The minimum usual value, μ-2σ is 17.8 and the maximum usual value, μ+2σ is 54.04
How to find the minimum and maximum usual values?From the information, n = 108, p = 0.24
minimum usual value μ-2σ
maximum usual value μ+2σ
Find the mean, μ:
μ = np = 108 × 0.24 = 35.92
Find the variance, n(1-p):
n(1-p) = 108 ×( 1-0.24) = 82.08
Find the standard deviation, σ:
σ = √82.08 = 9.06
minimum usual value, μ-2σ:
μ-2σ = 35.92 - (2×9.06) = 17.8
maximum usual value, μ+2σ:
μ+2σ = 35.92 + (2×9.06) = 54.04
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Can someone explain how to do this? Normally i’d know how to do it but I’m clueless. HELP!!!
The length of unknown side of the triangle will be 18 inch.
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
The two triangles are shown in figure.
Now,
Since, Both the triangle are similar.
Hence, There corresponding sides of the triangle are similar.
So, We get by definition of proportion visit:
⇒ 4 / 12 = 6 / x
⇒ 1/3 = 6/x
⇒ x = 6 × 3
⇒ x = 18 in
Thus, The length of unknown side of the triangle = 18 inch.
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Determine whether the triangles are congruent. If so, name the postulate or theorem that justifies your answer.
By Side - Angle - Side Congruence Rule the given triangles are Congruent
What is SAS Rule of Congruence?
That is stated in the SAS regulation. If two sides and the included angle of one triangle equal two sides and the included angle of another, the triangles are congruent. An included angle is one created by the intersection of two specified sides.
Solution:
By Side - Angle - Side Congruence Rule the given triangles are Congruent
Since, two sides are equal andd the angle included between the sides is equal to
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The mean of a sample is a) Always equal to the mean of the population b) Always smaller than the mean of the population c) Computed by summing the data values and dividing the sum by (n -1) d) Computed by summing all the data values and dividing the sum by the number of items e) None of the above answers is correct. #11 Since the mode is the most frequently occurring data value, it a) Can never be larger than the mean b) Is always larger than the median c) Is always larger than the mearn d) Must have a value of at least two e) None of the above answers is correct. #12. The difference between the largest and the smallest data values is the a) Variance b) Interquartile range c) Range d) Coefficient of variation e) None of the above answers is correct. #18 Let X and Y be independent random variables with Calculate E (X+1) (Y-1) 1 a) 1 b) 9/2 c) 16 d) 17 e) 27 f) None of these
The expected value of X + 1 (Y - 1) can be calculated using the formula E(X + 1)(Y - 1) = E(X)E(Y) + E(X) - E(Y) + 1. Thus, the expected value of X + 1 (Y - 1) = 9/2 * 9/2 + 9/2 - 9/2 + 1 = 17. Therefore, the correct answer is d) 17.
The expected value of X + 1 (Y - 1) is a measure of the average value of the product of two independent random variables, X and Y. To calculate this expected value, we can use the formula E(X + 1)(Y - 1) = E(X)E(Y) + E(X) - E(Y) + 1. Since X and Y are independent random variables, we know that E(X) = E(Y) = 9/2. Plugging this value into the formula, we get E(X + 1)(Y - 1) = 9/2 * 9/2 + 9/2 - 9/2 + 1 = 17. This is the expected value of X + 1 (Y - 1). Therefore, the correct answer is d) 17.
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A market receives the following sell orders. How are they ranked? That is, in whatorder will they be executed (1=first, 2=second, …, 5=last)
The sell order with the fifth lowest price (lowest bid) will be ranked fifth and will be executed last. In this case, the sell order with a price of $14 and a quantity of 10 will be executed last.
1. $10 - 20
2. $11 - 30
3. $12 - 50
4. $13 - 40
5. $14 - 10
1. The sell order with the lowest price (highest bid) is ranked first and will be executed first. In this case, the sell order with a price of $10 and a quantity of 20 will be executed first.
2. The sell order with the second lowest price (second highest bid) will be ranked second and will be executed second. In this case, the sell order with a price of $11 and a quantity of 30 will be executed second.
