The circumference of the tree trunk is 7.85
feet. If the tree trunk is cut, what will be
the diameter of the tree stump?
Use 3.14 for π.
Hint: C = πd
diameter [?] feet please explain how you got this answer for future problems
Answers
Answer:
2.5 feet
Step-by-step explanation:
Since circumference is just pi(we're using 3.14 in this case) * diameter, which is our answer, we need to divide the circumference(which is 7.58) BY 3.14, which is pi. This leaves us with the diameter, which is 2.5. The unit is already feet, so we needn't do anything about that.
Related Questions
Which geometry or geometries are common for complexes with a coordination number of 4?.
Answers
Complexes with a coordination number 4 mostly adopt tetrahedral and squar planar geometries.
What is geometry?Geometry is a subfield of mathematics that examines the measurement and relationships of surfaces, solids, solid surfaces, angles, and points.Ge and metria, two Greek terms that signify "measuring," are the origin of the word geometry. The foundation of geometry has been the method of geometry devised by the Ancient Greeks for more than 2000 years.The calculation of a triangle's angles is a geometry example.Plane geometry, solid geometry, and spherical geometry are the three most popular types of geometry.Complexes with a coordination number 4 mostly adopt tetrahedral and squar planar geometries.
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Scalcet8 4. 2. 26. suppose that 2 ≤ f '(x) ≤ 4 for all values of x. what are the minimum and maximum possible values of f(4) − f(1)? ≤ f(4) − f(1) ≤ show my work (optional)
Answers
The minimum value of f(4) - f(1) is 6.
The maximum value of f(4) - f(1) is 12.
In the question, we are given that, 2 ≤ f'(x) ≤ 4 for all values of x.
Taking the given inequality as (i).
We are asked to find the minimum and maximum possible values of f(4) - f(1).
We multiply (i) by dx throughout, to get:
4dx ≤ f'(x)dx ≤ 5dx.
To find this, we integrate (i) in the definite interval [4, 1] with respect to dx, to get:
[tex]\int_{1}^{4}2dx \leq \int_{1}^{4}f'(x)dx \leq \int_{1}^{4}4dx\\\Rightarrow [2x]_{1}^{4} \leq [f(x)]_{1}^{4} \leq [4x]_{1}^{4}\\\Rightarrow 2*4 - 2*1 \leq f(4)-f(1) \leq 4*4 - 4*1\\\Rightarrow 6 \leq f(4) -f(1) \leq 12[/tex]
Thus, the minimum value of f(4) - f(1) is 6.
The maximum value of f(4) - f(1) is 12.
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(6.04)the equation of the line of best fit of a scatter plot is y = −5x − 2. what is the slope of the equation? −5 −2 2 5
Answers
Answer:
slope = - 5
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - 5x - 2 ← is in slope- intercept form
with slope m = - 5
Write two different integers x, y, and z, and meet the following conditions. they do not all have the same sign and x-y-z=0
Answers
Two different integers are the same numbers, which have different signs.
What is integers?An integer is a number that includes negative and positive numbers, including zero. It does not include any decimal or fractional part. A few examples of integers are: -5, 0, 1, 5, 8, 97.
Given that,
x, y, and z are three integers. They follow the one condition: x-y-z = 0.
Any number in the number system that has only two signs, either + or -, So we consider that the third integer is 0 because 0 is a whole number that has neither a positive nor a negative sign.
The remaining two integers are the same numbers, but they have different signs to follow the given condition.
x-y-z = 0
x = y+z
Let y,z are the same numbers, They have different signs and x = 0.
Note: The value of x is always negative and y's value is always positive.
Example:
x = 0, y = +6, z = -6
x-y-z = 0
x = y+z
0 = +6-6
0 = 0
Hence, two different integers are the same numbers, which have different signs.
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Which choice is equivalent to the expression below?
5x√2-3√2+x√2
Answers
Answer:
You did not list any choices but if you simplify that the answer is 6√2x-3√2
Step-by-step explanation:
If they want you to factor it instead of simplifying the answer is 3√2(2x-1)
Answer:
[tex]6x\sqrt{2} - 3\sqrt{2}[/tex]
Step-by-step explanation:
So you haven't provided any options, but I'm assuming they want it in most simplified form.
