On each roll of a 6-sided die, we have 6 possible outcomes.
Then if we roll it twice, we will have 36 outcomes.
The outcomes where the sum is 4 are:
roll 1 roll 2 sum
1 3 4
3 1 4
2 2 4
Son in 3 out of 36 outcomes the sum can be 4, then the probability opf rolling a sum of 4 is given by the quotient:
P = 3/36
P = 1/12
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marks) There are more than 600 million bacteria in a person's body. Work out and write your answer correct to 1 significant figure the number of bacteria there would be in the people of a town with a population of 200 thousand. (Write answer in scientific notation)
Answer: The number of bacteria in the people of a town with a population of 200 thousand would be 200,000 * 600 million = 120 x 10^9 bacteria.
Step-by-step explanation:
Which of the following lists of properties contains only those that are characteristic properties of a substance? Odensity, solubility, melting point O boiling point, mass, density O volume, density, temperature O solubility, mass, volume
Of the lists of properties you provided, only the list of "identity, solubility, melting point" contains only those that are characteristic properties of a substance.
Identity refers to the name or chemical formula of the substance, which is unique to that substance and can be used to identify it.
Solubility refers to the ability of a substance to dissolve in a solvent, such as water. The solubility of a substance can also be used to identify it, as different substances have different solubility's.
Melting point refers to the temperature at which a solid substance will change into a liquid. Like solubility, the melting point of a substance is also a characteristic property that can be used to identify it.
On the other hand, boiling point, mass, and density are not always characteristic properties of a substance. While they can give us information about a substance, they are not unique to that substance and cannot be used to identify it.
Volume and temperature are not considered characteristic properties of a substance, as they are dependent on external factors, such as the pressure and the amount of the substance being measured.
In conclusion, the list of "identity, solubility, melting point" contains only those properties that are characteristic of a substance and can be used to identify it.
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Determine if the triangle below is a right triangle. If it is not, compute what the hypotenuse would have to be for the triangle to be a right triangle. A. No, the hypotenuse should be 98 B. No, the hypotenuse should be 99 C. No, the hypotenuse should be 94 D. Yes
The triangle will by a right triangle if the sum of the squared side lengths is equals to the squared length of the hypotenuse.
What is the Pythagorean Theorem?The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.
Hence, a triangle will only be a right triangle if the Pythagorean Theorem is respected, hence the sum of the squared side lengths must be compared to the square of the hypotenuse length.
Missing InformationThe problem is incomplete, hence the procedure to verify whether the triangle is a right triangle was presented.
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concerning the relationship between the chi squared test and two proportion z test with a two sided alternative hypothesis, which of the following statements is true?The x^2 test statistic is equal to the z test statistic. The x^2 test statistic is equal to the z test statistic squared. The x^2 test statistic is not equal to the z test statistic squared. The x^2 test statistic is not equal to the alternative hypotheses value squared.
The concept is the Chi-square test, a statistical test for comparing observed results to expected results. The answer is option A.
The test statistic x^2 is equivalent to the test statistic Z. Homogeneity 2x2 The chi-square statistic (and the test) is equivalent to a two proportion test.
The chi-square test is a statistical test used to compare observed results to expected results.The purpose of this test is to determine whether the difference between the observed and expected data is due to chance or to the relationship between the variables being studied. The
Two Ratio Z-Test is a statistical hypothesis test used to determine whether two ratios are different from each other. When you run the test, the z-statistic is calculated from two independent samples, and the null hypothesis is that the two proportions are equal.
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A wage earner receives a gross pay of $983.15 for 52.5 hours of work. What is his hourly rate of pay if a regular workweek is 44 hours and overtime is paid at time-and-a-half the regular rate of pay?
What is the intrest amount after borrowing $83,500 at a rate of 4.005% over 6 years? Round your answer to the nearest cent
The amount of interest nearest to cent will be $22,184.62.
What is compound interest?A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.
We know that the compound interest is given as
A = P(1 + r)ⁿ
Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.
The borrowing amount $83,500 at a rate of 4.005% over 6 years. Then the interest is given as,
I = A - P
I = $83,500 (1.04005)⁶ - $83,500
I = $105,684.62 - $83,500
I = $22,184.62
The amount of interest nearest to cent will be $22,184.62.
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Peggy invests $8, 400 at 6 1/2% interest for 10 years compounded semiannually. Find the amount of money in the account at the end of the term.
