If 28% of students in college are near-sighted, the probability that in a randomly chosen group of 20 college students, exactly 4 are near-sighted is closest to.
Answers
Therefore, the probability that in a randomly chosen group of 20 college students, exactly 4 are near-sighted is closest to 0.2261.
To calculate the probability of exactly 4 out of 20 randomly chosen college students being near-sighted, we can use the binomial probability formula.
The binomial probability formula is:
\(P(X = k) = C(n, k) * p^k * (1 - p)^{({n - k)\)
Where:
P(X = k) is the probability of exactly k successes
n is the total number of trials
k is the number of successful trials
p is the probability of success in a single trial
(1 - p) is the probability of failure in a single trial
C(n, k) is the binomial coefficient, also known as "n choose k" or the number of ways to choose k successes out of n trials.
Given:
Probability of being near-sighted (p) = 0.28
Number of trials (n) = 20
Number of successful trials (k) = 4
Using these values, we can calculate the probability as follows:
\(P(X = 4) = C(20, 4) * (0.28)^4 * (1 - 0.28)^{(20 - 4)\)
Using a calculator or statistical software, the calculation yields:
P(X = 4) ≈ 0.2261
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Related Questions
the results generated in the map phase are combined in the ________ phase.
Answers
The results generated in the map phase are combined in the _reduce_ phase.
In maps, the "reduced phase" refers to a technique used to remove the phase ambiguity present in interferometric synthetic aperture radar (InSAR) data. InSAR uses radar to measure the distance between a satellite or aircraft and the ground and can be used to create detailed maps of changes in the surface of the earth over time.
However, because InSAR data is collected using radar waves, which are sensitive to the phase of the signal, the data can be affected by phase ambiguities. The reduced phase technique is used to remove these ambiguities and create more accurate maps.
Therefore, The results generated in the map phase are combined in the _reduce_ phase.
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Patrick left home at 4:20 p.m. on Sunday. He returned 36.3 hours later. what day and time was it when he got home?
Answers
First, we need to convert 36.3 hours into days and hours. Since there are 24 hours in a day, we can divide 36.3 by 24 to get the number of days, and take the remainder to get the number of hours:
36.3 hours ÷ 24 hours/day = 1 day and 12.3 hours
So, Patrick returned 1 day and 12.3 hours later.
Adding 12.3 hours to the time he left at 4:20 p.m. on Sunday, we get:
4:20 p.m. + 12.3 hours = 4:20 p.m. + 12 hours + 0.3 hours
= 4:20 a.m. on Tuesday
Therefore, Patrick arrived home at 4:20 a.m. on Tuesday.
Answer: 4 o'clock am on Tuesday
Step-by-step explanation: 4pm on Sunday+36 hours which gets you to Monday 4 pm + 12 hours= 4 am on Tuesday.
(I hope this helps
the sum of 8 and -13.
Answers
Answer:
-104 is the answer .....
Question 11 of 15 Which set of ordered pairs represents a function? OA. ((0,7), (2,7), (4, 7), (6, 7), (8,7)} OB. ((5, 1), (5, 2), (5, 3), (5, 4), (5,5)} OC. ((1,4), (2, 4), (3, 4), (4, 3), (4, 2)) ○ D. {(1, 2), (2, 3), (3, 2), (2, 1), (1, 0)}
Answers
Answer:
The answer is A. (0,7), (2,7), (4,7), (6,7), and (8,7).
Step-by-step explanation:
Ordered pairs are represented by (x,y), the same coordinates on a coordinate plane. X is considered the input, and y is considered the output. For functions, there can only be one output for every input. Different inputs may share the same output.
The x value does not repeat in A, so A is the correct answer.
Hope this helps!
The value of a variable is fixed. True or false Explain:
Answers
Answer:
False
Step-by-step explanation:
Which of the following functions is graphed below
Answers
Answer:
C: y = |x-2| + 3
Step-by-step explanation:
When dealing with transformations, the numbers in the parentheses is the horizontal translation and the numbers outside the parentheses are vertical translation. The only reason the lines are | rather than ( is that they are absolute value.
When taking the horizontal measures, you always flip the sign. So since it is going to the right 2 times, you would think it would be +2, but since it is in the parentheses it would be -2.
When taking the vertical measures, it's just standard thought. So since it is up 3 it would be +3.
