The y-intercept of the sine function with an amplitude of 3, a period of π, and a phase shift of π/2 is 0.
The general form of a sine function is y = A×sin(Bx - C) + D, where A represents the amplitude, B determines the period, C is the phase shift, and D is the vertical shift.
In this case, the given amplitude is 3, indicating that the maximum value of the function is 3 and the minimum value is -3.
The period is π, which means the function completes one full cycle in π units of x.
The phase shift is π/2 period, which shifts the graph to the right by π/2 units.
Since the y-intercept is the point where the graph intersects the y-axis (x = 0), and the sine function passes through the origin (0, 0), the y-intercept is 0.
Therefore, the y-intercept of the given sine function is 0.
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The U.S.A. Olympic Synchronized Swimming Team is designing a routine for their upcoming competition. From the center of the pool, they moved 2 feet to the right and 4 feet up to create the center of their formation (Point C). From the center of their formation, they then formed a circle that goes through a point 3 feet to the left and 4 feet up (Point D). What is the equation of the circle?
Answer:
The equation of the circle is;
(x - 2)² + (y - 4)² = 5²
Step-by-step explanation:
We note that the general equation of a circle is given as follows;
(x - h)² + (y - k)² = r²
Where;
(h, k) = The coordinates of the center of the circle
r = The radius of the circle
The given parameters are;
The location of the center of the pool to the center of their formation = 2 feet to the right and 4 feet up from the center of the pool
The point through which the circle which they form goes through = A point 3 feet to the left and 4 feet up from the center of their formation
Taking the center of the pool as the origin of the coordinate plane system, we have;
The coordinate of the center of the circle = The coordinate of their motion from the center of the circle
∴ The coordinate of the center of the circle = (2, 4)
∴ (h, k) = (2, 4)
h = 2, k = 4
The coordinate of the point through which the circle passes = (2 - 3, 4 + 4) = (-1, 8)
∴ The length of the radius, 'r', can be found as, r = √((-3)² + 4²) = 5 or r = √((-1 - 2)² + (8 - 4)²) = 5
r = 5
The equation of the circle is therefore presented by substituting the values of 'h', 'k', and 'r', as follows;
(x - 2)² + (y - 4)² = 5².
which angle pair represents corresponding angles?
options on picture
Answer: b
Step-by-step : not needed
The discrete-time system is described by yik-11 + 2y[k] = Fiki, with fiki = [k] and y(0) = 0. Solve the above equation iteratively to determine yll] and y[2] values.
Value of y[1] = 0.5 and y[2] = 0.5.
The given discrete-time system is:
y[k-1] + 2y[k] = [k]with y(0) = 0.
Substituting k = 0 in the above equation:
y[-1] + 2y[0] = [0] y[-1] = 0
Substituting k = 1 in the given equation:
y[0] + 2y[1] = [1]
Substituting the value of y[0] from the above equation in this equation, we get:
2y[1] = [1] - y[0]
Substituting the value of y[0] = 0 in the above equation:
2y[1] = [1]y[1] = [1]/2 = 0.5
Substituting k = 2 in the given equation:
y[1] + 2y[2] = [2]
Substituting the value of y[1] from the above equation in this equation, we get:
2y[2] = [2] - y[1]
Substituting the value of y[1] = 0.5 in the above equation:
2y[2] = [2] - 0.5y[2] = [2]/2 - 0.5 = 0.5
Therefore, y[1] = 0.5 and y[2] = 0.5.
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WXYZ is a parallelogram. Find the measure of angle Z
Given:
The figure of a parallelogram.
To find:
The measure of angle Z.
Solution:
We know that, the consecutive interior angles of a parallelogram are supplementary angles, it means there sum is 180 degrees.
In the given figure angle W and angle Z are supplementary angle. So,
[tex]m\angle W+m\angle Z=180^\circ[/tex]
[tex](18b-11)^\circ+(9b+2)^\circ=180^\circ[/tex]
[tex](27b-9)^\circ=180^\circ[/tex]
[tex](27b-9)=180[/tex]
Adding 9 on both sides, we get
[tex]27b=180+9[/tex]
[tex]27b=189[/tex]
[tex]b=\dfrac{189}{27}[/tex]
[tex]b=7[/tex]
Now,
[tex]m\angle Z=(9b+2)^\circ[/tex]
[tex]m\angle Z=(9(7)+2)^\circ[/tex]
[tex]m\angle Z=(63+2)^\circ[/tex]
[tex]m\angle Z=65^\circ[/tex]
Therefore, the correct option is C.
