Which of the following sets of ordered pairs represents a function?
A.
{ (0, -2), (-27, -13), (-10, -5), (-27, -12) }
B.
{ (-7, -14), (-9, -18), (-5, -10), (-6, -12) }
C.
{ (1, -1), (1, -27), (1, -26), (1, -17) }
D.
{ (81, 1), (81, -1), (83, 4), (86, 6) }

Answers

Answer 1

Answer: B

Step-by-step explanation:

For the set of ordered pairs to be a function, each x-value has to correspond to only one y-value.

In option A, the x-value of -27 corresponds to both -13 and -12.

In option C, the x-value of 1 corresponds to -1, -27, -26, and -17.

In option D, the x-value of 81 corresponds to both 1 and -1.


Related Questions

Could you solve the table

Answers

The relation is decreasing by a factor of 2 each time, so:

[tex]\begin{gathered} y-9=-2(x-0) \\ y=-2x+9 \end{gathered}[/tex]

Therefore:

[tex]\begin{gathered} y(100)=-2(100)+9 \\ y(100)=-200+9 \\ y(100)=-191 \end{gathered}[/tex]

Answer:

-191

Use synthetic division to determine whether the first expression is a factor of the second. If it is, indicate the factorization. (If the first expression is not a factor of the second, enter DNE.)x − 2, 3x4 − 6x3 − 8x + 16(x − 2)=

Answers

Find out the division

3x^4-6x^3-8x+16 : (x-2)

3x^3-8

-3x^4+6x^3

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

-8x+16

8x-16

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

0

The remainder is zero

that means

The expression (x-2) is a factor of the polynomial

so

3x^4-6x^3-8x+16=(x-2)(3x^3-8)

.. Find the values indicated. For g = {(-1,0), (-3,3), (-5, 6), (-7,9), (-9, 12)} g(-3) = g(-9) = g(-7)=

Answers

Given:

g = {(-1,0), (-3,3), (-5, 6), (-7,9), (-9, 12)}

So,

To find g(-3), we need to find the term that contains -3 in the location of x of the order pair

So, g(-3) = 3

And by the same manner, we will find the others

So,

g(-9) = 12

g(-7) = 9

which of these is closest to the unit distance between points M and M' ?

Answers

the coordinate of M is (-3, -5)

it is given that M is translated 6 unit right , and 5 unit up.

so the coordinate of M' is (-3+6 , -5 + 5) = (3, 0)

so, the distance between M and M' is,

[tex]d=\sqrt[]{(3-(-3))^2+(0-(-5))^2}[/tex][tex]\begin{gathered} d=\sqrt[]{6^2+5^2} \\ d=\sqrt[]{36+25} \\ d=\sqrt[]{61} \end{gathered}[/tex]

d = 7.81

so, the closest to the unit distance is 8

thus, the answer is option D

Sharel spent the day at the mall. First, she bought five phones for $35each. Later, she found two five dollar bills. Write the total change to

Answers

if Sharel bought 5 phenes for 35 each, se spent 5 times 35 = $175

And when she found two $5 bills, it is like she received 2 times 5 = $10

Normally, expenses are negative numbers and earning are positive numbers, in this case

-$175 + $10 = - $165

Sothe answer is -165

A shoe salesman earns a commission of 30%
of all shoe sales made.
Yesterday he sold 3 pairs of shoes for $70 each and 2 pairs of shoes for $80
each. How much did he earn in commission yesterday?

Answers

Answer: $111 is earn by shoe salesman as commission .

Step-by-step explanation:

As given the statement in the question be as follow.

Shoes salesman sold 3 pairs of shoes for $70 each and 2 pairs of shoes for $80 each.

Total cost of the pair of shoes = 3 × 70 + 2 × 80

                                                 = 210 + 160

                                                 = $ 370

As given

shoe salesman earns a commission of 30% of all shoe sales made.