3. The sell order with the third lowest price (third highest bid) will be ranked third and will be executed third. In this case, the sell order with a price of $12 and a quantity of 50 will be executed third.
4. The sell order with the fourth lowest price (fourth highest bid) will be ranked fourth and will be executed fourth. In this case, the sell order with a price of $13 and a quantity of 40 will be executed fourth.
5. The sell order with the fifth lowest price (lowest bid) will be ranked fifth and will be executed last. In this case, the sell order with a price of $14 and a quantity of 10 will be executed last.
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Jill Paa obtained a $1,450 installment loan to pay for a new laptop computer for her classwork. She agreed to
repay the loan in 18 monthly payments at an APR of 8%.
The monthly payment is $966.76.
What is monthly payment?
The amount paid each month to repay the loan over the course of the loan is known as the monthly payment. When a loan is taken out, not only the principal, or the original lent amount, but also the interest that accrues, must be repaid.
Given the amount of the loan is $1,450.
The number of installment is 18.
The APR of the loan is 8%.
The monthly rate of interest is 8%/12 = 2/3%
The formula of monthly installment is
[tex]M=P[\frac{r}{1-(1+r)^{-n}} ][/tex]
P = principal = 1,450
r = rate of interest = 2/3%
n = number of instalment = 18
[tex]M=1450[\frac{0.67}{1-(1+0.67)^{-n}} ][/tex]
M = 966.76
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What is this question's answer?
The surface area of the figure given which is a rectangular prism is 1362cm²
Surface Area of Rectangular PrismThe total region or area covered by all the faces of a rectangular prism is defined as the surface area of a rectangular prism. A rectangular prism is a three-dimensional shape. It has six faces, and all the faces are rectangular-shaped. Therefore, both the bases of a rectangular prism must also be rectangles.
The surface area of the prism is calculated by the formula
A = 2[(lw) + (lh) + (wh)]
A = Surface areal = length of the prismh = height of prismw = width of prismTo solve this problem, we have to divide the prism into two different parts and solve for the area.
For the first rectangular prism;
h = 14cmw = 14cml = 8cmA = 2[(lw) + (lh) + (wh)]
A = 2[(8 * 14) + (8 * 14) + (14 * 14)]
A = 840cm²
The area of the second figure will be;
l = 8cmh = 17cmw = 5cmA = 2[(8 * 17) + (17 * 5) + (8 * 5)]
A = 552cm²
The total surface area of the figure is 840cm² + 552cm² = 1362cm²
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One sweater + 3 shirts =$37
3 sweaters + 2 shirts =$55. Find the price of one sweater and the price of one shirt
Answer: One sweater: $13 and One shirt: $8
Step-by-step explanation: You have to use elimination. The first formula would be 1x + 3y = 37 and the other is 3x + 2y = 55. Once you use elimination, you just solve a one step equation. When you get x = 13, you plug the 13 into one of the formulas to get 8.
Write the equation of a line passing through (-6,8) and is perpendicular to the line y=x+9 in point slope form and slope intercept form.
The equation of the line in point slope form and slope intercept form are y - 8 = -(x + 6) and y = -x + 2. respectively.
How to represent equation in slope intercept form and point slope form?The equation of a line in slope intercept form is as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, equation of a line passing through (-6,8) and is perpendicular to the line y = x + 9.
Perpendicular lines have slopes that are the opposite of the reciprocal of each other.
Therefore, the slope is - 1.
Hence,
y = -x + b
Using (-6, 8)
8 = -(-6) + b
b = 8 - 6
b = 2
Therefore, the slope intercept form is y = -x + 2.
The equation of the line in point slope form is represented as follows:
y - y₁ = m(x - x₁)
where
m = slope
Using (-6, 8)
Therefore, the equation in point slope form is y - 8 = -(x + 6)
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Write an equation in standard form of the line that contains the point (-2,3) and is parallel to (has the same slope as) the line
y = 4x-1.
Answer:
y=4x+11
Step-by-step explanation:
Solve the problem by finding x. I don’t know how to? Do you.