Answer:1200
Step-by-step explanation:1200
Assume that program runs in f (n) microseconds; where f (n) is the function given on the left. Fill in how large an input can be calculated, given cach of the runtimes given along the top. have filled in two values for you: You do not need to fill in every box, but should have at least of every row filled in, and at least half of the rows complete: second minute hour day month year Ign Vnl n lgn 72 1000 2n Show some calculations, O some of your code if you use code: What row is the most sucktastic one? Why? Do you have any non-integer answers?
The row with the most sucktastic runtime is the one with[tex]2^n[/tex], as it takes exponentially longer to run than the other runtimes.
No, we do not have any non-integer answers.
Second: 72
Minute: 1000
Hour: [tex]2^(17)[/tex]
Day: [tex]2^25[/tex]
Month: [tex]2^30[/tex]
Year: [tex]2^35[/tex]
Second: f(n) = 72 => n = 72
Minute: f(n) = 1000 => n = 1000
[tex]Hour: f(n) = 2^n = > n = 17Day: f(n) = 2^n = > n = 25 Month: f(n) = 2^n = > n = 30Year: f(n) = 2^n = > n = 35[/tex]
Seconds: The runtime for an input of size n is 72 microseconds, so the largest input that can be calculated in a second is 72.
Minutes: The runtime for an input of size n is 1000 microseconds, so the largest input that can be calculated in a minute is 1000.
Hours: The runtime for an input of size n is[tex]2^n[/tex] microseconds, so the largest input that can be calculated in an hour is [tex]2^17.[/tex]
Days: The runtime for an input of size n is [tex]2^n[/tex] microseconds, so the largest input that can be calculated in a day is [tex]2^25[/tex]
Months: The runtime for an input of size n is [tex]2^n[/tex] microseconds, so the largest input that can be calculated in a month is [tex]2^30.[/tex]
Years: The runtime for an input of size n is [tex]2^n[/tex] microseconds, so the largest input that can be calculated in a year is [tex]2^35.[/tex]
The row with the most sucktastic runtime is the one with [tex]2^n[/tex], as it takes exponentially longer to run than the other runtimes. Therefore, the longer the time period, the larger the input size that can be calculated. No, we do not have any non-integer answers as the runtimes of the inputs are in microseconds and the input size is given as an integer.
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Assuming that the math module has been imported, which of the following expressions evaluates to True?
a. math.hypot (3,4) == math.sqrt (25)
b. math.hypot (2,5) == math.trunc (2.5)
c. math.hypot (2,5) == math.true (2.5)
d. math.cell (2,5) == math.floor (2.5)
After evaluating these expression it seems to be the option (a) math.hypot(3,4) == math.sqrt(25) evaluate that is True
The math.hypot function calculates the Euclidean distance between two points in a 2D space, which is equivalent to the length of the hypotenuse of a right triangle with sides of length a and b (where a and b are the arguments to math.hypot).
In this case, math.hypot(3, 4) calculates the length of the hypotenuse of a right triangle with sides of length 3 and 4, which is equal to 5.
The expression math.sqrt(25) calculates the square root of 25, which is equal to 5. Since math.hypot(3, 4) and math.sqrt(25) both evaluate to 5, the expression math.hypot(3, 4) == math.sqrt(25) evaluates to True.
The other expressions are not evaluating to True:
b. math.hypot(2,5) != math.trunc(2.5)
c. math.hypot(2,5) != math.true(2.5)
d. math.cell(2,5) does not exist. It is likely a typo for math.ceil which is not equal to math.floor(2.5)
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when constructing bins for a frequency distribution of quantitative data, which of the following principles should generally be followed?
When constructing bins for a frequency distribution, it is important to have equal widths, choose the number of bins based on the sample size, and consider outliers in the data.
A frequency distribution is a representation of data that shows the number of observations in each category or bin.
One of the most important principles is to have an equal number of observations in each bin. This is known as having equal widths for the bins.
To calculate the width of a bin, divide the range of the data by the number of bins desired. The range is then divided into equal parts, each of which becomes a bin width.
Another principle is to have the number of bins chosen based on the sample size.
A rule of thumb is to have at least five observations in each bin, but more bins may be necessary for larger samples.
Additionally, the choice of bin width can also be influenced by outliers in the data. If there are extreme values in the data, it may be necessary to create a separate bin for those values, so they do not dominate the frequency distribution.
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A tower that is 118 feet tall casts a shadow 130 feet long. Find the angle of elevation of the sun to the nearest degree.
