The least positive integer N such that the set of 1000 consecutive integers beginning with 1000 N is 282.
Let x² appear before 1000N so:
(x+1)² − x² >1000⟹ x ≥ 500
Let A = [1000N, 1000(N+1)]
So I let x=500
then, x²=250000
, obviously this is impossible since the set has a square already.
So now I need to set some number, k² ≥ 5012 = 0 (mod1000)
So I need to solve the quadratic residue:
Lets see: 500²=250000
and 501²=251001
and 502²=252004
501²=500²+1000+ ∑ (12k−1)
502²=500²+2(1000)+∑ (12k−1)
The final answer is: N=282
All whole numbers and negative numbers are considered integers. This means that if we combine negative numbers with whole numbers, a collection of integers results.
An integer, which can comprise both positive and negative integers, including zero, is a number without a decimal or fractional portion. Integers include things like -5, 0, 1, 5, 8, 97, and 3,043.
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what is the mean of the sampling distribution equal to, what is the symbol for it, and how is it calculated? give the equation for the mean of the sampling distribution and show the number(s) that is/are used in the calculation
The mean of the sampling distribution is the average value of the mean of a large number of samples of the same size, taken from the same population. The symbol for the mean of the sampling distribution is usually represented by the Greek letter "mu" (μ). It is calculated as the sum of all the sample means divided by the number of samples.
The equation for the mean of the sampling distribution is given as:
μ = (1/n) * Σ x
where:
μ = mean of the sampling distribution
n = number of samples
Σ x = sum of the sample means
x = mean of each individual sample
The mean of the sampling distribution represents the center of the distribution and provides an estimate of the population mean. In this equation, the mean of each individual sample (x) is calculated first, and then those sample means are summed and divided by the number of samples (n) to find the mean of the sampling distribution (μ).
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Solve for the value of A
(Can someone help me please)
Which statement proves that the two circles are similar?
The circles A and C are similar because A can be mapped onto C by a translation of 3 units to the right and 5 units up, followed by a dilation about its center by a scale factor of 2.5.
The circles A and C are similar because A can be mapped onto C by a translation of 3 units to the left and 5 units down, followed by a dilation about its center by a scale factor of 0.4.
The circles A and C are similar because A can be mapped onto C by a translation of 3 units to the right and 5 units up, followed by a dilation about its center by a scale factor of 0.4.
The circles A and C are similar because A can be mapped onto C by a translation of 3 units to the left and 5 units down, followed by a dilation about its center by a scale factor of 2.5.
The circle's A and C are similar because A can be mapped onto C by a translation of 3 units to the left and 5 units down, followed by a dilation about its center by a scale factor of 2.5. Option D is correct.
The circle is the locus of a point whose distance from a fixed point is constant i.e center (h, k). The equation of the circle is given by
(x - h)² + (y - k)² = r²
Here,
To prove that the two circles are similar, circle A can be mapped onto C by a translation of 3 units to the right and 5 units up, followed by a dilation about its center by a scale factor of 2.5.
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A rectangular soccer field with a length of 100 yards and a width of 60 yards what is the length of the diagonal? Round to the nearest tenth
Answer: 116.7 yards.
Step-by-step explanation: The length of the diagonal of a rectangular soccer field with a length of 100 yards and a width of 60 yards can be found using the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (the diagonal) is equal to the sum of the squares of the lengths of the other two sides. In this case, the two sides of the triangle are 100 yards and 60 yards.
So, the diagonal can be found by:
d = √(100^2 + 60^2)
d = √(10000 + 3600)
d = √(13600)
d = 116.74 yards
Rounding to the nearest tenth, the length of the diagonal is 116.7 yards.
The length of the diagonal of the rectangular soccer field is 116.7 yards.
The line from one corner of a rectangle to the opposite center through the center is called a diagonal.