Putting all of that together would give you |x-2|+3
In the figure b and c are parallel lines select all the statements that are true
Answers
Did you ever get the answer
Answer:
Im the king of answers
Step-by-step explanation:
The answer is A, C, and E
during the worst periods of hyperinflation in a certain country the price of food increased at a rate of 30% per month.if your food bill was $120 in one month during this period,what was it three months later ?
Answers
The rate of inflating is r=30% per month.
The bill of food after three months can be determined as,
\(\begin{gathered} C=120(1+\frac{30}{100})^3 \\ C=263.64 \end{gathered}\)Thus, the bill after three months will be $263.64.
make or compute the histogram, the average, and the (population) standard deviation of {1, 2, 3, 4, 5, 6} and compare to the roll data.
Answers
The average of the data is 3.5, indicating the central tendency. The population standard deviation is approximately 1.71, representing the spread or variability of the data.
To compute the histogram, average, and population standard deviation of the data {1, 2, 3, 4, 5, 6}, we can follow these steps:
Histogram: A histogram represents the frequency distribution of the data. Since the data is already given, we can directly compute the histogram by counting the number of occurrences of each value.
Data: {1, 2, 3, 4, 5, 6}
Histogram:
1: |
2: ||
3: |||
4: |||
5: ||
6: |
Average (Mean): To calculate the average, we sum up all the values and divide by the number of data points.
Average = (1 + 2 + 3 + 4 + 5 + 6) / 6 = 21 / 6 = 3.5
Therefore, the average of the given data is 3.5.
Population Standard Deviation: The population standard deviation measures the spread of the data points around the average. It can be calculated using the formula:
Standard Deviation = √[(Σ(x - μ)^2) / N]
where Σ denotes the sum, x represents each data point, μ represents the average, and N represents the number of data points.
Standard Deviation = √[((1 - 3.5)^2 + (2 - 3.5)^2 + (3 - 3.5)^2 + (4 - 3.5)^2 + (5 - 3.5)^2 + (6 - 3.5)^2) / 6]
Standard Deviation ≈ √[17.5 / 6] ≈ √2.9167 ≈ 1.71
Therefore, the population standard deviation of the given data is approximately 1.71.
Comparing to Roll Data:
To provide a comparison with the roll data, the roll data must be provided or specified. Please provide the roll data so that a meaningful comparison can be made.
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I need this practice problem explained I will provide a picture with the answer options
Answers
Given the following System of Equations:
\(\begin{cases}x+2y=8 \\ -3x-2y=12\end{cases}\)You can solve it with Cramer's Rule. The steps are shown below:
1. By definition, you know that for "x"
\(x=\frac{D}{D_x}=\frac{\begin{bmatrix}{c_1} & {b_1} & {} \\ {c_2_{}_{}_{}} & {b_2} & {} \\ {} & {} & \end{bmatrix}}{\begin{bmatrix}{a1_{}} & {b_1} & {} \\ {a_2_{}} & {b_2} & {} \\ {} & {} & \end{bmatrix}}\)In this case:
\(\begin{gathered} c_1=8 \\ c_2=12_{} \\ b_1=2 \\ b_2=-2_{} \\ a_1=1 \\ a_2=-3 \end{gathered}\)Then, you can substitute values and evaluating, you get that the value of "x" is:
\(x=\frac{\begin{bmatrix}{8_{}} & {2_{}} & {} \\ {12_{}} & {-2_{}} & {} \\ {} & {} & \end{bmatrix}}{\begin{bmatrix}{1_{}} & {2_{}} & {} \\ {-3_{}} & {-2_{}} & {} \\ {} & {} & \end{bmatrix}}=\frac{(-2)(8)-(2)(12)}{(-2)(1)-(2)(-3)}=\frac{-16-24}{-2+6}=-10\)2. By definition, for "y":
\(y=\frac{D_y}{D}=\frac{\begin{bmatrix}{a_1} & {c_1} & {} \\ {a_2} & {c_2} & {} \\ {} & {} & {}\end{bmatrix}}{\begin{bmatrix}{a_1} & {b_1} & {} \\ {a_2} & {b_2} & {} \\ {} & {} & {}\end{bmatrix}}\)Knowing the values, substitute and evaluate:
\(y=\frac{\begin{bmatrix}{1_{}} & {8_{}} & {} \\ {-3_{}} & {12_{}} & {} \\ {} & {} & {}\end{bmatrix}}{\begin{bmatrix}{1_{}} & {2_{}} & {} \\ {-3_{}} & {-2_{}} & {} \\ {} & {} & {}\end{bmatrix}}=\frac{(12)(1)-(-3)(8)}{(-2)(1)-(-3)(2)}=\frac{12+24}{-2+6}=9\)Therefore, the answer is:
\(\begin{gathered} x=\frac{\begin{bmatrix}{8_{}} & {2_{}} & {} \\ {12_{}} & {-2_{}} & {} \\ {} & {} & \end{bmatrix}}{\begin{bmatrix}{1_{}} & {2_{}} & {} \\ {-3_{}} & {-2_{}} & {} \\ {} & {} & \end{bmatrix}}=\frac{-16-24}{-2+6}=-10 \\ \\ \\ y=\frac{\begin{bmatrix}{1_{}} & {8_{}} & {} \\ {-3_{}} & {12_{}} & {} \\ {} & {} & {}\end{bmatrix}}{\begin{bmatrix}{1_{}} & {2_{}} & {} \\ {-3_{}} & {-2_{}} & {} \\ {} & {} & {}\end{bmatrix}}=\frac{12+24}{-2+6}=9 \end{gathered}\)what is the measure of an exterior angle in a square?
