Answer:
a) 8259888
b) 34220
c) 45057474
Step-by-step explanation:
Given,
The total number of transistor = 65,
In which, the defective transistor = 6,
So, the number of non defective transistor = 65 - 6 = 59,
Since, out of these transistor 5 are selected,
a) Thus, the number of ways = the total possible combination of 5 transistors = [tex]{65}C_ 5[/tex]
[tex]=\frac{65!}{(65-5)!5!}[/tex]
[tex]=8259888[/tex]
b) The number of samples that contains exactly 3 defective transistors = the possible combination of exactly 3 defective transistors = [tex]{6}C_3\times {59}C_2[/tex]
[tex]=\frac{6!}{(6-3)!3!}\times \frac{59!}{(59-2)!\times 2!}[/tex]
[tex]=20\times 1711[/tex]
[tex]=34220[/tex]
c) The number of sample without any defective transistor = The possible combination of 0 defective transistor = [tex]^6C_0\times ^{59}C_5[/tex]
[tex]=1\times 45057474[/tex]
[tex]=45057474[/tex]
(a) 8259888 ways, (b) 34220 samples and (c) 5006386 samples.
Let's solve each part:
(a) There are 65 total transistors, and we want to select 5 of them. So, the number of ways to select a sample is the number of combinations of 65 things taken 5 at a time. This can be calculated using the combination formula:
Number of combinations = [tex]C(n, k) = \frac{n!}{ k! \times (n-k)!)}[/tex]
where:
n is the total number of items (65 transistors)
k is the number of items to select (5 transistors)
Plugging in the values:
[tex]C(65, 5) = \frac{65!}{ 5! \times (65-5)!)} = 8259888[/tex]
(b) We want samples that contain exactly 3 defective transistors. We can achieve this by selecting 3 defective transistors from the 6 available and 2 non-defective transistors from the remaining 59 (65 total - 6 defective).
So, the number of ways to select this specific scenario is:
Number of ways to choose 3 defective transistors out of 6: C(6, 3)
Number of ways to choose 2 non-defective transistors out of 59: C(59, 2)
Using the combination formula again:
[tex]C(6, 3) \times C(59, 2) = (\frac{6!}{ (3! \times 3!)}) \times (\frac{59!} { (2! \times 57!)}) = 34220[/tex]
(c) Samples with no defective transistors simply means selecting all 5 transistors from the 59 non-defective ones.
Therefore:
[tex]C(59, 5) = \frac{59!}{ (5! \times 54!)} = 5006386[/tex]
3. (6 Points). Solve the initial value problem y'-y.cosx=0, y(pi/2)=2e
Answer:
[tex]y=2e^{sin(x)}[/tex]
Step-by-step explanation:
Given equation can be re written as
[tex]\frac{\mathrm{d} y}{\mathrm{d} x}-ycos(x)=0\\\frac{\mathrm{d} y}{\mathrm{d} x}=ycos(x)\\\\=> \frac{dy}{y}=cox(x)dx\\\\Integrating \\ \int \frac{dy}{y}=\int cos(x)dx \\\\ln(y)=sin(x)+c[/tex]............(i)
Now it is given that y(π/2) = 2e
Applying value in (i) we get
ln(2e) = sin(π/2) + c
=> ln(2) + ln(e) = 1+c
=> ln(2) + 1 = 1 + c
=> c = ln(2)
Thus equation (i) becomes
ln(y) = sin(x) + ln(2)
ln(y) - ln(2) = sin(x)
ln(y/2) = sin(x)
[tex]y= 2e^{sinx}[/tex]
The mean score for all NBA games during a particular season was less than 106 points per game. If a hypothesis test is performed, how should you interpret a decision that fails to reject the null hypothesis? There is not sufficient evidence to reject the claim μ < 106. There is sufficient evidence to reject the claim μ < 106. There is not sufficient evidence to support the claim μ < 106. There is sufficient evidence to support the claim μ < 106.
Answer:
As given in the problem statement
mean score was less than 106
H0:mean score<106
so There is sufficient evidence to reject the claim μ < 106. is correct option.
A pile of 42 coins worth $4.90, consisting of nickels and quarters. How many nickels are there?
Answer:14
Step-by-step explanation:
A nickel is 5 cents (20% of dollar)
and a quarter is 25 cents (25% of dollar)
We have given a pile of 42 coins worth of $4.90
Let x be the no nickels and
y be the no of quarter
therefore
x+y=42 -----1
[tex]\frac{x}{4}[/tex]+[tex]\frac{y}{20}[/tex]=4.90 ---2
Solving [tex]\left ( 1\right )&\left ( 2\right )[/tex] we get
x=14 & y=28
Therefore no of nickels is 14 & no of quarters is 28
54% of U.S. adults have very little confidence in newspapers. You randomly select 10 U.S. adults. Find the probability that the number of U.S. adults who have very little confidence in newspapers is (a) exactly five, (b) at least six, and (c) less than four.
Answer:
[tex]P(5)=0.238[/tex]
[tex]P(x\geq 6)=0.478[/tex]
[tex]P(x<4)=0.114[/tex]
Step-by-step explanation:
In this case we can calculate the probability using the binomial probability formula
[tex]P(X=x)=\frac{n!}{x!(n-x)!}*p^x*(1-p)^{n-x}[/tex]
Where p is the probability of obtaining a "favorable outcome " x is the number of desired "favorable outcome " and n is the number of times the experiment is repeated. In this case n = 10 and p = 0.54.
