Answers
Answer:
[tex]\textsf{The parabola has a vertex at $\left(\:\boxed{-3}\:,\boxed{-7}\:\right)$, has a p-value of $\boxed{-1}$ and it}[/tex]
[tex]\textsf{$\boxed{\sf op\:\!ens\;to\;the\;left}$\:.}[/tex]
Step-by-step explanation:
The given directrix of the parabola is x = -2, which is a vertical line.
The directrix is perpendicular to the axis of symmetry. Therefore, this means that the parabola has a horizontal axis of symmetry.
The focus of a parabola is a fixed point located inside the curve. The x-coordinate of the given focus is x = -4. As this is to the left of the directrix, it means that the parabola opens to the left.
The standard form of a horizontal parabola is:
[tex]\boxed{(y-k)^2=4p(x-h)}[/tex]
where:
Vertex = (h, k)Focus = (h+p, k)Directrix: x = (h - p)Axis of symmetry: y = kAs the focus is (-4, -7), then:
[tex]\begin{aligned}(h+p, k)&=(-4,-7)\\\\\implies k&=-7\\\implies h+p&=-4\end{aligned}[/tex]
As the directrix is x = -2, then:
[tex]h - p=-2[/tex]
To find the value of h, sum the equations involved h and p to eliminate p:
[tex]\begin{array}{crcccr}&h &+& p& =& -4\\+&h& -& p& = &-2\\\cline{2-6}&2h&&& =& -6\\\cline{2-6}\\\implies &h&&&=&-3\end{array}[/tex]
To find the value of p, substitute the found value of h into one of the equations:
[tex]\begin{aligned}-3 - p&=-2\\p&=-3+2\\p&=-1\end{aligned}[/tex]
Therefore, the values of h, k and p are:
h = -3k = -7p = -1The parabola has a vertex at (-3, -7), has a p-value of -1 and it opens to the left.
The parabola has a vertex at (-3, y), has p-value of 1 and it equation is
(x + 3)² = 4y.
What is the equation of the parabola?To find the equation of the parabola with the given focus and directrix, we can use the standard form equation of a parabola:
(x - h)² = 4p(y - k)
where (h, k) is the vertex of the parabola and "p" is the distance from the vertex to the focus (and also from the vertex to the directrix).
Given:
Focus: (-4, -7)
Directrix: x = -2
1. Finding the vertex:
Since the directrix is a vertical line, the vertex lies on the line that is equidistant from the focus and directrix. In this case, it lies on the line x = (-4 + (-2))/2 = -3.
Therefore, the vertex of the parabola is (-3, y).
2. Finding the p-value:
The distance from the vertex to the focus (and also to the directrix) is the same. In this case, the distance is |-3 - (-4)| = 1.
Therefore, the value of "p" is 1.
3. Writing the equation of the parabola:
Using the vertex (-3, y) and the p-value of 1, we can write the equation of the parabola:
(x - h)² = 4p(y - k)
(x - (-3))² = 4(1)(y - y)
Simplifying, we get:
(x + 3)² = 4(y - y)
(x + 3)² = 4y
So, the equation of the parabola is (x + 3)² = 4y.
The vertex of the parabola is (-3, y) and the p-value is 1.
Learn more on equation of parabola here;
https://brainly.com/question/29635857
#SPJ1
Related Questions
At what points is the function y=sinx/3x continuous?
Answers
Answer: [tex](-\infty, 0) \cup (0, \infty)[/tex]
Step-by-step explanation:
The graph of [tex]\frac{\sin x}{x}[/tex] is continuous for all real [tex]x[/tex] except [tex]x=0[/tex], and multiplying this by [tex]1/3[/tex] does not change this.
A village P is 12 km from village Q. It takes 3 hours 20 minutes to travel from Q to P and back to Q by a boat. If the boat travels at a speed of 6 km/h from P to Q and (6 + x) km/h back to P, find the value of x.
Answers
Answer:
Hope this helps and have a nice day
Step-by-step explanation:
To find the value of x, we can use the formula:
Time = Distance / Speed
Let's calculate the time taken to travel from Q to P and back to Q.
From Q to P:
Distance = 12 km
Speed = 6 km/h
Time taken from Q to P = Distance / Speed = 12 km / 6 km/h = 2 hours
From P to Q:
Distance = 12 km
Speed = (6 + x) km/h
Time taken from P to Q = Distance / Speed = 12 km / (6 + x) km/h
Given that the total time taken for the round trip is 3 hours 20 minutes, we can convert it to hours:
Total time = 3 hours + (20 minutes / 60) hours = 3 + (1/3) hours = 10/3 hours
According to the problem, the total time is the sum of the time from Q to P and from P to Q:
Total time = Time taken from Q to P + Time taken from P to Q
Substituting the values:
10/3 hours = 2 hours + 12 km / (6 + x) km/h
Simplifying the equation:
10/3 = 2 + 12 / (6 + x)
Multiply both sides by (6 + x) to eliminate the denominator:
10(6 + x) = 2(6 + x) + 12
60 + 10x = 12 + 2x + 12
Collecting like terms:
8x = 24
Dividing both sides by 8:
x = 3
Therefore, the value of x is 3.
