The requried coordinate locations of the respective checkpoints at the Reflections of You obstacle course are A' (0,5), B' (9,5), and C' (4,5).
To find the reflected coordinates of each checkpoint in the y-axis, we need to negate the x-coordinate while keeping the y-coordinate the same.
For checkpoint A(0,5), the reflected coordinates A' will be (-0,5) or just (0,5) since reflecting a point over the y-axis does not change its y-coordinate.
For checkpoint B(-9,5), the reflected coordinates B' will be (9,5) since negating -9 gives us 9 and the y-coordinate remains the same.
For checkpoint C(-4,5), the reflected coordinates C' will be (4,5) since negating -4 gives us 4 and the y-coordinate remains the same.
Therefore, the coordinate locations of the respective checkpoints at the Reflections of You obstacle course are A' (0,5), B' (9,5), and C' (4,5).
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a) the perpendicular bisector of any line
XY.
b) the bisector of any angle XYZ.
c) the perpendicular from any point Z to line
XY.
The locus of points equidistant
from lines XY and YZ.
The locus of points equidistant
from points X and Y.
The shortest line from point
Z to line XY.
The line from point Z to the
midpoint of the line XY.
The locus of points equidistant
from points X and Z.
The locus of points equidistant
from lines XY and XZ.
At the perpendicular bisector of any line
XY and the bisector of any angle XYZ, the correct option is A. The locus of points equidistant from lines XY and YZ.
How to explain the bisectorAngle bisector is a locus or set of points that bisects an angle and is equidistant from two intersecting math that create an angle
The perpendicular bisector is a set of points that bisects a line generated by Linking two points and are equidistant from two points.
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A manager's sample estimated the standard deviation of number of credit cards per employee to be 3 cards. You are researching the average number of credit cards per employee. You want to know how many people you should survey if you want to know, at a 95% confidence level, that the sample mean credit cards per employee is within 1point of the true number of credit cards per employee.
Use a calculator to find the value of z that you should use in the sample size formula
To find the value of z for a 95% confidence level, we can use a z-score table or a calculator. The z-score corresponding to a 95% confidence level is 1.96.
To determine the sample size, we can use the formula:
n = (z^2 * s^2) / E^2
where:
n = sample size
z = z-score (1.96 for 95% confidence level)
s = estimated standard deviation (3 cards)
E = margin of error (1 card)
Plugging in the values, we get:
n = (1.96^2 * 3^2) / 1^2
n = 34.56
We need to round up to the nearest whole number, so the sample size should be 35 people. This means that if we randomly select 35 employees and calculate their average number of credit cards, we can be 95% confident that the true average number of credit cards per employee is within 1 card of our sample mean.
To determine the required sample size for your survey with a 95% confidence level and a margin of error of 1 point, you'll need to use the sample size formula and find the appropriate z-value.
The sample size formula is: n = (z^2 * σ^2) / E^2
Where:
- n is the sample size
- z is the z-value corresponding to the desired confidence level (95% in this case)
- σ is the estimated standard deviation of the population (3 credit cards per employee)
- E is the margin of error (1 point)
For a 95% confidence level, the z-value is approximately 1.96. You can find this value using a z-table or an online calculator.
Now, plug the values into the formula:
n = (1.96^2 * 3^2) / 1^2
n = (3.8416 * 9) / 1
n ≈ 34.5744
Since you cannot survey a fraction of a person, round up to the nearest whole number. Therefore, you should survey approximately 35 people to achieve a 95% confidence level with a margin of error of 1 point for the average number of credit cards per employee.
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In an arithmetic sequence, U2= 5 and U3= 11.
Find the common difference.
Find the first term.
Find the sum of the first 20 terms
The common difference is 6, and the sum of the first 20 terms for the arithmetic sequence 1120.
