The phase shift for the given equation is π/8.
What is phase shift?In the study of waveforms and the transmission of signals, the phrase "phase shift" is frequently used. It speaks of the movement caused by two impulses as they spread over time. A signal processing device like an electronic amplifier or a low- or high-pass filter that applies specific operations to the signal and causes the output signal phase to change from its initial input signal phase can be the culprit behind this displacement.
The general form of a sinusoidal function is y = A sin(Bx - C) + D, where A is the amplitude, B is the frequency (and also related to the period T by T = 2π/B), C is the phase shift, and D is the vertical shift.
Comparing this form to the given equation y = -3sin(4x - π/2) - 1, we can see that the amplitude A is 3, the frequency B is 4, and the vertical shift D is -1. To find the phase shift C, we need to rearrange the equation to isolate the argument of the sine function:
y + 1 = -3sin(4x - π/2)
Dividing both sides by -3, we get:
(sin(4x - π/2)) / (-1/3) = -(y + 1) / 3
Recall that sin(θ - π/2) = cos(θ), so we can rewrite the argument of the sine function as:
4x - π/2 = 4(x - π/8)
Now, the equation becomes:
(sin[4(x - π/8)]) / (-1/3) = -(y + 1) / 3
Comparing this to the standard form y = A sin(Bx - C) + D, we can see that B = 4 and A/B = -1/3, so A = -4/3. Thus, we have:
y = (-4/3) sin[4(x - π/8)] - 1
The phase shift is the horizontal shift of the graph, which is given by C = π/8. Therefore, the phase shift for the given equation is π/8.
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The line joining (-3p, 0) to (-1, 5) is parallel to the line joining (p, 1) to (2p, 3). Find p.
Answer:
write ✍️
Step-by-step explanation:
justification for the following line translation . line 1 3p-
Ten cards numbered 1 thru 10 are placed in a box. If a card is de random from the box, what is the probability of drawing a prime a 10% b 25% c 40% d 50%
The probability of drawing a prime is 40%.
Calculating probability:To calculate the probability of drawing a prime number, use the formula
P(E) = Number of favorable outcomes / Total number of outcomes
Where P(E) is the probability of event E, and we determine the number of favorable outcomes and total possible outcomes based on the given conditions.
Here we have
Ten cards numbered 1 to 10 are placed in a box.
The total number of outcomes will get in a random experiment = 10
Here set of prime numbers from 1 to 10 = {2, 3, 5, 7}
Number of favorable outcomes that are getting prime number = 4
Hence, the probability of getting a prime number
= 4/10 = 2/5 = 0.4 = 40% [ Multiplied by 100 ]
Therefore,
The probability of drawing a prime is 40%.
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how many 1/3s are in three
The perimeter of a rectangle is 34 feet. The length, l, of the garden is 14.38. the length, l, of the garden is 5 more than 2 times the width. Find the measurement of the width of the garden
The width of the garden is 4 feet.
What is Rectangle ?
A rectangle is a quadrilateral with four right angles, opposite sides that are parallel, and equal in length. It is a type of parallelogram where the adjacent sides are equal in length, but the opposite sides are not necessarily equal.
Let's start by using the formula for the perimeter of a rectangle:
Perimeter = 2(length + width)
We know that the perimeter is 34 feet, so we can plug in that value and simplify:
34 = 2(l + w)
17 = l + w
We also know that the length is 5 more than 2 times the width, so we can write an equation for that:
l = 2w + 5
We can substitute this expression for l into the first equation:
17 = (2w + 5) + w
Simplifying, we get:
17 = 3w + 5
12 = 3w
w = 4
Therefore, the width of the garden is 4 feet.
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(1/x-y)-(2/2x+y)+(1/x+y)-(2/2x-y)
Answer:
6xy^2/(x-y)(x+y)(2x+y)(2x-y)
Step-by-step explanation:
1 - 2 + 1 - 2
x-y 2x+y x+y 2x-y
= take LCM
Then simplify.
Answer:
-2x+2/x
Step-by-step explanation:
for acute angles A and B it is known that sin A - 28/53 and tan B = 4/3. find the value of cos(A+B) in simplest form
For acute angles A and B it is known that sin A - 28/53 and tan B = 4/3. , , the value of cos(A+B) in simplest form is -15/53.