To do this, we simply combine like terms, and in this case you can see the [tex]\sqrt{2}[/tex] as a variable, if it makes it easier to think about why we can combine terms. So just like how we can do: [tex]2y + y = 3y[/tex] we can do the same thing here, since sqrt(2) constant and it's in each expression.
So if it makes a bit easier to represent, I'll rewrite the equation such that sqrt(2) = y
[tex]5xy-3y+xy[/tex]
So in here, think of y as the variable and the 5x, -3, and x as the coefficients.
In doing this we can combine the terms by adding them, since they all have the same "variable" (sqrt(2))
[tex](5x-3+x)y[/tex]
Simplify this expression to get
[tex](6x-3)y[/tex]
Now just plug the sqrt(2) back in as y and you get the expression
[tex](6x-3)\sqrt{2}[/tex]
Since we can't combine the 6x and -3 in any way, we we can just distribute this back into the sqrt(2)
[tex]6x\sqrt{2} - 3\sqrt{2}[/tex]
Find the circumference of a circle with radius of 4.2in.
Answers
Answer: 26.39
Step-by-step explanation:
2xπxr
2 into 22/7into 4.2
2 into 22 into 0.6
26.4 is the circumference of circle
The data in the table can be entered into a calculator to determine a linear equation of best fit where x represents the number of years with a company and y represents an employee’s salary in dollars.
What conclusion can be drawn from the correlation coefficient associated with this linear equation?
Answers
Based on the given table which shows the number of years with a company in relation to the employee salary, the conclusion that can be drawn is There is a weak positive correlation between the variables.
What is the correlation between the values?When two variables are said to be positively correlated, then it means that when one variable increases, the other variable would increase as well.
If the correlation between them is strong, then the increase between the variables would be more uniform i.e. we can tell with higher accuracy, how the increase in one variable would affect the other.
In the table, we see that with every increase in the number of years with the company, there is an increase in the salary. This means that there is a positive correlation.
The increase is not uniform however. Sometimes it increases by $1,000, and other times by $7,000. As the increase is not uniform, it means that the correlation is weak.
In conclusion, there is a weak positive correlation between number of years and salary.
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Can someone help ???????
Answers
So if you divide 2 by 120 it will be 60
So x/y = 60
x equals 2 so that means z equals 2
Then divide 2 by 2 and you will get one
So add 60 by one so you get 61
Answer: 61
A coin is flipped 15 times where each flip comes up either heads or tails. How many possible outcomes (a) contain exactly four tails (b) contain at least three heads?
Answers
Using the arrangements formula, it is found that:
a) There are 1365 possible outcomes that contain exactly four tails.
b) There are 1,307,674,399,889 possible outcomes that contain at least three heads.
What is the arrangements formula?The number of possible arrangements of n elements is given by the factorial of n, that is:
[tex]A_n = n![/tex]
When there are repetitions, the number of ways is given as follows:
[tex]A_{n}^{n_1, n_2, \cdots, n_n} = \frac{n!}{n_1!n_2! \cdots n_n!}[/tex]
In which [tex]n_1, n_2, \cdots, n_n[/tex] are the numbers of repetitions.
Item a:
11 heads and 4 tails, hence:
[tex]A_{15}^{11,4} = \frac{15!}{11!4!} = 1365[/tex]
There are 1365 possible outcomes that contain exactly four tails.
Item b:
The total number is:
[tex]A_{15} = 15! = 1,307,674,400,000[/tex]
With no heads:
[tex]A_{15}^{15,0} = \frac{15!}{15!0!} = 1[/tex]
With one head:
[tex]A_{15}^{14,1} = \frac{15!}{14!1!} = 15[/tex]
With two heads:
[tex]A_{15}^{13,2} = \frac{15!}{13!2!} = 95[/tex]
Hence the number of outcomes with less than three heads is:
1 + 15 + 95 = 111
With at least three heads, the number of outcomes is:
[tex]1,307,674,400,000 - 111 = 1,307,674,399,889[/tex]
There are 1,307,674,399,889 possible outcomes that contain at least three heads.