Answer:
x = 3
Step-by-step explanation:
speed = distance / time
time = distance / speed
Total time from P to Q to P:
T = 3h 20min
P to Q :
s = 6 km/h
d = 12 km
t = d/s
= 12/6
t = 2 h
time remaining t₁ = T - t
= 3h 20min - 2h
= 1 hr 20 min
= 60 + 20 min
= 80 min
t₁ = 80/60 hr
Q to P:
d₁ = 12km
t₁ = 80/60 hr
s₁ = d/t₁
[tex]= \frac{12}{\frac{80}{60} }\\ \\= \frac{12*60}{80}[/tex]
= 9
s₁ = 9 km/h
From question, s₁ = (6 + x)km/h
⇒ 6 + x = 9
⇒ x = 3
The table displays the scores of students on a recent exam. Find the mean of the
scores to the nearest 10th.
Score Number of Students
70
6
75
80
85
90
95
3
9
5
7
8
2
Answers
The mean of the scores to the nearest tenth is 83.7.
What is the mean?Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.
Given the question above, we need to find the mean of the scores to the nearest tenth.
We can find the mean by using the formula below:
[tex]\text{Mean} = \dfrac{\text{Sum of all the observations}}{\text{Total number of observations}}[/tex]
Now,
[tex]\text{Mean} = \dfrac{70(6)+75(3)+80(9)+85(5)+90(7)+95(8)}{6+3+9+5+7+8}[/tex]
[tex]\text{Mean} = \dfrac{420+225+720+425+630+760}{38}[/tex]
[tex]\text{Mean} = \dfrac{3180}{38}[/tex]
[tex]\text{Mean} = 83.7[/tex]
Therefore, the mean of the scores to the nearest tenth is 83.7.
Read more about the mean at:
https://brainly.com/question/32056327
A store has a sale with 20% off every item. When you enter the store, you receive a coupon that states that you receive an additional 30% off. Is this equal to a 50% discount? Explain your answer
Answers
Answer: Nope
Step-by-step explanation:
No, receiving a 20% discount followed by an additional 30% discount does not result in a total discount of 50%.
To understand why, let's consider an example with an item priced at $100.
If there is a 20% discount applied initially, the price of the item would be reduced by 20%, which is $100 * 0.20 = $20. So the new price after the first discount would be $100 - $20 = $80.
Now, if there is an additional 30% discount applied to the $80 price, the discount would be calculated based on the new price. The 30% discount would be $80 * 0.30 = $24. So the final price after both discounts would be $80 - $24 = $56.
Comparing the final price of $56 to the original price of $100, we can see that the total discount is $100 - $56 = $44.
Therefore, the total discount received is $44 out of the original price of $100, which is a discount of 44%, not 50%.
Hence, receiving a 20% discount followed by an additional 30% discount does not result in a total discount of 50%.
What is the range of this function?
Answers
The range of the given graph is expressed as:
Option A: {-∞, ∞}
What is the range of the given function?The range of a function is defined as the set of all the possible output values of y. The formula to find the range of a function is y = f(x).
In a relation, it is only a function if every x value corresponds to only one y value,
Now, looking at the given graph, we see that At x = 0, the function is also y = 0.
However, between 0 and π intervals, we see that the graph approaches positive and negative infinity and as such we can tell that the range is expressed as: {-∞, ∞}
Read more about Range of Function at: https://brainly.com/question/7954282
#SPJ1
Find the volume of the solid obtained by rotating the region
bounded by the graphs y=(x-4)^3,the x-axis, x=0, and x=5
about the y-axis? (Express numbers in exact form. Use symbolic
notation and fractions where needed.)
Answers
Answer:
Step-by-step explanation:
To find the volume of the solid obtained by rotating the region bounded by the graphs y = (x - 4)^3, the x-axis, x = 0, and x = 5 about the y-axis, we can use the method of cylindrical shells.
The formula for the volume of a solid obtained by rotating a region bounded by the graph of a function f(x), the x-axis, x = a, and x = b about the y-axis is given by:
V = 2π ∫[a, b] x * f(x) dx
In this case, the function f(x) = (x - 4)^3, and the bounds of integration are a = 0 and b = 5.
