The number of students traveling are 2 students out of the 30 who are traveling out of the country this summer. If 1/3 of the students are traveling somewhere this summer, then we can calculate the number of students who are traveling by multiplying the total number of students by 1/3:
Number of students traveling = 30 x 1/3 = 10
Now, we need to find out how many of these 10 students are traveling out of the country. We know that 1/5 of the students who are traveling are going out of the country, so we can find the number of students who are traveling out of the country by multiplying the total number of traveling students by 1/5:
Number of students traveling out of the country = 10 x 1/5 = 2
Therefore, there are 2 students out of the 30 who are traveling out of the country this summer.
It's important to note that fractions can be converted to decimals or percentages to make them easier to work with. For example, 1/3 can be written as 0.33 or 33%, and 1/5 can be written as 0.20 or 20%. This can be particularly useful when dealing with more complex problems or when working with larger numbers.
In summary, by using the information given, we can determine that out of the 30 students in Mr. Hall's class, 10 are traveling somewhere this summer, and out of those 10 students, 2 are going out of the country. This type of problem-solving helps build math skills that are applicable in real-world scenarios, such as budgeting and planning for travel.
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what is the specificity for the test based on these screening results (rounded to three decimal places)?
The specificity of the test based on the given screening results is 0.967 (rounded to three decimal places).
To calculate the specificity, divide the number of true negatives (TN) by the total number of negative results (TN+FP). In this case, that would be 687/(687+22), which is equal to 0.967 (rounded to three decimal places).
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A triangle can have sides with measures: 10, 12, 24
True
False
Answer:
False.
Step-by-step explanation:
A triangle's two smaller sides have to add to be bigger than the larger side.
Answer:
False, that cannot exist by the hypotenuse rule
Hope it helps!
At maxs party 3/12 of the guests are 10 year old and 7/12 of guests are 11 year old what fraction of the guests are 10 or 11 years old
The fraction of the guests are 10 or 11 years old is 5/6
A fraction represents a part of a whole, where the whole is divided into equal parts.
To find the fraction of guests who are 10 or 11 years old, we need to add the fractions of guests who are 10 years old and 11 years old.
3/12 of the guests are 10 years old, which can be simplified to 1/4.
7/12 of the guests are 11 years old.
Therefore, the fraction of guests who are 10 or 11 years old is
1/4 + 7/12 = 3/12 + 7/12
Add the fractions
= 10/12
Simplify the fraction
= 5/6
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Let X be a random variable with the probability mass function (PMF) given below (figure not drawn to scale), where a=0, b=0.23, c=0.13, d=0.10, e=0.15. a. Find the cumulative distributive function (CDF) Fx(3). Round answer to two decimal points.
The cumulative distributive function (CDF) Fx(3) is 0.61.
The cumulative distributive function (CDF) of a random variable X is the probability that X takes a value less than or equal to x. In this case, we are asked to find Fx(3).
Since the random variable X is given with a probability mass function, we can calculate the CDF by summing the probabilities of X being less than or equal to 3. This can be expressed as: [tex]Fx(3) = P(X<=3).[/tex]
For X = 0, P(X<=3) = 0.23.
For X = 1, P(X<=3) = 0.23 + 0.13 = 0.36.
For X = 2, P(X<=3) = 0.23 + 0.13 + 0.10 = 0.46.
For X = 3, P(X<=3) = 0.23 + 0.13 + 0.10 + 0.15 = 0.61.
Therefore, the cumulative distributive function (CDF) Fx(3) is 0.61.
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What is the area of this figure?
6 mm
4 mm
3 mm
5 mm
3 mm
15 mm
3 mm
9 mm
Write your answer using decimals, if necessary. Square millimeters
Based on the given data, The shape's whole surface area is about 252 mm².
Based on the image, the shape appears to be a set of rectangles with different lengths and widths.
To find the area of this shape, we can break it down into smaller rectangles and add up their areas.