Here given that,
Length of the rectangular soccer field, l = 100 yards
Width of the rectangular soccer field, w = 60 yards
To find the length of the diagonal d,
The formula is
d = sqrt(l^{2} + w^{2} )
d = sqrt(100^2 + 60^2)
= sqrt(10,000 + 3600)
=sqrt (13,600)
= 116.61
=116.7 yards
Therefore, the length of the diagonal of a rectangular soccer field = 116.7 yards
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suppose your mp3 player contains 100 songs. 10 of those songs are by your favorite group (say pink floyd one of my favorite bands). suppose the shuffle feature is used to play the songs in random order. note that after a shuffle all the 100 songs are played before the next shuffle.
1. What is the probability that the first U2 song heard is the 5th song played? 2. What is the probability that one of the first five songs played is a U2 song?
Probability is a measure of how likely something is to occur. It is expressed as a number between 0 and 1, where 0 indicates that an event is impossible and 1 indicates that an event is certain. For example, if there is a 20% chance of rain, the probability of rain is 0.2. Probability is often used to calculate the likelihood of different outcomes in a situation.
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The Hurricane Hunters took the following measurements from a hurricane over several days as it developed. Using the graph, what would be the wind speed of a hurricane with an air pressure
of 937 kPa?
A. 235
B. 182
C. 203
D. 222
The wind speed of a hurricane with an air pressure of 937 kPa is 203, hence option C is correct answer.
What is point - slope form?A straight line is represented using its slope and a point on the line using point slope form. This indicates that the point slope form is used to get the equation of a line whose slope is'm' and which passes through a point. The equation of a straight line can be expressed in several ways. Point slope shape is one of them. The point slope form's equation is as follows: y - y1 = m (x - x1)
From the given graph we can observe that the two coordinates of the wind and pressure are:
(x1, y1) = (934, 206)
(x2, y2) = (922, 218)
The slope of the line is given by:
m = (y2 - y1) / (x2 - x1)
m = (218 - 206) / (922 - 934)
m = - 12/ 12
m = - 1
Using the point-slope form we have:
y - y1 = m (x - x1)
Substituting the values:
y - 206 = -1 (x - 934)
y - 206 = -x + 934
y = -x + 934 + 206
y = -x + 1140
Substitute the value of x = 937kPa:
y = -x + 1140
y = -937 + 1140
y = 203
Hence, the wind speed of a hurricane with an air pressure
of 937 kPa is 203, hence option C is correct answer.
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the population density of city A is 6,000 people per square mile l. city B is a dilation of city A with scale factor 1.2 if city B has 3/5 of the population of city A what is the population density of city B
The population density in city B is 6000 people per square mile considering it has 3/5 of the population in city A.
What is the population density in city A?The population density in city A is 6,000.
What is the population density in city B?It is known that city B, is bigger than city 1.2 times bigger than city A, so this means:
1 mile in city A = 1.2 miles in city B
Using this, and knowing that the population in city B is 0.6 times that of the one in city A, let's calculate the density:
0.6 x 6000 / 1.2 = 3,000 people per square mile
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Let Set A be {1, 3, 5, 7, 9}, and let Set B be {0, 2, 4, 6, 8}. Then:
Find the set union of A and B.
Find the set intersection of A and B.
Are A and B disjoint?
(Show your work)
Answer:
1) A and B = {1, 3, 5, 7, 9, 0, 2, 4, 6, 8}
2) Yes, A and B are disjoint.
Step-by-step explanation:
The set union of A and B is the set containing all the elements of Set A and Set B. So it would be:
Set A U B = {1, 3, 5, 7, 9, 0, 2, 4, 6, 8}
The set intersection of A and B is the set containing all the elements that are common to both Set A and Set B. So it would be:
Set A ∩ B = {} (empty set)
Yes, A and B are disjoint because they have no elements in common.
expand the logarithm as much as possible. rewrite the expression as a sum, difference, or product of logs. ln (1/g^k) Enclose arguments of functions in parentheses and include a multiplication sign between terms. For example, ln(1/gk)
The expression of logarithmic function, f(x) = ln (1/gᵏ) after all possible expansion is equals to the f(x) = - k × ln( g).
