The probability that more than 8 hours are needed to grade all of the exams is about 52%
What is the probability of a standard normal distribution?The probability of a standard normal distribution is the area under the curve of the normal distribution function within a specified interval.
Let X represent the random variable to grade an exam, and let Y represent the total time to grade all exams
The number of students = 50
Therefore;
Y = 50·X
The properties of the normal distribution indicates that we get;
E(Y) = E(50·X) = 50·E(X) = 50 × 9.7 = 485
Var(Y) = Var(50·X) = 50²·Var(X) = 50² × 1.92² = 9025
The standard deviation, SD(Y) = √(Var(Y)) = √(9025) = 95
The probability that more than 8 hours are needed can be found using the z-score of the normal distribution as follows;
8 hours = 480 minutes
Z = (480 - 485)/95 ≈ -0.0526
The probability obtained from a standard normal table, is therefore;
P(Z > -0.0526) = 1 - 0.48006 ≈ 0.52
The probability that more than 8 hours are needed to grade all students is therefore about 0.52 or 52%
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a runner wants to run 11.7 km . she knows that her running pace is 6.7 mi/h .how many minutes must she run
The number of minutes she must run to reach her goal is 65.1 minutes.
The time she must run for is found by dividing the distance by the speed:
Time = Distance / Speed
We need to convert the distance from kilometers to miles before substituting values into the formula.
11.7 km = 11.7 / 1.609344 = 7.270043 miles
The formula now becomes:
Time = 7.270043 miles / 6.7 mi/h
Time = 1.085081 h
To get the time in minutes, we need to convert the time in hours to minutes. There are 60 minutes in an hour, so there are
Time = 1.085081 h x (60 minutes/1 hour)
Time = 65.104863 minutes = 65.1 minutes
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please help
there are 2 possible answers
Let x be the number of boys in a class and y be the number of girls. Which equation represents 2 boys for
every 5 girls? Select all that apply.
A. x=2y-5
B. x=5y-2
C. 5x=2y
D. x=2 1/2y
E. x=2/5y
Answer:
C, E
Step-by-step explanation:
You want the equations that represent 2 boys for every 5 girls in a class.
RatioThe number of boys is represented by x, and the number of girls is represented by y, so you have ...
x : y = 2 : 5
As fractions, this is ...
x/y = 2/5
Other representationsMultiplying by 5y gives ...
5x = 2y . . . . . . matches equation C
Dividing by 5, we have ...
x = 2/5y . . . . . . matches equation E
Assume a jar has five red marbles and four black marbles. Draw out two marbles with and without replacement. Find the requested probabilities. (Enter the probabilities as fractions.)
(a) P(two red marbles)
with replacement without replacement (b) P(two black marbles)
with replacement without replacement (c) P(one red and one black marble)
with replacement without replacement (d) P(red on the first draw and black on the second draw)
with replacement without replacement
The probability of selecting another black marble is 3/7. As a result, the probability of drawing two black marbles in a row without replacement
(a) P(two red marbles) with replacement:The probability of drawing a red marble from a jar with five red marbles and four black marbles is 5/9, as there are five red marbles and nine total marbles. As a result, the probability of selecting two red marbles in a row with replacement is:P(two red marbles with replacement) = (5/9) × (5/9) = 25/81without replacement:When the first marble is removed, there are now only eight marbles remaining in the jar. Because there are only four black marbles in the jar, the probability of drawing a red marble is now 5/8. Therefore, the probability of selecting two red marbles in a row without replacement is:P(two red marbles without replacement) = (5/9) × (5/8) = 25/72(b) P(two black marbles)with replacement:For the first draw, there are four black marbles in the jar and a total of nine marbles. Therefore, the probability of drawing a black marble on the first draw is 4/9. Since the first marble was not removed, there are now eight marbles in the jar, including three black ones, and there are a total of nine marbles. Therefore, the probability of selecting another black marble is 3/9 or 1/3.
The probability of drawing two black marbles in a row with replacement is:P(two black marbles with replacement) = (4/9) × (1/3) = 4/27without replacement:Since the first marble was removed, there are only eight marbles in the jar, and there are four black ones. Therefore, the probability of selecting a black marble is 4/8 or 1/2. When the first black marble is removed, there are only seven marbles left, including three black ones. Therefore, the probability of selecting another black marble is 3/7. As a result, the probability of drawing two black marbles in a row without replacement is:P(two black marbles without replacement) = (4/9) × (3/7) = 12/63(c) P(one red and one black marble)with replacement:When one red and one black marble are selected with replacement, there are nine marbles in the jar for each draw. The probability of selecting one red and one black marble in a row is:P(one red and one black marble with replacement) = 2 × (5/9) × (4/9) = 40/81without replacement:Since there are five red and four black marbles in the jar, the probability of selecting a red marble first is 5/9. Once the red marble has been drawn and removed, there are only eight marbles remaining, including four black ones. As a result, the probability of selecting a black marble is 4/8 or 1/2.
