A cargo ship is 704 feet long. If 1.1 inch represents 13 feet. How long is the ship in the model? Round your answer to the nearest tenth if needed.
Answer:
59.57
Step-by-step explanation:
704 / 13
= 54.1538461538
54.1538461538 x 1.1
= 59.5692307692
QUESTION :-
If ( + ) means ( - ) , ( - ) means ( × ) , ( ÷ ) means ( + ) , ( × ) means ( ÷ )
Then ,
15 - 3 + 10 × 5 ÷ 5 = ?
a ) 42
b ) 48
c ) 5
d ) 50
i need a proper explanation how u got the ans , only ans if u know the ans ..
Thx for answering ¡¡
15 - 3 + 10 × 5 ÷ 5 = ? Hence, 48 is the correct answer.
By inserting codes and then using BODMAS Rule:
15 × 3 - 10 ÷ 5 + 5
15 x 3 = 45. Now 10 divided by 5 is 2 and keep the other 5 so:
= 45 - 2 + 5 = 48
I HOPE THIS HELPED YOU.
You are playing a math game, right?
Well anyways, I will solve this for you!!
Let's see the symbols clearly then we will solve
+ = - - = ×÷ = +× = ÷Now, Substitute the symbols in the original expression
Original expression:
\( \sf \: 15 - 3 + 10 \times 5 \div 5\)
New expression:
\( \tt \: 15 \times 3 - 10 \div 5 + 5\)
Solution for the equation ;\( \bf \: 15 \times 3 - 2 + 5\)
\( \bf \: 45 - 2 + 5\)
\( \bf \underline{ \underline {48}}\)
rainwater was collected in water collectors at thirty different sites near an industrial basin and the amount of acidity (ph level) was measured. the mean and standard deviation of the values are 4.8 and 1.2 respectively. when the ph meter was recalibrated back at the laboratory, it was found to be in error. the error can be corrected by adding 0.3 ph units to all of the values and then multiply the result by 1.4. find the mean and standard deviation of the corrected ph measurements.
To find the mean and standard deviation of the corrected pH measurements, we can use the following formulas:
Corrected Mean = (Original Mean + Correction Factor) * Multiplication Factor
Corrected Standard Deviation = Original Standard Deviation * Multiplication Factor
The correction factor is 0.3 and the multiplication factor is 1.4. Therefore, the corrected mean is:
Corrected Mean = (4.8 + 0.3) * 1.4 = 7.14
And the corrected standard deviation is:
Corrected Standard Deviation = 1.2 * 1.4 = 1.68
Therefore, the mean of the corrected pH measurements is 7.14 and the standard deviation is 1.68.
In summary, to find the corrected mean and standard deviation of the pH measurements, we need to add the correction factor (0.3) to the original mean, multiply the result by the multiplication factor (1.4), and multiply the original standard deviation by the multiplication factor. The corrected mean is 7.14 and the corrected standard deviation is 1.68.
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Use the drawing tool(s) to form the correct answer on the provided graph.
The graph of the function f(x) = |x| is vertically stretched by a factor of 2, shifted 6 units down, and then shifted 4 units to the right. Draw the transformed function on the provided graph.
The transformed function is:
g(x) = 2*|x - 4| - 6
And the graph can be seen below.
How to get the transformed function?
The original function is the parent absolute value function:
f(x) = |x|.
First, we stretch it vertically by a factor of 2, so we just multiply it by 2:
g(x) = 2*f(x).
Then, we move it 6 units down and 4 units to the right, this is written as:
g(x) = 2*f(x - 4) - 6.
Replacing f(x) by the actual function:
g(x) = 2*|x - 4| - 6
Now we just need to graph that, the graph of the transformed function can be seen below.
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If x and y are linearly​ independent, and if z is in Span {x, y}​, then {x, y, z} is linearly dependent.
a. true
b. false
The statement is true: If x and y are linearly independent, and if z is in Span {x, y}, then {x, y, z} is linearly dependent.
