The explanation provides a step-by-step process to determine the minimum trips required for the miners to cross the river.
To determine the minimum number of trips required for the miners to cross the river, we need to carefully consider the constraints given.
First, A and B can cross together because the maximum combined weight of their cargoes is 90 kg (40 + 50) which is less than 100 kg.
Then, A returns alone, carrying B's cargo, leaving B and C on the other side. B and C cross together as the combined weight of their cargoes is 40 kg (20 + 20) which is less than 100 kg.
Finally, B returns and takes A's cargo, crossing with C's cargo. In total, the minimum number of trips needed is 9 (Option A).
Theo had a balance of-$4 in his savings account.after making a deposit he has $25 in his account what is the overall
Suppose the leftmost digits of two numbers are 8 and 3 can u tell which number is greater? Explain
Mira's kitchen sink holds up to 103.468 liters of water. Round this amount to the nearest liter.
The nearest liters is 103 L(liters).
While rounding a figure to the nearest whole number, the figure closest to the decimal point is considered.
If the figure that is closest to the decimal point is more than 5, it would be taken as one and added to the first unit of the figures which is 3.
But if the figure is less than 1, it's taken as Zero.
From the liters given, 4 which is closest to the decimal point is less than 5. This is therefore taken as 0
Therefore, the nearest liters is 103 L(liters).
Learn more here:
https://brainly.com/question/21420385
Factor the polynomial 4x4 – 20x2 – 3x2 + 15 by grouping. What is the resulting expression? (4x2 + 3)(x2 – 5) (4x2 – 3)(x2 – 5) (4x2 – 5)(x2 + 3) (4x2 + 5)(x2 – 3)
Answer:
Hi there! The answer is to this question is
B. (4x2 – 3)(x2 – 5)
Hope this helps :D
The factored form of the polynomial 4x⁴ – 20x² – 3x² + 15 is (4x² – 3)(x² – 5). The correct option is B.
What is a polynomial?A polynomial in mathematics is an expression made up of coefficients and indeterminates and involves only the operations of multiplication, addition, subtraction, and non-negative integer exponentiation of variables.
Given polynomial is 4x⁴ – 20x² – 3x² + 15. The polynomial by grouping can be solved as below:-
P = 4x⁴ – 20x² – 3x² + 15
P = 4x² ( x² - 5) -3 ( x² - 5 )
P = (4x² – 3)(x² – 5)
Hence, the factored form of the polynomial 4x⁴ – 20x² – 3x² + 15 is (4x² – 3)(x² – 5).
To know more about polynomials follow
https://brainly.com/question/2833285
#SPJ6
Gymnast Clothing manufactures expensive soccer cleats for sale to college bookstores in runs of up to 500. Its cost (in dollars) for a run of x pairs of cleats is C(x) = 3050 + 8x + 0.1x2 (0 ≤ x ≤ 500). Gymnast Clothing sells the cleats at $150 per pair. Find the revenue and profit functions. How many should Gymnast Clothing manufacture to make a profit? Revenue = 150x Correct: Your answer is correct. Profit = 150x−(3050+8x+0.1x2) Correct: Your answer is correct. At least Incorrect: Your answer is incorrect. pairs
To find the profit maximizing quantity, we must calculate and compare total revenue, marginal revenue, total cost, and marginal cost for each unit level, and graph the total revenue, total cost, marginal revenue, and marginal cost curves. The profit maximizing quantity is where marginal revenue equals marginal cost.
Explanation:To determine the profit maximizing quantity, we need to calculate total revenue, marginal revenue, total cost, and marginal cost for each output level of the winter coats sold by Doggies Paradise Inc. Since the firm is perfectly competitive and dog coats sell for $72 each, the marginal revenue is equal to the price, thus $72 for each additional unit sold.
Let's calculate these values and summarize them in a table:
Total Revenue (TR) = Price (P) imes Quantity (Q) = $72 imes QMarginal Revenue (MR) = Change in TR / Change in Q = $72 (constant for each unit since P is constant)Total Cost (TC) = Fixed Costs (FC) + Variable Costs (VC)Marginal Cost (MC) = Change in TC / Change in QThe marginal cost can be found by taking the difference in total variable costs for each additional unit produced plus the fixed costs. It's important to compare MR and MC for each output to find the profit maximizing quantity, where MR=MC. Graphing these will illustrate the intersection point that denotes the optimal output level. The total revenue and total cost curves can also help visualize the point at which profit is maximized, as this is where the distance between the TR and TC curves is largest.
A conjecture and a portion of the flowchart proof used to prove the conjecture are shown.
Which equation best represents the information that should be in the box labeled 1?
3x = 9
3x = 26
3x = 27
3x = 30
Answer:
The correct option is 3.
Step-by-step explanation:
Given: [tex]\overline {PQ}\cong \overline{QR}[/tex], [tex]PQ=3x-1,QR=26[/tex].
