The values of A and B in the general solution (y'') + (9y') + (14y) = 0 are A = -7 and B = -2, respectively.
To determine the values of A and B in the general solution of the second-order linear differential equation (y'') + (9y') + (14y) = 0, where A > B, we need to compare the characteristics of the equation with the given general solution.
The given general solution is in the form y = C1exp(AX) + C2exp(BX), where C1 and C2 are arbitrary constants.
To find A and B, we compare the general solution with the differential equation (y'') + (9y') + (14y) = 0.
The characteristic equation for the given differential equation is obtained by substituting y = exp(kX) into the differential equation, where k is a constant.
By doing this, we get the equation [tex]k^2[/tex] + 9k + 14 = 0.
Solving this quadratic equation, we find the roots k1 = -2 and k2 = -7.
Since the general solution contains terms of the form exp(AX) and exp(BX), we can set A = -7 and B = -2, as A > B.
This choice of A and B ensures that the general solution satisfies the given differential equation.
Therefore, the values of A and B in the general solution (y'') + (9y') + (14y) = 0 are A = -7 and B = -2, respectively.
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Which expression is equivalent to the given expression?
Step-by-step explanation:
D. In 2 _ In
maaf kalo salah
6,6 and 7 units down and 5 units left where is t'
Answer:
it's 1,-1
Step-by-step explanation:
hoped I helped. I'm good at these.
On January 1, 2020, SugarBear Company acquired equipment costing $150,000, which will be depreciated on the assumption that the equipment will be useful for five years and have a residual value of $12,000. The estimated output from this equipment is as follows: 2020-15.000 unit; 2021-24,000 units; 2022-30,000 units: 2023-28,000 units: 2024-18,000 units. The company is now considering possible methods of depreciation for this asset.
Required
Calculate what the depreciation expense would be for each year of the asser's life, if the company chooser
The straight-line method 1. The units-of-production method
li. The double-diminishing-balance atlad
D. Bnefly discuss the criteria that a company sad ce seer when selecting a depreciation method.
When the total number of units produced over the five-year period is 125,000 units, the depreciation will be $1.20 pee unit.
How to calculate the valueThe total number of units produced over the five-year period is 125,000 units. Therefore, the depreciation expense for each year would be calculated as follows:
Depreciation expense = (Cost of asset - Residual value) / Total number of units produced
Depreciation expense = ($150,000 - $12,000) / 125,000 units
Depreciation expense = $1.20 per unit
There are several factors that a company should consider when selecting a depreciation method. These factors include:
The type of asset being depreciated.The useful life of the asset.The expected pattern of depreciation.The tax implications of the different methods.The type of asset being depreciated is an important factor to consider because different assets have different useful lives and expected patterns of depreciation. For example, a machine that is expected to be used for five years would be depreciated using a different method than a building that is expected to be used for 30 years.
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ABM Services paid a $4.15 annual dividend on a day it closed at a price of $54 per share. What
was the yield?
Answer:
Yield per share = 7.68% (Approx.)
Step-by-step explanation:
Given:
Dividend paid = $4.15
Price per dividend = $54
Find:
Yield per share
Computation:
Yield per share = [Dividend paid / Price per dividend]100
Yield per share = [4.15 / 54]100
Yield per share = [0.0768]100
Yield per share = 7.68% (Approx.)
Consider a branching process whose offspring generating function is o(s) = (1/6) + (5/6)s2. Obtain the probability of ultimate extinction. Enter your answer as an integer of the form m or a fraction of the form m/n. Do not include spaces. Consider a branching process whose offspring generating function is o(s) = (5/6) + (1/6)s?. Obtain the mean time to extinction. Write your answer to two decimal places. Do not include spaces. Use the Excel spreadsheet "Mean Time to Extinction" in the Resources section of the unit Moodle page to help you with the calculation.
Probability of ultimate extinction: To get the probability of ultimate extinction in a branching process, we need to calculate the value of o(q) = q where q is the probability of ultimate extinction.
Now, o(s) = (1/6) + (5/6)s²
Therefore, for the probability of ultimate extinction,
o(q) = q = (1/6) + (5/6)q²=> 6q² - 5q + 1 = 0
On solving the quadratic equation,
we get q = 1 or q = 1/6.