U2 = 5
U3 = 11
Finding the common difference (d)
U3 - U2
= 11 - 5
= 6
Finding the first term (U1):
U1 = U2 - (2 - 1) × d
= 5 - (2 - 1) × 6
= 5 - 6
= -1
Finding the sum of the first 20 terms:
Sn = n/2 × (2U1 + (n - 1)d)
Sn = 20/2 × (2 × -1 + (20 - 1) × 6)
= 10 × (-2 + 19 × 6)
= 10 × (-2 + 114)
= 10 × 112
= 1120
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1) Use the method of cylindrical shells to find the volume generated by rotating the region bounded by y=e^(?x^2), y=0, x=0, and x=1 about the y -axis.
2) Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line.
y=sqrt(x?1), y=0, x=5 about the line y=5
3) Use the Shell Method to compute the volume of the solids obtained by rotating the region enclosed by the graphs of the functions y=x^2 , y=8?x^2 and to the right of x=1.5 about the y -axis.
Answer: Number Question #1 - To find the volume generated by rotating the region bounded by y=e^(−x^2), y=0, x=0, and x=1 about the y-axis using the method of cylindrical shells, we can integrate the volume of each cylindrical shell. The radius of each shell will be x, and the height will be e^(−x^2).
Thus, the volume is given by:
V = ∫[0,1] 2πxe^(−x^2) dx
Using u-substitution with u=−x^2 and du/dx=−2x, we can rewrite this integral as:
V = ∫[0,−1] −πe^udu
Evaluating the integral, we get:
V = π/2(e^0 − e^(−1)) ≈ 0.436
Therefore, the volume generated by rotating the region about the y-axis is approximately 0.436 cubic units.
Number Question #2 - To find the volume of the solid obtained by rotating the region bounded by y=sqrt(x−1), y=0, x=5 about the line y=5, we can again use the method of cylindrical shells. In this case, the radius of each shell will be 5−y, and the height will be x−1.
Thus, the volume is given by:
V = ∫[0,4] 2π(5−y)(x−1)dy dx
Integrating with respect to y first, we get:
V = ∫[1,5] π(x−1)(5−y)^2 dx
Expanding and simplifying, we get:
V = 2π/3 [(5x−x^2−13)∣[1,5]]
Evaluating the integral, we get:
V = (32π/3)
Therefore, the volume of the solid obtained by rotating the region about y=5 is (32π/3) cubic units.
Number Question #3 - To find the volume of the solid obtained by rotating the region enclosed by the graphs of y=x^2, y=8−x^2, and to the right of x=1.5 about the y-axis using the method of cylindrical shells, we can integrate the volume of each cylindrical shell. The radius of each shell will be x, and the height will be (8−x^2)−x^2=8−2x^2.
Thus, the volume is given by:
V = ∫[1.5,2] 2πx(8−2x^2)dx
Integrating, we get:
V = (32π/3) − (9π/2)
Therefore, the volume of the solid obtained by rotating the region about the y-axis is (32π/3) − (9π/2) cubic units.
Hasina is making green tea lattes. She steams milk to mix with hot tea. Hasina has 12 fl oz of hot tea. Based on the ratio in the recipe,how much milk does Hasina need to steam?
The amount of milk Hasina need to steam cannot be calculated with the given information
Calculating how much milk does Hasina need to steam?From the question, we have the following parameters that can be used in our computation:
Size = 12 fl oz
Mix type = steams milk to mix with hot tea
The available parameters is not enough to determine the ratio
Assuming that we have
Ratio of steam to hot tea is 1 : 2
Then the steam would be:
Steam = 12/2
Simplify
Steam = 6 oz
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The line plot represents the wait time in line for a ride at a local fair.
A line plot titled Wait Time at the Fair. The horizontal line labeled Time in Minutes begins at 8, with every one unit labeled up to 20. There is one dot above 10, 11, 14, 16, and 17. There are two dots above 13. There are four dots above 12 and 15.
Which of the following best describes the shape of the data, and why?
The data is skewed and means that the wait times were less than 13 minutes for all the rides.
The data is bimodal, and it might mean that the wait times for the most popular rides were 12 and 15 minutes long.
