The circumference of the circle is 340 units.
What is circle ?
In geometry, a circle is a two-dimensional shape consisting of all points that are a fixed distance (called the radius) from a given point (called the center). A circle is a set of points that are equidistant from the center.
Let's use the formula relating the length of an arc to the circumference of a circle:
Length of arc = (central angle / 360) x circumference
Plugging in the given values, we get:
17 = (18/360) x circumference
Simplifying and solving for the circumference, we get:
circumference = 17 x (360/18) = 17 x 20 = 340
Therefore, the circumference of the circle is 340 units.
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1. State the converse, contrapositive, and inverse of the conditional statement “A positive integer is a prime only if it has no divisors other than 1 and itself”.
Answer:
Step-by-step explanation:
A contrapositive statement changes "if not p then not q" to "if not q to then, not p." The converse of the conditional statement is “If Q then P.” The contrapositive of the conditional statement is “If not Q then not P.” The inverse of the conditional statement is “If not P then not Q.” if p → q, p → q, then, ∼ q →∼ p ∼ q →∼ p
A Note about Notation: Be careful with the notation a|b
. This does not represent the rational number ab
. The notation a|b
represents a relationship between the integers a
and b
and is simply a shorthand for “ a
divides b
.” "Divides" as in a|b
is a relation (true or false), while "divided by" as in ab
or a/b
is an operation (results in a number).
The definition for “divides” can be written in symbolic form using appropriate quantifiers as follows: A nonzero integer m
divides an integer n
provided that (∃q∈Z)(n=m⋅q).
Compare the following box plots below. Which of the following statements is NOT true?
Class B has a higher median
Class A has greater variability
Both A and B have students who are only children
Over half of the students in class A have two or more siblings
Comparing the box plots, the statements which are not true are Class A has greater variability and over half of the students in Class A have two or more siblings.
Based on the given box plots, we can make the following observations:
a) Class B has a higher median: True. We can see from the plot that the median line for Class B (represented by the orange line inside the box) is higher than the median line for Class A (represented by the blue line inside the box).
b) Class A has greater variability: False. We can see from the plot that the boxes for both classes have similar lengths, indicating similar variability. However, Class A has a few more outliers compared to Class B, which indicates some extreme values that are far from the median.
c) Both A and B have students who are only children: True. We can see from the plot that both classes have a box plot labelled "0" indicating that some students in each class are only children.
d) Over half of the students in class A have two or more siblings: False. We can see from the plot that the box labelled "2+" in Class A only covers about a third of the box, indicating that less than a third of the students have two or more siblings. Therefore, the statement is not true.
Therefore, the answer is b) Class A has greater variability and d) Over half of the students in Class A have two or more siblings.
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URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
The correct answer is (B) Function A is decreasing, while function B is also decreasing AND Function A is steeper.
Which worksheet helps you figure out how much you can spend and invest?
Answer:
A monthly budget worksheet cause it shows your income and expenditure, so you are able to spend within your budget and it helps you know your disposable income
A submarine is 1,275.5 feet below sea level. It dives down 215.5 feet and then rises 125.5 feet. Finally, the sub dives down another 122.4 feet. Assume sea level is at an elevation of 0 feet.
After diving dοwn 215.5 feet, rising 125.5 feet, and diving dοwn anοther 122.4 feet, the submarine is at a depth οf 1,063.1 feet belοw sea level.
What is the arithmetic οperatiοn?The fοur fundamental οperatiοns οf arithmetic are additiοn, subtractiοn, multiplicatiοn, and divisiοn οf twο οr mοre quantities. Included in them is the study οf numbers, especially the οrder οf οperatiοns, which is impοrtant fοr all οther areas οf mathematics, including algebra, data management, and geοmetry. The rules οf arithmetic οperatiοns are required in οrder tο answer the prοblem.
Starting at a depth οf 1,275.5 feet belοw sea level, the submarine dives dοwn an additiοnal 215.5 feet:
1,275.5 - 215.5 = 1,060 feet belοw sea level
Then the submarine rises 125.5 feet:
1,060 + 125.5 = 1,185.5 feet belοw sea level
Finally, the submarine dives dοwn anοther 122.4 feet:
1,185.5 - 122.4 = 1,063.1 feet belοw sea level
Therefοre, after diving dοwn 215.5 feet, rising 125.5 feet, and diving dοwn anοther 122.4 feet, the submarine is at a depth οf 1,063.1 feet belοw sea level.
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Explain how to simplify this expression: (7a + 9) + (4a - 7).