Thus, the probability of ultimate extinction is 1/6. Mean time to extinction:
To calculate the mean time to extinction, we can use the formula, E(T) = (1/o'(1))
where o'(1) is the first derivative of the generating function o(s) evaluated at s = 1.
Now, o(s) = (5/6) + (1/6)s=> o'(s) = (1/6)
On substituting s = 1, o'(1) = (1/6).
Thus, E(T) = (1/o'(1))= (1/ (1/6))= 6
The mean time to extinction is 6.
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CAN SOMEONE IN THIS APP HELP PLEASE
Answer:
15 feet
Step-by-step explanation:
The distance from the foot of the ladder to the person is 6 feet. The person is also 6 feet. Therefore that mini triangle's length and width are both 6 feet.
The distance from the foot of the ladder to the wall is 15 feet. This is now a simple ratio. The length of the mini triangle is 6 to length of the larger triangle, 15. The height ratio is the mini triangle is 6 to the bigger triangle, x.
The height of the bigger triangle is the height of the wall. (Since the two are similar, then we can automatically deduce the height is 15.) But if you wanted to work out the ratio above ^^ you would multiply the 6 diagnol to the 15 and then divide by the last 6 to get 15.
Population 1,2,4,5,8 · Draw all possible sample of size 2 W.O.R · Sampling distribution of Proportion of even No. · Verify the results
Question:
A population consists 1, 2, 4, 5, 8. Draw all possible samples of size 2 without replacement from this population.
Verify that the sample mean is an unbiased estimate of the population mean.
Answer:
[tex]Samples: \{(1,2),(1,4),(1,5),(1,8),(2,4),(2,5),(2,8),(4,5),(4,8),(5,8)\}[/tex]
[tex]\hat p = \frac{3}{5}[/tex] --- proportion of evens
The sample mean is an unbiased estimate of the population mean.
Step-by-step explanation:
Given
[tex]Numbers: 1, 2, 4, 5, 8[/tex]
Solving (a): All possible samples of 2 (W.O.R)
W.O.R means without replacement
So, we have:
[tex]Samples: \{(1,2),(1,4),(1,5),(1,8),(2,4),(2,5),(2,8),(4,5),(4,8),(5,8)\}[/tex]
Solving (b): The sampling distribution of the proportion of even numbers
This is calculated as:
[tex]\hat p = \frac{n(Even)}{Total}[/tex]
The even samples are:
[tex]Even = \{2,4,8\}[/tex]
[tex]n(Even) = 3[/tex]
So, we have:
[tex]\hat p = \frac{3}{5}[/tex]
Solving (c): To verify
[tex]Samples: \{(1,2),(1,4),(1,5),(1,8),(2,4),(2,5),(2,8),(4,5),(4,8),(5,8)\}[/tex]
Calculate the mean of each samples
[tex]Sample\ means = \{1.5,2.5,3,4.5,3,3.5,5,4.5,6,6.5\}[/tex]
Calculate the mean of the sample means
[tex]\bar x = \frac{1.5 + 2.5 +3 + 4.5 + 4 + 3.5 + 5 + 4.5 + 6 + 6.5}{10}[/tex]
[tex]\bar x = \frac{40}{10}[/tex]
[tex]\bar x = 4[/tex]
Calculate the population mean:
[tex]Numbers: 1, 2, 4, 5, 8[/tex]
[tex]\mu = \frac{1 +2+4+5+8}{5}[/tex]
[tex]\mu = \frac{20}{5}[/tex]
[tex]\mu = 4[/tex]
[tex]\bar x = \mu = 4[/tex]
This implies that [tex]\bar x[/tex] is an unbiased estimate of the [tex]\mu[/tex]
Pip was thinking of a number. Pip halves the number and gets an answer of 87.2. Form an
equation with x from the information.
X/2= 87.2
to find X:
87.2 X 2= 174.4
therefore X is 174.4
What is -a⁻² if a = -5?
Answer:
25
Step-by-step explanation:
First, plug -5 in for a, -(-5)^2. We treat the negative on the outside of the paranthese as a -1 so we do -1 times -5 and we get 5. Then we square 5 and get 25.
how do you solve this ?
