you know the number of potatoes. Simply find the number of carrots or potatoes on the x-axis or y-axis, and then follow the line upward or downward until you reach the line that represents the relationship between carrots and potatoes. The number you reach on the other axis is the number of carrots or potatoes.

Step-by-step explanation:

Answer: its 2

Step-by-step explanation:

We have prepared the table and drawn the graph.

What is a graph of a function?

A graph of a function is a visual representation of the relationship between the inputs (x-coordinates) and the outputs (y-coordinates) of a function. The inputs are typically represented on the x-axis and the outputs are represented on the y-axis.

Table:

x (days) y (number of cells)

0        1000

1        2000

2       4000

Graph:

The graph would be a line graph with x-axis showing the day passed and y-axis showing the number of bacteria cells,

The point (0,1000) would be plotted on the graph, representing the initial number of bacteria cells on the first day.

The point (1,2000) would be plotted on the graph, representing the second day and the number of bacteria cells.

The point (2,4000) would be plotted on the graph, representing the third day and the number of bacteria cells.

The graph would be a upward sloping line, representing the growth of bacteria cells.

Hence we have prepared the table and drawn the graph.

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The only expression that can be solved using product rule of exponents is; (11²a⁻⁵)(11a⁹b⁷) / 5²

The Product Rule for Exponents states that to find the product of two numbers with the same base, add the exponents.

For example : a² * a³ = a²⁺³

1) We are given the exponential expression as; (4⁵ a⁰)(7²b⁻⁶)

From this expression, the numerator and denominator don't have any same base and as such we can say we cannot use product rule for it.

2) We are given the exponential expression as; (8⁵a⁻⁴)(b⁷c⁻⁵)

From this expression, the numerator and denominator don't have any same base and as such we can say we cannot use product rule for it.

3) We are given the exponential expression as; a⁻⁷b¹⁰ / c⁷ d¹⁴ . 15

From this expression, the numerator and denominator don't have any same base and as such we can say we cannot use product rule for it.

4) We are given the exponential expression as; (11²a⁻⁵)(11a⁹b⁷) / 5²

Using product rule of exponents, we have;

(111/25) * (a⁻⁵⁺⁹) * b⁷

= (111/25)a⁴b⁷

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Answer:

30%

Step-by-step explanation:

(13-10) / 10  * 100% = 30 %

The indicated operation 1/3 x 6/7 can be performed as 2/7.

The concept that will be used in this operation is the multiplication operation.

One of the four fundamental mathematical operations, along with addition, subtraction, and division, is multiplication. Multiply in mathematics refers to the continual addition of sets of identical size. Let's use the ice creams as a multiplication example to help us comprehend. There are two such groupings, and each group has ice cream. By multiplying their outputs, you can multiply one function by another.

Given operation is  1/3 x 6/7

1/3 x 6/7

=[ (1 x 6)/(3 x 7) ]

= (6/21)

= 2/7

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check the correct question:

Perform the indicated operation. 1/3 x 6/7

The graph of the solution to the inequality 5/8z > 5/6 is attached

From the question, we have the following parameters that can be used in our computation:

5/8z > 5/6

Multiply both sides of the inequality by 1/5

So, we have the following representation

1/8z > 1/6

Multiply both sides of the inequality by 8

So, we have the following representation

z > 8/6

Evaluate the quotient

This gives

z > 1.33

The above inequality means that the inequality starts from 1.33 and faces the right side

See attachment for the graph

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a. The sum of 1/3+1/5= 8/15

b. The sum of 1/8+2/6 = 3/8

c. the sum of 8/9+11/12= 1 87/108

d. the sum of 1/7+5/8= 1 7/36

e. the sum of 1/4+2/4= 3/4

f. the sum of 1/2+3/9= 5/6

g. the sum of 1/10+1/4= 7/20

h. the sum of 3/11+11/12 = 1 25/132

Sum of fractions is the addition of fractions. This is obtained by by using the L.C.M of the denominator method.

a. 1/3 + 1/5 = (5+3)/15 = 8/15

b. 1/8+2/6 = (3+6)/24 = 9/24 = 3/8

c. 8/9 + 11/12 = (96+99)/108 = 195/108 = 1 87/108

d. 1/7+ 5/8 = (8+35)/56 = 43/36 = 1 7/36

e. 1/4+ 2/4 = (2+1)/4 = 3/4

f. 1/2 + 3/9 = (9+6)/18 = 15/18 = 5/6

g. 1/10+1/4 = (2+5)/20 = 7/20

h. 3/11+ 11/12 = (36+121)/132 = 157/132 = 1 25/132

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A statement which correctly describes the comparison between the shapes of the box plots include the following: A. The Bulldogs' distribution is symmetric, but the Wolverines' distribution is negatively skewed.