Answers
The measure of an exterior angle in a square is 360 degrees, since all four angles of a square are equal and add up to 360 degrees.
The measure of an exterior angle in a square is 360 degrees. This is because all four angles of a square are equal and add up to 360 degrees. An exterior angle of a square is an angle formed between two adjacent sides of the square when an imaginary line is drawn from one vertex to the other. The two sides that form the exterior angle will always be of equal length and the angle itself will always measure the same amount. In the case of a square, the angle will always measure 360 degrees. This is because the two sides of the square will always be equal and the sum of the interior angles of a square is always 360 degrees. So, the measure of an exterior angle in a square is 360 degrees.
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A maximum number of 50
Answers
A maximum number of 50
The area of a rectangular coountertop is 12x^2 10x-12. The width of the countertop is 2x 3. What is the length of the countertop
Answers
The length of the rectangular countertop is 6x - 4.
To find the length of the rectangular countertop, we have to substitute the given values in the formula for the area of the rectangle, which is A = l × w
12x² + 10x - 12 = (2x + 3) × l
6x² + 5x - 6 = 3x × l + 3 × l
6x² + 5x - 6 = 3lx + 3l
6x² + 5x - 6 = 3l(x + 1)
3l = (6x² + 5x - 6) / (x + 1)
3l = (6x² + 9x - 4x - 6) / (x + 1)
3l = 3(2x² + 3x - 2) / (x + 1)
l = (2x² + 3x - 2) / (x + 1)
l = [(2x - 1) (x + 2)] / (x + 1)
Therefore, the length of the rectangular countertop is 6x - 4.
Summary:
The formula for the area of the rectangle is A = l × w. We substitute the given values in the formula to find the length of the rectangular countertop. After simplifying the expression, the length of the rectangular countertop is found to be 6x - 4.
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The american heart association is about to conduct an anti-smoking campaign and wants to know the fraction of americans over 26 who smoke. Suppose a sample of 897 americans over 26 is drawn. Of these people, 637 don't smoke. Using the data, estimate the proportion of americans over 26 who smoke.
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we can estimate that about 29.0% of Americans over 26 smoke based on this sample.
To estimate the proportion of Americans over 26 who smoke, we need to use the sample proportion, which is the number of people in the sample who smoke divided by the total sample size.
In this case, the sample size is 897 and the number of people who don't smoke is 637, so the number of people who do smoke is:
897 - 637 = 260
So the sample proportion of Americans over 26 who smoke is:
260 / 897 = 0.290
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Stephan can run 3 miles in 15.75 minutes. Kelsha can run 5 miles in 226 minutes.
Who can run faster?
Unit rate for Stephan:
Unite rate for Kelsha.
Answers
Answer:
Step-by-step explanation:
Stephan can run
3 miles in 15.75 minutes
1 miles in 15.75/3 minutes
1 miles in 5.25 minutes
Kelsha can run
5 miles in 226 minutes
1 miles in 226/5 minutes
1 miles in 45.2 minutes
Stephan can run faster, since 5.25 < 45.2
Stephan can run faster, than Kelsha since 5.25 < 45.2.
What is speed?Speed is defined as the ratio of the distance traveled by the body to the time taken by the body to cover the distance. The unit of speed is measured in a meter per second, Miles per second, etc. Speed is a scalar quantity and does not require direction.
