Answer:
a) [tex]P(X=0)=(4C0)(0.75)^0 (1-0.75)^{4-0}=0.0039[/tex]
[tex]P(X=1)=(4C1)(0.75)^1 (1-0.75)^{4-1}=0.0469[/tex]
[tex]P(X=2)=(4C2)(0.75)^2 (1-0.75)^{4-2}=0.211[/tex]
[tex]P(X=3)=(4C3)(0.75)^2 (1-0.75)^{4-3}=0.422[/tex]
[tex]P(X=4)=(4C4)(0.75)^2 (1-0.75)^{4-4}=0.316[/tex]
b) [tex] E(X) = np = 4*0.75=3[/tex]
c) [tex] Sd(X) =\sqrt{np(1-p)}=\sqrt{4*0.75*(1-0.75)}=0.866[/tex]
d) [tex] P(X \geq 3) \geq 0.98[/tex]
And the dsitribution that satisfy this is [tex]X\sim Binom(n=9,p=0.75[/tex]
Step-by-step explanation:
Previous concepts
The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".
Let X the random variable of interest, on this case we now that:
[tex]X \sim Binom(n=4, p=1-0.25=0.75)[/tex]
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
Part a
[tex]P(X=0)=(4C0)(0.75)^0 (1-0.75)^{4-0}=0.0039[/tex]
[tex]P(X=1)=(4C1)(0.75)^1 (1-0.75)^{4-1}=0.0469[/tex]
[tex]P(X=2)=(4C2)(0.75)^2 (1-0.75)^{4-2}=0.211[/tex]
[tex]P(X=3)=(4C3)(0.75)^2 (1-0.75)^{4-3}=0.422[/tex]
[tex]P(X=4)=(4C4)(0.75)^2 (1-0.75)^{4-4}=0.316[/tex]
Part b
The expected value is givn by:
[tex] E(X) = np = 4*0.75=3[/tex]
Part c
For the standard deviation we have this:
[tex]Sd(X) =\sqrt{np(1-p)}=\sqrt{4*0.75*(1-0.75)}=0.866[/tex]
Part d
For this case the sample size needs to be higher or equal to 9. Since we need a value such that:
[tex] P(X \geq 3) \geq 0.98[/tex]
And the dsitribution that satisfy this is [tex]X\sim Binom(n=9,p=0.75[/tex]
We can verify this using the following code:
"=1-BINOM.DIST(3,9,0.75,TRUE)" and we got 0.99 and the condition is satisfied.
To find the probabilities of different numbers of successes ranging from 0 to 4 in a group of parolees, we can use the binomial probability formula. The expected number of parolees who will not be repeat offenders can be calculated by multiplying the probability of success by the total number of parolees. The standard deviation can also be calculated using a formula. To be about 98% sure that three or more parolees will not become repeat offenders, Alice should counsel a group size of at least 13 parolees.
Explanation:To find the probabilities of different numbers of successes, we can use the binomial probability formula. Given that the probability of success is 0.25 and the number of trials is 4, we can calculate the probabilities as follows:
P(0) = (1-0.25)^4 = 0.316P(1) = 4C1 * 0.25^1 * (1-0.25)^3 = 0.421P(2) = 4C2 * 0.25^2 * (1-0.25)^2 = 0.281P(3) = 4C3 * 0.25^3 * (1-0.25)^1 = 0.047P(4) = 4C4 * 0.25^4 * (1-0.25)^0 = 0.008The expected number of parolees who will not be repeat offenders can be calculated by multiplying the probability of success (0.25) by the total number of parolees (4), which gives an expected value of 1 parolee. The standard deviation can be calculated using the formula sqrt(n * p * (1-p)), where n is the number of trials and p is the probability of success. In this case, the standard deviation is sqrt(4 * 0.25 * (1-0.25)) ≈ 0.866.
To determine the size of the group that Alice should counsel to be about 98% sure that three or more parolees will not become repeat offenders, we can use the binomial cumulative distribution function. We need to find the smallest value of n (the number of trials) such that P(X ≥ 3) > 0.98, where X represents the number of successes. Solving this inequality, we find that Alice should counsel a group size of at least 13 parolees.
