Answer:
106,218
Step-by-step explanation:
159,327/3= 53,109·2
Answer:
2/3 of 159,327 = 106,218
Step-by-step explanation:
159,327 divided by two thirds is 106,218
HELP!!!!In 2004, school lunch Rockwell high school was $2.20.In 2009 the costs increased to $3.25. Find the annual rate of change in the price for school lunch from 2004 to 2009.
a. $0.20 per year
b. $0.21 per year
c. $1.05 per year
d. $0.18 per year
Answer:
$0.21 per year
Step-by-step explanation:
$0.21 times 5 years equals $1.05
So its $0.21
The annual rate of change is $0.21 per year
Cost of lunch in 2004 = $2.20
Cost of lunch in 2009 = $3.25
Difference in cost = $3.25 - $2.20 = $1.05
Number of years = 2009 - 2004 = 5 years
The annual rate of change will be:
= Difference in cost / Years taken
= $1.05/5
= $0.21 per year.
Therefore, the annual rate of change is $0.21 per year.
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A husband and wife discover that there is a 6% probability of their passing on a hereditary disease to any of their children. If they plan to have three children, what is the probabllity of the event that I6 at least one child wil inherit the disease? The probability is E%. (Round to one decimal place as needed.)
The probability that at least one child will inherit the hereditary disease is approximately 16.9%.
To calculate the probability that at least one child will inherit the hereditary disease, we can use the concept of complementary probabilities.
The probability of the event "at least one child inherits the disease" is equal to 1 minus the probability that none of the children inherit the disease.
The probability that a child does not inherit the disease is 1 minus the probability that they do inherit the disease, which means it is 1 - 0.06 = 0.94.
Since the couple plans to have three children, we multiply the probability of not inheriting the disease for each child:
Probability of none of the children inheriting the disease = 0.94^3 = 0.830584.
Finally, we subtract this value from 1 to get the probability of at least one child inheriting the disease:
Probability of at least one child inheriting the disease = 1 - 0.830584 = 0.169416 or 16.9% (rounded to one decimal place).
Therefore, the probability that at least one child will inherit the hereditary disease is approximately 16.9%.
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find the exact value of cos(A+B) given that sin(A)=-1/2, with angle A in quadrant 4, and sin(B)=1/4, with angle B in quadrant 2
Answer:
cos(A + B) = [tex]\frac{-3\sqrt{5}+1}{8}[/tex]
Step-by-step explanation:
Let us revise some rule of trigonometry
sin²(x) + cos²(x) = 1cos(x + y) = cos(x) cos(y) - sin(x) sin(y)The sign of the trigonometry functions in the four quadrants
In the 1st quadrant: sin(x) and cos(x) are positive valuesIn the 2nd quadrant: sin(x) is positive value, cos(x) is negative valueIn the 3rd quadrant: sin(x) and cos(x) are negative valuesIn the 4th quadrant: sin(x) is negative value, cos(x) is positive valueIn the given question
→ Angle A is in the 4th quadrant
∵ sin(A) = -1/2
→ Use the 1st rule above to find cos(A)
∵ (-1/2)² + cos²(A) = 1
∴ 1/4 + cos²(A) = 1
→ Subtract 1/4 from both sides
∴ cos²(A) = 3/4
→ Take square root for both sides
∴ cos(A) = ±√(3/4)
→ In the 4th quadrant cos is a positive value
∴ cos(A) = (√3)/2
→ Angle B is in the 2nd quadrant
∵ sin(B) = 1/4
→ Use the 1st rule above to find cos(B)
∵ (1/4)² + cos²(B) = 1
∴ 1/16 + cos²(B) = 1
→ Subtract 1/16 from both sides
∴ cos²(B) = 15/16
→ Take square root for both sides
∴ cos(B) = ±√(15/16)
→ In the 2nd quadrant cos is a negative value
∴ cos(B) = (-√15)/4
Let us find the exact value of cos(A + B)
→ By using the 2nd rule above
∵ cos(A + B) = cos(A) cos(B) - sin(A) sin(B)
∴ cos(A + B) = [tex](\frac{\sqrt{3}}{2})(-\frac{\sqrt{15}}{4})-(-\frac{1}{2})(\frac{1}{4}) =-\frac{3\sqrt{5}}{8}+\frac{1}{8}[/tex]
∴ cos(A + B) = [tex]\frac{-3\sqrt{5}+1}{8}[/tex]
Each time any customer enters a coffee shop, there
is a probability of that their order will include a
latte.