Describe Angles?In geometry, an angle is the measure of the amount of turn between two lines that intersect at a point, called the vertex of the angle. Angles are typically measured in degrees, but can also be measured in radians.
Angles can be classified based on their measures. An angle that measures less than 90 degrees is called an acute angle, while an angle that measures exactly 90 degrees is called a right angle. An angle that measures greater than 90 degrees but less than 180 degrees is called an obtuse angle, while an angle that measures exactly 180 degrees is called a straight angle. Finally, an angle that measures greater than 180 degrees but less than 360 degrees is called a reflex angle.
We can start by using the identity:
cos(A + B) = cos A cos B - sin A sin B
To find cos A and sin A, we can use the identity:
sin² A + cos² A = 1
sin A = √(1 - cos² A)
We are given sin A = 28/53, so we can solve for cos A:
sin² A + cos² A = 1
(28/53)² + cos² A = 1
cos² A = 1 - (28/53)²
cos A = ± √[(53/53)² - (28/53)²]
Since A is acute, we take the positive root:
cos A = √(1 - (28/53)²)
To find sin B and cos B, we can use the identity:
tan B = sin B / cos B
We are given tan B = 4/3, so we can solve for sin B and cos B using the Pythagorean identity:
sin² B + cos² B = 1
sin B = (4/3) cos B
(4/3)² cos² B + cos² B = 1
cos² B = 1 / ((4/3)² + 1)
cos B = √(1 / ((4/3)² + 1))
sin B = (4/3) cos B
Now we can substitute all of these values into the formula for cos(A + B):
cos(A + B) = cos A cos B - sin A sin B
cos(A + B) = √(1 - (28/53)²) √(1 / ((4/3)² + 1)) - (28/53) (4/3) √(1 / ((4/3)² + 1))
cos(A + B) = (√((53² - 28²) / 53²)) (√(9 / (16 + 9))) - (4/3) (28/53) (√(9 / (16 + 9)))
cos(A + B) = (45/53) (√(9/25)) - (112/265) (√(9/25))
cos(A + B) = (9/53) - (24/53)
cos(A + B) = -15/53
Therefore, cos(A + B) = -15/53.
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What is 2 3/4 + -1 1/8
Answer:
hope it helps.
Help with math problems
The answer choice which is not a true statement include the following: C. the solution set of |3k + 3| ≤ -9 is {k|-4 ≥ k ≥ 2}.
What is an inequality?In Mathematics and Geometry, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the inequality symbols;
Greater than (>).Less than (<).Greater than or equal to (≥).Less than or equal to (≤).In order to determine the solution set to the given inequality, we would write out the absolute value function (inequality) as shown below.
|3k + 3| ≤ -9
Since |3k + 3| would always be positive and negative nine (-9) is negative, |3k + 3| will always be greater than negative nine (-9), and as such, the inequality cannot be true and has no solution set.
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Dean qualifies for a 5-year loan from his credit union with a 5.25% APR. Assuming he uses the $4,300 as a down payment. You have already calculated his loan amount and his monthly payment. Considering all the monthly payments and the down payment, what will be the total amount that he pays for the car if he gets the loan and pays it off as scheduled? Round to two decimal places.
The total amount that he will pay for the car will be $17,093.40, assuming a loan amount of $15,000, a down payment of $4,300, a 5-year loan term, and a 5.25% APR.
Assuming that Dean has used the $4,300 as a down payment, his loan amount would be the total cost of the car minus the down payment, which is not given in the question.
However, assuming that the loan amount is $15,000 (which would be the case if the total cost of the car was $19,300), the monthly payment would be $284.89.
To calculate the total amount that Dean pays for the car over the course of the loan, we can multiply the monthly payment by the number of payments (60 payments over 5 years) and add the down payment:
Total amount = (Monthly payment x Number of payments) + Down payment
Total amount = ($284.89 x 60) + $4,300
Total amount = $17,093.40
Therefore, if Dean gets the loan and pays it off as scheduled, the total amount that he will pay for the car will be $17,093.40.