The data is symmetric and means that the wait times were around 13 minutes for all the rides.
The data is skewed and means that the wait times were over 13 minutes for all the rides.
The shape of the data of the line plot is best described by the option
The data is bimodal, and it might mean that the wait times for the most popular rides were 12 and 15 minutesWhat is a line plot?A line plot is a graphical display of data as check marks showing the frequency of a data point above a number line.
The description of the line plot can be presented as follows;
The number of dota above the points marked 10, 11, 14, 16, and 17 = One dot each
The number of dots above the point marked 13 = Two dots
The number of dots above the points marked 12, and 15 = Four dots each
The above description of the line plot indicates;
The mode of the dataset are 12 and 15, therefore;
The data set is bimodalThe option that best describes the shape of the data, is therefore;
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Find the probabilities for the values of n
and \(p\_ when the conditions for the binomial distribution are met
The probability that two batteries used sequentially will remaining greater than 4 years is about 6.95%.
The time to failure of a single rechargeable battery is exponentially distributed with a median of three years. which means that the opportunity that a single battery will ultimate more than 4 years is given via:
P(X > 4) = e^(-4/3) ≈ 0.2636
Wherein X is the time to failure of a single battery.
Assuming that the two batteries are used sequentially and independently, the chance that each batteries will remaining more than four years is given by means of the made from their man or woman probabilities:
P(X1 > 4 and X2 > 4) = P(X1 > 4) * P(X2 > 4)
For the reason that two batteries are used successionally, the probability of the alternate battery lasting further than 4 times is analogous to the chance of the first battery lasting redundant than 4 years
P(X1 > 4 and X2 > 4) = P(X > 4)^2 ≈ 0.0695
Consequently, the probability that two batteries used sequentially will remaining greater than 4 years is about 0.0695 or 6.95%.
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Arrivals at a telephone booth are considered to be Poisson, with an average time of 10 minutes between successive arrivals. The length of a phone call is distributed exponentially with mean 3 minutes. The probability that an arrival does not have to wait before service is A0.3B0.7C0.5D0.9
The probability that an arrival does not have to wait before service is 0.7 (Option B).
To calculate the probability that an arrival does not have to wait before service, we need to use the Poisson and exponential distributions.
First, we can calculate the average number of arrivals per hour:
60 minutes / 10 minutes per arrival = 6 arrivals per hour
Next, we can use the exponential distribution to calculate the probability that a phone call is less than or equal to 10 minutes (the time between arrivals):
P(call length ≤ 10 minutes) = 1 - e^(-10/3) ≈ 0.957
This means that there is a 95.7% chance that a phone call will end before the next arrival.
Finally, we can use the Poisson distribution to calculate the probability that there are no arrivals in the 10-minute window between the end of a phone call and the next arrival:
P(no arrivals in 10 minutes) = e^(-6) ≈ 0.002
So the probability that an arrival does not have to wait before service is:
P(no wait) = P(call length ≤ 10 minutes) * P(no arrivals in 10 minutes)
P(no wait) = 0.957 * 0.002
P(no wait) ≈ 0.002
Therefore, the answer is A) 0.3.
We're given that arrivals at a telephone booth follow a Poisson distribution with an average time of 10 minutes between arrivals, and the length of a phone call is exponentially distributed with a mean of 3 minutes. We need to find the probability that an arrival does not have to wait before service.
Step 1: Calculate the arrival rate (λ) and service rate (μ)
The average time between arrivals is 10 minutes, so the arrival rate λ is 1/10 arrivals per minute.
The average length of a phone call is 3 minutes, so the service rate μ is 1/3 calls per minute.
Step 2: Calculate the traffic intensity (ρ)
The traffic intensity ρ is the ratio of the arrival rate to the service rate.
ρ = λ/μ = (1/10) / (1/3) = 3/10 = 0.3
Step 3: Calculate the probability that an arrival does not have to wait (P_0)
For an M/M/1 queue (Poisson arrivals and exponential service times with a single server), the probability that an arrival does not have to wait before service is given by P_0 = 1 - ρ.
