The probability that more than 240 flights in a random sample of 400 commercial airline flights will arrive on time is approximately 1 or 100%.
To solve this problem using a normal approximation, we need to calculate the mean (μ) and standard deviation (σ) of the binomial distribution and then use the normal distribution to approximate the probability.
Given:
Probability of an airline flight arriving on time (success): p = 0.84
Number of trials (flights): n = 400
Number of flights arriving on time (successes): x > 240
First, we calculate the mean and standard deviation of the binomial distribution using the following formulas:
Mean (μ) = n * p
Standard Deviation (σ) = √(n * p * (1 - p))
μ = 400 * 0.84 = 336
σ = √(400 * 0.84 * 0.16) = √(53.76) ≈ 7.33
Now, we can use the normal distribution to find the probability that more than 240 flights will arrive on time. Since we're interested in the probability of x > 240, we will calculate the probability of x ≥ 241 and then subtract it from 1.
To use the normal distribution, we need to standardize the value of 240:
z = (x - μ) / σ
z = (240 - 336) / 7.33
z ≈ -13.13
Now, we can find the probability using the standard normal distribution table or a calculator. Since the value of z is extremely low, we can approximate it as:
P(x > 240) ≈ P(z > -13.13)
From the standard normal distribution table or calculator, we find that P(z > -13.13) is essentially 1 (close to 100%).
Therefore, the probability that more than 240 flights in a random sample of 400 commercial airline flights will arrive on time is approximately 1 or 100%.
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In each of the following graphs, find the lengths of the line segments shown. Write your answers (in simplest
radical form if they are not integers.
(a)
B
(b)
Q
The length of the two segments, written as radicals, are:
AB = √117
PQ = √244
How to find the length of the segments shown?Remember that for a segment whose endpoints are (x₁, y₁) and (x₂, y₂), the length of the segment is:
L = √( (x₂ - x₁)² + (y₂ - y₁)²)
First, for the segment AB the endpoints are:
A = (-4, -4)
B = (2, 5)
Then the length is:
L = √( (-4 - 2)² + (-4 - 5)²)
L = √117
For the segment PQ the endpoints are:
P = (-6, 8)
Q = (6, -2)
The length is:
L = √( (-6 - 6)² + (8 + 2)²)
L = √244
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What is the vertical displacement of the basic graph to produce a graph of
OA Sunits down
B. 2 units down
OC units down
OD
units up
SUBMIT
The vertical displacement is of 2 units down, the correct option is B.
What is the vertical displacement?Remember that for a function f(x), a vertical displacement of N units is written in general form as:
g(x) = f(x) + N
If N > 0, the translation is upwards.
if N < 0, the translation is downwards.
Here we assume that we start with the parent cosine function:
y = cos(x)
And the transformed function is:
y = -2 - cos(x - π)
So we have some transformations, but the vertical translation is of 2 units down. So the correct option is B.
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DUE TDYYYYYY!!!!!!!!
The data on the box plots indicates;
6. a) 46 years, b) 24 years, c) 75%
7. a) 70 seconds and 58 seconds, b) 50%, c) 25%
8. a) 32 inches and 44 inches, b) 50%, c) The data vary least between the lower quartile and the median
What is a box plot?A box plot also known as a box and whisker plot displays the five number summary of a dataset.
