The ratio of the surface area to volume of a right rectangular prism with a square base and a height that is triple the base edge is 6:1.
Let x be the length of one side of the square base of the prism. Then the height of the prism is 3x. The surface area of the prism is given by 2x² + 4(x)(3x) = 14x², since there are two square faces with area x² each and four rectangular faces with area x(3x) each.
The volume of the prism is x²(3x) = 3x³. Therefore, the ratio of surface area to volume is (14x²)/(3x³) = 14/3x = 4.67/x. Since x is a length, it must be positive, so the ratio is minimized when x is as large as possible.
Therefore, the smallest possible ratio is when x approaches infinity, and in this limit, the ratio approaches 0. However, in the real world, x must be finite, so the ratio is always greater than 0.
We can see that the ratio decreases as x increases, so the smallest possible ratio occurs when x is as small as possible.
The smallest possible positive value of x is 0.000000...01, which is very close to 0 but not equal to 0. Therefore, the ratio is always greater than 0 but can be made arbitrarily small.
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a roulette wheel has the numbers from 1 to 36, as well as 0 and 00. when an odd number comes up, you win $1; otherwise, you lose $1. what is the expected gain (or loss) from a single trial? what is the variance of the gain (or loss)?
The predicted gain (or loss) from a single trial is 53 cents per game on average.
A roulette wheel has the number 1 through 36, as well as 0 and 00. If you wager $1 that an odd number would show up, you will win or lose $1 depending on whether or not that occurrence occurs. If random variable X represents your net benefit, X=1 with probability 18/38 and X=-1 with probability 20/38.
E(X) = 1(18/38) – 1 (20/38) = -$.053
On average, the casino wins 5 cents for each game.
If the stakes are raised, the casino makes even more money:
E(X) = 10(18/38) – 10 (20/38) = -$.53
If the cost is $10 for each game, the casino wins an averaged of 53 cents per game. If 10,000 games are played in a single night, that's a cool $5300.
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Chris and Alex are friends who have summer jobs as waiters. The distribution of Chris’s weekly tips is approximately normal with mean $225 and standard deviation $25. Alex works at a different restaurant; the distribution of his weekly tips is approximately normal with mean $240 and standard deviation $15. Assuming their weekly tips are independent, which is the probability that Chris will make more in tips than Alex in a randomly selected week? Show your work.
(A) 0.067
(B) 0.159
(C) 0.227
(D) 0.303
(E) 0.354
Marilyn is buying a birthday present for her son from his favorite store. She has a $25 store credit that will help cover the cost of his gift. Marilyn wants to spend less than $31 after applying the store credit. If p represents the cost of the present, then this situation can be modeled by the inequality,
p - 25 < 31
Which value could be a possible cost for the present and a solution to Marilyn’s inequality?
57
58
56
55
Answer: 55
Step-by-step explanation: 55 - 25 = 30
just subtract all the answers by 25 and try to find something lower then 31
A pizza maker determined an annual profit in dollars
2
from selling pizzas using f(n) = 65n -0.04n² where
n is the number of pizzas sold. What is the annual
profit if the pizza maker sells 300 pizzas?
A. $18,500
B. $3,600
C. $7,800
D. $15,900
Answer:
Given, the annual profit equation is f(n) = 65n - 0.04n².
When the number of pizzas sold, n = 300, the annual profit will be:
f(300) = 65(300) - 0.04(300)²
= 19500 - 0.04(90000)
= 19500 - 3600
= $15,900
Therefore, the annual profit if the pizza maker sells 300 pizzas is $15,900. Answer: D.
Step-by-step explanation:
We have two rational expressions: The first rational expression has (y² - 13y +36) in the numerator and (y² + 2y - 3) in the denominator. The second rational expression has (y²-y-12) in the numerator and(y²-2y+1) in the denominator .Simplify them
We are given two rational expressions: one with (y² - 13y + 36) in the numerator and (y² + 2y – 3) in the denominator, and the other with (y² - y – 12) in the numerator and (y² - 2y + 1) in the denominator. We need to simplify these rational expressions.
