If Joao scored a goal in 60% of the soccer games last season, then we can expect him to score a goal in about 60% of the games he plays this season.
So, if Joao plays in 10 games this season, we can estimate that he will score a goal in approximately 60% of those games.
To calculate the actual number of games he is expected to score a goal in, we can use the formula:
Expected number of goals = Total number of games x Probability of scoring a goal
Plugging in the numbers, we get:
Expected number of goals = 10 x 0.6 = 6
Therefore, based on the experimental probability from last season, we can estimate that Joao will score a goal in around 6 games out of the 10 he plays this season.
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Use the random list of 100 numbers below and the assignations 0-4 to represent girls and 5-9 to represent boys to answer the question. Determine how many groups contain at least three girls and use the information to answer the questions below.
The example's random list had 25 groups containing three girls, a probability of 25 %. The amount of groups of this random list is (more or less than) ______ the example's random list. The probability of the this random list is therefore (lower or higher then) ________ the example's random list.
The probability of this random list is therefore the same as the example's random list, which is 25%.
What is the probability?To determine the number of groups containing at least three girls, we need to count the number of groups where there are at least 3 numbers between 0 and 4.
We can do this by counting the number of groups that have 0, 1, or 2 numbers between 0 and 4, and subtracting this from the total number of groups:
Number of groups with 0, 1, or 2 numbers between 0 and 4:
Number of groups with 0 numbers between 0 and 4 = 6 choose 0 * 94 choose 4 = 5,414,200
Number of groups with 1 number between 0 and 4 = 6 choose 1 * 94 choose 3 = 291,301,200
Number of groups with 2 numbers between 0 and 4 = 6 choose 2 * 94 choose 2 = 5,111,640
Total number of groups = 100 choose 5 = 75,287,520
Number of groups with at least 3 numbers between 0 and 4:
= Total number of groups - Number of groups with 0, 1, or 2 numbers between 0 and 4
= 75,287,520 - (5,414,200 + 291,301,200 + 5,111,640)
= 64,460,480
The amount of groups of this random list is the same as the example's random list (both have 100 groups).
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Plsss help
The following two-way frequency table displays the number of adults and children attending a sporting event.
Sporting Event Attendance
Males Females Total
Adults 804 641 1,445
Children 431 268 699
Total 1,235 909. 2,144
What percentage of males attending the sporting event are adults?
A.
55. 64%
B.
65. 1%
C.
37. 5%
D.
34. 9%
The percentage of males attending the sporting events that are adults is:
65.10%.
How to obtain the percentage?A percentage is one example of a proportion, as it is obtained by the number of desired outcomes divided by the number of total outcomes, and then multiplied by 100%.
The number of males attending sporting events is given as follows:
1235.
Of those 1235 males, 804 are adults, hence the percentage of males attending the sporting events that are adults is given as follows:
p = 804/1235 x 100%
p = 65.10%.
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PLEASE HELP I NEED THIS QUICK!!!
The number of ways to travel the route is given as follows:
18 ways.
What is the Fundamental Counting Theorem?The Fundamental Counting Theorem states that if there are m ways to do one thing and n ways to do another, then there are m x n ways to do both.
This can be extended to more than two events, where the number of ways to do all the events is the product of the number of ways to do each individual event, according to the equation presented as follows:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
The options for this problem are given as follows:
Providence to Boston: 3 ways.Boston to Syracuse: 3 ways.Syracuse to Pittsburgh: 2 ways.Hence the total number of ways is given as follows:
3 x 3 x 2 = 18 ways.
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Which is an expression in terms of π that represents the area of the shaded part of ⊙R
The general expression would be A_shaded = πr² - (1/2)r²θ(π/180).
To find an expression in terms of π that represents the area of the shaded part of circle R, we need to :
1. Identify the radius (r) of circle R.
2. Determine the area of the entire circle using the formula A_circle = πr².
3. Identify the angle measure (θ) in degrees of the sector corresponding to the shaded part.
4. Convert the angle measure to radians by multiplying by (π/180).
5. Calculate the area of the sector using the formula A_sector = (1/2)r²θ.
6. Subtract the area of the sector from the area of the entire circle to find the area of the shaded part: A_shaded = A_circle - A_sector.
