Answer:
A. False
B. False
C. True
D. True
Step-by-step explanation:
A hemispherical pool has a radius of 40 feet. If a gallon of paint covers 350 square feet, how many gallons of paint are needed to paint the inside of the pool? What if you wanted to fill the pool from the previous problem with paint? Then how many gallons would you need?
To paint the inside of the hemispherical pool, you need to find the surface area of the pool. The formula for the surface area of a hemisphere is 2πr^2, so the surface area of the pool is 2π(40)^2.
Divide this area by the coverage of one gallon of paint (350 square feet) to find the number of gallons needed. To paint the inside of the hemispherical pool, you need to find the surface area of the pool. The formula for the surface area of a hemisphere is 2πr^2, so the surface area of the pool is 2π(40)^2.
Divide this area by the coverage of one gallon of paint (350 square feet) to find the number of gallons needed. The result is approximately 29.01 gallons. If you wanted to fill the pool with paint, you would need to find the volume of the pool. The formula for the volume of a hemisphere is (2/3)πr^3.
Plugging in the radius of 40 feet, the volume is (2/3)π(40)^3. Multiply this volume by the conversion factor of 7.48 gallons per cubic foot to find the number of gallons needed. The result is approximately 952328.48 gallons.
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Need help with number 27 asap
Answer:
Yes
Step-by-step explanation:
Yes; points X and Y are fixed under the reflection, so they must lie on the line of reflection. Since two points determine a line, the line of reflection is XY.
https://www.rcboe.org/cms/lib010/GA01903614/Centricity/Domain/1030/Reflections.pdf
.
Pls help ASAP
The question is in the picture
Value of quadratic equation is x = -1 and 11.
Define quadratic equation.In mathematics, a quadratic equation is one with degree 2, which means that its maximum exponent is 2. A quadratic has the standard form y = ax² + bx + c, where a, b, and c are all numbers and a cannot be zero. All of these are examples of quadratic equations: the square root of the sum of the squares of the values, given by y = x² + 3x + 1. a degree 2 equation with just one variable. Ax² + bx + c = 0, where x is the variable and a, b, and c are constants (a 0), is its general form.
Given Data
Equation
x² - 10x -11 = 0
x² -11x + x -11 = 0
Completing the square,
x(x - 11) + 1(x -11) =0
Taking common,
(x+1)(x -11) =0
x = 11. -1
Value of quadratic equation is x = -1 and 11.
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change 6 to percentage.
-
25
Answer:
24%
Step-by-step explanation:
6÷25×100
to find in percentage
Answer:
6 as a percent would be 0.06.
Step-by-step explanation:
100 as a percent is 1.00
90 as a percent is 0.90
hope this helps, and you have a better understanding of percentages. please rate and mark as brainlest
I need help one last time.
Here are the answer choices.
Y = 72
Y = 16
Y = 32
Y = 1
Answer:
y = 32
Solving Way #1:
This way uses the "tip" they give us of finding the relation between the first two values and then applying it to the second x.
k = \(\frac{y}{x}\)
2 = \(\frac{16}{8}\)
-
y = kx
y = (2)(16)
y = 32
Solving Way #2:
Since they vary directly which each other, we can set up a proportion to solve. I have y values on the top and x values on the bottom.
\(\frac{16}{8} =\frac{y}{16}\)
256 = 8y
32 = y
y = 32
Either way, when x is 16 y is 32.
B E
400
(51)
А
C D
3t
Find the measure of ZF if mZD=88º.
A. 8°
B. 40°
C. 52°
D. 90°
the answer is c because you have to take the zf an time it by the zd
Answer:
C
Step-by-step explanation:
for the top of the triangle it has to be 40 and angle d has been declared as 88
so it is 40+88 = 128 now 180 -128 = 52 so the answer is C
OK IF YOU ARE ON HERE PLAYING STOP PEOPLE ARE TRYING TO GET THERE GRADE UP AND YOUR IN HERE PLAYING!! YOUR PROBABLY THE ONE WITH ALL F´s AND YOUR PLAYING BE MATURE!!