Answer:
x = 37 mm
Step-by-step explanation:
using the Pythagorean theorem:
m² = 13² - 5² = 169 - 25 = 144
m = √144 = 12 mm
x² = 12² + 35² = 144 + 1225 = 1369
x = √1369 = 37 mm
Answer:
x=37.3
Step-by-step explanation:
Since we're looking for "x" we need to use "the Pythagorean theorem".
13mm will be our "A" and 35mm will be our "B" will "x" being the hypotenuse.
Since x is the hypotenuse, it needs to be a number greater than 13 and 35.
c=√(a² + b²)
Making it c=√(13² + 35²)
Making C=37.336 or 37.3
Therefore making, x=37.3
help ASAP Ill give you brainliest
Answer:
none of these
Step-by-step explanation:
There are 3 boys walking
There are a total of 20 people
3/20 = 0.15
That is 15 percent, therefore none of these answers.
Step-by-step explanation:
any has at least one mode
Nahla Burtoni is buying her first home for $125,000. She has been granted
a mortgage loan at an annual interest rate of 8.5% for 20 years with a
$25,000 down payment. Closing costs are 2% of the amount of the
mortgage loan and will be financed as part of the mortgage. What is the
actual amount financed with the mortgage?
O $100,000
O $102,000
O $120,000
O $125,000
Answer: the answer is B!!!!!!!!!!!!!!
Step-by-step explanation:
Problem 3. Reformulate the following LP by the big-M method (only the reformulation is required, no need to solve the LP).
max 2x1 + x2 + X3 x
s.t.
X2+x3≥5
X1 X2 ≥1
x1 + x2+3x3 ≤ 25
X1, X2, X3 0
The reformulated problem includes the original variables x₁, x₂, x₃, and the additional slack variables s₁, s₂, and s₃. The objective function and constraints remain the same, but the problem has been transformed into an equality form suitable for applying the big-M method or other linear programming techniques.
To reformulate the given linear programming problem using the big-M method, we introduce additional binary variables and big-M constants. The reformulated problem is as follows:
maximize 2x₁ + x₂ + x₃
subject to:
x₂ + x₃ + s₁ = 5
x₁ - x₂ + s₂ = 1
x₁ + x₂ + 3x₃ + s₃ = 25
x₁, x₂, x₃, s₁, s₂, s₃ ≥ 0
where s₁, s₂, and s₃ are slack variables, and we choose a large positive constant M to represent infinity.
Introducing slack variable s₁ for the inequality constraint x₂ + x₃ ≥ 5:
We add s₁ to the left-hand side of the inequality to transform it into an equation: x₂ + x₃ + s₁ = 5.
Introducing slack variable s₂ for the inequality constraint x₁ - x₂ ≥ 1:
We subtract s₂ from both sides of the inequality to transform it into an equation: x₁ - x₂ + s₂ = 1.
Introducing slack variable s₃ for the inequality constraint x₁ + x₂ + 3x₃ ≤ 25: We subtract s₃ from the left-hand side of the inequality to transform it into an equation: x₁ + x₂ + 3x₃ + s₃ = 25.
Since all variables in the original problem are non-negative (x₁, x₂, x₃ ≥ 0), we explicitly state this in the reformulation.
Therefore, the reformulated problem includes the original variables x₁, x₂, x₃, and the additional slack variables s₁, s₂, and s₃. The objective function and constraints remain the same, but the problem has been transformed into an equality form suitable for applying the big-M method or other linear programming techniques.
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Incomplete question:
Reformulate the following LP by the big-M method (only the reformulation is required, no need to solve the LP).
maxₓ 2x₁ + x₂ + x₃
s.t.
x₂+x₃ ≥ 5
x₁ - x₂ ≥ 1
x₁ + x₂+ 3x₃ ≤ 25
x₁, x₂, x₃ ≥0
Let Y_1.... Y_n be a random sample from a distribution with the density function
f_θ(y) = 3θ^3/y^4 y≥θ≥0
Is there a UMP test at level a for testing H_o: θ ≤ θ_o vs. H_1 : θ> θ_o? If so, what is the test?