(a) exactly five
This is:
[tex]x=5,\ n=10,\ p=0.54.[/tex]
So:
[tex]P(X=5)=\frac{10!}{5!(10-5)!}*0.54^x*(1-0.54)^{10-5}[/tex]
[tex]P(5)=0.238[/tex]
(b) at least six
This is: [tex]x\geq 6,\ n=10,\ p=0.54.[/tex]
[tex]P(x\geq 6)=P(6) + P(7)+P(8)+P(9) + P(10)[/tex]
[tex]P(x\geq 6)=0.478[/tex]
(c) less than four
This is: [tex]x< 4,\ n=10,\ p=0.54.[/tex]
[tex]P(x<4)=P(3) + P(2)+P(1)+P(0)[/tex]
[tex]P(x<4)=0.114[/tex]
This question is based on the probability. Therefore, the required probabilities are : (a) [tex]P(5) = 0.238[/tex], (b)[tex]P(x \geq 6) = 0.478[/tex] and (c) [tex]P(x <4) = 0.114[/tex].
Given:
54% of U.S. adults have very little confidence in newspapers. You randomly select 10 U.S. adults.
We have to find the probability that the number of U.S. adults who have very little confidence in newspapers is (a) exactly five, (b) at least six, and (c) less than four.
According to the question,
[tex]P(5) = 0.238\\P(x \geq 6) = 0.478\\P(x <4) = 0.114[/tex]
In this we have to calculate the probability using the binomial probability formula,
[tex]P(X=x) = \dfrac{n!}{x!(n-x)!} \times p^{x} \times (1-p)^{n-x}[/tex]
Where, p is the probability of obtaining a "favorable outcome ", x is the number of desired "favorable outcome " and n is the number of times the experiment is repeated. In this case n = 10 and p = 0.54.
(a) exactly five
x=5, n= 10, p = 0.54
[tex]P(X=5)= \dfrac{10!}{5!(10-5)!} \times 0.5^{x} \times (1-0.54)^{10-5}[/tex]
P(X=5) = 0.238
(b) at least six
[tex]x\geq 6, n=10, p=0.54\\P(x\geq 6) = P(6) + P(7) + P(8) + P(9)+P(10)\\P(x\geq 6) = 0.478[/tex]
(c) less than four
[tex]x< 6, n=10, p=0.54\\P(x< 4) = P(3) + P(2) + P(1) + P(0)\\P(x< 4) = 0.114[/tex]
Therefore, the answers are : (a) [tex]P(5) = 0.238[/tex], (b)[tex]P(x \geq 6) = 0.478[/tex]
and (c) [tex]P(x <4) = 0.114[/tex].
For more details, please refer this link:
https://brainly.com/question/795909
Eliminate the parameter and obtain the standard form of the rectangular equation. Hyperbola: x = h + b tan(θ), y = k + a sec(θ) Use your result to find a set of parametric equations for the line or conic. (When 0 ≤ θ ≤ 2π. Set your center at the origin. Enter your answers as a comma-separated list of equations.) Hyperbola: vertices: (0, ±2); foci: (0, ± 5 )
The standard form of the hyperbola is derived using trigonometric identities and substituted values. The given hyperbola has vertices (0,±2) and foci (0,±5), which yields a = 2, and c = 5. Using these, the standard form of the hyperbola would be y²/4 - x²/21 = 1, and the parametric equations are x = sqrt(21) tan(θ), y = 2 sec(θ).
Explanation:To eliminate the parameter and obtain the standard form of the rectangular equation for a hyperbola, use the properties of trigonometric identities and apply the Pythagorean identity tan²(θ) + 1 = sec²(θ). Now, express tan(θ) and sec(θ) in terms of x and y, and substitute these into the Pythagorean identity to obtain the equation of the hyperbola.
In this case, tan(θ) = (x - h) / b and sec(θ) = (y - k) / a. Substitute these into the Pythagorean identity to get ((x - h) / b)² + 1 = ((y - k) / a)². Rearrange to obtain ({(x - h)²}/{b²}) - ({(y - k)²}/{a²}) = 1. This is the standard form of the hyperbola equation centered at (h, k).
For the specific hyperbola given with vertices (0,±2) and foci (0,±5), you can determine that a = 2, and c = 5. Using the relationship c² = a² + b² (for hyperbolas), you can find b = sqrt(c² - a²) = sqrt((5)² - (2)²) = sqrt(21).
So, the standard form of the equation would be y²/4 - x²/21 = 1. The parametric equations revert back to the original equation with specific values, i.e., x = sqrt(21) tan(θ) and y = 2 sec(θ).
Learn more about Hyperbola here:https://brainly.com/question/27799190
#SPJ3
An inverted pyramid is being filled with water at a constant rate of 50 cubic centimeters per second. The pyramid, at the top, has the shape of a square with sides of length 6 cm, and the height is 14 cm. Find the rate at which the water level is rising when the water level is 6 cm.
The rate at which the water level is rising when the water level is 6 cm is 8.33 cm/s.
Explanation:We can find the rate at which the water level is rising by using similar triangles. Let the height of the water level be h (in cm). Since the pyramid is inverted, the volume of water inside the pyramid is given by V = (6-h)^2 * h. Taking the derivative of both sides with respect to time, we get dV/dt = 50. Solving for dh/dt, we find that the rate at which the water level is rising is dh/dt = 50 / (12 - h).
When the water level is 6 cm, we substitute h = 6 into the equation to find the rate at which the water level is rising. dh/dt = 50 / (12 - 6) = 50 / 6 = 8.33 cm/s. Therefore, when the water level is 6 cm, the rate at which the water level is rising is 8.33 cm/s.
NEED HELP ASAP!!!!!!!!!!!!