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In the xy-coordinate plane, line l is perpendicular to the y-axis and passes through the point (5, -3).Which of the following is an equation of line l?A. x = 0B. x = 5C. y = −3D. y + 3 = x + 5E. y − 3 = x + 5
Answer:
C. y = -3
Step-by-step explanation:
Line L is perpendicular to the y-axis, so line L is just a straight horizontally line going from left to right.
This mean that the x-coordinate they gave us is irrelevant since our flat line is going to pass through all possible x-values. The only thing we need to focus on the the y-value.
So we know that the line passes through (__, -3)
the equation y = -3 gives us a horizontal line that passes through (__, -3).
Therefore answer is C.
Answer A and B are wrong because they gave us vertical lines, we want horizontal lines. D and E are wrong because those are diagonal lines, we want flat horizontal lines.
Find the area of the largest isosceles triangle that can be inscribed in a circle of radius r
Answer:
(3/4)(√3)r²
Step-by-step explanation:
The largest such triangle is an equilateral triangle. It will have a side length of r√3. The area can be found a number of ways, one of which is to use the formula for the area of an equilateral triangle of side length s:
A = s²·(√3)/4
Using s=r√3, we get ...
A = (3/4)(√3)r²
If stewart and patrick can finish a science project together in 20 minutes, and Patrick works four times as quickly as Stewart, how long would it take Patrick to complete the project alone?
Answer:
It would take 25 minutes for Patrick to complete the project alone.
Step-by-step explanation:
They did the project in 20 minutes, that is, 100% of the project, so:
[tex]x + y = 1[/tex]
In which x is the percentage that Patrick worked and y is the percentage that Stewart worked.
Patrick works four times as quickly as Stewart, so x = 4y.
So
[tex]x + y = 1[/tex]
[tex]4y + y = 1[/tex]
[tex]5y = 1[/tex]
[tex]y = 0.2[/tex]
-----------
[tex]x = 4y = 4*0.2 = 0.8[/tex]
Patrick did 80% of the project in 20 minutes. We can solve this problem by a simple rule of three, in which the time it would take for him to complete the project alone is 100%. So
20 minutes - 0.8
x minutes - 1
[tex]0.8x = 20[/tex]
[tex]x = 25[/tex]
It would take 25 minutes for Patrick to complete the project alone.
Patrick, who works four times as quickly as Stewart, would take 25 minutes to complete the project alone.
Explanation:This question is about rates and can be solved using algebra. Let's denote the rate at which Stewart can do the work as S and the rate at which Patrick does the work as P. Since Patrick works four times as quickly as Stewart, P=4S. The rate at which they work together is S+P. According to the question, together they can complete the job in 20 minutes, so their combined rate is 1 job per 20 minutes or 1/20. Therefore, S + P = 1/20.
Substitute P=4S into the equation, we get S + 4S = 1/20, which simplifies to 5S = 1/20. Solve this equation, we find that S = 1/100. So Stewart alone would finish the job in 100 minutes. Since Patrick is four times faster, Patrick alone would complete it in 100/4 = 25 minutes.
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Question 9 (5 points)
Lines a, b, and care coplanar. Lines a and b intersect. Line c intersects only with line b. Draw and label a figure
for this relationship.
Answer:
Lines 'a' and 'c' are parallel. Line 'b' is non parallel to 'a' and 'c'.
Step-by-step explanation:
Picture is attached with the answer as a solution to it.
In the question it is give that line 'c' only intersect with line 'b' and not with, so the only way that two lines won't intersect here 'a' and 'c' is that lines are parallel. If the lines are not parallel then those lines will definitely meet.
A football team won 10 matches out of the total number of matches they played if their win percentage was 40 then how many matches did they play in all
Answer:the football team played 25 games in all
Step-by-step explanation:
Let x represent the total number of matches that the football team played.
The football team won 10 matches out of the total number of matches they played. if their win percentage was 40, it means that
10/x × 100 = 40
1000 = 40x
x = 1000/40 = 25
What is the next term of the sequence -3, 6, -12, 24, ...? Que
Answer:
-48
Step-by-step explanation:
Let me know if you need anything
Answer:
-48
Step-by-step explanation:
next in a row is always equal previous one multiple by -2
-3*(-2)=6
6*(-2)=-12
-12*(-2)=24
24*(-2)=-48
Explain how to graph a quadratic equation to someone who does not
know how. Make sure you explain how to find the vertex-
formula to use. You should also teach them how to tell whether the
graph opens up or down and how to find the maximum or minimum
and zeros/solutions.