In mathematics, the logarithmic function is defined as inverse function to exponent function and defined as f(x) = logₐx where a is base of function. Properties of Logarithmic Functions :
Product Rule : logₐ MN = logₐ M + logₐ N , with the same base, multiply two numbers result add the exponents.Quotient Rule : logₐ M/N = logₐ M – logₐ N, with the same base, divide two numbers result add the exponents.Power Rule : Raise an exponential expression to power and multiply the exponents. Logₐ Mᵖ = p logₐ MZero Exponent Rule, logₐ 1 = 0.We have, a natural logarithmic function, i.e., base = 10, f(x) = ln (1/gᵏ) and we have to expand it. To expand logarithms means write them as a sum or difference product of logarithms. The order to apply rules is quotient rule, product rule and then power rule. So, f(x) = ln (1/gᵏ)
applying quotient rule,
=> f(x) = ln(1) - ln( gᵏ)
Appling power rule,
=> f(x) = ln(1) - k ln( g)
Applying Zero Exponent Rule,
=> f(x) = 0 - k × ln( g)
Hence, the required expansion is f(x) = - k × ln( g).
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Find an ordered pair (x, y) that is a solution to the equation.
-x+2y=7
Answer:
To find an ordered pair (x, y) that is a solution to the equation -x + 2y = 7, we can substitute any values of x and y that satisfy the equation. For example, let x = 3, then we can solve for y:
-3 + 2y = 7
2y = 10
y = 5
So (3, 5) is an ordered pair that is a solution to the equation.
 Need help will reward
When investing, the principal is the money that is kept in an investment account.
What is meant by principal investment?
Cash held in an investment account serves as the principal while investing. The amount you really borrow when you take out a loan—before interest is applied—is known as the principle.
Senior employees at venture capital firms, principals are ranked above associates and analysts. They are less senior than partners, but they could be on the partner track. Principals can assist the company in sourcing and carrying out deals, much like an associate.
When you sell an investment, you normally only need to pay taxes if you make a profit. To determine whether you made a profit or loss, you must deduct the cost basis of your investment—typically, the price you paid—from the sale price.
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The principal for amount $2496.76 at 1% compound interest annually for 3 years is $ 2420.03.
What does the term "primary investment" mean?When investing, the principal is the money that is kept in an investment account. The principle of a loan is the amount that you actually borrow when you apply for one, before interest is added.
Principals are the most senior personnel in venture capital firms, ahead of associates and analysts. They are not as senior as partners, but they might be moving toward becoming partners. Similar to an associate, principals can help the business find and close deals.
You typically only have to pay taxes on an investment sale if you make a profit. You must subtract the cost basis of your investment, which is often the price you bought, from the sale price to establish if you made a profit or a loss.
Using the formula,
Amount = P(1 + R/100)ⁿ
Where P = principle amount,
R = rate of interest,
n = time period,
It is given that
Amount = $2496.79
Rate of interest (R ) = 1%
(n) time period = 3,
Putting the above values in the formula,
2496.76 = P (1 + 1/100)³
⇒ 2496.76 = P (101/100)³
⇒ 2496.76 / (101/100)³ = P
⇒ P = 2496.76 / 1.03
⇒ P = $ 2420.03
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Faked numbers in tax returns, invoices, or expense account claims often display patterns that aren't present in legitimate records. Some patterns, like too many round numbers, are obvious and easily avoided by a clever crook. Others are more subtle. It is a striking fact that the first digits of numbers in legitimate records often follow a model known as Benford's law. Call the first digit of a randomly chosen legitimate record ????X for short. The histogram of the probability distribution for ????X is shown here.
What is the shape of this histogram?