Answer:
p(0) = 800
p(8) = 997
Step-by-step explanation:
p(t) = 800 * (1.028)^t
The current price is when t=0
p(0) = 800 * (1.028)^0
= 800(1)
= 800
The price in 8 years
p(8) = 800 * (1.028)^8
=997.7802522414861936754688
To the nearest dollar
= 998
Answer:
[tex]p(0)=\$\ 800[/tex]
[tex]p(8)=\$\ 998[/tex]
Step-by-step explanation:
The function that the mode in the price is a function of exponential growth
[tex]p(t)=800(1.028)^t[/tex]
If t represents time in years, then to find the current price we do [tex]t = 0[/tex]
Then:
[tex]p(t=0)=800(1.028)^0[/tex]
[tex]p(0)=800(1)[/tex]
[tex]p(0)=\$\ 800[/tex]
To find the price after 8 years substitute t = 8 in the equation
[tex]p(t=8)=800(1.028)^8[/tex]
[tex]p(8)=\$\ 998[/tex]
The production department of Celltronics International wants to explore the relationship between the number of employees who assemble a subassembly and the number produced. As an experiment, 2 employees were assigned to assemble the subassemblies. They produced 11 during a one-hour period. Then 4 employees assembled them. They produced 18 during a one-hour period. The complete set of paired observations follows.
Number of Assemblers One-Hour Production (units)
2 11
4 18
1 7
5 29
3 20
The dependent variable is production; that is, it is assumed that different levels of production result from a different number of employees.
a. Draw a scatter diagram.
b. Based on the scatter diagram, does there appear to be any relationship between the number of assemblers and production? Explain.
c. Compute the correlation coefficient.
Answer:
We are given that The dependent variable is production; that is, it is assumed that different levels of production result from a different number of employees.
Number of Assemblers(x) One-Hour Production(y) (units)
2 11
4 18
1 7
5 29
3 20
a. Draw a scatter diagram.
Solution : Refer the attached figure
b. Based on the scatter diagram, does there appear to be any relationship between the number of assemblers and production? Explain.
Solution: The equation that shows the relationship between the number of assemblers and production is [tex]y=5.1x+1.7[/tex]
Where y is One-Hour Production (units) and x is the Number of Assemblers
c.Compute the correlation coefficient.
Solution:
Formula of correlation coefficient:[tex]r=\frac{n(\sum xy)-(\sum x)(\sum y)}{[n \sum x^2 -(\sum x)^2][n \sum y^2 -(\sum y)^2]}[/tex]
x y xy [tex]x^2[/tex] [tex]y^2[/tex]
2 11 22 4 121
4 18 72 16 324
1 7 7 1 49
5 29 145 25 841
3 20 60 9 400
Sum: 15 85 306 55 1735
n=5
Substitute the values in the formula :
[tex]r=\frac{5(306)-(15)(85)}{[5 (55) -(15)^2][5 (1735) -(85)^2]}[/tex]
[tex]r=0.00351[/tex]
The correlation coefficient is 0.00351
The number of measles cases increased 13.6 % to 57 cases this year, what was the number of cases prior to the increase? (Express your answer rounded correctly to the nearest whole number)
Answer:
The number of cases prior to the increase is 50.
Step-by-step explanation:
It is given that the number of measles cases increased by 13.6% and the number of cases after increase is 57.
We need to find the number of cases prior to the increase.
Let x be the number of cases prior to the increase.
x + 13.6% of x = 57
[tex]x+x\times \frac{13.6}{100}=57[/tex]
[tex]x+0.136x=57[/tex]
[tex]1.136x=57[/tex]
Divide both the sides by 1.136.
[tex]\frac{1.136x}{1.136}=\frac{57}{1.136}[/tex]
[tex]x=50.176[/tex]
[tex]x\approx 50[/tex]
Therefore the number of cases prior to the increase is 50.
You invest $1600 in an account paying 5% interest compounded daily. What is the account's effective annual yield? Assume 360 days in a year.
The account's effective annual yield is ___% (Round to two decimal places as needed)
Answer:
5.13%.
Step-by-step explanation:
Amount accumulated in 1 year
= 1600(1 + 0.05/360)^360
= $1682.03
Account's effective annual yield
= 82.03 * 100 / 1600 %
= 5.13%.
The account's effective annual yield (EAY) for an investment of $1600 with a 5% interest rate compounded daily (assuming a 360-day year) is approximately 5.12% when rounded to two decimal places.
The student has invested $1600 in an account that offers 5% interest compounded daily with the assumption of a 360-day year. To find the effective annual yield, we use the formula for compound interest and the definition of effective annual yield (EAY), which accounts for the compounding effect:
EAY = (1 + r/n)n - 1
Where:
In this case:
Now, substituting the values, we get:
EAY = (1 + 0.05/360)360 - 1
Calculating this out:
EAY = (1 + 0.0001388888889)360 - 1
EAY
to find the EAY:
EAY = ((1 + (0.05/360))^360) - 1
After calculating the above expression, the approximate effective annual yield comes out to be:
EAY = 0.05116 or 5.116%
Therefore, after rounding to two decimal places as required, the effective annual yield of the account is 5.12%.
A fair coin is flipped 4 times. What is the probability that at least two heads are flipped?
The probability of flipping at least two heads in four tosses of a fair coin is calculated using the binomial distribution, and the total probability is found to be 0.6875 or 68.75%.
To calculate the probability of flipping at least two heads in a series of four coin tosses with a fair coin, we need to consider all the possible outcomes in which we can get at least two heads. The different numbers of heads that can be obtained are 0, 1, 2, 3, or 4. To find the probability of each specific event, we use the binomial distribution formula, which for flipping two heads is:
P(2 heads) = (4 choose 2) × (0.5)² × (0.5)² = 6 × 0.25 × 0.25 = 0.375.
We can also find the probabilities of obtaining three and four heads:
P(3 heads) = (4 choose 3) × (0.5)³ × (0.5)¹ = 4 × 0.125 × 0.5 = 0.25,
P(4 heads) = (4 choose 4) × (0.5)⁴ = 1 × 0.0625 = 0.0625.
Next, we add these probabilities together to get the total probability of flipping at least two heads:
Total probability = P(2 heads) + P(3 heads) + P(4 heads) = 0.375 + 0.25 + 0.0625 = 0.6875.
Therefore, the probability of flipping at least two heads in four tosses of a fair coin is 0.6875 or 68.75%.