Yes, there is a uniformly most powerful (UMP) test at level a for testing for the given density function.
The test is based on the likelihood ratio, where the critical region is (θ_o, ∞) and the test statistic is (nθ_o^3)/Y(n), where Y(n) is the largest observation in the sample.
To obtain the UMP test at level a for testing H_0: θ ≤ θ_o vs. H_1: θ > θ_o, we need to find the likelihood ratio test with the largest power for all possible alternatives. The likelihood ratio test is constructed as the ratio of the likelihood function under H_0 to the likelihood function under H_1. By algebraic manipulation, we obtain the likelihood ratio test statistic as (nθ_o^3)/Y(n), where Y(n) is the largest observation in the sample.
Under H_0, this test statistic has a chi-squared distribution with one degree of freedom. Therefore, the critical region for rejecting H_0 at level a is the right tail of the chi-squared distribution with one degree of freedom, which is (θ_o, ∞).
This test is UMP because it has the highest power for all possible alternatives. This is because the distribution of Y(n) is stochastically increasing in θ, which means that for a given sample size n, the probability of obtaining an observation larger than a threshold value increases as θ increases.
Therefore, the likelihood ratio test statistic decreases as θ increases, which means that the rejection region (θ_o, ∞) has the highest power for all possible alternatives. Hence, the test based on the likelihood ratio is the UMP test at level a for testing H_0: θ ≤ θ_o vs. H_1: θ > θ_o for the given density function
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What is the diameter of a satellite dish with a circumference of 957.7?
Answer:
The diameter would be 305 m
Step-by-step explanation:
Answer:
305 assuming your using 3.14 for pi
Step-by-step explanation:
A submarine was situated 475 feet below sea level. if it ascends 150 feet, what is its new position relative to the sea level?
Answer:
325 feet below sea level i believe
Step-by-step explanation:
What number is equal to (1/6)^4?
Answer:
1/5
Step-by-step explanation:
i searched it up yikessssssss
The value of the given term is 1296.
What is a fraction?A fraction consisting of a quotient and remainder is a mixed fraction. we can convert the mixed fraction to improper fraction by first dividing the numerator by denominator and then taking the quotient as whole number and remainder as the numerator of proper fraction keeping the denominator same.
We are given the number as [tex]\dfrac{1}{6} ^{-4}[/tex]
Here we can see that the power is negative so we can just reciprocal the term.
Then we get;
6^4
this means 6 x6x6x6 = 1296
The correct value is 1296.
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Can you help me in this please No links or spams or bots or report
Answer:
Monday - 7 hr 30 mins
Wednesday - 9 hr 30 mins
Friday - 7 hr
Saturay - 5 hr 30 mins
---------------------------------------------------------------
If you earn $12.40 per hour, first you must find how many hours you worked total - in this case, 29 hr and 30 mins.
So you would be making $359.60 per week.
A student in your class mentally calculates 8+9 by noting that 8 is "1 less than 9", and, since 2 x 9 = 18, then 8 + 9 must be "1 less than 18," or 17. The equations representing this method are as follows: 1.8+9 (9-1) +9 ii. (9-1)+9=9+(9-1) iii. 9+ (9-1) (9+9)-1 iv. (9+9)-1-18-1 V. 18-1 17 Which properties of addition is the student implicitly using?
The student is implicitly using the commutative property and the associative property of addition.
i. (9-1) + 9: The student uses the commutative property, which states that the order of adding numbers does not affect the sum. They rearrange the terms to (9-1) + 9, recognizing that adding 9 after subtracting 1 is the same as adding 9 before subtracting 1.
ii. (9-1) + 9 = 9 + (9-1): Here, the student demonstrates the associative property. The associative property states that the grouping of numbers being added does not affect the sum. They regroup the terms to show that adding (9-1) first and then adding 9 is equivalent to adding 9 first and then subtracting 1.
iii. 9 + (9-1): The student does not explicitly demonstrate a property here. They simply perform the calculation of adding 9 and (9-1), recognizing that 9 minus 1 is 8.
iv. (9+9)-1-18-1: In this step, the student performs the subtraction calculations but does not demonstrate any particular property.
v. 18-1: Finally, the student calculates the subtraction and arrives at the answer 17.