The shape of the histogram for the first digit of a randomly chosen legitimate record following Benford's law is a logarithmic curve, with the first digit "1" appearing most frequently, followed by "2," and so on, with the frequency of each digit decreasing as the digit increases.
What is tax return?A tax return is a document filed with a tax authority (such as the IRS) that reports an individual's or a business's taxable income, expenses, and other information for a given tax year. The purpose of a tax return is to determine how much tax an individual or business owes or to claim a refund if they overpaid their taxes during the year.
Benford's law is a mathematical principle that predicts the frequency of occurrence of digits in many real-life sets of data. According to the law, in such datasets, the first digit is likely to be a "1" more often than any other digit, followed by "2", and so on, with "9" being the least likely first digit. The law has been shown to hold true for many types of data, including population sizes, stock prices, and physical constants.
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A couple has $5,000 to invest and has to choose between three investment options.
Option A: 2 1/4% annual interest compounded quarterly
Option B: 3% annual interest compounds every 4 months
Option C: 4 1/2 annual interest compounded semi-annually
If they plan on no deposits and no withdrawals for 5 years, which option will give them the largest balance after 5 years? Use a mathematical model for each option to explain your choice.
Answer:C
Step-by-step explanation:Basically time goes on and it starts off with a less percentage based off the amount of weeks later to add up to the most
Using Compound Interest, The largest balance is $780255, so the option A will give them the largest balance after 5 years.
What is Compound Interest?Even though there are several ways to define an investor, compound interest helps investors. When banks lend money and utilize the income they earn to finance other loans, for instance, they profit from compound interest. When depositors earn interest on their bank accounts, bonds, or other investments, compound interest benefits them.
It's crucial to remember that although while "compound interest" includes the word "interest," the idea extends beyond the contexts in which the expression is typically employed, such as bank accounts and loans.
We will calculate compound interest in every case:
Using formula
[tex]Amount = P(1 + \frac{r}{m})^{t}[/tex]
option A: balance after 5 years:
[tex]5,000 (1+ 2 \frac{1}{4}\%) ^{4\times 5} = $7802.55[/tex]
option B:
balance after 5 years:
[tex]5000 (1+ 3\%)^{3\times 5} = $7789.84[/tex]
option C:
balance after 5 years:
[tex]5,000 (1+ 4\frac{1}{2}\%) ^{3\times 5} = $7764.85[/tex]
The largest balance is $780255, so the option A will give them the largest balance after 5 years.
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How to divide decimals
Answer: READ BELOW
Step-by-step explanation:
To divide decimals, you can follow these steps:
1. Move the decimal point in the divisor (the number you're dividing by) to the right, counting the number of places you move it.
2. Move the decimal point in the dividend (the number you're dividing into) the same number of places to the right.
3. Divide the numbers as if they were whole numbers.
4. Place the decimal point in the quotient (the result) the same number of places from the right as the number you counted when moving the decimal points in step 1 and 2.
For example:
To divide 12.5 by 2.5, you would move the decimal point in 2.5 two places to the right to get 25, and move the decimal point in 12.5 two places to the right to get 1250. Then divide 1250 by 25 to get 50. Finally, place the decimal point two places from the right in the quotient 50 to get the final answer of 0.50.
The elements of Matrix C are shown below.
C11 = 3
C12 = 1
C13=-9
C14 = 8
C21 = 2
C22=2
C23 =0
C24 = 5
C31 = 16
C32 = 1
C33=-3
c34=11
if matrix c equals matrix d, which of the following is matrix d?
If matrix c equals matrix d, then matrix d is [tex]\left[\begin{array}{cccc}3&1&-9&8\\2&2&0&5\\16&1&-1&11\end{array}\right][/tex], hence option B is the correct answer.
What is matrix?A collection of numbers lined up in rows and columns to form a rectangular array is called a matrix. The elements, or entries, of the matrix are the integers. In addition to numerous mathematical disciplines, matrices find extensive use in the sectors of engineering, physics, business, and statistics.