By following these steps, you will obtain an expression in terms of π that represents the area of the shaded part of circle R. However, the general expression would be A_shaded = πr² - (1/2)r²θ(π/180).
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HELP ME PLEASE AND YOU GET BRAINLIEST PLEASE HELP ME FAST
Answer:
48
Step-by-step explanation:
can be divided into two 4x6 rectangles. Therefore, the area is 4x6 + 4x6 = 48
Draw a triangle with one side length of 5 units and another side length
of 7 units. What additional piece of information will guarantee that only
one triangle can be drawn?
It should be noted that to craft a triangle with an edge measuring 5 units of length, another side 7 units in magnitude, we can get underway by sketching an uninterrupted line of 7-units duration.
How to explain the informationSubsequently, draw an additional segment arriving at a peak of 5-units from the starting point of the former line. From the end-point of the line calculated as 7 units, draw a joined line towards the conclusion of the 5 unit-length section. This enables two distinctive triangles:
Also, to guarantee that just a single triangle can be drawn, it is imperative to recognize the angle resting between the two assigned sides. In case we are endowed with the inclination between both varying lengths of five and seven units, then only an original composition of triangle can be constructed.
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¿Cómo se escribe la multiplicación 713 × 49, descomponiendo ambos números?
The decomposition of 713 × 49 has been provided below
How to decompose the problemTo multiply 713 and 49, we can use the distributive property and decompose the second number as follows:
49 = 40 + 9
Then, we can multiply each part of the sum by 713:
713 × 40 + 713 × 9
To calculate this, we can use the multiplication table and then add the results:
713
x 40
28520
713
x 9
6417
Then, we add the two results:
713 × 40 = 28520
713 × 9 = 6417
34997
Therefore, the multiplication 713 × 49, decomposed as 713 × 40 + 713 × 9, equals 34,997.
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When you get home from school, there is 7/8 of a pizza left. You eat 1/2 of it. How much pizza is left over?
Answer: 3/8
Step-by-step explanation:
7/8-1/2
Find common denominator which is 8 and you get that from 1/2 by multiplying 4 on the top and bottom and so you wind up with 4/8 and 7/8-4/8 is 3/8
A political candidate feels that she performed particularly well in the most recent debate against her opponent. Her campaign manager polled a random sample of 400 likely voters before the debate and a random sample of 500 likel voters after the debate. The 95% confidence interval for the true difference (post-debate minus pre-debate) in proportions of likely voters who would vote for this candidate was (-0. 014, 0. 064). What was the difference (pre- debate minus post-debate) in the sample proportions of likely voters who said they will vote for this candidate?
The difference in the sample proportions of likely voters who said they will vote for this candidate is 0.025.
The range of the 95% confidence interval for the actual difference between the proportions of probable voters who would support this candidate before and after the debate was (-0.014, 0.064). To find the difference (pre-debate minus post-debate) in the sample proportions of likely voters who said they will vote for this candidate, we need to find the midpoint of the confidence interval, which is the point estimate of the true difference.
In the given question, the interval is (-0.014, 0.064), then the expression for the likely difference is
(0.064 + (-0.014))/2 = 0.050/2
= 0.025
Hence, the difference in the sample proportions of likely voters who said they will vote for this candidate is 0.025.
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Find the area of the triangle. 8 m
5 m
Question content area bottom
Part 1
The area of the triangle is 1 m cubed. (Type a whole number. )
The area of the triangle is 20 square meters.
The formula to find the area of a triangle is A = 1/2 * base * height. In this case, the base of the triangle is 8 meters and the height is 5 meters. Therefore, the area of the triangle is A = 1/2 * 8 m * 5 m = 20 m^2.
We can also check our answer by using the formula A = (b * h) / 2, where b is the base and h is the height of the triangle. Substituting the values given in the question, we get A = (8 m * 5 m) / 2 = 20 m^2. Therefore, the area of the triangle is 20 square meters.
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Find the divergence of vector fields at all points where they are defined
div ( (2x^2 - sin(xz)) i + 5j - (sin (Xz)) k)
The divergence of vector fields at all points where they are defined ar 4x - 2xcos(xz) for all points in R3.