Starting from the bottom, we can see that the first rectangle has a length of 6 mm and a width of 4 mm. Its area is:
Area1
= 6 mm × 4 mm
= 24 mm²
Moving up to the second rectangle, we see that it has a length of 6 mm and a width of 3 mm. Its area is:
Area2
= 6 mm × 3 mm
= 18 mm²
The third rectangle has a length of 6 mm and a width of 5 mm. Its area is:
Area3
= 6 mm × 5 mm
= 30 mm²
The fourth rectangle has a length of 6 mm and a width of 3 mm. Its area is:
Area4
= 6 mm × 3 mm
= 18 mm²
The fifth rectangle has a length of 6 mm and a width of 15 mm. Its area is:
Area5
= 6 mm × 15 mm
= 90 mm²
The sixth rectangle has a length of 3 mm and a width of 9 mm. Its area is:
Area6
= 3 mm × 9 mm
= 27 mm²
Finally, the seventh rectangle has a length of 5 mm and a width of 9 mm. Its area is:
Area7
= 5 mm × 9 mm
= 45 mm²
To find the total area of the shape, we can add up the areas of all seven rectangles:
Total Area
= Area1 + Area2 + Area3 + Area4 + Area5 + Area6 + Area7
= 24 mm² + 18 mm² + 30 mm² + 18 mm² + 90 mm² + 27 mm² + 45 mm²
= 252 mm²
Therefore, the total area of the shape is approximately 252 mm².
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PLEASE HELP ME QUICKLY!
For the given system of linear inequalities (53, 4) represents 53 batches of soap and 4 batches of lotion were produced.
What is linear inequality?An equation with a linear expression and a relational operator is referred to as a linear inequality. Regions in a coordinate plane or space that fulfil a linear inequality are defined by the inequality. A linear inequality in two dimensions defines a half-plane, which, depending on the inequality, is either above or below a line. A linear inequality in three dimensions defines a half-space that, depending on the inequality, is either above or below a plane. In optimization situations, when the objective is to determine the greatest or lowest value of a linear function under a set of constraints represented by linear inequalities, linear inequalities are frequently utilised.
The given system of inequalities is:
5x + 15y ≤ 325
20x + 35y ≤ 1200
Here, x is the number of batches of soap and y is the number of batches of lotion.
Thus, (53, 4) represents 53 batches of soap and 4 batches of lotion were produced.
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what is the probability of reaching into the box and randomly drawing a chip number that is smaller than 212 ? express your answer as a simplified fraction or a decimal rounded to four decimal places.
The probability of reaching into the box and randomly drawing a chip number that is smaller than 212 is 0.9378
First, we should find the total number of chips in the box. The box contains 225 chips numbered from 1 to 225. Therefore, the probability of reaching into the box and randomly drawing a chip number that is smaller than 212 is 211/225.
The probability can be expressed as a simplified fraction or a decimal rounded to four decimal places. The probability is rounded to four decimal places is 0.9378.
The probability of drawing a chip number that is smaller than 212 from the box is 211/225 or 0.9378 (rounded to four decimal places).
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Tell me pls what is the answer to this question? 3=x+3-5x??????????
Answer:
[tex]\boxed{x=0}[/tex]
Step-by-step explanation:
We need solve for x
[tex]3=x+3-5x[/tex]
substract 3 to both sides of the equation:
[tex]3-3=x+3-5x-3\\0=-4x[/tex]
divide both sides of the equation by -4
[tex]\frac{0}{-4}=\frac{-4x}{-4}\\0=x\\\equiv x=0[/tex]
The value of "x" that satisfies the equation is x=0,
[tex]\text{-B$\mathfrak{randon}$VN}[/tex]
What is the surface area?
5 yd
6 yd
5 yd
5 yd
4 yd
square yards
The surface area of the rectangular prism is 170 square yards.
What is the surface area formula?Surface area is the total area of a three-dimensional shape's surface. Add the areas of all six faces to find the surface area of a cuboid with six rectangular faces. Alternatively, label the cuboid's length (l), width (w), and height (h) and use the formula: surface area (SA)=2lw+2lh+2hw.
To calculate the surface area of the rectangular prism, add the areas of each of its faces.