30% is written is decimal form

= 0.30

Commission earns = 0.30 × Total cost of the pair of shoes .

                              = 0.30 × 370

                              = $ 111

Therefore $111 is earn by shoe salesman as commission .

Boris's cat will be having four kittens. Boris performs asimulation by tossing a coin to model whether thesekittens will be male or female.• Let'heads (H) = female kitten• Let tails (T) = male kittenThe results of the simulation are:

Answers

Given:

Boris performs a simulation by tossing a coin to model whether these kittens will be male or female.

The total number of sample space is, N = 10.

Head for female kitten

T for male kitten.

The objective is to find the probability that at least three of the kittens will be male.

Fromthe obtained simulation, the number of sample space with at least thee tail (T) is, n(T)=4

Now, the probability of at least three of the kittens will be male can be calculated by,

[tex]undefined[/tex]

4) Using the number line to help you, decide which fraction is larger or if they are equal: one/twos or three/fifths. Label each fraction on the number line.

Answers

Explanation:

The number line is between 0 to 1. There are 10 smaller lines in between

Each of the small lines represent 1/10 or 0.1

one/twos is the same as 1/2 = 0.5

three/fifths is the same as 3/5 = 0.6

From the above, 0.6 is greater than 0.5

Showing both numbers on the number line:

A Snack company can pack 15 granola bars in a box how many boxes are needed for 600 granola bars ?

Answers

Answer:40

Step-by-step explanation: 15 bars to a box.

600 bars in total.

600/15= 40

40 boxes of granola bars

If a number with two places to the right of the decimal place is added to a number with three places to the right of thedecimal place then the answer should be reported as having how many numbers to the right of the decimal place

Answers

Let the number with two places to the right of the decimal place be represented as 20.45 and the number with three places to the right of the decimal place be 20.456

Required:

When we add the two numbers, how many numbers to the right of the decimal place is it going to have?

We can know this by adding the two fictitious numbers:

[tex]20.45\text{ + 20.456 = 40.906}[/tex]

Here we can see that

An inspector found 18 defective radios during an inspection. If this is 0.024% of the total number of radios inspected, how many radios were inspected?

Answers

Total number of defected radios is 18

Let the total number of defective radios be taken as y

If 0.024% of the total number of radios inspected are defective, i.e 0.024% of y

[tex]\frac{0.024}{100}y=18[/tex]

Solve for y, by cross multiplying

[tex]\begin{gathered} \frac{0.024}{100}y=18 \\ 0.024y=18\times100 \\ \text{Divide both sides by 0.024} \\ \frac{0.024y}{0.024}=\frac{1800}{0.024} \\ y=75000 \end{gathered}[/tex]

Hence, the number of radios inspected, y, is 75000

Please help me with my Calc hw, it is not outside scope of brainly tutor. I am following along diligently, thanks!

Answers

ANSWER

[tex]-2\sqrt[]{1+\cos(x)}+C[/tex]

EXPLANATION

To solve this integral we have to use the substitution method. Let u = 1 + cos(x), then du is,

[tex]du=-\sin (x)dx[/tex]

Thus, dx is,

[tex]dx=\frac{du}{-\sin (x)}[/tex]

Replace the function and the differential in the integral,

[tex]\int \frac{\sin(x)}{\sqrt[]{1+\cos(x)}}dx=\int \frac{\sin(x)}{\sqrt[]{u}}\cdot\frac{du}{-\sin (x)}[/tex]

The sin(x) cancels out,

[tex]\int \frac{\sin(x)}{\sqrt[]{u}}\cdot\frac{du}{-\sin(x)}=-\int \frac{1}{\sqrt[]{u}}du[/tex]

We have to find a function whose derivative is 1/√u. This function is √u since its derivative is,

[tex]\frac{d}{du}(\sqrt[]{u})=\frac{1}{2\sqrt[]{u}}[/tex]