The divergence of the given vector field F = (2x^2 - sin(xz)) i + 5j - (sin (xz)) k can be found using the formula for divergence:
div(F) = (∂Fx/∂x) + (∂Fy/∂y) + (∂Fz/∂z)
Here, Fx = (2x² - sin(xz)), Fy = 5, and Fz = -sin(xz). Taking the partial derivatives, we get:
∂Fx/∂x = 4x - zcos(xz)
∂Fy/∂y = 0
∂Fz/∂z = -xcos(xz)
Therefore, the divergence of F is:
div(F) = (∂Fx/∂x) + (∂Fy/∂y) + (∂Fz/∂z) = 4x - zcos(xz) - xcos(xz) = 4x - 2xcos(xz)
The divergence of F is defined for all points where F is defined, which is the entire 3-dimensional space. So, the divergence of F is 4x - 2xcos(xz) for all points in R3.
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Part 3
sales tax is 8%
basketballs are 20% off
you have two customers john and david. john has $250 and
david has $150. john is coaching a baseball team and wants
to buy 10 baseball bats for his team. david wants to buy 3
pairs of running shoes for his kids. will each person be able
to buy the items that they want? explain.
baseball bats are 5% off
running shoes are 15% off
i
tax
with
discount
total
cost
john
david
John will be able to buy the 10 baseball bats for his team with some money left over is -$6.50 and David will be able to buy the 3 pairs of running shoes for his kids with some money left over is $12.30.
Based on the given information, we can calculate the total cost for each customer after factoring in the sales tax and discounts.
For John:
The cost of 10 baseball bats without any discounts or tax would be 10 * $25 = $250.
Since baseball bats are 5% off, John will get a discount of 0.05 * $250 = $12.50.
So, the cost of 10 baseball bats after discount is $250 - $12.50 = $237.50.
Adding 8% sales tax to this amount, the total cost for John will be $237.50 + (0.08 * $237.50) = $256.50.
For David:
The cost of 3 pairs of running shoes without any discounts or tax would be 3 * $50 = $150.
Since running shoes are 15% off, David will get a discount of 0.15 * $150 = $22.50.
So, the cost of 3 pairs of running shoes after discount is $150 - $22.50 = $127.50.
Adding 8% sales tax to this amount, the total cost for David will be $127.50 + (0.08 * $127.50) = $137.70.
Therefore, John will be able to buy the 10 baseball bats for his team with some money left over ($250 - $256.50 = -$6.50) and David will be able to buy the 3 pairs of running shoes for his kids with some money left over ($150 - $137.70 = $12.30).
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Find the missing values assuming continuously compounded interest. (Round your answers to two decimal places.)
Initial Investment: $100
Annual % Rate: ?
Amount of time it takes to double: ?
Amount after 10 years: $1405
Answer:
Annual % Rate: 26.43%
Amount of time it takes to double: 2.62yr
Step-by-step explanation:
Solving for r(Annual%Rate)
A=P⋅e^(r⋅t)
1405=100⋅^(r⋅10)
1405=100⋅e(^10r)
1405/100=100/100⋅e^(10r)
14.05 = e^(10r)
log(14.05) = log(e^10r)
1.1476 = 10r⋅log(e)
1.1476/log(e) = 10r
1.1476/10⋅log(e) = r
r = 0.26426
=26.43%
Now we have r=26.43%. We can use this information to solve for t, the time period to double the initial investment:
2P = Pe^(rt)
2 = e^(0.2643t)
ln(2) = 0.2643t
t = ln(2)/0.2643
t = 2.62yr
A point in the figure is chosen at random. Find the probability that the point lies in the shaded region of the circle.
To find the probability that the point lies in the shaded region of the circle, we need to compare the area of the shaded region to the total area of the circle. Let's say the radius of the circle is r.
The area of the shaded region can be found by subtracting the area of the unshaded region from the total area of the circle. The unshaded region is a square with side length equal to the radius of the circle. Therefore, its area is r^2. The total area of the circle is πr^2. So the area of the shaded region is:
πr^2 - r^2 = r^2(π - 1)
Now, if we choose a point at random from the circle, any point has an equal chance of being chosen. So the probability of choosing a point in the shaded region is equal to the area of the shaded region divided by the total area of the circle:
P(shaded) = (r^2(π - 1))/πr^2 = π - 1
Therefore, the probability of choosing a point in the shaded region of the circle is π - 1.
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What is the area of a regular hexagon with side length of 12. 7 and apothem length of 11?