Answer:
x = e^3 +7
Step-by-step explanation:
ln ( x-7) = 3
To solve for x, raise each side to base e
e ^ ( ln ( x-7) ^= e^3
x-7 = e^3
Add 7 to each side
x-7+7 = e^3 +7
x = e^3 +7
Which of the following are true? 1. If velocity is constant and positive, then distance traveled during a time interval is the velocity multiplied by the length of the interval. 2. If velocity is positive but decreasing, using the velocity at the beginning of each subinterval in a rectangle sum gives an overestimate of the distance traveled. Select one:a. Both 1 and 2 b. Just 1 c. Neither 1 or 2 d. Just 2
According to the statement given, Distance = Velocity X time = V1 X (t2 - t1), but this is the overestimate value
What is velocity?Velocity is the rate at which a moving object's location changes as observed from a specific frame of reference and measured at a specific time standard.
1. Distance = velocity X time
= V X (t2 - t2)
2. According to the statement given,
Distance = Velocity X time
= V1 X (t2 - t1)
but this is the overestimate value, because
Distance = Area under velocity - time curve
therefore, statement 2 is correct
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the questions in this activity refer back to prelab 0, which would be a good place to look if you need any help. in test a, suppose you make 100 experimental measurements of some quantity and then calculate mean, standard deviation, and standard error of the numbers you obtain. in test b, suppose you make 400 experimental measurements of the same quantity and you again calculate mean, standard deviation, and standard error. 1)which of the following statements is the most likely description of the comparison of the standard deviations found in test a and test b ?
For measurements of the same quantity, there won't be a significant difference in the standard deviation.
The standard deviation for Tests A and B is almost the same.
Total quantity in test a = n1 = 100
Total quantity in test b = n2=400
We know that the standard error is defined as: [tex]S E=\frac{\sigma}{\sqrt{n}}[/tex]
where we have, for test A [tex]$$S E_A=\frac{\sigma}{\sqrt{100}}$$[/tex]
and for Test B [tex]$$S E_B=\frac{\sigma}{\sqrt{400}}=\frac{1}{2} * \frac{\sigma}{\sqrt{100}}$$[/tex]
So, from here, we can conclude that,
The standard error in Test A is twice as big as in Test B.
The complete question will be:
Which of the following statements is the most likely description of the comparison of the standard errors found in Test A and Test B?
The standard errors found in Test A and Test B will be about the same.
The standard error found in Test A will about be twice as big as the standard error found in Test B.
The standard error found in Test A will about be four times as big as the standard error found in Test B.
The standard error found in Test B will about be twice as big as the standard error found in Test A.
The standard error found in Test B will about be four times as big as the standard error found in Test A.
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Which of the following are rational numbers? Select three that apply.
[tex] \sqrt{?} [/tex]
[tex] \sqrt{9} [/tex]
[tex] \sqrt{5} [/tex]
[tex] \sqrt{3} [/tex]
[tex] \sqrt{8} [/tex]
[tex] \sqrt{4} [/tex]
The rational numbers are √9, √4, √1. Options A, B and F
What are rational numbers?
A rational number is defined as a number expressed as the ratio of two integers, such that the denominator should not be equal to zero.
These numbers can be expressed as quotients of two integers.
It is a number whose decimal form is finite or recurring in nature.
It is determined by dividing an integer with another integer, an exception is made with zero.
It is important to note the following;
The square roots of perfect squares are rational numbers The square roots of non-perfect squares are not rational numbersFrom the numbers given, the rational numbers are;
√9, √4, √1
Hence, the values are √9, √4, √1
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Please help…
Geometry
The proof that shows that ∠B ≅ ∠D by the CPCTC is explained in the table below.
What is CPCTC?CPCTC is a postulate that stands for "corresponding parts of congruent triangles are congruent". It says that if you prove that two triangles are congruent to each other, then every of their corresponding parts are congruent.
Therefore, the proof below shows how to use CPCTC to prove that ∠B ≅ ∠D.