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Use what you know about reflections of functions
to match the graph to the function rule.
Answers
The answers are :
y = 3ˣ ⇒ b
y = 3⁻ˣ ⇒ a
y = -3ˣ ⇒ c
For y = 3ˣ, we will get a graph that will increase exponentially in the direction of positive y-axis.
For y = 3⁻ˣ, we will get a graph that will decrease exponentially in the direction of positive x-axis.
For y = -3ˣ, we will get a graph that will decrease exponentially in the direction of negative y-axis.
Find x. A. 4–√6 B. 16√6/3 C. 4√6/3 D. 32√3/3
Answers
Answer:
Step-by-step explanation:
12
The length and breadth of a rectangular park 25m and 12m. find the distance covered by a boy who takes 4 rounds of the garderean. also find its a
Answers
Answer:296 m
I’m assuming “breadth” is width and garderean is just the park.
(25+25+12+12) times 4.
A is never defined
Hank is currently reading a book that is 250 pages long. if he can read 10 pages every 15 minutes, how many hours will it take him to read the book?
Answers
Answer:
The answer is B, 2.78 hours
Step-by-step explanation:
Answer:
6 hours 15 minutes, or 6.25 hours
Step-by-step explanation:
We assume Hank reads at a constant rate. His reading time will be proportional to the number of pages.
ProportionWe know that 15 minutes is 1/4 hour, so the proportion can be written ...
hours/pages = (book hours)/(250 pages) = (1/4 hour)/(10 pages)
Multiplying by 250 pages gives ...
book hours = 250(1/4 hour)/10 = 25/4 hour = 6 1/4 hour
It will take Hank 6 1/4 hours to read the book.
Joseph has a bag filled with 3 red, 3 green, 15 yellow, and 9 purple marbles. Determine P(not red) when choosing one marble from the bag.
10%
30%
50%
90%
Question 2(Multiple Choice Worth 2 points)
(Sample Spaces LC)
List the sample space for rolling a fair seven-sided die.
S = {1, 2, 3, 4, 5, 7}
S = {1, 2, 3, 4, 5, 6, 7, 8}
S = {1}
S = {7}
Question 3(Multiple Choice Worth 2 points)
(Sample Spaces LC)
Which event will have a sample space of S = {h, t}?
Flipping a fair, two-sided coin
Rolling a six-sided die
Spinning a spinner with three sections
Choosing a tile from a pair of tiles, one with the letter A and one with the letter B
Question 4(Multiple Choice Worth 2 points)
(Theoretical Probability MC)
A group of students was surveyed in a middle school class. They were asked how many hours they work on math homework each week. The results from the survey were recorded.
Number of Hours Total Number of Students
0 1
1 8
2 2
3 5
4 9
5 7
6 3
Determine the probability that a student studied for exactly 1 hour. Round to the nearest hundredth.
0.03
0.23
0.30
0.77
Question 5(Multiple Choice Worth 2 points)
(Likelihood MC)
A spinner is given.
A spinner divided into eight equal colored sections, with one orange, two purple, two yellow, and three blue.
Which statement about probability is true?
The probability of landing on orange is greater than the probability of landing on purple.
The probability of landing on yellow is less than the probability of landing on blue.
The probability of landing on orange is equal to the probability of landing on yellow.
The probability of landing on purple is equal to the probability of landing on blue.
Question 6(Multiple Choice Worth 2 points)
(Experimental Probability MC)
Sandy used a virtual coin toss app to show the results of flipping a coin 50 times, 400 times, and 2,000 times. Explain what most likely happened in Sandy's experiment.
Sandy's experimental probability was closest to the theoretical probability in the experiment with 2,000 flips.
Sandy's experimental probability was closest to the theoretical probability in the experiment with 400 flips.
Sandy's experimental probability was closest to the theoretical probability in the experiment with 50 flips.
Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.