6. The data from the ages of the teachers at the Carter Middle School indicates that we get;
The minimum age = 24 years
Q₁ = 30 years
Q₂ = 46 years
Q₃ = 54 years
The maximum of the data = 66 years
Therefore;
a) The median age, Q₂ = 46 years
b) The interquartile range = 54 years - 30 years = 24 years
c) The percentage of the teachers that are at least 30 years (30 years or more) = (100 - Q₁)% = (100 - 25)% = 75%
7. The five number summary of the track and field running times are;
The minimum = 58 s
Q₁ = 60 s
Q₂ = 63 s
Q₃ = 65 s
The maximum of the data = 70 s
a) The maximum and minimum run times are; 70 seconds and 58 seconds
b) The median run time is 63, and the maximum run time is 70, therefore, the percentage of runners that had a runtime between 63 and 70 is 50%
c) The first quartile or 25th percentile running time is 60 seconds, therefore, the percentage of runners that have a time of at most 60 seconds is 25%
8. The five number summary of the data of the wingspan of the birds are;
The minimum = 24
Q₁ = 32 inches
Q₂ = 36 inches
Q₃ = 44 inches
The maximum of the data = 72 inches
The above five number summary for the wingspan indicates;
a) The lower and upper quartiles are; Q₁ = 32 inches and Q₃ = 44 inches
b) 3 feet = 36 inches, therefore;
The median, Q₂ = 36 inches, therefore, the percentage that have a wingspan of no more than 3 feet (3 feet or less) is 50%
c) The variability of the data from the box and whiskers chart indicates that the quartile the data values vary least is between Q₁ and Q₂
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I NEED HELP ASAP 100 POINTZZZZZZZZ
A square with sides measuring 7 millimeters each is drawn within the figure shown. A point within the figure is randomly selected.
What is the approximate probability that the randomly selected point will lie inside the square?
Responses
4.7%
4.7%
7.4%
7.4%
16.6%
16.6%
26.1%
Answer:
To find the probability that the randomly selected point will lie inside the square, we need to find the area of the square and the area of the figure, and then divide the area of the square by the area of the figure.
The area of the square is 7 mm x 7 mm = 49 mm^2.
To find the area of the figure, we can divide it into a rectangle and two right triangles. The rectangle has dimensions of 8 mm x 14 mm, so its area is 8 mm x 14 mm = 112 mm^2. Each right triangle has base 8 mm and height 6 mm, so each triangle has an area of (1/2) x 8 mm x 6 mm = 24 mm^2. The total area of the figure is therefore 112 mm^2 + 24 mm^2 + 24 mm^2 = 160 mm^2.
The probability of selecting a point inside the square is then 49 mm^2 / 160 mm^2, which is approximately 0.3063 or 30.63%.
Therefore, the answer is closest to 26.1%, which is the third option.
Step-by-step explanation:
20. Which of the following is the function for the graph below?
The quadratic function that represents the given graph is:
y = ¹/₂(x − 4)² - 1
How to write a quadratic equation in vertex form?The general form of a quadratic equation in Vertex Form is expressed as:
y = a(x − h)² + k,
where
(h, k) is the vertex.
From the given graph, we can see that the coordinates of the vertex is (4, -1). Thus, we have:
y = a(x − 4)² - 1
Looking at the four given options from Option A to Option D, we can deduce that only given option that gives us the coordinates of the quadratic curve vertex is option D.
Thus, we can conclude that the quadratic function that truly represents the given parabolic graph curve is:
y = ¹/₂(x − 4)² - 1
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Ladonna borrowed 2000$ to purchase a car the total amount she will need pay includes 2000 200 in interest and 75$ in loan fees what is the finance charge on Lasonnas loan
Answer:
i don't know fam how will I be able to answer that
Urgent please!!
If there are 100 students, (66 who have over 70% in homework with 62 of those 66 students passing the exam and 4 failing, and 34 students who have below a 70% in homework, with only 8 passing and 26 failing) what is the probability that a student has under 70% or did not pass the final exam?
The probability that a student has under 70% or did not pass the final exam is 26/100.
Given that,
Total number of students = 100
Number of students who has over 70% = 66
Number of students who has under 70% = 34
Number of students who have under 70% and passing the exam = 8
Number of students who have under 70% and did not pass the exam = 26
Probability that a student has under 70% or did not pass the final exam is,
P = 26/100
Hence the required probability is 26/100.
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An employee is considering two job offers . First offer : $ 57,000 yearly salary with a 6 % matching 401k Second offer : $ 63,000 yearly salary with a 5 % matching 401k The employee plans to stay at either job for at least 4 years , assumes there are no salary increases , and will make 401k contributions at the same rate the company matches . After 4 years , the total value of the first offer , including gross income and total 401k contributions , is $ 255,360 . Which job has the better overall pay structure , and by how much ?