As a result, the probability of drawing one red and one black marble without replacement is:P(one red and one black marble without replacement) = (5/9) × (4/8) + (4/9) × (5/8) = 20/36 + 20/36 = 10/18 = 5/9(d) P(red on the first draw and black on the second draw)with replacement:There are nine marbles in the jar for each draw. The probability of selecting a red marble first is 5/9. When the red marble is returned to the jar, there are still nine marbles in the jar, but now there are only four black marbles. The probability of selecting a black marble on the second draw is 4/9. As a result, the probability of drawing a red marble first and a black marble second with replacement is:P(red on the first draw and black on the second draw with replacement) = (5/9) × (4/9) = 20/81without replacement:Since there are five red and four black marbles in the jar, the probability of selecting a red marble first is 5/9. Once the red marble has been drawn and removed, there are only eight marbles remaining, including four black ones. As a result, the probability of selecting a black marble is 4/8 or 1/2. As a result, the probability of drawing a red marble first and a black marble second without replacement is:P(red on the first draw and black on the second draw without replacement) = (5/9) × (4/8) = 5/18
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Ryan buys some jumpers to sell on a stall. He spends £190 buying 80 jumpers. He sells 50% of the jumpers for £12 each. He then puts the rest of the jumpers on a Buy one get one half price offer. He manages to sell half the remaining jumpers using this offer. How much profit does Ryan make?
Ryan makes a profit of £240. the total sales now amount to £600. By subtracting the cost of the jumpers, i.e. £190, from the total sales, we calculate that Ryan makes a profit of £240.
Ryan spends £190 to buy 80 jumpers. He sells 50% of the jumpers, i.e. 40 jumpers, at £12 each. This brings the total sales to £480. Then, he puts the remaining 40 jumpers on a Buy one get one half price offer. He sells 20 of the remaining jumpers using this offer. Therefore, the total sales now amount to £600. By subtracting the cost of the jumpers, i.e. £190, from the total sales, we calculate that Ryan makes a profit of £240.
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In tests of significance about an unknown parameter of some population, which of the following is considered strong evidence against the null hypothesis?
A. The value of an estimate of the unknown parameter based on a simple random sample from the population is not equal to zero.
B. The value of an estimate of the unknown parameter lies within 2 units of the sample value.
C. We observe a value of an estimate of the unknown parameter based on a simple random sample from the population that is very consistent with the null hypothesis
D. We observe a value of an estimate of the unknown parameter based on a simple random sample from the population that is very unlikely to occur if the null hypothesis is true.
In tests of significance about an unknown parameter of some population, "We observe a value of an estimate of the unknown parameter based on a simple random sample from the population that is very unlikely to occur if the null hypothesis is true" is considered strong evidence against the null hypothesis. The correct answer is Option (D).
We apply the principle of hypothesis testing to test a population's claims in inferential statistics. The null hypothesis (H₀) is always a statement about the population parameter that we believe to be true. However, we use the sample data to decide whether the null hypothesis is true or not. When we perform the hypothesis testing, we must consider the level of significance, the sample size, and the nature of the test.
The value of an estimate of the unknown parameter based on a simple random sample from the population that is very unlikely to occur if the null hypothesis is true is considered strong evidence against the null hypothesis. In other words, if the value of the test statistic is greater than the critical value, we can reject the null hypothesis. Consequently, we will have sufficient evidence to support the alternative hypothesis.
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The vertex of the parabola below is at the point (5, -3). Which of the equations
below could be the one for this parabola?-ہے
A. y=-3(x-5)^2-3
B. x=3(y-5)^2-3
C. x=3(y+3)^2+5
D. x=-3(y+3)^2+5
None of the available options match the parabola's equation.
Which might be the parabola's equation?To determine the equation of a parabola, we can utilize the vertex form. Assuming we can read the coordinates (h,k) from the graph, the aim is to utilize the coordinates of its vertex (maximum point, or minimum point), to formulate its equation in the form y=a(xh)2+k, and then to determine the value of the coefficient a.
A parabola's vertex form is given by:
[tex]y = a(x-h)^2 + k[/tex]
where (h,k) is the parabola's vertex.
[tex]y = a(x-5)^2 - 3[/tex]
These values are substituted into the equation to produce:
[tex]-15 = a(2-5)^2 - 3[/tex]
[tex]-15 = 9a - 3[/tex]
[tex]-12 = 9a[/tex]
[tex]a = -4/3[/tex]
[tex]y = (-4/3)(x-5)^2 - 3[/tex]
This equation is expanded and simplified to produce:
[tex]y = (-4/3)x^2 + (32/3)x - 53[/tex]
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A sample of size 25 is drawn from a normal population with a population standard deviation of 100. Suppose the mean of the sample is x(bar) = 35. Recall that z0.025=1.96. A 95% confidence interval for the population mean is equal to
The 95% confidence interval for the population mean is equal to (30.4,39.6).