Question 7(Multiple Choice Worth 2 points)
(Experimental Probability MC)
There are 10 brown, 10 black, 10 green, and 10 gold marbles in bag. A student pulled a marble, recorded the color, and placed the marble back in the bag. The table below lists the frequency of each color pulled during the experiment after 40 trials..
Outcome Frequency
Brown 13
Black 9
Green 7
Gold 11
Compare the theoretical probability and experimental probability of pulling a brown marble from the bag.
The theoretical probability, P(brown), is 50%, and the experimental probability is 25%.
The theoretical probability, P(brown), is 50%, and the experimental probability is 22.5%.
The theoretical probability, P(brown), is 25%, and the experimental probability is 13.0%.
The theoretical probability, P(brown), is 25%, and the experimental probability is 32.5%.
Question 8(Multiple Choice Worth 2 points)
(Experimental Probability MC)
A student randomly draws a card from a standard deck of 52 cards. He records the type of card drawn and places it back in the deck. This is repeated 20 times. The table below shows the frequency of each outcome.
Outcome Frequency
Heart 7
Spade 3
Club 6
Diamond 4
Determine the experimental probability of drawing a spade.
0.15
0.25
0.35
0.50
Answers
The probability of not choosing red when choosing one marble from the bag is 90%.
S = {1, 2, 3, 4, 5, 7}
Flipping a fair, two-sided coin.
probability that a student studied for exactly 1 hour is 0.23.
The probability of landing on yellow is less than the probability of landing on blue.
Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.
The theoretical probability, P(brown), is 25%, and the experimental probability is 32.5%.
The experimental probability of drawing a spade is 0.15.
How to compute the probability?The probability of not choosing red when choosing one marble from the bag will be:
= (3 + 15 + 9)/30
= 27/30
= 90%
The sample space for rolling a fair seven-sided die will be S = {1, 2, 3, 4, 5, 7}.
The event that will have a sample space of S = {h, t} will be flipping a fair, two-sided coin.
The probability that a student studied for exactly 1 hour will be:
= 8/(1+8+2+5+9+7+3)
= 8/35
= 0.23
The true statement is that the probability of landing on yellow is less than the probability of landing on blue.
Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.
The theoretical probability, P(brown), is 25%, and the experimental probability is 32.5%. This was 13/40 = 32.5%.
The experimental probability of drawing a spade will be:
= 3/(7+3+6+4)
= 3/20
= 0.15.
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Answer: the sample space of the experiment from simultaneously flipping a coin and rolling a die consisted of: 2 × 6 = 12 possible outcomes.
Step-by-step explanation:
The sample space of 52 cards is all 52 possible outcomes, which is {Ace of Hearts, two of hearts, three of hearts...etc}.
Select the correct answer.
Which expression is equivalent to 3/2?
Answers
Answer:
Here is the full list of equivalent fractions to 32. 3/2, 6/4, 96, 12/8, 15/10, 18/12, 21/14, 24/16, 27/18, 30/20, 33/22, 36/24, 39/26, 42/28, 45/30, 48/32, 51/34, 54/36, 57/38, 60/40
Step-by-step explanation:
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Lou received requests for 150 tickets for their art show. The number of requests was 120% of the number of tickets they had. How many tickets do they have?
Answers
Answer:
180
Step-by-step explanation:
If she received requests for 150 tickets, and that is 120% of what they have, you would find 20% of 150. You would do this because 100% of 150 is 150, now you need to add the other 20%, so you have to find 20% of 150. Which is 30. You would then add that to 150 sine it is 120% of what they have. So, they have 180 tickets
how 4-digit positive integers have four differennt digits, where the leading digit is not zero, the integer is a multiple of 5, and 5 is the largets digt
Answers
Answer:
There are 9 possible thousands digits, because 0 cannot be the leading digit.
There are 2 possible ones digits, 0 and 5.
If the ones digit is 5:
There are 5 possible thousands digits: 1, 2, 3, and 4.For each possible thousands digit, there are 5 possible hundreds digits. (We used one of the digits above to be the thousands digit, but 0 is a possible hundreds digit.)For each possible pair of thousands-and-hundreds digits, there are 4 possible tens digits.