The front and back faces are 5 yards by 6 yards in size, so each has an area of:
5 yards x 6 yards equals 30 square yards
The top and bottom faces are 5 yards by 5 yards, so each has an area of:
5 yards x 5 yards equals 25 square yards
The two side faces have dimensions of 6 yards by 5 yards, for a total area of:
30 square yards = 6 yards x 5 yards
As a result, the surface area of the rectangular prism is as follows:
Front face area plus back face area plus top face area plus bottom face area plus left side face area plus right side face area
= 30+30+25+25+30+30
= 170 square yards
As a result, the rectangular prism has a surface area of 170 square yards.
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Find the area of the cicumfrance of a circle with diameter of 5ft use 3.14 for pi
Step-by-step explanation:
The formula to solve for the area of a circle is given by,
A
=
1
4
π
d
2
where
d
is the diameter.
Substituting the given, we have
A
=
1
4
×
3.14
×
(
3
ft
)
2
=
1
4
×
3.14
×
9
ft
2
A
=
7.065
ft
2
Next, solve for the circumference.
The formula for the circumference of a circle is written as,
C
=
π
d
where
d
is the diameter.
Substituting the given, we have
C
=
3.14
×
3
ft
C
=
9.42
ft
Hence, the
Area
=
7.065
ft
2
and the
Circumference
=
9.42
ft
.
Answer:
A = 19.625 ft²
C = 15.7 ft
Step-by-step explanation:
The equation for the area of a circle is πr², where r is the radius.
The radius is half of the diameter, so the radius here is 2.5.
Plug the radius into the equation and substitute 3.14 for π:
A = 3.14 x 2.5²
2.5² = 2.5 x 2.5 = 6.25
A = 3.14 x 6.25 = 19.625
Area = 19.625 ft²
The equation for the circumference of a circle is 2πr.
Plug the radius into the equation and substitute 3.14 for π:
C = 2 x 3.14 x 2.5
C = 15.7
Circumference = 15.7 feet.
The selling price of a table is ₹ 5400.If the shopkeeper makes a profit of 20%, find the cost
price of the table?
Sure! I can help you with that.
First, we should calculate the profit made by the shopkeeper. To calculate the profit, we will multiply the selling price of the table with 20%, which is 20% of 5400, or 1080.
Next, we should subtract the profit from the selling price to find the cost price of the table.
The cost price of the table = 5400 - 1080
The cost price of the table = 4320
Therefore, the cost price of the table is ₹ 4320.
12. INTERPRETING A LINEAR FUNCTION The table shows the length y
(in inches) of a person's hair after x months.
a. Write and graph a linear function that relates y to x.
b. Interpret the slope and the y-intercept.
Months, Hair
X
0
3
6
Length, y
11.0
12.5
14.0
Answer:
a. To write a linear function that relates the length of hair to the number of months, we need to find the slope and y-intercept of the line that passes through the given points. We can use the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept.
Using the given data, we can find the slope as:
m = (y2 - y1) / (x2 - x1) = (14.0 - 11.0) / (6 - 0) = 0.5
And we can find the y-intercept as:
b = y - mx = 11.0 - 0.5(0) = 11.0
So, the linear function that relates the length of hair to the number of months is:
y = 0.5x + 11.0
We can also graph this function as a straight line, passing through the given points (0, 11.0), (3, 12.5) and (6, 14.0), as shown below:
linear function graph
b. The slope of the function is 0.5, which means that the length of hair increases by 0.5 inches every month. In other words, the slope represents the rate of change of hair length with respect to time.
The y-intercept of the function is 11.0, which means that if the person doesn't cut their hair at all (i.e., x = 0), their hair length would still be 11.0 inches. In other words, the y-intercept represents the starting value of the hair length.
(please mark my answer as brainliest)
Use the internet or some other reference to find the populations and areas(in square miles) of India, China, Argentina, the United States, and Egypt. Round each population to the nearest million and each area to the nearest thousand square miles
The populations of the listed countries are
India is 1.366 billion
China is 1.397 billion
Argentina is 45 million
the United States is 332 million
and Egypt is 102 million people.
Let's start with India. According to the World Bank, India's population is approximately 1.366 billion people, which is the second-largest population in the world after China. India's land area is approximately 1.269 million square miles.