P_0 = 1 - 0.3 = 0.7
So, the probability that an arrival does not have to wait before service is 0.7 (Option B).
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(Chapter 13) Suppose f is twice continuously differentiable. At an in ection point of the curve y = f(x), the curvature is 0.
The curvature is zero at the origin, but f(x) is not twice continuously differentiable function at x = 0, because f''(x) does not exist at x = 0. Therefore, the statement is not necessarily true.
An inflection point is a point on a curve where the sign of the curvature changes. At an inflection point, the curvature may be zero, but it may also be undefined. Moreover, even if the curvature is defined and equal to zero at an inflection point, it does not necessarily imply that the function is twice continuously differentiable at that point.
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Question 2 (Essay Worth 30 points)
(10.08 HC)
The function h is defined by the power series =h of x is equal to x cubed plus the quantity x to the fourth power over 3 end quantity plus the quantity x to the fifth power over 5 end quantity plus x to the sixth power over 7 end quantity plus the quantity x to the seventh power over 9 end quantity plus dot dot dot equals the summation from n equals 0 to infinity of the quantity x to the power of n plus 3 end quantity over the quantity 2 times n plus 1 end quantity period
Part A: Determine the interval of convergence of the power series for h. (10 points)
Part B: Find h ′(−1) and determine if the new series converges or diverges. Justify your response and discuss the relationship between the radius of convergence and interval of convergence of h(x) and h ′(x). (10 points)
Part C: Determine if the power series h(x2) has any points of inflection. Justify your answer. (10 points)
Answer:
I'm not sure if this what your looking for as an answer, but I hope it helped!
The function h(x) is given as the power series:
=h(x) = x³ + (x⁴/3) + (x⁵/5) + (x⁶/7) + (x⁷/9) + ...
Part A: To determine the interval of convergence, we use the ratio test:
lim(n→∞) |(x^(n+4))/(2(n+2)+1) * (2n+1)/(x^n+3)| = lim(n→∞) |x|^2/2 = |x|^2/2
The ratio test tells us that the series converges if |x|²/2 < 1 and diverges if |x|²/2 > 1. Therefore, the interval of convergence is -√2 < x < √2.
Part B: To find h′(−1), we differentiate the power series term by term:
h′(x) = 3x² + 4x³/3 + 5x⁴/5 + 6x⁵/7 + 7x⁶/9 + ...
h′(−1) = 3(−1)² + 4(−1)³/3 + 5(−1)⁴/5 + 6(−1)⁵/7 + 7(−1)⁶/9 + ...
= 3 − 4/3 + 1/5 − 6/7 + 1/9 − ...
= ∑(n=0 to ∞) (−1)^n * (2n+3)/(2n+1)
We can use the alternating series test to show that the series converges. The terms decrease in absolute value, and the limit of the terms approaches zero. Therefore, h′(−1) converges.
The relationship between the radius of convergence and interval of convergence of h(x) and h′(x) is that the radius of convergence of h′(x) is the same as that of h(x), but the interval of convergence may be different due to the behavior at the endpoints.
Part C: To determine if h(x²) has any points of inflection, we differentiate twice:
h(x²) = (x²)³ + ((x²)⁴/3) + ((x²)⁵/5) + ((x²)⁶/7) + ((x²)⁷/9) + ...
h′(x) = 3x⁴ + 4x⁵/3 + 5x⁶/5 + 6x⁷/7 + 7x⁸/9 + ...
h″(x) = 12x³ + 20x⁴/3 + 30x⁵/5 + 42x⁶/7 + 56x⁷/9 + ...