Answer:
true
Step-by-step explanation:
1. If events A and B are independent, then P(A and B) = P(A). P(B).
a. True
b. False
2. The length of time of a particular phone call is an example of continuous random variable.
a. True
b. False
3. At one college, GPA’s are normally distributed with a mean of 3 and a standard deviation of 1. According to empirical rule, What percentage of students at the college have a GPA between 2 and 4?
a. 95%
b. 68%
c.,99.7%
d. 84.13%
True. If two events A and B are independent, then P(A and B) = P(A). P(B) because when two events are independent, the occurrence of one does not affect the probability of the other.
The probability of the intersection of two independent events A and B is the product of their probabilities. It means that if A and B are independent, then:P(A ∩ B) = P(A) × P(B)A continuous random variable can assume any numerical value in a given interval or range. For example, the length of a phone call can be any value greater than zero and can be decimal. A continuous random variable can be measured and expressed in decimal points or fractions. The empirical rule also called the 68-95-99.7% rule, states that for a normal distribution, approximately:
68% of the data fall within one standard deviation of the mean,
95% of the data fall within two standard deviations of the mean, and
99.7% of the data fall within three standard deviations of the mean.
Since the mean GPA of the students at the college is 3 and the standard deviation is 1, then 68% of students have a GPA between (3 - 1) and (3 + 1) which is 2 and 4. Thus, the correct option is b. 68%.
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A radio tower is located 350 feet from a building. From a window in the building, a person determines that
the angle of elevation to the top of the tower is 38° and that the angle of depression to the bottom of the
tower is 26°. How tall is the tower?
feet
The height of the tower is approximately 294.56 feet.
How tall is the tower?Let's denote the height of the tower as h. Then, we can use the tangent function to set up two equations:
tan(38°) = h / (350)
tan(26°) = (h - x) / (350), where x is the height of the bottom of the tower above the ground.
We can solve for h by eliminating x from these equations. To do this, we can solve the second equation for x:
x = h - 350 * tan(26°)
Then, we can substitute this expression for x into the first equation:
tan(38°) = h / 350
tan(26°) = (h - (h - 350 * tan(26°))) / 350
Simplifying the second equation, we get:
tan(26°) = tan(38°) - tan(26°)
tan(26°) + tan(26°) = tan(38°)
2 * tan(26°) = tan(38°)
tan(26°) = tan(19°)
Now we can solve for h:
h = 350 * tan(38°)
h ≈ 350 * 0.7813
h ≈ 273.45 feet
Therefore, the tower is approximately 273.45 feet tall.
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This graph shows the amount of (s) money in Jack's account after (w) weeks.
Which equation represents the amount of (s) money in Jack's account after (w) weeks?
Answer:
s=6w
Step-by-step explanation:
the graph goes up by 6 on the y axis for everyone one that the x moves
Answer:
d
Step-by-step explanation:
to carry a suitcase on an airplane, the length width height of the box must be less than or equal to 60 inches. (a) assuming the height is fixed, what is the maximum volume of the box in terms of the height, h ? (b) what height allows you to have the maximum volume?
The maximum volume of the box in terms of the height h is (30 - h/2)^2 x h, and the height that allows us to have the maximum volume is 40 inches
To answer your question, let's first understand that the volume of a box is given by the formula V = L x W x H, where L is the length, W is the width and H is the height. Since we are assuming the height is fixed, we can rewrite this formula as V = L x W x h.
Now, we know that the length plus width plus height of the box cannot exceed 60 inches. Therefore, we have the equation L + W + h = 60, which we can solve for L or W in terms of h. Let's solve for L: L = 60 - W - h.
Substituting this value of L into the formula for volume, we get V = (60 - W - h) x W x h. We can simplify this equation by expanding the brackets and collecting like terms to get V = -W^2h + 60Wh - h^2.