Answer:
To compare the two job offers, we need to calculate the total value of each offer after four years. Let's start with the first offer:
- Yearly salary: $57,000
- 401k matching: 6% of salary, so $3,420 per year
- Total yearly income: $57,000 + $3,420 = $60,420
- Total 401k contribution after 4 years: $3,420 x 4 = $13,680
- Total gross income after 4 years: $60,420 x 4 = $241,680
- Total value after 4 years (including 401k contributions): $241,680 + $13,680 = $255,360
Now let's do the same calculation for the second offer:
- Yearly salary: $63,000
- 401k matching: 5% of salary, so $3,150 per year
- Total yearly income: $63,000 + $3,150 = $66,150
- Total 401k contribution after 4 years: $3,150 x 4 = $12,600
- Total gross income after 4 years: $66,150 x 4 = $264,600
- Total value after 4 years (including 401k contributions): $264,600 + $12,600 = $277,200
Therefore, the second job offer has a better overall pay structure by $21,840 ($277,200 - $255,360).
Write the equation of the conic section shown below.
Please help 100 pts math
(x+4)² + (y-4)² = 9 is the measure of the equation of the circle.
Equation of a circleThe given diagram is a circle and the general formula of a circle is expressed as:
(x-a)² + (y-b)² = r²
where;
(a, b) is the centre
r is the radius
The centre is at (-4, 4). The radius of the circle is expressed as:
r² = (4-4)² + (-1+4)²
r² = 3²
r² = 9
Substitute the centre and square of the radius to have (x+4)² + (y-4)² = 9
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Answer:
[tex](x+4)^2+(y-4)^2=9[/tex]
Step-by-step explanation:
From observation of the given diagram, we can see that the graphed conic section is a circle with center (-4, 4) that passes through point (-1, 4).
The equation of a circle in standard form is:
[tex]\boxed{(x-h)^2+(y-k)^2=r^2}[/tex]
where:
(h, k) is the center.r is the radius.The radius of a circle is the distance from the center of the circle to any point on its circumference.
As the center and given point have the same y-coordinate, the radius is the distance between their x-coordinates. Therefore:
[tex]r = -1-(-4)=-1+4=3[/tex]
To write the equation of the circle, substitute h = -4, k = 4 and r = 3 into the formula:
[tex](x-(-4))^2+(y-4)^2=3^2[/tex]
[tex](x+4)^2+(y-4)^2=9[/tex]
Therefore, the equation of the graphed conic section (circle) is:
[tex]\boxed{(x+4)^2+(y-4)^2=9}[/tex]
Every animal cost the zoo money. Some of the things that the zoo needs to
pay for are food for the animals, enrichment materials, upkeep of the exhibit,
landscape of the exhibit, and more. The total cost of an animal is the cost of
food and the other expenses. Let the other expenses total $15,000 a week.
Food costs $7 a pound. Write an expression for how much it costs to keep
an adult of your animal for one week where x is the number of pounds your
adult animal eats in a day.
The total cost of an animal is the cost of food and the other expenses. Let
the other expenses total $15,000 a week. Food costs $7 a pound.
Write an expression to show how much it costs per week to keep the baby
animal where x is the number of pounds one adult eats in a day. Simplify
your expression
Please help???
Answer:
First, let's establish a few facts based on your question:
1. The food costs $7 per pound.
2. An adult animal eats x pounds of food per day.
3. There are other costs totaling $15,000 per week.
4. We are assuming a 7-day week.
Now, let's write an expression for the total cost of keeping an adult animal for one week.
The food cost for one day for an adult animal is 7x dollars (because the animal eats x pounds of food per day, and each pound costs $7).
So, an adult animal's food cost for one week (7 days) is 7x * 7 dollars.
Plus the other expenses of $15,000 per week, the total cost for one week becomes:
7x * 7 + 15,000
This simplifies to:
49x + 15,000
This expresses the total cost of keeping an adult animal for one week.