The simplified expression would be 11a + 2.
Simplifying an expressionIn order to simplify the given expression, we first need to combine like terms.
The terms can be combined by adding their coefficients:
(7a + 4a) = 11a(9 - 7) = 2Now we can substitute these combined terms back into the original expression:
(7a + 9) + (4a - 7) = 7a + 4a + 9 - 7
And then simplify further:
= 11a + 2
Therefore, the simplified form of the expression (7a + 9) + (4a - 7) is 11a + 2.
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Writing equations of lines
Anthony purchased a $227 stereo system at Wrigley's Department Store. He paid $47 down and agreed to pay the balance in 12 equal monthly payments. The finance charge was 9.6% simple interest. What was the amount of each payment
Answer:
Calculation:
Total Amount: $227
Down Payment: $47
Interest Rate: 9.6% (0.096)
Number of Payments: 12
Remaining Balance: $227 - $47 = $180
Remaining Balance with Interest: $180 + (9.6/100 * $180) = $197.68
Amount of Payment: $197.68 / 12 = $16.47
Answer: The amount of each payment is $16.47.
Are conditional probabilities always dependent?
Answer:
Two events are said to be independent if one event occurring does not affect the probability that the other event will occur. However, if one event occurring or not does, in fact, affect the probability that the other event will occur, the two events are said to be dependent.
If one event occurs or not, it does, in fact, affect the probability that the other event will occur, and then the two events are said to be dependent.
Given the following functions find and simplify (f-g)(1) f(x)=-x^2-x-3 g(x)=-1
To find (f-g)(1), we first need to find f(1) and g(1): f(1) = -(1)^2 - 1 - 3 = -5 g(1) = -1 Now we can substitute these values into (f-g)(x) = f(x) - g(x) and simplify: (f-g)(1) = f(1) - g(1) = (-5) - (-1) = -4 Therefore, (f-g)(1) = -4.
HELP PLSSSSSSSSSSSSSSSS
Answer:
H
Step-by-step explanation:
% of 11 year olds is 24
% of 12 year olds is 16
then ratio of
11 year olds : 12 year olds
= 24 : 16 ( divide both parts by 8 )
= 3 : 2
Tom and John are engaged in buying and selling certain products A and B. Tom BUYS 5 of product A but
SELLS twice as much of product B. John on the other hand SELLS three times what Tom BOUGHT of
product A and BUYS 13 of product B. At the end of the business day, John banks Ksh 110,000/- while
Tom banks Ksh 230,000.
Under the assumption that the sale prices for product A and B are the same for the two men, and the costs prices for the products A and B are also the same for the two men, obtain the following:
The price for product A which was determined as Ksh 42,727.27 and the price for product B as 44,363.63
Question: If there was a mark up of 25% on the cost price and a discount of 15% on the sale price, how
much would each of the partners have banked at the end of the business day?
Product A is priced at Ksh 55,000, while Product B is priced at Ksh 32,000.
How to calculate Product A and B?Assume that the selling price for both the two items A and B is "S" and the cost price for both is "C". Using this knowledge, we can create two equations that relate the costs and revenues of the two items, one for Tom and one for John:
Tom: 5C - 2(5S) = [tex]P_1[/tex]
John: 3(5C) - 13C = [tex]P_2[/tex]
where [tex]P_1[/tex] and [tex]P_2[/tex] represent Tom's and John's respective profits.
We are aware that John deposits Ksh. 110,000 while Tom deposits Ksh. 230,000 at the end of the business day. Thus, we can say:
[tex]P_1[/tex] = 230,000 - 5C
[tex]P_2[/tex] = 110,000 - 18C
These values are what we obtain when we enter them into the equations for Tom and John:
5C - 2(5S) = 230.000 - 5C
When we simplify these equations, we obtain:
10C - 10S = 230,000
2C = 110,000
Solving for C, we get:
C = 55,000
We may determine S by adding this value back into the original equation:
10(55,000) - 10S = 230,000
Simplifying this equation, we get:
S = 32,000
Therefore, the price for product A is Ksh 55,000 and the price for product B is Ksh 32,000.
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Solve the systems by elimination.
10x + 10y = 40
5x + 3y = 8
Answer:
x = -2, y = 6
Step-by-step explanation:
First, find the opposite of 10 by multiplying 5x+3y=8 by -2 to eliminate 10x.
