an appliance store sold 360 microwave ovens last year. Of that amount, 3/8 were apartment-sized models. The number of apartment-sized models sold for the year was what?
multiply:
360 * 3/8 = 360*3 =1080
1080/8 = 135 were apartment sized
Generate a process that would generate random numbers between –1 and 1 for x and y positions of 10000 points and count how many points fall with the circle, then determine an estimated version of π. (see below to generate floating point random numbers. this generation is not needed to describe the process, but to implement the process)
The question is about using the Monte Carlo method to estimate the value of π, by generating random points in a square, counting how many fall inside a unit circle, and finally using this count to calculate π.
Explanation:This question involves the implementation of a famous problem in computational mathematics known as the Monte Carlo method for estimating the value of π:
First, initialize a variable, say 'count', to 0. This variable will keep track of the number of points falling within the circle.Next, carry out a 'for' loop to generate 10000 points. Each point will have x and y coordinates, each a random floating point number between -1 and 1.For each generated point (x, y), calculate the distance from the point to the origin (0,0), which is sqrt(x^2 + y^2). If this distance is less than or equal to 1, it means that the point lies within the unit circle, so increment the 'count' variable by one.After all 10000 points have been generated and tested, 'count' will hold the total number of points lying within the circle. To determine an estimation of π, use the formula 4 * (count / total_number_of_points).This process is based on the mathematical fact that the ratio of the area of a unit circle to the square it is inscribed in is π/4.
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solve the following equation for 2 + √4y -3 = 11
Final answer:
To solve the equation 2 + √(4y - 3) = 11 for y, subtract 2 from both sides, square both sides to remove the square root, then solve for y to find that y = 21.
Explanation:
The question asks to solve the equation 2 + √(4y - 3) = 11 for y. To solve for y, follow the steps below:
First, subtract 2 from both sides of the equation to isolate the square root term: √(4y - 3) = 9.
Now, square both sides of the equation to eliminate the square root: (√(4y - 3))^2 = 9^2, which simplifies to 4y - 3 = 81.
Add 3 to both sides of the equation to isolate the term with y: 4y = 84.
Finally, divide both sides by 4 to solve for y: y = 21.
Therefore, the solution to the equation is y = 21.
is a integer a rational number
How many gallons of a 80% antifreeze solution must be mixed with 60 gallons of 30% antifreeze to get a mixture that is 70% antifreeze?
how many gallons will it take to mow a lawn if you maintain the rate of 1/2 gallon of gasoline per 1/4 mowed
Suppose John opens a savings account with $1,000 that compounds interest daily. The APR at the time John deposits the account is 3.5%. He makes no withdrawals or deposits. What is his APY to the nearest hundredth of a percent after 1 year?
Find the derivative of f (x)=(x^2+1)^3 (x^2+2)^6 using chain rule.
Let a be a rational number and b be an irrational number. Which of the following are true statements?
A. The sum of a and b is never rational
B. The product of a and b is rational
C. b^2 is sometimes rational
D. a^2 is always rational
E. √a is never rational
F. √b is never rational
how many times larger is the value of the 8 in 80,351 than the value of the 8 in 95,852
find two consecutive odd integers whose product is 1 less than 6 times their sum. Domain for the smallest : {-1, 1, 11}
True or false: the standard deviation is the square root of the variance.
Answer:
True. The standard deviation is indeed the square root of the variance.
Explanation:
The standard deviation measures the dispersion or spread of data points around the mean in a dataset. It quantifies the average distance of data points from the mean. Mathematically, it's the square root of the variance, which is the average of the squared differences between each data point and the mean. By taking the square root, we return to the original scale of the data, making the standard deviation more interpretable. A higher standard deviation indicates greater variability, while a lower standard deviation suggests that the data points are closer to the mean, signifying less variability within the dataset.
How many elements are in the set (A,B,C)
Write the number 63 in four different ways
Solution:
we have been asked to write the number 63 in four different ways. It can be done as follows
[tex]63=60+3[/tex]
Here we are just adding 3 to 60 and finally we get 63.
[tex]63=6\times10+3[/tex]
This one of the many way of writing 63.
[tex]63=70-7[/tex]
Here we have used the concept of subtraction to write 63.
[tex]63=7\times10-7[/tex]
Concept of subtraction and multiplication to write the number 63.
Hence the four ways have been written.
Write an equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of the given equation.
(−5,−7); y=−2x+1
Write an equation for the line in slope-intercept form.
Answer:
y=-2x-19
Step-by-step explanation:
this is the right answer , i tried the other answer for this and it said it was wrong so
what percent of 1600 is 20?