The term quadratic comes from the word quadrate meaning square or rectangular. Similarly, one of the definitions of the term quadratic is a square. In an algebraic sense, the definition of something quadratic involves the square and no higher power of an unknown quantity; second degree. So, for our purposes, we will be working with quadratic equations which mean that the highest degree we'll be encountering is a square. Normally, we see the standard quadratic equation written as the sum of three terms set equal to zero. Simply, the three terms include one that has an [tex]x^{2}[/tex], one has an x, and one term is "by itself" with no [tex]x^{2}[/tex] or x.
There are 70 students in a school band. 40%are sixth graders,20% are seventh graders and the rest are eighth graders.How many sixth graders are there.
Answer:the number of sixth graders is 28
Step-by-step explanation:
Total number of students in the school band is 70. 40% are sixth graders. 20% are seventh graders and the rest are eighth graders. This means that the percentage of eighth graders is 100 - (40+20) = 100 - 60 = 40%
This means that the number of sixth graders would be 40% of the total number of students in the school band. It becomes
40/100 × 70 = 0.4×70 = 28
Find the probability of rolling a sum less than 6 or a sum greater than 8 when a pair of dice is rolled?
Answer:
[tex]\frac{5}{9}\approx0.556[/tex]
Step-by-step explanation:
A pair of dice is rolled so the outcome space will be.
[tex]S= \{(1,1),(1,2),(1,3),(1,4),(1,5),(1,6)\\(2,1),(2,2),(2,3),(2,4),(2,5),(2,6)\\(3,1),(3,2),(3,3),(3,4),(3,5),(3,6)\\(4,1),(4,2),(4,3),(4,4),(4,5),(4,6)\\(5,1),(5,2),(5,3),(5,4),(5,5),(5,6)\\(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)\}[/tex]
Total number of elements [tex]=36[/tex]
Possible outcomes in which sum is less than [tex]6[/tex] or greater than [tex]8[/tex]
[tex]S_{1} = \{(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3),(3,1),(3,2),(3,6),\\(4,1),(4,5),(4,6),(5,4),(5,5),(5,6),(6,3),(6,4),(6,5),(6,6)\}[/tex]
Number of element in this space [tex]=20[/tex]
P(sum is less than [tex]6[/tex] or greater than [tex]8[/tex])
[tex]=\frac{Favourable\ outcomes}{total\ outcomes} \\=\frac{20}{36}\\ =\frac{5}{9}[/tex]
Virenas Scout troop is trying to raise at least $650 this spring. How many boxes of cookies must they sell at $4.50 per box in order to reach their goal?
Answer:
145
Step-by-step explanation:
To find the number of boxes to reach the goal, divide the goal amount by the box amount:
[tex]650 \div 4.50 \approx144.444444[/tex]
Since you can't sell .444444 of a box, you must sell 145 boxes.
Sally is interested in taking a job in a city which she's not familier with the cost of living. She is especially concerned about the cost of housing and is interested in the average cost of a three bedroom home. Which of the following averages will be most influenced by three bedroom homes owned by millionaires?
a.mode
b.median
c.mean
d.none of the above
Answer:
c.Mean
Step-by-step explanation:
We have been given that the Sally is interested in taking a job in a city in which she's not familiar with the cost of living. She is especially concerned about the cost of housing and is interested in the average cost of a three bedroom home.
We know that in a normal distribution all central tendencies (mean, mode, median) are equal.
When a very large or very small valued data point is added to data set, mean is mostly affected by that outlier.
We know that mode of a data set is the point that appears at-most in the data set, so outliers doesn't affect mode.
Median of a data set is less affected by outliers.
The price of the three bedroom homes owned by millionaires will be greater than prices of houses owned by people in the neighborhood.
Therefore, mean will be most influenced by three bedroom homes owned by millionaires.
Jade took a math test with 20 questions is worth an equal number of points. The test is worth 100 points in total. Write an equation that can be used to calculate jade's score based on the number of questions she got right on the test.