PLEASE HELP!
The area of the regular hexagon with a side length of 12.7 and apothem length of 11 is approximately 416.61 square units.
To find the area of a regular hexagon, you can use the formula , where A is the [tex]A =\frac{3\sqrt{3} }{2} (s^{2} )[/tex]area, s is the length of one side, and √3 is the square root of 3.
However, since the apothem length is given, you can also use the formula , where ap is the apothem length and p is the perimeter of the hexagon.
First, let's find the perimeter of the hexagon. Since a hexagon has six sides, the perimeter will be 6 x 12.7 = 76.2.
Next, we can use the apothem length of 11 and the side length of 12.7 to find the length of the radius of the circle inscribed in the hexagon. This is because the apothem is the distance from the center of the hexagon to the midpoint of any side, and the radius is the distance from the center to any vertex.
Using the Pythagorean theorem, we can find the radius:
[tex]r^2 = ap^2 + (\frac{s}{2} )^{2}[/tex]
[tex]r^2 = 11^2 + (\frac{12.2}{7} )^{2}[/tex]
[tex]r^2 = 121 + 40.1225[/tex]
[tex]r^2 = 161.1225[/tex]
[tex]r = \sqrt{161.1225}[/tex]
[tex]r = 12.69[/tex]
Now that we know the radius, we can use the formula for the area of a regular polygon in terms of the radius: A = (1/2) x r x ap x n, where n is the number of sides (which is 6 for a hexagon).
Plugging in the values we have:
[tex]A = \frac{1}{2} (12.69)(11)(6)[/tex]
[tex]A = 416.61[/tex]
Therefore, the area of the regular hexagon with a side length of 12.7 and apothem length of 11 is approximately 416.61 square units.
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Linus received 12 marks more in Test 2 than his score in Test 1. This was a 15%
improvement. He then made another 4-mark improvement in Test 3.
(a) What was his score for Test 1?
(b) What was the percentage increase in his test score from Test 2 to Test 3?
Give your answer correct to 1 decimal place.
(a) Linus's score for Test 1 is 80. (b) The percentage increase in his test score from Test 2 to Test 3 is 4.3%.
(a) Let's denote Linus's score in Test 1 as "x." Since he received 12 more marks in Test 2, his score for Test 2 is "x + 12." The 15% improvement means that (x + 12) is 115% of x:
x + 12 = 1.15x
Now, we can solve for x:
12 = 0.15x
x = 12 / 0.15
x = 80
So, Linus's score in Test 1 was 80.
(b) Linus made a 4-mark improvement in Test 3, so his score was (x + 12) + 4, which is (80 + 12) + 4 = 96. To find the percentage increase from Test 2 to Test 3, we can use the formula:
Percentage increase = ((New score - Old score) / Old score) * 100
Percentage increase = ((96 - 92) / 92) * 100
Percentage increase = (4 / 92) * 100
Percentage increase ≈ 4.35
The percentage increase in his test score from Test 2 to Test 3 is approximately 4.3% (correct to 1 decimal place).
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1.
(03. 01 MC)
Part A: Find the LCM of 8 and 9. Show your work. (3 points)
Part B: Find the GCF of 35 and 63. Show your work. (3 points)
Part C: Using the GCF you found in Part B, rewrite 35 + 63 as two factors. One factor is the GCF and the other is the sum of two numbers that do not have a common factor. Show your work. (4 points)
The LCM of 8 and 9 is 72. The GCF of 35 and 63 is 7.35 + 63 can also be written as 7 X 14.
Part A
Here we have been given 2 numbers 8 and 9. We need to find the LCM. LCM is the Lowest Common Multiple. It is the smallest number which can be divided by all the mentioned number. To take the LCM of 8 and 9 we first will factorize them
8 = 2 X 2 X 2
9 = 3 X 3
Here we see that 8 and 9 do not have any common factor. Hence we need to simply multiply them together to get
8 X 9 = 72
Part B.
We need to find GCF of 35 and 63. GCF or the Greatest common factor is the highest number that can divide all the given numbers. Here too we will first factorize 35 and 63.
35 = 5 X 7
63 = 3 X 3 X 7
Here we see that between the numbers, 7 is the only common factor
Hence, 7 is the GCF.