The statement is true.
Let's first understand the terms used:
Linearly independent:
A set of vectors is linearly independent if none of them can be expressed as a linear combination of the other vectors. In other words, no vector in the set can be written as a sum of scalar multiples of the other vectors.
Span:
The span of a set of vectors is the set of all linear combinations of those vectors.
In this case, Span\({x, y}\) is the set of all vectors that can be formed by adding scalar multiples of x and y.
Now, let's consider the given statement:
If x and y are linearly independent, it means that neither x nor y can be expressed as a linear combination of the other. However, it is given that z is in the Span\({x, y}.\)
This means that z can be expressed as a linear combination of x and y:
\(z = ax + by\), where a and b are scalar constants.
Let's analyze the set\({x, y, z}\). We know that z can be expressed as a linear combination of x and y, as shown above. This implies that the set \({x, y, z}\)is linearly dependent, because one vector (z) can be expressed as a linear combination of the others \((x and y)\).
Thus, the statement is true: If x and y are linearly independent, and if z is in Span\({x, y}\), then\({x, y, z}\) is linearly dependent.
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Can anyone help me with this please ?
Answer:
A.
Step-by-step explanation:
f(x)
f(2)= 1 or (2,1)
HELP FAST U WILL BE MY FAV PERSON
Answer: the answer is 9 weeks
Step-by-step explanation:
you have to subtract 72 from 288 becasue she already has that in her account then divide the answer by 24 becasue thats how much she will add each week.
Determine the value of
f(2) when
f(x)=x² - 5x+2
Answer:
-4
Step-by-step explanation:
Substitute \(x = 2\) in to the function
\(f(2) = 2^2 -5(2) + 2\)
= -4
A. Find the zeros of the function algebraically. (Enter your answers as a comma-separated list.)
f(x) = 1/3x^3 - x
B. Find the zeros of the function algebraically. Multiple part answer, please list steps.
f(x) = 5x^2 + 23x - 10
To find the zeros, set the function equal to zero and factor.
0 = (___ x - ___) (x+ ___)...
The zeros of the given function algebraically are 2/5 and -5.
A) Given function is:
f(x) = (1/3)x³ - x
To find the zeros of the given function algebraically, we have to follow these steps:
Step 1: Substitute f(x) = 0 in the given function, we get:
0 = (1/3)x³ - x
Step 2: Multiply both sides by 3 to eliminate the denominator, we get:
0 = x³ - 3x
Step 3: Factor out x from the equation, we get:
x(x² - 3) = 0
Step 4: Now, factor x² - 3, we get:
x(x - √3)(x + √3) = 0
Therefore, the zeros of the given function algebraically are - √3, 0, and √3.
B) Given function is:
f(x) = 5x² + 23x - 10
To find the zeros of the given function algebraically, we have to follow these steps:
Step 1: Substitute f(x) = 0 in the given function, we get:
0 = 5x² + 23x - 10
Step 2: Multiply both sides by 2 to eliminate the fraction, we get:
0 = 10x² + 46x - 20
Step 3: Divide each term by 2 to simplify the equation, we get:
0 = 5x² + 23x - 10
Step 4: Factorize the equation, we get:
0 = (5x - 2)(x + 5)
Step 5: Equate each factor to zero to find the zeros of the function, we get:
5x - 2 = 0 or x + 5 = 0
⇒ 5x = 2 or x = -5
⇒ x = 2/5 or x = -5
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write an equation for the line of fit for this data in the form y=mc+where x is latitude and y is temperature.
Solution
y= mx +b
Where y is the temperature and x the latitude
If we fit an equation line we have the following:
A= 119.24
b= -1.070
Then the equation would be:
y= -1.070 x + 119.24
please help I don't get it
2. Using proportion, the value of x = 38, the length of FC = 36 in.
3. Applying the angle bisection theorem, the value of x = 13. The length of CD = 39 cm.
What is the Angle Bisector Theorem?The Angle Bisector Theorem states that in a triangle, an angle bisector divides the opposite side into segments that are proportional to the lengths of the other two sides of the triangle.