So there are 5 x 5 x 4 = 100 possible 4-digit numbers that end in 5 with no repeated digit and no digit larger than 5.
If the ones digit is 0:
There are 5 possible thousands digits.For each possible thousands digit, there are 4 possible hundreds digits.For each possible pair of thousands-and-hundreds digits, there are 6 possible tens digits.
So there are 5 x 4 x 6 = 120 possible 4-digit numbers that end in 0 with no repeated digit and no digit larger than 5.
100+120=220
Answer: 220 possible numbers.
Solve the equation 5(x + 2) = 6x + 3x − 14, and show your work. (5 points)
Answers
Evaluate the following expression. "5 less than 15"
A. -10
B. 8
C. 20
D. 10
Answers
Answer: 10
Step-by-step explanation: 5 less than 15 is 10 because 15 - 5 is 10. If it was 15 less from 5, only then it would be -10.
Answer:
5 less than 15 is Option D, 10. This is because using mathematical symbols, it says 15-5 which equals to 10.
Consider the word pencil. if all of the letters are used, and the first letter can’t be n or l, how many ways can the letters be arranged?
Answers
480 Ways can the letters be arranged.
What is the meaning of probability ?
Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.First letter can't be n or l
= 4! × [tex]5P_{3}[/tex]
= 24 × 5! /3!
= 24 × 5 × 4
= 480
Therefore, 480 ways can the letters be arranged.
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Answer: 480 ways
Step-by-step explanation:
jaquan washes cars for his neighbors on the weekends. Jaquan uses the same amount of water for each car he washes. the point on the following coordinate plane show how much water jaquan uses for 2,5, and 8. How much water does Jaquan use for 6 cars?
help me plsss
Answers
The amount of water for washing x cars is y = 12x, and 72 gallons would be needed to wash 6 cars.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The standard form of a linear equation is given as:
y = mx + b
Where m is the rate of change and b is the y intercept (initial value of y)
Let y represent the amount of water Jaquan uses to wash x cars, Using the point (2, 24) and (5, 60):
y - 24 = [(60 - 24)/(5- 2)](x - 2)
y = 12x
For 6 cars:
y = 12(6) = 72
The amount of water for washing x cars is y = 12x, and 72 gallons would be needed to wash 6 cars.
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Answer: Jaquan uses 72 L to wash 6 cars
Step-by-step explanation:
Translate the sentence into an equation.
15 less than Taryn's age is 20
use the variable a to represent Taryn's age.
answer choices:
a. 20-a = 15
b. 15-a = 20
c. a-15= 20
d. 20-15 = a
Answers
Answer: c. a-15= 20
Step-by-step explanation:
The answer is c because a represents her age and 15 less than that would mean that you have to subtract 15 from her age which is represented by a, and then 15 less than a would equal 20, so a-15=20
Assume you took $5,000 out of the bank to purchase a car worth $5,000. How much did you net worth change?
Answers
Your net worth change by zero dollars.
What is net worth?Net worth is the difference between asset and liability.
In other words net worth is the sum of all assets owned by a person or a company, minus any obligations or liabilities.
Therefore, since he took $5,000 out of the bank to purchase a car worth $5,000 his net worth will change by zero dollars.
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Instructions: Find the volume of each figure. Round your answers to the nearest tenth, if necessary.
Answers
The volume of the cone is 84.9 km³
How to find the volume of a cone?Volume of a cone = 1 / 3 πr²h
where
h = heightr = radiusTherefore,
radius = 3 km
height = √9.5² - 3²
height = √81.25
height = 9.01387818866
height = 9.014 km
Volume of a cone = 1 / 3 × 3.14 × 3² × 9.014
volume of the cone = 254.732197612 / 3
volume of the cone = 84.9107325372
volume of the cone = 84.9 km³
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g(a) = 4a + 5
f(a) = a² + 2a
Find: g(f(a))
Answers
Step-by-step explanation:
g(f(a))=4(a²+2a) + 5
= 4a²+8a+5
Maria and Franco are mixing sports drinks for a track meet.