10x+10y=40
-2(5x+3y=8)
10x+10y=40
-10x-6y=-16 (Subtract 10y - 6y) (Subtract 40 - 16)
4y = 24 (Divide by 4 on both sides)
y = 6
Substitute 6 in the y value in any of the equations.
10x+10(6)=40 (Replaced 10y with 10(6) )
10x+60=40
-60 = -60 (Subtract 60 from both sides)
10x = -20 (Divide by 10 on both sides)
10 10
x = -2
A school bus has 22 rows of seats, and 4 students can be seated in each row. Students riding in the bus have filled 19 rows of seats, and 1/2 of the remaing seats. How many seats on the bus are empty?
Thus, remaining seats on the school bus that are empty is found as: 6 seats.
Explain about the fraction of number:The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.
The number of parts by which the whole has already been divided is shown by the denominator. It is positioned in the fraction's lower portion, just below fractional bar.How several sections of both the fraction are displayed or chosen is shown in the numerator. It is positioned well above fractional bar in the upper portion of the fraction.Given data:
Total rows of seats = 22Number of seats in each row = 4Filled rows = 191/2 of the remaining.Total seats in bus = Total rows of seats * Number of seats in each row
Total seats in bus = 22 * 4
Total seats in bus = 88
Filled seats = 19 * 4 = 76
Left seats = 88 - 76 = 12
Now, 1/2 of the 12 seats is filled = 6 seats.
remaining seats = 6
Thus, remaining seats on the school bus that are empty is found as: 6 seats.
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Jacob drove from Nicktown to Binghamton at
an average speed of 70 mph. If it took him 4
hours to get there, how far is Binghamton from
Nicktown?
A. 17.5 miles
B. 210 miles
C. 280 miles
D. 300 miles
(3, -3) and (8, 12)
Step-by-step explanation:
what did you ask the question? ask it clearly please?? if you ask clearly the question. we also give answer
You are the casting director for a local production of the play Rent. There are six distinct parts available, but you have tventy-three volunteers. In how many different ways can this play be cast?
Hamilton had a 21-man company in its first (currently only ongoing) production. There are 720 ways that can play as cast.
Hamilton had a 21-man company in its first (currently only ongoing) production, so we really know a little about our army of volunteers (all of which I think are good enough to hold the show to a high standard), but that's not necessarily the case. The problem - Thomas Kail and Andy Blanken buehler use their team of 11 in their Broadway productions to great effect, but a team of the same size. It's an art choice.
When it comes to the main body, there are actually 14 named locations, with a lot of work through singing and/or dialogue, in addition to the many things the members use from Kail products. This prevents all volunteers from being an essential part because that leaves us only 3 people in total which seems a bit lackluster in some big productions.
One solution is to have some minor roles played by the band members - for example James Madison, King George III, Peggy Schuyler and Maria Reynolds - so now we have 9 key characters and 8 groups that we need to succeed. compact performance.
My preference is to follow a Broadway production, so we have 10 main actors, so the ensemble is 7 people. If necessary, with the help of a small part of the main cast, we can expand the group in many performances.
Therefore, there are 10!/7! = 720 ways .
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simplify -2(2x - 5) -4x
Answer: -8x +10
Step-by-step explanation:
-2(2x -5) -4x
1. simplify parthentheses
-4x +10 -4x
add like terms
-8x +10
Please help with the question below
please write the answer in a decimal
Answer
15.71 cm
Explanation
In a class of 20 children, 8 had one sister, 6 had 2 sisters. The mean number of children was 1. how many children had no sisters
There are no children in the class who have no sisters. This is because the mean number of children is 1, and some children have more than one sibling to Balance out those who have only one.
To solve this problem, we need to use some basic principles of statistics and probability. Let's start by identifying the key information provided in the problem. We know that there are 20 children in the class, and that some of them have sisters. Specifically, 8 children have one sister and 6 children have two sisters. We also know that the mean (average) number of children is 1, which means that on average, each child has one sibling.
To find out how many children had no sisters, we can use the following formula:
Total number of children - (number of children with one sister x 1) - (number of children with two sisters x 2) = number of children with no sisters
Using the values from the problem, we get:
20 - (8 x 1) - (6 x 2) = 0
This means that there are no children in the class who have no sisters. While this may seem counterintuitive, it's important to remember that the mean number of children is 1, which means that some children must have more than one sibling in order to balance out the others who have only one.
In summary, the answer to the question is that there are no children in the class who have no sisters. This is because the mean number of children is 1, and some children have more than one sibling to balance out those who have only one.