The baby animal usually eats less than an adult. We can't establish an exact formula if we don't have a specific proportion or ratio. Let's assume a baby animal eats half the amount of an adult animal (0.5x); you could adjust this as per the actual ratio for your specific animal.
So, a baby animal's food cost for one day is 7*0.5x dollars.
A baby animal's food cost for one week (7 days) is 7*0.5x * 7 dollars.
So, adding the other expenses of $15,000 per week, the total cost for one week becomes:
7*0.5x * 7 + 15,000
This simplifies to:
24.5x + 15,000
This would be the expression for the total cost of keeping a baby animal for one week, assuming it eats half the amount of an adult. You can adjust the 0.5 factor to match your specific animal's actual food consumption ratio of the baby to the adult.
Cindy, Inc. sells a product for $10 per unit. The variable expenses are $6 per unit, and the fixed expenses total $35,000 per period. By how much will net operating income change if sales are expected to increase by $40,000?
A) $16,000 increase
B) $5,000 increase
C) $24,000 increase
D) $11,000 decrease
Answer: it is a $16,000 increase
In which quadrants is cosine positive?
A. I and II
B. I and III
C. II and IV
D. I and IV
D. I and IV are the quadrants the cosine function is positive
To determine in which quadrants the cosine function is positive, we need to consider the signs of cosine in different quadrants of the Cartesian coordinate system.
The unit circle is a useful tool to understand the behavior of trigonometric functions. In the unit circle, the x-coordinate represents the cosine value, while the y-coordinate represents the sine value. The cosine function is positive in the quadrants where the x-coordinate is positive.
Quadrant I is the top-right quadrant, where both the x and y coordinates are positive. In this quadrant, cosine is positive because the x-coordinate is positive.
Quadrant II is the top-left quadrant, where the x-coordinate is negative, but the y-coordinate is positive. In this quadrant, cosine is negative because the x-coordinate is negative.
Quadrant III is the bottom-left quadrant, where both the x and y coordinates are negative. In this quadrant, cosine is negative because the x-coordinate is negative.
Quadrant IV is the bottom-right quadrant, where the x-coordinate is positive, but the y-coordinate is negative. In this quadrant, cosine is positive because the x-coordinate is positive.
Based on this analysis, we can conclude that cosine is positive in Quadrant I and Quadrant IV. Therefore, the correct answer is D. I and IV.
It's important to note that this applies to the standard unit circle and the principal values of cosine. When considering periodicity and multiple revolutions around the unit circle, the positive regions of cosine will repeat every 360 degrees or 2π radians.
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Multiple choice: which function has an amplitude of 5 and a period of pie/3 ?
A) f(x)= 5 cos 6x
B) f(x)= 1/5 cos 6x
C) f(x)= 5 cos 2/3 x
D) f(x)= 3 cos 5x
Option C) f(x) = 5 cos (2/3 x) is the Function that has an amplitude of 5 and a period of π/3.
The function that has an amplitude of 5 and a period of π/3 is:
C) f(x) = 5 cos (2/3 x)
To determine the correct option, let's analyze the components of the function.
The general form of a cosine function is f(x) = A cos (Bx), where A represents the amplitude and B represents the frequency.
Given that the amplitude is 5, we can eliminate options A and B since they have amplitudes of 6 and 1/5, respectively.
Now, look at the period of the function. The period (T) of a cosine function is calculated as T = 2π/B, where B represents the frequency.
In this case, the period is given as π/3, which means T = π/3.
To find the frequency B, we can rearrange the formula: B = 2π/T.
Substituting T = π/3 into the formula, we get B = 2π/(π/3) = 2π * 3/π = 6.
Comparing the frequency B of option C (B = 2/3) with the calculated frequency (B = 6), we can see that they match.
Therefore, the correct function with an amplitude of 5 and a period of π/3 is:
C) f(x) = 5 cos (2/3 x).
In conclusion, option C) f(x) = 5 cos (2/3 x) is the function that has an amplitude of 5 and a period of π/3.
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Find the area of the trapezoid. Leave your answer in simplest radical form.