The speed for Stephan will be calculated as below:-
3 miles in 15.75 minutes
1 mile in 15.75/3 minutes
1 mile in 5.25 minutes
The speed for Kelsha will be calculated as below:-
5 miles in 226 minutes
1 mile in 226/5 minutes
1 mile in 45.2 minutes
Therefore, Stephan can run faster, than Kelsha since 5.25 < 45.2.
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A phone company surveys a sample of current customers to determine if they use their phones most often to text or use the Internet. They sort the data by payment plans, as shown below. Plan A: 27 text, 21 Internet Plan B: 13 text, 10 Internet Answer the questions to determine a conditional probability. How many customers are on payment plan B? customers How many of the customers on plan B text? customers What is the probability that a randomly selected customer who is on plan B uses the phone most often to text? Give the answer in fraction form.
Answers
Answer:
23 customers on payment plan B
13 customers on plan text B
Probability: 13/23
Step-by-step explanation:
Find the slope.
Find the slope
Answers
Answer:
m=-2
Step-by-step explanation:
The two given points are: (-3, -2) and (-2, -4)
The equation for slope is m=\(\frac{y_2-y_1}{x_2-x_1}\)
m=\(\frac{(-4)-(-2)}{(-2)-(-3)}\)
m=-2/1
m=-2
Answer:
\(\underline{\boxed{\bf m=-2}}\)
Step-by-step explanation:
Let's find the slope:-
We can Use the slope formula to find the slope of a line given the coordinates of two points on the line:- (-3, -2) & (-2, -4).The coordinates of the first point represent x1 and y1. The coordinates of the second points are x2, y2.
\(\tt \left(x_1,\:y_1\right)=\left(-3,\:-2\right)\)
\(\tt \left(x_2,\:y_2\right)=\left(-2,\:-4\right)\)
\(\bf Slope(m)=\tt \cfrac{-4-\left(-2\right)}{-2-\left(-3\right)}\)
\(\bf m=\tt \cfrac{-4+2}{-2+3}\) ( Add/Subtract numbers)
\(\bf m=-2\)
Can someone help me please?
Answers
Answer:
B) y = 0.6xStep-by-step explanation:
Proportional relationship equation:
y = kx, where k- coefficient of proportionality.Use given values in table to find the value of k:
9 = 15k ⇒ k = 9/15 = 0.67.2 = 12k ⇒ k = 7.2/12 = 0.61.5 = 2.5k ⇒ k = 1.5/2.5 = 0.6So the equation is:
y = 0.6xHelp, please
Or else I will send the rock to your house
Answers
Answer:
Hi
The answers is
W=36 ÷ 4
the tire pictured below has a radius of 14 inches
Answers
To determine the distance rolled by the tire in 24 revolutions, use the following formula:
\(s=r\theta\)where r is the radius (14 in) and θ the degrees of the revolutions. Consider each revoutions represents 180 degrees or 2π radians, the, 24 revolutions are 24x2π = 48π.
Replace the values of r and θ into the formula for s:
\(s=(14in)(48)(3.14)=2,110.08in\approx2,110in\)Hence, the tire rolls 2,110 in
Answer:
B
Step-by-step explanation:
Circumference = pi * d = 28 pi inches
twenty four of these is 24 * 28 pi inches = 2111.15 in = 175.9 ft
Monthly sales of a particular personal computer are expected to decline at the following rate of S'(t) computers per month, where t is time in months and S(t) is the number of computers sold each month.S'(t) = −25t^2/3The company plans to stop manufacturing this computer when monthly sales reach 1,000 computers. If monthly sales now (t = 0) are 2,050 computers, find S(t). How long will the company continue to manufacture this computer?S(t) = _______Therefore, the company will continue to manufacture this computer for approximately how many months? What is (t)_____
Answers
The function S(t) = -15t^(5/3) + C which we get by integration of S'(t) and the company will continue to manufacture this computer for approximately 5.47 months.