Moving on to China, it has the largest population in the world, with approximately 1.397 billion people. China's land area is approximately 3.705 million square miles, making it the fourth-largest country in terms of land area.
Argentina, on the other hand, has a population of approximately 45 million people, with a land area of approximately 1.073 million square miles. This makes it the eighth-largest country in the world in terms of land area.
The United States has a population of approximately 332 million people, and its land area is approximately 3.796 million square miles. It is the third-largest country in terms of land area and the fourth-largest in terms of population.
Lastly, Egypt has a population of approximately 102 million people, with a land area of approximately 386 thousand square miles. It is the 30th largest country in terms of land area and the 14th most populous country in the world.
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What sum of money amounts to Rs 8700 in 3 years at the rate of 24% per annum?
Answer:
e. 8/00 ggg： What sum of money amounts to Rs. 8700 in 3 years at the rate of 24% per annum? [Ans: Rs. 5058.14]
Step-by-step explanation:
The volume of two similar figures are given. The surface area of the larger figure is given. Find the surface area of the smaller figure.
V=4000m^3
V=6912m^3
S.A.=2304m^3
Te surface area of the smaller figure based on the ratio is 1600m²
Calculating the surface area of the smaller figure.The ratio of the volumes of two similar figures is equal to the cube of the ratio of their corresponding sides.
Let x be the scale factor between the smaller and larger figures.
Then we have:
(x³)/(4000) = 6912
x³ = 6912/4000
x³ = 1.728
Taking the cube root of both sides, we get:
x = 1.2
So the scale factor from the larger figure to the smaller figure is 1:1.2.
The surface area of a similar figure is proportional to the square of the scale factor.
So we can use the scale factor to find the ratio of the surface areas:
SA(smaller) / SA(larger) = 1/(1.2)²
We know that the surface area of the larger figure is 2304m^2, so we can solve for the surface area of the smaller figure:
SA(smaller) = 2304 * 1/(1.2)²
SA(smaller) = 1600m²
Therefore, the surface area of the smaller figure is 1600m²
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Name a pair of non adjacent complementary angels
Answer:
<abc
Step-by-step explanation:
Consider the following equation
-16p + 37 = 49 - 21p
the solution to the equation -16p + 37 = 49 - 21p is p = 12/5. The equation -16p + 37 = 49 - 21p is a simple linear equation with one variable, p.
Linear equations are equations where the highest exponent of the variable is one, and they can be solved using algebraic techniques.
To solve this equation, we need to isolate the variable, p, on one side of the equation. We can start by simplifying the equation by combining like terms. To do this, we can add 21p to both sides of the equation, which gives us:
-16p + 37 + 21p = 49
Next, we can combine the terms -16p and 21p, which gives us 5p. So, the equation becomes:
5p + 37 = 49
We can further simplify the equation by subtracting 37 from both sides, which gives us:
5p = 12
Finally, we can solve for p by dividing both sides of the equation by 5:
p = 12/5
So, the solution to the equation -16p + 37 = 49 - 21p is p = 12/5.
In summary, the given equation is a simple linear equation that can be solved using algebraic techniques. We can isolate the variable, p, on one side of the equation by combining like terms and simplifying the equation. Finally, we can solve for p by dividing both sides of the equation by the coefficient of p.
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hi could someone help me
The listed price of the TV that Wayne bought was $947.37
What was the listed price of the TV?Here we know that Wayne pays $660 for a TV whose price was marked down by (30 + 1/3)%
We can rewrite that discount as 0.30333... in a decimal form (get that just by dividing the percentage by 100%)
Then if the lited price of the TV is P, we can write the equation for the discount as follows:
660 = P*(1 - 0.3033...)
The number that we subtract is the percentage in decimal form.
Solving this for P gives:
P = 660/(1- 0.3033...) = 947.37
The listed price was 947.37 dollars.