Substituting these values into the formula, we have:
V = 2π ∫[0, 5] x * (x - 4)^3 dx
To evaluate this integral, we can expand the cubic term and then integrate:
V = 2π ∫[0, 5] x * (x^3 - 12x^2 + 48x - 64) dx
V = 2π ∫[0, 5] (x^4 - 12x^3 + 48x^2 - 64x) dx
Integrating each term separately:
V = 2π [1/5 x^5 - 3x^4 + 16x^3 - 32x^2] evaluated from 0 to 5
Now we can substitute the bounds of integration:
V = 2π [(1/5 * 5^5 - 3 * 5^4 + 16 * 5^3 - 32 * 5^2) - (1/5 * 0^5 - 3 * 0^4 + 16 * 0^3 - 32 * 0^2)]
Simplifying:
V = 2π [(1/5 * 3125) - 0]
V = 2π * (625/5)
V = 2π * 125
V = 250π
Therefore, the volume of the solid obtained by rotating the region bounded by the graphs y = (x - 4)^3, the x-axis, x = 0, and x = 5 about the y-axis is 250π cubic units.
Triangle ABC has the following coordinates: A=(5,-5), B=(3,-3), C=(5,-3) What are the coordinates of triangle A'B'C' if it is created by dilating triangle ABC with the origin (0,0) as the center of dilation and with a scale factor of 3?
Answers
Answer:A' = (15, -15), B' = (9, -9), and C' = (15, -9)
Step-by-step explanation:
To dilate triangle ABC with a center of dilation at the origin (0,0) and a scale factor of 3, you need to multiply the coordinates of each vertex by the scale factor.
Let's calculate the coordinates of triangle A'B'C':
For point A:
x-coordinate of A' = scale factor * x-coordinate of A = 3 * 5 = 15
y-coordinate of A' = scale factor * y-coordinate of A = 3 * (-5) = -15
Therefore, A' = (15, -15)
For point B:
x-coordinate of B' = scale factor * x-coordinate of B = 3 * 3 = 9
y-coordinate of B' = scale factor * y-coordinate of B = 3 * (-3) = -9
Therefore, B' = (9, -9)
For point C:
x-coordinate of C' = scale factor * x-coordinate of C = 3 * 5 = 15
y-coordinate of C' = scale factor * y-coordinate of C = 3 * (-3) = -9
Therefore, C' = (15, -9)
Hence, the correct coordinates of triangle A'B'C' are A' = (15, -15), B' = (9, -9), and C' = (15, -9).
5 In a Survery of 130 people 80 claimed to be CDO partisans and 60 claimed to be Anc partisan. If 30 of them are both ANC and CDO how many people are none of these two parties
Answers
Answer: there are 20 people who claimed to be neither CDO partisans nor ANC partisans.
Step-by-step explanation:
To determine the number of people who are none of these two parties, we need to subtract the total number of people who claimed to be CDO partisans, ANC partisans, and those who claimed to be both from the total number of people surveyed.
Total surveyed people = 130
Number claiming to be CDO partisans = 80
Number claiming to be ANC partisans = 60
Number claiming to be both ANC and CDO = 30
To find the number of people who are none of these two parties, we can calculate it as follows:
None of these two parties = Total surveyed people - (CDO partisans + ANC partisans - Both ANC and CDO)
None of these two parties = 130 - (80 + 60 - 30)
None of these two parties = 130 - 110
None of these two parties = 20
f(x)=x^2. What is g(x)?
Answers
Answer:
D, g(x) = 1/4 x^2
Step-by-step explanation:
You can try plugging in the x and y values into each equation. The answer to this would be D, where if you plug in 2 as the x value, you get 1/4 * 4 which equals 1. This also makes sense because 2x would have a narrower curve while 1/2x would have a wider curve.
Pls geometry work help
Answers
Answer:
Step-by-step explanation:
Given:
<RPS = 35
<PAQ = 130
Solution:
If <PAQ = 130 then <QAR =50
because they are a linear pair that add to 180
<QAR = mQR = 50
mRS = 2(<RPS) >inscribed angle
mRS = 2(35)
mRS = 70
<PAQ = 130
<PAQ = mPQ
<PSQ = 1/2 (mPQ) >inscribed angle
<PSQ = 1/2 (130)
<PSQ = 65
<PBS = 180 - <RPQ - PSQ >triangle
<PBS = 180 - 35-65
<PBS = 80
<PBS = <QBR >vertical angles
<QBR = 80
<ABQ = 180- <QBR >linear pair
<ABQ = 180 - 80
<ABQ= 100
<AQB = 180 - <ABQ - <QAR >triangle
<AQB = 180 -100 - 50
<AQB = 30
<AQB = <AQS
<AQS =30
mRS = 70
mPS = 180-mRS 180 for semicircle
mPS = 180 - 70
mPS = 110
Aschalew is able to do apiece of work in 15 days and Abay can do the same work in 20 daya. if they can work together for 4 days, what is the fraction of the work left?
Answers
Answer:
8/15
Step-by-step explanation:
1/15(4 + 1/20(4)
4/15 + 4/20 I can reduce 4/20 to 1/5
4/15 + 1/5
4/15 + 3/15 = 7/15
Together they can get 7/15 of the job done. 15/15 - 7/15 is 8/15.