63 can also be written as 63 = 7 X 9
Hence we can write 35 + 3
= (7 X 5) + (7 X 9)
Taking 7 common we get
7(5 + 9)
= 7 X 14
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A digital timer counts down from 5 minutes (5:00) to 0:00 one second at a time. For how many seconds does at least one of the three digits show a 2?
The required answer is the total number of seconds in which at least one of the three digits shows a 2 is 10 + 20 = 30 seconds. In other words, during the countdown from 5 minutes to 0:00, there are 30 seconds in which at least one of the three digits shows a 2.
To determine the number of seconds in which at least one of the three digits on a digital timer shows a 2 while counting down from 5 minutes (5:00) to 0:00, we need to consider the various possibilities.
Step 1: Determine the total number of seconds in 5 minutes.
There are 60 seconds in a minute, so 5 minutes would be equal to 5 * 60 = 300 seconds.
Step 2: Consider each second from 0 to 300 and check if any of the three digits (hundreds, tens, or ones) contains the digit 2.
To simplify the calculation, we can focus on the ones digit for the first 60 seconds (from 0:00 to 0:59). In this range, the ones digit contains the digit 2 ten times (2, 12, 22, 32, 42, 52, 62, 72, 82, 92). So, in the first minute, there are 10 seconds in which the ones digit shows a 2.
For the remaining 240 seconds (from 1:00 to 4:59), we need to consider both the tens and ones digits. In each minute within this range, the tens digit can have a digit 2 for all ten seconds (20, 21, 22, ..., 29). Additionally, the ones digit can have a digit 2 for ten seconds in each minute. So, in the remaining 240 seconds, there are 10 * 2 = 20 seconds in which at least one of the tens or ones digits shows a 2.
Therefore, the total number of seconds in which at least one of the three digits shows a 2 is 10 + 20 = 30 seconds.
Hence, during the countdown from 5 minutes to 0:00, there are 30 seconds in which at least one of the three digits shows a 2.
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Medical records at a doctor’s office reveal that 12% of adult patients have seasonal allergies. Select a random sample of 100 adult patients and let p^ = the proportion of individuals in the sample who have allergies.
(a) Calculate the mean and standard deviation of the sampling distribution of p^.
(b) Interpret the standard deviation from part (a).
(c) Would it be appropriate to use a normal distribution to model the sampling distribution of p^ ? Justify your answer
We know that both np and nq are greater than or equal to 10, it is appropriate to use a normal distribution to model the sampling distribution of p^ in this case.
(a) To calculate the mean and standard deviation of the sampling distribution of p^, we'll use the formulas:
Mean (μ) = p
Standard deviation (σ) = √(p*q/n)
where p is the proportion of individuals with allergies (0.12), q is the proportion of individuals without allergies (1 - p = 0.88), and n is the sample size (100).
Mean (μ) = 0.12
Standard deviation (σ) = √(0.12 × 0.88 / 100) = 0.02887
(b) The standard deviation of 0.02887 in this context represents the variability in the proportions of individuals with allergies that we would expect to observe in different random samples of 100 adult patients each. It quantifies the dispersion of p^ around the true population proportion.
(c) To determine if it's appropriate to use a normal distribution to model the sampling distribution of p^, we can check if both np and nq are greater than or equal to 10:
np = 100 × 0.12 = 12
nq = 100 × 0.88 = 88
Since both np and nq are greater than or equal to 10, it is appropriate to use a normal distribution to model the sampling distribution of p^ in this case.
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() Jamison works as a server at a local restaurant. He made $42.80 in tips on
Thursday night. He made 2 1/4 times that amount in tips on Friday night. How much
in tips did he earn on Friday?
Therefore, Jamison made $96.30 in tips on Friday night.
What is equation?An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides, left-hand side (LHS) and right-hand side (RHS), connected by an equal sign (=). The LHS and RHS can contain numbers, variables, operators, and functions, and the equal sign indicates that the value of the expression on the LHS is equal to the value of the expression on the RHS.
Here,
Jamison made $42.80 in tips on Thursday night.
To find out how much he made in tips on Friday night, we need to multiply the Thursday amount by 2 1/4, which is the same as multiplying it by 9/4.