We can see that h″(x) is always positive, so h(x²) does not have any points of inflection.
write 36 as a product of prime factors write the factors in order from smallest to largest
Answer:{2,2,3,3}
Step-by-step explanation:
six by six is 36 and 2 times three would give you six
Answer:
(2,2,3,3)
Step-by-step explanation:
The function f(x) is shown on the graph. The graph shows a downward opening parabola with a vertex at 3 comma 25, a point at negative 2 comma 0, a point at 8 comma 0, a point at 0 comma 16, and a point at 6 comma 16. What is the standard form of the equation of f(x)?
The equation of the parabola in standard form is f(x) = -(x - 3)² + 25
the vertex of the parabola is given as (3, 25), we know that the equation of the parabola can be written in vertex form as:
f(x) = a(x - 3)² + 25
where a is a constant that determines the shape of the parabola.
The point (6, 16) lies on the parabola
so we can substitute x = 6 and y = 16 into the equation above to find 'a'.
16 = a(6 - 3)² + 25
-9 = 9a
Dividing both sides by 9, we get:
a = -1
Now we know that the equation of the parabola is:
f(x) = -(x - 3)² + 25
Hence, the equation of the parabola in standard form is f(x) = -(x - 3)² + 25
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The diagram in Fig. 15.17 is an equi- lateral triangle with its given dimen- sions in cm. Find the perimeter of the triangle. x+8 y +4 4x-y
The perimeter of the equlateral triangle is 42 units
Finding the perimeter of the triangle.The dimensions of the triangle are given as
x + 8, y + 4 and 4x - y
The side lengths of an equilateral triangle are equal
So, we have
x + 8 = y + 4
4x - y = y + 4
When evaluated, we have
x = 6 and y = 10
So, we have
Perimeter = 3 * (y + 4)
This gives
Perimeter = 3 * (10 + 4)
Evaluate
Perimeter = 42
Hence, the perimeter is 42 units
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consider the function l(x,y)shown in the contour diagram at the right.l(x,y)is the percentage a student earns on an exam as a function of x,the number of hours the student slept the night before,and y.how full their stomach is before the exam on a scale of 1 to 10.
Sleeping is more important than the having full stomach when it comes to doing well on an exam
Based on the contour diagram, it seems that the percentage a student earns on an exam (l) is affected by both x and y. In other words, the more hours a student sleeps (x), the higher their percentage in the exam tends to be. Similarly, the fuller a student's stomach is (y), the higher their percentage in the exam tends to be.
It's important to note that the impact of x and y on l isn't necessarily equal. For example, if a student sleeps for 10hours (x=10) and has a full stomach (y=10), their percentage in the exam appears to be close to 100%. However, if they only sleep for 5 hours (x=5) and have a full stomach (y=10), their percentage in the exam appears to be closer to 70%. This suggests that sleeping is more important than having a full stomach when it comes to doing well on an exam.
Overall, this function seems to demonstrate that the amount a student sleeps and their level of hunger can impact their performance on an exam. However, it's important to note that this is just one function and may not apply to every student or every exam.
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Need Help ASAP
10 points. please help
The length of the arc BC is given as follows:
Arc BC = 10π units.
What is the measure of the circumference of a circle?The circumference of a circle of radius r is given by the equation presented as follows:
C = 2πr.
The radius in this problem is of 10 units, hence the length of the whole circumference is of:
C = 20π units.
The entire circumference is of 360º, hence arc BC is half the circumference, and it's length is given as follows:
Arc BC = 10π units.
Missing InformationThe problem asks for the length of arc BC.
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4. The department of fish and wildlife want to estimate the size of alligator population in
Louisiana. The department issued 937 tags to hunters in 2018. The average length of the
alligators was 11.2 ft with a standard deviation of 2.06 feet. What is the mean and
standard deviation of the population?
solve:
cos theta = -0.37
give your answer to 1 decimal place
Answer: Not sure which one you need my guess would be RADIANS
Step-by-step explanation:
For COS THETA RADIANS = 1.9
For COS THETA DEGREES = 111.7
Sorry if its wrong
A square pyramid is sliced in such a way that the plane cuts in a direction perpendicular to the base but does not pass through the vertex, what is the resulting cross section?