Statement Reason
1. BC ≅ CD 1. Given
2. AC ≅ EC 2. Given
3. ∠ACB ≅ ∠ECD 3. Vertical angles theorem
4. ΔACB ≅ ΔECD 4. SAS theorem
5. ∠B ≅ ∠D 5. CPCTC
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Consider n independent flips of a coin having probability p of landing on heads. Say that a changeover occurs whenever an outcome differs from the one preceding it. For instance, if n=5 and the outcome is HHTHT, then there are 3 changeovers. Find the expected number of changeovers. Hint: Express the number of changeovers as the sum of n-1 Bernoulli random variables.
The expected number of transitions is 22p(1-p) when take into account n separate coin flips with a p percent chance of landing on heads.
Given that,
Take into account n separate coin flips with a p percent chance of landing on heads. Say a changeover happens any time an outcome diverges from the one that came before it. For instance, there are 3 changeovers if n=5 and the result is HHTHT.
We have to determine the anticipated number of transitions.
We know that,
Independent flips,
n =12
Probability of heads =p
Probability of tails =(1-p)
Let m=1,2,...n
If mth term may be head then (m+1)th outcome could be head or vice-versa.
Probability of change overs from mth to (m+1)th outcome =2p(1-p)
So, the expected changeovers is given by
E[change overs] = (n-1) *2p(1-p)
= (12-1) × 2p(1-p)
=11 × 2p(1-p)
=22p(1-p)
Therefore, the expected number of transitions is 22p(1-p) when take into account n separate coin flips with a p percent chance of landing on heads.
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Suppose you want to purchase a $ 195000 house. If you put 20% down and finance the rest in a 15 year mortgage at an interest rate of 4%, what will your monthly payments be?
Monthly payment
The monthly payment on a principal of $156000 with interest rate of 4% over a time period of 15 years is $1153.91
Monthly PaymentThe monthly payment is the amount paid per month to pay off the loan in the time period of the loan. When a loan is taken out it isn't only the principal amount, or the original amount loaned out, that needs to be repaid, but also the interest that accumulates.
The formula of monthly payment is given as;
A = P [r(1 + r)ⁿ] / [(1 + r)ⁿ - 1]
A = Monthly paymentr = ratep = principaln = number of paymentThe principal of the loan can be calculated as 20 % of 195000
20 / 100 = x / 195000
0.2 = x / 195000
x = 39000
The principal is 195000 - 39000 = 156000
The principal is 156000, rate is 4% and time is 15 year
Substituting the values into the formula
A = 156000[0.04(1 + 0.04)¹⁸⁰] / [(1 + 0.06)¹⁸⁰ - 1]
A = 1153.91
The monthly payment is $ 1,153.91
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Complete the square to solve the equation below.
Check all that apply.
will mark brainliest
x2 + 8x- 5 = 15
A. x=3
B. x=-2
C. x= -10
D. x= 2
Answer:
+2 or –10
Step-by-step explanation:
x² + 8x –5 = 15
x² + 8x = 15 + 5
x² + 8x = 20
using completing the square method
(½(8))² to be applied in both sides
x² + 8x + 16 = 20 + 16
factorise the LHS
(x+4)² = 36
x + 4 = √36
x + 4 = ±6
x = –4±6
x = –4 + 6 or –4–6
x = +2 or –10
pls mark as brainliest
43. Ford Davis borrowed $14,000 of a non-interest-bearing, simple discount, 8% , 90-day note. Assume ordinary interest. What are Ford's proceeds?
A. $14,000
B. $13,720
C. $13,000
D. $17,320
Answer: B. $13,720
Step-by-step explanation: To calculate Ford's proceeds, we need to first find the discount, which is equal to the interest on the loan multiplied by the principal amount of the loan. The interest is 8% of $14,000, or $1,120. The discount is then $1,120 * 90/360, or $310. The proceeds are equal to the principal amount minus the discount, or $14,000 - $310 = $13,720.
