Let f(x)=3x and g(x)=x^2+5. Perform function operation g(x)/f(x). State the domain.
On Monday, Amie rides her bike from home to school. After school, she bikes to work. After work, she bikes home. Based on the information in the diagram below, about how many miles does Amie bike on Monday?
The answer is D: 13.1 miles
Find the circumference of the circle. Use pi = 3.14. A. 3 m B. 18.84 m C. 6 m D. 28.26 m
The circumference of the circle.
A. r = 3 m, C = 18.84 m
B. r = 18.84 m, C = 118,315 m
C. r = 6 m, C = 37.68 m
D. r = 28.26 m, C = 177,473 m
Further explanationCircles are two-dimensional builds which are sets of equidistant points at a point called the center point
The distance of these points to the center is called the radius of the circle. While the circle field is an area which is bounded by a circle
There are terms - terms commonly used in circles:
1. The center point 2. Radius 3. Arc 4. Circumference 5. Segment 6. Chord 7. Annulus 8. Diameter 9. Disc 10. LensWhereas circumference formula
C = 2. π. r
π = 3.14
r = radius
In the question is known radius as follows:
A. r = 3 mthen
C = 2.3.14. 3
C = 18.84 m
B. r = 18.84 mC = 2.3.14. 18.84
C = 118,315 m
C. r = 6 mC = 2.3.14. 6
C = 37.68 m
D. r = 28.26 mC = 2.3.14. 28.26
C = 177,473 m
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Is the expression 2f + 4f + 2 – 3 equivalent to 6f – 1? 6f – 1 evaluated at f = 9 is 53. 2f + 4f + 2 – 3 evaluated at f = 9 is also 53. 6f – 1 evaluated at f = 3 is 17. what is 2f + 4f + 2 – 3 evaluated at f = 3?
Answer: 17
Step-by-step explanation:
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there were 13,426 eligible voters for a certain election. On election day 8,206 people cast their vote. What was the percent of voter turn-out?
Final answer:
The percent of voter turnout in this election was 61.1%.
Explanation:
Voter turnout refers to the percentage of eligible voters who cast a ballot in an election.
To calculate the percent of voter turn-out, you need to divide the number of people who cast their vote by the total number of eligible voters, then multiply by 100 to get the percentage.
Number of people who cast their vote: 8,206
Total number of eligible voters: 13,426
To calculate the percent of voter turnout we use the following formula:
Divide the number of people who voted by the number of eligible voters.
Multiply the result by 100 to get a percentage.
= (8,206 / 13,426) × 100
= 0.611 × 100
= 61.1%
Therefore, the percent of voter turnout in this election was 61.1%.
Here are four decimal numbers: 0.98, 0.3, 0.26, 0.627 order from smallest to largest.
WZ←→− is tangent to circle O at point B.
What is the measure of ∠OBZ?
80º
90º
160º
180º
WZ is tangent to circle O at point B. The measure of [tex]\angle OBZ[/tex] is [tex]90^{\circ}[/tex].
Given,line wz is tangent to circle O at point B.
We have to find out the measure of [tex]\angle OBZ[/tex].
What is a tangent?A tangent to a circle is a straight line which touches the circle at only one point. This point is called the point of Tangency.
The tangent to a circle is perpendicular to the radius at the point of tangency.
Here in circle O, WZ is the tangent which touches the circle at point B,
so B is the point of tangency and the [tex]\angle OBZ[/tex] is [tex]90^{\circ}[/tex].
Hence the correct option is B. [tex]90^{\circ}[/tex]
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A classic counting problem is to determine the number of different ways that the letters of "personnel""personnel" can be arranged. find that number.
The number of different ways in which the letter of “PERSONNEL” can be arranged is [tex]\boxed{\bf 90,720}[/tex].
Further explanation:
A permutation is an arrangement of objects in their order in which we find number of ways that can occur in a period of time.
If all the letters are different then the number of arrangement can be written as follows:
[tex]\boxed{\begin{aligned}P(n)&=n!\\&=n\cdot (n-1)\cdot (n-2)...2\cdot 1\end{aligned}}[/tex]
The number of different permutation can be calculated as follows:
[tex]\boxed{p(n)=\dfrac{n(n-1)(n-2)...2\cdot 1}{n_{1}!\cdot n_{2}!}}[/tex]
Here, [tex]n_{1}[/tex] and [tex]n_{2}[/tex] are the different kind of object such that [tex]n_{1}+n_{2}+n_{3}+\cdot \cdot+n_{k}=n[/tex].
Given:
The given word is “PERSONNEL”.
Calculation:
Step 1:
First consider that all the letters are different i.e, repetition of letter is allowed.
The given word “PERSONNEL” has [tex]9[/tex] letters.