To find the maximum volume, we need to find the value of W that maximizes this equation. We can do this by differentiating the equation with respect to W and setting the derivative equal to zero. After some calculations, we get W = 30 - h/2.
Substituting this value of W back into the equation for volume, we get V = (30 - h/2)^2 x h. To find the height that gives us the maximum volume, we can differentiate this equation with respect to h and set the derivative equal to zero. After some calculations, we get h = 40 inches.
Therefore, the maximum volume of the box in terms of the height h is (30 - h/2)^2 x h, and the height that allows us to have the maximum volume is 40 inches.
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What is the minimum possible value of a European call if S = 52;
K = 50, r (annual rate of interest) = 24% and time remaining to
maturity is 3 months? (10 pts)
Note: Use simple rate of interes
The minimum possible value of the European call option is approximately 2.8752.
Given the parameters S = 52 (current stock price), K = 50 (strike price), r = 24% (annual interest rate), and a time to maturity of 3 months, we can calculate the minimum call option value.
The Black-Scholes formula for European call option pricing is as follows:
C = S * N(d1) - K * e^(-r*T) * N(d2)
Where:
C = Call option price
S = Current stock price
N = Cumulative standard normal distribution function
d1 = (ln(S/K) + (r + σ^2/2) * T) / (σ * sqrt(T))
d2 = d1 - σ * sqrt(T)
K = Strike price
r = Annual interest rate
T = Time to maturity (in years)
e = Euler's number (approximately 2.71828)
σ = Implied volatility of the underlying asset
Using the provided values, we can calculate the minimum call option value as follows:
d1 = (ln(52/50) + (0.24 + 0^2/2) * (3/12)) / (0.24 * sqrt(3/12))
= (ln(1.04) + 0.12 * 0.25) / (0.24 * 0.1443)
= (0.0392 + 0.03) / 0.0346
= 1.7507
d2 = 1.7507 - 0.24 * sqrt(3/12)
= 1.7507 - 0.24 * 0.1443
= 1.7507 - 0.0346
= 1.7161
N(d1) = N(1.7507) ≈ 0.9599 (using standard normal distribution table)
N(d2) = N(1.7161) ≈ 0.9569 (using standard normal distribution table)
C = 52 * 0.9599 - 50 * e^(-0.24 * (3/12)) * 0.9569
= 49.9152 - 50 * e^(-0.06) * 0.9569
≈ 49.9152 - 50 * 0.9408
≈ 49.9152 - 47.040
≈ 2.8752
Therefore, the minimum possible value of the European call option is approximately 2.8752.
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Consider the right triangle shown below where a=10.16 and b=11.57. Note that θ and ϕ are measured in radians.
What is the value of tan(ϕ)?
What is the value of sin(ϕ)?
What is the value of ϕ?
What is the value of θ?
In order to find the value of tan(ϕ), sin(ϕ), ϕ, and θ, we must first find the values of c and θ using the Pythagorean Theorem and SOH CAH TOA respectively.
Then, we can use these values to find the trigonometric functions of ϕ and θ.
Using the Pythagorean Theorem, we have:
c² = a² + b²c² = (10.16)² + (11.57)²c ≈ 15.13
Using SOH CAH TOA, we have:
tan(θ) = opposite/adjacent tan(θ)
= 11.57/10.16tan(θ) ≈ 1.14θ ≈ 0.86 radians
Since the triangle is a right triangle, we know that ϕ = π/2 - θϕ ≈ 0.70 radians
Using SOH CAH TOA, we have:
sin(ϕ) = opposite/hypotenuse
sin(ϕ) = 10.16/15.13sin(ϕ) ≈ 0.67
Using the identity tan(ϕ) = sin(ϕ)/cos(ϕ), we can find the value of tan(ϕ) by finding the value of cos(ϕ).cos(ϕ) = cos(π/2 - θ)cos(ϕ) = sin(θ)cos(ϕ) ≈ 0.40tan(ϕ) ≈ sin(ϕ)/cos(ϕ)tan(ϕ) ≈ (0.67)/(0.40)tan(ϕ) ≈ 1.68[
Therefore, the value of tan(ϕ) is approximately 1.68, the value of sin(ϕ) is approximately 0.67, the value of ϕ is approximately 0.70 radians, and the value of θ is approximately 0.86 radians.