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Use the given information to find the minimum sample size required to estimate an unknown population mean μ.
How many business students must be randomly selected to estimate the mean monthly earnings of business students at one college? We want 95% confidence that the sample mean is within $135 of the population mean, and the population standard deviation is known to be $538.
54
62
43
86
Answer:
the correct answer is option B.
Step-by-step explanation:
We can use the formula for the margin of error for a confidence interval for a population mean with a known population standard deviation:
Margin of error = z*σ/√n
where z is the critical value from the standard normal distribution for the desired confidence level (95% in this case), σ is the population standard deviation, and n is the sample size.
We are given that the margin of error is $135 and σ is $538. We need to find the sample size, n. To do this, we first need to find the appropriate value of z for a 95% confidence level. Using a standard normal distribution table or calculator, we can find that z = 1.96.
Substituting the values into the margin of error formula and solving for n, we have:
$135 = 1.96*($538)/√n
Squaring both sides and solving for n, we get:
n = [1.96*($538)/$135]^2 ≈ 62
Therefore, a sample size of 62 business students must be randomly selected to estimate the mean monthly earnings of business students at one college with 95% confidence that the sample mean is within $135 of the population mean, assuming the population standard deviation is known to be $538.
So the correct answer is option B.
A bird flying at 15 m
above sea level dives vertically 2 m
into the sea to catch a fish and returns to its initial height.
What was the total vertical distance it travelled?
The bird covered 34 metres of vertical space overall. Warm-blooded, feathery animals with the ability to fly are known as birds.
The bird soared 15 m above the water, dove 2 m vertically, and descended to a depth of the water that was 15 + 2 = 17 m below its starting height. The bird must fly 17 m vertically upwards in order to cover the same distance in the other direction in order to return to its starting height.
Consequently, the bird travelled a total vertical distance of 34 metres (17 metres when diving and 17 metres while returning to its starting height).
Hence, the bird covered 34 metres of vertical space overall.
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The number of students who ride the school bus is 110%of the number of students who walk.How many students ride the school bus
If the number of students who walk is represented by x, then the number of students who ride the school bus is 110% of x, which can be written as:
1.10x
This is because 110% can be written as 1.10 (since 110% means 110 out of 100).
So, if we know the value of x, we can multiply it by 1.10 to find the number of students who ride the school bus.
However, we don't know the value of x in this problem. Therefore, we cannot find the exact number of students who ride the school bus.
Answer:If the number of students who walk is represented by x, then the number of students who ride the school bus is 110% of x, which can be written as:
1.10x
This is because 110% can be written as 1.10 (since 110% means 110 out of 100).
So, if we know the value of x, we can multiply it by 1.10 to find the number of students who ride the school bus.
However, we don't know the value of x in this problem. Therefore, we cannot find the exact number of students who ride the school bus.
Step-by-step explanation:
A bag contains 8 red marbles, 3 blue marbles, and 1 green marble. Find P(not blue). a. 9 c. One-fourth b. Four-thirds d. three-fourths Please select the best answer from the choices provided A B C D
Answer:
The probability of not getting a blue marble is the probability of getting either a red or a green marble. P(not blue) = P(red or green) P(red or green) = P(red) + P(green) P(red or green) = 8/12 + 1/12 P(red or green) = 9/12 P(not blue) = 3/4 Therefore, the answer is D. three-fourths.
Can someone please help ASAP!
The correct answer for this would be: Triangles BCA and DAC are congruent according to the Angle-Side-Angle (ASA) Theorem.
What is a Parallelogram?
A parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size.
According to the ASA theorem, if the included side of one triangle and its two angles are comparable to the parts of another triangle, then the triangles are said to be congruent.
Check the attached file for the image of this problem.
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Jeremy and Leslie are each flying their own drones in a flat field with their drones hovering between the two of them. Jeremy's drone is closer to him than to Leslie, and Leslie's drone is closer to her than to Jeremy. Jeremy's drone is 30 meters above the ground, and he is located 50 meters to
the left from the point directly below the drone. The angle of elevation from Leslie's location on the ground to her dronp is 55°, and the distance between her location on the ground and her drone is 70 meters.