$42.80 x 9/4 = $96.30
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Find the maximum volume of a box inscribed in the tetrahedron bounded by the coordinate planes and the plane x + 1/7y + 1/6z = 1. (Use symbolic notation and fractions where needed.) the maximum volume of the box: ...
The maximum volume of the box is 5/49, which occurs at vertex 3.
How to find the maximum volume of a box inscribed in the tetrahedron bounded by the coordinate planes?Let the length, width, and height of the box be x, y, and z respectively. Then the volume of the box is given by V = xyz.
The tetrahedron is bounded by the coordinate planes and the plane x + 1/7y + 1/6z = 1. We can find the vertices of the tetrahedron as follows:
(0, 0, 0)
(7, 0, 0)
(0, 6, 0)
(0, 0, 6)
We can see that the maximum values of x, y, and z occur at different vertices of the tetrahedron.
Therefore, we need to find the coordinates of the vertices of the box at each vertex of the tetrahedron.
At vertex 1, we have x = 0, y = 0, and z = 0. The distance from this vertex to the plane is 1, so the maximum value of x is 1.
Therefore, we set x = 1 and solve for y and z:
1 + 1/7y + 1/6z = 1
y = 0
z = 0
At vertex 2, we have x = 7, y = 0, and z = 0. The distance from this vertex to the plane is 6/7, so the maximum value of y is 6/7.
Therefore, we set y = 6/7 and solve for x and z:
x + 1/7(6/7) + 1/6z = 1
x = 5/6
z = 1/7
At vertex 3, we have x = 0, y = 6, and z = 0. The distance from this vertex to the plane is 5/6, so the maximum value of z is 5/6.
Therefore, we set z = 5/6 and solve for x and y:
x + 1/7y + 1/6(5/6) = 1
x = 4/7
y = 3/7
At vertex 4, we have x = 0, y = 0, and z = 6. The distance from this vertex to the plane is 1/7, so the maximum value of x is 7.
Therefore, we set x = 7 and solve for y and z:
7 + 1/7y + 1/6(6) = 1
y = -42/7
z = 1/6
Now we can calculate the volume of the box at each vertex of the tetrahedron:
V1 = 1(0)(0) = 0
V2 = 5/6(6/7)(1/7) = 5/294
V3 = 4/7(3/7)(5/6) = 5/49
V4 = 7(-42/7)(1/6) = -49/6
Therefore, the maximum volume of the box is 5/49, which occurs at vertex 3.
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please help me with this Pythagoras theorum
Step-by-step explanation:
18 m = hypotenuse = c
5 m = b
a² + b² = c²
a² + (5)² = (18)²
a² + 25 = 324
a² = 324 - 25
a² = 299
a = √299
a = 17.29 or 17.3 m
perimeter = a + b + c
= 17.3 + 18 + 5
= 40.3 m
#CMIIWfor each of these relations on the set {1,2,3,4}, decide whether it is reflexive, whether it is symmetric, and whether it is transitive. Which of these relations are equivalence relations?(a) {(2,2),(2,3),(2,4),(3,2),(3,3),(3,4)}. (b) {(1,1),(1,2),(2,1),(2,2),(3,3),(4,4)}. (c) {(2,4),(4,2)}.
The relation is not an equivalence relation. (a) {(2,2),(2,3),(2,4),(3,2),(3,3),(3,4)}:
Reflexive: (2,2), (3,3) are present, but (1,1) and (4,4) are not present. Hence, not reflexive.
Symmetric: (2,3) is present, but (3,2) is also present. Hence, not symmetric.
Transitive: No counterexample to transitivity exists. Hence, it is transitive.
Therefore, the relation is not an equivalence relation.
(b) {(1,1),(1,2),(2,1),(2,2),(3,3),(4,4)}:
Reflexive: (1,1), (2,2), (3,3), (4,4) are present. Hence, reflexive.
Symmetric: (1,2) is present, but (2,1) is also present. Hence, symmetric.
Transitive: No counterexample to transitivity exists. Hence, it is transitive.
Therefore, the relation is an equivalence relation.
(c) {(2,4),(4,2)}:
Reflexive: (2,2) and (4,4) are not present. Hence, not reflexive.
Symmetric: (2,4) is present, but (4,2) is not present. Hence, not symmetric.
Transitive: No counterexample to transitivity exists. Hence, it is transitive.
Therefore, the relation is not an equivalence relation.