20√3 in² is the required area of the trapezoid in simplest form
Area of a trapezoidThe formula for calculating the area of a trapezoid is expressed as:
A = 1/2(a+b)*h
where
a and b are the sides
h is the height of the trapezoid
Given the following
a = 14in
b =26 in
For the height:
tan 60 = h/6
h = 6tan60
h = √3
Substitute
A = 1/2(14 + 26)*√3
A = 20√3 in²
Hence the area of the trapezoid in its simplest radical form is 20√3 in²
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Help me understand this please
The sine of the angle θ in this problem is given as follows:
[tex]\sin{\theta} = \pm \frac{\sqrt{17}}{7}[/tex]
What is the unit circle?For an angle [tex]\theta[/tex] the unit circle is a circle with radius 1 containing the following set of points with the trigonometric ratios of an angle θ: [tex](\cos{\theta}, \sin{\theta})[/tex].
Hence the relation between sine and cosine is given as follows:
sin²(θ) + cos²(θ) = 1.
The cosine for this problem is given as follows:
[tex]\cos{\theta} = \frac{4\sqrt{2}}{7}[/tex]
The square of the cosine is then given as follows:
[tex]\cos^2{\theta} = \frac{32}{49}[/tex]
Then the sine is obtained as follows:
sin²(θ) + 32/49 = 1
sin²(θ) = 17/49
[tex]\sin{\theta} = \pm \frac{\sqrt{17}}{7}[/tex]
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Explain how you would determine the input value of the function f(x) = 4x + 3/4 given a specific output value?
We can set up an equation and solve it for the input. If the output is A, then we will get:
x = A/4 - 3/16
How to find the input?Let's say that we know that the output is f(x) = A, then we can write the equation:
A= 4x + 3/4
Now we can solve that for x.
A = 4x + 3/4
A - 3/4 = x
(A - 3/4)/4 = x
A/4 - 3/16 = x
That is the input for the given output.
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Condense each expression to a single logarithm. I know the answer, I just don’t understand how to get there. Any in-depth answer appreciated.
The condensed form of the given expression is log₆√(660).
To condense the expression (log₆ 5)/2 + (log₆ 12)/2 + (log₆ 11)/2 into a single logarithm, we can use the properties of logarithms.
As we know that the property of logarithms that states:
logₐ(b) + logₐ(c) = logₐ(b x c)
Applying this property to the given expression, we have:
(log₆ 5)/2 + (log₆ 12)/2 + (log₆ 11)/2 = log₆(5 x 12 x 11)/2
Now, we simplify the inside of the logarithm:
5 x 12 x 11 = 660
Substituting this back into the expression, we have:
(log₆ 5)/2 + (log₆ 12)/2 + (log₆ 11)/2 = log₆(660)/2
log₆(660)/2 = (1/2) log₆(660)
Finally, we can further simplify the expression by using the property:
logₐ(xⁿ) = n logₐx.
log₆√(660)
So, the condensed form of the expression is:
log₆√(660)
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A cylinder has been cut out of a solid. Find the volume of the remaining solid. ( i want to learn how to solve this but have found no useful things online please help!!!!!)
The volume of the remaining solid is approximately 417.17 [tex]cm^3.[/tex]
To find the volume of the remaining solid after a cylinder has been cut out, you need some additional information. Specifically, you need the dimensions of the original solid and the dimensions of the cylinder that was cut out. With that information, you can calculate the volume of both the original solid and the cylinder, and then subtract the volume of the cylinder from the volume of the solid to find the volume of the remaining solid.
Let's assume that the original solid is a cylindrical prism and the cylinder that was cut out is aligned with the length of the prism. Here's a step-by-step process to find the volume of the remaining solid:
Determine the dimensions of the original solid:
Let's say the length, width, and height of the original solid are represented by L, W, and H, respectively.
Determine the dimensions of the cylinder:
The cylinder should have the same length as the original solid, so its length is also L. Let's denote the radius of the cylinder as r and its height as h.
Calculate the volume of the original solid:
The volume of a cylindrical prism is given by the formula V = L × W × H.