That means that they have 8/15 left to do.
Helping in the name of Jesus.
Adults are encouraged to visit the dentist at least once a year. In the 2019 National College Health
Assessment, 28,021 out of a random sample of 38,433 college students said they had a dental exam in
the last 12 months.
¹American College Health Association-National College Health Assessment (2020). Undergraduate student
reference group data report, Fall 2019. https://www.acha.org/NCHA/ACHA-
NCHA Data/Publications and Reports/NCHA/Data/Reports ACHA-NCHAIIl.aspx
Use the appropriate data analysis tool to construct a 99% confidence interval to estimate the
population proportion of college students who said they had a dental exam in the last 12 months.
Lower Bound
Upper Bound
Answers
The boundaries of the 99% confidence interval are
Lower bound = 0.7232Upper bound = 0.7348Constructing the 99% confidence intervalFrom the question, we have the following parameters that can be used in our computation:
Selected, x = 28021
Sample, n = 38433
This means that the proportion, p is
p = 28021/38433
p = 0.729
The 99% confidence interval is then calculated as
CI = p ± z * √(p * (1 - p)/n)
Where
z = 2.576 i.e. the z-score at 99% confidence interval
So, we have
CI = 0.729 ± 2.576 * √(0.729 * (1 - 0.729)/38433)
Evaluate
CI = 0.729 ± 0.0058
Evaluate
CI = (0.7232, 0.7348)
Hence, the confidence interval is (0.7232, 0.7348)
Read more about confidence interval at
https://brainly.com/question/32801070
#SPJ1
Which rectangles are similar? Four rectangles have a length of 3 c m and a height of 5 c m, a length of 2 point 5 c m and a height of 5 point 5 c m, a length of 2 point 5 c m, and a height of 2 c m, and a length of 5 c m and a height of 4 c m respectively.
Answers
The rectangles that are similar are Rectangle 3 and Rectangle 4.
To determine which rectangles are similar, we need to compare their corresponding side lengths.
Rectangle 1:
Length: 3 cm
Height: 5 cm
Rectangle 2:
Length: 2.5 cm
Height: 5.5 cm
Rectangle 3:
Length: 2.5 cm
Height: 2 cm
Rectangle 4:
Length: 5 cm
Height: 4 cm
To determine similarity, we need to compare the ratios of the corresponding side lengths of the rectangles.
Comparing Rectangle 1 with Rectangle 2:
Length ratio: 3 cm / 2.5 cm = 1.2
Height ratio: 5 cm / 5.5 cm ≈ 0.91
The length ratio and height ratio are not equal, so Rectangle 1 and Rectangle 2 are not similar.
Comparing Rectangle 1 with Rectangle 3:
Length ratio: 3 cm / 2.5 cm = 1.2
Height ratio: 5 cm / 2 cm = 2.5
The length ratio and height ratio are not equal, so Rectangle 1 and Rectangle 3 are not similar.
Comparing Rectangle 1 with Rectangle 4:
Length ratio: 3 cm / 5 cm = 0.6
Height ratio: 5 cm / 4 cm = 1.25
The length ratio and height ratio are not equal, so Rectangle 1 and Rectangle 4 are not similar.
Comparing Rectangle 2 with Rectangle 3:
Length ratio: 2.5 cm / 2.5 cm = 1
Height ratio: 5.5 cm / 2 cm = 2.75
The length ratio and height ratio are not equal, so Rectangle 2 and Rectangle 3 are not similar.
Comparing Rectangle 2 with Rectangle 4:
Length ratio: 2.5 cm / 5 cm = 0.5
Height ratio: 5.5 cm / 4 cm = 1.375
The length ratio and height ratio are not equal, so Rectangle 2 and Rectangle 4 are not similar.
Comparing Rectangle 3 with Rectangle 4:
Length ratio: 2.5 cm / 5 cm = 0.5
Height ratio: 2 cm / 4 cm = 0.5
The length ratio and height ratio are equal, so Rectangle 3 and Rectangle 4 are similar.
Therefore, the rectangles that are similar are Rectangle 3 and Rectangle 4.
for more such question on rectangles visit
https://brainly.com/question/2607596
#SPJ8
Purchasing a Car
Now you have to decide how to save enough money to purchase a used car in three years. You have the
$1000 that you saved up and you plan to continue working. According to your estimates, you can save an
additional $60 per month to put towards the car purchase. After conducting some research at the banks,
you have decided on two options (see below). You need to figure out which option will yield the most
money after the three years.
Option #1-CD for 3 years
Interest rate of 3% compounded monthly.
No money can be added to the CD.
However you can save your money on the side.
Option # 2-CD for 1 year
Interest rate of 2% compounded quarterly.