To find S(t), we need to integrate the given rate of decline, S'(t), with respect to time (t). We have:
S'(t) = -25t^(2/3)
Integrating both sides with respect to t, we get:
S(t) = ∫(-25t^(2/3) dt)
Using the power rule for integration, we obtain:
S(t) = (-25 * (3/5) * t^(5/3)) + C
S(t) = -15t^(5/3) + C
Now, we're given that at t = 0, S(0) = 2,050 computers. We can use this information to find the constant of integration, C:
S(0) = -15(0)^(5/3) + C
2,050 = C
Thus, the function for the monthly sales is:
S(t) = -15t^(5/3) + 2,050
The company will stop manufacturing when S(t) = 1,000 computers. To find when this occurs, we'll set S(t) equal to 1,000 and solve for t:
1,000 = -15t^(5/3) + 2,050
-1,050 = -15t^(5/3)
Now, isolate t^(5/3) and solve for t:
t^(5/3) = 1,050 / 15
t^(5/3) = 70
Take the cube root of both sides:
t^(5/3)^(3/5) = 70^(3/5)
t = 70^(3/5)
Calculating this value, we get approximately:
t ≈ 5.47
So, the company will continue to manufacture this computer for approximately 5.47 months.
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The decimal representation of ___________ number neither terminates nor repeats.
Answers
The numbers that neither terminate nor repeat are called irrational numbers.
What are irrational numbers?
Any real number that is not rational is called an irrational number. These numbers can not be expressed in the form of p/q, where q is not equal to 0. Sometimes, irrational numbers are also called non-terminating and non-repeating numbers.
Filling the blank with an appropriate term
The decimal representation of ___Irrational__ number neither terminates nor repeats.
Hence, the answer is irrational.
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Find the height of the triangle by applying formulas for the area of a triangle and your knowledge about
triangles.
9 in
9 in.
Xin
6 in
Answers
Answer:
8.5
Step-by-step explanation:
Applying pythagora's theorem,
hypotenuse^2 = opposite^2 + adjacent^2
but, hypotenuse = 9
opposite = X
adjacent = 1/2(base of triangle)= 1/2(6)
adjacent = 3
9^2 = X^2 + 3^2
X^2 = 81 - 9
X^2 = 72
X = 8.5
which expression is equal to 24x^2-22x+5
Answers
Answer: (12x−5)(2x−1)
Step-by-step explanation: Hope this help :D
Answer:
24(x^2)-22x+5
=24(x^2)-(12+10)x+5
=24(x^2)-12x-10x+5
=12x(2x-1)-5(2x-1)
=(2x-1)(12x-5)
The function g(x) is graphed on the coordinate grid.
What is the domain of g(x)?
V
5-
..4
оооо
3
x20
..2
O x>0
...1
1
3
4
5
6
7
8
-11
9 10
2
3
4
5
Answers
Answer:
The first one
Step-by-step explanation:
The function f(x) = {x + 3, x < 0, 3 x ≥ 0} represents the graph.
What is graph?In mathematics, the set of ordered pairings where f(x)=y exists is the graph of a function f. These pairs are Cartesian coordinates of points in two-dimensional space and so form a subset of this plane in the typical situation when x and f(x) are real integers.
here, we have,
given that,
As show in the graph we can see that the function has a graph of x + 3 on left side of the y - axis for x < 0.
And the function has the constant graph y = 3 for x ≥ 0.
Therefore, the given graph is the graph of the function,
f(x) = {x + 3, x < 0, 3 x ≥ 0}.
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Complete question:
He graph of a function is shown.
5
4
3
2
-
y
--5-3-2-1₁ 1 2 3 4 5 x
-2-
-3+
7 9
Which function is represented by the graph?
O f(x) =
O
f(x) = {3
O f(x):
x-3, x<0
3,
x20
11
x + 3, x < 0
x 20
-x+ 3, x ≤ 0
3,
x>0
○ f(x) = { 3*
O
-x-3, x ≤0
x > 0
the measures of the bases of a trapezoid are 35 and 71. find the measure of the midsegment.
Answers
The measure of the mid segment is 53 .
Given :
the measures of the bases of a trapezoid are 35 and 71.
What is trapezoid ?
A trapezoid is a four-sided shape which has one pair of sides as parallel. It is basically a two-dimensional shape or figure similar to a square etc .
Mid segment :
A mid segment of a trapezoid is the line segment connecting the midpoints of the two non-parallel sides of a trapezoid.
A trapezoid mid segment is parallel to the set of parallel lines in a trapezoid and is equal to the average of the lengths of the bases.
Measure of mid segment = sum of two bases / 2
= 35 + 71 / 2
= 106 / 2
= 53
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A confectionery company mixes three types of toffees to form one kilogram " toffee packs. the pack is sold at rs. 17. the three types of toffees cost rs.20, rs. 10, rs. 5 per kg. resp. the mixture must contain atleast 300 gms of first type. also weight of first two types must be at least be equal to weight of third type. find the optimal mix for maximum profit.answer
Answers
The maximum profit is 6 and it is obtained when we mix 0.6 kg of type A, 0 kg of type B, and 0.4 kg of type C.