Calculate the volume of the cylinder:
The volume of a cylinder is given by the formula V = π × [tex]r^2[/tex] × h.
Subtract the volume of the cylinder from the volume of the original solid to find the volume of the remaining solid:
V_remaining = V_original - V_cylinder.
Here's an example to illustrate the process:
Example:
Let's say the original solid is a cylindrical prism with dimensions L = 10 cm, W = 6 cm, and H = 8 cm. The cylinder that was cut out has a radius of r = 2 cm and a height of h = 5 cm.
Volume of the original solid:
V_original = L × W × H = 10 cm × 6 cm × 8 cm = 480 [tex]cm^3.[/tex]
Volume of the cylinder:
V_cylinder = π × [tex]r^2[/tex] × h = π × [tex](2 cm)^2[/tex] × 5 cm ≈ 62.83 [tex]cm^3.[/tex]
Volume of the remaining solid:
V_remaining = V_original - V_cylinder = 480[tex]cm^3[/tex]- 62.83 [tex]cm^3[/tex] ≈ 417.17 [tex]cm^3.[/tex]
Therefore, the volume of the remaining solid is approximately 417.17 [tex]cm^3.[/tex]
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Look at the square below. It is divided into 100 squares. If you needed to color in 28%, how many squares would you color?
square divided into 100 smaller squares, 10 x 10
To find the number of squares you would need to color if you need to color in 28% of a square divided into 100 smaller squares, 10 x 10, you would follow these steps:First, find what 28% of 100 is.
To do this, you can multiply 100 by 0.28:100 x 0.28 = 28Next, you know that there are 100 smaller squares in the larger square, so you can multiply the number of smaller squares by the percentage you need to color:100 x 0.28 = 28You would need to color in 28 smaller squares out of the 100 smaller squares in the larger square.
Therefore, you would color in 28% of the square. It's important to note that you could also express 28% as a fraction or decimal:28% = 28/100 = 0.28By using these equivalent forms of 28%, you can solve the problem in a few different ways.
But the simplest method is to multiply the total number of squares in the square by the percentage that needs to be shaded. Therefore, if you needed to color 28% of a square divided into 100 smaller squares, 10 x 10, you would color in 28 smaller squares.
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find the slope and y-intercept.
The slope and the y-intercept of the line y = 4x + 5 are given as follows:
Slope of 4.y-intercept of 4.How to define a linear function?The slope-intercept equation for a linear function is presented as follows:
y = mx + b
The coefficients m and b represent the slope and the intercept, respectively, and are explained as follows:
m represents the slope of the function, which is by how much the dependent variable y increases or decreases when the independent variable x is added by one.b represents the y-intercept of the function, representing the numeric value of the function when the input variable x has a value of 0. On a graph, the intercept is given by the value of y at which the graph crosses or touches the y-axis.The function for this problem is given as follows:
y = 4x + 5.
Hence the slope and the intercept are given as follows:
m = 4.b = 5.Missing InformationThe problem asks for the slope and the intercept of y = 4x + 5.
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This is algebra 1 and can u help me my friends because is describe the error in solving x^2+3x=18 by graphing
The error is that the x-intercept of the given equation is x = -6 and x = 3 not, x = 0 and x = -3.
The equation should now be written as a quadratic equation with the variable zero.
x² + 3x - 18 = 0
Use the quadratic formula or factor the quadratic equation.
The equation can be factored in this situation as follows:
(x + 6)(x - 3) = 0
Set each factor equal to zero and solve for x.
x + 6 = 0 or x - 3 = 0
Solving the first equation:
x + 6 = 0
x = -6
Solving the second equation:
x - 3 = 0
x = 3
Therefore, the solutions to the equation x² + 3x = 18 are x = -6 and x = 3.
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4. In the above figure (not drawn to scale), AC=110,CB=20, AD=190, and BD = 40. Find ZAEC.
A. 75°
B. 105°
O C. 90°
O D. 150°
The angle ∠AEC in the chord intersection is 75 degrees.