Maria uses cup of powdered mix for every 2 gallons of water. Franco uses
1 cups of powdered mix for every 5 gallons of water. Whose sports drink is
stronger? Explain how you found your answer
Answers
Answer:Maria
Step-by-step explanation: Maria uses a cup per 2 gallons while Franco uses a cup for 5 gallons. Maria has a 1:16 ratio while Franco has a ratio of 1: 80 because a gallon is 16 cups. It is clear now that Franco has a smaller ratio so, Maria's sports drink is stronger.
A triangle has side lengths of (2b + 5c) centimeters, (10b + 7d) centimeters, and
(4d-3c) centimeters. Which expression represents the perimeter, in centimeters,
of the triangle?
Answers
The perimeter of the triangle can be express as follows:
12b + 11d + 2c
How to find perimeter of a triangle?The perimeter of a figure is the sum of the whole sides of the figure.
A triangle has three sides. Therefore, the perimeter of a triangle is the sum of the three sides.
Therefore, the sides of the triangle are of lengths (2b + 5c) centimetres, (10b + 7d) centimetres, and (4d-3c) centimetres.
Hence, the perimeter of the triangle can be represented as follows:
Perimeter of the triangle = 2b + 5c + 10b + 7d + 4d - 3c
Perimeter of the triangle = 2b + 10b + 7d + 4d + 5c - 3c
Perimeter of the triangle = 12b + 11d + 2c
Therefore, the perimeter of the triangle can be express as follows:
12b + 11d + 2c
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A function is shown: f(x) = 36x² - 1.
Choose the equivalent function that best shows the x-intercepts on the graph
Answers
Based on the given function, the equivalent function that best shows the x-intercepts on the graph is f(x) = (6x - 1)(6x + 1)
What are equivalent functions?Equivalent functions are different functions that have equal values when evaluated and compared
How to determin the equivalent function that best shows the x-intercepts on the graph?
The function is given as:
f(x) = 36x^2 - 1
Express 1 as 1^2
f(x) = 36x^2 - 1^2
Express 36x^2 as (6x)^2
f(x) = (6x)^2 - 1^2
Apply the difference of two squares.
This is represented as:
(a + b)(a - b) = a^2 - b^2
So, we have the following equation
f(x) = (6x - 1)(6x + 1)
Based on the given function, the equivalent function that best shows the x-intercepts on the graph is f(x) = (6x - 1)(6x + 1)
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A scientist uses a submarine to study ocean life. She begins 88 feet below sea level. • After traveling down for 6 seconds, she's 182 feet below sea level. Find the rate of change in the submarine's elevation in feet per second. Round your answer to the nearest tenth.
Answers
Answer:
original ft below sea level =88 feet
In six seconds goes to 182 feet
Amount of feet covered in 6 seconds=182-88=94 ft
Step-by-step explanation:
rate in feet per second = 94/6=15.66
rounding to nearest tenth=15.7ft/s
PLEASE HELP ME SOLVE THE QUESTION BELOW
Ann and Tom want to establish a fund for their grandson's college education. What lump sum must they deposit at 12 % annual interest rate, compounded quarterly , in order to have 20,000$ in the fund at the end of 10 years?
Answers
For Ann and Tom to have $20,000 at the end of 10 years, they must deposit a sum of $6,131.14.
What is the principal?
To calculate the sum of money they must deposit, use the compound interest formula.
From the compound interest formula;
P = A / ( 1 + r/n )^(nt)
Given that;
Final amount A = 20,000Interest rate r = 12% = 12/100 = 0.12Compound n = quarterly = 4Time t = 10 yearsPrincipal P = ?P = A / ( 1 + r/n )^(nt)
P = 20,000 / ( 1 + 0.12/4 )^(4×10)
P = 20,000 / ( 1.03)^40
P = 20,000 / 3.26203779
P = $6,131.14
Therefore, for Ann and Tom to have $20,000 at the end of 10 years, they must deposit a sum of $6,131.14.
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