Given the elements of the matrix C.
The matrix c is represented by its rows and columns element, and the arrangements are:
C11 = 3 C12 = 1 C13=-9 C14 = 8
C21 = 2 C22=2 C23 =0 C24 = 5
C31 = 16 C32 = 1 C33=-3 C34=11
Hence, the matrix C is:
[tex]\left[\begin{array}{cccc}3&1&-9&8\\2&2&0&5\\16&1&-1&11\end{array}\right][/tex]
From the given option we observe that the matrix d that is similar to matrix c is option B.
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The correct question is:
Problem 3.24 Effective interest rate and APR Aruna invested Rs 150,000 eighteen months ago. Currently, the investment is worth Rs 168,925. Aruna knows the investment has paid interest every three months, but she does not know what the yield on her investment is. Compute both annual percentage rate (APR) and the effective annual rate of interest on her investment. Ans: 8%; 8.24%
Answer: 8.24%
Step-by-step explanation:
To calculate the annual percentage rate (APR) and the effective annual rate of interest on Aruna's investment, we need to know the following information:
The initial investment amount (Rs 150,000)
The final investment amount (Rs 168,925)
The time period of the investment (18 months)
The frequency of interest payments (every 3 months)
The interest earned on the investment is the difference between the final investment amount and the initial investment amount. In this case, the interest earned is:
Rs 168,925 - Rs 150,000 = Rs 18,925.
Calculate the interest rate per period: To find the interest rate per period, divide the interest earned by the initial investment amount and multiply by the number of periods per year. In this case, the interest rate per period is:
(Rs 18,925 / Rs 150,000) * (4 periods per year) = 0.08%.
Calculate the APR: The APR is the interest rate per period multiplied by the number of periods in the investment. In this case, the APR is:
0.08% * 18 months = 8%.
The effective annual rate of interest takes into account the compounding of interest over time. To calculate the effective annual rate of interest, we use the formula:
(1 + r/n)^n - 1, where r is the interest rate per period and n is the number of compounding periods per year.
In this case, the effective annual rate of interest is:
(1 + 0.08%/4)^4 - 1 = 8.24%.
So the annual percentage rate (APR) is 8% and the effective annual rate of interest is 8.24%
Shakil and Omar both walk to the same shop from different starting points.
The distance-time graphs show information about their journeys.
How much shorter in km was the distance Omar had to walk?
Distance is the number of units between two points.
Shakil's distance was 15 km shorter than Omar's
How to interpret the graphs
From Shakil's graph, the highest distance from home is 10 kmFrom Omar's graph, the highest distance from home is 25 kmCalculate the difference between these distances
d=25km-10km
Evaluate the differences
d=15km
Hence, Shakil's distance was 15 km shorter than Omar's
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The polynomial function F(x) = 2x^2 + 4has a critical point at which of the following x values? A. x=0 B. ×= 4 C. X=2 D. X= -2
Answer:
The critical point of the function F(x) = 2x^2 + 4 is x = 0.
Step-by-step explanation:
A. x=0
The critical point of a polynomial function is the value of x at which the function changes from increasing to decreasing or vice versa. To find the critical point of a polynomial function, we need to find the value of x that makes the first derivative of the function equal to zero.
The first derivative of F(x) = 2x^2 + 4 is F'(x) = 4x
Setting F'(x) = 0, we get:
4x = 0
x = 0
Therefore, the critical point of the function F(x) = 2x^2 + 4 is x = 0.
What is the equation of the curve that passes through the point (1,8) if the slope of the curve at any point X is given by dy/dx= 3x^2+2
Refer to the attached images.
Let (Y1, Y2) denote the coordinates of a point chosen at random inside a unit circle whose center is at the origin. That is, Y1 and Y2 have a joint density function given by
f (y1, y2) = 1/ π , y^2 1 + y^2 2 ≤ 1, 0, elsewhere.