3
If the order includes a latte, there is a probability of
3 that it will also include a cookie.
4
If the order does not include a latte, there is a
2
probability of that it will include a cookie.
What is the probability that the next customer to
enter the shop will order a cookie?
The probability that the next customer to enter the shop will order a cookie is given as follows:
31/60.
How to calculate a probability?The parameters that are needed to calculate a probability are listed as follows:
Number of desired outcomes in the context of a problem or experiment.Number of total outcomes in the context of a problem or experiment.Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.
The outcomes in which a cookie is ordered are given as follows:
3/4 of 1/3 -> includes a latte.2/5 of 2/3 -> does not include a latte.Hence the probability is obtained as follows:
3/4 x 1/3 + 2/5 x 2/3 = 1/4 + 4/15 = 15/60 + 16/60 = 31/60.
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5. 37°. If maN = (13x)° what is the value of x and the maN?
The value of x is approximately 2.8462° and the value of maN is 37°.
To find the value of x and maN, we need to use the given information. According to the question, maN is equal to (13x)°.
To solve for x, we can set up an equation:
maN = (13x)°
Now, since we know that maN is equal to 37°, we can substitute this value into the equation:
37° = (13x)°
To isolate x, we divide both sides of the equation by 13:
37° / 13 = (13x)° / 13
This simplifies to:
2.8462° ≈ x°
Therefore, the value of x is approximately 2.8462°.
Now, let's find the value of maN. We already know that maN is equal to (13x)°. Substituting the value of x that we just found, we get:
maN = (13 * 2.8462)°
Simplifying the multiplication:
maN = 37°
So, the value of maN is 37°.
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Choose the expression that is equivalent to both −x/y and x/−y.
Answer:
1÷y/-x
Step-by-step explanation:
1÷y/-x
1×-x/y
-x/y
6(4+x)-1=27-(x+5) can someone help me please, I'm confused
Answer:
X=16
Step-by-step explanation:
Solving for variable 'x'.
Add '-6x' to each side of the equation.
20 + 4x + -6x = -12 + 6x + -6x
Combine like terms: 4x + -6x = -2x
20 + -2x = -12 + 6x + -6x
Combine like terms: 6x + -6x = 0
20 + -2x = -12 + 0
20 + -2x = -12
Add '-20' to each side of the equation.
20 + -20 + -2x = -12 + -20
Combine like terms: 20 + -20 = 0
0 + -2x = -12 + -20
-2x = -12 + -20
Combine like terms: -12 + -20 = -32
-2x = -32
Divide each side by '-2'.
x = 16
Simplifying
x = 16
Help me solve this problem please
Answer:
C. 16
Step-by-step explanation:
y^2-z^2
(-5)^2-(-3)^2
25-9
16
Answer:
Step-by-step explanation:
y = - 5
y^2 = (-5)^2
y^2 = 25
z = - 3
z^2 = (-3)^2
z^2 = 9
y^2 - z^2 = 25 - 9 = 16
6.5x-10=4.5x+6 can someone give a step by step answer plz
Answer:
[tex]\huge{\bold{\boxed{\sf{x = 8 }}}}[/tex]
Step-by-step explanation:
[tex]6.5x - 10 = 4.5x + 6[/tex]
Move 4.5x to left hand side and change its sign.
Similarly, move 10 to right hand side and change its sign.
⇒[tex]6.5x - 4.5x = 6 + 10[/tex]
Subtract 4.5x from 6.5x
⇒[tex]2x = 6 + 10[/tex]
Add the numbers: 6 and 10
⇒[tex]2x = 16[/tex]
Divide both sides by 2
⇒[tex]\frac{2x}{2} = \frac{16}{2}[/tex]
Calculate
⇒[tex]\boxed{\sf{ x = 8 }}[/tex]
Hope I helped!
Best regards!
~[tex]\sf{TheAnimeGirl}[/tex]
Select all the true statements:
A) Two squares with the same side lengths are always congruent
B) Two rectangles with the same side lengths are always congruent
C) Two rhombuses with the same side lengths are always congruent
D) Two parallelograms with the same side lengths are always congruent
E) Two quadrilaterals with the same side lengths are always congruent
Answer:
A and C
Step-by-step explanation:
A) Two squares with the same side lengths are always congruent
C) Two rhombuses with the same side lengths are always congruent.