If a square pyramid is sliced in a way that the plane cuts in a direction perpendicular to the base but doesn't pass through the vertex, the resulting cross-section will be a trapezoid.
This trapezoid will have one pair of parallel sides and one pair of non-parallel sides.
To understand why the resulting cross-section is a trapezoid, imagine a square pyramid standing on its base. Now, imagine slicing the pyramid horizontally, parallel to the base. The resulting cross-section would be a square.
However, if we change the direction of the slice to be perpendicular to the base, but not passing through the vertex, the resulting cross-section will not be a square. Instead, it will be a trapezoid, with one set of parallel sides corresponding to the base of the pyramid, and the other set of sides corresponding to the slice that was made.
This type of cross-section is commonly seen in architectural and engineering designs, where different shapes need to be created by slicing or intersecting 3D shapes. Understanding the resulting cross-section of different slicing techniques is essential to ensure the proper fit and function of the final product.
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The circle passes through the point ( 3 , 6 ) What is its radius?
Answer: 5
Step-by-step explanation: The center of the circle will be (–3, 6), and the radius, which is the distance from (–3,6), will be 5. The standard form of a circle is given below: (x – h)2 + (y – k)2 = r2, where the center is located at (h, k) and r is the length of the radius. In this case, h will be –3, k will be 6, and r will be 5.
Consider the spinner shown to answer the following questions. To break the code of puzzle three you will need to enter the numeric answer to each question, separated by a dash. Make sure to not add any labels, spaces, or commas. Be sure to convert all your answers to decimals.
For example, 32-085-7-.63-2
PLEASE HELP (photo below)
The missing values are:
1. 0.16667
2. 0.16667
3. 0.16667
4. 0.16667
5. 0.6667
6. 0.5
7. 0.5
We have a spinner having 6 sections.
1. Probability (getting e)
= 1/6
= 0.16667
2. Probability (getting D)
= 1/6
= 0.16667
3. Probability (getting vowel)
= 2/6
=1/3
= 0.16667
4. Probability (getting C)
= 1/6
= 0.16667
5. Probability (getting consonant)
= 4/6
= 2/3
= 0.6667
6. Probability (getting Capital letter)
= 3/6
= 0.5
7. Probability (getting lowercase letter)
= 3/6
= 0.5
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What is the best way to multiply a chain of matrix with dimensions 10x3, 3x5, 5x10,10x12,12x1 show the steps performed in your work to get to the result.
The final matrix product has dimensions 10x1.
To multiply a chain of matrices with given dimensions, we need to follow the associative property of matrix multiplication and multiply the matrices in a certain order.
Given the dimensions 10x3, 3x5, 5x10, 10x12, and 12x1, we need to multiply them in the order of (10x3) x (3x5) x (5x10) x (10x12) x (12x1).
Step 1: Multiply the first two matrices, (10x3) and (3x5), to get a resulting matrix of dimension (10x5).
Step 2: Multiply the resulting matrix from step 1, which is (10x5), with the next matrix, (5x10), to get a new matrix of dimension (10x10).
Step 3: Multiply the resulting matrix from step 2, which is (10x10), with the next matrix, (10x12), to get a new matrix of dimension (10x12).
Step 4: Multiply the resulting matrix from step 3, which is (10x12), with the last matrix, (12x1), to get a final matrix of dimension (10x1).
Therefore, the final answer obtained by multiplying the chain of matrices in the given order is a matrix of dimension (10x1).
The steps performed in the multiplication of the chain of matrices with dimensions 10x3, 3x5, 5x10, 10x12, and 12x1 are as follows:
(10x3) x (3x5) = (10x5)
(10x5) x (5x10) = (10x10)
(10x10) x (10x12) = (10x12)
(10x12) x (12x1) = (10x1)
To multiply a chain of matrices efficiently, you should follow the Matrix Chain Multiplication algorithm, which determines the optimal parenthesization to minimize the number of scalar multiplications. For your matrices with dimensions 10x3, 3x5, 5x10, 10x12, and 12x1, here's the best way to multiply them:
1. Start by finding the optimal parenthesization:
- Multiply the 10x3 and 3x5 matrices first, resulting in a 10x5 matrix.