1. Calculate whose drone is higher. Show all work.
2. The angle elevation from the lower drone to the higher drone is 25 degrees. Use this information to calculate the distance between Jeremy and Leslie. Show all work.
3. Jeremy now flies his drone vertically so that it is the same height as Leslie’s drone. Draw a new diagram that includes Jeremy, Leslie, and the drones after Jeremy flies his drone to the same height as Leslie’s.
4. Explain why the angle of elevation from Jeremy’s location on the ground to his drone is different from the angle of elevation between Leslie’s location on the ground and her drone, given that both drones are at the same elevation above the ground.
5. Calculate the angle of elevation from Jeremy’s location on the ground to his drone to validate your reasoning. Show all work.
The solutions are explained below.
Given that, Jeremy and Leslie are each flying their own drones in a flat field with their drones hovering between the two of them. The figure is attached.
Height of Jeremy's drone = 30 m
Height of Leslie's drone = x m
h / 70 = sin 53°
h = 70 × sin 53°
h = 57.34
Therefore, Leslie's drone is higher than Jeremy's drone.
Difference of height = 57.34 - 30 = 27.34 m
27.34 / x = tan25°
x = 58.63 m
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PERCENTAGES QUESTIONSS
So, the answer in its simplest form is 1/200.a) Here's the completed frequency tree: Drink tea.
So, the number of people who drink at least 3 cups of tea each day is:[tex]10 * 0.2 = 2[/tex]Therefore, the fraction of the 400 people who drink at least 3 cups of tea each day is: 2 / 400This fraction can be simplified by dividing both the numerator and the denominator by their greatest common factor, which is 2:1 / 200So, the answer in its simplest form is 1/200.
What is fraction?A fraction is a numerical quantity representing a part of a whole or a ratio between two quantities. It is expressed as one number (the numerator) divided by another number (the denominator), separated by a horizontal line. The numerator represents the number of parts being considered, while the denominator represents the total number of equal parts that make up the whole. For example, in the fraction 3/4, the numerator is 3, which represents three parts out of a total of four equal parts. Fractions can be used to represent many different types of quantities, such as parts of a whole, ratios, percentages, and probabilities.
b) Out of the 400 people, 10 said yes to drinking tea, and 20% of those (or 0.20*10 = 2) said they drink at least 3 cups each day. Therefore, the fraction of people who drink at least 3 cups of tea each day is 2/400, which simplifies to 1/200.
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At one college, GPAs are normally distributed with a mean of 2.9 and a standard deviation of 0.6. Find the 70th percentile.
The GPA corresponding to the 70th percentile at the college is approximately 3.246 based on standard deviation.
We can use the conventional normal distribution table or a calculator with a normal distribution function to determine the 70th percentile of GPAs at a college, which are normally distributed with a mean of 2.9 and a standard deviation of 0.6.
The inverse normal distribution function with a mean of 2.9, a standard deviation of 0.6, and a percentile of 70 can be used on a calculator. This results in:
[tex]3.246 for invNorm(0.7, 2.9, 0.6).[/tex]
As a result, the GPA that represents the 70th percentile is roughly 3.246.
We can determine the z-score corresponding to the 70th percentile, which is 0.5244, by using a common normal distribution table. Thus, we may apply the equation z = (x - ) /, where x is the GPA that corresponds to the 70%ile, is the mean, and is the standard deviation, and all three variables have values of 2.9. After finding x, we obtain:
0.5244 = (x - 2.9) / 0.6
x = 3.246
Once more, doing so yields the same outcome as using a calculator.
In conclusion, the GPA at the college that represents the 70th percentile is roughly 3.246.
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Let f(x)=2x-1, h(x) = -x-5.
Find (f o h)(-3).
(foh)(-3)=
So, (f o h)(-3) = 3. This is the value of the composite function (f o h) at -3. Please note that (f o h)(-3) is equivalent to f(h(-3))
What is function?An input and an output are connected by a function. It functions similarly to a machine with an input and an output. Additionally, the input and output are somehow connected. The traditional format for writing a function is f(x) "f(x) =... "
To find (f o h)(-3), we need to first evaluate h(-3), and then plug that result into the function f(x).