Two geometric shapes are called congruent if they have the same size and the same shape.
A square has all four sides equal, therefore two squares with the same side lengths are always congruent in all respect (shape and area). Two rhombuses with the same side lengths are always congruent. Two rectangles are congruent if both of them have the opposite sides are equal. Two parallelograms are said to be congruent if all four corresponding sides are equal in length & one corresponding internal angle is equal.Therefore the true statements are A and C.
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Find w = a + bi = [tex]\sqrt{z}[/tex] where a and b are real numbers.
[tex]\sqrt{-7-24i}[/tex]
The calculated values of w are w = -3 + 4i and w = 3 - 4i
How to calculate the value of wFrom the question, we have the following parameters that can be used in our computation:
w = a + bi
Also, we have
[tex]\sqrt{-7 - 24i}[/tex]
This means that
[tex]a + bi = \sqrt{-7 - 24i}[/tex]
Square both sides
So, we have
(a + bi)² = -7 - 24i
Expand the exponent
a² + 2abi - b² = -7 - 24i
When both sides of the equation are compared, we have
a² - b² = -7
2ab = -24
When solved for a and b, we have
a = -3 and b = 4 or a = 3 and b = -4
Recall that
w = a + bi
So, we have
w = -3 + 4i and w = 3 - 4i
Hence, the values of w are w = -3 + 4i and w = 3 - 4i
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Root diameter of a thread is another name of O a. main diameter b. Base diameter O c. minor diameter. Od. Major diameter Clear my choice
The root diameter, also known as the minor diameter, is the smallest diameter of a thread. It is an important dimension in thread design and influences the fit and functionality of threaded connections.
In thread terminology, the root diameter refers to the smallest diameter of a threaded object. It is also known as the minor diameter or the base diameter. The root diameter is measured at the bottom of the thread grooves or valleys, where the threads meet the unthreaded portion of the object.
The minor diameter is an essential parameter in thread design and measurement. It determines the size of the internal thread or the mating external thread that will fit into it. It plays a crucial role in ensuring proper engagement and functionality of threaded connections. The root diameter is typically smaller than the major diameter, which is the largest diameter of the thread. The difference between the major diameter and the minor diameter determines the depth of the thread.
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How many fluid ounces are there in 8 pints 5 cups?
Kyle and his friends had a pie-eating contest. Kyle ate 1/9 of his apple pie. Bobby ate
5/ 6 of his peach pie. Joanie ate 1/3of her blueberry pie. Evie ate 2/3of her cherry pie. How much pie was left?
Answer:
37/18 pie in total, for individual see below
Step-by-step explanation:
kyle has 8/9 apple pie left
bobby has 1/6 of peach pie left
joanie has 2/3 of blueberry pie left
evie has 1/3 of cherry pie left
so in total: 8/9+1/6+2/3+1/3=19/18+1=37/18
Suppose the random variables X1 and X 2 have the covariance matrix 2 1 E - ( 1 4 l with the eigenvalues and corresponding eigenvectors given as follows A1 = 4414, el = (0.383,0.924)T, A2 2 1.586, .22 = (0.924, —0.383)T. (a) [1 marks] Use the above eigenvalues and eigenvectors, write down the singular value decomposition expression for E. (b) [3 marks] Explain how to generate random vectors from the multivariate normal distribution N01, 2), where a = (050)1' and E is given above. (c) [2 marks] Use the following four N (0, 1) random numbers —0.626, 0.184, —0.836, 1.5 to generate 2 random vectors (each has the dimension of 2 X 1) from a N(u, E) with it : (0,0)T. ((1) [2 marks] Calculate the factor loadings if we use only the second eigen value and vector (i.e. 62 and A2 ) to perform Factor Analysis. (c) [2 marks] Hence calculate the corresponding specific variances for the two random variables. (f) [2 marks] Using your answers in (d) and (e) express the random vari— ables X1, X2 in terms of the obtained factor loadings.
a) E = UΣV^T, b) Generate a vector of independent standard normal random variables, z = (z1, z2)^T, c) x1 = μ + E^(1/2)z1, x2 = μ + E^(1/2)z2, d) the factor loading is the square root of 1.586 multiplied by the vector (0.924, -0.383), e) 1 - (0.924^2 * 1.586), f) X1 = μ1 + (factor loading for X1) * F1, X2 = μ2 + (factor loading for X2) * F2.