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Find X. round to nearest tenth using law of cosines, please help!
Step-by-step explanation:
Using the modified picture attached to this answer;
Parameters
x = Angle X
8 = x
19 = y
14 = z
Therefore,
Using Cosine rule
x² = y² + z² - 2·y·z·cos X
Masking Cos X the subject of the formula,
Cos X = (y² + z² - x²) / (2·y·z)
Cos X = (19² + 14² - 8²) / (2·19·14)
Cos X = (361 + 196 - 64) / 532
Cos X = (557 -64) / 532
Cos X = 493 / 532
Cos X = 0.92669
But, since we are looking for angle X, we have to divide both sides by Cos, therefore having;
X = Cos-¹ [0.92669]
Since 1 / Cos = Cos-¹
Therefore,
X = 22.075
And since x, our unknown, is equal to angle X, then,
x = 22.1 (to the nearest tenth)
An international fast food chain is looking at opening a new franchise in Emerald, Queensland. They contact a marketing research firm to help them assess the level of interest in the restaurant within the town. From a list of all the residential addresses in Emerald, the firm selects a simple random sample of 100 and mails a brief questionnaire to each. The population of interest is
Select one:
a. all people in Emerald, Queensland.
b. all adults in Emerald, Queensland.
c. the 100 addresses to which the questionnaire was mailed.
d. the people in Emerald who eat fast food.
e. all residential addresses in Emerald, Queensland.
The population of interest is: A. all people in Emerald, Queensland.
The population of interest refers to the group of individuals that the research is trying to draw inferences about. In this case, the international fast food chain is looking to assess the level of interest in opening a franchise in Emerald, Queensland.
Therefore, the population of interest is all people who live in Emerald, Queensland, as they are the group that the research is trying to understand. The sample of 100 addresses that the research firm selected is just a subset of this population and the questionnaires are being sent to them to infer about the entire population.
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What is the value of w in the equation 10(2) -4(-w)=36
Answer:
w = 4
Step-by-step explanation:
10(2)-4(-w)=36
20+4w=36
4w=36-20
4w=16
w=16/4
w=4
Linda got a prepaid debit card with $20 on it. For her first purchase with the card, she bought some bulk ribbon at a craft store. The price of the ribbon was 14 cents per yard. If after that purchase there was $17. 06 left on the card, how many yards of ribbon did Linda buy?
Therefore, Linda bought 21 yards of ribbon. Hence, Linda bought 94 yards of ribbon.
The number of yards of ribbon Linda bought, we need to calculate the difference between the initial balance on the card and the remaining balance after the purchase.
The initial balance on the card was $20. To find the amount spent on ribbon, we subtract the remaining balance ($17.06) from the initial balance. $20 - $17.06 = $2.94
Now, we need to determine how many yards of ribbon Linda could purchase with $2.94, given that the price of the ribbon is 14 cents per yard.
To find the number of yards, we divide the total amount spent ($2.94) by the price per yard (14 cents): $2.94 ÷ $0.14 = 21
Therefore, Linda bought 21 yards of ribbon.
Hence, Linda bought 94 yards of ribbon.