Note that a coefficient 1/2 is missing, so to cancel it out, we have to multiply by 2. Don't forget the constant of integration,

[tex]-\int \frac{1}{\sqrt[]{u}}du=-2\sqrt[]{u}+C[/tex]

Finally, we have to replace u with the function we substituted before,

[tex]-2\sqrt[]{u}+C=-2\sqrt[]{1+\cos (x)}+C[/tex]

Hence, the result of the integral is,

[tex]-2\sqrt[]{1+\cos(x)}+C[/tex]

A publisher for promising new novel figures fixed costs at $61,000 and variable cost at $1.50 for each book produced if the book is sold to distributors for $15 each how many must be produced and sold for publisher to break even?

Answers

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given information

[tex]\begin{gathered} For\text{ the cost price function:} \\ Fixed\text{ cost=\$61,000 = constant} \\ Variable\text{ cost = \$1.50 }\times\text{ number of books} \\ Let\text{ x be the number of books produced} \end{gathered}[/tex]

The function for the cost price becomes:

[tex]61000+1.5x[/tex]

STEP 2: Get the function for the selling price

The function for the selling price becomes:

[tex]\text{ \$}15x[/tex]

STEP 3: Calculate the number of books required to break even

To get the breakeven, the cost price will be equal to selling price. Therefore,

[tex]\begin{gathered} 61000+1.5x=15x \\ Subtract\text{ 1.5x from both sides} \\ 61000+1.5x-1.5x=15x-1.5x \\ 61000=13.5x \\ Divide\text{ both sides by 13.5} \\ \frac{61000}{13.5}=\frac{13.5x}{13.5} \\ 4518.518519=x \\ x\approx4519 \end{gathered}[/tex]

Hence, the number of books that must be produced and sold to get a breakeven is approximately 4519

In the circle below, if arc AB is congruent to arc CD, chord AB = 3x - 6 and chord CD = x + 12, find x.

Answers

Solution

We will equate the two values

[tex]\begin{gathered} 3x-6=x+12 \\ \\ 3x-x=12+6 \\ \\ 2x=18 \\ \\ x=9 \end{gathered}[/tex]

The answer is

What is the mean for the data shown in the dot plot?

Answers

We will determine the mean as follows:

[tex]x=\frac{1(4)+4(5)+3(6)+2(7)+1(10)}{11}\Rightarrow x=6[/tex]

So, the mean will be 6.

Last month, Ebony had 110 dollars in achecking account. The current balance is146 dollars. What is the percent change inthe account balance from last month to thismonth? Round your answer to the nearest whole percent.

Answers

Problem

Last month, Ebony had 110 dollars in a

checking account. The current balance is

146 dollars. What is the percent change in

the account balance from last month to this

month? Round your answer to the nearest whole percent.

Solutiion

For this case we can use the following formula:

[tex]\text{Change}=\frac{\text{Actual}-\text{Before}}{\text{Before}}\cdot100[/tex]

And replacing we got:

[tex]\text{Change}=\frac{146-110}{110}\cdot100=32.72[/tex]

And then the answer wounded to the nearest percent would be:

33%

If f(x)=x squared + 3x - 10 then over which of the following intervals is f(x)<0 ?

Answers

Given data:

The given function is f(x)= x^2 +3x-10.

The given inequality is,

[tex]\begin{gathered} f(x)<0 \\ x^2+3x-10<0 \\ x^2+5x-2x-10<0 \\ x(x+5)-2(x+5)<0 \\ (x+5)(x-2)<0 \\ -5Thus, the value of x is -5

Please help with the question below (please try to answer in maximum 10/15 minutes).