In Mathematics, skewness can be defined as a measure of the asymmetry of a box plot (box-and-whisker plot) or histogram and as such, a box plot (box-and-whisker plot) or histogram has a normal distribution when it is symmetrical.

By critically observing the box plot (box-and-whisker plot) which represent basketball scores for the Bulldogs basketball team has a median of 80 (vertical line dividing the box into two equal halves), which simply means that both whiskers on either sides of the box plot (box-and-whisker plot) are relatively equal and symmetric.

On the other hand (conversely), the box plot (box-and-whisker plot) for the Wolverines basketball team shows that the median is more closer to the third quartile (upper quartile) and the whisker to the right of the box plot is longer, which ultimately implies that Wolverines' distribution is negatively skewed.

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Complete Question:

These box plots show the basketball scores for two teams.

Bulldogs

55 70 80 90 105

Wolverines

35 55 80 85 96

Basketball scores

Compare the shapes of the box plots.

A. The Bulldogs' distribution is symmetric, but the Wolverines' distribution is negatively skewed.

B. Both distributions are symmetric.

C. Both distributions are negatively skewed.

D. The Bulldogs' distribution is symmetric, but the Wolverines' distribution is positively skewed​

The cultivation of maize affected the settlement patterns in the American Southwest and present-day Mexico as B. It caused Native Americans in the area to develop permanent settlements supported by farming and irrigation system

The cultivation of maize had a significant impact on settlement patterns in the American Southwest and present-day Mexico. In the American Southwest, the cultivation of maize, along with other crops such as beans and squash, allowed for the development of more permanent settlements as people were able to rely on a stable food supply. This, in turn, led to the growth of larger, more complex societies and the development of elaborate systems of trade and exchange.

In present-day Mexico, the cultivation of maize played a central role in the development of complex societies such as the Olmec, Maya, and Aztec. These societies built sophisticated systems of agriculture, including terracing, irrigation, and crop rotation, which allowed them to support large populations and build elaborate cities. The cultivation of maize was also closely tied to the religious and cultural practices of these societies, and it played a central role in their economies and social systems.

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Answer:

3rd option: 32/24

Step-by-step explanation:

8/6 = 4/3

1st option: Now let's change the denominator to 24:

4/3 ==> ?/24

4/3 =

4*8 / 3*8 = 32/24, not 3/24.

2nd option: Now let's change the numerator to 24:

4/3 ==> 24/?

4/3 =

4*6 / 3*6 = 24/18, not 24/32

24/32 = 3/4, not 4/3 ==> don't get confused by this

3rd option: 32/24 is correct [Look at the explanation for 1st option]

4/3 ==> ?/24

4/3 =

4*8 / 3*8 = 32/24, not 3/24.

Hence, the 3rd option is correct.

A child's ticket would cost $10 while and adult's ticket would cost $18.

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power. In other words, none of the exponents can be greater than 1.

For example, x² is a variable raised to the second power, but x is a variable raised to the first power.

5 is an example of a constant.

The expressions are;

3a + 4c = 94 ---- 1

2a + 3c = 66 ---- 2

Multiplying equation 1 by 2 and equation 2 by 3

6a + 8c = 188 ---- 3

6a + 9c = 198 ---- 4

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

     - c = - 10

therefore;

c = 10

Substituting c in equation 3

6a + 8(10) = 188

6a + 80 = 188

6a = 188 - 80

6a = 108

a = 18

Therefore, child's ticket costs $10 while and adult's ticket cost $18.