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Let v=⟨1,4,3⟩ - v = ⟨ 1 , 4 , 3 ⟩ - Calculate v×i,v×j,v×k
The cross product of two vectors v and i, v and j, and v and k are as follows:
v × i = ⟨ 4 , -1 , 0 ⟩ v × j = ⟨ -3 , 0 , 1 ⟩ v × k = ⟨ 0 , -3 , -4 ⟩The cross product of two vectors v and i, v and j, and v and k can be computed using the following formula:
For two vectors a and b the cross product is given by a × b = a1b2 − a2b1 i + a2b3 − a3b2 j + a3b1 − a1b3 k
Therefore, for v = ⟨1,4,3⟩ and i, j, and k the corresponding cross product calculations are:
v × i = 1 × 4 − 4 × 1 i + 4 × 3 − 3 × 4 j + 3 × 1 − 1 × 3 k = 4 i − 12 j + 3 k = ⟨ 4 , −1 , 0 ⟩v × j = 1 × 3 − 4 × 3 i + 4 × 1 − 3 × 1 j + 3 × 4 − 1 × 4 k = −3 i + 4 j − 12 k = ⟨ −3 , 0 , 1 ⟩v × k = 1 × 1 − 4 × 4 i + 4 × 4 − 3 × 1 j + 3 × 3 − 1 × 4 k = 0 i − 12 j − 4 k = ⟨ 0 , −3 , −4 ⟩Therefore, the cross product of two vectors v and i, v and j, and v and k is given by:
v × i = ⟨ 4 , -1 , 0 ⟩ v × j = ⟨ -3 , 0 , 1 ⟩ v × k = ⟨ 0 , -3 , -4 ⟩For more such questions on Cross product.
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*MUST ANSWER ASAPPP PLS *
Answer:
$20
Step-by-step explanation:
if you look at the lowest point in the graph and match it up with the y intercept (the cost) then the answer is $20.
can someone solve 3y − 3 = 2y + 6
step by step
Answer:
\(y = 9\)
Step-by-step explanation:
1) Add 3 to both sides.
\(3y = 2y + 6 + 3\)
2) Simplify 2y + 6 + 3 to 2y + 9.
\(3y = 2y + 9\)
3) Subtract 2y from both sides.
\(3y - 2y = 9\)
4) Simplify 3y - 2y to y.
\(y = 9\)
Therefor, the answer is y = 9.
Answer:
3y-3=2y+6
3y-2y=3+6 (You will group like terms)
therefore,y=9
Which of the following appear in the diagram below?
Check all that apply.
z
A. YX
B. ZXYZ
C. ZYXZ
D. YW
Answer:
A , B, D
Step-by-step explanation:
YX is the segment joining points Y and X and is defined (A)
∠ XYZ is the angle between XY and YZ and is defined (B)
∠ YXZ is the angle between YX and XZ
However there is no segment joining XZ ← not defined
YW is the segment joining points Y and W and is defined (D)
The number of students enrolled at a college is 16,000and grows 6% each year. Complete parts (a) through (e).
The growth of the population after .t. years would be \(y_t = 16000^{(1.06t)}\).
What is the formula for exponential growth and exponential decaying function?The formula for exponential growth is \(y = y_0e^{(kt)}.\)
The formula for exponential decay is \(y = y_0e^{(-kt)}.\).
Given, The number of students enrolled at a college is 16,000 and grows 6% each year.
Now, 6% in terms of decimals is 0.06 hence k = 1 + 0.06 = 1.06.
The initial amount is 16000.
So, After t number of years, the population would be, \(y_t = 16000^{(1.06t)}\).
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Suppose there are two individuals in the society, and 4 possible allocations. The net benefit for each individual in each allocation is given below: (The two numbers in each of the following brackets indicate the net benefits for individual 1 and individual 2, respectively.)
Outcome A: (10,25)
Outcome B: (20,10)
Outcome C: (14,20)
Outcome D: (15,15)
Suppose it is impossible to make transfers between the two individuals.
____ are Pareto efficient outcomes.
a. A and C only
b. A,C, and D
c. A and B only
d. C and D only
e. A only
f. A,B,C, and D
only Outcome D is a Pareto efficient outcome. In this given scenario, "A and D" are Pareto efficient outcomes.What is Pareto efficiency? Pareto efficiency is a state of allocation of resources in which it is impossible to make any one individual better off without making at least one individual worse off.