Find P(Y1 ≤ Y2).
Solve using polar coordinates.
To solve this problem using polar coordinates, we need to change from rectangular coordinates to polar coordinates, which represent points in the plane as pairs of polar coordinates (r,θ).
Given that Y1 = rcos(θ) and Y2 = rsin(θ), the condition Y1 ≤ Y2 is equivalent to 0 ≤ θ ≤ π/2. Hence, the required probability can be expressed as:
P(Y1 ≤ Y2) = ∫∫_{0<=θ<=π/2, 0<=r<=1} f(r,θ) dr dθ
where f(r,θ) = 1/π, 0 <= r <= 1.
The integration yields P(Y1 ≤ Y2) = 1/2.
Therefore, the probability that Y1 is less than or equal to Y2 for a point chosen randomly inside the unit circle is 1/2.
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You can drive 150 miles on 3/4 of a tank of gas in 3 hours. How far can you drive on one tank of gas
Answer: 200 miles
Step-by-step explanation: First divide 150 by 3 = 50, then multiply by 4 = 200 miles.
You can drive 200 miles with one tank of gas.
Step-by-step explanation:1. Identify the data.3/4 of a tank ---> 150 miles
1 full tank ---> x amount of miles
2. Solve the rule of 3.x = (1 full tank * 150 miles) / 3/4 of a tank
x = (1 * 150) / 3/4= 200 miles.
Check the attached image to better understand how a rule of 3 is solved. Beware that this procedure only applied when there is direct proportionality between the variables.
3. Conclude.You can drive 200 miles with one tank of gas.
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A few crystals of solid are added to the beaker. They did not dissolve after further mixing. Classify the solution. A. The solution is unsaturated. B. The solution is saturated. C. You cannot classify the solution because you do not know the concentration of the solution. An alloy is an example of a ________ solution A.gas/solid B. liquid/liquid C. solid/solid
When a solute does not dissolve in a solvent on further mixing, it is a saturated solution. An alloy is an example of solid/solid solution.
A saturated solution means a solution which has maximum solute concentrate. It cannot dissolve more solute in normal temperature. In such a solution system, if we add further crystals of solid, it will not dissolve. It has attained an equilibrium state. The amount of solute that dissolves will be equal to the amount which precipitates.
An alloy is a mixture of solid with solids. It can be two metals or a metal and a non-metal. It is a homogenous mixture of solid substances, so it is also called as solid solution. The metal in higher concentration acts as the solvent and the one with lower concentration acts as solute.
So saturated solutions does not dissolve further solute particles. Alloy are solid/solid solutions.
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y=3(x+3)−4 using the given table of values and following the instructions below
Answer:
y = 3x + 5
Step-by-step explanation:
y = 3x + 5
y = 3x + 9 - 4
y = 3x + 5
If you need more help, comment on my answer. K? feel free to comment. lol.
Let T: R2→R2 be the linear transformation that first rotates points clockwise through 30∘ and then reflects points through the line y=x. Find the standard matrix A for T.
A = ?
The standard matrix A is [ (1/2, √3/2) (√3/2, -1/2) ]
To find the standard matrix of a linear transformation, we need to find the images of the standard basis vectors under the transformation.
The standard basis vectors in R2 are (1,0) and (0,1). Let's find their images under T.
The image of (1,0) under a 30∘ clockwise rotation is (√3/2, 1/2). The image of this under reflection through the line y=x is (1/2, √3/2).
The image of (0,1) under a 30∘ clockwise rotation is (-1/2, √3/2). The image of this under reflection through the line y=x is (√3/2, -1/2).