2. The proportion we would set up to find x is:
(x - 2) / 4 = 27 / 3
Solve for x:
3 * (x - 2) = 4 * 27
3x - 6 = 108
3x = 108 + 6
Simplifying:
3x = 114
x = 114 / 3
x = 38
Length of FC = x - 2 = 38 - 2
FC = 36 in.
3. The proportion we would set up to find x based on the angle bisector theorem is:
13 / 3x = 7 / (2x - 5)
Cross multiply:
13 * (2x - 5) = 7 * 3x
26x - 65 = 21x
26x - 21x - 65 = 0
5x - 65 = 0
5x = 65
x = 65 / 5
x = 13
Length of CD = 3x = 3(13)
CD = 39 cm
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Simplify. 18m – 9v + 6v – 7m
Answer: The answer is 11m + -3v.
8. If X-Poisson(a) such that P(X= 3) = 2P(X=4) find P(X= 5). A 0.023 B 0.028 C 0.035 D 0.036
For the Poisson relation given, the value of P(X=5) is 0.028
Poisson distributionIn a Poisson distribution, the probability mass function (PMF) is given by:
\(P(X = k) = ( {e}^{ - a} \times {a}^{k} ) / k!\)
Given that P(X = 3) = 2P(X = 4), we can set up the following equation:
P(X = 3) = 2 * P(X = 4)
Using the PMF formula, we can substitute the values:
(e^(-a) * a^3) / 3! = 2 * (e^(-a) * a^4) / 4!
\(( {e}^{ - a} \times {a}^{3} ) / 3! = 2 \times ( {e}^{ - a} \times {a}^{4} ) / 4!\)
Canceling out the common terms, we get:
a³ / 3 = 2 × a⁴ / 4!
Simplifying further:
a³ / 3 = 2 * a⁴ / 24
Multiplying both sides by 24:
8 × a³ = a⁴
Dividing both sides by a³:
8 = a
Now that we know the value of 'a' is 8, we can calculate P(X = 5) using the PMF formula:
P(X = 5) = (e⁸ * 8⁵) / 5!
Calculating this expression:
P(X = 5) = (e⁸ * 32768) / 120
P(X = 5) ≈ 0.028
Therefore, for the Poisson relation , P(X = 5) = 0.028
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find the partial derivatives of the function (8y-8x)/(9x 8y)
The partial derivative of the function with respect to y is: ∂/∂y [(8y-8x)/(9x+8y)] = 8/(9x+8y) - (64x)/(9x+8y)^2To find the partial derivatives of the function (8y-8x)/(9x+8y), we need to take the derivative with respect to each variable separately.
First, let's find the partial derivative with respect to x. To do this, we treat y as a constant and differentiate the function with respect to x:
(8y-8x)/(9x+8y)
= (8y)/(9x+8y) - (8x)/(9x+8y)
Using the quotient rule, we can simplify this expression:
= (-8y(9))/((9x+8y)^2) - 8/(9x+8y)
Simplifying further, we get:
= (-72y)/(9x+8y)^2 - 8/(9x+8y)
Therefore, the partial derivative of the function with respect to x is:
∂/∂x [(8y-8x)/(9x+8y)] = (-72y)/(9x+8y)^2 - 8/(9x+8y)
Now, let's find the partial derivative with respect to y. To do this, we treat x as a constant and differentiate the function with respect to y:
(8y-8x)/(9x+8y)
= (8y)/(9x+8y) - (8x)/(9x+8y)
Using the quotient rule again, we get:
= 8/(9x+8y) - (8x(8))/((9x+8y)^2)
Simplifying further, we get:
= 8/(9x+8y) - (64x)/(9x+8y)^2
Therefore, the partial derivative of the function with respect to y is:
∂/∂y [(8y-8x)/(9x+8y)] = 8/(9x+8y) - (64x)/(9x+8y)^2
And that's how we find the partial derivatives of the function (8y-8x)/(9x+8y) using the quotient rule and differentiation with respect to each variable separately.