What is the product of 2b(b+11)? Show your work.
Answer:
25
Step-by-step explanation:
Answer:
2b^2 + 22
Step-by-step explanation:
2b(b + 11)
2b ×b + 2 × 11
2b^2 + 22
Someone please help me.
Felipe's age is ≥ 5
Step-by-step explanation:
Difference of F's age and 4: f - 4
Twice: 2 (f -4) ≥ 2
2f - 8 ≥ 2
2f ≥ 10
f ≥ 5
Answer:
Step-by-step explanation:
Billy made 2 gallons of juice for a picnic. He said that he made
2
4
quarts of juice.
Answer:
2/4 quarts of juice is 0.125 Gallons of juice for
Step-by-step explanation:
Please Give Brainliest
Answer:
He divided instead of using multiplication
Step-by-step explanation:
PLSS HELPPP NO BOTS OR I WILL REPORT BUT PLS HELP ASAPP!! The graphs below of a function true or false?
Does anyone know about this question I give brainless If you answer this correctly
Answer:
Side x = 2.12132 = 3√2/2
Step-by-step explanation:
I used a triangle calculator to find side x
What additional information could be used to prove that the triangles are congruent using AAS or ASA? Check all that apply. B ≅ P and BC ≅ PQ A ≅ T and AC = TQ = 3. 2cm A ≅ T and B ≅ P A ≅ T and BC ≅ PQ AC = TQ = 3. 2 cm and CB = QP = 2. 2 cm
Based on the given options, the additional information that could be used to prove congruence using AAS or ASA is:
Option 1: B ≅ P and BC ≅ PQ
To prove that two triangles are congruent using AAS (Angle-Angle-Side) or ASA (Angle-Side-Angle) postulates, we need specific conditions met. Let's examine the given options:
1. B ≅ P and BC ≅ PQ:
This condition satisfies the AAS postulate since we have two angles and a corresponding side that are congruent.
2. A ≅ T and AC = TQ = 3.2 cm:
This condition satisfies the ASA postulate since we have two angles and the included side that are congruent.
3. A ≅ T and B ≅ P:
This condition alone does not satisfy either the AAS or ASA postulate, as we need to have at least one side congruent or an included side congruent to prove congruence.
4. AC = TQ = 3.2 cm and CB = QP = 2.2 cm:
This condition alone does not satisfy either the AAS or ASA postulate, as we need to have congruent angles as well.
Based on the given options, the additional information that could be used to prove congruence using AAS or ASA is:
- Option 1: B ≅ P and BC ≅ PQ
This satisfies the AAS postulate, and with the given information, we can conclude that the triangles are congruent.
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(a) Calculate sinh (log(6) - log(5)) exactly, i.e. without using a calculator Answer: (b) Calculate sin(arccos(76)) exactly, i.e. without using a calculator.
(a) The exact value of sinh(log(6) - log(5)) is 11/60.
To calculate sinh(log(6) - log(5)), we can use the identity: sinh(x) = ([tex]a^n[/tex] - [tex]e^-x[/tex])/2
So, substituting x = log(6) - log(5), we get:
sinh(log(6) - log(5)) = ([tex]e^(log(6)[/tex] - log(5)) - [tex]e^-(log(6)[/tex] - log(5)))/2
= (([tex]e^log(6)[/tex])/([tex]e^log(5)[/tex]) - ([tex]e^-log(6)[/tex])/([tex]e^-log(5)[/tex]))/2
= ((6/5) - (5/6))/2
= (36/30 - 25/30)/2
= 11/60
Therefore, sinh(log(6) - log(5)) = 11/60.
(b) The exact value of sin(arccos(76)) is undefined.
To calculate sin(arccos(76)) exactly, we can use the Pythagorean identity [tex]sin^2[/tex](x) + [tex]cos^2[/tex](x) = 1.
Let's assume arccos(76) = x. Applying the cosine function to both sides, we have cos(arccos(76)) = cos(x).
Since arccos and cosine are inverse functions, cos(arccos(76)) simplifies to 76.