(a) The singular value decomposition (SVD) expression for the covariance matrix E can be written as: E = UΣV^T, where U is an orthogonal matrix consisting of the eigenvectors of E, Σ is a diagonal matrix with the square roots of the eigenvalues of E on the diagonal, and V^T denotes the transpose of the matrix V.
(b) To generate random vectors from the multivariate normal distribution N(0, E), where a = (0, 0)^T and E is given, you can follow these steps:
1. Compute the matrix square root of E, denoted as E^(1/2), by performing the eigenvalue decomposition of E: E = QΛQ^T, where Q is a matrix of the eigenvectors of E and Λ is a diagonal matrix with the eigenvalues of E on the diagonal.
2. Generate a vector of independent standard normal random variables, z = (z1, z2)^T.
3. Compute the random vector x = μ + E^(1/2)z, where μ is the mean vector (0, 0)^T.
(c) Using the provided N(0, 1) random numbers (-0.626, 0.184, -0.836, 1.5), and assuming these correspond to z1, z2, z3, and z4 respectively:
1. Take the first two values (-0.626 and 0.184) as z1 and z2, and compute the random vector x1 = μ + E^(1/2)z1.
2. Take the next two values (-0.836 and 1.5) as z3 and z4, and compute the random vector x2 = μ + E^(1/2)z2.
(d) When using only the second eigenvalue and eigenvector (A2 and e2) for factor analysis, the factor loadings can be calculated as the square root of the eigenvalue multiplied by the corresponding eigenvector. In this case, the factor loading is the square root of 1.586 multiplied by the vector (0.924, -0.383).
(e) The specific variances for the two random variables can be obtained by subtracting the squared factor loadings from their respective eigenvalues. For the first random variable (X1), the specific variance is 4 - (0.383^2 * 1.586). For the second random variable (X2), the specific variance is 1 - (0.924^2 * 1.586).
(f) The random variables X1 and X2 can be expressed in terms of the obtained factor loadings as:
X1 = μ1 + (factor loading for X1) * F1,
X2 = μ2 + (factor loading for X2) * F2,
where μ1 and μ2 are the means of X1 and X2 respectively, and F1 and F2 are the latent factors associated with X1 and X2, respectively.
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Add.
=
-5+ (-5) = 0
.
- 3 + 6
Answer:
-30
Step-by-step explanation:
-5 + (-5) = -10
-10 times 3 = -30
-3 + 6 = 3
Answer:
Step-by-step explanation:
1 = -10
2= + 3 = 13
Gordon, Henry and Sarah share £48 in a ratio 2:3:1. How much money does each person get?
Answer:
Gordon gets 16£, Henry gets 24£ and Sarah gets 8£
Step-by-step explanation:
Let the ratio be 2x + 3x + 1x
Total amount = £48
So;
2x + 3x + x = 48
6x = 48
x = 48 / 6
x = 8
Now
2x = 16
3x = 24
x = 8
11m — 5 = —60
It's solve for m, please help I'm confused
Answer:
I believe its -5
Step-by-step explanation:
It makes sense lol
Find the HCF of 96 and 108
Step-by-step explanation:
it may help you to understand.
Find the slope and the y-interept of the line
y=-3/2x+6
Answer:
The correct answer is that the slope is 32.
Step-by-step explanation:
Using the slope-intercept form, the slope is 32 .
Identify the slope and y intercept in the equation: y = -x + 5
Answer:
m = -1
y-int (0, 5)
General Formulas and Concepts:
Slope-Intercept Form: y = mx + b
m - slope
b - y-intercept
The y-intercept is the y value when x = 0.
Another way to reword that is when the graph crosses the y-axis.
Step-by-step explanation:
Step 1: Define equation
y = -x + 5
Step 2: Define parts
Slope m = -1
y-intercept = 5
what is the repricol of 2 ???