Simplifying the first rational expression:
The numerator of the first expression, y² - 13y + 36, can be factored as (y – 4)(y – 9).
The denominator, y² + 2y – 3, can be factored as (y + 3)(y – 1).
Therefore, the first rational expression simplifies to (y – 4)(y – 9) / (y + 3)(y – 1).
Simplifying the second rational expression:
The numerator of the second expression, y² - y – 12, can be factored as (y – 4)(y + 3).
The denominator, y² - 2y + 1, can be factored as (y – 1)(y – 1) or (y – 1)².
Therefore, the second rational expression simplifies to (y – 4)(y + 3) / (y – 1)².
By factoring the numerator and denominator of each rational expression, we obtain the simplified forms:
First rational expression: (y – 4)(y – 9) / (y + 3)(y – 1)
Second rational expression: (y – 4)(y + 3) / (y – 1)²
These simplified expressions are in their simplest form, with no common factors in the numerator and denominator that can be further canceled.
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find two numbers that have the given product and the given sum 12,8
Answer:
What?
Step-by-step explanation:
This is a Muti-Question From 3 different Questions ____________________________________________________________________Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. Bonnie withdrew $1,200 from her savings account. She spent of the money on travel arrangements. She spent of the remaining amount at the hardware store. Finally, she treated her friend to lunch with some of the remaining money. After lunch, Bonnie had $300.50 left. How much money did Bonnie spend on lunch? Bonnie spent $_____ on lunch. __________________________________________________________________ Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. At the farmers market, Nathaniel buys two dozen oranges at $3.50 per dozen, four kilograms of apples at $3.25 per kilogram, two kilograms of carrots at $1.90 per kilogram, and one kilogram of potatoes for $1.20. He received a 5% discount off his total bill. How much money did Nathaniel spend on fruits and vegetables at the farmers market? Nathaniel spent $______ at the farmers market. __________________________________________________________________ elect the correct answer. A basketball team played 15 games and won 80% of them. If the team expects to play 30 games in all, how many more games must it win to finish the season with a 90% winning percentage? A. 12 B. 14 C. 15 D. 27 Please Help me with these 3 Questions!
Answer:
23.75
Step-by-step explanation:
IM GANNA HELP FOR THE SECOND ONE CUZ THE FIRST QUESTION DOESNT HAVE SOME VALUES AND THE THIRD IS KINDA HARD
BUT I HOPE I HELPED
the question:
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. At the farmers market, Nathaniel buys two dozen oranges at $3.50 per dozen, four kilograms of apples at $3.25 per kilogram, two kilograms of carrots at $1.90 per kilogram, and one kilogram of potatoes for $1.20. He received a 5% discount off his total bill. How much money did Nathaniel spend on fruits and vegetables at the farmers market? Nathaniel spent $______ at the farmers market.
nathaniel got 2 dozen so 7$ for the oranges
4 kg so 13$ for apples
2 kg so 3.8$ for carrots
1 kg so 1.2$ for potatoes
LETS ADD IT TOGETHER
25$ TOTAL
DISCOUNT=5%
5% OF 25 IS 1.25
SO 25-1.25=23.75
SO NATHANIEL SPENT 23.75$ IN ALL
HOPE I HELPED
PLS MARK BRAINLIEST
DESPERATELY TRYING TO LEVEL UP
✌ -ZYLYNN JADE ARDENNE
JUST A RANDOM GIRL WANTING TO HELP PEOPLE!
PEACE!
Lydia buys 5 pounds of apples and 3 pounds of bananas for a total of $8.50. Ari buys 3 pounds of apples and 2 pounds of bananas for a total of $5.25. This system of equations represents the situation, where x is the cost per pound of apples, and y is the cost per pound of bananas.