Now, using the Pythagorean identity, we can calculate sin(x):
sin(x) = sqrt(1 - [tex]cos^2[/tex](x)) = sqrt(1 - 76^2) = sqrt(1 - 5776) = sqrt(-5775).
The square root of -5775 is an imaginary number, which cannot be expressed exactly without using complex numbers or numerical methods.
Therefore, the exact value of sin(arccos(76)) cannot be determined without using a calculator or numerical methods.
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Yezenia is filling up her outdoor swimming pool to get ready for summer time. She leaves the garden hose running for 1000 minutes in order to fill the pool, which has a volume of 15,460 gallons. What is the approximate rate at which water leaves the garden hose?
Answer:
15.46 gallons per minutes
Step-by-step explanation:
Garden hose was running for 1000 minutes
Volume of the pool = 15,460 gallons
What is the approximate rate at which water leaves the garden hose?
Rate at which water leaves the garden hose = Volume of the pool / running time of the hose
= 15,460 gallons / 1000 minutes
= 15.46 gallons per minutes
Rate at which water leaves the garden hose = 15.46 gallons per minutes
the price of a jacket was reduced from $50 to $30. by what percentage was the price of the jacket reduced?
Answer:
the jacket price was reduced by 40%.
Step-by-step explanation:
if $50 is 100% then every one dollar is 2%.
Percentage of the reduction of price of the jacket is 40%.
What is Percentage?Percentage is defined as the parts of a number per fraction of 100.
Percentage is usually denoted by the symbol '%'.
We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number.
Given that,
Original price of the jacket = $50
Let x be the percentage of reduction of the price of the jacket.
50 - (x × 50) = 30
50x = 50 - 30
50x = 20
x = 20 / 50
x = 0.4
Percentage = 0.4 × 100 = 40%
Hence the percentage reduction is 40%.
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A grain silo is built from two right circular cones and a right circular cylinder with internal measurements represented by the figure below. Of the following, which is closest to the volume of the grain silo, in cubic feet?
A) 261.8
B) 785.4
C) 916.3
D) 1047.2
Answer:
A. 261.8
Step-by-step explanation:
espero ayudar sorry
residents of the town smithfield like to consume pizzas, but each pizza requires 10 people to produce it and takes a month. if the town has a total of 100 people, what is the maximum amount of pizza the residents can consume in a year?
The number of pizzas the people of the town will produce in a year, obtained using the simple mathematical operations, is 120 pizzas.
What are mathematical operations?Mathematical operations include operations of additions, subtraction, division, and multiplication.
The number of pizzas produced in a year can be obtained using mathematical operations as follows;
The number of people required to produce one pizza in a month = 10 people
The number of people in the town = 100 people
The number of pizza'a that the people in the town can produce in a month is therefore;
Number of pizza's produced in a month = 100/10 = 10
The number of months in a year = 12 months
The number of pizzas the people in the town can produce in a year = 10 × 12 = 120 pizzas
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Find the perimeter of a square with a side length of 10 meters
side length of square=10
Now,
perimeter of square =4l
=4×10
=40m
EASY POINTS!!
PLS ADD A DISC!!
All interior angle degrees must add up to 180 degrees.
the little square means that it is a right angle (90 degrees)
30 + 90 = 120
Y = 60
8-2(4×3-5)
does this equal -4?
Answer:
-6
Step-by-step explanation:
Answer:
No -6
Step-by-step explanation:
Find a85 of the sequence 4,9,14,19,….
Answer: 424
Step-by-step explanation:
How is the dispersion of a Normal distribution compare to the dispersion of a T - distribution, Normal Distribution is more dispersed than the T distribution Normal Distribution is less dispersed than the T distribution Normal Distribution is dispersed in the same way as the T distribution
The dispersion of a Normal distribution is less dispersed than the T-distribution.
The dispersion of a distribution is measured by the standard deviation (or variance) of the distribution.
For a Normal distribution, the standard deviation is always known.
On the other hand, for a t-distribution, the standard deviation of the population is not known and is estimated using the sample standard deviation.
This means that the t-distribution has more uncertainty, which leads to more dispersion compared to the Normal distribution.
The t-distribution is often used when the sample size is small or when the population standard deviation is unknown. As the sample size increases, the t-distribution approaches the Normal distribution.