You can add money at the end of each year.
You will renew it each year for 3 years.
Work Shown:
Answers
Answer:
Step-by-step explanation:
To determine which option will yield the most money after three years, let's calculate the final amount for each option.
Option #1 - CD for 3 years:
Principal (initial investment) = $1000
Interest rate = 3% per year (compounded monthly)
No additional money can be added
To calculate the final amount, we can use the formula for compound interest:
A = P * (1 + r/n)^(n*t)
Where:
A = Final amount
P = Principal (initial investment)
r = Interest rate (as a decimal)
n = Number of times the interest is compounded per year
t = Number of years
For Option #1:
P = $1000
r = 3% = 0.03 (as a decimal)
n = 12 (compounded monthly)
t = 3 years
A = $1000 * (1 + 0.03/12)^(12*3)
Calculating the final amount for Option #1, we get:
A = $1000 * (1 + 0.0025)^(36)
A ≈ $1000 * (1.0025)^(36)
A ≈ $1000 * 1.0916768
A ≈ $1091.68
Option #2 - CD for 1 year:
Principal (initial investment) = $1000
Interest rate = 2% per year (compounded quarterly)
Money can be added at the end of each year
To calculate the final amount, we need to consider the annual additions and compounding at the end of each year.
First Year:
P = $1000
r = 2% = 0.02 (as a decimal)
n = 4 (compounded quarterly)
t = 1 year
A = $1000 * (1 + 0.02/4)^(4*1)
A ≈ $1000 * (1.005)^(4)
A ≈ $1000 * 1.0202
A ≈ $1020.20
At the end of the first year, the total amount is $1020.20.
Second Year:
Now we add an additional $60 to the previous amount:
P = $1020.20 + $60 = $1080.20
r = 2% = 0.02 (as a decimal)
n = 4 (compounded quarterly)
t = 1 year
A = $1080.20 * (1 + 0.02/4)^(4*1)
A ≈ $1080.20 * (1.005)^(4)
A ≈ $1080.20 * 1.0202
A ≈ $1101.59
At the end of the second year, the total amount is $1101.59.
Third Year:
Again, we add $60 to the previous amount:
P = $1101.59 + $60 = $1161.59
r = 2% = 0.02 (as a decimal)
n = 4 (compounded quarterly)
t = 1 year
A = $1161.59 * (1 + 0.02/4)^(4*1)
A ≈ $1161.59 * (1.005)^(4)
A ≈ $1161.59 * 1.0202
A ≈ $1185.39
At the end of the third year, the total amount is $1185.39.
Comparing the final amounts:
Option #1: $1091.68
Option #2: $1185.39
Therefore, Option #2 - CD for 1 year with an interest rate of 2% compounded quarterly and the ability to add money at the end of each year will yield the most money after three years.
need help with tshdjkdkdndndndndkd
Answers
The length of this line segment is: B. 2√13 units.
How to determine the distance between the coordinates for each points?In Mathematics and Geometry, the distance between two (2) end points that are on a coordinate plane can be calculated by using the following mathematical equation:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Where:
x and y represent the data points (coordinates) on a cartesian coordinate.
By substituting the given end points into the distance formula, we have the following;
Distance = √[(4 + 2)² + (1 + 3)²]
Distance = √[(6)² + (4)²]
Distance = √[36 + 16]
Distance = √52
Distance = 2√13 units.
Read more on distance here: brainly.com/question/12470464
#SPJ1
A rectangular piece of metal is 5 in longer than it is wide. Squares with sides 1 in lòng are cut from the four corners
and the flaps are folded upward to form an open box. If the volume of the box is 234 in³, what were the original
dimensions of the piece of metal?
Answers
The original dimensions of the piece of metal were 15 inches by 20 inches.
To solve this problem, we can use the given information to set up an equation. Let's assume that the width of the rectangular piece of metal is x inches. According to the problem, the length of the piece of metal is 5 inches longer than its width, so the length would be (x+5) inches.
When squares with sides 1 inch long are cut from the four corners, the width and length of the resulting box will be reduced by 2 inches each. Therefore, the width of the box will be (x-2) inches and the length will be ((x+5)-2) inches, which simplifies to (x+3) inches.
The height of the box will be 1 inch since the flaps are folded upward.
Now, let's calculate the volume of the box using the formula Volume = length * width * height.
Substituting the values, we have:
234 = (x+3)(x-2)(1)
Simplifying the equation, we get:
234 = x^2 + x - 6
Rearranging the equation, we have:
x^2 + x - 240 = 0
Now, we can solve this quadratic equation either by factoring or by using the quadratic formula. Let's use factoring to find the values of x.
Factoring the equation, we have:
(x+16)(x-15) = 0
Setting each factor equal to zero, we get:
x+16 = 0 or x-15 = 0
Solving for x, we have:
x = -16 or x = 15
Since the width cannot be negative, we take x = 15 as the valid solution.