Solve for z in the system of equations.
x + y - z = -5
2x - y + z = 8
x - 4y + 3z = 5
Answer:
z = 20
Step-by-step explanation:
Elimination Method:We can use the elimination method in a systems of 3 equations, just as we did when we were solving systems of 2 equations. While the method we apply it is the same, we have to apply it multiple times as elimination gets rid of one variable (usually) and since we're dealing with 3 variables, that still leaves us with 2 variables and we need to cancel once more.
Applying Elimination Method:
We want to develop two linear equations, by applying elimination twice to each equation at least once, and then from there we can apply elimination once more.
Since we're solving for "z", we don't want to immediately cancel it out. So let's use the following two equations:
[tex]x+y-z=-5\\\\x-4y+3z[/tex]
Let's cancel out the "x", by manipulating one equation to be -x. We can do this by multiplying one equation by -1, but remember we have to apply this to both sides of the equation. Let's do it to the top one (you could also do it to the bottom one)
[tex]-1(x+y-z)=-(-5)\implies -x-y+z=5[/tex]
So now let's add the two equations:
[tex]\ \ \ (-x-\ y+\ z)=5\\+(\ \ x-4y + 3z) = 5\\ ------------\\ -5y+4z=10[/tex]
Now let's apply the same thing, but to the middle and bottom equation. Since they don't have the same absolute value coefficients (ignoring the sign) we need to multiple one by a value other than just negative one. So let's multiply the bottom equation by -2 so that the bottom will have a -2x which will cancel when adding it to 2x
[tex]-2(x - 4y + 3z) = -2(5)\\-2x + 8y - 6z = -10[/tex]
Now let's add the equations:
[tex]\ \ \ (\ \ 2x-y+z)=8\\+(-2x + 8y - 6z)=-10\\\\-----------\\7y - 5z = -2[/tex]
So now we have the two equations:
[tex]7y-5z=-2\\-5y+4z=10[/tex]
From here we can apply any method we want, from here I'll use substitution. Since we want to get rid of the "y", let's solve for "y" in terms of z, so once we substitute we have no "y" terms left.
[tex]7y-5z=-2\\7y=5z-2\\y=\frac{5z-2}{7}[/tex]
Now let's plug this into the second two-variable equation we made.
[tex]-5(\frac{5x-2}{7})+4z=10\\\\\frac{-25x+10}{7}+4z=10\\\\\frac{-25}{7}z+\frac{10}{7} + \frac{28}{7}z = \frac{70}{7}\\\\\frac{-25+28}{7}z = \frac{70-10}{7}\\\\\frac{3}{7}z = \frac{60}{7}\\\\z = \frac{60}{7} * \frac{7}{3}\\\\z = 20[/tex]
you are playing blackjack in a casino. the casino is using a single, 52 card deck. shuffling the deck takes time. so rather than shuffling the deck after each hand, the casino deals three hands before shuffling. the used cards are put to the side and not used again until the deck is reshuffled. after two hands, you observe that the following cards have been removed from the deck.
2,2,4,5,6,8,8,10,J,J (ten cards total)
What is the probability that you will be dealt a blackjack on the next hand?
The probability of being dealt a blackjack on the next hand is 4.8%. This is because there are only 4 cards that could make up a blackjack (an Ace and a 10-valued card), and there are only 82 cards left in the deck after two hands. Therefore, the probability of being dealt a blackjack is 4/82, or 4.8%.
The probability of being dealt a blackjack on the next hand is 4.8%. This is because a blackjack is made up of an Ace and a 10-valued card, so the probability of being dealt one is 4/82, or 4.8%. This is because after two hands, there are only 82 cards left in the deck. Of those 82 cards, there are only 4 that can make up a blackjack. Therefore, the probability of being dealt a blackjack is 4/82, or 4.8%. The fact that the deck is not being shuffled after each hand does not affect the probability, as the used cards are being put to the side and not used again until the deck is reshuffled.
Probability of blackjack = (number of cards that can make a blackjack / total number of cards remaining in the deck)
Probability of blackjack
= (4 / 82)
Probability of blackjack
= 4.8%
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Assume that the probability that there is a significant accident in a nuclear power plant during one year’s time is .001. If a country has 100 nuclear plants, estimate the probability that there is at least one such accident during a given year.
please help with explantion
The estimate probability that there is at least one such accident during a given year, P(X≥1) is equals to the 0.0952..