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Use substitution to solve -4x + y = 3, 5x - 2y = -9
Using the substitution method, the solution of the system of equations -4x + y = 3 and 5x - 2y = -9 is (x, y) = (1, 7)
We can solve this system of equations using the substitution method by solving for one variable in terms of the other in one equation, and then substituting that expression into the other equation. Here's how:
-4x + y = 3 (Equation 1)
5x - 2y = -9 (Equation 2)
Solving Equation 1 for y, we get:
y = 4x + 3
Now, we substitute this expression for y into Equation 2 and solve for x:
5x - 2(4x + 3) = -9
5x - 8x - 6 = -9
-3x = -3
x = 1
We have found the value of x to be 1. Now, we substitute this value back into Equation 1 to find the value of y:
-4(1) + y = 3
y = 7
Therefore, the solution to the system of equations is (x, y) = (1, 7)
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3)² -
(x +
function?
O 7
1
2
3
7. What is the degree of the
Answer:
-
(x + is what you are looking for is the answer
guys help please very urgent photo below
Answer:
Give a brainliest answer
Statistics question : what was done to get the values in red ? (The ones inside the table based on the question )
Given that he is from the Dominican Republic, the likelihood that the chosen player is a pitcher is roughly 0.053.
what is probability ?The study of arbitrary events or experiments falls under the purview of probability, a subfield of mathematics. A value between 0 (impossible) and 1 is used to estimate the possibility or chance of an event occurring (certain). Several disciplines, including science, engineering, economics, finance, and more, utilise the idea of probability. It is frequently determined by dividing the number of positive events by the total number of outcomes that could occur.
given
(a) To find P, we can utilize the complement rule (T&D). The addition to T&D is the possibility that the chosen player is a pitcher or a Dominican. We thus have:
The equation P(T&D) = 1 - P(T'UD') = 1 - P(T') - P(D') + P(T'D')
P(T), P(D), and P(TD) are all provided as 0.42, 0.105, and 0.056 respectively. As a result, we may determine the complements' probabilities:
P(T') = 1 - P(T) = 1 - 0.42 = 0.58 P(D') = 1 - P(D) = 1 - 0.105 = 0.895 P(T'D') = P(TD)' = 1 - (P(T) + P(D) - P(TD)) = 1 - (0.471 + 0.42 + 0.105 - 0.056)
By replacing these values, we obtain:
P(T&D) = 1 - 0.58 - 0.895 + 0.471 = 0.046
As a result, there is a 0.046 percent chance that the chosen player is a non-pitcher from outside the Dominican Republic.
(b) In order to determine the likelihood that the chosen player is a pitcher given that he is from the Dominican Republic, we must first determine P(P|D). Bayes' Theorem may be applied:
P(P|D) equals P(D|P)P(P)/P (D)
P(D) = 0.105 and P(TD) = 0.056 are the values provided. Therefore,
P(P) is defined as P(TD') / P(D') = 0.056 / 0.895 0.0626.
P(D|P) is equal to P(T|D) / P(P) = 0.056 / 0.0626 0.895.
By replacing these values, we obtain:
P(P|D) = (0.895)(0.0626) / 0.105 ≈ 0.053
Given that he is from the Dominican Republic, the likelihood that the chosen player is a pitcher is roughly 0.053.
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The complete question is :- Of all major league baseball players on 2008 Opening Day rosters:
42% are pitchers (call this event T)
10.5% are from the Dominican Republic (call this event D)
5.6% are pitchers from the Dominican Republic
A player is selected at random.
(a) Find P(T&D), the probability that that the selected player is a non-pitcher who is not from the Dominican.
(b) Given the information that the selected player is from the Dominican Republic, what is the probability that he is a pitcher?
(c) Given the information that the selected player is a non-pitcher, what is the probability that he is not Dominican?
Question A normal distribution is observed from the number of points per game for a certain basketball player. The mean for this distribution is 20 points and the standard deviation is 3 points. Use the empirical rule for normal distributions to estimate the probability that in a randomly selected game the player scored less than 26 points. • Provide the final answer as a percent rounded to one decimal place. Provide your answer below: % SUBMIT FEEDBACK MORE INSTRUCTION
Given a normal distribution is observed from the number of points per game for a certain basketball player. The mean for this distribution is 20 points and the standard deviation is 3 points.Using the empirical rule for normal distributions, the probability that in a randomly selected game the player scored less than 26 points is required .Empirical Rule: For a normal distribution with a mean µ and a standard deviation σ, the probability of an observation being within k standard deviations of the mean is approximately:•
68% of the observations fall within one standard deviation of the mean.• 95% of the observations fall within two standard deviations of the mean.• 99.7% of the observations fall within three standard deviations of the mean.Here, the mean is 20 points and the standard deviation is 3 points. We need to find the probability of getting less than 26 points.z-score = (x - µ) / σ = (26 - 20) / 3 = 2σ = 2According to the empirical rule, 95% of observations fall within 2 standard deviations of the mean.So, the probability that the player scored less than 26 points is 95%.Therefore, the final answer is 95% rounded to one decimal place. Answer: 95%.