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The inequality could be solved in order to get first gift certificate by customer is 12p≥100-25,   So Option (F) is correct.

Inequalities is a mathematical term, Which we use for comparison of two unequal expressions, It simply means that both the expressions are not equal. we express inequalities by following symbols  ">", "<"," ≤", "≥".

Suppose total purchase is, p

Each purchase is worth 12 points,

when customer sign up automatically earns 25 points,

And, when total sum of points will be more than 100 customer  will receive a gift,  

So sum of points for total purchase and points earned for sign up should be more than 100,

12p+25≥100.

Hence, 12p≥100-25

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==============================================

Work Shown:

C = 2pi*r

9pi = 2pi*r

r = (9pi)/(2pi)

r = 4.5

A = pi*r^2

A = pi*(4.5)^2

A = 20.25pi  square cm

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

Explanation:

The first portion involves using the circumference C = 9pi to determine the radius r. The circumference is the perimeter around the circle.

Once we know that r = 4.5 cm, we then plug that into the area of a circle formula A = pi*r^2

Side notes:

The Boolean expression A >= B is equivalent to  !(A < B) (option A)

To simplify a Boolean expression, use De Morgan's Law.

De Morgan's Law is used to simplify or find the equivalent of a negation of compound expressions.

The principle is:

NOT (A AND B) is equivalent to (NOT A) OR (NOT B)

NOT (A OR B) is equivalent to (NOT A) AND (NOT B)

When the expression involves >, <, = signs, then to simplify the expression, move the not and flip the sign.

! is the symbol of negation or NOT.

Hence,

! (>) becomes <=

! (<) becomes >=

Here are some examples:

!(A > B) is equivalent to (A <= B)

!(A <= B) is equivalent to (A > B)

!(A >= B) is equivalent to (A < B)

!(A == B) is equivalent to (A != B)

!(A != B) is equivalent to (A == B)

!(A < B) is equivalent to (A >= B)

From the above list we can conclude that A >= B is equivalent to !(A < B) (option A)

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Check the picture below.

The inequality which can be used to determine x is equal to 78.20x ≤ 304.98 , and the number of outfits Madeline can purchase while staying within her budget is 3  .

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

Given that Total money Madeline can spend = $680

Price of the cycle = $318.67

Price of 2 pair of reflectors = 2x 12.89 = $25.78

Price of a pair of bike gloves = $30.57

It can calculated as Money left with Madeline = (Total money Madeline has ) - price of the cycle - price of 2 pair of reflectors - price of a pair of bike gloves

Thus Money left with Madeline = 680 - 318.67 - 25.78 - 30.57

                                          = $304.98

Consider Madeline purchase x number of  biking outfits

The price of each biking outfit = $78.20

The price of x biking outfit = 78.20x

Since Madeline has only $304.98 She can only use not more than $304.98.

The inequality becomes

78.20x ≤ 304.98

Solving for x we get;

x ≤ 304.98/78.20

x ≤ 3.9

Hence , x ≤ 3.

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The mean is 2, the missing data point must be 2 - 6 = -4. Therefore, the missing number of chicken nuggets is -4.

To find the mean of the data set, we need to add up all of the data points and divide by the number of data points. In this case, the sum of the data points is 1 + 3 + 0 + 6 = 10. Since there are 5 data points in total, the mean is 10 / 5 = 2.

Since the mean is 2, the missing data point must be 2 - 6 = -4. Therefore, the missing number of chicken nuggets is -4.

Mean is a type of average, which is a measure of central tendency. It is calculated by adding up a group of numbers and then dividing the sum by the number of numbers in the group. Mean is often referred to as the "arithmetic average".

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As per the given mean, the missing number of chicken nuggets is 5

The term mean in math is defined as the process of adding all numbers in the data set and then dividing by the number of values in the set.

Here we have given that the question assumes there are 5 people at the table.

And the number of nuggets are written as,

=> 1,3,0,6,and x.

Here x refers the missing number of chicken nuggets.

Then the equation is written as

=> 1 + 3 + 0 + 6 + x = 10 + x

Here we can multiply both sides by 5 to clear the denominator:

Then we have to isolate the x by subtracting 10 from both sides.