The standard matrix of T is then the matrix whose columns are the images of the standard basis vectors:
A = [ (1/2, √3/2) (√3/2, -1/2) ]
= [tex]\left[\begin{array}{cc}1/2&\sqrt{3} /2\\\sqrt{3} /2&-1/2\end{array}\right][/tex]
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Please help me solve this
Extra points
Answer:
X + 9
Step-by-step explanation:
sum is addition
the sum of the measures of the interior angles of a convex polygon is given. classify the polygon by the number of sides in both examples
The polygons are classified as;
33. 3 sides
34. 23 sides
What is a polygon?A polygon can be defined as a plane figure that is described by a finite number of straight line segments which are all connected to form a closed polygonal chain.
The different types of polygons are;
Triangle with 3 sidesQuadrilateral with 4 sidesPentagon with 5 sidesHexagon with 6 sidesHeptagon with 7 sidesOctagon with 8 sidesNonagon with 9 sidesDecagon with 10 sidesFrom the information given,
The polygon has a measure of 180 degrees
The formula for calculating the sum of the angles of a polygon is;
(n-2) 180
(3-2)180
180. It is a triangle
(23--2) 180
21(60)
3960. It has 23 sides
Hence, the values are 3 and 23
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divisions: 5. The cost of warehouse space is allocated to three inventories: raw materials, work- in-process, and finished goods. The inventories use the warehouse space in the ratio of one-third to one-sixth to three-eighths, respectively. If the total warehouse space is 9.6 million square metres, at a cost of $11.55 million, how much of the cost should be allocated to each of the inventories?
The cost allocation to each inventory is:
Raw materials: $11.52 millionWork-in-process: $11.52 millionFinished goods: $11.52 millionHow to solve the following?We can use the ratio of warehouse space usage to calculate the cost allocation to each inventory. Let's first calculate the warehouse space usage for each inventory.
Raw materials: 1/3 * 9.6 million square metres = 3.2 million square metres
Work-in-process: 1/6 * 9.6 million square metres = 1.6 million square metres
Finished goods: 3/8 * 9.6 million square metres = 4.8 million square metres
Next, we can calculate the cost allocation for each inventory by dividing the total cost by the corresponding warehouse space usage.
Raw materials: $11.55 million / 3.2 million square metres = $3.6 million/million square metres
Work-in-process: $11.55 million / 1.6 million square metres = $7.2 million/million square metres
Finished goods: $11.55 million / 4.8 million square metres = $2.4 million/million square metres
Finally, we can multiply the cost per million square metres by the warehouse space usage for each inventory to find the total cost allocation.
Raw materials: $3.6 million/million square metres * 3.2 million square metres = $11.52 million
Work-in-process: $7.2 million/million square metres * 1.6 million square metres = $11.52 million
Finished goods: $2.4 million/million square metres * 4.8 million square metres = $11.52 million
So, the cost allocation to each inventory is:
Raw materials: $11.52 million
Work-in-process: $11.52 million
Finished goods: $11.52 million
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Six different colored dice are rolled. Of interest is the number of dice that show a one.Find the probability that all six dice show a one.
The probability that all six dice show a one is 1/46656
How to determine the probabilityFrom the question, we have the following parameters that can be used in our computation:
Number of dices = 6
Outcome = all 1
The probability of rolling a one on one die is 1/6.
So the probability of rolling a one on all six dice is:
(1/6) * (1/6) * (1/6) * (1/6) * (1/6) * (1/6) = (1/6)^6
So the probability of all six dice showing a one is 1/46656
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Please help! If you get it right I'll give you Brainlist!
4 cm Equals 1 day on the x axis
2 cm = 5 0 C on the y axis
To determine the temperature on a specific day:
Trace the vertical line parallel to the y axis from the position on the x axis to the point where this vertical line crosses the graph.
Trace a horizontal line parallel to the x axis from that point until it meets the y axis at the desired location.
To locate the day at a specific temperature, trace a horizontal line parallel to the x axis from the temperature point on the y axis to the point where this horizontal line meets the graph.
Now, trace a vertical line parallel to the y axis from that position until it crosses the x axis at the desired location.