Answer:
[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
this is because
[tex]2=\frac{2}{1}[/tex]
and the reciprocal of this is [tex]\frac{1}{2}[/tex]
[tex]\frac{2}{1}[/tex] → [tex]\frac{1}{2}[/tex]
∠A=6x+5 ∘ space, start color blueD, angle, A, equals, 6, x, plus, 5, degree, end color blueD \qquad\green{\angle B=4x + 45^\circ}∠B=4x+45 ∘ space, start color green, angle, B, equals, 4, x, plus, 45, degree, end color green Solve for xxx and then find the measure of \blueD{\angle A}∠Astart color blueD, angle, A, end color blueD: \blueD{\angle A} =∠A=start color blueD, angle, A, end color blueD, equals ^\circ ∘ degree Stuck?Watch a video or use a hint.
Answer:
Step-by-step explanation:
Find the required figure in the attachment. From the figure, <A = <B (alternate interior angle)
Given
∠A=6x+5
∠B=4x+45
Since <A = <B hence;
6x+5 = 4x+45
Collect the like terms
6x-4x = 45-5
2x = 40
Divide both sides by 2;
2x/2 = 40/2
x = 20
Hence the value of x is 20°
Next is to get the measure of <A
Since <A = 6x+5
Substitute x = 20° into the expression
<A = 6(20)+6
<A = 120+6
<A = 126°
Hence the measure of <A is 126°
Answer:
125
Step-by-step explanation:
It's right on khan
Ms. Lawrence had $550 in her bank account. Thr next day she withdrew $120 to buy groceries. She deposited $200 two days later. Four days later she used her debit card to buy new shoes that cost $89. What was her bank account balance after these transactions?
Answer:
$541
Step-by-step explanation:
1). $550 - $120 = $430 left in her bank account.
2). $430 + $200 = $630 in her bank account.
3). $630 - $89 = $541 left in her bank account.
(Withdraw means removing some of your money out of your bank account, and deposit means putting money back in your bank account)
So, therefore, after all of those transactions, Ms. Lawrence's bank account has $541.
Hope this helps! <3
Determine two integers whose sum is 6 and whose difference is -2.
A medical screening program administers three independent fitness tests. Of the persons taking the tests. 90% pass test I. 65% pass test II, and 50% pass test III. A participant is chosen at random. (a) What is the probability that she will pass all three tests? (b) What is the probability that she will pass at least two of the three tests? (a) Probability is . (Round to four decimal places as needed.)
a. The probability that she will pass all three tests is 0.2925.
b. The probability that she will pass at least two of the three tests is 0.8150 (rounded to four decimal places).
To calculate the probability of passing all three tests, we need to multiply the probabilities of passing each individual test since the events are independent.
(a) Probability of passing all three tests:
P(passing test I) = 90% = 0.9
P(passing test II) = 65% = 0.65
P(passing test III) = 50% = 0.5
P(passing all three tests) = P(passing test I) * P(passing test II) * P(passing test III)
= 0.9 * 0.65 * 0.5
= 0.2925
Therefore, the probability that she will pass all three tests is 0.2925.
(b) To calculate the probability of passing at least two of the three tests, we can sum up the probabilities of passing exactly two tests and passing all three tests.
Probability of passing exactly two tests:
P(passing two tests) = [P(passing test I) * P(passing test II) * (1 - P(passing test III))] +
[P(passing test I) * (1 - P(passing test II)) * P(passing test III)] +
[(1 - P(passing test I)) * P(passing test II) * P(passing test III)]
P(passing two tests) = [0.9 * 0.65 * (1 - 0.5)] + [0.9 * (1 - 0.65) * 0.5] + [(1 - 0.9) * 0.65 * 0.5]
= 0.2925 + 0.1575 + 0.0725
= 0.5225
Probability of passing all three tests: 0.2925 (calculated in part (a))
P(passing at least two tests) = P(passing two tests) + P(passing all three tests)
= 0.5225 + 0.2925
= 0.8150
Therefore, the probability that she will pass at least two of the three tests is 0.8150 (rounded to four decimal places).
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2) Solve the Equation
Answer:
0
Step-by-step explanation:
I will give you branilest!
This size running track is usually called a 400-meter track. However, if a person ran as close to the "inside" as possible on the track, they would run less than 400 meters in one lap. How far away (in meters) from the inside border would someone have to run to make one lap equal exactly 400 meters?
Solution
The two straightaway sections of the track are each 84.39 meters. The two semi-circular sections can be joined to form a circle whose radius is 36.5 meters and so the diameter of this circle is 2×36.5=73 meters. The circumference of this circle will be π×73 meters and so the total perimeter of the track is
2×84.39+π×73≈398.12.
So the perimeter of the track is less than 400 meters.