Answers

Solution:

Given the dimensions of the composite figure below

[tex]\begin{gathered} For\text{ the cuboid:} \\ l=12\text{cm} \\ w=4\text{ cm} \\ h=3cm \\ For\text{ the triangular prism:} \\ a=3\text{ cm} \\ b=4\text{ cm} \\ c=13\text{ cm} \\ h=5\text{ cm} \end{gathered}[/tex]

To find the surface area, SA, of the composite figure, the formula

[tex]SA=2(lh)+2(wh)+(lw)+2(\frac{1}{2}lh)+(bc)+(ah)[/tex]

Substitute the values of the variables into the formula above

[tex]\begin{gathered} SA=2\left(12\cdot3\right)+2\left(3\cdot4\right)+\left(12\cdot4\right)+2\left(\frac{1}{2}\left(12\cdot5\right)\right)+\left(13\cdot4\right)+\left(4\cdot5\right) \\ SA=2(36)+2(12)+(48)+(60)+(52)+20 \\ SA=72+24+48+60+52+20 \\ SA=276\text{ cm}^2 \end{gathered}[/tex]

Hence, the surface area, SA, is

[tex]276\text{ cm}^2[/tex]

The ratio of the lengths of corresponding sides of two similar triangles is 5:8. The smaller triangle has an area of 87.5cm^2. What is the area of the larger triangle

Answers

Question:

Solution:

Remember the following theorem: the ratio of the areas of two

similar triangles is equal to the ratio of the squares of their corresponding sides. Then, here A1 and A2 are areas of two similar triangles, and S1 and S2 are their corresponding sides respectively :

S1 : S2 = 5 : 8

then

[tex]\frac{S1}{S2}=\frac{5}{8}[/tex]

now, A1 = 87.5. Thus, according to the theorem, we get the following equation:

[tex](\frac{5}{8})^2=\frac{87.5}{A2}[/tex]

this is equivalent to:

[tex]\frac{25}{64}=\text{ }\frac{87.5}{A2}[/tex]

by cross-multiplication, this is equivalent to:

[tex](A2)(25)\text{ = (64)(87.5)}[/tex]

solving for A2, we get:

[tex]A2\text{ =}\frac{(64)(87.5)}{25}=224[/tex]

so that, we can conclude that the correct answer is:

The area of the larger triangle is

[tex]224cm^2[/tex]

Find the areas of the figure. Area of Parallelogram, Trapezoid and Composite figure. Round to the nearest hundredth where necessary.

Answers

Let

A₁ be the area of the parallelogram

A₂ be the area of the trapezoid

Solving for the area of the parallelogram

Given the following dimensions

b = 23 cm

h = 14 cm

The area is solved using

[tex]\begin{gathered} A_1=bh \\ A_1=(23\text{ cm})(14\text{ cm}) \\ A_1=322\text{ cm}^2 \end{gathered}[/tex]

The area of the parallelogram therefore is 322 square centimeters.

Solving for the area of the trapezoid.

Given the following dimensions

b₁ = 15 cm

b₂ = 34 cm

h = 19 cm

The area is solved using

[tex]\begin{gathered} A_2=\frac{b_1+b_2}{2}\cdot h \\ A_2=\frac{15\text{ cm}+34\text{ cm}}{2}(19\text{ cm}) \\ A_2=\frac{49\text{ cm}}{2}(19\text{ cm\rparen} \\ A_2=(24.5\text{ cm})(19\text{ cm}) \\ A_2=465.5\text{ cm}^2 \end{gathered}[/tex]

The area of the trapezoid is 465.5 square centimeters.

Solving for the area of the composite figure.

Get the sum of the two areas to get the area of the composite figure, we have

[tex]\begin{gathered} A_{\text{total}}=A_1+A_2 \\ A_{\text{total}}=322\text{ cm}^2+465.5\text{ cm}^2 \\ A_{\text{total}}=787.5\text{ cm}^2 \end{gathered}[/tex]

Therefore, the area of the composite figure is 787.5 square centimeters.

Help please I’ll give 10 points

Answers

Choose the right symbol for the following

What are Symbols?