Answer:
[tex]Jade's\,score=5*right\,answers[/tex]
Step-by-step explanation:
Because all the questions have the same point, we can find the weight (value) of each question dividing the total points by the total number of answers questions:
[tex]\frac{100}{20}= 5[/tex]
Now with the weight of each question the only thing we should to do is to multiply it by the number of the questions she got right:
[tex]Jade's\,score=5*right\,answers[/tex]
Let check if our equation works, if Jade got all the answers right, we expect she got a 100 score. Let verify on the equation
[tex]Jade's\,score=5*(20)=100[/tex], that's what we expected
If she got 10 right answers, we expect 50 score and if she got 0 right answers, we expect 0 score, let check again:
[tex]Jade's\,score=5*(10)=50[/tex]
[tex]Jade's\,score=5*(0)=0[/tex]
Again, we obtain the expected scores, so we can conclude our equation works.
To find Jade's score on the math test, calculate the points per question by dividing the total points (100) by the number of questions (20). Each question is worth 5 points. Jade's score is the number of questions she got right multiplied by 5 points.
Explanation:To calculate Jade's score on a math test with 20 questions that is worth a total of 100 points, we can start by finding out how many points each correct answer is worth. Since the total points are evenly distributed among the questions, we divide the total points by the number of questions.
Each question is worth 5 points (100 points total ÷ 20 questions).
Let x represent the number of questions Jade got right. The equation to calculate Jade's score is then:
Score = 5 × x
To find Jade's score, we simply multiply the number of questions she got right by 5. For example, if Jade answered 16 questions correctly, her score would be 80 points (5 points/question × 16 questions).
involving a carnival fishpond. Assume that the pond contains 100 fish: 78 purple, 21 blue, and 1 silver. A contestant pays $0.65 to randomly catch one fish and receives $0.40 if the fish is purple, $0.80 if the fish is blue, and $13.00 if the fish is silver. How much (on average) does the carnival gain on each play?
Answer:
On average the carnival gain on each play
= 0.04 dollars
Step-by-step explanation:
Given that a pond contains 100 fish: 78 purple, 21 blue, and 1 silver.
Fish Purple Blue Silver total
Frequency 78 21 1 100
Prob 0.78 0.21 0.01 1
Revenue 0.4 0.8 13
game fee 0.65 0.65 0.65
Net revenue -0.25 0.15 12.35
Net Rev*Prob -0.195 0.0315 0.1235 -0.04
Thus we get per player expected net revenue is -0.04
This would be gain for Carnival
Hence On average the carnival gain on each play
= 0.04 dollars
Final answer:
To calculate the carnival's average gain per play, determine the expected payoff for each fish type, subtract the cost to play, and sum these amounts. The carnival gains an average of $0.61 per play.
Explanation:
The student's question involves calculating the average gain for a carnival on each play of a carnival fishpond game. To find this, we need to determine what the carnival earns on average based on the probabilities of catching each type of fish (purple, blue, or silver) and the payoff for each.
Let's calculate the expected profit (gain) per play for the carnival. The probability and payoff for each type of fish are:
Purple fish: Probability = 78/100, Payoff = $0.40
Blue fish: Probability = 21/100, Payoff = $0.80
Silver fish: Probability = 1/100, Payoff = $13.00
The expected payoffs for the carnival from catching each type of fish are:
Purple: 78/100 * $0.40
Blue: 21/100 * $0.80
Silver: 1/100 * $13.00
Subtract the contestant's cost ($0.65) from each expected payoff to find the expected gain. Then, sum these expected gains to find the overall average gain for the carnival.
The carnival's expected gain is:
Expected Gain per Play = (78/100 * $0.40) + (21/100 * $0.80) + (1/100 * $13.00) - $0.65
Calculating:
Expected Gain per Play = ($0.3120) + ($0.1680) + ($0.1300) - $0.65
Expected Gain per Play = $0.61
This calculation shows that on average, the carnival gains $0.61 for each play of the fishpond game.
PLEASE HELP ME!!!! I CANT DO THIS!!! WILL GIVE BRAINLIEST!!!!
Divide 27x^3 − 72x^2 + 36x by 9x.
A. 3x^2 − 8x + 4
B. 3x^2 + 8x − 4
C. 3x^3 − 8x + 4
D. 3x^3 + 8x − 4
Susan buys the item listed below at a grocery store. 2 packages of chicken priced at $12.36 per package. 1/2 pound of broccoli priced at $1.98 per pound. 1gallon of milk priced at $3.49 per gallon. There is no sales tax on the food she buys. Susan pays for the items and recevies $0.80 in change. What amount of money does Susan use to pay for the items?