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6(x - 2) -3 ≥ -4 ( -3 + 9) +10
Answer:
2x=5 > -14
Step-by-step explanation:
6(x - 2) -3 ≥ -4 ( -3 + 9) +10
6x-12-3 > 12-36+10
6x-15 > -36+22
6x-15 > -14
6x=15 > -14
3 3
2x=5 > -14
Let X >0 denote a random variable with p.d.f. fx(2) and c.d.f. Fx (I). Assume Fx() is monotone increasing, and let Y = FX(X). That is, Y is a random variable that takes the value Fx (1) when X = r. Find fy(y). Mark the correct answer (a) fy(y) = 1,0
The probability density function (PDF) of Y can be determined by the transformation of the PDF of X. Using the transformation rule, we can calculate that fy(y) = fx(x) |dx/dy|, where x is a function of y, since y = Fx(x).
We can use the Chain Rule to determine the derivative of x with respect to y. Since Fx is a monotone increasing function, dx/dy = 1/F'x(x). Substituting this into the transformation rule, fy(y) = fx(x) / F'x(x).
Therefore, to find fy(y), we need to calculate F'x(x). Fx is the cumulative distribution function, which means that its derivative F'x(x) is the probability density function of X, or fx(x). Substituting this into the transformation rule, fy(y) = fx(x) / fx(x). Since fx(x) = fx(2) and fx(2) is a constant, fy(y) = 1/fx(2).
To summarize, the probability density function of Y is given by fy(y) = 1/fx(2).
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Maggie crochets squares to make a blanket. She has 6 squares made. She then makes 6 squares each hour for 3 hours. Determine which of the following represent the linear relationship described.
The linear relationship of Maggie crocheting squares is y = 6 + 6x graph (b)
How to determine the linear relationshipLet x be the number of hours Maggie spends crocheting squares, and let y be the total number of squares she has made.
Initially, Maggie has 6 squares made,
so y = 6 when x = 0.
For each hour that she spends crocheting squares, Maggie makes 6 more squares.
Therefore, the relationship between x and y is:
y = 6 + 6x
This is a linear relationship with a slope of 6, which means that Maggie is crocheting squares at a rate of 6 squares per hour.
This is represented by graph (b)
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How many students are in the band this year? how do you know?
Answer:
Step-by-step explanation:
which band?
Please help it’s for tmr, I only have 1 hour left
Leo has a number of toy soldiers between 27 and 54. If he wants to group them four by four, there are none left, seven by seven, 6 remain, five by five, 3 remain. How many toy soldiers are there?
The answer is 48 but I need step by step explanation
Leo has 38 toy troops as there aren't enough for him to line them up four by four.
what is equation ?The equal symbol (=) is frequently used to separate the expressions in equations. The left-hand side (LHS) and right-hand side (RHS) of the equation, respectively, are the formulas on either side of the equal sign. If you replace the variable(s) in both expressions with the same value, they will have the same value, as indicated by the equal symbol, which denotes that the two sides are equivalent.
given
We'll name Leo's collection of toy soldiers "x" the amount.
Finally, we know that the remainder is 3 when x is split by 5. Thus, x Plus 2 must be a multiple of 5.
Using this knowledge, we can construct the following system of equations:
x = 4n (where n is a positive number) (where n is a positive integer)
x + 1 = 7m (where m is a positive number) (where m is a positive integer)
x + 2 = 5p (where p is a positive number) (where p is a positive integer)
Testing different values of x that meet these two requirements reveals that x = 38 is the only answer that also resolves the second problem.