Many operations in mathematics are carried out using mathematical symbols. Mathematical quantities are easy to refer to thanks to the symbols. It's interesting to consider how entirely dependent mathematics is on numbers and symbols. In addition to referring to various amounts, math symbols also show how two quantities relate to one another. The primary purpose of all mathematical symbols is to carry out mathematical operations under distinct conceptions.

1) 0.02 > 0.002

2) 0.05 < 0.5

3) 0.74 < 0.84

4) 0.74 > 0.084

5) 1.2 < 1.25

6) 5.130 = 5.13

7) 3.201 > 3.099

8) 0.159 < 1.590

9) 8.269 > 8.268

10) 4.60 > 4.060

11) 302.026 > 300.226

12) 0.237 > 0.223

13) 3.033 < 3.303

14) 9.074 < 9.47

15) 6.129 < 6.19

16) 567.45 > 564.75

17) 78.967 > 78.957

18) 5.346 < 5.4

19) 12.112 < 12.121

20) 26.2 = 26.200

21) 100.32 > 100.232

To learn more about Symbols click on the link

https://brainly.com/question/25421984

#SPJ13

Tiffany deposited two checks into her bank account this month.One check was for $50, and the second check was for $22.Her balance at the end of the month was $306, and she made no withdrawals.Which expression shows Tiffany's balance at the beginning of the month?

Answers

Answer:

Tiffany's balance at the beginning of the month = $229

Explanations:

First Deposit = $50

Second Deposit = $22

End of the month balance = $306

Balance at the beginning of the month = End of the month balance - (First Deposit + Second deposit)

Balance at the beginning of the month = 306 - (50 + 22)

Balance at the beginning of the month = 306 - 77

Balance at the beginning of the month = $229

hello can you help me with this trigonometry question and this a homework assignment

Answers

You have:

sin 2A = -√7/4

In order to determine the value of sin A, first calculate the value of angle A by using sin⁻¹ over the previous equation, just as follow:

sin⁻¹(sin 2A) = sin⁻¹(-√7/4) In this way you cancel out the sin

2A = -41.41° divide by 2 both sides

A = -41.41°/2

A = -20.705°

however, take into account that angle A is in the third quadrant. Then, it is necessary to consider the result A=-20.705° is respect to the negative x-axis.

To obtain the angle respect the positive x-axis (the normal way), you simply sum 180° to 20.705°:

20.705 + 180° = 200.705°

Next, use calculator to calculate sinA:

sin(200.705°) = -0.3535

Pedro can't decide which size pizza to order. The 10-inch cheese and sausage pizza is $4.99, while the 12-inch deluxe is $5.99. If he gets the 10-inch pizza, the total price will be divided among 3people. If he chooses the 12-inch pizza, then the total price will be divided among 4 people. Which is the better buy? How much will each person pay? (Use 3.14 for r.)A. 10-inch pizza; $1.50B. 12-inch pizza; $1.50C. 10-inch pizza; $1.66 D. 12-inch pizza; $1.66

Answers

Answer: The better buy is the the 12-inch deluxe for $5.99.

B. 12-inch pizza; $1.50

Explanation:

From the information given, the 10-inch cheese and sausage pizza is $4.99, while the 12-inch deluxe is $5.99. If he gets the 10-inch pizza. We would calculate the area of both pizzas by applying the formula for calculating the area of a circle which is expressed as

Area = πr^2

where

π = 3.14

r is the radius of the circle

For the 10-inch cheese and sausage pizza,

diameter = 10

r = 10/2 = 5

Area = 3.14 x 5^2 = 78.5

If it is divided among 3 people,

each person gets 78.5/3 = 26.2 in^2

Amount that each person pays = 4.99/3 = $1.66

This means that each person pays $1.66 for 26.2 in^2

For the 12-inch cheese and sausage pizza,

diameter = 12

r = 12/2 = 6

Area = 3.14 x 6^2 = 113.04

If it is divided among 4 people,

each person gets 113.04/4 = 28.26 in^2

Amount that each person pays = 5.99/4 = $1.5

This means that each person pays $1.5 for 28.26 in^2

Thus, the better buy is the the 12-inch deluxe for $5.99.