Therefore, the number of ways for arranging nine letters can be calculated as follows:
[tex]\begin{aligned}P(9)&=9\cdot (9-1)\cdot (9-2)\cdot \cdot 2\cdot 1\\&=9\cdot 8\cdot 7\cdot 6\cdot 5\cdot 4\cdot3 \cdot 2\cdot 1\\&=362,880\end{aligned}[/tex]
Therefore, the different arrangements of the given word is [tex]362,880[/tex].
Step 2:
Since, the letter N and E is repeated two times in given word “PERSONNEL” then the half of the arrangement is repeated of these two letters.
Use the formula for finding the number of distinguishable permutation. It can be calculated as follows:
[tex]\begin{aligned}\text{Number of permutation}&=\dfrac{362880}{2!\cdot 2!}\\&=\drac{362880}{4}\\&=90,720\end{aligned}[/tex]
The number of different ways that the letter of “PERSONNEL” can be arranged is [tex]90,720[/tex].
Thus, the number of different ways that the letter of “PERSONNEL” can be arranged is [tex]\boxed{\bf 90,720}[/tex].
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Answer details:
Grade: High school
Subject: Mathematics
Chapter: Permutation
Keywords: Permutation, combination, personnel, counting, arrangement, different ways, order, letters, different ways, repetition, arranged objects, distinguishable permutation, counting problem.
The number of different ways to arrange the letters of 'personnel' is calculated using combinatorics and permutation formulas, resulting in 151,200 unique arrangements.
To find the number of different ways to arrange the letters of the word "personnel", we must use the principles of combinatorics and permutations.
The word 'personnel' consists of 9 letters with repetitions: there are three E's, two N's, one P, one S, one O, and one L. To count the number of unique arrangements, we start with the total factorial of all letters, which is 9!, but then we need to account for repeated letters by dividing by the factorials of the frequency of each repeating letter.
This results in the following permutation formula:
N! / (n1!)n2!...nk!
Where N is the total number of letters, and n1, n2, ..., nk are the number of times each unique letter is repeated.
So for 'personnel': 9! / (3!)(2!) = 151,200
There are therefore 151,200 unique ways to arrange the letters in 'personnel'.
The parent secant function is shifted 2 units down, and its period is changed to pi. Which of the following is the graph of the transformed function?
Thank you!
Make a box-and-whisker plot for the data. what is the median value? 56 32 48 52 51 53 48 38 35 42 40 46 54 50
Answer:
Median = 48.
Step-by-step explanation:
Given : 56 32 48 52 51 53 48 38 35 42 40 46 54 50.
To find : what is the median value.
Solution : We have given 56 32 48 52 51 53 48 38 35 42 40 46 54 50.
Step (1) : Arrange in ascending order
32 , 35 , 38 ,40 , 42 , 46 , 48, 48 ,, 50 ,51, 52 ,53 ,54 , 56.
Total numbers = 14 ,
Formula of median for even numbers : [tex](\frac{n+1}{2})^{th} ,(\frac{n}{2})^{th} \\Mean\ of\ (\frac{n+1}{2})^{th} ,(\frac{n}{2})^{th}\ term\ is\ the\ median[/tex].
Here , n = 14
Step (2): [tex](\frac{14}{2})^{th} ,(\frac{14}{2}+1)^{th}[/tex]
[tex](7^{th} ,(8)^{th}[/tex] terms are 48 , 48
Step (3) :Mean of [tex](7^{th} ,(8)^{th}[/tex] = [tex](\frac{48+48}{2})[/tex] .
Median = 48.
Therefore, Median = 48.
Which inequality represents all possible solutions of -7n < -14?
Emily added 5 grams of water into 20 grams of 50% salt solution.
She made ___ grams of ___% salt solution.
A merchant uses the rule: selling price equals cost + 10% of cost. This is a function. Why?
Answer:
y=x+0.10
Step-by-step explanation:
To ensure that you do not have a total consumption budget, which two categories should be added to your budget
Given △ABC where A(2, 3), B(5, 8), C(8, 3), RS is the midsegment parallel to AC, ST is the midsegment parallel to AB, and RT is the midsegment parallel to BC, determine if the statements are true or false.
Select True or False for each statemen
In 1987 the average price of gasoline was $0.94. Today the price of gas is about $3.00. What is the percent increase from 1987 to today? (explain the problem please)
Answer:
-219.1% decrease
Step-by-step explanation:
.94-3.00=-2.06
-2.06/.94=-2.191
-2.191*100=-219.1 decrease
Quadrilateral ABCD is inscribed in this circle. What is the measure of ∠A ? Enter your answer in the box.
Answer: The answer is 137°.
Step-by-step explanation: Given that the quadrilateral ABCD is inscribed in a circle, where measure of angle C is 43°. We are to find the measure of ∠A.
Since the quadrilateral ABCD is inscribed in a circle, so it will be a cyclic quadrilateral. Also, the sum of opposite angles of a cyclic quadrilateral is 180°.