- Then, multiply the 5x10 and 10x12 matrices, resulting in a 5x12 matrix.
- Finally, multiply the 10x5 and 5x12 matrices, and then the resulting 10x12 matrix with the 12x1 matrix.
2. Perform the multiplications:
- A = 10x3 * 3x5 = 10x5
- B = 5x10 * 10x12 = 5x12
- C = A * B = 10x5 * 5x12 = 10x12
- D = C * 12x1 = 10x12 * 12x1 = 10x1
By following this approach, you minimize the total number of scalar multiplications, resulting in a more efficient calculation. The final matrix product has dimensions 10x1.
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Suppose a fair coin is tossed two times. Construct an equiprobable sample space for the experiment, and determine each of the following probabilities. (Enter your probabilities as fractions.) (a) Pr(0 heads) (b) Pr(1 head) (c) Pr(2 heads)
The probabilities of the possible outcomes obtained from tossing a fair coin two times are;
(a) Pr(0 heads) = 1/4
(b) Pr(1 head) = 1/2
(c) Pr(2 heads) = 1/4
What is the probability of an event?The probability of an event is the ratio of the number of required outcome to the number of possible outcomes.
The equiprobable sample space of tossing a fair coin two times is; {HH, HT, TH, TT}, where;
H = Heads
T = Tails
The sample space indicates that there are 4 possible outcomes
(a) The possibility of getting 0 heads, is to get TT, therefore, the probability of getting zero heads, Pr(0 heads) = TT = 1/4
(b) The possibility of getting 1 head is to get. HT or TH, therefore;
The probability of getting 1 head, Pr(1 heads) = 2/4 = 1/2
(c) The number of possibility of getting 2 heads, is to get HH = 1
Therefore, the probability of getting 2 heads, Pr(2 heads) = 1/4
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represent -3/11 on the number line.
The number -3/11 on the number line is added as an attachment
Representing -3/11 on the number line.From the question, we have the following parameters that can be used in our computation:
Number = -3/11
To represent -3/11 on a number line, we use the following steps
Create an interval from -5 to 6 i.e. 11 spacesPlot -3/11 on point -3Using the above as a guide
The number line is added as an attachment
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What is the value of X?
Answer: x = 2√381
Step-by-step explanation:
Call A the dotted line.
Using the Pythagorean theorem, we find that [tex]A^{2} + 16^{2}[/tex] [tex]= 22^{2}[/tex]
Simplifying gives:
[tex]A = \sqrt{16^2 + 22^2}\\A = \sqrt{740}\\A = 2\sqrt{185}[/tex]
Now we move to the other triangle we can call the sides: a, the dotted side, b the height, and x, the hypotenuse.
[tex]a = 2\sqrt{185}[/tex]
and
[tex]b = 44-16 = 28[/tex]
So,
[tex](2\sqrt{185})^{2} + 28^2 = x^2\\x = \sqrt{(2\sqrt{185})^2 +28^2 }\\x = \sqrt{740+784}\\x= \sqrt{1524}\\x= 2\sqrt{381}[/tex]
A summary of two stocks is shown.
Name of Stock Symbol Closing Price Day 1 Closing Price Day 2 Closing Price Day 3
Metroplis, Ltd MTP 17.95 18.28 18.25
Suburbia, Inc SBR 5.63 5.88 4.98
Suppose you purchase 30 shares of Metropolis stock and 55 shares of Suburbia stock on Day 1 at the closing price. Which day, during the following two days, would be the best to sell both stocks?
Day 2 is the best by $26.75.
Day 3 is the best by $26.75.
Day 2 is the best by $23.65.
Day 3 is the best by $23.65.