5x + 3y = 8.5
3x + 2y = 5.25
If you multiply the first equation by 2, what number should you multiply the second equation by in order to eliminate the y terms when making a linear combination?
Complete the multiplication and add the equations. What is the result?
What is the price per pound of apples? $
What is the price per pound of bananas? $
Answer: The price per pound of apples is $ 1.25 and the price per pound of bananas is $ 0.75.
Step-by-step explanation: Given that lydia buys 5 pounds of apples and 3 pounds of bananas for a total of $8.50 whereas Ari buys 3 pounds of apples and 2 pounds of bananas for a total of $5.25.
We are to find the price per pound of apples and bananas.
The cost per pound of apples is represented by x dollars and the cost per pound of bananas is represented by y dollars.
Then, according to the given information, the system of equations describing the situation is as follows:
Multiplying equation (i) by 2, we have
and multiplying equation (ii) by 3, we have
To eliminate y, we subtract equation (iv) from equation (iii) and we arrive at
From equation (i), we get
Thus, the price per pound of apples is $ 1.25 and the price per pound of bananas is $ 0.75.
Answer:Bro the answer is price per pound of apples is $1.25
and the price per pound of bannanas is $0.75
Chose the step below that correctly uses the division property to begin solving the equation: 2x - 14 = 4.
(PLS HELP ASAP) A basketball player scored 351 points last year. If the player plays 18 games this year, how many points will he need to average per game to beat last year’s total?
Answer:
I think it's 19 I'm pretty sure
Answer:
20
Step-by-step explanation:
The first step would be to divide 351 by 18 to see what score he would need to tie his previous record. The answer to that would be 19.5, so if you round to the nearest whole, you would get 20.
This figure represents a box that is filled with board games.
What is the volume of the box in terms of board games?
4 board games
16 board games
36 board games
144 board games
Answer:
16 board games.
Step-by-step explanation:
The volume of the box is 6 x 6 x 4 (144).
The volume of 1 board game is 3 x 3 x 1 (9).
144/9 = 16
consider a data set corresponding to readings from a distance sensor: 9, 68, 25, 72, 46, 29, 24, 93, 84, 17 if normalization by decimal scaling is applied to the set, what would be the normalized value of the first reading, 9?
If decimal scaling normalization is applied to the given data set, the normalized value of the first reading, 9, would be 0.09.
To normalize the first reading, 9, we divide it by 100. Therefore, the normalized value of 9 would be 0.09.By applying the same normalization process to each value in the data set, we would obtain the normalized values for all readings. The purpose of normalization is to scale the data so that they fall within a specific range, often between 0 and 1, making it easier to compare and analyze different variables or data sets.
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Can someone plz help I’m being timed it’s only one problem!!!!
Answer:
10 and 12
Step-by-step explanation:
Is my guess
Answer:
10 and 12
Step-by-step explanation:
also if you wouldn't mind giving brainliest i'm just trying to rank up. Only if u dont mind though.
B is the midpoint of AC . If AB =3x-4 and BC =2x+5, what is the length of BC ?
Answer:
23
Step-by-step explanation:
AB = BC = (1/2)AC
3x - 4 = 2x + 5
x = 9
BC = 2x + 5 = 2 × 9 + 5 = 23
for rotation, when swapping the x and y and making the y negative, what happens if the new y is already negative
When you perform a 2D rotation of a point by swapping the x and y coordinates and negating the new y coordinate, the sign of the y-coordinate will change based on the quadrant in which the original point lies.
If the original point lies in the first or fourth quadrant, the new y-coordinate will be negative after rotation. In this case, if the new y-coordinate is already negative, then you do not need to negate it again.
On the other hand, if the original point lies in the second or third quadrant, the new y-coordinate will be positive after rotation. In this case, if the new y-coordinate is already negative, then you need to negate it to correctly represent the rotation.