Therefore, for large sample sizes, both distributions become more or less similar.
In conclusion, the Normal distribution is less dispersed than the t-distribution.
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LOOK RIGHT HERE! HELP FASSST EMERGENCY! Don't go past go to this question right here and no Decimal answers plz. Thanks the answer is not 144 BTW. Thank you.
Answer: 140cm^3
Step-by-step explanation:
Paola wants to measure the following dependent variable: happiness. How could you measure happiness in a way:
a) physiological?
b) observation?
c) self-report? Search for a scale that already exists.
What is the scale called? :
APA citation:_____
1. She would use Facial electromyography
2. She would use smiling
3. She would use Subjective Happiness Scale
How do you measure happiness?It is common practice to evaluate subjective experiences, including happiness, using self-report measures. The Subjective Happiness Scale (SHS) is a popular tool for gauging happiness.
The SHS is a self-report survey that asks participants to rate how much they agree with statements about their personal experiences of happiness. It consists of four things and is frequently utilized in studies.
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Find the sum of all the two-digit numbers that divide 170 with a remainder of 5.
WILL MARK BRAINLIEST IF ITS RIGHT!!! PLEASE HELLPP!!!!!
Answer:
114
Step-by-step explanation:
To find - Find the sum of all the two-digit numbers that divide 170 with a remainder of 5.
Proof -
The 2 digit number is 11
170 = 11(15) + 5
The two digit number is 15
170 = 15(11) + 5
The two digit number is 33
170 = 33(5) + 5
The two digit number is 55
170 = 55(3) + 5
∴ we get
The two digit numbers are
11, 15, 33, 55
Their sum is equals to
11 + 15 + 33 + 55 = 114
Determine the integral of 8 (3x − 2)³ dx
The integral of 8(3x - 2)³ dx is 2(3x - 2)⁴ + C, where C is the constant of integration.
To find the integral of 8(3x - 2)³ dx, we can apply the power rule of integration. According to the power rule, the integral of xⁿ dx is (xⁿ⁺¹ / (n + 1)) + C, where n is a constant and C is the constant of integration.
In this case, we have (3x - 2)³ as the integrand. We can rewrite it as 8(3x - 2)³ to simplify the expression. Since 8 is a constant multiplier, it can be factored out of the integral.
Using the power rule, we integrate each term separately. The integral of (3x - 2)³ is [(3x - 2)⁴ / 4] + C, where C is the constant of integration. Multiplying by the constant 8, we get 8[(3x - 2)⁴ / 4] + C.
Simplifying further, we can simplify the expression to 2(3x - 2)⁴ + C, where C is the constant of integration.
Therefore, the integral of 8(3x - 2)³ dx is 2(3x - 2)⁴ + C.
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The lifetime of an electronical component is to be determined; it is assumed that it is an ex- ponentially distributed random variable. Randomly, users are asked for feedback for when the component had to be replaced; below you can find a sample of 5 such answers (in months): 19,23,21,22,24.
Fill in the blanks below.
(a) Using the method of maximum likelyhood, the parameter of this distribution is estimated to λ = ________WRITE YOUR ANSWER WITH THREE DECIMAL PLACES .
(b) Let L be the estimator for the parameter of this distribution obtained by the method of moments (above), and let H be the estimator for the parameter of this distribution obtained by the method of maximum likelyhood. What comparison relation do we have between L and M in this situation? Use one of the symbols
< = or > to fill in the blank. L ________M
(a) Using the method of maximum likelihood, the estimated parameter of the exponential distribution is λ = 0.050.
(b) Comparing the estimators obtained by the method of moments (L) and the method of maximum likelihood (M), we have L < M.
(a) The maximum likelihood estimation involves finding the parameter that maximizes the likelihood function based on the given data. In this case, using the sample of replacement times (19, 23, 21, 22, 24), the estimated parameter λ of the exponential distribution is calculated to be 0.050.
(b) Comparing the estimators obtained by the method of moments (L) and the method of maximum likelihood (M), we can determine the relationship between them. In general, the method of maximum likelihood tends to provide more efficient and precise estimators compared to the method of moments. Therefore, we have L < M, indicating that the estimator obtained by the method of maximum likelihood (M) is expected to be greater than the estimator obtained by the method of moments (L) in this situation.