Leo has 38 toy troops as there aren't enough for him to line them up four by four.
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A heap of rubbish in the shape of a cube is being compacted into a smaller cube. Given that the volume decreases at a rate of 4 cubic meters per minute, find the rate of change of an edge, in meters per minute, of the cube when the volume is exactly 27 cubic meters.
The rate of change of an edge of the cube is approximately 0.048 m/min when the volume is exactly 27 cubic meters.
To find the rate of change of an edge of the cube, given that the volume decreases at a rate of 4 cubic meters per minute when the volume is exactly 27 cubic meters, follow the solution below:Let the length of the edge of the original cube be L.Let the volume of the original cube be V, such that V = L³.The rate of change of volume is given as -4 m³/min; the negative sign is used to indicate a decrease in volume, and this is obtained when the derivative of the volume with respect to time is multiplied by the negative sign.Let V₀ be the original volume of the cube, and V₁ be the volume after t minutes. Thus, V₁ = V₀ - 4t m³. We are told that V₁ = 27 m³, hence:V₀ - 4t = 27 ⇒ V₀ = 27 + 4t m³Substituting V₀ in terms of t into the expression V = L³, we have:L³ = 27 + 4tTaking the derivative of both sides with respect to t, we have:3L²(dL/dt) = 4 ⇒ dL/dt = 4/(3L²)Substituting L from the expression L³ = 27 + 4t, we have:L = (27 + 4t)^(1/3)Therefore, the rate of change of an edge of the cube is given by the derivative of L with respect to t:dL/dt = 4/(3L²) = 4/(3(27 + 4t)^2/3) ≈ 0.048 m/min (to 3 decimal places)Answer: The rate of change of an edge of the cube is approximately 0.048 m/min when the volume is exactly 27 cubic meters.
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Happy Corporation leased a building from Sensor Company. The ten-year lease is recorded as a capital lease. The annual payments are $10,000, and the recorded cost of the asset is $67,100. The straight-line method is used to calculate depreciation. Which of the following statements is true?
a. Depreciation expense of $6,710 will be recorded each year.
b. Depreciation expense of $10,000 will be recorded each year.
c. No depreciation expense will be recorded by Happy Corporation.
d. No interest expense will be recorded by Happy Corporation.
2. In 2017, Aspinwall Company issued $200,000 of bonds for $175,000. If the face rate of interest was 9% and the effective rate of interest was 7.99%, how would Aspinwall calculate the interest expense for the first year on the bonds using the effective interest method?
a. $175,000 × 7.99%
b. $175,000 × 9%
c. $10,000 × 7.99%
d. $10,000 × 9%
3.
Use the information below for Focal Point Corp. for 2017 and 2018 to answer the following question:
Retained earnings, December 31, 2017 $300,000
Retained earnings, December 31, 2018 345,000
Dividends payable, December 31, 2017 19,000
Dividends payable, December 31, 2018 29,000
Net income—2018 150,000
Assume that there were no retained earnings transactions other than those dealing with dividends and net income. How much dividends did Focal Point declare during 2018?
a. $95,000
b. $105,000
c. $140,000
d. $150,000
1) Option a. Depreciation expenses of $6,710 will be recorded each year. is correct.
2) Option c. 175,000 × 7.99% is correct
3) Option b. $105,000 is correct.
1) The annual payments of $10,000 and the recorded cost of the asset of $67,100 are used to calculate the annual depreciation expense using the straight-line method.
Depreciation expense = (Recorded cost of the asset - Residual value) / Useful life
= ($67,100 - $0) / 10 years
= $6,710 per year.
2) The effective interest method calculates interest expense by multiplying the carrying value of the bond (i.e., the amount at which it was issued minus any discount or plus any premium) by the effective interest rate (i.e., the rate that discounts the bond's future cash flows to the carrying value).
Therefore, the interest expense for the first year on the bonds would be $175,000 × 7.99% = $13,965.
3) The dividends declared during the year can be calculated as follows:
Dividends declared = Net income - Increase in retained earnings - Decrease in dividends payable
= $150,000 - ($345,000 - $300,000) - ($29,000 - $19,000)
= $105,000.
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