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Which statement is true for the equation 4x − 4x − 5 = −5?
A. It has no solution.
B. It has one solution.
C. It has two solutions.
D. t has infinitely many solutions.
Answer:
Step-by-step explanation:
It would have no solution. Every time x is something, the 4x-4x will cancel each other out leaving the -5=-5
convert into power notation -1/81
Answer:
-1/9^2 is the power notation for your questions
Step-by-step explanations
CAN SOEMBODYY JUST PLSS IM BEGGIN HEL PMEEEEEEEEEEEEEEEEEEEEEEEE
Answer:
Hi, there
Question 1: B. 6x^3(x-6)
Question 2: A. (8x+3)^2
Question 3: A. (5x+9y)(5x-9y)
Question 4: D.(x-2)(x-3)
Step-by-step explanation:
Hope this helps :)
Find the next two terms in this
sequence.
50, 40, 31, 23, 16, | ? ],[?]
Answer:
8, 0
Step-by-step explanation:
can anyone please help me
Answer:
1. x = 9°
angleA=36°
angleB=54°
2. x = 28°
angleA=28°
angleB=62°
Step-by-step explanation:
1. 6x + 4x = 90° (By ASP)
2. 2x + 6 + x = 90° (By ASP)
The first two of three consecutive multiples of 9 sum to 2511. What are the numbers?
Answer:
First = 1251
Second = 1260
Third = 1268
Step-by-step explanation:
First: 9x
Second: 9(x+1)
Third: 9(x+2)
\({ \tt{first + second = 2511}} \\ { \tt{9x + 9(x + 1) = 2511}} \\ { \tt{9x + 9x + 9 = 2511}} \\ { \tt{18x = 2502}} \\ { \tt{x = 139}}\)
First = 9 × 139 = 1251
First = 9 × 139 = 1251Second = 9(139 + 1) = 1260
First = 9 × 139 = 1251Second = 9(139 + 1) = 1260Third = 9(139 + 2) = 1268
someone help please bro i need help right now
The linear function represented by the table is:
y = 8x + 6
How to find the linear function?A general linear function can be written in slope-intercept form as:
y = a*x + b
Where a is the slope and b is the y-intercept.
The y-intercept is the value that the function takes when x = 0, here we can see that we have the pair (0, 6), then the y-intercept is 6.
y = a*x + 6
Now we want to find the value of a. Using any other of the pairs in the table (like (3, 30) for example)
We can replace the points in the equation and then solve it for a.
Using the second point (1, 14) we will get:
14 = a*1 + 6
Now we can solve that for a.
14 = a + 6
14 - 6 = a
8 = a
The linear function is:
y = 8x + 6
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Suppose that a deck of 52 cards contains 26 red cards and 26 black cards (and assume the red cards are numbered 1 to 26, and so are the black cards). Say we use the 52 cards to randomly distribute 13 cards each among two players (2 players receive 13 card each). a. How many ways are there to pass out 13 cards to each of the two players? b. What is the probability that player 1 will receive 13 cards of one color and player 2 receive 13 cards of the other color?
(A) the number of ways to pass out 13 cards to each of the two players is (52! / (13! × 13!)) × (39! / (26! × 13!)) (B) We can calculate probability by dividing the number of favorable outcomes by the total number of possible outcomes. (26! / (13! × 13!))²] / [(52! / (13! × 13!)) × (39! / (26! × 13!))]
A) To determine the number of ways to distribute 13 cards to each of the two players, we can use the concept of combinations. Since the order of distribution does not matter, we'll use the formula for combinations:
C(52, 13) × C(39, 13)
= (52! / (13! × (52 - 13)!)) × (39! / (13! × (39 - 13)!))
Simplifying this expression:
= (52! / (13! × 39!)) × (39! / (13! × 26!))
= (52! / (13! × 13! × 26!)) × (39! / (26! × 13!))