Therefore, the original dimensions of the piece of metal were 15 inches in width and (15+5) = 20 inches in length.
For more such questions on original dimensions
https://brainly.com/question/31552973
#SPJ8
A message is coded into the binary symbols 0 and 1 and the message is sent over a communication channel.
The probability a 0 is sent is 0.4 and the probability a 1 is sent is 0.6. The channel, however, has a random error that
changes a 1 to a 0 with probability 0.1 and changes a 0 to a 1 with probability 0.2. Show your work below.
a. What is the probability a 1 is received?
b. If a 1 is received, what is the probability a 0 was sent?
Answers
Answer:
A: the probability that a 1 is received is 0.56.
B: the probability that a 0 was sent given that a 1 is received is (2/25) * (1 - P(0 sent)).
Step-by-step explanation:
To solve this problem, we can use conditional probabilities and the concept of Bayes' theorem.
a. To find the probability that a 1 is received, we need to consider the two possibilities: either a 1 was sent and remained unchanged, or a 0 was sent and got flipped to a 1 by the random error.
Let's denote:
P(1 sent) = 0.6 (probability a 1 is sent)
P(0→1) = 0.2 (probability a 0 is flipped to 1)
P(1 received) = ?
P(1 received) = P(1 sent and unchanged) + P(0 sent and flipped to 1)
= P(1 sent) * (1 - P(0→1)) + P(0 sent) * P(0→1)
= 0.6 * (1 - 0.2) + 0.4 * 0.2
= 0.6 * 0.8 + 0.4 * 0.2
= 0.48 + 0.08
= 0.56
Therefore, the probability that a 1 is received is 0.56.
b. If a 1 is received, we want to find the probability that a 0 was sent. We can use Bayes' theorem to calculate this.
Let's denote:
P(0 sent) = ?
P(1 received) = 0.56
We know that P(0 sent) + P(1 sent) = 1 (since either a 0 or a 1 is sent).
Using Bayes' theorem:
P(0 sent | 1 received) = (P(1 received | 0 sent) * P(0 sent)) / P(1 received)
P(1 received | 0 sent) = P(0 sent and flipped to 1) = 0.4 * 0.2 = 0.08
P(0 sent | 1 received) = (0.08 * P(0 sent)) / 0.56
Since P(0 sent) + P(1 sent) = 1, we can substitute 1 - P(0 sent) for P(1 sent):
P(0 sent | 1 received) = (0.08 * (1 - P(0 sent))) / 0.56
Simplifying:
P(0 sent | 1 received) = 0.08 * (1 - P(0 sent)) / 0.56
= 0.08 * (1 - P(0 sent)) * (1 / 0.56)
= 0.08 * (1 - P(0 sent)) * (25/14)
= (2/25) * (1 - P(0 sent))
Therefore, the probability that a 0 was sent given that a 1 is received is (2/25) * (1 - P(0 sent)).
A message is coded into the binary symbols 0 and 1 and the message is sent over a communication channel. The probability a 0 is sent is 0.4 and the probability a 1 is sent is 0.6. The channel, however, has a random error that changes a 1 to a 0 with probability 0.2 and changes a 0 to a 1 with probability 0.1. (a) What is the probability a 0 is received? (b) If a 1 is received, what is the probability a 0 was sent?
Assume that at the current exchange rate, the British pound is worth $1.65 in American dollars. You have some dollar bills and several British pound coins. There are 17 items altogether, which have a total value of $20.25 in American dollars. How many American dollars and how many British pound coins do you have?
Answers
Answer:
So we have $11.64 in American dollars and £5 in British pound coin
Step-by-step explanation:
To solve this problem, we can use a system of equations. Let x be the number of American dollars and y be the number of British pound coins. Then we have:
x + y/1.65 = 20.25 (since each British pound coin is worth 1.65 American dollars)
x = 17 - y (since there are 17 items altogether)
Substituting the second equation into the first, we get:
(17 - y) + y/1.65 = 20.25
Multiplying both sides by 1.65, we get:
28.05 - y + y = 33.4125
y = 33.4125 - 28.05
y = 5.3625
Therefore, we have 5 British pound coins and:
x = 17 - y = 17 - 5.3625 = 11.6375
Use the perimeter formula to find the perimeter of the rectangle.
a vertical rectangle with one side length labeled 11 inches and another side length labeled 9 inches
40 inches
31 inches
22 inches
18 inches
Answers
Answer:
Perimeter = 40 inches
Step-by-step explanation:
The formula for the perimeter of a rectangle is given by:
P = 2l + 2w, where,
P is the perimeter,l is the length,and w is the width.Thus, we can allow the 11-inch side to represent the length and the 9-inch side to represent the width and plug in 11 for l and 9 for w in the perimeter formula to find P, the perimeter of the rectangle:
P = 2(11) + 2(9)
P = 22 + 18
P = 40
Thus, the perimeter of the rectangle is 40 inches.