Given:
f(x) = -2x - 1
h(x) = -x - 5
First, we evaluate h(-3):
h(-3) = -(-3) - 5
h(-3) = 3 - 5
h(-3) = -2
Now, we plug the result of h(-3) into the function f(x):
f(h(-3)) = f(-2)
f(h(-3)) = -2(-2) - 1
f(h(-3)) = 4 - 1
f(h(-3)) = 3
So, (f o h)(-3) = 3. This is the value of the composite function (f o h) at -3. Please note that (f o h)(-3) is equivalent to f(h(-3)), which means we first evaluate h(-3) and then plug that result into f(x). I hope this helps! Let me know if you have any further questions. :)
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QUESTION 3
If y varies inversely as x, find the inverse variation equation for the situation.
y = 1/8 when x = 40
[tex]yx=5[/tex]
Explanation:
If [tex]y[/tex] varies inversely as [tex]x[/tex] then
[tex]y\times x=k[/tex] for some constant [tex]k[/tex]
Since [tex]y = \frac{1}{8}[/tex] when [tex]x=40[/tex]
[tex]\huge \text(\dfrac{1}{8}\huge \text)\times(40)=k[/tex]
[tex]\longrightarrow k=5[/tex]
Need some help
50 points!!
Answer:
145°
Step-by-step explanation:
The exterior angle 3 is equal to the sum of angle 1 and 2.
Using substitution we can say that:
5x + 4x + 10 = 10x -5
9x + 10 = 10x -5
10x-9x=10+5
x= 15
We have just found that the value of x is equal to 15.
By substituting this back to the angle 3 expression, 10x-5, we get
10(15) - 5
150 - 5
145°
A utility company in a western city of the United States expects the consumption of electricity to increase by 11%/year during the next decade, due mainly to the expected increase in population. If consumption does increase at this rate, find the amount by which the utility company will have to increase its generating capacity in order to meet the needs of the area at the end of the decade.
The utility company will have to increase its generating capacity by approximately 185.3% to meet the expected increase in electricity consumption over the next decade.
Exponential growth:The problem involves the use of the exponential growth formula in mathematics, where we are given the current consumption of electricity in a city and we are asked to find the expected consumption of electricity after a certain period of time, assuming a fixed annual growth rate.
We can use the formula:
C = C₀ × (1 + r)ⁿHere we have
A utility company in a western city in the United States expects the consumption of electricity to increase by 11%/year during the next decade, due mainly to the expected increase in population.
Let C₀ be the current consumption of electricity in the western city of the United States, and let C₁₀ be the expected consumption of electricity at the end of the decade.
We can use the following formula to calculate C₁₀:
C₁₀ = C₀ × (1 + r)ⁿ
Where r is the annual growth rate, n is the number of years
The amount by which the utility company will have to increase its generating capacity in order to meet the needs of the area at the end of the decade is given by the difference between C₁₀ and C₀
That is:
Amount of increase = C₁₀ - C₀
Substituting the values given in the problem, we get:
C₁₀ = C₀ (1 + 0.11)¹⁰
C₁₀/C₀ = (1.11)¹⁰
C₁₀/C₀ = (1.11)¹⁰
C₁₀ = C₀ × 2.84
Therefore, the amount by which the utility company will have to increase its generating capacity in order to meet the needs of the area at the end of the decade is:
Amount of increase =C₁₀ - C₀ = 2.853 × C₀ - C₀ = 1.853 × C₀
Therefore,
The utility company will have to increase its generating capacity by approximately 185.3% to meet the expected increase in electricity consumption over the next decade.
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A school newspaper took a survey of 100 students the results of the survey showed that 43 students are fans of Buffalo Bills 27 students are fans of New York Jets and 48 students do not like either team how many of the students surveyed are fans of both the Buffalo Bills and the New York Jets?
Answer: 18 students
Step-by-step explanation: 43+27+48=118 118-100=18
Find the value of x, y, and z in the rhombus below.