= (52! / (13! × 13! × 26!)) × (39! / (26! × 13!))
= (52! / (13! × 13!)) × (39! / (26! × 13!))
Therefore, the number of ways to pass out 13 cards to each of the two players is (52! / (13! × 13!)) × (39! / (26! × 13!)).
B) To calculate the probability that player 1 will receive 13 cards of one color and player 2 will receive 13 cards of the other color, we need to find the favorable outcomes and divide it by the total number of possible outcomes.
The favorable outcome is when player 1 receives 13 cards of one color and player 2 receives 13 cards of the other color.
For player 1 to receive 13 red cards, there are C(26, 13) ways, and for player 2 to receive 13 black cards, there are C(26, 13) ways.
Therefore, the number of favorable outcomes is C(26, 13) ×C(26, 13).
The total number of possible outcomes is the same as the answer to part A, which is C(52, 13) × C(39, 13).
Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes.
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There are approximately \(6.54 \times 10^{11}\) ways to distribute 13 cards to each of the two players, and the probability that player 1 will receive 13 cards of one color and player 2 will receive 13 cards of the other color is approximately 0.76%.
a. To determine the number of ways to pass out 13 cards to each of the two players, we can use the concept of combinations. We need to select 13 cards out of the total 52 cards for the first player, and then the remaining 13 cards will automatically go to the second player. The number of ways to choose 13 cards out of 52 is given by the combination formula: \(52_C_{13} = \frac{52!}{(13!(52-13)!)}\). Evaluating this expression, we find that there are approximately \(6.54 \times 10^{11}\) ways to distribute the cards.
b. The probability that player 1 will receive 13 cards of one color and player 2 will receive 13 cards of the other color depends on the specific color that each player receives. Let's consider the case where player 1 receives all red cards and player 2 receives all black cards. There are 26 red cards and 26 black cards, so the probability of player 1 receiving all red cards is given by: \(\frac{26_C_{13} \times 26_C_0}{52_C_{13}}\). Evaluating this expression, we find that the probability is approximately 0.0076, or 0.76%.
In conclusion, there are approximately \(6.54 \times 10^{11}\) ways to distribute 13 cards to each of the two players, and the probability that player 1 will receive 13 cards of one color and player 2 will receive 13 cards of the other color is approximately 0.76%.
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Find the lateral surface area of this
cylinder. Round to the nearest tenth.
12cm
3 cm
?] cm2
lateral surface area of this cylinder is 1584/7 or 226.28...cm square.
The lateral area of the cylinder is 226.2 cm² .
What is lateral surface area of cylinder?The lateral surface of an object is all of the sides of the object, excluding its base and top. The lateral surface area is the area of the lateral surface.
For a right circular cylinder of radius r and height h, the lateral area is the area of the side surface of the cylinder:
A = 2πrh.
According to the question
radius of cylinder = 3 cm
height of cylinder = 12 cm
The lateral area of the cylinder:
A = 2πrh
A = 2 * \(\frac{22}{7}\) * 3 * 12
A = 226.2 cm²
Hence, the lateral area of the cylinder is 226.2 cm² .
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Please help I’ll mark as brainliest!! And explain why too
Answer:
A=2 B=1
Step-by-step explanation:
B is distributive because you have to foil the x out of the parenthesis
A is because when three or more numbers are added (or multiplied), the sum (or the product) is the same regardless of the grouping of the addends.
Chapter 5: Solving Linear Equations by Graphing > Section Exercises 5.4 > Exercise 1
Previous
The method to solve the equation system graphically is discussed below.
What is function?A function is a relation between a dependent and a independent function.
Given is to solve a given system of linear equations.
Since the linear equations are not given, we can assume the system of equations to be -
ax + by + c = 0
dx + ey + f = 0
We will discuss how to solve the equations graphically. The steps are -
It is important to remember that a linear equation has one solution set.Plot the graph of both the lines on the graph paper. Both the graphs would be straight line.Now, the point of intersection, will give the solution set for the given system of linear equations.Therefore, the method to solve the equation system graphically is discussed above.