Prove: [tex]x=9[/tex]
[tex]\overline {PQ}\cong \overline{QR}[/tex] (Given)
[tex]PQ=QR[/tex] (Segment congruent postulate)
[tex]3x-1=26[/tex] (Substitution property of equality)
Add 1 on both sides.
[tex]3x-1+1=26+1[/tex] (Addition property of equality)
[tex]3x=27[/tex]
Divide both sides by 3.
[tex]x=9[/tex] (Division property of equality)
Hence proved.
The required equation for box 1 is 3x=27.
Therefore the correct option is 3.
3. List all measurements that you can make with the 10-oz and 6-ov glasses. You can combine both cups for this process. If the measurements were not included in your process to solve, prove how you can make specific measurements. 4. Make observations about your findings Is there anything that you notice? Make a conjecture. Do you think what you found will work in all cases (for example if you were to use odd measurements rather than even)? 5. Vary the problem in an attempt to prove your conjecture. You can vary the problem by changing the target amount to find or changing the size of the glasses. Since you have already found all possible measurements for the 10-oz and 6-oz glass, your task is to change the glass sizes.
The ways that can be used to illustrate the measurement will be:
Use an object as a reference pointChoose an appropriate vessel to pour your liquid into. Place your vessel on a flat surface and bring yourself down to eye level.How to illustrate the information?It should be noted that the measurements that one can make with the 10-oz and 6-ov glasses include measuring cups of water, etc.
It is important to have some visual aids as a reference for the correct amount. It is important to clearly see the amount being poured as the fluid is slowly poured into the vessel.
In mathematics, the conjecture is a conclusion or a proposition which is proffered on a tentative basis without proof.
In conclusion, use an object as a reference point, choose an appropriate vessel to pour your liquid into, and then place the vessel on a flat surface and bring yourself down to eye level.
Learn more about measurement on:
https://brainly.com/question/24842282
#SPJ1
One-Half cup of black provides 15% of the potassium you need daily. You must get the remaining 2890 milligrams from other sources. How many milligrams of potassium should you consume daily?
In 12 hours, how many more kilometers could the yellow car go than the red car if the red car has an average speed of 217/km per hour and the yellow car has 242 km per hour?
Zach has 3/4 hour to play video games. it takes him 1/12 hour to set uo the system. Each round of his favorite game takes 1/6 hour. How many rounds can he play
Final answer:
After setting up the system, Zach has 2/3 hour left to play. Since each round takes 1/6 hour, he can play 4 full rounds of his favorite game.
Explanation:
Zach has 3/4 hour to play video games, and it takes him 1/12 hour to set up the system. Each round of his favorite game takes 1/6 hour. To find out how many rounds he can play, we need to subtract the setup time from the total available time and then divide by the time each game takes.
Subtract the setup time from the total time: 3/4 hour - 1/12 hour.Calculate the common denominator and subtract: 9/12 hour - 1/12 hour = 8/12 hour, which simplifies to 2/3 hour.Divide the remaining time by the time per round: 2/3 hour ÷ 1/6 hour.Calculate the number of rounds: 2/3 hour × 6/1 hour = 4 rounds.Zach can play 4 full rounds of his favorite game.
The area of a square garden is one sixteenth
1.
16 squared 2. How long is each side?
Shona is buying a rug for her room. Store A has the rug for $45 with a 10% discount. Store B has the same rug for $46 and is offering a $10 off coupon. The sales tax is 6% on either purchase. If Shona only has $40 to spend, which store will she purchase the rug from, and how much will she have left over?
Estimate 45.8 divided by 23.6
The largest butterfly in the world is found in Papua,New Guinea.The female butterfly of the species weighs about 9/10 ounce.Use a decimal to write the female's weight.
what property was used to rewrite the polynomial expression
(x+5)+3(a+(6x)y) to (5+x)+3(a+(6x)y)
What is 0.61 repeating as a fraction and how did you get the answer
Answer:
the answer is 61/99
Step-by-step explanation:
How much will you save if you buy an item listed at $75.50 at a 25% discount?
drew adds 1/2 cup of wheat flour and 2 3/4 cup of white flour to his muffin batter. how many cups of flourdoes drew add
A 1 1/4
B 2 2/3
C 3 1/4
D 3 3/4
Answer:3 and 1/4 is the answer
Step-by-step explanation:
Chris needs a graphing calculator for math class. He finds a $60 model on sale for 15% off. If he decides to buy this calculator, how much will the sale price be?
there are 16 sixth graders and 20 seventh graders in a club. the club wants to organize members into equal size groups. each group will only have sixth or only seventh graders.
how many students will be in each group if each group has the greatest number if club members
Which phrase correctly describes the following expression?(5+23)
The expression (5+23) is correctly described as a simple addition, resulting in a sum of 28. It exemplifies the basic operation of adding two numbers together, an essential mathematical skill.