What are the given allocations and benefits of individuals? The net benefit for each individual in each allocation is given below: (The two numbers in each of the following brackets indicate the net benefits for individual 1 and individual 2, respectively.) Outcome A: (10, 25) Outcome B: (20, 10) Outcome C: (14, 20)Outcome D: (15, 15) Which of the outcomes are Pareto efficient?
Now, let's see which of the given outcomes are Pareto efficient: Outcome A: If we take Outcome A, then individual 1 gets 10 and individual 2 gets 25 as their net benefits. But the allocation isn't Pareto efficient because if we take Outcome B, then individual 1 gets 20 which is greater than 10 as his net benefit, and the net benefit for individual 2 would become 10 which is still greater than 25. Therefore, Outcome A isn't Pareto efficient. Outcome B: If we take Outcome B, then individual 1 gets 20 and individual 2 gets 10 as their net benefits.
But the allocation isn't Pareto efficient because if we take Outcome C, then individual 1 gets 14 which is less than 20 as his net benefit, and the net benefit for individual 2 would become 20 which is greater than 10. Therefore, Outcome B isn't Pareto efficient.Outcome C: If we take Outcome C, then individual 1 gets 14 and individual 2 gets 20 as their net benefits. But the allocation isn't Pareto efficient because if we take Outcome A, then individual 1 gets 10 which is less than 14 as his net benefit, and the net benefit for individual 2 would become 25 which is greater than 20. Therefore, Outcome C isn't Pareto efficient.
Outcome D: If we take Outcome D, then individual 1 gets 15 and individual 2 gets 15 as their net benefits. The allocation is Pareto efficient because there is no other allocation where one individual will be better off without harming the other individual.Therefore, only Outcome D is a Pareto efficient outcome.
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this is a question on a review assignment that i’m stuck on , my summer school teacher said i could get help if i needed. any help would be greatly appreciated
Answer:
may be 3549 cube inch while rounded up.
identify three examples of molecules that are proteins?
HELP PLEASE
Step-by-step explanation:
I really don't know sorry
TRUE/FALSE. we use anova to test for differences between population means by examining the amount of variability between the samples relative to the amount of variability within the samples.
We use ANOVA to test for differences between population means by examining the amount of variability between the samples relative to the amount of variability within the samples. Hence, it is TRUE
What is ANOVA ?The statistical analysis tool known as analysis of variance (ANOVA) divides the observed aggregate variability present in a data set into two categories: systematic variables and random components. The random factors have no statistical impact on the presented data set, whereas the systematic factors do. The ANOVA test is used by analysts to ascertain how independent factors in a regression analysis affect the dependent variable.
ANOVA basically stands for analysis of the variance.
Analysis of variance, or ANOVA, is a statistical method that separates observed variance data into different components to use for additional tests.A one-way ANOVA is used for three or more groups of data, to gain information about the relationship between the dependent and independent variables.If no true variance exists between the groups, the ANOVA's F-ratio should equal close to 1Hence, according to above statements, given fact is true.
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1 in 10,000 white tailed deer on the east coast of the united states carries the lyme disease bacteria. you randomly select a white-tailed deer from a population on the east coast. what is the probability that the deer you select carries the lyme disease bacteria?
The probability of selecting a white-tailed deer that carries the Lyme disease bacteria is 1 in 10,000, or 0.0001. This means that out of every 10,000 white-tailed deer on the east coast, only one is expected to carry the Lyme disease bacteria.
If we assume that each deer in the population has an equal chance of carrying the bacteria, then the probability of selecting a deer that carries the bacteria can be calculated using the formula for probability:
Probability = Number of desired outcomes / Total number of possible outcomes
In this case, the number of desired outcomes is one (since we want to select a deer that carries the bacteria), and the total number of possible outcomes is the total number of white-tailed deer in the population. Since we don't know the exact number of deer in the population, we can assume that it is very large, so we can use an approximation:
Probability ≈ 1 / (Very large number)
Therefore, the probability of selecting a white-tailed deer from the east coast population that carries the Lyme disease bacteria is very close to 0.0001 or 1 in 10,000.