What's the annual percentage yield for money invested at the rate of 3.2% compounded continuously?
Answer:__________ %
Convert your answer into a percentage. Round your answer to 2 decimal places.
Answer:
The Annual percentage yield is 3.25%.
Step-by-step explanation:
Given : Money invested at the rate of 3.2% compounded continuously.
To find : What's the annual percentage yield?
Solution :
Money invested at the rate of 3.2% compounded continuously.
The compounded continuously formula is
[tex]A=Pe^{rt}[/tex]
Where, P is the principal P=1
t is the time t=1
r is the interest rate r=3.2%=0.032
Substitute the value in the formula,
[tex]A=Pe^{rt}[/tex]
[tex]A=1\times e^{0.032}[/tex]
[tex]A=1.0325[/tex]
The Annual percentage yield is
[tex]APY=(A-1)\times 100[/tex]
[tex]APY=(1.0325-1)\times 100[/tex]
[tex]APY=0.0325\times 100[/tex]
[tex]APY=3.25\%[/tex]
Therefore, The Annual percentage yield is 3.25%.
The population of an Asian country is growing at the rate of 0.7% annually. If there were 3,942.000 residents in the city in 1995. Find how many to the nearest ten thousand) are living in that city in 2000. Use y = 3,942,000(2.7)0.0074 a) 370,000 b) 4,000,000 c) 4.160,000 d) 4.320,000
Answer:
b) 4,000,000
Step-by-step explanation:
Let the population is measured since 1995,
Given,
The initial population, P = 3,942,000,
Annual rate of growing, r = 0.7% = 0.007,
If y represents the population after t years
So, the population after t years would be,
[tex]y=Pe^{rt}[/tex]
[tex]y=3942000(2.7)^{0.007x}[/tex]
Therefore, the population after 5 years,
[tex]y=3942000(2.7)^{0.007\times 5}=3942000(2.7)^{0.035}=4081448.78924\approx 4000000[/tex]
Hence, the population in 2000 would be approximately 40,00,000.
Option 'b' is correct.
By using the accurate population growth formula P = P0(1 + r)^n and substitifying the given values, the population of the Asian country in 2000 would be approximately 4,160,000 residents.
Explanation:
The question involves the concept of exponential growth, specifically applied to the population growth of an Asian country. Now, in given formula y = 3,942,000(2.7)^0.0074, we should use the correct growth rate formula to solve the problem which should be P = P0(1 + r)^n since the population growth is annually and continuous. Here, P0 is the initial population (3,942,000), r is the growth rate (0.7% or 0.007) and n is the number of years (2000-1995 = 5 years).
Using this formula, if you substitute these values in, you should get:
P = 3,942,000(1 + 0.007)^5
If you calculate this out, you reach a population of approximately 4,160,000 residents at the end of year 2000. Thus, answer 'c' is the correct option. Please remember exponential growth is a concept necessary for understanding population dynamics across multiple fields like demography, biology and mathematical modeling.
Learn more about Population Growth here:https://brainly.com/question/18415071
#SPJ3
13. Determine whether B = {(-1, 1,-1), (1, 0, 2), (1, 1, 0)} is a basis of R3.
Answer: Yes, the given set of vectors is a basis of R³.
Step-by-step explanation: We are given to determine whether the following set of three vectors in R³ is a basis of R³ or not :
B = {(-1, 1,-1), (1, 0, 2), (1, 1, 0)} .
For a set to be a basis of R³, the following two conditions must be fulfilled :
(i) The set should contain three vectors, equal to the dimension of R³
and
(ii) the three vectors must be linearly independent.
The first condition is already fulfilled since we have three vectors in set B.
Now, to check the independence, we will find the determinant formed by theses three vectors as rows.
If the value of the determinant is non zero, then the vectors are linearly independent.
The value of the determinant can be found as follows :
[tex]D\\\\\\=\begin{vmatrix} -1& 1 & -1\\ 1 & 0 & 2\\ 1 & 1 & 0\end{vmatrix}\\\\\\=-1(0\times0-2\times1)+1(2\times1-1\times0)-1(1\times1-0\times1)\\\\=(-1)\times(-2)+1\times2-1\times1\\\\=2+2-1\\\\=3\neq 0.[/tex]
Therefore, the determinant is not equal to 0 and so the given set of vectors is linearly independent.
Thus, the given set is a basis of R³.
caps hock Guess and Check (or use Algebra) to solve #3 & # 4 3. Plato has 36 coins in nickels, dimes, and quarters. The number of nickels is three less than twice the number of dimes. The total value of the coins is $5.20. How many of each type of coin does Plato have? mel 36 coinsin d
4. Katy bought a ski hat that was marked down 35% to $15.60. What was the price of the hat before the markdown? (Hint: She was in Oregon where they do not have sales tax). 35 9. douon 15.60 5. Sele amo ont 621.06
Answer:
Part 1:
Let the nickels be = n
Let the dimes be = d
Let the quarters be = q
Plato has 36 coins in nickels, dimes, and quarters. So, equation forms:
[tex]n+d+q=36[/tex] .....(1)
The number of nickels is three less than twice the number of dimes.
[tex]n=2d-3[/tex] ....(2)
The total value of the coins is $5.20.
[tex]0.10d+0.05n+0.25q=5.20[/tex] .... (3)
Substituting n=2d-3 in (1) and (3)
[tex]2d-3+d+q=36[/tex]
=> [tex]3d+q=39[/tex] ....(4)
[tex]0.10d+0.05(2d-3)+0.25q=5.20[/tex]
=> [tex]0.10d+0.10d-0.15+0.25q=5.20[/tex]
=> [tex]0.20d+0.25q=5.35[/tex] ...(5)
Multiplying (4) by 0.25 and subtracting (5) from (4)
[tex]0.75d+0.25q=9.75[/tex] now subtracting (5) from this we get;
[tex]0.55d=4.4[/tex]
=> d = 8
Substituting d = 8 in [tex]3d+q=39[/tex]
[tex]3(8)+q=39[/tex]
[tex]24+q=39[/tex]
=> q = 15
Substituting values of d and q in [tex]n+d+q=36[/tex], we get n
[tex]n+8+15=36[/tex]
[tex]n=36-23[/tex]
=> n = 13
Therefore Plato has 13 nickels, 15 quarters and 8 dimes.