How to find the angle when chord intersect?If two chords intersect inside a circle, then the measure of the angle formed is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle.
Therefore, let's use the chord intersection to find the angle ∠AEC as follows:
∠AEC = 1 /2 (110 + 40)
∠AEC = 1 / 2 (150)
∠AEC = 75 degrees
Therefore,
∠AEC = 75 degrees
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(06.03 HC)
Let sin8= and <0<.
2
2√2
5
Part A: Determine the exact value of cos 20. (5 points)
0
Part B: Determine the exact value of sin
2
(5 points)
Answer:
Part A:
To determine the exact value of cos 20, we can use the trigonometric identity cos^2θ + sin^2θ = 1. Since sin^2θ = (sin 8)^2 = (2√2/5)^2 = 8/25, we can solve for cos^2θ as follows:
cos^2θ = 1 - sin^2θ
cos^2θ = 1 - 8/25
cos^2θ = 17/25
Taking the square root of both sides, we get:
cosθ = ±√(17/25)
Since 0 < θ < π/2 (given that θ is acute), cosθ is positive. Therefore:
cosθ = √(17/25)
cosθ = √17/5
So, the exact value of cos 20 is √17/5.
Part B:
To determine the exact value of sin (2θ), we can use the double-angle formula for sine, which states that sin (2θ) = 2sinθcosθ. Given that sin 8 = 2√2/5 and cosθ = √17/5 (from Part A), we can substitute these values into the formula:
sin (2θ) = 2(sin 8)(cosθ)
sin (2θ) = 2(2√2/5)(√17/5)
sin (2θ) = (4√2√17)/25
sin (2θ) = (4√34)/25
So, the exact value of sin (2θ) is (4√34)/25.
Step-by-step explanation:
The PTO is selling raffle tickets to raise money for classroom supplies. A raffle ticket costs $4. There is 1 winning ticket out of the 280 tickets sold. The winner gets a prize worth $62. Round your answers to the nearest cent.
What is the expected value (to you) of one raffle ticket? $
Calculate the expected value (to you) if you purchase 12 raffle tickets. $
What is the expected value (to the PTO) of one raffle ticket? $
If the PTO sells all 280 raffle tickets, how much money can they expect to raise for the classroom supplies? $
The expected values of the raffle ticket for you are given as follows:
One ticket: -$3.76.12 tickets: -$45.12.For the PTO, the expected values are given as follows:
One ticket: $3.76.12 tickets: $45.12.What is the mean of a discrete distribution?The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.
For you, the distribution is given as follows:
P(X = 62) = 1/280.P(X = -4) = 279/280.Hence the expected value for one ticket is given as follows:
E(X) = 62/280 - 4 x 279/280
E(X) = -$3.76.
For twelve tickets, the expected value is given as follows:
12 x -3.76 = -$45.12.
For the PTO, we use the inverse signals, as the distribution is the inverse, that is:
P(X = -62) = 1/280.P(X = 4) = 279/280.More can be learned about the expected value of a discrete distribution at https://brainly.com/question/27899440
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AB is a tangent to circle C. Find mA
hello
sum of a triangle's inner angles are 180°, hence;
A = 180 - (42 + 90) = 48°
Based on the graph of the general solution to the differential equation dy over dx equals 2 times x minus 2 times y comma which of the following statements is true?
The slopes along the y-axis are horizontal.
The slopes along the x-axis are horizontal.
The slopes are all positive in Quadrant 4.
The slopes are all positive in Quadrant 1.
Answer:
The slopes along the y-axis are horizontal.
Step-by-step explanation:
The statement "The slopes along the y-axis are horizontal" is true based on the graph of the general solution to the differential equation dy/dx = 2x - 2y. This is because when x = 0, the slope of the solution curve is equal to -2y, which means the slope is horizontal or zero when y = 0.
The statement "The slopes along the x-axis are horizontal" is false because the slope of the solution curve at the point (0,0) is -2(0) = 0, which means the slope is horizontal at this point only.
The statement "The slopes are all positive in Quadrant 4" is false because the slope is negative in Quadrant 4.