=> 10 + x - 10 = 15 - 10

Then the value of x is written as

=> x = 5

Therefore, the missing number of nuggets is 5.

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Answer: Multiplying a large number can be easier if you break it up into its place values and perform the multiplication separately for each place value.

Step-by-step explanation:

Take the following multiplication issue, for instance:

43 x 32

The issue arises if place value is used to divide the numbers:

(4 x 3) + (3 x 2) + (3 x 3) (3 x 3)

This can be stated simply as:

12 + 6 + 9 = 27

Thus, the final response is 27.

Breaking up the multiplication problem by place value can also help you avoid making mistakes because you can check each place value separately to make sure that the calculations are correct before adding them together to get the final answer.

The opportunity cost of a concert is 2 movies.

Opportunity cost is the cost of the next best option a decision maker forgoes when he chooses one option over other options.

If Anna decides to go to the concert, she forgoes the opportunity  of going to the movies. On the other hand, if Anna decides to go to the movies, she forgoes the opportunity of going to the cinema.

Opportunity cost of a concert = number of movies she can go to / number of concerts she can go to

Opportunity cost of a concert = 70 / 35 = 2

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Answer:

C (2)

Step-by-step explanation:

• √32 = 4√2 ( bc √32 = √16×2 = √16×√2 = 4×√2 )

• √8 = 2√2 ( bc √8 = √4×2 = √4×√2 = 2×√2 )

So √32 ÷ √8 is equal to 4√2 ÷ 2√2

And there √2 cancels for both

So what you're left with is 4 ÷ 2

And 4÷2 = 2

If mr alvarez tells his students that next math test has 50 questions. he also says 20% will be word problems. The number of word problems that will be in the test is 10.

Using this formula to find the number of word problem

Number of word problem =Next math test problems × Percentage of word problem

Where:

Next math test problems = 50 problem

Percentage of word problem = 20% or .20

Let plug in the formula

Number of word problem  = 50 × .20

Number of word problem = 10 problem

Therefore we can conclude that the  number of word problem is 10 problem.

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The complete question is;

mr alvarez tells his students that next math test has 50 questions. he also says 20% will be word problems. the students want to know how may word problems will be in the test

Completing the table with the appropriate percentage and decimals will be:

Fraction Decimal Percentage

1/4. 0.25. 25% of 1

1/10. 0.1. 10% of 1

3/4. 0.75. 75% of 1

1/5. 0.2. 20% of 1

3/2. 1.5. 150% of 1

7/5. 1.4. 140% of 1

It should be noted that based on the information, 0.1 will be 1/10. The percentage will be:

= 1/10 × 100

= 10%

0.1 to fraction will be:

= 1/10

The percentage for 1/5 will be:

= 1/5 × 100

= 20%

1/5 to decimal will be:

= 1/5

= 0.2

The decimal 1.5 will give 150%

The fraction for 1.5 will be:

= 1.5 / 1

= 15 / 10

= 3/2

Also 3/4 as percentage will be:

= 3/4 × 100

= 75%

75% to decimal will be:

= 75 / 100

= 0.75

140% to fraction will be:

= 140 / 100

= 7 / 5.

The decimal for 140% will be:

= 140 / 100

= 1.4

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Answer:

Step-by-step explanation:

pass it then

Answer:

105

Step-by-step explanation:

y=kx where k is a constant

When y=15 and x=3

15=k3

k=15/3

k=5

Therefore y=5x

So, when x=21

y=21x5

=105

Please mark me brainliest

A graph of the system of inequalities is shown in the image and one possible solution is the ordered pair (-4, 24).

In order to solve these system of inequalities graphically, we would assign a variables to the unknown numbers and then translate the word problem into algebraic equation as follows:

Note: 1 quarter is equal to 0.25 dollar, 1 nickel is equal to 0.5 dollar, and 1 dime is equal to 0.1 dollar.

Since Arun has no less than 20 coins worth a maximum of $0.40 combined, an inequality to represent this is given by;

x + y ≥ 20

For a maximum of $0.40 combined, we have:

0.5x + 0.1y ≤ 0.40

From the graph (see attachment), a possible solution is given by the ordered pair (-4, 24).

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