So, the student implicitly uses the commutative property and the associative property of addition in their mental calculation.
Brayden invests money in an account paying a simple interest of 3.3% per year. If he invests $30 and no money will be added or removed from the investment, how much will he have in one year, in dollars and cents?
Answer:
$30.99
Step-by-step explanation:
The formula for simple interest is I = PRT where I = interest earned, P = principal amount borrowed/deposited, R = rate as a decimal, and T = time in years.
I = (30)(0.033)(1)
I = 0.99
Then add that to the amount deposited ($30) and you're done.
30 + 0.99 = $30.99
Please let me know if you have questions.
The answer is $29.01
If S=4 [tex]\pi[/tex] [tex]r^{2}[/tex] the value of S When R= 10[tex]\frac{1}{2}[/tex]
Each sample of water has a 10% chance of containing a particular organic pollutant. Assume that the samples are independent with regard to the presence of the pollutant. Find the probability that in the next 18 samples, exactly 2 contains the pollutant.
(a) P(x≥≥4)
(b) P(x≤≤4).
(c) P(3≤≤x≤≤7)
The probability that in the next 18 samples, exactly 2 contain the pollutant is
P(x = 2) =[tex]C(18, 2) (0.1)^2 (0.9)^16[/tex]
= 0.252.
The given is Each sample of water has a 10% chance of containing a particular organic pollutant.
Assume that the samples are independent with regard to the presence of the pollutant.
We need to find the probability that in the next 18 samples, exactly 2 contain the pollutant.
We can use the Binomial distribution formula to solve this problem.
The binomial distribution formula is given by:
P(x) = [tex]C(n, x) px qn-x[/tex]
Where n is the number of trials, x is the number of successes, p is the probability of success, and q is the probability of failure.
Since there is a 10% chance of containing a particular organic pollutant, the probability of success is:
p = 0.1
The probability of failure is:
q = 1 - p
= 1 - 0.1
= 0.9
Number of trials (samples) is n = 18
(a) To find P(x≥≥4)
We need to find the probability that 2 or more samples contain the pollutant.
We can do this by subtracting the probability that less than 2 samples contain the pollutant from 1.
P(x ≥ 2) = 1 - P(x < 2)P(x < 2)
= P(x = 0) + P(x = 1)P(x = 0)
= C(18, 0) (0.1)0 (0.9)18
= [tex]0.9^18[/tex]
P(x = 1) = [tex]C(18, 1) (0.1)^1 (0.9)^17[/tex]
= 0.33
P(x < 2) = [tex]0.9^18[/tex]+ 0.33
= 0.335
P(x ≥ 2) = 1 - 0.335
= 0.665
(b) To find P(x≤≤4)
We need to find the probability that 4 or less samples contain the pollutant.
P(x ≤ 4) = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3) + P(x = 4)P(x = 0)
= C(18, 0) (0.1)0 (0.9)18
= [tex]0.9^18[/tex]
P(x = 1) = [tex]C(18, 1) (0.1)^1 (0.9)^17[/tex]
= 0.33
P(x = 2) = [tex]C(18, 2) (0.1)^2 (0.9)^16[/tex]
= 0.053
P(x = 3) = [tex]C(18, 3) (0.1)^3 (0.9)^15[/tex]
= 0.0047
P(x = 4) =[tex]C(18, 4) (0.1)^4 (0.9)^14[/tex]
= 0.0003
P(x ≤ 4) = 0.9^18 + 0.33 + 0.053 + 0.0047 + 0.0003
= 0.288
(d) To find P(3≤≤x≤≤7)
We need to find the probability that between 3 and 7 (inclusive) samples contain the pollutant.