20 is 1.25% of 1600.
(Part / Whole) * 100 = Percentage
20 by 1600:
20 / 1600 = 0.0125.
Multiply the result by 100 to get the percentage:
0.0125 * 100
= 1.25%.
So, 20 is 1.25% of 1600.
The sum of three consecutive numbers is 72. What is the largest of these numbers?
25 Is the largest number too add up to the sum.
What do March 16, 1948, Feb. 25, 1950, and Aug. 8, 1964 have in common??
Find the degree of the term -5x squared
Q=3X+9XZ solve for X
The required solution is X=Q/3+9Z.
It is required to find the solution is X.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. Equation, statement of equality between two expressions consisting of variables and/or numbers.
Given:
The given expression is
Q=3X+9XZ
We move all terms to the left side and equate to find the value of x we have.
Q=X(3+9Z)
By taking common to x and divide and move each term to left side, we have
X=Q/3+9Z
Therefore, the required solution is X=Q/3+9Z.
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A restaurant uses 44 pounds of potatoes for a party of 1212 people. If they are cooking potatoes for a party of 60 people, what should they do?
Solve for W
A=2Lw+2Lh+2wh
Is a measure of dispersion that indicates how much scores in a sample vary around the mean of the sample?
julia has just gotten a new job paying 80,000 a year . what would be her estimated federal taxes?
Julia estimated federal taxes will be $ 22,400.
What is Percentage?To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. With the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.
Given:
Julia has just gotten a new job paying 80,000 a year .
From the figure the tax will be of 28%.
So, Julia estimated federal taxes will be
= 80,000 x 28/100
= 800 x 28
= $ 22,400
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Find the equation of the curve that passes through the point 0, 1 6 and whose slope at each point (x, y) is − x 12y .
The equation is [tex]\(x^2 + 12y^2 - 3072 = 0\),[/tex] obtained from integrating [tex]\(12y \, dy = -x \, dx\)[/tex] with the initial condition.
To find the equation of the curve passing through the point (0, 16) with a slope given by [tex]\( \frac{{dy}}{{dx}} = -\frac{x}{12y} \),[/tex] you can use separation of variables.
Given that [tex]\( \frac{{dy}}{{dx}} = -\frac{x}{12y} \)[/tex], we can rewrite it as:
[tex]\[ 12y \, dy = -x \, dx \][/tex]
Now, integrate both sides:
[tex]\[ \int 12y \, dy = \int -x \, dx \]\[ 6y^2 = -\frac{1}{2}x^2 + C \][/tex]
Given that the curve passes through the point (0, 16), substitute these values into the equation:
[tex]\[ 6(16)^2 = -\frac{1}{2}(0)^2 + C \]\[ 6(256) = C \]\[ C = 1536 \][/tex]
Therefore, the equation of the curve is:
[tex]\[ 6y^2 = -\frac{1}{2}x^2 + 1536 \][/tex]
This can also be written in standard form as:
[tex]\[ x^2 + 12y^2 - 3072 = 0 \][/tex]
So, the equation of the curve is [tex]\( x^2 + 12y^2 - 3072 = 0 \).[/tex]
subtract the quotient of 15/3 from the sum of 33 and 7
quotient is division
so 15/3 = 5
sum is addition so 33+7 = 40
40-5 = 35
Estimate sin pi/3 if sin pi/2 = 1 and sin 0 = 0 and sin pi = 0
To estimate the value of sin pi/3, which is roughly 1.047 or 60 degrees, we can use standard trigonometric values. Since pi/3 is closer to pi/2 than pi, where sin achieves its maximum of 1, the value of sin pi/3 should be closer to 1 than 0. Standard trigonometric values confirm that sin pi/3 = sqrt(3)/2 = 0.866.
Explanation:To estimate sin pi/3, we can make use of some standard values in trigonometry. Pi is roughly 3.14, hence pi/3 is roughly 1.047. The sin function gives a result of 1 at pi/2 (or 90 degrees), 0 at 0, and again 0 at pi (or 180 degrees). Thus, it achieves its maximum at pi/2 and then decreases to 0 at pi. Intuitively, since pi/3 (or 60 degrees) is closer to pi/2 than to pi, the sin value at pi/3 should be closer to 1 than to 0. From the standard trigonometric values, we know that sin pi/3 = sqrt(3)/2 which is roughly 0.866.
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1.4t-0.4(t-3.1)=5.8
What is T?
What is the standard form of 14 ten thousands + 12 thousands
translate into an algebraic expression: the difference of six times a number and 8