Therefore, we have
[tex]\angle A+\angle C=180^\circ\\\\\Rightarrow \angle A+43^\circ=180^\circ\\\\\Rightarrow \angle A=180^\circ-43^\circ\\\\\Rightarrow \angle A=137^\circ.[/tex]
Thus, the required answer is 137°.
Jaylyn rode her bicycle in a bike-a-thon she wrote 33.48 miles in 2.7 hours if she rode at the same speed what was her speed in miles per hours
Write a proportion to find how many points xx a student needs to score on a test worth 80 points to get a test score of 80%.
Answer:cross multiply to solve
100x = 50*78
x = 50*78/100
x = 39 points needed to score a 78%
Step-by-step explanation:hope this helps:D
What is the quotient
Raina's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Raina $4.40 per pound, and type B coffee costs $5.80 per pound. This month, Raina made 171 pounds of the blend, for a total cost of $856.00 . How many pounds of type A coffee did she use?
i just tried to solve this everyway i know possible when you get the answer lmk please.
-r+8(-5r-2) what is the equivalent expression
-41r+16
Answer:
Step-by-step explanation:
What does it mean if a statistic is resistant? choose the correct answer below.
a. extreme values (very large or small) relative to the data do not affect its value substantially.
b. changing particular data values affects its value substantially.
c. an estimate of its value is extremely close to its actual value.
d. extreme values (very large or small) relative to the data affect its value substantially?
A statistic is said to be resistant if it isn't significantly affected by outliers or extreme values in the data. It remains relatively stable when extreme values are added or removed from the dataset.
Explanation:In statistics, when a statistic is described as resistant, it is typically referring to its ability not to be affected by outliers or extreme values (very large or small) in a dataset. In other words, a resistant statistic is relatively stable and does not change dramatically if an extreme value is added to, or removed from, the dataset. So, the correct answer is: a. extreme values (very large or small) relative to the data do not affect its value substantially.
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Helppppppp!!!!!!!!!!!!!!!!!!
Just a quick math question.
When converting 18 quarts into gallons, I would have to divide by 4 to get the answer which is 4.5, but why am I dividing by 4? Where did 4 come from?
A car is traveling at a speed of 44 feet per second. What is the car’s speed in miles per hour? How many miles will the car travel in 4 hours? In your computations, use the fact that 1 mile is equal to 5280 feet. Do not round your answers
Car travels at speed of 44 feet per second. Converted to miles per hour, it's 30 mph. In 4 hours, it travels 120 miles, using the conversion factor 1 mile = 5280 feet.
To find the car's speed in miles per hour, you can use the conversion factor:
1 mile = 5280 feet
So, first, we need to convert the car's speed from feet per second to miles per hour.
Find out how many feet the car travels in an hour, and then we'll convert that to miles:
1 hour = 60 minutes
1 minute = 60 seconds
So, in 1 hour, there are 60 minutes × 60 seconds = 3600 seconds.
Now, if the car is traveling at a speed of 44 feet per second, in 1 hour, it would travel:
44 feet/second × 3600 seconds/hour = 158,400 feet/hour
Now, convert this to miles:
158,400 feet/hour / 5280 feet/mile = 30 miles/hour
So, the car's speed is 30 miles per hour.
To find out how many miles the car will travel in 4 hours at this speed:
4 hours × 30 miles/hour = 120 miles
The car will travel 120 miles in 4 hours.
Therefore, speed of the car is 30 miles/hour and it travels 120 miles in 4 hours.
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An aquarium is 18 in. high, 12 in. wide, and 24 in. long. How much water can the aquarium hold? (V = lwh)
The table gives the probability distribution of the number of books sold in a day at a bookstore. What is the probability of 16 or more books being sold on a given day?
number of books sold in a day
0-5
6-10
11-15
16-20
21-25
probability
0.110
0.206
0.464
0.201
?
The probability of 16 or more books being sold on a given day is 0.22 or 22%.
What is probability?Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.
The table gives the probability distribution of the number of books sold in a day at a bookstore.
The missing probability will be
We know that the sum of all the outcomes must be one.
0.110 + 0.206 + 0.464 + 0.201 + x = 1
On solving, we have
x = 0.019
The number of books sold in a day Probability
0-5 0.110
6-10 0.206
11-15 0.464
16-20 0.201
20-25 0.019
The probability of 16 or more books being sold on a given day will be
[tex]\rm P(x \geq 16) = 0.201 + 0.019 = 0.22[/tex]
The probability of 16 or more books being sold on a given day is 0.22 or 22%.
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Please help
1.
(05.08 MC)
Given the equation `1/(x-1)+2/x=x/(x-1)`
Part A: What values of x that would make the equation no solution? Why?
Part B: What is the solution of the equation. Show all of your steps.
(10 points)
2.
(05.09 MC)
Max and Maggie have to clean the house. It takes Max 10 hours to clean the house, while Maggie can complete the task in 6 hours. How long will it take for them to work together? Explain each step in solving this equation. (10 points)