The amount that each person pays is

B. 12-inch pizza; $1.50

wich choice shows the correct solution to 2544÷8?

Answers

ANSWER:

318

STEP-BY-STEP EXPLANATION:

We have the following operation:

[tex]2544÷8[/tex]

So the answer is 318

The correct solution to 2544/8 is the number 318

using first principles to find derivatives grade 12 calculus help image attached much appreciated

Answers

Given: The function below

[tex]y=\frac{x^2}{x-1}[/tex]

To Determine: If the function as a aximum or a minimum using the first principle

Solution

Let us determine the first derivative of the given function using the first principle

[tex]\begin{gathered} let \\ y=f(x) \end{gathered}[/tex]

So,

[tex]f(x)=\frac{x^2}{x-1}[/tex][tex]\lim_{h\to0}f^{\prime}(x)=\frac{f(x+h)-f(x)}{h}[/tex][tex]\begin{gathered} f(x+h)=\frac{(x+h)^2}{x+h-1} \\ f(x+h)=\frac{x^2+2xh+h^2}{x+h-1} \end{gathered}[/tex][tex]\begin{gathered} f(x+h)-f(x)=\frac{x^2+2xh+h^2}{x+h-1}-\frac{x^2}{x-1} \\ Lcm=(x+h-1)(x-1) \\ f(x+h)-f(x)=\frac{(x-1)(x^2+2xh+h^2)-x^2(x+h-1)}{(x+h-1)(x-1)} \end{gathered}[/tex][tex]\begin{gathered} f(x+h)-f(x)=\frac{x^3+2x^2h+xh^2-x^2-2xh-h^2-x^3-x^2h+x^2}{(x+h-1)(x-1)} \\ f(x+h)-f(x)=\frac{x^3-x^3+2x^2h-x^2h-x^2+x^2+xh^2-2xh-h^2}{(x+h-1)(x-1)} \\ f(x+h)-f(x)=\frac{x^2h+xh^2-2xh+h^2}{(x+h-1)(x-1)} \end{gathered}[/tex][tex]\begin{gathered} \frac{f(x+h)-f(x)}{h}=\frac{x^{2}h+xh^{2}-2xh+h^{2}}{(x+h-1)(x-1)}\div h \\ \frac{f(x+h)-f(x)}{h}=\frac{x^2h+xh^2-2xh+h^2}{(x+h-1)(x-1)}\times\frac{1}{h} \\ \frac{f(x+h)-f(x)}{h}=\frac{h(x^2+xh^-2x+h^)}{(x+h-1)(x-1)}\times\frac{1}{h} \\ \frac{f(x+h)-f(x)}{h}=\frac{x^2+xh-2x+h}{(x+h-1)(x-1)} \end{gathered}[/tex]

So

[tex]\lim_{h\to0}\frac{f(x+h)-f(x)}{h}=\frac{x^2-2x}{(x-1)(x-1)}=\frac{x(x-2)}{(x-1)^2}[/tex]

Therefore,

[tex]f^{\prime}(x)=\frac{x(x-2)}{(x-1)^2}[/tex]

Please note that at critical point the first derivative is equal to zero

Therefore

[tex]\begin{gathered} f^{\prime}(x)=0 \\ \frac{x(x-2)}{(x-1)^2}=0 \\ x(x-2)=0 \\ x=0 \\ OR \\ x-2=0 \\ x=2 \end{gathered}[/tex]