-----------------------------------------------------------------------------------------
Part 2:
Let the original price of the ski hat be = x
Original price was marked down by 35% means value was lowered by 35%.
So, we can calculate as:
[tex]x-\frac{35x}{100}=15.60[/tex]
=> [tex]\frac{65x}{100}=15.60[/tex]
=> [tex]65x=1560[/tex]
x = 24
Hence, the original price was $24 but after 35% marking down, it was available for $15.60.
Find a parametric representation for the surface. The part of the plane z = x + 3 that lies inside the cylinder x2 + y2 = 9. (Enter your answer as a comma-separated list of equations. Let x, y, and z be in terms of s and/or θ.)
You can use
[tex]x=u\cos v[/tex]
[tex]y=u\sin v[/tex]
[tex]z=u\cos v+3[/tex]
with [tex]0\le u\le3[/tex] and [tex]0\le v\le2\pi[/tex].
The parametric equations for the part of the plane z = x + 3 that lies inside the cylinder x² + y² = 9 can be written as x = 3cos(θ), y = 3sin(θ), and z = 3cos(θ) + 3.
Explanation:The parametric representation of a surface can be found by expressing the variables x, y, and z in terms of parameters. Given the cylinder equation x² + y² = 9, we can express x and y in terms of a single parameter θ as follows:
x = 3cos(θ)y = 3sin(θ)Here we've used the parametric equations for a circle of radius 3. Moving further with the given plane equation z = x+3, we substitute x from our parametric equations above:
z = 3cos(θ) + 3So, the parametric representation for the given surface is:
x = 3cos(θ)y = 3sin(θ)z = 3cos(θ) + 3Learn more about Parametric Representation here:https://brainly.com/question/34159526
#SPJ2
8 Line in the xy-plane contains points from each of Quadrants II, III, and IV, but no points from Quadrant I. Which of the following must be true? A) The slope of line is undefined. B) The slope of line is zero. C) The slope of line is positive. D) The slope of line is negative. CONTINUE
Answer:
The correct option is D.
Step-by-step explanation:
The slope of a line is the change in y with respect to x.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
If the slope of a line is undefined it means it is a vertical line and a vertical line can not passes through three quadrants. So, option A is incorrect.
If the slope of a line is 0 it means it is a horizontal line and a horizontal line can not passes through three quadrants. So, option B is incorrect.
If the slope of a line is positive it means the value of y increases as x increases.
Since it is an increasing line, therefore after a certain period both x and y will positive. It means the line will passes through first quadrant. So, option C is incorrect.
If the slope of a line is negative it means the value of y decreases as x increases. It can passes through each of Quadrants II, III, and IV.
Therefore the correct option is D.
Maria needed 88 gallons of gas to fill her car's gas tank. The mileage odometer read 40 comma 00040,000 miles. When the odometer read 40 comma 18040,180, Maria filled the tank with 99 gallons. At the end of the trip, she filled the tank with 1616 gallons, and the odometer read 40 comma 48440,484 miles. How many miles per gallon did she get for the entire trip?
Answer:
about 29,748.3
Step-by-step explanation:
4000040000 - 4018040180 = 18000180
(11 gallons were used there^)
4018040180 - 4048440484 = 30400304
1616+11 = 1627 total gallons
18000180 + 30400304 = 48400484
48400484/ 1627 = 29,748.3
A card is drawn at random from a standard deck of 52 cards. Find the following conditional probabilities. a) The card is a spade, given that it is black. b) The card is black, given that it is a spade. c) The card is a seven, given that it is black. d) The card is a king, given that it is a face card.
To find the conditional probabilities, you need to use the definition of conditional probability. Given that a card is black, the probability that it is a spade is 1/2. Given that a card is a spade, the probability that it is black is 2. Given that a card is black, the probability that it is a seven is 1/13. Given that a card is a face card, the probability that it is a king is 1/3.
Explanation:To find these conditional probabilities, we need to use the definition of conditional probability:
P(A|B) = P(A and B) / P(B)
a) The card is a spade, given that it is black:
In a standard deck of cards, there are 26 black cards and 13 spades. So, P(S|B) = P(S and B) / P(B) = 13/26 / 26/52 = 1/2
b) The card is black, given that it is a spade:
P(B|S) = P(B and S) / P(S) = 26/52 / 13/52 = 26/13 = 2
c) The card is a seven, given that it is black:
In a standard deck of cards, there are 4 black sevens and 26 black cards. So, P(7|B) = P(7 and B) / P(B) = 4/26 / 26/52 = 1/13
d) The card is a king, given that it is a face card:
In a standard deck of cards, there are 4 kings and 12 face cards. So, P(K|F) = P(K and F) / P(F) = 4/52 / 12/52 = 1/3
Exercise 2.2 gave the following data (in increasing order) for the attribute age: 13, 15, 16, 16, 19, 20, 20, 21, 22, 22, 25, 25, 25, 25, 30, 33, 33, 35, 35, 35, 35, 36, 40, 45, 46, 52, 70. (a) Use smoothing by bin means to smooth these data, using a bin depth of 3. Illustrate your steps. Comment on the effect of this technique for the given data. (b) How might you determine outliers in the data? (c) What other methods are there for data smoothing?