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Peter observes that 75% of the birds at his bird feeder are finches. The results from 20-simulation trials of the model showed that finches are a
guaranteed bird type for 80% of the birds.
Based on the results from the simulation trials, what should Peter conclude about his hypothesis if he predicted that birds at his bird feeder woul
continue with the same percentage of finches as before?
A. Reject the hypothesis.
B. Conclude the alternate hypothesis was correct.
C. Conclude that 80% of the birds at the bird feeder should always be finches.
D. Conclude the hypothesis was correct.
Option A "Reject the hypothesis" is the appropriate conclusion in this case.
As per the question,
Based on the results from the simulation trials, Peter should conclude that his hypothesis should be rejected.
The simulation showed that finches are a guaranteed bird type for only 80% of the birds, which is lower than the observed percentage of 75% finches at Peter's bird feeder.
This indicates that the predicted percentage of finches continuing at the same rate is not supported by the simulation results.
Therefore, option A "Reject the hypothesis" is the appropriate conclusion in this case.
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Ling bought d donuts to share with coworkers. There were 6 donuts in each box. Write an expression that shows how many boxes of donuts Ling bought.
the expression would be used as follows:
Number of boxes of donuts (N) = 6 x Number of donuts (D)
Ling bought 108 boxes of donuts.
This expression is a mathematical equation that uses multiplication to calculate the number of boxes of donuts Ling bought.
What is mathematical equation?Equations are used to solve problems involving unknowns, such as how much a person owes for groceries or how many people are required to complete a certain task.
The expression that would show how many boxes of donuts Ling bought is:
Number of boxes of donuts (N) = 6 x Number of donuts (D)
In this expression, N represents the number of boxes of donuts Ling bought and D represents the number of donuts. This expression can be used to calculate the number of boxes of donuts Ling bought when the number of donuts is known.
For example, if Ling bought 18 donuts, the expression would be used as follows:
Number of boxes of donuts (N) = 6 x Number of donuts (D)
N = 6 x 18
N = 108
Therefore, Ling bought 108 boxes of donuts.
This expression is a mathematical equation that uses multiplication to calculate the number of boxes of donuts Ling bought. The expression can be used whenever the number of donuts is known and can be used to calculate the number of boxes of donuts Ling bought.
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Janct was driving home from work at a speed of 40 mph. Realizing she forgot her documents as she arrived home, she then drove back to work at a speed of 60 mph. What is her average speed for the entire trip?
A. 48 mph
B.49 mph
C. 50 mph
D. 52 mph
Answer: 50 mph
Step-by-step explanation:
3
5
6
ft = 3
5
6
× 1 ft = 3
5
6
× 12 in Write 3
5
6
feet as a single fraction greater than one. Then, complete the expression PLEASE HELP ASAP
The complete expression of given question is :
3 5/6 feet = 23/6 feet = 46 inches.
What do you mean by term Mixed Fraction ?A mixed fraction is a type of fraction that consists of a whole number and a proper fraction. For example, 3 1/2, 2 2/3, and 5 3/8 are all mixed fractions. The whole number part represents a number of whole units, while the fraction part represents a part of a unit.
To write 3 5/6 feet as a single fraction greater than one, we can convert the mixed number to an improper fraction. To do this, we multiply the whole number (3) by the denominator of the fraction (6), and add the numerator (5), then put the result over the denominator. Like this:
3 5/6 = (3 x 6 + 5)/6 = 23/6
Therefore, 3 5/6 feet can be written as the improper fraction 23/6 feet.
To complete the expression, we can use the fact that 1 foot is equal to 12 inches. Therefore, we can convert 23/6 feet to inches by multiplying it by 12:
23/6 feet × 12 inches/1 foot = 23/6 × 12 inches
Simplifying the fraction, we get:
23/6 × 12 inches = 276/6 inches = 46 inches
Therefore, the expression is:
3 5/6 feet = 23/6 feet = 46 inches.
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- w/5 + 9 = 13 what w
Answer:
w = -20
"The beautiful thing about learning is that no one can take it away from you." :)
The temperature of one furnace is 1400°C and cools at a rate of 2.5°C per minute. The temperature of another furnace is 1200°C and is heated at a rate of 1.5°C per minute. Write an equation that models when the temperature of the two furnaces will be equal.
Answer:
1400 - 2.5t = 1200 + 1.5t
t = 50
Step-by-step explanation:
A trapezoid has an
area of 35 mm².
What is the height
of the trapezoid?
8 mm
6 mm
The height of the trapezoid is 7 mm.