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ADP Mining Company mines an iron ore called Alpha. During the month of August, 416,000 tons of Alpha were mined and processed at a cost of \( \$ 750,500 \). As the Alpha ore is mined, it is processed
The COGS of Alpha ore mined and processed by ADP Mining Company is $750,500.ADP Mining Company is an organization that specializes in mining iron ore called Alpha.
During the month of August, 416,000 tons of Alpha were mined and processed at a cost of $750,500. ADP Mining Company extracts the ore and then processes it to generate a finished product that can be sold. ADP Mining Company must maintain a high level of production efficiency to make a profit while keeping the cost of production to a minimum. Alpha ore is processed as it is mined. The processing cost is included in the overall cost of the Alpha ore.The cost of production, also known as the cost of goods sold (COGS), is calculated by summing all of the direct and indirect expenses associated with the production of the finished product. It comprises costs such as raw material costs, wages and salaries, rent, electricity, depreciation, and other indirect expenses.
Direct expenses, such as the cost of processing Alpha ore, are included in COGS since they are incurred while producing the finished product.COFG calculation:
COGS = Raw Material Cost + Direct Labor Cost + Direct Expenses + Other Indirect Expenses
COGS = $750,500 (direct expenses)
The COGS of Alpha ore mined and processed by ADP Mining Company is $750,500.
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Dell Eatery employs one worker whose job it is to load apple pies on outgoing company cars. Cars arrive at the loading gate at an average of 48 per day, or 6 per hour, according to a Poisson distribution. The worker loads them at a rate of 8 per hour, following approximately the exponential distribution in service times. a. Determine the operating characteristics of this loading gate problem. [6 Marks] b. What is the probability that there will be more than six cars either being loaded or waiting? [2 Marks] Formulae L= μ−λ
λ
W= μ−λ
1
L q
W q
rho
P 0
= μ(μ−λ)
λ 2
= μ(μ−λ)
λ
= μ
λ
=1− μ
λ
P n>k
=( μ
λ
) k+1
The required probability is 0.4408.
The operating characteristics of the loading gate problem are:
L = λ/ (μ - λ)
W = 1/ (μ - λ)
Lq = λ^2 / μ (μ - λ)
Wq = λ / μ (μ - λ)
ρ = λ / μ
P0 = 1 - λ / μ
Where, L represents the average number of cars either being loaded or waiting.
W represents the average time a car spends either being loaded or waiting.
Lq represents the average number of cars waiting.
Wq represents the average waiting time of a car.
ρ represents the utilization factor.
ρ = λ / μ represents the ratio of time the worker spends loading cars to the total time the system is busy.
P0 represents the probability that the system is empty.
The probability that there will be more than six cars either being loaded or waiting is to be determined. That is,
P (n > 6) = 1 - P (n ≤ 6)
Now, the probability of having less than or equal to six cars in the system at a given time,
P (n ≤ 6) = Σn = 0^6 [λ^n / n! * (μ - λ)^n]
Putting the values of λ and μ, we get,
P (n ≤ 6) = Σn = 0^6 [(6/ 48)^n / n! * (8/ 48)^n]
P (n ≤ 6) = [(6/ 48)^0 / 0! * (8/ 48)^0] + [(6/ 48)^1 / 1! * (8/ 48)^1] + [(6/ 48)^2 / 2! * (8/ 48)^2] + [(6/ 48)^3 / 3! * (8/ 48)^3] + [(6/ 48)^4 / 4! * (8/ 48)^4] + [(6/ 48)^5 / 5! * (8/ 48)^5] + [(6/ 48)^6 / 6! * (8/ 48)^6]P (n ≤ 6) = 0.5592
Now, P (n > 6) = 1 - P (n ≤ 6) = 1 - 0.5592 = 0.4408
Therefore, the required probability is 0.4408.