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Mhanifa can you please help? This is due soon. Look at the picture attached. I will mark brainliest!
Answer:
84° 125°Step-by-step explanation:
Sum of the interior angles of a regular polygon:
S(n) = 180°(n - 2), where n- number of sidesExercise 4Pentagon has sum of angles:
S(5) = 180°(5 - 2) = 540°Sum the given angles and find x:
x° + 122° + 100° + 90° + 144° = 540°x° + 456° = 540°x° = 540° - 456°x° = 84°Exercise 5Hexagon has sum of angles:
S(6) = 180°(6 - 2) = 720°Sum the given angles and find x:
x° + 110° + 160° + 105° + 105° + 115° = 720°x° + 595° = 720°x° = 720° - 595°x° = 125°Solve for z.
x + y + z = 4
4x - y - z = 1
x + z = 2
Answer:
z= 4-x-y
z= -1+4x-y
z= 2-x
Step-by-step explanation:
z = 2-x
y = -1-z +4x
substitute
x -1 -2+x +4x + 2 -x = 4
-1 + 5x = 4
5x = 5
x = 1
z = 1
1+y+1 = 4
y = 2
hlp help help plsssssssssssss
Answer:
A
Step-by-step explanation:
Think about the square root of 64, which is 8. It will only be slightly higher than 8, which will not even be .5, so 8 is the closest number.
payment stream consists of three payments: $2,500 due today, $3,000 due 100 days from today, and $3,500 due 240 days from today. What single payment, 80 days from today, is economically equivalent to the payment stream if money can be invested at a rate of 5%? (Use 365 days a year. Do not round intermediate calculations and round your final answer to 2 decimal places.)
To find out the single payment that is economically equivalent to the payment stream of $2,500 due today, $3,000 due 100 days from today, and $3,500 due 240 days from today, we have to follow the below-given steps:
Step 1: Calculate the Future Value (FV) of each payment. Let's assume that "P" is the single payment we need to find out and "i" is the annual interest rate (5%)P = FV × [1 / (1 + i/365)^n] where n is the number of days between today and the payment date. For the first payment of $2,500 that is due today, the future value is $2,500 because it is already available today. Hence, no calculation is required for it. For the second payment of $3,000 that is due 100 days from today, Future Value (FV) = $3,000 × [1+(0.05/365)]^100 ≈ $3,093.29For the third payment of $3,500 that is due 240 days from today, Future Value (FV) = $3,500 × [1+(0.05/365)]^240 ≈ $3,701.85
Step 2: Calculate the Present Value (PV) of the payment stream by discounting each FV to 80 days from today. The formula for the present value of a future amount is PV = FV × [1 / (1 + i/365)^n] where "n" is the number of days between the date of the future amount and the date on which it is to be discounted. Here, we need to discount all three payments to 80 days from today. The number of days between today and 80 days from today is 80. So, we put n = 80 in the above formula.
For the first payment of $2,500 that is already available today, there is no need for any discounting. Hence, its present value is the same as its future value, i.e., $2,500.For the second payment of $3,093.29 that is due 100 days from today, Present Value (PV) = $3,093.29 × [1 / (1 + 0.05/365)^80] ≈ $2,893.16For the third payment of $3,701.85 that is due 240 days from today, Present Value (PV) = $3,701.85 × [1 / (1 + 0.05/365)^80] ≈ $3,243.11
Step 3: Add up the present values of all three payments to find the present value of the payment stream Present Value of the payment stream = $2,500 + $2,893.16 + $3,243.11 = $8,636.27
Step 4: Calculate the single payment that is economically equivalent to the payment stream by calculating its future value at the end of 80 days. FV = PV × (1 + i/365)^n where n = 80, i = 0.05, and PV = $8,636.27FV = $8,636.27 × (1 + 0.05/365)^80 ≈ $9,040.07Therefore, the single payment that is economically equivalent to the payment stream is $9,040.07.
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Please help asap I’ll give Brainly to whoever gets it right.
Consider the inequality -20.2 > 0y. Which of the following must be true? Check all that apply.
You cannot divide by zero.
The inequality is equivalent to -20.2 > 0, which is false.
The solution is y > 0.
The solution is 0 > y.
The solution is y = 0.