A small college has 204 student athletes. The number of students who play soccer is 52. The number of students who play volleyball is 31. The probability that a student plays in both volleyball and soccer is 5/204.What is the probability that a randomly selected student athlete in this school: Plays both soccer and volleyball? Plays volleyball?
Answers
To calculate the probabilities, we can use the following information:
Total number of student athletes = 204
Number of students who play soccer = 52
Number of students who play volleyball = 31
Probability of a student playing both soccer and volleyball = 5/204
1. Probability that a student plays both soccer and volleyball:
Let's denote the probability of playing both soccer and volleyball as P(Soccer and Volleyball). From the given information, we know that the number of students who play both soccer and volleyball is 5.
P(Soccer and Volleyball) = Number of students who play both soccer and volleyball / Total number of student athletes
P(Soccer and Volleyball) = 5 / 204
2. Probability that a student plays volleyball:
We want to find the probability of a student playing volleyball, denoted as P(Volleyball).
P(Volleyball) = Number of students who play volleyball / Total number of student athletes
P(Volleyball) = 31 / 204
Therefore, the probability that a randomly selected student athlete in this school plays both soccer and volleyball is 5/204, and the probability that they play volleyball is 31/204.
for similar questions on probabilities.
https://brainly.com/question/251701
#SPJ8
The area of a triangular road sign is 70 square ft. If the base of the sign measures 14 ft, what is the height of the sign?
Answers
Answer:
height = 10 ft
Step-by-step explanation:
the area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )
given A = 70 and b = 14 , then
[tex]\frac{1}{2}[/tex] × 14 × h = 70
7h = 70 ( divide both sides by 7 )
h = 10 ft
subtract (9x^2+4x) from ( -4x^2-7)
Answers
Answer: -13x² - 4x - 7
Step-by-step explanation:
We will subtract (9x² + 4x) from (-4x² - 7).
Given:
-4x² - 7 - (9x² + 4x)
Distribute the negative:
-4x² - 7 - 9x² - 4x
Reorder terms by degree:
-4x² - 9x² - 4x - 7
Combine like terms:
-13x² - 4x - 7
0.005627 to 3 decimal places
Answers
(i) Correcting the figures to 3 decimal places:
-0.005627 ≈ -0.006
0.0056 ≈ 0.006
-0.0049327 ≈ -0.005
0.0049 ≈ 0.005
-0.001342 ≈ -0.001
(ii) Correcting the figures to 3 significant figures:
-0.005627 ≈ -0.00563
0.0056 ≈ 0.00560
-0.0049327 ≈ -0.00493
0.0049 ≈ 0.00490
-0.001342 ≈ -0.00134
(i) When rounding to 3 decimal places, we look at the fourth decimal place and round the figure accordingly. If the fourth decimal place is 5 or above, we round up the preceding third decimal place. If the fourth decimal place is less than 5, we simply drop it.
(ii) When rounding to 3 significant figures, we consider the digit in the third significant figure. If the digit in the fourth significant figure is 5 or above, we round up the preceding third significant figure. If the digit in the fourth significant figure is less than 5, we simply drop it.
Rounding to the correct number of decimal places or significant figures is important to maintain precision and accuracy in calculations and measurements. It helps to ensure that the reported values are appropriate for the level of precision required in a given context.
For more such questions on significant figures
https://brainly.com/question/30169
#SPJ8
Express in simplest radical form show work
Answers
Answer:
-33x√2
Step-by-step explanation:
[tex]-5x\sqrt{98}+2\sqrt{2x^2}\\\\= -5x\sqrt{2*7^{2} } + 2(x\sqrt{2} )\\\\= -5x(7)(\sqrt{2} ) + 2x\sqrt{2} \\\\= -35x\sqrt{2} +2x\sqrt{2} \\\\= (-35+2)x\sqrt{2}\\ \\=-33x\sqrt{2}[/tex]
I've been stuck on this problem for a minute, anyone able to show me what to do?
Use the following duration times (seconds) of 24 eruptions of the Old Faithful geyser in Yellowstone National
Park. The duration times are sorted from lowest to highest.
110 120 178 213 234 234 235 237 240 243 245 245
250 250 251 252 254 255 255 259 260 266 269 273
Describe how to calculate the limits to determine outliers for this data set? Identify any outliers.
Answers
Answer:
1. 01= 234, 03= 255 (since the data is
already sorted)
2. I0R = 255 - 234= 21
3. Lower limit = 234- 1.5 * 21= 203.5
Upper limit = 255+ 1.5 * 21= 285.5
4. Outliers: 110, 120, 178 (below the
lower limit), and 273 (above the upper
limit)
. Julio compró ropa por un costo de $5000, por la cual dejó el 20% de apartado. ¿Con cuánto dinero termina de pagar la ropa?