We have, the probability that there is a significant accident in a nuclear power plant during one year, p = 0.01
Total nuclear plants in country , n = 100
we have to calculate probability that there is at least one such accident during a given year.
Using Binomial Probability distribution,
X ~ Bin( 100, 0.01)
P(X= x ) = ⁿCₓ(p)ˣ (1-p)⁽ⁿ⁻ˣ⁾
Thus, the probability that there is at least one such accident during a given year, P(X≥1)
= 1 - P(there is no such event, P(X= 0)
= 1 - P(X= r ) = 1 - ⁿCᵣpʳ(1-p )⁽ⁿ⁻ʳ⁾
where p is probability of success
r = 0 , n = 100, p = 0.001
plugging all known values in above formula,
P(X≥ 1) = 1 - ¹⁰⁰C₀ (0.001)⁰(1- 0.001)⁽¹⁰⁰⁻⁰⁾
= 1 - ¹⁰⁰C₀ (0.001)⁰(0.999)¹⁰⁰
= 1 - 1 ×1 ×0.904792
=1 - 0.904792
=0.0952
Hence, required probability is 0.0952.
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i need help with this problem
The weight of a medium-sized orange selected at random from a large bin of oranges at a local supermarket is a random variable with mean μ = 12 ounces and standard deviation σ = 1.2 ounces. Suppose we independently select two oranges at random from the bin. The difference in the weights of the two oranges (the weight of the first orange minus the weight of the second orange) is a random variable with a standard deviation equal to
The standard deviation of the difference in the weights of the two oranges is equal to sqrt(1.2^2 + 1.2^2) = 1.7 ounces.
What do you mean by standard deviation?
The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
The standard deviation of the difference in the weights of the two oranges is equal to the square root of the sum of the squares of the standard deviations of the two oranges. This is because the weights of the two oranges are independent random variables.
Therefore, the standard deviation of the difference in the weights of the two oranges is equal to sqrt(1.2^2 + 1.2^2) = 1.7 ounces.
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PLEASE HELP WILL MARK BRAINLIEST
Answer: [tex]\cos P=r/q[/tex]
Step-by-step explanation:
Cosine is defined as adjacent/hypotenuse.
In relation to [tex]\angle P[/tex], the adjacent side is [tex]r[/tex] and the hypotenuse is [tex]q[/tex].
So, [tex]\cos P=r/q[/tex].
the table compares the average daily temperature and ice cream sales each day using technology, determine the line of fit, where x represents the average daily temperatures and y represents the total icecream sales. round values to the nearest tenth
Answer:
representa 48
Step-by-step explanation:
Real numbers a and b satisfy the equations 3ª = 815+2 and 125=5ª-3. What is ab?
(A) -60
(B)-17
(C) 9
(D) 12
(E) 60
By solving a simultaneous linear equation, it can be calculated that-
Value of ab = 60
What is simultaneous linear equation?
At first it is important to know about linear equation
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Here, a simultaneous linear equation needs to be solved
[tex]3^a = 81^{b+2}[/tex] and [tex]125^b = 5^{a-3}[/tex]
[tex]3^a = 3^{4(b+2)}[/tex]
a = 4(b + 2)
a = 4b + 8
a - 4b = 8 ... (1)
[tex]125^b = 5^{a-3}\\5^{3b} = 5^{a-3}\\[/tex]
3b = a - 3
a - 3b = 3 .... (2)
Subtracting (1) from (2)
b = -5
Putting the value of b in (2)
a - 3(-5) = 3
a + 15 = 3
a = 3 - 15
a = -12
Value of ab = (-12) [tex]\times[/tex](-5) = 60
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a bag of mixed peanuts and cashews contains pounds of peanuts that cost per pound and pound of cashews that cost per pound
The number of pounds of peanuts needed is 29.167.