Answer:
42°
Step-by-step explanation:
A right-angled triangle can formed in this scenario (image attached), where:
θ = angle of elevation of the sun
Opposite side = The height of the tower
Adjacent side = Length of the shadow
Trigonometric function will be used to determine the angle of elevation:
tanθ = [tex]\frac{opposite}{adjacent}[/tex]
[tex]= \frac{118 feet}{130 feet}[/tex]
feet in the numerator and denominator will cancel each other out completely:
θ =[tex]tan^{-1} (\frac{118}{130})[/tex]
θ = 42.23°
∴ θ = 42° (Rounded to the nearest degree)
Suppose that, in 1998, Japan produced 0.528 million pounds of corn. The total world production that year totaled 71 million pounds of corn. What percent of the world's total production of pounds of corn is contributed by Japan? Round your answer to the nearest tenth.
Find the volume of a frustum of a pyramid with square base of side 22, square top of side 13 and height 20.
The volume of a frustum of a pyramid with given dimensions is 6260 cubic units.
What is frustum of pyramid?
The top of a conventional pyramid is removed to create the frustum, which is a pyramid. It is known as a truncated pyramid for this reason. The height of a pyramid is represented by the letter h and is the distance from its base to its summit. Similar to it, it has two bases and a slant height indicated by the letter "s" (top and bottom).
We are given frustum of a pyramid with square base of side 22, square top of side 13 and height 20.
We know that volume of frustum of pyramid(V) = h(b^2 + a^2 + ab)/3
We are given b = 22, a = 13 and h = 20
From this, we get
⇒V = h(b^2 + a^2 + ab)/3
⇒V = 20(22^2 + 13^2 + 22*13)/3
⇒V = 20(484 + 169 + 286)/3
⇒V = 20(939)/3
⇒V = 20*313
⇒V = 6260 cubic units
Hence, the volume of a frustum of a pyramid with given dimensions is 6260 cubic units.
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Find and simplify each of the following for f(x) = 4x² - 6x + 9.
(A) f(x + h) =
(Do not factor.)
A bag contains 8 green candies and 4 red candies. You randomly select one candy at a time to eat. If you eat five candies, there are relatively prime positive integers m and n so that m n is the probability that you do not eat a
green candy after you eat a red candy. Find m + n.
If m/n is the probability that you do not eat green candy after you eat a red candy, then m + n is 6.
A bag contains 8 green candies and 4 red candies. If you eat five candies, there are relatively prime positive integers m and n so that m/n is the probability that you do not eat green candy after you eat a red candy. Below list the ways to accomplish this ordering along with their respective probabilities:
GRRRR : [tex]\frac{8}{12}\times\frac{4}{11} \times\frac{3}{10} \times\frac{2}{9} \times\frac{1}{8}[/tex]
GGRRR : [tex]\frac{8}{12}\times\frac{7}{11} \times\frac{4}{10} \times\frac{3}{9} \times\frac{2}{8}[/tex]
GGGRR : [tex]\frac{8}{12}\times\frac{7}{11} \times\frac{6}{10} \times\frac{4}{9} \times\frac{3}{8}[/tex]
GGGGR : [tex]\frac{8}{12}\times\frac{7}{11} \times\frac{6}{10} \times\frac{5}{9} \times\frac{4}{8}[/tex]
GGGGG : [tex]\frac{8}{12}\times\frac{7}{11} \times\frac{6}{10} \times\frac{5}{9} \times\frac{4}{8}[/tex]
The sum is [tex]\frac{8\times3\times4(2+14+42+70+70)}{12.11.10.9.8}[/tex]
Probability that you do not eat green candy after you eat a red candy =[tex]\frac{1}{5}[/tex]
so m = 1 and n = 5
m + n =6
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Find one possible missing coordinate so that the point becomes a solution to the given inequality.
(x,9)
is a solution to 8x−7
.
Answer:
x=2Step-by-step explanation:
y=8x-7
9=8x-7
9+7=8x-7+7
16=8x
16/8=8x/8
2=x
In a box containing 36 strawberries, 2 of them are rotten. Kyle randomly picked 5 of these strawberries.a. What is the probability of having at least 1 rotten strawberry among the 5?b. How many strawberries should be picked so that the probability of having exactly 2rotten strawberries among them equals 2/35?
a) The probability of having at least 1 rotten strawberry among the 5 is 0.262.
b) 1 strawberry must be picked so that the probability of having exactly 2 rotten strawberries among them equals 2/35.
What is probability?
Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.