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show work/steps please
Find the Taylor series for f centered at 6 if f(n) (6) = (-1)"n! 4"(n + 2) Σ n = 0 What is the radius of convergence R of the Taylor series? R = = X
The Taylor series for f centered at 9, given f^(n)(9) = (-1)^n n!/6^n (n + 2), is f(x) = f(9) - (x-9)/2 + (x-9)^2/12 - (x-9)^3/432 + (x-9)^4/10368 - ... .
To find the Taylor series for f centered at 9, we need to use the formula
f(x) = f(a) + f'(a)(x-a)/1! + f''(a)(x-a)^2/2! + f'''(a)(x-a)^3/3! + ...
where f'(x) represents the first derivative of f(x) with respect to x, f''(x) represents the second derivative of f(x) with respect to x, and so on.
In this case, we are given the nth derivative of f(x) evaluated at x = 9, so we can plug in the values and simplify the formula
f(9) = f(9) (since we're centering the series at 9)
f'(9) = (-1)^1 (1!/6^1)(1 + 2) = -1/2
f''(9) = (-1)^2 (2!/6^2)(2 + 2) = 1/6
f'''(9) = (-1)^3 (3!/6^3)(3 + 2) = -1/36
f''''(9) = (-1)^4 (4!/6^4)(4 + 2) = 1/216
and so on. So the Taylor series for f centered at 9 is
f(x) = f(9) - (x-9)/2 + (x-9)^2/2! * 1/6 - (x-9)^3/3! * 1/36 + (x-9)^4/4! * 1/216 - ...
or, simplifying the coefficients
f(x) = f(9) - (x-9)/2 + (x-9)^2/12 - (x-9)^3/432 + (x-9)^4/10368 - ...
This is the Taylor series for f centered at 9, based on the given information.
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The given question is incomplete, the complete question is:
Find the Taylor series for f centered at 9 if f^(n)(9) = (-1)^n n!/6^n (n + 2)
A right rectangular prism has a length of 1 foot, a width of 1 3/8 feet, and a height of 5/8 foot. unit cubes with side lengths of 1/8 foot are added to completely fill the prism with no space remaining. how many cubes can fit inside the prism? explain how to find the number by using the volume formula. explain how to find the number by using the side lengths of the prism and the cubes.
The number of cubes of dimensions of [tex]\frac{1}{8}[/tex] foot that can fit into a rectangular prism of a length of 1 foot, a width of 1 [tex]\frac{3}{8}[/tex] foot, and a height of [tex]\frac{5}{8}[/tex] foot is 55.
Volume of cuboid = l * b * h
where l is the length
b is the breadth
h is the height
l = 1 foot
b = 1 [tex]\frac{3}{8}[/tex] foot = [tex]\frac{11}{8}[/tex] foot
h = [tex]\frac{5}{8}[/tex] foot
Volume of cuboid = 1 * [tex]\frac{11}{8}[/tex] * [tex]\frac{5}{8}[/tex]
= [tex]\frac{55}{64}[/tex] cubic foot
Volume of cube = [tex]s^3[/tex]
where s is the side
s = [tex]\frac{1}{8}[/tex] foot
Volume = [tex]\frac{1}{8}^3[/tex]
= [tex]\frac{1}{64}[/tex] cubic foot
Number of cubes = [tex]\frac{\frac{55}{64} }{\frac{1}{64} }[/tex]
= 55
The number of cubes that fit into the prism is 55.
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The path r(t)=(t) i+(3t2+5) j describes motion on the parabola y=3x2+5. Find the particles velocity and acceleration vectors at t=5
The particle's velocity vector at t=5 is v(5) = 1i + 30j, and the acceleration vector at t=5 is a(5) = 0i + 6j.
To find the particle's velocity, we take the derivative of the path r(t) with respect to time:
v(t) = r'(t) = i + 6t j
Substituting t=5, we get:
v(5) = 1i + 30j
To find the particle's acceleration, we take the derivative of the velocity with respect to time:
a(t) = v'(t) = 0i + 6j
Substituting t=5, we get:
a(5) = 0i + 6j
Note that the acceleration vector is constant, which is expected since the particle is moving along a parabolic path, and the curvature of the path remains constant.
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Find the area of the polygon
ASAP PLEASE HELP!!!!