Answer:
Susan payed $30 for her purchase
Step-by-step explanation:
Chicken: $12.36 per package (x2) = $24.72
Broccoli: $1.98 per pound (x1/2) = $0.99 +
Milk: $3.49 per gallon (x1) = $3.49
-and no added sales tax ____________
$29.20
If Susan got $0.80 in return, then she must have payed $30 to begin with.
Answer:
The amount of money that Susan use to pay for the items = $30
Step-by-step explanation:
2×(12.36)+0.5×(1.98)+(3.49)+(0.8) = 30.
:)
The first round of the 2010 FIFA World Cup consisted of several groups of four teams each. Within each group, each of the four teams played each other once. How many matches were there in each group?
Answer:There are 6 matches in each group
Step-by-step explanation:
The first round of the 2010 FIFA World Cup consisted of several groups of four teams each. Within each group, each of the four teams played each other once. Assuming the teams are A, B, C and D.. The way the teams in the group play each other would be
AB, CD first group matches.
AC, BD second group matches.
AD, BC. Third group matches
Therefore, the number of matches in each group would be 6
Help please!! Stuck on this question!! ∠ABC is adjacent to ∠CBD. If the m∠ABC=4x+23, m∠CBD=6x+7, and m∠ABD=130°, what is the measure of angle ABC?
Answer:
63 degrees
Step-by-step explanation:
add 4x + 23 and 6x + 7, then equal that to 130. When you find x, plug it into 4x+23 and get 63.
Leiff goes online to buy a new video game. He finds a site that currently has a promotion of 15% off on all orders over $50. Leiff decides to buy his video game, with a price tag of $128, at this site because he knows that he will get the 15% discount when he checks out. Leiff pays 5.3% sales tax on the discounted price and pays a shipping fee of $4.75. What is the total of Leiff’s online purchase?
Answer:
$119.32
Step-by-step explanation:
Leiff decides to buy his video game, with a price tag of $128, at this site
he will get the 15% discount when he checks out.
100-15= 85%
Discounted price=85% of 128 is [tex]0.85 \cdot 128=108.8[/tex]
Leiff pays 5.3% sales tax on the discounted price
5.3% is 0.053
sales tax amount=0.053 times 108.8=5.7664
So we add the sales tax amount and shipping fee
[tex]108.8+5.7664+4.75=119.32[/tex]
So $119.32 is the total amount
The total of Leiff’s online purchase is $119.31.
To calculate the total of Leiff's online purchase, we need to first calculate the discount on the video game.
The discount is calculated by multiplying the original price of the video game by the discount rate.
Discount = $128 * 15%
= $19.20
The discounted price of the video game is the original price minus the discount.
Discounted price = $128 - $19.20
= $108.80
The sales tax is calculated by multiplying the discounted price of the video game by the sales tax rate.
Sales tax = $108.80 * 5.3%
= $5.76
The total cost of the video game, including the discount and sales tax, is:
Total cost = $108.80 + $5.76
= $114.56
The total cost of Leiff's online purchase is the cost of the video game plus the shipping fee.
Total cost = $114.56 + $4.75
= $119.31
Therefore, the answer is $119.31.
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Graph the inverse of the function.
Answer:
The graph of the inverse function is the same that the graph of the original function
Step-by-step explanation:
step 1
Find the equation of the function in the graph
Let
f(x) ---> the function in the graph
we know that
Is a linear function
take the points (0,6) and (6,0)
Find the slope of the linear function
[tex]m=(0-6)/(6-0)\\m=-1[/tex]
Find the the equation of the linear function in slope intercept form
[tex]f(x)=mx+b[/tex]
we have
[tex]m=-1[/tex]
[tex]b=6[/tex] ---> the y-intercept is given
substitute
[tex]f(x)=-x+6[/tex]
step 2
Find the inverse of the function f(x)
Let
y=f(x)
[tex]y=-x+6[/tex]
Exchange the variables (x for y and y for x)
[tex]x=-y+6[/tex]
Isolate the variable y
[tex]y=-x+6[/tex]
Let
[tex]f^{-1}(x)=y[/tex]
[tex]f^{-1}(x)=-x+6[/tex]
[tex]f^{-1}(x)=f(x)[/tex]
In this problem the graph of the inverse function is the same that the graph of the original function
Graphing the inverse of a function is achieved by flipping the graph over the line y = x. In science, graphs of inversely proportional variables like P and V form a hyperbola, but these can be 'linearized' for clarity and accuracy. Often, a regression analysis is utilized to find the best fitting line within a set of data plots.