The probability that Kyle selects exactly k rotten strawberries among the five she randomly picks is -
P( exactly k rotten strawberries) = [tex]\frac{(^2c_k)(^{34}c_{5-k}) }{^{36}c_5}[/tex]
since if she picks k of the 2 rotten strawberries, Kyle must also select 5 - k of the 36 -2 = 34 good strawberries.
Therefore, the probability that Kyle picks at least one rotten strawberry is -
P(at least 1 rotten strawberry) = P(exactly 1 rotten strawberry) + P(exactly 2 rotten strawberries)
P(at least 1 rotten strawberry) =[tex]\frac{(^2c_1)(^{34}c_{4}) }{^{36}c_5} + \frac{(^2c_2)(^{34}c_{3}) }{^{36}c_5}[/tex]
P(at least 1 rotten strawberry) = [(2 × 46376) / 376992] + [(1 × 5984) / 376992]
P(at least 1 rotten strawberry) = (92752 / 376992) + (5984 / 376992)
P(at least 1 rotten strawberry) = 0.246 + 0.016
P(at least 1 rotten strawberry) = 0.262
The probability of selecting exactly 2 rotten strawberries among n is
P(exactly 2 rotten strawberries) = [tex]\frac{(^2c_2)(^{34}c_{n-2}) }{^{36}c_n} = \frac{(^{34}c_{n-2}) }{^{36}c_n}[/tex]
The value for n is 2/35.
P(exactly 2 rotten strawberries) =[tex]\frac{(^{34}c_{\frac{-33}{35}}) }{^{36}c_{\frac{2}{35} }}[/tex]
P(exactly 2 rotten strawberries) = 1 / 1
P(exactly 2 rotten strawberries) = 1
Therefore, the probability is 0.262 and 1 strawberry must be picked.
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You take a package to the local shipping company. They charge a fixed base cost of $6 per package plus an additional $0.39 per pound. If P represents the number of pounds of your package, and C is the total cost of shipping your package, write the linear equation that represents the relationship between P and C
The linear equation that represents the relationship between P and C will be C = 0.39P + 6.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
You take a bundle to the nearby delivery organization. They charge a proper base expense of $6 per bundle in addition to an extra $0.39 per pound.
Let 'P' be the number of pounds and 'C' be the total cost. Then the equation is given as,
C = 0.39P + 6
The linear equation that represents the relationship between P and C will be C = 0.39P + 6.
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The length of a rectangle is 2 ft longer than it’s width if the perimeter of the rectangle is 36ft find it’s area
Answer:
two of the sides are x and the other two sides are x+2
x+x+x+2+x+2 = 36
4x = 32
x = 8
the sides are 8, 8, 10, 10
area is length x width
8 x 10 = 80
answer: 80ft
Step-by-step explanation:
Baseball The table shows the height of a baseball hit, with
x representing the time (in seconds) and y representing
the baseball's height (in feet). Use a graphing calculator
to find the best-fitting model for the data.
Time, x
2 4 6 8
0
Helght, y 3 28 40 37 26
Oy 1.553x² +15.1782 -3.37
Oy -1.553x² - 15.178x + 3.37
Oy = -1.553x² +15.178x + 3.37
Oy 1.553x² +15.178x + 3.37
Answer: The best-fitting model for the data is a parabolic equation with the form y = ax^2 + bx + c. The coefficients a, b, and c represent the parameters that best describe the relationship between the time (x) and the height (y) of the baseball.
Based on the information provided, the best-fitting model is:
y = 1.553x^2 + 15.178x + 3.37
where y is the height of the baseball (in feet), x is the time (in seconds), 1.553 is the coefficient for x^2, 15.178 is the coefficient for x, and 3.37 is the constant term. This equation represents the best fit of the data to a parabolic function.
Step-by-step explanation:
CAN ANYONE WRITE ME A SENTENCE USING THE WORD (YEARS)!
Answer:
Happy New Years sir it is 12:00 in the morning.
Step-by-step explanation:
yes
TBill rates 2016 Here are a plot and regression output showing the federal rate on 3-month Treasury bills from 1950 to 1980, and a regression model fit to the relationship between the Rate (in %) and Years Since 1950 (www.gpoaccess.gov/eop/). a. What is the correlation between Rate and Year? b. Interpret the slope and intercept. c. What does this model predict for the interest rate in the year 2020?
The correlation between Rate and Year is positive. The slope of the regression line is 0.0275 and the intercept is -9.8086. The model predicts that the interest rate in 2020 will be 2.38%.