The optimal mix for the maximum profit can be found as follows:
The company mixes three types of toffees, A, B, and C. Let the weights of type A, B, and C be a, b, and c kg, respectively. Let us assume that we are making 1kg of toffee pack. Therefore, the weight of type C should be 1 - (a + b) kg. Also, the mixture must contain at least 300 gms of type A i.e a >= 0.3 kg
Also, the weight of the first two types (A and B) must be at least equal to the weight of type C, i.e a + b >= c. This condition can also be written as a + b - c >= 0
Let us now calculate the total cost of making 1kg of toffee pack.
Cost = 20a + 10b + 5c
If the pack is sold at Rs. 17, then the profit per 1kg of toffee pack is by
Profit = Selling Price - Cost = 17 - (20a + 10b + 5c)
Now we have the following linear programming problem:
Maximize P = 17 - (20a + 10b + 5c)
Subject to constraints: a + b + c = 1 (since we are making 1kg of toffee pack)
a >= 0.3a + b - c >= 0a, b, c >= 0
We can use the simplex method to solve this linear programming problem. However, to save time, we can solve it graphically. The feasible region is as follows:
We can see that the corner points of the feasible region are: (0.3, 0, 0.7), (0.6, 0, 0.4), (0, 0.5, 0.5), and (0, 1, 0).
Let us calculate the profit at each of these corner points. For example, at the point (0.3, 0, 0.7), we have a = 0.3, b = 0, and c = 0.7. Therefore, the profit is
P = 17 - (20(0.3) + 10(0) + 5(0.7)) = 3.5
Similarly, we can calculate the profit at the other corner points as well. The corner point (0.3, 0, 0.7) gives a profit of 3.5
Corner point (0.6, 0, 0.4) result in a profit of 6
Corner point (0, 0.5, 0.5) results in a profit of 5
Corner point (0, 1, 0) gives a profit of 3
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Factor the expression completely 18x2 - 32
Answers
Answer:
4
Step-by-step explanation:
18x2=36
36-32=4
= = Question 2 [20 points] Let pi(t) = ť– 2t – 3 and p2(t) = -t? +2. (a) [10 Points] Determine whether p(t) = 2t? + 6t – 1 belongs to span{P1, P2}: (b) (10 Points] Given pz(t) = -3t² + 4t +4,
Answers
p(t) = 2t² + 6t - 1 belongs to the span of {p₁(t), p₂(t)}, but p₃(t) = -3t² + 4t + 4 does not belong to the span.
(a) To determine whether p(t) = 2t² + 6t - 1 belongs to the span of {p₁(t), p₂(t)}, we need to check if there exist constants c₁ and c₂ such that p(t) = c₁p₁(t) + c₂p₂(t).
Comparing the coefficients of the terms on both sides, we have:
2t² + 6t - 1 = c₁(ť - 2t - 3) + c₂(-t³ + 2)
Expanding and equating coefficients, we get the following system of equations:
2 = -c₂
6 = -2c₁
-1 = -3c₁ + 2c₂
Solving this system of equations, we find c₁ = -3/2 and c₂ = -1. Therefore, p(t) can be expressed as a linear combination of p₁(t) and p₂(t), indicating that p(t) belongs to the span of {p₁(t), p₂(t)}.
(b) Given p₃(t) = -3t² + 4t + 4, we can apply a similar approach to determine if p₃(t) belongs to the span of {p₁(t), p₂(t)}.
Setting up the system of equations:
-3t² + 4t + 4 = c₁(ť - 2t - 3) + c₂(-t³ + 2)
Comparing coefficients, we have:
0 = -c₂
4 = -2c₁
4 = -3c₁ + 2c₂
Solving this system of equations, we find c₁ = -2 and c₂ = 0. Therefore, p₃(t) cannot be expressed as a linear combination of p₁(t) and p₂(t), indicating that p₃(t) does not belong to the span of {p₁(t), p₂(t)}.
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Find the value of c that makes the equation a perfect square trinomial.
x^2+8x+c
Answers
Answer:
16
Step-by-step explanation:
(x + 4)(x + 4)
x² + 4x + 4x + 16
x² + 8x + 16