Answer:
Step-by-step explanation:
13, 15, 16, 16, 19, 20, 20, 21, 22, 22, 25, 25, 25, 25, 30, 33, 33, 35, 35, 35, 35, 36, 40, 45, 46, 52, 70.
a) Smoothing by bin means
Each bin has depth of 3
Dividing data into bins
so, Bin 1= 13, 15, 16
Bin 2= 16, 19, 20
Bin 3= 20, 21, 22
Bin 4= 22, 25, 25
Bin 5= 25, 25, 30
Bin 6= 33, 33, 35
Bin 7 = 35, 35, 35
Bin 8= 36, 40, 45
Bin 9= 46, 52, 70
Now, smoothing data by bin mean
so, Bin 1= 13, 15, 16 = (13+15+16)/3 = 15 Bin 1 = 15,15,15
Bin 2= 16, 19, 20 = (16+19+20)/3 = 18 Bin 2 = 18,18,18
Bin 3= 20, 21, 22= (20+21+22)/3 = 21 Bin 3 = 21,21,21
Bin 4= 22, 25, 25 = (22+25+25)/3 = 24 Bin 4 = 24,24,24
Bin 5= 25, 25, 30 =(25+25+30)/3 = 27 Bin 5 = 27,27,27
Bin 6= 33, 33, 35 = (33+33+35)/3 = 34 Bin 6 = 34,34,34
Bin 7 = 35, 35, 35 = (35+35+35)/3 = 35 Bin 7 = 35,35,35
Bin 8= 36, 40, 45 = (36+40+45)/3 = 40 Bin 8 = 40,40,40
Bin 9= 46, 52, 70=(46+52+70)/3 = 56 Bin 9 = 56,56,56
This technique is used to smooth the data. Data may have noise, using binning techniques we can remove noise from the data. It helps in providing more accurate results
b) How might you determine outliers in the data?
Outliers are the data that are abnormal to other data points. Outliers can be found by Box and whisker chart (box plot). Inter Quartile range can also be used to identify outliers
c) What other methods are there for data smoothing?
Other methods of smoothing data are
a) binning by boundaries
b) Exponential smoothing
c) Random walk
The correct statement will be that the method of binning is extensively used for smoothening the data and cancels the noise a data contains. Outliers of a data can be determined using the quartile range.
There are different methods of data smoothening, such as binning with the help of boundaries, binning with the help of outliers, exponential binning, etc.
Binning of attributes.The bins will be created using the depth of 3 as,
Bin 1- 13,15,16 ; Bin 2- 16,19,20 ; Bin 3 20, 21, 22 ; Bin 4- 22,25,25 ; Bin 5- 25, 25, 30 ; Bin 6- 33,33,35 ; Bin 7- 35,35,35 ; Bin 8- 36,40,45 ; Bin 9- 46,52,70.
The vales of bins will be averaged and rounded off to the nearest whole numbers, considering bins as b in the following way.
[tex]b1= \dfrac {13+15+16}{3}\\\\b1= 14.67[/tex]
Continuing further in similar ways, we will find the values of remaining bins as
b2- 18b3- 21b4- 24b5- 27b6- 34b7- 35b8- 40b9- 56The outliers in the data can be found by using the box plot method and quartile range functions. Normally, such outliers are referred to as the mismatching data in a bin.
There are various different methods for smoothing the data. Some ways of smoothing the data are exponential smoothing, random walk smoothing, boundary binning method, etc.
Hence, the data is smoothened using the binning method and the values obtained are as above.
Learn more about bin data here:
https://brainly.com/question/6103918
2- suppose a ball is thrown upward to a height of h0 meters . each time the ball bounces, it rebounds to a fraction r of its previous height . let hn be the hight after the nth term biunces. cosider the following value of h0 and r
a- find the first 4 terms of the sequence of heights(hn)
b- find a general expression for the nth term of the sequence (hn)
h0=20 , r=0.5
Answer:
a) 40, 50, 55, 57.5
b) [tex]S_n=h_0+2h_0\sum_{n=1}^{\infty}r^n[/tex]
Step-by-step explanation:
h₀ = Initial height of the ball =20
r = Rebound fraction = 0.5
a) The series of bouncing balls is given by
Sₙ=h₀+2h₀(r¹+r²+r³+r⁴.........rⁿ)
S₁=h₀+2h₀r¹=20+2×20×0.5=40
S₂=h₀+2h₀(r¹+r²)=20+2×20×(0.5+0.5²)=50
S₃=h₀+2h₀(r¹+r²+r³)=20+2×20×(0.5+0.5²+0.5³)=55
S₄=h₀+2h₀(r¹+r²+r³+r⁴)=20+2×20×(0.5+0.5²+0.5³+0.5⁴)=57.5
b) General expression for the nth term of the sequence
[tex]S_n=h_0+2h_0\sum_{n=1}^{\infty}r^n[/tex]
Final answer:
The first 4 heights after each bounce form a geometric sequence with the first term h₀ being 20 meters and subsequent terms being 10, 5, and 2.5 meters. The general expression for the nth term (hn) is given by the formula hₙ = 20 * (0.5)ⁿ
Explanation:
Given an initial height h₀ of 20 meters and a rebound fraction r of 0.5, the sequence of heights after each bounce forms a geometric sequence.
The first height is h₀ which is 20 meters. Subsequent heights can be found by multiplying the previous height by the rebound fraction r.
Third term : h2 = h= 10 * 0.5 = 5 meters
General Expression for the nth Term (b)
The nth term (hₙ) of the sequence can be found using the formula for the nth term of a geometric sequence:
hₙ = h₀ * rⁿ
For this particular sequence:
hₙ = 20 * (0.5)ⁿ
A cable provider wants to contact customers in a particular telephone exchange to see how satisfied they are with the new digital TV service the company has provided. All numbers are in the 443 exchange, so there are 10 comma 000 possible numbers from 443-0000 to 443-9999. If they select the numbers with equal probability: a) What distribution would they use to model the selection? b) What is the probability the number selected will be an even number? c) What is the probability the number selected will end in 666?