Explanation:The phrase that correctly describes the following expression (5+23) is simple addition. This expression simply requires adding the two numbers within the parentheses, leading to an answer of 28. Unlike complex expressions that involve multiple operations and rules such as the distributive property or the order of operations (parentheses, exponents, multiplication and division, and addition and subtraction), this expression only requires basic addition.
The concept of addition is fundamental in mathematics, allowing for the combining of two or more numbers to find their total. Such operations are building blocks for more complex arithmetic and algebraic tasks.
It's also important to note that the order in which numbers are added does not change the sum, a principle known as the commutative property of addition.
Morgan has $60 to spend on clothes. He wants to buy a pair of jeans for $25 and spend the rest on t-shirts. Each t-shirt costs $5. Which inequality represents the number of t-shirts he can purchase? x ≥ 7 x ≤ 16 x ≤ 7 x ≥ 16
Answer:
x ≤ 7
Step-by-step explanation:
the larger of two numbers is nine less than four times the smaller number. If the sum od the two numbers is 76, find both numbers
Answer:
17 and 59
Step-by-step explanation:
Let's find the answer by assuming the following:
L=larger number
S=smaller number
The first condition is: 'L' is nine less than four times 'S' but, because:
(four times 'S') is the same as 4*S then:
('L' is nine less than four times 'S') is equal to ('L' is nine less than 4*S), which means:
L+9=4*S (eq. 1)
Second condition is: the sum of the two numbers is 76, so:
L+S=76 which can be written as:
S=76-L using this relation in eq. 1 we have:
L+9=4*S
L+9=4*(76-L)
L+9=304-4L
L+4L=304-9
5L=295
L=295/5
L=59
And also we have:
L+S=76
S=76-L
S=76-59
S=17
In conclusion, the two numbers are 17 and 59.
The perimeter of a square is 12p +4. One side of the square equals? Explain your answer.
We know that a square, by definition, has four congruent sides.
So, simply divide the perimeter by 4, and you will get the expression equivalent to each side: 12p+4/4
3p+1 is equal to one side of the square
Find the remaining trigonometric ratios of θ based on the given information.
csc θ = 2 and cos θ is positive
To find the remaining trigonometric ratios of θ given that csc θ = 2 and cos θ is positive, we calculate sin θ, cos θ, tan θ, cot θ, and sec θ.
Explanation:To find the remaining trigonometric ratios of θ, we are given that csc θ = 2 and cos θ is positive. Based on this information, we can determine the values of the other trigonometric ratios.
The reciprocal of sin θ is csc θ, so we can find sin θ by taking the reciprocal of 2. Therefore, sin θ = 1/2.
Since cos θ is positive and sin θ is positive (since 1/2 is positive), we know that θ is in the first quadrant. In the first quadrant, all the trigonometric ratios are positive. Therefore, cos θ = √(1 - sin²θ) = √(1 - (1/2)²) = √(1 - 1/4) = √(3/4) = √3/2.
Finally, we can find the remaining trigonometric ratios:
tan θ = sin θ / cos θ = (1/2) / (√3/2) = 1/√3 = √3/3cot θ = 1/tan θ = √3/3sec θ = 1/cos θ = 2/√3 = 2√3/3cos θ = √3/2Learn more about Trigonometric Ratios here:https://brainly.com/question/31675053
#SPJ2
What is the area of Figure ABCD?
a) 54 square inches
b) 60 square inches
c) 66 square inches
d) 72 square inches
How to rewrite 3x4-1+2
melissa is making clothes for her dolls.She has 7/8 yard of fabric.Each doll shirt requires 2/7 of a yard of fabric.How many shirts can she make for her dolls?
The sum of two consecutive integers is 150. what are the two integers ?
The numbers are 74.5 and 75.5
What is algebra?Algebra is a branch of mathematics that deals with symbols and the arithmetic operations across these symbols. These symbols do not have any fixed values and are called variables. In our real-life problems, we often see certain values that keep on changing. But there is a constant need to represent these changing values. Here in algebra, these values are often represented with symbols such as x, y, z, p, or q, and these symbols are called variables. Further, these symbols are manipulated through various arithmetic operations of addition, subtraction, multiplication, and division, with an objective to find the values.
Given number:
150
let the consecutive number be x and x+1
Now, according to the question
x+x+ 1= 150
2x + 1 = 150
2x= 149
x= 149/2
x= 74.5
hence, the numbers are 74.5 and 75.5
Learn more about algebra here:
https://brainly.com/question/953809
#SPJ2
A butter block weighs 200g the dimension of the block is 8cm by 5cm by 6cm what is the density to 3 decimal places?
Density of butter block is 0.833 g/cm³
Given that;Weight of butter block = 200 g
Dimension of Butter block = 8cm by 5 cm by 6 cm
Find:Density of butter block
Computation:Density of butter block = Weight of butter block / Volume of butter block
Weight of butter block
Density of butter block = 200 / [(8)(5)(6)]
Density of butter block = 200 / 240
Density of butter block = 0.833 g/cm³
Learn more:https://brainly.com/question/2745718?referrer=searchResults