P(3 ≤ x ≤ 7) = P(x = 3) + P(x = 4) + P(x = 5) + P(x = 6) + P(x = 7)P(x = 3)
= [tex]C(18, 3) (0.1)^3 (0.9)^15[/tex]
= 0.0047
P(x = 4) = C(18, 4) (0.1)^4 (0.9)^14
= 0.0003
P(x = 5) = [tex]C(18, 5) (0.1)^5 (0.9)^13[/tex]
= 0.00001
P(x = 6) = [tex]C(18, 6) (0.1)^6 (0.9)^12[/tex]
= 2.15e-07
P(x = 7) = [tex]C(18, 7) (0.1)^7 (0.9)^11[/tex]
= 4.7e-10
P(3 ≤ x ≤ 7) = 0.0047 + 0.0003 + 0.00001 + 2.15e-07 + 4.7e-10
= 0.00471
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Suppose that the NY state total population remains relatively fixed 20Mil, with 8.4Mil of the people living in the city and remaining are in the suburbs. Each year 3.5% of the people living in the city move to the suburbs, and 1.7% of the suburban population moves to the city. What is the long-term distribution of population, after 100 years (what is the population in the city and in the suburbs)? Plot population of city and suburbs over period of 100 years. Submit, 1) answer(s), 2) Matlab code, 3) graph(s)
After 100 years, the long-term distribution of population in the city and suburbs of New York state can be calculated based on the given migration rates. The population in the city and suburbs will stabilize at approximately 3.96 million and 16.04 million, respectively. The population distribution can be visualized using a graph that shows the population of the city and suburbs over the 100-year period.
To calculate the long-term population distribution, we can use the concept of equilibrium. Let C represent the population in the city and S represent the population in the suburbs. The equilibrium equations can be written as follows:
C = C - 0.035C + 0.017S
S = S + 0.035C - 0.017S
Simplifying these equations, we have:
C = 0.965C + 0.017S
S = 0.035C + 0.983S
Solving these equations simultaneously, we find that C stabilizes at approximately 3.96 million and S stabilizes at approximately 16.04 million.
To plot the population of the city and suburbs over the 100-year period, you can use the following MATLAB code:
Copy code
years = 0:100;
C = zeros(1, 101);
S = zeros(1, 101);
C(1) = 8.4;
S(1) = 20 - C(1);
for i = 2:101
C(i) = 0.965*C(i-1) + 0.017*S(i-1);
S(i) = 0.035*C(i-1) + 0.983*S(i-1);
end
plot(years, C, 'b', 'LineWidth', 2);
hold on;
plot(years, S, 'r', 'LineWidth', 2);
xlabel('Years');
ylabel('Population');
legend('City', 'Suburbs');
title('Population of City and Suburbs Over 100 Years');
This MATLAB code calculates and plots the population of the city (in blue) and suburbs (in red) over the 100-year period.
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which dashed line is an asymptote for the graph?
Answer:
the graph has two vertical asymptotes, line q intersects the line at -8 and is the more important one.
Step-by-step explanation:
This is visible based off of the picture.
Let x = 9a - 7, where a is an integer. What is x mod 3?
For x = 9a - 7, where a is an integer, the value of x mod 3 is determined using the remainder when x is divided by 3, and it is equal to 2.
To find the value of x mod 3, we need to determine the remainder when x is divided by 3.
The expression x = 9a - 7, where a is an integer, allows us to calculate x mod 3.
To find x mod 3, we substitute the given expression x = 9a - 7 into the equation:
x mod 3 = (9a - 7) mod 3.
To simplify the expression, we can use the properties of modular arithmetic.
First, we can rewrite 9a as (3 × 3a) and distribute the modulus operator:
(9a - 7) mod 3 = ((3 × 3a) - 7) mod 3.
Next, we can separate the modulus operation:
((3 × 3a) - 7) mod 3 = ((3 × 3a) mod 3 - 7 mod 3) mod 3.
Since 3 is congruent to 0 mod 3, the first term becomes 0:
((3 × 3a) mod 3 - 7 mod 3) mod 3 = (0 - 7 mod 3) mod 3.
The second term, 7 mod 3, can be simplified as the remainder when 7 is divided by 3, which is 1:
(0 - 7 mod 3) mod 3 = (0 - 1) mod 3 = -1 mod 3.
Finally, we can find the remainder when -1 is divided by 3, which is 2:
-1 mod 3 = 2.
Therefore, x mod 3 is equal to 2.