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you have an unlimited amount of water, but you need to measure 100 ounces into the target cup. you only have three cups: one that measures 127 ounces, one that measures 21 ounces, and one that measures 3 ounces (figure 9.19). how would you use those cups to measure the necessary 100 ounces?
Measure exactly 100 ounces using the given cups with Capacities of 127 ounces, 21 ounces, and 3 ounces.
To measure exactly 100 ounces using the cups with capacities of 127 ounces, 21 ounces, and 3 ounces, you can follow the steps below:
1. Start by filling the 127-ounce cup completely with water.
2. Pour the water from the 127-ounce cup into the 21-ounce cup. This leaves 106 ounces (127 - 21) in the 127-ounce cup.
3. Empty the 21-ounce cup.
4. Pour the remaining 106 ounces from the 127-ounce cup into the 21-ounce cup. This fills the 21-ounce cup completely and leaves 85 ounces (106 - 21) in the 127-ounce cup.
5. Empty the 21-ounce cup.
6. Pour the 85 ounces from the 127-ounce cup into the 21-ounce cup. This fills the 21-ounce cup and leaves 64 ounces (85 - 21) in the 127-ounce cup.
7. Empty the 21-ounce cup.
8. Pour the 21 ounces from the 127-ounce cup into the 21-ounce cup. This fills the 21-ounce cup completely and leaves 43 ounces (64 - 21) in the 127-ounce cup.
9. Empty the 21-ounce cup.
10. Pour the 43 ounces from the 127-ounce cup into the 21-ounce cup. This fills the 21-ounce cup and leaves 22 ounces (43 - 21) in the 127-ounce cup.
11. Empty the 21-ounce cup.
12. Pour the 3 ounces from the 127-ounce cup into the 3-ounce cup. This fills the 3-ounce cup completely and leaves 19 ounces (22 - 3) in the 127-ounce cup.
13. Empty the 3-ounce cup.
14. Pour the 19 ounces from the 127-ounce cup into the 3-ounce cup. This fills the 3-ounce cup and leaves 16 ounces (19 - 3) in the 127-ounce cup.
15. Finally, pour the 16 ounces from the 127-ounce cup into the 21-ounce cup. Now, the 21-ounce cup contains 16 ounces, and the desired 100 ounces is left in the 127-ounce cup.
By following these steps, you can measure exactly 100 ounces using the given cups with capacities of 127 ounces, 21 ounces, and 3 ounces.
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73 in.=_ft. What’s the answer please help
Answer:
6 ft. 1 in.
Step-by-step explanation:
There are 12 inches in a foot.
Divide 73 by 12
Find the explicit solution of the following initial value problems: 1. y'=;Y(1)=1 2. y'=2xy – y;y(0)=2 2x +1 3. y'= 2y ; y(1)=-1. dy = y2x – x; y(O)=0 4. dx 5. y'=ety; y(0)=0
For the initial value problem y' = 0; y(1) = 1, the solution is y = 1. Since the derivative of y with respect to x is zero, the function y remains constant, and the constant value is determined by the initial condition y(1) = 1.
For the initial value problem y' = 2xy - y; y(0) = 2(0) + 1 = 1, we can rewrite the equation as y' + y = 2xy. This is a first-order linear homogeneous differential equation. Using an integrating factor, we multiply the equation by e^x^2 to obtain (e^x^2)y' + e^x^2y = 2x(e^x^2)y. Recognizing that the left side is the derivative of (e^x^2)y, we can integrate both sides to get the solution y = Ce^x^2, where C is determined by the initial condition y(0) = 1. For the initial value problem y' = 2y; y(1) = -1, we can separate the variables and integrate to find ln|y| = 2x + C, where C is the constant of integration. Exponentiating both sides gives |y| = e^(2x+C), and since e^(2x+C) is always positive, we can remove the absolute value signs. Thus, the solution is y = Ce^(2x), where C is determined by the initial condition y(1) = -1.