The statement "The slopes are all positive in Quadrant 1" is false because the slope is negative in Quadrant 1.
Therefore, the only true statement is "The slopes along the y-axis are horizontal."
Solve x/8 = sin 34°
Give your answer to 1 d.p.
Step-by-step explanation:
Using a calculator, we find sin 34° to be approximately 0.559193.
Multiplying both sides of the equation x/8 = sin 34° by 8, we get x = 8(sin 34°).
Substituting the value we found for sin 34°, we get x = 8(0.559193) ≈ 4.4735
Rounding to 1 decimal place, x ≈ 4.5.
Therefore, x/8 = sin 34° is solved for x to be approximately 4.5.
En la carnicería hemos comprado 2 kg y cuarto de ternera, 5 kg y dos cuartos de pollo y
4 kg y tres cuartos de lomo de cerdo. Expresa en forma de fracción y número decimal el
total de carne que hemos comprado.
Answer:
Step-by-step explanation:
[tex]\frac{25}{2}[/tex]
Please help. Unnecessary answers will be reported.
King Arthur's Sword has a blade that is made of a regular hexagon and a regular pentagon. What is the amplitude of the tip of King Arthur's Sword?
Assuming that the blade of King Arthur's Sword is symmetrical and that the hexagon and pentagon have equal side lengths, we can find the amplitude of the tip by constructing a regular 15-sided polygon (a pentadecagon) with the hexagon and pentagon as two of its sides.
To do this, we can start by drawing a regular hexagon. We then draw a regular pentagon with one of its vertices coinciding with one of the vertices of the hexagon. Next, we draw a line segment connecting the other endpoint of the pentagon to the next vertex of the hexagon, and we draw another regular pentagon with one of its vertices coinciding with this endpoint. We repeat this process until we have constructed the pentadecagon.
The amplitude of the tip of the sword is the distance between the center of the pentadecagon and one of its vertices. This value is difficult to calculate exactly, but we can use the fact that a regular n-sided polygon has each of its vertices equidistant from its center. Since the pentadecagon has 15 vertices, the amplitude of the tip is approximately equal to the radius of a circle that touches each vertex of the pentadecagon.
Using some trigonometry and the fact that the interior angles of a regular pentagon and hexagon are known values, we can calculate that the amplitude of the tip is approximately 1.618 times the side length of each polygon. Therefore, if we know the side length of the hexagon and pentagon, we can multiply that value by approximately 1.618 to find the amplitude of the tip.
A bucket contains six white balls and five red balls. A sample of four balls is selected
at random from the bucket, without replacement. What is the probability that the
sample contains...
Exactly two white balls and two red balls??
At least two white balls?
Answer: 80.30%
Step-by-step explanation:
To calculate the probability, we need to determine the total number of possible samples and the number of samples that satisfy the given conditions.
Exactly two white balls and two red balls:
The total number of ways to choose four balls from a bucket of 11 balls is given by the combination formula: C(11, 4) = 11! / (4! * 7!) = 330.
The number of ways to choose exactly two white balls and two red balls can be calculated as follows: C(6, 2) * C(5, 2) = (6! / (2! * 4!)) * (5! / (2! * 3!)) = 15 * 10 = 150.
Therefore, the probability of selecting exactly two white balls and two red balls is 150/330 ≈ 0.4545 or approximately 45.45%.
At least two white balls:
To calculate this probability, we need to consider the following possibilities:
Selecting exactly two white balls and two red balls: We calculated this in the previous question, and the probability is 150/330 ≈ 0.4545 or approximately 45.45%.
Selecting three white balls and one red ball: C(6, 3) * C(5, 1) = (6! / (3! * 3!)) * (5! / (1! * 4!)) = 20 * 5 = 100.
Selecting four white balls and no red ball: C(6, 4) = 6! / (4! * 2!) = 15.
Adding up these possibilities, the total number of favorable outcomes is 150 + 100 + 15 = 265.
Therefore, the probability of selecting at least two white balls is 265/330 ≈ 0.8030 or approximately 80.30%.