Answer:
a) uniform
b) 1/2
c) 1/1000
Step-by-step explanation:
a) "numbers with equal probability" have a uniform distribution.
__
b) Even numbers make up 1/2 of all numbers.
__
c) There are ten such numbers in the range, so the probability is ...
10/10000 = 1/1000
The selection of telephone numbers can be modeled using a Uniform distribution. The probability of selecting an even number is 1/2, while the chance of selecting a number ending in 666 is 0.001.
Explanation:The questions asked can be explained using probability theory, a branch of mathematics.
a) To model the selection of the telephone numbers, one would use a Uniform distribution. This is because every number in the range has an equal chance of being selected.
b) The probability that the selected number is even relies on the last digit of the telephone number. As the last digit could be 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9, each with equal probability, the chance that it is even (0, 2, 4, 6, or 8) is 1/2 or 50%.
c) The probability that the selected number ends in 666 is much lower. Since there are 10,000 possible numbers, and only 10 of them end in 666 (443-0666, 443-1666, etc. through 443-9666), the probability is 10 in 10,000 or 0.001 (0.1%).
Learn more about Probability Theory here:https://brainly.com/question/33441869
#SPJ2
If ( 43.65 ) ( 8.79 ) / x = ( 0.4365 ) ( 87.9 ) then value of x is:
(a) .01 (b) 0.1 (c) 1 (d) 10 (e) 100
Need step-by-step solution
i will mark your answer Brainliest
Answer:
(d) 10
Step-by-step explanation:
Multiply by x and divide by its coefficient:
(43.65)(8.79) = (0.4365)(87.9)x
(43.65)(8.79)/((0.4365)(87.9)) = x
At this point, any calculator can give you the answer. It is, perhaps, more satisfying to work out the answer without a calculator.
x = (43.65)/(0.4365) × (8.79)/(87.9)
In the first quotient, the numerator is 100 times the denominator; in the second, the denominator is 10 times the numerator.
x = (100) × (1/10) = 100/10
x = 10
_____
Moving the decimal point to the right 1 place multiplies the numerical value by 10.
The value of x in the given equation that satisfies the condition is 10.
Explanation:In this question, we're given a mathematical expression in which the value of x is unknown. We're looking for the value of x that satisfies the equation:
( 43.65 ) ( 8.79 ) / x = ( 0.4365 ) ( 87.9 )
To solve this equation for x, we can start by noting the similarity between the left and right sides. We have larger numbers on the left side that appear, in reduced form, on the right side.
Follow these steps:
Multiply 43.65 and 8.79 to get 383.985.Multiply 0.4365 and 87.9 to get 38.3985.Divide 383.985 by 38.3985 to get 10.So, the correct option would be (d) 10.
Learn more about Algebra here:https://brainly.com/question/32436021
#SPJ2
The coefficient of x^3y^4 in (3x+2y)^7 is
Answer:
The coefficient is 15120.
Step-by-step explanation:
Since, by the binomial expansion formula,
[tex](x+y)^n=\sum_{r=0}^n^nC_r x^{n-r} y^r[/tex]
Where, [tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]
Thus, we can write,
[tex](3x+2y)^7 = \sum_{r=0}^n ^7C_r (3x)^{7-r} (2y)^r[/tex]
For finding the coefficient of [tex]x^3y^4[/tex],
r = 4,
So, the term that contains [tex]x^3y^4[/tex] = [tex]^7C_4 (3x)^3 (2y)^4[/tex]
[tex]=35 (27x^3) (16y^4)[/tex]
[tex]=15120 x^3 y^4[/tex]
Hence, the coefficient of [tex]x^3y^4[/tex] is 15120.
Answer:[tex][/tex]
Coefficient of [tex]x^3y^4[/tex] in [tex](3x+2y)^7[/tex] is 15120
Step-by-step explanation:
We know that [tex](x+y)^{n}[/tex]) can be expanded in (n+1) terms by using binomial theorem and each term is given as
[tex]n_C_{r}x^{n-r}y^{r}[/tex]
Here value of r is taken from n to 0
we have to determine the coefficient of [tex]x^3y^4[/tex] in [tex](3x+2y)^7[/tex]
in this problem we have given n=7
We have to determine the coefficient of [tex]x^3y^4[/tex]
it means in the expansion we have to find the the 3rd power of x and therefore
r=n-3
here n=7
therefore, r=7-3=4
Hence the coefficient of [tex]x^3y^4[/tex] can be determine by using formula
[tex]n_C_{r}x^{n-r}y^{r}[/tex]
here n=7, r=4
[tex]7_C_{4}x^{7-4}y^{4}[/tex]
=[tex]\frac{7\times 6\times 5\times 4}{1\times 2\times 3\times 4} (3x)^3(2y)^4[/tex]
=[tex]15120x^3y^4[/tex]
Therefore the coefficient of [tex]x^3y^4[/tex] in [tex](3x+2y)^7[/tex] is 15120
find lim ?x approaches 0 f(x+?x)-f(x)/?x where f(x) = 4x-3
If [tex]f(x)=4x-3[/tex]:
[tex]\displaystyle\lim_{\Delta x\to0}\frac{(4(x+\Delta x)-3)-(4x-3)}{\Delta x}=\lim_{\Delta x\to0}\frac{4\Delta x}{\Delta x}=4[/tex]
If [tex]f(x)=4x^{-3}[/tex]:
[tex]\displaystyle\lim_{\Delta x\to0}\frac{\frac4{(x+\Delta x)^3}-\frac4{x^3}}{\Delta x}=\lim_{\Delta x\to0}\frac{\frac{4x^3-4(x+\Delta x)^3}{x^3(x+\Delta x)^3}}{\Delta x}[/tex]
[tex]\displaystyle=\lim_{\Delta x\to0}\frac{4x^3-4(x^3+3x^2\Delta x+3x(\Delta x)^2+(\Delta x)^3)}{x^3\Delta x(x+\Delta x)^3}[/tex]
[tex]\displaystyle=\lim_{\Delta x\to0}\frac{-12x^2\Delta x-12x(\Delta x)^2-4(\Delta x)^3}{x^3\Delta x(x+\Delta x)^3}=-\frac{12}{x^4}[/tex]
Suppose a company did $3,000,000 in annual maintenance in 2013 and expects 85% of those to renew for 2014. Suppose that product sales for 2013 were $3,000,000 (which included free maintenance in 2013) and 60% of those were expected to pay an annual maintenance of 20% of the purchase price in 2014. What will be the annual maintenance collected in 2014?