Explanation:To graph the inverse of a function, you observe the function as a set of points in a 2D space (on a graph) and flip each point over the line y = x. This results in a new function, which is the inverse. When it comes to more specific functions like pressure and volume relationships, this is shown when plotting the inverse of the pressure (P^-1) versus the volume (V), or the inverse of volume (V^-1) versus the pressure (P).
Scientists often linearize data when graphs have curved lines because they're difficult to read accurately at low or high values. If you plot P (pressure) versus V (volume), you will get a hyperbola. This kind of function can be 'linearized' to make it easier to understand and interpret.
Finally, in many cases, such as plotting data points of inflation rate versus unemployment rate, the resulting graph can be analysed using a statistical process called regression. This helps to find the best fitting line for the set of data plots, which can often not perfectly fit the line.
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What is the proper time sequence of the following three political movements/parties, from earliest to latest?
Answer:
The proper time sequence of the three political parties/movements, from earliest to latest is as follow:
Greenback party, Populist Party, Progressive movement.Step-by-step explanation:
Greenback party is such an American political party with the ideology of against the monopoly. It was founded in 1874 and dissolved in 1889. They worked for the rights of the farmers and workers of industries. They ran three candidates for the presidential elections in their era of political life. Populist Party is such an American party that is also known as People's Party which was founded in 1892 and dissolved in 1908. They fought for anti-corruption and were supporter of state control of railways. The women played a very active role in this party.Progressive Moment is also known as Progressive Era that was ended in 1920. This era demanded the reforms in the political system and gave rise to the social activism. The issues like corruption, industrialization and many such issues came in limelight.Amc "for each $x$" in [0,1], define f(x) = 2x for how many values of x in [0,1] if f 2005 (x) = 1/2?
Answer:
[tex]2^{2005}[/tex]
Step-by-step explanation:
We are given [tex]f^{[2005]}(x) = \frac {1}{2}[/tex].
Hence, [tex]f(f^{[2004]}(x))=\frac{1}{2}[/tex].
Assume [tex]y=f^{[2004]}(x)[/tex].
Hence, [tex]f(y)=\frac{1}{2}[/tex] or [tex]y=\frac{1}{4}[/tex] or [tex]y=\frac{3}{4}[/tex].
So we can conclude that [tex]f^{[2004]}(x)=\frac{1}{4}[/tex] or [tex]f^{[2004]}(x)=\frac{3}{4}[/tex].
So we can find [tex]f(f^{[2003]}(x))=\frac{1}{4}[/tex] orf(f^{[2003]}(x))=\frac{3}{4}.
Assume [tex]z=f^{[2003]}(x)[/tex].
Hence, [tex]f(z)=\frac{1}{8}[/tex] or f(z)=\frac{7}{8} or f(z)=\frac{5}{8} or f(z)=\frac{3}{8}.
Therefore, we double the number of possible solutions for each iteration.
Thus, the number of solutions is [tex]2^{2005}[/tex].
Prove the identity cos x + cos y = 2cos(x+y/2) cos(x-y/2).
a. Show that x+y/2+x-y/2=x
b. Find a similar expression using x+y/2 and x-y/2 that equals y.
C. Use parts (a) and (b) to prove the identity.
Answer:
Step-by-step explanation:
cos(c+d)=cos c cos d-sin c sin d ...(1)
cos(c-d)=cos c cos d+sin c sin d ...(2)
add (1) and (2)
cos (c+d)+cos (c-d) =2 cos c cos d ...(3)
put c+d=x
c-d=y
add
2c=x+y
c=(x+y)/2
subtract
2d=x-y
d=(x-y)/2
substitute in (3)
[tex]cos~ x+cos~ y=2 cos (\frac{x+y}{2}) ~cos (\frac{x-y}{2})[/tex]
To prove the identity cos x + cos y = 2cos((x+y)/2) cos((x-y)/2), we need to show that x+y/2+x-y/2=x and find a similar expression using x+y/2 and x-y/2 that equals y. Once we have these expressions, we can use them to prove the identity.