A quadrilateral with one set of parallel opposite sides is referred to as a trapezium.
To find the height of a trapezoid when the area and the lengths of the parallel bases are given, we can use the formula:
h = 2A / ([tex]b_1 + b_2[/tex])
where
h is the height,
A is the area,
[tex]b_1[/tex] and [tex]b_2[/tex] are the lengths of the parallel bases.
As per given information in the question.
Using the given area of 35 mm² and the lengths of the parallel bases,
For [tex]b_1[/tex] = 8 mm and [tex]b_2[/tex] = 6 mm
we get:
h = 2 x 35 / (8 + 6) = 7 mm
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Mary Lou Mason purchased baby bottles for $4.56, baby formula for $12.45, and a pacifier for $2.13. For all purchases she must pay the state sales tax of 6.5 percent and the county tax of 1.5 percent. What is the tax on her purchases? Show all of your work.
Answer:
$1.53
Step-by-step explanation:
You want to know the total tax on purchases of $4.56, 12.45, and 2.13 if the tax rate is the sum of 6.5% and 1.5%.
TaxThe tax is the product of the tax rate and the total of purchases. The tax rate will be the sum of the state and county tax rates:
6.5% +1.5% = 8% = 8/100
The attached calculation shows the tax is $1.53 after rounding to cents.
The tax rate on Mary Lou Mason's purchases is $1.53.
What is meant by rate?
In mathematics, rate usually refers to the ratio of two quantities that have different units of measurement.
To calculate the total tax on Mary Lou Mason's purchases, we need to first calculate the total cost of her purchases, including both the prices of the items and the sales tax.
The total cost of Mary Lou Mason's purchases before taxes is:
$4.56 + $12.45 + $2.13 = $19.14
To calculate the sales tax, we need to multiply the total cost of the purchases by the sum of the state and county tax rates:
6.5% + 1.5% = 8%
So the sales tax rate is 8%.
To calculate the total tax on Mary Lou Mason's purchases, we multiply the total cost of the purchases by the sales tax rate:
$19.14 x 8% = $1.53
Therefore, the tax on Mary Lou Mason's purchases is $1.53.
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Find the maximum value of = √ subject to the cost constraint K + 4L = 16.
Estimate the change in the optimal value of Q if the cost constraint is changes to K +
4L = 17
Answer:
This problem can be solved using the method of Lagrange multipliers. Let's define the Lagrangian function as: L(K, L, λ) = Q - λ(K + 4L - 16) Taking partial derivatives with respect to K, L, and λ, we get: dL/dK = 0 => 1 - λ = 0 => λ = 1 dL/dL = 0 => 1 - 4λ = 0 => λ = 1/4 dL/dλ = K + 4L - 16 = 0 Solving the last equation for K, we get: K = 16 - 4L Substituting this into the Lagrangian function, we get: L = Q - λ(16 - 4L + 4
A hand of 10 cards is dealt from a well-shuffled standard 52-card deck of cards. What is the probability that the hand contains 3 Jacks?
a) 0.048617
b) 0.018617
c) 0.038617
d) 0.068617
e) 0.028617
A hand of 10 cards is dealt from a well-shuffled standard 52-card deck of cards. The probability that the hand contains 3 Jacks is 0.018617. So correct option is b.
Describe combinations?In mathematics, combinations refer to the ways of selecting a group of items from a larger set without considering the order of the items. Combinations are used to count the number of possible outcomes in situations where order does not matter, such as selecting a group of people to form a committee, or selecting a subset of items from a larger collection.
The number of possible combinations of r items selected from a set of n items is given by the formula:
C(n, r) = n! / (r! * (n - r)!)
where n! represents the factorial of n, which is the product of all positive integers up to n, and r! represents the factorial of r.
To solve this problem, we need to find the probability of selecting exactly 3 jacks out of 10 cards from the 52-card deck.
The probability of selecting a jack from the deck is 4/52, since there are four jacks in the deck. The probability of not selecting a jack is 48/52, since there are 48 non-jack cards in the deck.
Using the formula for the probability of a specific combination of events occurring (nCr), where n is the total number of cards in the deck, and r is the number of jacks we want to select:
P(3 jacks) = (4/52)³(48/52)⁷ × 10C3
10C3 is the combination of 10 cards taken 3 at a time, which is equal to 10!/(3!7!) = 120.
Therefore, P(3 jacks) = (4/52)³(48/52)⁷ × 120 ≈ 0.018617
So, the answer is b) 0.018617.
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