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Based on Exercise 9, prove that τ and σ are multiplicative. That is, prove that if m and n are relatively prime, then τ(mn)=τ(m)τ(n) and σ(mn)= σ(m)σ(n).
To prove that τ and σ are multiplicative, we need to show that if m and n are relatively prime, then τ(mn) = τ(m)τ(n) and σ(mn) = σ(m)σ(n).
To prove τ(mn) = τ(m)τ(n), we can start by considering the prime factorization of m and n. Let's say m = p₁^a₁ * p₂^a₂ * ... * pₖ^aₖ and n = q₁^b₁ * q₂^b₂ * ... * qₙ^bₙ, where p₁, p₂, ..., pₖ and q₁, q₂, ..., qₙ are distinct prime numbers. Since m and n are relatively prime, none of their prime factors overlap.
Now, the divisors of mn are the numbers of the form p₁^x₁ * p₂^x₂ * ... * pₖ^xₖ * q₁^y₁ * q₂^y₂ * ... * qₙ^yₙ, where 0 ≤ xᵢ ≤ aᵢ and 0 ≤ yⱼ ≤ bⱼ. Thus, the number of divisors of mn, τ(mn), can be calculated by multiplying the number of divisors of m, τ(m), with the number of divisors of n, τ(n). Hence, τ(mn) = τ(m)τ(n).
To prove σ(mn) = σ(m)σ(n), we can again use the prime factorization of m and n. Similar to the previous proof, the sum of divisors of mn, σ(mn), can be calculated by multiplying the sum of divisors of m, σ(m), with the sum of divisors of n, σ(n). Hence, σ(mn) = σ(m)σ(n).
Therefore, we have proved that τ and σ are multiplicative when m and n are relatively prime.
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We have shown that both τ and σ are multiplicative functions, satisfying the properties τ(mn) = τ(m)τ(n) and σ(mn) = σ(m)σ(n) for relatively prime numbers m and n.
To prove that τ (the number of positive divisors) and σ (the sum of positive divisors) are multiplicative functions, we need to show that for any two relatively prime numbers, m and n, the following properties hold:
1. τ(mn) = τ(m)τ(n)
2. σ(mn) = σ(m)σ(n)
Let's start with property 1:
1. τ(mn) = τ(m)τ(n)
If m and n are relatively prime, it means that they do not share any prime factors. Therefore, the divisors of mn are formed by taking a divisor of m and a divisor of n. Each divisor of mn can be uniquely expressed as the product of a divisor of m and a divisor of n.
Since the number of divisors of mn is equal to the product of the number of divisors of m and the number of divisors of n, we can conclude that τ(mn) = τ(m)τ(n).
Now let's move on to property 2:
2. σ(mn) = σ(m)σ(n)
Similar to property 1, we can express the sum of divisors of mn as the sum of products, where each product is formed by taking a divisor of m and a divisor of n. Again, since m and n are relatively prime, their divisors are distinct.
Using the distributive property, we can expand the sum of products as the sum of two separate terms: one involving the divisors of m and another involving the divisors of n. The sum of divisors of mn is therefore equal to the product of the sum of divisors of m and the sum of divisors of n.
Hence, we can conclude that σ(mn) = σ(m)σ(n).
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Andre went to a sporting goods store that was having a different sale. He bought a baseball glove and 2 packages of socks. The baseball glove normally costs $34. The baseball glove is not discounted. One package of socks normally costs $6. On sale, one package of socks cost $4. The sales tax rate is 7.75%. What percentage of the total regular price (before tax) was his savings?
Please help this is due today and I have even tried cheating
Answer:
8.7%
Step-by-step explanation:
Divition then Multiply
Answer: 8.7%
Step-by-step explanation:
You have to divide then multiply
help me help me ………….
Answer:
not similar
Step-by-step explanation:
not similar--it doesn't work out for the angles to be similar
if we find the angle x of the right-hand triangle, we can tell it would be 41 degrees
meaning that these triangles are not similar