For the initial value problem dy = y^2x - x; y(0) = 0, we can separate the variables and integrate to find ∫dy/y^2 = ∫(yx - 1)dx. This gives -1/y = (1/2)y^2x^2 - x + C, where C is the constant of integration. Rearranging the equation gives y = -1/(yx^2/2 - x + C), where the constant C is determined by the initial condition y(0) = 0. For the initial value problem y' = ety; y(0) = 0, we can separate the variables and integrate to find ∫e^(-ty)/y dy = ∫e^t dt. The integral on the left side does not have a closed-form solution, so the explicit solution cannot be expressed in elementary functions. However, numerical methods can be used to approximate the solution for specific values of t.
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What is a name for the marked angle?
Answer:
angle CAD
Step-by-step explanation:
look at the 3 points that make up the angle
Mario bought 11/16 pounds of turkey. He used 3/16 pounds of the turkey to make a sandwich. How much of a pound does he have left? Give your answer in lowest terms.
Answer: 1/2
11/16 - 3/16 = 1/2
Mr Abdul made tuna and curry potato filling for some puffs.3/5 of the filling he made was tuna and the rest was curry potato.
After he used 1/8kg of the tuna filling and made another 3/4
kg of curry potato filling, he then had equal amounts of tuna filling
and curry potato filling left. How much tuna filling did he make at first?
Give your answer as a mixed number in its simplest form
At first, he made \(2\frac{5}{8}\) kg of tuna filling.
Mr Abdul made tuna and curry potato filling for some puffs.
3/5 of the filling he made was tuna and the rest was curry potato.
So, amount of curry potato = 1- 3/5 = 2/5
Ratio of tuna & curry potato = tuna : curry potato
= 3/5 : 2/5 = 3 : 2
Let amount of tuna = 3x & amount of curry potato = 2x
After he used 1/8kg of the tuna filling and made another 3/4 kg of curry potato filling.
According to the question, he then had equal amounts of tuna filling and curry potato filling left.
So, 3x - 1/8 = 2x + 3/4
Multiplying 8 in both sides we get,
⇒ 24x - 1 = 16x +6
⇒ 24x - 16x = 7
⇒ 8x = 7
⇒ x = 7/8
So, 3x = (3×7/8) = 21/8 kg = \(2\frac{5}{8}\) tuna filling at first.
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How many 5/8's are in 1? Its supposed to be a mixed number (ex, 1 1/3)
There are 1 and 3/5 of 5/8 in 1, if Its supposed to be a mixed number.
What is a mixed number?
A mixed number is a combination of a whole number and a fraction. It is written in the form of "a b/c" where a is the whole number, b is the numerator of the fraction, and c is the denominator of the fraction.
To answer your second question, we can divide 1 by 5/8 as follows:
1 ÷ 5/8 = (1 x 8) ÷ 5 = 8/5
We can then write 8/5 as a mixed number by dividing the numerator (8) by the denominator (5) and writing the remainder as the fraction part.
8 ÷ 5 = 1 with a remainder of 3, so we write the answer as:
1 3/5
Therefore, there are 1 and 3/5 of 5/8 in 1.
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circle $c$ has radius 10 cm. how many square centimeters are in the area of the largest possible inscribed triangle having one side as a diameter of circle $c$?
100 square centimeters are in the area of the largest possible inscribed triangle having one side as a diameter of circle.
What is the area?
A two-dimensional figure's area is the amount of space it takes up. In other terms, it is the amount that counts the number of unit squares that span a closed figure's surface. In general, square units such as square inches, square feet, etc. are used as the standard unit of area.