Multiply the number of pounds of each type and multiply by the cost per pound to get the total cost of that part contribution to the total. Add them together and set it equal to the final total pounds (50) multiplied by its cost per pound ($2.90)
There are 5 pounds of mixed nuts.
let x = pounds of peanuts
cost of each pound of peanuts is $1.50
45 - x = pounds of cashews
Cost of each pound of cashew is $4.50
This way total pounds = 50
5 pounds($6) + x pounds ($1.50) + (45-x)pounds($4.50) = 50 pounds($2.90)
30 + 1.50x + 202.5 - 4.50x = 145
-3x = -87.5
x = 29.167
Therefore, the number of pounds of peanuts needed is 29.167.
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Disclaimer
The question given by you is incomplete, the abouve asnwer is done as per a similar question, the question is
A merchant has 5 pounds of mixed nuts that cost $30. he wants to add peanuts that cost $1.50 per pound and cashews that cost $4.50 per pound to obtain 50 pounds of a mixture that costs $2.90 per pound. how many pounds of peanuts are needed?
use the formulas for lowering powers to rewrite the expression in terms of the first power of cosine, as in example 4. cos4(x) sin2(x)
The expression in terms of first power of cosine cos4x*sin2x = 1/16 + cos(2x)/16 - cos(4x)/16 - cos(4x)cos(2x)/16.
How to lower the power of expression in trigonometry?
The cosecant and cotangent functions, which exist in the numerator and denominator, can be used to simplify a trigonometric statement by writing it in terms of the sine and cosine functions.sin2x+cos2x = 1 and cos2x = (1+cos(2x))/2
Using the first identity, we have sin2x = 1-cos2x.
So we have that cos4x*sin2x = cos4x(1-cos2x)
Expanding, we have cos4x-cos6x.
Since cos2x= (1+cos(2x))/2, this implies cos4x = ((1+cos(2x))/2)² and cos6x=((1+cos(2x))/2)³.
Expanding each one, we have
cos4x - cos6x = 1/4(1+2cos(2x) + cos2(2x)) - 1/8(1+3cos(2x) + 3cos2(2x) + cos3(2x)).
Simplifying we get
cos4x - cos6x = 1/8 + 1/8(cos(2x) - cos2(2x) - cos3(2x)).
cos2(2x) = 1/2(1+cos(4x)) and cos3(2x)
= cos2(2x)*cos(2x)
= 1/2(1+cos(4x)) * cos(2x)
= 1/2(cos(2x) + cos(4x)*cos(2x))
Substituting, we get
cos4x - cos6x = 1/8 + 1/8(cos(2x) - 1/2(1+cos(4x)) - 1/2(cos(2x) + cos(4x)*cos(2x)))
Cleaning it up, we get
cos4x*sin2x = 1/16 + cos(2x)/16 - cos(4x)/16 - cos(4x)cos(2x)/16.
Hence, The expression in terms of first power of cosine cos4x*sin2x = 1/16 + cos(2x)/16 - cos(4x)/16 - cos(4x)cos(2x)/16.
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rearrange the formula to make x the subject 4(x-3)/a=y
Answer:
x=3+ay/4a
Step-by-step explanation:
4(x-3)/a=y
a*4(x-3)/a=a*y
4a(x-3)=ay
4a(x-3)/4a=ay/4a
x-3=ay/4a
x-3+3=3+ay/4a
x=3+ay/4a
If f(x)=3x²-1 and g(x)=x+2, find (f+g)(x).
A. 4x² +1
B. 3x²+x+1
C. 3x²+x-1
D. 3x³ -2
The addition of function f(x) = 3 · x² - 1 and function g(x) = x + 2 is equal to (f + g)(x) = 3 · x² + x + 1. (Correct choice: B)
How to find the resulting expression of the addition of two functions
New functions can be created by combining functions, the most common operations are listed below:
AdditionSubtractionMultiplicationDivisionCompositionIn this problem we must determine the expression that is the result of the addition of two functions, whose definition is shown below:
(f + g) (x) = f(x) + g(x)
First, use the definition of the addition of two functions:
(f + g)(x) = (3 · x² - 1) + (x + 2)
Second, simplify the algebraic expression:
(f + g)(x) = 3 · x² + x + 1
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