Answers
Julio bought clothes for $5000 with a 20% down payment, which amounts to $1000. Hence, he ends up paying $4000 for the clothes.
Julio's clothing purchase involved a total cost of $5000. To secure the purchase, he made a down payment of 20% of the total cost. To calculate the down payment, we multiply the total cost by the down payment percentage:
Down payment = 20% * $5000
Down payment = 0.20 * $5000
Down payment = $1000
The down payment amount is $1000. To determine the final amount that Julio ends up paying for the clothes, we need to subtract the down payment from the total cost:
Total cost - Down payment = $5000 - $1000
Total cost - Down payment = $4000
Therefore, Julio ends up paying $4000 for the clothes.
For more such information on: down payment
https://brainly.com/question/1698287
#SPJ8
The question probable may be:
Julio bought clothes for a cost of $5000, for which he left a 20% down payment. How much money does he end up paying for the clothes?
This year, the number of raffle tickets sold for a school's extracurricular activities fundraiser is 848. It is estimated that the number of raffle tickets sold will increase by 5% each year. Find the total number of raffle tickets sold at the end of 9 years.
Select the correct answer below:
9,158
9,351
9,818
10,666
Answers
This year, the number of raffle tickets sold for a school's extracurricular activities fundraiser is 848. It is estimated that the number of raffle tickets sold will increase by 5% each year.
The total number of raffle tickets sold at the end of 9 years is approximately 9,818.
To find the total number of raffle tickets sold at the end of 9 years, we need to calculate the number of tickets sold each year and sum them up.
Starting with the initial number of tickets sold, which is 848, we will increase this number by 5% each year for a total of 9 years.
Year 1: 848 + (5% of 848) = 848 + 42.4 = 890.4
Year 2: 890.4 + (5% of 890.4) = 890.4 + 44.52 = 934.92
Year 3: 934.92 + (5% of 934.92) = 934.92 + 46.746 = 981.666
Year 9: Ticket sales at the end of 9 years = Number of tickets sold in Year 8 + (5% of Year 8 sales)
Year 9: Total = 1,399.585 + 69.97925 = 1,469.56425 ≈ 1,469.56
The total number of raffle tickets sold at the end of 9 years is approximately 1,469.56.
The correct option is 9,818.
For more questions on raffle tickets
https://brainly.com/question/2083262
#SPJ8
Quadrilateral EFGH is an isosceles trapezoid with bases EH and FG. The measure of angle HGF is (9y + 3)°, and the measure of angle EFG is (By + 5)°.
What is the measure of angle HGF?
Answers
The correct Option is A. The measure of angle HGF is 20°.
Quadrilateral EFGH is an isosceles trapezoid with bases EH and FG.
The measure of angle HGF is (9y + 3)°, and the measure of angle EFG is (By + 5)°.
To find the measure of angle HGF, we need to solve for the value of y.
Since EFGH is an isosceles trapezoid, the opposite angles are congruent.
Therefore, the measure of angle EFG is also (9y + 3)°.
To find the value of y, we can set the two expressions equal to each other: (9y + 3)° = (By + 5)°.
Next, we can solve for y by isolating it.
We subtract 3° from both sides: 9y = By + 2.
To get y by itself, we subtract By from both sides: 9y - By = 2.
Finally, we can factor out y: y(9 - B) = 2.
To solve for y, we divide both sides by (9 - B): y = 2 / (9 - B).
Now that we have the value of y, we can substitute it back into the expression for angle HGF: (9y + 3)°.
Thus, the measure of angle HGF is (9(2 / (9 - B)) + 3)°.
Therefore, The correct Option is A.
For more questions on angle
https://brainly.com/question/25770607
#SPJ8
If FE =14 find the length of BC
Please give a very in-depth explanation and I will mark Brainliest!!
Answers
HI Your answer is 42
I have calculated it you can trust me
Well you have marked right in the pic
PLEASE MARK AS BRAINLIEST
simplify each expression 4(x+2)+(8+2x)
Answers
The simplified form of the expression for 4( x + 2 ) + ( 8 + 2x ) is 6x + 16.
What is the simplified form of the expression?Given the expresion in the equestion:
4( x + 2 ) + ( 8 + 2x )
To simplify the expression 4( x + 2 ) + ( 8 + 2x ), first, apply distributive property by distributing 4 to the terms ( x + 2 ):
4( x + 2 ) + ( 8 + 2x )
4 × x + 4 × 2 + 8 + 2x
4x + 8 + 8 + 2x
Collect and add like terms:
4x + 2x + 8 + 8
Add 4x and 2x
6x + 8 + 8
Add the constants 8 + 8
6x + 16
Therefore, the simplified form is 6x + 16.
Learn about PEMDAS here: brainly.com/question/36185
#SPJ1