(-x-8)
107⁰
(3y-1)
(-42-7)
Step-by-step explanation:
It is not clear from the given information which angles and sides are being referred to as "107⁰", "-x-8", "-42-7", and "3y-1". However, we can use some properties of rhombuses to solve for x, y, and z.
Opposite angles in a rhombus are equal. Therefore, if one angle is 107⁰, then the opposite angle is also 107⁰.
The diagonals of a rhombus are perpendicular bisectors of each other. This means that they intersect at a right angle and divide each other into two equal parts.
The diagonals of a rhombus bisect each other's angles. This means that the angles formed by each diagonal with the sides of the rhombus are equal.
Using these properties, we can set up some equations to solve for x, y, and z:
Let's assume that "-x-8" and "-42-7" are the lengths of the diagonals of the rhombus, and that "3y-1" is the length of one of the sides.
Since the diagonals bisect each other's angles, we know that the angles formed by each diagonal with the side of the rhombus are equal. Let's call each of these angles "z":
-z + 107⁰ + z = 180⁰ (sum of angles in a triangle)
107⁰ = 180⁰ - 2z
2z = 73⁰
z = 36.5⁰
Now let's use the fact that the diagonals are perpendicular bisectors of each other:
(-x-8)/2 = (-42-7)/2
-x-8 = -49
-x = -41
x = 41
Finally, let's use the fact that the sides of a rhombus are equal:
-x-8 = 3y-1
41-8 = 3y-1
33 = 3y
y = 11
Therefore, the values of x, y, and z in the rhombus are:
x = 41
y = 11
z = 36.5⁰
PART A: A can of cat food measures 1" tall and a diameter of 3.5". What is the volume of cat food in the can? To solve Give your answer in cubic inches. Round to the nearest hundredth.
PART B: Cat food is sold by ounces (weight).
If the can holds 5.8 ounces, write a ratio to show cubic inches (your answer from slide 3) to ounces.
A)The volume of cat food in the can is 9.62 cubic inches .
B) A ratio to show cubic inches to ounces is 4.83.
What is a cylinder?
A cylinder is a three-dimensional geometric shape that has two congruent circular bases connected by a curved surface.
The volume of a cylinder can be calculated using the formula
=> [tex]V = \pi r^2h,[/tex]
where r is the radius of the circular base, h is the height of the cylinder, and π is the mathematical constant pi (approximately equal to 3.14).
To find the volume of the cat food in the can, we need to use the formula for the volume of a cylinder,
Since the diameter is 3.5 inches, the radius is half of that, which is 1.75 inches. The height is 1 inch.
So,[tex]V=3.14\times(1.75)^2\times1[/tex] = 9.62 cubic inches (rounded to the nearest hundredth).
Therefore, the volume of cat food in the can is approximately 9.62 cubic inches.
Now ,To find the ratio of cubic inches to ounces,
Since the can holds 5.8 ounces of cat food, we can find the volume of cat food in cubic inches by dividing the weight by the density:
=> 5.8 ounces / 1.2 ounces per cubic inch
= 4.83 cubic inches (rounded to the nearest hundredth).
Therefore, a ratio to show cubic inches to ounces is 4.83.
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1 1/9 x 2 2/5 as a mixed number in simplest form
Answer:
2 [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
1 1/9 x 2 2/5 = ?
1 1/9 = 10/9
2 2/5 = 12/5
[tex]\frac{10}{9}[/tex] x [tex]\frac{12}{5}[/tex] = [tex]\frac{120}{45}[/tex] = [tex]\frac{8}{3}[/tex] = 2 [tex]\frac{2}{3}[/tex]
So, the answer is 2 [tex]\frac{2}{3}[/tex]
1. (100 pts) Consider two players A and B in a contest. The first one who wins a game wins the
contest. In the case of 5 successive draws, the contest is declared drawn. The probability that A
wins a game is 0.2. The probability that B wins a game is 0.5. And, thus, the probability of a draw
is 0.3. The winning or draw of each game is independent of previous games. The duration of the
contest is defined as the total number of games that are played before a winner is determined or
the contest is declared drawn.
(a) What is the PMF of the duration of the contest?
(b) What is the probability that the duration is at least 4?
The probability that the duration is at least 4 is 0.0053 (rounded to four decimal places).