At critical point the range of value of x is 0 and 2

Let us test the points around critical points

[tex]\begin{gathered} f^{\prime}(x)=\frac{x(x-2)}{(x-1)^2} \\ f^{\prime}(0)=\frac{0(0-2)}{(0-1)^2} \\ f^{\prime}(0)=\frac{0(-2)}{(-1)^2}=\frac{0}{1}=0 \\ f^{\prime}(2)=\frac{2(2-2)}{(2-1)^2}=\frac{2(0)}{1^2}=\frac{0}{1}=0 \end{gathered}[/tex][tex]\begin{gathered} f(0)=\frac{x^2}{x-1}=\frac{0^2}{0-1}=\frac{0}{-1}=0 \\ f(2)=\frac{2^2}{2-1}=\frac{4}{1}=4 \end{gathered}[/tex]

The function given has both maximum and minimum point

Hence, the maximum point is (0,0)

And the minimum point is (2, 4)

It’s supposed to answer in simplest formIf I die is rolled one time find the probability of

Answers

A die can have 6 possible outcomes.

The probability of an event is calculated using the formula:

[tex]P=\frac{number\text{ }of\text{ }required\text{ }outcomes}{number\text{ }of\text{ }total\text{ }outcomes}[/tex]

Therefore, the probability of rolling a 1 is gotten to be:

[tex]P=\frac{1}{6}[/tex]

The probability is 1/6.

A sample of 7 students was taken to see how many pencils they were carrying.2, 3, 2, 5, 7, 1, 41. Calculate the sample mean.2. Calculate the standard deviation.

Answers

Sample mean = 3.43

sample standard deviation = 2.07

Explanation:

Given: 2, 3, 2, 5, 7, 1, 4

Total numbers = 7

1) Sample mean is calculated by finding the average of the data set

[tex]\begin{gathered} \text{Sample mean = }\frac{su\text{ m of data set}}{number\text{ of data set}} \\ \text{sample mean = }\frac{2+3+2+5+7+1+4}{7} \\ \text{sample mean = 24/7 } \\ \text{sample mean = }3.43 \end{gathered}[/tex]

2) We have sample standard deviation and population standard deviation.

SInce the question asked for sample mean, we will be calculating sample standard deviation.

Standard deviation is calculated as:

[tex]\begin{gathered} s\tan dard\text{ deviation = }\sqrt[]{\frac{\sum^{}_{}(x_1-mean)^2}{N-1}} \\ \\ s\tan dard\text{ deviation = }\sqrt[]{\frac{\sum ^{}_{}(2-3.43)^2+(3-3.43)^2+(2-3.43)^2+(5-3.43)^2+(7-3.43)^2+(1-3.43)^2+\mleft(4-3.43\mright)^2}{7-1}} \\ s\tan dard\text{ deviation = }\sqrt[]{\frac{25.7143}{6}}\text{ = }\sqrt[]{4.2857} \\ s\tan dard\text{ deviation = }2.07 \end{gathered}[/tex]

For what values of b will F(x) = logb x be a decreasing function?A.0 < b < 1B.0 > b > -1C.b > 0D.b < 0

Answers

Given:

There is a function given as below

[tex]F(x)=\log_bx[/tex]

Required:

For what value of b the given function in decreasing

Explanation:

The given function is logarithm function

also written as

[tex]F(x)=\frac{log\text{ x}}{log\text{ b}}[/tex]

The base b is determines that if the function is increasing or decreasing

here

for

[tex]0the given function is decreasing

for

[tex]b>1[/tex]

the given function is increasing

Final answer:

[tex]0

Dee, Sarah, Brett, and Betsy are splitting their dinner bill. After the tip, the total is $30.08. How muchdoes each owe if they split the bill four ways?

Answers

The four individuals Dee, Sarah, Brett and Betsy split their dinner bill four ways, which means its divided into four parts. Hence, after splitting, each person owes;

[tex]\begin{gathered} \text{Per person=}\frac{Total}{4} \\ \text{Per person=}\frac{30.08}{4} \\ \text{Per person=7.52} \end{gathered}[/tex]

This shows that when paying the bill, each of the four individuals will have to pay $7.52

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