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1. What does PEMDAS stand for?
P:
E:
M:
D:
A:
S:
Answer:
P- arenthesis
E- xpontent
M- ultiplication
D- ivision
A- ddition
S- ubtraction
Answer:
Step-by-step explanation:
p=parentheses
e=exponents
m=multiplication
d=division
a=addition
s=subtraction
Question 3
1 pts
meters, will the period of a pendulum be 3 seconds? Use the formulas T = a[.where the proportionality constant,
The acceleration of gravity on Mars is 3.69 For what length
2 TT
a. depends on the acceleration of gravity: a =
vg
0.92 meters
0.84 meters
0.66 meters
Greta bought a collar for her dog. The
original price was $12 but she had a
coupon for 10% off. How much money
did she save?
Answer:
She saved 1.20
Step-by-step explanation:
Purchase Price:
$12
Discount:
(12 x 10)/100 = $1.20
Final Price:
12 - 1.20 = $10.80
Tell whether the angles are complementary or supplementary. Then find the value of x.
Answer: Complementary x=15
Step-by-step explanation:
Complementary angles add up to 90°, supplementary angles add up to 180°.
We know they add up to 90 so...
3x+45=90
3x=45
x=15
Information from a poll of registered voters in a city to assess voter support for a new school tax was the basis for the following statements.
The poll showed 51% of the respondents in this city's school district are in favor of the tax. The approval rating rises to 58% for those with children in public schools. It falls to 45% for those with no children in public schools. The older the respondent, the less favorable the view of the proposed tax: 38% of those over age 56 said they would vote for the tax compared with 73% of 18- to 25-year-olds.
Suppose that a registered voter from this city is selected at random, and define the following events.
F = event that the selected individual favors the school tax
C = event that the selected individual has children in the public schools
O = event that the selected individual is over 56 years old
Y = event that the selected individual is 18–25 years old
Use the given information to estimate the values of the following probabilities. (1) P(F) (ii) P(FIC) (iii) PCFCS) (iv) P(FIO)
The probability that the selected individual has children in public schools AND favors the school tax is 0.32
The probability that the selected individual favors the school tax AND has children in public schools is 0.32.
The probability that the selected individual favors the school tax AND does NOT have children in public schools is 0.2.
The probability that the selected individual favors the school tax AND is over 56 years old is 0.15.
The probability that the selected individual favors the school tax AND is 18-25 years old is 0.45.
Based on the given information, the probability of event F (the selected individual favors the school tax) is 0.54, as 54% of the respondents are in favor of the tax. The probability of event C (the selected individual has children in public schools) is 0.59, as the approval rating rises to 59% for those with children in public schools. The probability of event O (the selected individual is over 56 years old) is 0.37, as only 37% of those over age 56 said they would vote for the tax. The probability of event Y (the selected individual is 18-25 years old) is 0.71, as 71% of 18- to 25-year-olds said they would vote for the tax.
Using these probabilities, we can estimate the values of the following probabilities:
(1) P(CF) is the probability that the selected individual has children in public schools AND favors the school tax. Based on the given information, we can multiply the probabilities of events C and F: P(CF) = 0.59 * 0.54 = 0.318, or approximately 0.32.
(ii) P(FIC) is the probability that the selected individual favors the school tax AND has children in public schools. This is the same as P(CF), so P(FIC) = 0.32.
(iii) P(FIN) is the probability that the selected individual favors the school tax AND does NOT have children in public schools. To calculate this, we can use the fact that the approval rating falls to 44% for those with no children in public schools. So, P(FIN) = 0.44 * (1 - 0.59) = 0.18, or approximately 0.2.
(iv) P(FTO) is the probability that the selected individual favors the school tax AND is over 56 years old. To calculate this, we can use the fact that the approval rating for those over 56 years old is only 37%. So, P(FTO) = 0.37 * (1 - 0.59) = 0.1523, or approximately 0.15.
(v) P(FY) is the probability that the selected individual favors the school tax AND is 18-25 years old. To calculate this, we can use the fact that the approval rating for those 18-25 years old is 71%. So, P(FY) = 0.71 * (1 - 0.37) = 0.4477, or approximately 0.45.
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