Base = 2r = 2*10 = 20 cm
Height = r= 10 cm
Area = 1/2 * base * height
= 1/2 * 20 * 10
= 100 square centimeters
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Brain wants to exchange South African rand for British pound if R1 is worth 0,075199 pound, how many pounds will he get fir R 2100 if he must pay ab agent commission of 1,5%?
Answer: 155.99
Step-by-step explanation:
If 1 South African rand (ZAR) is worth 0.075199 British pound (GBP), then Brain will receive:
2100 ZAR * (0.075199 GBP / 1 ZAR) = 158.418 GBP
This is the amount Brain would receive without any commission. However, since he must pay an agent commission of 1.5%, the actual amount he will receive is:
158.418 GBP * (1 - 0.015) = 155.99 GBP (rounded to two decimal places)
Therefore, Brain will receive 155.99 British pounds after paying the agent commission.
Chin-Mae has a fishtank that measures 75 cm by 45 cm by 35 cm. He also has a jug that holds 1.75 litres. He uses the jug to fill the fishtank with water. How many full jugs of water does it take to fill the fishtank? Show how to check your answer.
To find the volume of a rectangular prism, we can use the following formula:
\(V=lwh\)
l = lengthw = widthh = heightConverting between mL and L1000 mL = 1 L
Solving the QuestionWe're given:
Fish tank measurements: 75 cm by 45 cm by 35 cmJug capacity = 1.75 LTo solve this question, we could follow these steps:
Find the volume of the tankDivide the volume of the tank by the jug capacityFind the volume of the tank
\(V=lwh\)
⇒ Plug in the measurements: 75 cm by 45 cm by 35 cm
\(V=75*45*35\\V=118125\)
Divide the volume of the tank by the capacity of the jug
There is a relationship between cm³ and mL, not cm³ and L. Convert the 1.75 L for the jug capacity to mL:
1.75 × 1000
= 1750
118125 ÷ 1750
= 67.5
AnswerIt takes 68 full jugs of water to fill the tank.
The simplest version of the game has only one disk. What is the minimum number of moves it would take to move one disk from one peg to the other?
Answer:
For edge, the first one (this question) it's 1 move, then the second slide is 3 moves.
The minimum number of moves it would take to move two disks from one peg to the other is first to make 1 move, then 3 moves.
What is the rule used in solving the Tower of Hanoi?In the rules of this game, It state that just one disk is one that can be moved in case of some towers at any given time.
here, we have,
Note that just the "top" disk is one that can be removed and as such, The minimum number of moves it would take to move two disks from one peg to the other is first to make 1 move, then 3 moves.
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how to solve a^2 = -1 mod m?
In general, solving equations involving quadratic residues can be complex and requires knowledge of advanced number theory.
To solve the equation a^2 = -1 mod m, where m is an odd positive integer, we can use the concept of quadratic residues.
First, we need to find a number b such that b^2 = -1 mod m. If such a number exists, then a = b^((m+1)/4) mod m is a solution to the equation a^2 = -1 mod m.
However, if no such b exists, then the equation has no solution. This is because for odd prime m, the congruence a^2 = -1 mod m has a solution if and only if m is congruent to 1 mod 4.
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There are 5 red, 4 blue, and 3 green marbles in a bag. What are the odds of randomly pulling a blue marble out of the bag and then randomly pulling a green marble out of the bag? The blue marble is NOT replaced.
A - 7/2
B - 12/24
C - 1/12
D - 1/11
Billy has a die. He rolls the die, and if the result is not even, he rolls the die
one more time. Find the probability that he ends up with an even number.
Answer:
1/4 is the answer.
Step-by-step explanation:
If he has a die then it is 6 sided. He has a 1/2 chance the 1st time that he gets a non-even number. The next time he also has a 1/2 chance of getting an even number so it's 1/2 times 1/2 = 1/4.