Explanation:To prove the identity cos x + cos y = 2cos((x+y)/2) cos((x-y)/2), we need to show that x+y/2+x-y/2=x and find a similar expression using x+y/2 and x-y/2 that equals y. Once we have these expressions, we can use them to prove the identity.
To prove x+y/2+x-y/2=x, we can combine like terms by simplifying the expression. Combining x terms, we have x+x=x. Combining y/2 terms, we have y/2-y/2=0. Therefore, the equation is proven.To find a similar expression using x+y/2 and x-y/2 that equals y, we can subtract the two expressions. Subtracting, we have (x+y/2) - (x-y/2) = x - x + y/2 + y/2 = y. Therefore, the expression is x+y/2 - x-y/2 = y.Using parts (a) and (b), we can now prove the identity. Starting with the left-hand side of the identity (cos x + cos y), we can substitute in the expressions we found in parts (a) and (b). The left-hand side becomes 2cos((x+y)/2) cos((x-y)/2), which is equal to the right-hand side of the identity. Therefore, the identity is proven.Learn more about Proving the identity here:https://brainly.com/question/32435277
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Executive Limousine rentals charges an initial fee of $200 and $40 per hour that the limousine is in service. Jet Limousine rentals charges an intial fee of $120 and $50 per hour that the limosine is in service. At how many hours of service do the two limousine rental companies charge the same amount?
At 8 hours of service, the two limousine rental companies charge the same amount.
Step-by-step explanation:
Given,
Initial fee of Executive Limousine rental = $200
Per hour charges of service = $40
Let,
x be the number of hours.
E(x) = 40x+200
Initial fee of Jet Limousine rental = $120
Per hour charges of service = $50
J(x) = 50x + 120
For the charges to be same;
E(x) = J(x)
[tex]40x+200=50x+120\\200-120=50x-40x\\80=10x\\10x=80[/tex]
Dividing both sides by 10
[tex]\frac{10x}{10}=\frac{80}{10}\\x=8[/tex]
At 8 hours of service, the two limousine rental companies charge the same amount.
Keywords: function, addition
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Which system of equations is represented by the matrix below?
Answer:
C
Step-by-step explanation:
The elements of the matrix need to match the coefficients in the equations.
Answer:
c.
Step-by-step explanation:
h
A trough is 8 feet long and has perpendicular cross section in the shape of an isosceles triangle (point down) with base 1 foot and height 2 feet. The trough is being filled with water at a rate of 1 cubic foot every 5 minutes. How fast is the water level rising whenthe water is 1/2 foot deep?
Answer:
Dh/dt = 0.082 ft/min
Step-by-step explanation:
As a perpendicular cross section of the trough is in the shape of an isosceles triangle the trough has a circular cone shape wit base of 1 feet and height h = 2 feet.
The volume of a circular cone is:
V(c) = 1/3 * π*r²*h
Then differentiating on both sides of the equation we get:
DV(c)/dt = 1/3* π*r² * Dh/dt (1)
We know that DV(c) / dt is 1 ft³ / 5 min or 1/5 ft³/min
and we are were asked how fast is the water rising when the water is 1/2 foot deep. We need to know what is the value of r at that moment
By proportion we know
r/h ( at the top of the cone 0,5/ 2) is equal to r/0.5 when water is 1/2 foot deep
Then r/h = 0,5/2 = r/0.5
r = (0,5)*( 0.5) / 2 ⇒ r = 0,125 ft
Then in equation (1) we got
(1/5) / 1/3* π*r² = Dh/dt
Dh/dt = 1/ 5*0.01635
Dh/dt = 0.082 ft/min
Graph the linear equation.
x = - 9
For model 5, the tip of the blade travels 0.18 mile per revolution. What is the approximate speed, in revolutions per minute, for model 5?
Answer:
19 revolutions per minute, for model 5.
Step-by-step explanation:
Consider the model shown below:
From the table:
The blade length for model 5 is 148 feet
Also the maximum blade tip speed is 200 miles per hour.
It is given that the tip of the blade travels 0.18 mile per revolution.
To find the number of revolution per hour simply divide the maximum speed of the blade with the revolution.
Number of revolutions per hour = [tex]\frac{200}{0.18}=1111.111[/tex]
We need to find the speed, in revolutions per minute, so divide the obtained revolution per hour with 60.
[tex]\frac{1111.11}{60} =18.52\approx19[/tex]
Hence, 19 revolutions per minute, for model 5.