The correlation between Rate and Year is positive, which means that as the years go by, the interest rate on 3-month Treasury bills is increasing. The slope of the regression line (0.0275) tells us that the average increase in the interest rate per year is 0.0275%. The intercept of the regression line (-9.8086) represents the interest rate in 1950.
This model predicts that the interest rate in 2020 will be 2.38%, which is obtained by plugging in 1970 for the Year variable and solving for the Rate. It's important to keep in mind that this model is based on historical data, and future interest rates may not follow the same pattern as in the past.
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Alice decides to finish her trip by riding a train 700 miles to Washington D.C. The train travels at an average speed of 80mph. What are the domain and range of the function this creates?
The range of the function is 8.75.
And the domain is all the positive integers.
What is a domain?The collection of all conceivable independent values that a function or relation may take is known as its domain.
Given:
Alice decides to finish her trip by riding a train 700 miles to Washington, D.C.
The train travels at an average speed of 80mph.
Let s be the average speed.
So, speed = distance / time
s = 700/t
t = 700/80
t = 8.75 hours.
The range of the function is 8.75.
And the domain is all the positive integers.
Therefore, the time it will take is 8.75 hours.
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Consider the cubic function g(x) = −2( + 4)^3 − 5. Please describe how this function has been transformed from the cubic parent function f(x) = x^3
The cubic function g(x) = -2(x + 4)³ - 5 can be obtained from f(x) = x³ by a translation of 4 units to the right, a vertical scaling by a factor of -2, and a reflection about the x-axis.
What are functions?Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
The cubic parent function f(x) = x³ has been transformed to the function g(x) = −2(x + 4)³ − 5 through a combination of translations, scaling, and reflection.
Translation: The parent function has been shifted 4 units to the right, resulting in x + 4 instead of x in the argument of the function.
Scaling: The parent function has been scaled vertically by a factor of -2, resulting in a coefficient of -2 in front of the argument.
Reflection: The parent function has been reflected on the x-axis, resulting in the negative sign in front of the argument.
Thus, g(x) = -2(x + 4)³ - 5 can be obtained from f(x) = x³ by a translation of 4 units to the right, a vertical scaling by a factor of -2, and a reflection about the x-axis.
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A car can be rented for $80 per week plus $0.25 per mile. How many miles can be driven if you have at most $110 to spend for weekly transportation?
Answer: Let x be the number of miles driven.
The cost of renting the car and driving x miles is 80 + 0.25x.
We want to find the maximum number of miles that can be driven given a budget of $110, so we set 80 + 0.25x = 110 and solve for x:
80 + 0.25x = 110
0.25x = 110 - 80
0.25x = 30
x = 120
So the maximum number of miles that can be driven is 120.
Step-by-step explanation:
Verify that the indicated function is an explicit solution of the given differential equation. Assume an appropriate interval I of definition for the solution.
By' +y=0; y e-x/8
When y = e-x/8,
y'--8
Thus, in terms of x,
Sy' + y =
0
Need Help?
X
Read It
X +ex/8
We have the DE, [tex]y'+y=0[/tex], verify that [tex]y=e^{\frac{-x}{8}}[/tex] is a solution.
We have, [tex]y=e^{\frac{-x}{8}}[/tex], find [tex]y'[/tex].
=> [tex]y'=\frac{-1}{8} e^{\frac{-x}{8}}[/tex]
Plug [tex]y[/tex] and [tex]y'[/tex] into the DE.
=> [tex]y'+y=0[/tex]
=>[tex](\frac{-1}{8} e^{\frac{-x}{8}})+(e^{\frac{-x}{8}})=0[/tex]
=> [tex]e^{\frac{-x}{8}}=\frac{1}{8} e^{\frac{-x}{8}}[/tex]
=> [tex]e^{\frac{-x}{8}}\neq \frac{1}{8} e^{\frac{-x}{8}}[/tex]
Thus, [tex]y=e^{\frac{-x}{8}}[/tex], is not a solution to the given DE.
A multimeter and an oscilloscope cost $574. The oscilloscope cost $356 more than the multimeter. Find the cost of the oscilloscope and the multimeter.
Answer:
oscilloscope: $465multimeter: $109Step-by-step explanation:
You want the costs of an oscilloscope and a multimeter when the sum of their costs is $574, and the difference of their costs is $356.
Sum and differenceLet o and m represent the costs of the oscilloscope and multimeter, respectively. Then the costs can be described by ...
o +m = 574
o -m = 356
SolutionAdding these two equations gives ...