What is probability?Probability is represented by a number between 0 and 1, with 0 denoting an impossibility and 1 denoting a certainty.
According to question:(a) Let X be the duration of the contest. Then X can take values from 1 to 6, where 1 indicates that A or B wins the first game, and 6 indicates that the contest ends in a draw after 5 successive draws.
We can find the PMF of X by considering the possible outcomes for each value of X.
P(X = 1) = P(A wins) + P(B wins) = 0.2 + 0.5 = 0.7
P(X = 2) = P(A loses, B loses, A wins or B wins) = 0.3 * 0.3 * (0.2 + 0.5) = 0.054
P(X = 3) = P(A loses, B loses, A loses, B loses, A wins or B wins) = [tex]0.3^4[/tex] * (0.2 + 0.5) = 0.01323
P(X = 4) = P(A loses, B loses, A loses, B loses, A loses, B loses, A wins or B wins) = [tex]0.3^6[/tex] * (0.2 + 0.5) = 0.00243
P(X = 5) = P(A loses, B loses, A loses, B loses, A loses, B loses, A loses, B loses, A wins or B wins) = [tex]0.3^8[/tex] * (0.2 + 0.5) = 0.0004374
P(X = 6) = P(5 successive draws) = [tex]0.3^5[/tex] = 0.00243
Therefore, the PMF of X is:
X 1 2 3 4 5 6
P(X) 0.7 0.054 0.01323 0.00243 0.0004374 0.00243
(b) To find the probability that the duration is at least 4, we need to add the probabilities of X = 4, X = 5, and X = 6.
P(X >= 4) = P(X = 4) + P(X = 5) + P(X = 6) = 0.00243 + 0.0004374 + 0.00243 = 0.0052974
Therefore, the probability that the duration is at least 4 is 0.0053 (rounded to four decimal places).
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Can someone help me with this?
Answer: 63,932
Step-by-step explanation:
September: 11,724
October: 14,380 + 11,724 = 26,104
November: 14,380 + 11,724 = 26,104
Combine all 3 months to get your answer= 63,932
Need help with question #4
Both the lines are parallel hence, they cannot intersect each other and value of H= (0,0).
What is an equation?A mathematical statement known as an equation consists of two algebraic expressions separated by equal signs (=) on either side.
It demonstrates the equality of the relationship between the printed statements on the left and right.
Left side equals right side in all formulas.
To find the values of unknowable variables, which stand in for unknowable quantities, you can solve equations.
A statement is not an equation if it lacks the equals sign.
When two expressions have the same value, a mathematical statement known as an equation will include the symbol "equal to" between them.
Hence, Both the lines are parallel hence, they cannot intersect each other and value of H= (0,0).
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what is the best estimate of 2/3+3/4
Let's add the fractions first and then we can estimate the sum.
[tex]= \dfrac{2}{3} +\dfrac{3}{4}[/tex]
change to common denominators
[tex]= \dfrac{8}{12} +\dfrac{9}{12}[/tex]
add numerators only
[tex]\dfrac{17}{12}[/tex] or [tex]1\dfrac{5}{12}[/tex] or [tex]1.42[/tex]
ANSWER: 13 is the best estimate of the answer. Normally we round up to 1.4 with a number like 1.42, but since that is not a choice, we can estimate 1 as the answer.
I need help, please show me the work and explain, I'm giving 50 points.
Answer:
Area_sector = 9.8 square inches
Step-by-step explanation:
A sector is a piece of a circle. Like a pie slice. We can use the angle given to find out what fraction of the circle we are looking for.
There are 360° in a circle. The sector is 125°. So the fraction of the circle we are looking for is (125/360) Of course this can be reduced, but we should just let the calculator handle it.
Now, the area of the whole circle is:
A = pi•r^2
A = pi • 3^2
The radius is given. r = 3
A = 9pi
They said to use 3.14 for pi
A = 28.26
This is the area of the whole circle, so we need to multiply by that fraction to find the area of the pie slice (sector)
Area_sector =
(125/360)28.26
= (0.3472222)28.26
= 9.8125
Round to the nearest tenth.
~= 9.8