Final answer:
To determine the speed in revolutions per minute for model 5, we need to know how far the blade tip travels in one minute. This would be divided by 0.18 miles, the distance per revolution, to find the RPM. Without the distance traveled in one minute, we cannot complete the calculation.
Explanation:
To calculate the approximate speed in revolutions per minute for model 5, where the tip of the blade travels 0.18 miles per revolution, we need to find how many revolutions it would complete in one minute. Assuming the tip travels at a constant speed, you would divide the distance it covers in one minute by the distance per revolution.
First, determine the distance traveled by the blade tip in one minute. Since no speed is given for one minute in the question, we cannot provide a direct answer; more information would be needed, such as the distance the blade tip travels in a given time frame. However, if we had information like this, we could proceed with a calculation:
Let's say the tip travels X miles in one minute. You would then divide X by 0.18 miles to find the number of revolutions per minute:
Revolutions per minute (RPM) = Distance in miles per minute / Distance per revolution
RPM = X miles / 0.18 mile
For example, if the tip travels 1.8 miles in one minute, then:
RPM = 1.8 miles / 0.18 mile = 10 RPM
Thomas Malthus, a political economist, showed that the human population would outstrip available resources unless kept in check by other factors such as famine, war, and disease. How did Charles Darwin apply this principle to his theory of evolution by natural selection?A. Darwin used this as a contrast to plant and animal populations, which live in balance with their available resources.B. Darwin used this to illustrate that because food supply remains relatively the same, plant and animal populations show little variation in size.C. Darwin realized this also applied to plant and animal populations, and this struggle for existence resulted in an opportunity for natural selection to act on differences within populations.D. Darwin used this to illustrate that as food supplies increase, populations increase.
Answer:
C. Darwin realized this also applied to plant and animal populations, and this struggle for existence resulted in an opportunity for natural selection to act on differences within populations.
Step-by-step explanation:
Thomas Malthus in his Malthusian theory of population concluded that since population increases geometrically and resources only increase arithmetically, there will reach a point in time when the resources will be not be able to sufficiently cater for the population.
The Charles Darwin theory of Evolution is based on five key observations and conclusions drawn from them. These observations and inferences are summarized as:
Species are more fertile. They birth more offspring than can grow to adulthood. Populations remain fairly stable with miniscule fluctuations. Food resources are limited, but are relatively constant most of the time.Based off these observations, it is seen that there will be a struggle amongst the members of the specie for the limited resources.
In sexually reproducing species, generally no two individuals are identical. Variation is rampant.Much of this variation is heritable.From the last two observations, the species that survive then pass on their traits to their offspring and the cycle repeats itself with each subsequent generation being better evolved than the previous ones.
Thus, Darwin discovered that the Malthusian theory of population also applies to plant and animal populations where scarcity of resources gives room for natural selection to take place due to the variation within populations.
Carly's family is moving out ,so she needs to pack the dishes .Dishes brake easily so she must wrap them up. She cuts a sheet of bubble wrap into two pieces .What is the fraction ?
1/2, or one half. since she cuts it into 2.
The Vega family has a cell phone plan that costs $75 per month including taxes and fees.The plan lets the 5 members of the Vega family share 1,000 of talk time per month and 400 text messages per month.Any minutes over 1,000 cost $1 per minute,and any texts over 400 cost $2 per text Because of a family emergency,the family uses 1,050 minutes and 415 texts in March.Write an expression you could use to find the amount of the Vega's cell phone bill for March.Evaluate the expression.Show your work.
Answer:the Vega's cell phone bill for March is $155
Step-by-step explanation:
Let x represent the number of talk time in minutes that the family uses for a month.
Let y represent the number of text messages that the family sends in a month.
Let z represent the total cost of using x talk time and sending y text messages in a month.
The cell phone plan costs $75 per month including taxes and fees. Any minutes over 1,000 cost $1 per minute,and any texts over 400 cost $2 per text. This means that the total cost of x minutes and y texts would be
z = 75 + 1(x - 1000) + 2(y - 400)
z = 75 + x - 1000 + 2y - 800
z = 75 - 1000 - 800 + x + 2y
z = x + 2y - 1725
Because of a family emergency,the family uses 1,050 minutes and 415 texts in March. The total cost would be
z = 1050 + 2(415) - 1725
z = 1050 + 830 - 1725 = $155