2o = (574+356) = 930
o = 465 . . . . . . . . . . . . divide by 2
Subtracting the second equation from the first gives ...
2m = 574 -356 = 218
m = 109 . . . . . . . . . . . . divide by 2
The oscilloscope costs $465; the multimeter costs $109.
__
Additional comment
This is the generic solution to a "sum and difference" problem: the higher value is half the sum of the given numbers, and the lower value is half their difference.
help me with this pls
Where the OADB is a sector of a circle, and Angle AOB = 80°, and the Radius of OB = 12cm,:
A circular sector (symbol: ) is the piece of a disk (a closed region circumscribed by a circle) contained by two radii and an arc, where the smaller area is known as the minor sector and the bigger as the major sector.
Given m∠AOB = 98°, OB = OA = 25cm (The radii are congruent) Thus,
m∠OAB = m∠OBA,
m∠OAB = (180 - 98) /2
m∠OAB = 41°
In the Right Triangle OBC, OB = 25cm, m∠OBC = 41°
Hence,
OC /OB = Sin ∠OBC ,
OC = OB (Sin ∠OBC )
= 25 * Sin41°
= 16.4cm; thus,
OC = 16.4cm
Where BC/OB = Cos ∠OBC,
BC = OB ( Cos ∠OBC)
= 25 * Cos 41° Thus,
BC = 16.4cm
The area of the ΔOAB = 1/2 * OA * OB * Sin98°
= 1/2 * 25 * 25 * Sin 98°
= 309.5cm²
The area of the Sector OADB = (98°/360°) * π * 25²
= 0.2722222222 * 3.14 * 25²
= 0.2722222222 * 3.14 * 252
= 534.5cm²
The percentage of the diagram that is shaded is given as:
309.5/534.5 * 100
= 0.5790458372 *100
= 57.9%
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c)If 2000 items sell when the price is 30 dollars and if the number of items that are sold decreases by 400 for every 1 dollar increase in price, find the rate of change of the profit when the item price is 30 dollars.
The rate of change of the profit when the item price is $30 is $3600 per dollar increase in price.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let's call the number of items sold at a price of $p as x(p).
Based on the information given, we can write an equation for x(p) as:
x(p) = 2000 - 400(p - 30)
The profit from selling the items at a price of $p is given by the product of the number of items sold and the price:
Profit(p) = x(p)×p
Taking the derivative of the profit function with respect to the price, we can find the rate of change of the profit:
dProfit/dp = dx/dp×p + x(p)
= -400 p + 400 ( 30) + 2000 - 400(p - 30)
= -400 p + 12000
When p = 30, the rate of change of the profit is:
dProfit/dp = -400(30 )+ 12000
= 3600
So the rate of change of the profit when the item price is $30 is $3600 per dollar increase in price.
Hence, the rate of change of the profit when the item price is $30 is $3600 per dollar increase in price.
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In the figure above, ABCD, BEFG, and DHIJ are squares with AB= 2(DH) and DH = 2(BE). If a point is chosen at random inside square ABCD, what is the probability it will be in the shaded region?
(A) 1/2
(B) 5/8
(C) 11/16
(D) 3/4
Answer:
[tex]\dfrac{11}{16}\\\\[/tex]
Option C
Step-by-step explanation:
We have the following information:
AB = 2DH
DH = 2BE or BE = DH/2
The area of square ABCD = (2DH)² = 4DH²
The area of square BEFG = BE² = (DH/2)² = DH²/4
The area of square DHFJ = DH²
Area of the unshaded region
= area of square BEFG + area or square DHFJ
= DH²/4 + DH² = DH²/4 + 4DH²/4 = 5DH²/4
Area of shaded region
= area of square ABCD - area of unshaded region
[tex]= AB^2 - \dfrac{5}{4}DH^2\\\\= 4DH^2 - \dfrac{5}{4} DH^2\\\\= \dfrac{4DH^2 \cdot 4}{4} - \dfrac{5}{4} \cdot DH^2[/tex]
[tex]= \dfrac{16DH^2 - 5DH^2}{4}= \dfrac{11DH^2}{4}[/tex]
[tex]\textrm{Probability of a point falling in the shaded region} =\dfrac{\textrm{Area of shaded region}}{\textrm{Total area of both regions}}\\\\= \dfrac{11DH^2/4}{4DH^2} = \dfrac{11}{16}\\\\[/tex]