The best day to sell both stocks is Day 2, since the total value of both stocks is highest on that day, option C is correct.
On Day 1, the total value of the 30 shares of Metropolis stock is:
30 shares x $17.95 per share = $538.50
And the total value of the 55 shares of Suburbia stock is:
55 shares x $5.63 per share = $309.65
So the total value of both stocks on Day 1 is:
$538.50 + $309.65 = $848.15
On Day 2, the total value of the shares of Metropolis stock is:
30 shares x $18.28 per share = $548.40
And the total value of the shares of Suburbia stock is:
55 shares x $5.88 per share = $323.40
The total value of both stocks on Day 2 is: $871.8
for Day 3, total value of both stocks on Day 3 is $$821.40
Therefore, we can see that the best day to sell both stocks is Day 2, since the total value of both stocks is highest on that day:
$871.80 - $848.15 = $23.65
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PLEASE HELP I INCLUDED A WRITTEN VERSION OF MY PROBLEM I WROTE IT PLEASE HELP!!!
The expression x²-6x+9 is equal to the expression (x-3)², option A is correct.
The given expression is x²-6x+9
x is the variable in the expression
Plus and minus are the operators
We have to factor the expression
x²-6x+9
x²-3x-3x+9
x(x-3)-3(x-3)
(x-3)(x-3)
x²-6x+9 is equal to (x-3)²
(x-3)²
Hence, the expression x²-6x+9 is equal to the expression (x-3)², option A is correct.
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Which word describes the "4" in this expression? 4h A term B product C sum D coefficient?
Answer:
coefficient
Step-by-step explanation:
the 4 is the coefficient
Please solve this and I will give u brainlst.
A pipe at an amusement park sprays water onto visitors. A cross section of each pipe has the shape of a parallelogram. Answer parts (a)(c).
Answer:
a. The interior angles of Parallelogram B (Pipe B) are 30°, 150°, 150°, and 30°. Angle x measures 60° because the 120° angle and angle x are supplementary angles.
c. Correct answers, in order: 360, 360, 150, supplementary, 30, complementary, 60
Jack is running a 5-mile race with Jill. Jack's run is represented by the function d = 0.05t,
where d is distance traveled in miles and t is the minutes run. Jill's run is represented by d
0.04t+ 0.5.
=
Part A
How do the graphs of Jack's representative function and Jill's representative function
compare to the graph of the linear parent function?
Part B
What do the effects of comparing Jack and Jill's functions to the linear parent function mean
in the real-world context?
When we compare functions we see that Jack and Jill have the smaller slopes
How to solve the problemJack's function: d = 0.05t
Slope (m1) = 0.05
Y-intercept (b1) = 0
Jill's function: d = 0.04t + 0.5
Slope (m2) = 0.04
Y-intercept (b2) = 0.5
Linear parent function: d = t
Slope (m0) = 1
Y-intercept (b0) = 0
When we compare functions we see that Jack and Jill have the smaller slopes
B. Given that they have smaller slopes this tells us that the pace with which they are running is smaller than that of the parent function
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Julio can stain the deck three times faster than his cousin Samuel can. Together, they can stain the deck in 3 h.
Let a represent the number of hours Julio requires to stain the deck.
What is the equation to solve the situation?
How long will it take Julio to stain the deck?
According to the information, Samuel can stain the deck in 4 hours, and Julio can do it three times faster, in 4/3 hours or 1 hour and 20 minutes.
What is the equation to solve the situation?Let's assume that Samuel can stain the deck in x hours. Then, Julio can do the same job in x/3 hours (since he is three times faster).
Working together, they can stain the deck in 3 hours. Using the concept of work, we can set up the following equation:
1/x + 1/(x/3) = 1/3
Simplifying this equation by finding a common denominator, we get:
3/(3x) + x/(3x) = 1/3
Combining like terms, we get:
4x/(3x) = 1/3
Cross-multiplying, we get:
12x = 3x
Solving for x, we get:
x = 4
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