Now, a) the forecast and actual temperatures are the same where the graphs of Both intersect on Tuesday, Friday, and Sunday.
b) Repeat step 1 to obtain the temperature for the graph forecast for the days of the week.
Mon 15 0 C Tuesday 20 0 C Wednesday 25 0 C
Thu −22.5 \s0\s C
Friday 15 0 C Saturday 30 0 C
Sun −35 \s0\s C
As a result, the highest expected temperature for the week is 35 0 C.
c) Repeat step 1 to determine the temperature for the real graph based on the days of the week.
Mon−17.5 \s0\s C
Tuesday 20 0 C Wednesday 30 0 C
Thu −15 \s0\s C
Friday 15 0 C Saturday 25 0 C
Sun −35 \s0\s C
So the week's minimum real temperature is 15 0 C.
d) The difference between actual and predicted temperatures for the week
Mon, 17.5−15=2.5 \s0 C
Tue, 20−20=0 \s0\s C
Wed, 30−25=5 \s0\s C
Thu, 15−22.5=−7.5 \s0\s C
Fri, 15−15=0 \s0\s C
Sat, 25−30=−5 \s0\s C
Sun, 35−35=0 \s0\s C
The actual temperature differs from the expected temperature by 7.5 degrees Celsius on Thursday.
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The actual temperature differs from the expected temperature by 7.5 degrees Celsius on Thursday. 4 cm Equals 1 day on the x axis. 2 cm = 5 0 C on the y axis
To determine the temperature on a specific day:
Trace the vertical line parallel to the y axis from the position on the x axis to the point where this vertical line crosses the graph.
Trace a horizontal line parallel to the x axis from that point until it meets the y axis at the desired location.
To locate the day at a specific temperature, trace a horizontal line parallel to the x axis from the temperature point on the y axis to the point where this horizontal line meets the graph.
Now, trace a vertical line parallel to the y axis from that position until it crosses the x axis at the desired location.
Now, a) the forecast and actual temperatures are the same where the graphs of Both intersect on Tuesday, Friday, and Sunday.
b) Repeat step 1 to obtain the temperature for the graph forecast for the days of the week.
Mon 15 0 C Tuesday 20 0 C Wednesday 25 0 C
Thu −22.5
Friday 15 0 C Saturday 30 0 C
Sun −35
As a result, the highest expected temperature for the week is 35 0 C.
c) Repeat step 1 to determine the temperature for the real graph based on the days of the week.
Mon−17.5
Tuesday 20 0 C Wednesday 30 0 C
Thu −15
Friday 15 0 C Saturday 25 0 C
Sun −35
So the week's minimum real temperature is 15 0 C.
d) The difference between actual and predicted temperatures for the week
Mon, 17.5−15=2.5
Tue, 20−20=0
Wed, 30−25=5
Thu, 15−22.5=−7.5
Fri, 15−15=0
Sat, 25−30=−5
Sun, 35−35=0
The actual temperature differs from the expected temperature by 7.5 degrees Celsius on Thursday.
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at a factory that produces pistons for cars machine 1 produces 616 satisfactory pistons and 84 unsatisfactory Pistons today. machine 2 produced 414 satisfactory pistons and 276 unsatisfactory Pistons today suppose that one piston from machine 1 and one piston from machine 2 are chosen at random from today's batch what is the probability that the piston from machine 1 is unsatisfactory and the piston from machine 2 is satisfactory do not round your answer decimal please
Answer:
The probability of getting unsatisfactory piston of machine 1 and satisfactory machine of piston 2 is 0.072
Step-by-step explanation:
p(E) = p(unsatisfactory Pistons of machine 1) = 84/700
p(F) = p(Satisfactory Pistons of machine 2) = 414/690
p(E and F) =
p(unsatisfactory piston of machine 1 and satisfactory machine of piston 2)
p(E and F) = p(E) . p(F)
= 84/700 . 414/690
= 0.072