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Is this answer right?
Answer:
Step-by-step explanation:
all angles are congruent:false
B.consecutive angles are congruent:false
corresponding angles are congruent:true.
c.diagonals bisect eachother:true.
d.diagonals bisect opposite angles:false.
You take a 30 year $400,000 mortgage at 9% compounded monthy. What will be your payment? How much principal will be outstanding at the halfway time (180payments)? Round to nearest $.
Group of answer choices
A) p = $3218 & P(180) = 317,322
B) p = $3281 & P(180) = 313,722
C) p = $3218 & P(180) = 313,722
D) p = $3281 & P(180) = 317,322
The principal will be outstanding at the halfway time C) p = $3218 & P(180) = 313,722.
What is principal?Principal is an amount of money borrowed or invested, on which interest is paid. It is the original sum of money that is invested or borrowed and not the interest that accumulates over time. Principal is the amount of money before any interest or other costs are added. Borrowers must pay back the principal plus interest when the loan is due. Investors can earn returns on their principal when an investment is successful.
The payment for a 30 year $400,000 mortgage at 9% compounded monthly is calculated using the following formula:
p = (400000 * (1 + (0.09/12))³⁶⁰)/(360 * (1 - (1 + (0.09/12))^⁻³⁶⁰))
Plugging in the given values, we get:
p = (400000 * (1 + (0.09/12))³⁶⁰)/(360 * (1 - (1 + (0.09/12))^-360)) = $3218
The amount of principal outstanding at the halfway time (180 payments) is calculated using the following formula:
P(180) = 400000 - (p * 180)
Plugging in the given values, we get:
P(180) = 400000 - (3218 * 180) = 313,722
Therefore, the answer is C) p = $3218 & P(180) = 313,722.
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If You take a 30 year $400,000 mortgage at 9% compounded monthy. the paynebt will be $3218 and P(180) = 317,322. The correct answer is A) p = $3218 & P(180) = 317,322.
What is probability?
Probability is a branch of mathematics that deals with the study of random events or phenomena. It involves the measurement of the likelihood or chance of an event occurring, based on the ratio of the number of favorable outcomes to the total number of possible outcomes.
To calculate the monthly payment for the mortgage, we can use the formula:
P = A / ((1 - (1 + r)^(-n)) / r)
where P is the monthly payment, A is the loan amount ($400,000), r is the monthly interest rate (9%/12 = 0.0075), and n is the total number of payments (30 years x 12 months/year = 360 payments).
P = 400000 / ((1 - (1 + 0.0075)^(-360)) / 0.0075)
P = $3,219.64 (rounded to the nearest cent)
Therefore, the monthly payment is $3,219.
To find the outstanding principal balance at the halfway time (180 payments), we can use the formula for the remaining balance of a loan after t payments:
P(t) = A * ((1 + r)^t - 1) / (r * (1 + r)^t)
where P(t) is the remaining principal balance after t payments.
P(180) = 400000 * ((1 + 0.0075)^180 - 1) / (0.0075 * (1 + 0.0075)^180)
P(180) = $313,721.87 (rounded to the nearest dollar)
Therefore, the correct answer is A) p = $3218 & P(180) = 317,322.
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-13.5=2.7s (im class so hurry)
Answer:
Step-by-step explanation:
2.7s = -13.5
27s = -135
s = -5
Answer:
\(s=-5\)
Step-by-step explanation:
\(-13.5=2.7s\)
Switch sides:
\(2.7s=-13.5\)
Multiply both sides by 10:
\(2.7s\times 10=-13.5\times 10\)
\(27s=-135\)
Divide both sides by 27:
\(\frac{27s}{27}=\frac{-135}{27}\)
\(s=-5\)
If y=x+2 changed to y=x-1 how would it change