20PTS
Hello!
This shape is a "Strange" shape, but if you look closer at it, you can see that it can be divided into "normal shapes" like rectangles and squares
On the bottom on the "polygon" we can dived it into 2 squares
One square would have the dimensions of 6 and 6
The other one would have 4 and 6
The formula of area is: Base*Height
So the first square would have an area of 36
The second square would have an area of 24
Now we solve for the big rectangle
On first thought, it may seem like the dimensions are 16 and 25, but it is actually 10 and 25. Because 16 is the whole height of the polygon.
So we subtract it by 6
So the big rectangle is 250
=================
Now we add the areas together to get a total result of 310
If you have questions, feel free to ask
What is the measure of JG
measure of arc JG = 160 degrees
Step-by-step explanation:Main Concept: Intersecting chords
Chords are line segments with ends points that are both on the edge of the circle. Intersecting chords are a pair of chords on the same circle that intersect.
In an extreme example, the chords may intersect at one of the end points, making the intersecting chords an inscribed angle.
Because Intersecting chords intersect, if the line segments are extended into lines, the lines form two pairs of vertical angles. Vertical angles are congruent. Given one vertical angle pair, they will contain two arcs (in the extreme case, the arc will have a measure of zero).
The measure of each of the vertical angles is the average of the two contained arcs.
This problem
For this problem, FG and HJ are chords of the same circle, and they intersect.
If we call the intersection P, angle GPJ is given with a measure of 100 degrees.
Angle GPJ and Angle FPJ form a vertical angle pair, so they are congruent, because vertical angles are congruent.
The measure of each of the vertical angles is the average of the two contained arcs.
The two arcs that this vertical angle pair contain are the arc JG and arc FH.
The measure of arc FH is given as 40 degrees.
Substitute these known quantities into the equation describing the relationship between one of the vertical angles and the contained arcs.
[tex]m \angle GPJ=\frac{1}{2}(m ~\text{arc}JG + m ~\text{arc}FH)[/tex]
[tex](100^o)=\frac{1}{2}(m ~\text{arc}JG + (40^o))[/tex]
Multiply both sides by 2...
[tex]200^o=m ~\text{arc}JG + 40^o[/tex]
Subtract 40 degrees from both sides...
[tex]160^o=m ~\text{arc}JG[/tex]
Alyssa makes $200 for every 8 hour shift she works as a personal trainer. She graphs the amount of money she earns on the y-axis, and number of hours she works the x-axis. What is the slope of the graph?
The slope of this graph is equal to 25.
How to calculate the slope of a line?In Mathematics and Geometry, the slope of any straight line can be determined by using this mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Based on the information provided above, we can reasonably infer and logically deduce that Alyssa made $200 for every 8 hour shift she works as a personal trainer. Additionally, the amount of money Alyssa earned would be plotted on the y-axis while the number of hours she work would be plotted on the x-axis of a graph;
Slope (m) = 200/8
Slope (m) = 25.
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1) paul wants to deposit $7,300 into a one-year cd at a rate of 4.85%, compounded quarterly.
a) what his ending balance after the year?
b) how much interest did he earn?
c) what is his annual percentage yield?
hint: use the compounding interest formula
Using the compounding interest formula:
a) His ending balance after the year will be $7,658.91.
b) The amount of interest he will earn is $358.91.
c) His annual percentage yield is 4.9166%.
a) To calculate the ending balance after one year, we'll use the compound interest formula: A = P(1 + r/n)^(nt), where A is the ending balance, P is the principal ($7,300), r is the interest rate (4.85% or 0.0485), n is the number of compounding periods per year (4 for quarterly), and t is the number of years (1).
A = 7300(1 + 0.0485/4)^(4*1) = 7300(1.012125)⁴ = 7300*1.049166 = $7,658.91
b) To find the interest earned, subtract the principal from the ending balance: Interest = A - P
Interest = $7,658.91 - $7,300 = $358.91
c) To calculate the annual percentage yield (APY), we'll use the formula: APY = (1 + r/n)^(n) - 1
APY = (1 + 0.0485/4)⁴ - 1 = 1.049166 - 1 = 0.049166 or 4.9166%
Paul's ending balance after one year is $7,658.91, he earns $358.91 in interest, and his annual percentage yield is 4.9166%.
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