Answer:
In year 2013 annual maintenance done = $ 3,000,000
Out of this 85% is expected to renew in 2014 = [tex]0.85\times3000000[/tex] = $2,550,000
Now Sales in 2013 = $3,000,000
60% of these sales = [tex]0.60\times3000000[/tex] = $1,800,000
Now out of this 60%, 20% annual maintenance was expected to be paid
In 2014 = [tex]0.20\times1800000[/tex] = $360000
So, Total annual maintenance in 2014 = [tex]2550000+360000[/tex]
= $2,910,000
(1 point) Suppose that for two random variables X and Y the joint density function is f(x,y)=6xe−x(y+6), for x>0 and y>0. Find each of the following. (a) fX|Y(x,y)= (b) fY|X(x,y)=
The question is about calculating the conditional probability density functions of two random variables X and Y given their joint density function. However, without the marginal density functions for X and Y, it is not possible to provide exact numerical answers. General formulas involve dividing the joint density function by the respective marginal density function.
Explanation:The question relates to the field of probability and statistics, specifically pertaining to joint density functions of two random variables (X and Y). We have the joint density function f(x, y) = 6xe^(−x(y+6)) where x > 0 and y > 0.
For the conditional probability density function, the general formula for fX|Y(x, y) is the joint density function divided by the marginal density function of Y. Similarly, for fY|X(x, y), it is the joint density function divided by the marginal density function of X.
However, the marginal density functions for X and Y are not specified in the question. Typically, to find these, one would integrate the joint density function with respect to the other variable. Due to this missing information, it's not possible to provide an exact numerical answer.
Learn more about Conditional Probability here:https://brainly.com/question/32171649
#SPJ2
1. Suppose you take a coin and flip it 4 times in a row. After each flip you record whether the coin landed heads or tails. What is the probability you’ll get at least 2 heads?
Answer:
25%
Step-by-step explanation:
Great question, since a regular coin has two sides one heads and one tails. That gives us a 50% probability of it landing on either side of the coin. Since we would like to know the probability of getting 2 heads in a row, we would need to multiply the probability of the first toss landing on heads with the second toss landing on heads, like so...
[tex]\frac{1}{2} *\frac{1}{2} =\frac{1}{4}[/tex]
So we can see that the probability of us getting two heads in a row is that of \frac{1}{4}[/tex] or 25%.
I hope this answered your question. If you have any more questions feel free to ask away at Brainly.
1. A box contains 4 red and 6 green balls. Two balls are drawn. You receive $10 if both are red and you pay $1 otherwise. What are your expected winnings?
Answer:
Your Winnings are $ -1
Step-by-step explanation:
Hello, great question. These types are questions are the beginning steps for learning more advanced Algebraic Equations.
Since we are not told what two balls were actually drawn, then the expected winnings would be of the greatest probability occurring. To figure this out we need to calculate the probability of getting two red balls consecutively and the probability of getting two different colors consecutively. Since there are a total of 10 balls the probabilities of getting one ball would be the following,
Red: [tex]\frac{4}{10} = 40%[/tex]
Green: [tex]\frac{6}{10} = 60%[/tex]
Now we need to know the probability of us getting 2 reds together, two greens, or one of each.
2 Reds: [tex]\frac{4}{10} *\frac{4}{10} = \frac{16}{100} = 16%[/tex]
2 Greens: [tex]\frac{6}{10} *\frac{6}{10} = \frac{36}{100} = 36%[/tex]
1 Each: [tex]\frac{4}{10} *\frac{6}{10} = \frac{24}{100} = 24%[/tex]
So we can see that the highest probability is getting 2 Greens in a row. Meaning you would have to pay $1
I hope this answered your question. If you have any more questions feel free to ask away at Brainly.
Solve the inhomogeneius linear ode by undetermined coefficients
Y"+4y=3sin2x
Answer with explanation:
The given non Homogeneous linear differential equation is:
y" +4 y'=3 Sin 2 x-------(1)
Put , u=y'
Differentiating once
u'=y"
Substituting the value of , y' and y" in equation (1)
⇒u' +4u =3 Sin 2x
This is a type of linear differential equation.
Integrating factor [tex]=e^{4t}[/tex]
Multiplying both sides of equation by Integrating factor
[tex]e^{4 x}(u'+4u)=e^{4x}3 \sin 2x\\\\ \text{Integrating both sides}\\\\ue^{4x}=\int {3 \sin 2x \times e^{4x}} \, dx \\\\ue^{4x}=\frac{3e^{4x}}{2^2+4^2}\times (4\sin 2x -2 \cos 2x)\\\\ue^{4x}=\frac{3e^{4x}}{20}\times (4\sin 2x -2 \cos 2x)+C_{1}\\\\ \text{Using the formula of}\\\\\int{e^{ax}\sin bx } \, dx=\frac{e^{ax}}{a^2+b^2}\times (a \sin bx-b \cos bx)+C[/tex]
where C and [tex]C_{1}[/tex] are constant of integration.
Replacing , u by , y' in above equation we get the solution of above non homogeneous differential equation
[tex]y'(x)=\frac{3}{20}\times (4\sin 2x -2 \cos 2x)+C_{1}e^{-4 x}[/tex]