For the first lane on the track, the straightaway sections are each 84.39 meters long. However, the curved sections form a circle whose radius is now 36.5+1.22=37.72 meters. The diameter of the circle will be 2×37.72=75.44 meters. So the perimeter of lane 1 is
2×84.39+π×75.44≈405.78.
So the perimeter of lane 1 on the track is more than 400 meters and is almost 8 meters more than the perimeter of the inside of the track.
Suppose we let x denote the distance from the inside of lane 1 which gives a perimeter of 400 meters. This perimeter will be consist of the two straight sections which contribute 2×84.39 meters to the perimeter. In addition, there will be two semi-circular sections of radius 36.5+x meters. Combining these gives a circle whose diameter is 2×(36.5+x) meters. So we want
2×84.39+π×2×(36.5+x)=400.
Rewriting this we find
2π×x=400−2×84.39−2π×36.5
Solving for x we find
x≈0.30.
Note that this value for x is not exact but approximate. It is accurate to within about two ten thousandths of a meter or a fraction of a millimeter. So approximately 30 centimeters from the inside of lane 1 the perimeter of the track is 400 meters.
Approximately 30 meters from the inside border will someone run to make one lap equal exactly 400 meters .
Given,
Track length = 400 meters.
The two straightaway sections of the track are each 84.39 meters. The two semi-circular sections can be joined to form a circle whose radius is 36.5 meters and so the diameter of this circle is 2×36.5=73 meters. The circumference of this circle will be π×73 meters and so the total perimeter of the track is:
2×84.39+π×73≈398.12.
So the perimeter of the track is less than 400 meters.
For the first lane on the track, the straightaway sections are each 84.39 meters long. However, the curved sections form a circle whose radius is now 36.5+1.22=37.72 meters. The diameter of the circle will be 2×37.72=75.44 meters. So the perimeter of lane 1 is
2×84.39+π×75.44≈405.78.
So the perimeter of lane 1 on the track is more than 400 meters and is almost 8 meters more than the perimeter of the inside of the track.
Suppose we let x denote the distance from the inside of lane 1 which gives a perimeter of 400 meters. This perimeter will be consist of the two straight sections which contribute 2×84.39 meters to the perimeter. In addition, there will be two semi-circular sections of radius 36.5+x meters. Combining these gives a circle whose diameter is 2×(36.5+x) meters. So we want
2×84.39+π×2×(36.5+x)=400.
Rewriting this we find
2π×x=400−2×84.39−2π×36.5
Solving for x we find
x≈0.30.
So approximately 30 centimeters from the inside of lane 1 the perimeter of the track is 400 meters.
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Evaluate the expression for x = 2
3x2 -8
23 Evaluate the expression for x = 3
5 - x²
ASAP WILL LITERALLY GIVE U 20 POR
Answer:
the last one is -4 the first one -2 I think
Step-by-step explanation:
im at this level of math
The graph represents a function with the form f(x) = asin(bx + c).
On a coordinate plane, a function has a maximum of 6 and minimum of negative 6. It completes one period at StartFraction 2 pi Over 3 EndFraction. It decreases through the y-axis at (0, 2).
Which values of a, b, and c are possible?
a = 6, b = 1, c = StartFraction pi Over 3 EndFraction
a = 6, b = 3, c = pi
a = 3, b = 1, c = StartFraction pi Over 3 EndFraction
a = 3, b = 6, c = pi
Answer:
a=6, b=3, c=pi
Step-by-step explanation:
Got it right on edge
Using sine function concepts, it is found that possible values for a, b and c are given by:
[tex]a = 6, b = 3, c = \pi[/tex]The standard sine function is given by:
[tex]y = a\sin{(bx + c)}[/tex]
In which:
The amplitude is 2a. The period is [tex]\frac{2\pi}{b}[/tex]. The horizontal shift is c.In this problem:
Maximum of 6 and minimum of negative 6, hence the amplitude is 12, that is, [tex]2a = 12 \rightarrow a = 6[/tex].The period is of [tex]\frac{2\pi}{3}[/tex], hence [tex]\frac{2\pi}{3} = \frac{2\pi}{b} \rightarrow b = 3[/tex].It passes through the y-axis at (0,2), which is one third of the maximum. Considering the shift, we have that [tex]c = \pi[/tex].You can learn more about the sine function at https://brainly.com/question/16818112