A confidence interval is a range of values that surrounds the point estimate, such as a sample mean, and provides a sense of the precision of the estimate. The confidence interval (CI) contains the estimated parameter at a given level of confidence, usually 95% or 99%.
The 95% confidence interval for the population mean is given by:
x(bar) ± Zα/2 * σ/√n
Where,
x(bar) = 35σ = 100n = 25Zα/2 = Z0.025 = 1.96
Substituting the values, we get:
CI = 35 ± 1.96 * 100/√25
CI = (30.4,39.6)
Hence, the 95% confidence interval for the population mean is (30.4,39.6).
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The mean height of 15 pupils is 159 cm. One of these pupils is 148 cm and leaves the group. Determine the new mean height of the group. Give your answer correct to 1 decimal place.
Using the mean formula we know that the new mean height of 14 people is 159.7 cm.
What is mean?A mean in math is the average of a data set, calculated by adding all numbers together and then dividing the total of the numbers by the number of numbers.
For illustration, with the dataset containing: 8, 9, 5, 6, 7, the mean is 7, as 8 + 9 + 5 + 6 + 7 = 35, 35/5 = 7.
The mean height given is 159 cm.
Let, x1, x2, x3 ..... x15 be the height of 15 people.
x1+x2+x3 ..... x15/15 = 159
x1+x2+x3 ..... x15 = 159 * 15 = 2385 cm ...(1)
Let, x1 = 148 cm, who leaves the group.
148+x2+x3 ..... x15 = 2385 cm
x2+x3 ..... x15 = 2237 cm
Now, we have 14 people.
New mean = x2+x3 ..... x15/14
= 2237/14
= 159.7 cm
Therefore, using the mean formula we know that the new mean height of 14 people is 159.7 cm.
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If the sum of two numbers is 10 and the product of the numbers is 15, then find the following:
(a) The difference of numbers.
(b) Sum of cube of the numbers.
Answer:
the numbers are
[tex] \sqrt{10} + 5 \\ - \sqrt{10} + 5[/tex]
Step-by-step explanation:
then there difference is
square root of 10 + 5 -(- square root of 10 +5)
=
[tex]2 \sqrt{10} [/tex]
and the cube of there sum is 15^3 = 15* 15* 15
= 3375
Calculate the volume of iron needed to create a rectangular prism with a base area of
2250 square cm. The prism has a cylinder missing through the center of the prism. The
radius of the cylinder is 25 cm and the height of the cylinder and the prism are both
100cm. Find the volume to the nearest tenth of a cubic cm.
The volume of iron needed to create the rectangular prism is approximately 28650.5 cubic cm.
what is volume?
Volume is the amount of space occupied by a three-dimensional object. It is a measure of how much an object can hold or how much space it takes up. The volume of a solid object is typically measured in cubic units, such as cubic centimeters (cm³) or cubic meters (m³).
The volume of the rectangular prism without the cylinder can be calculated as:
[tex]$$V_1 = A \times h$$[/tex]
where A is the base area and h is the height
[tex]$$V_1 = 2250 \times 100$$[/tex]
[tex]$$V_1 = 225000 \ \text{cubic cm}$$[/tex]
The volume of the cylinder can be calculated as:
[tex]$$V_2 = \pi r^2 h$$[/tex]
where r is the radius and h is the height
[tex]$$V_2 = \pi \times 25^2 \times 100$$[/tex]
[tex]$$V_2 = 196349.54 \ \text{cubic cm}$$[/tex]
The volume of the rectangular prism with the cylinder missing can be calculated as:
[tex]$$V = V_1 - V_2$$[/tex]
[tex]$$V = 225000 - 196349.54$$[/tex]
[tex]$$V = 28650.46 \ \text{cubic cm}$$[/tex]
Therefore, the volume of iron needed to create the rectangular prism with a base area of 2250 square cm, a cylinder missing through the center of the prism with a radius of 25 cm, and the height of the cylinder and the prism being 100 cm, is approximately 28650.5 cubic cm (rounded to the nearest tenth of a cubic cm).
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Can someone help me find the elevation of the sun I need the answers that are highlighted in yellow please help image below
Answer:
Step-by-step explanation:
a. ∠ACB
b. AC
c. AB
d. BC
e. tangent, opposite, adjacent
f. m∠ACB = tan⁻¹(34/45) = 37°
y=2x+1
2x-y=3
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
use the newton-raphson method to find an approximate value of 3√7 . use the method until successive approximations obtained by calculator are identical. an appropriate function to use for the approximation would be f (x) = A x^2 + B x^3 + C x + D where A= B= C= D=
If c1 = 2, then c2 = ___
2√3= ____
Find the height of an open cylinder of radius of 8cm given that it has a curved surface area of 1000cm²
The height of an open cylinder of radius of 8cm given that it has a curved surface area of 1000 cm² is equals to the 159.24 cm.
The area obtained after substracting the circular area from the total area of the cylinder is called as curved surface area. Curved surface area is calculated by formula, 2πrh
where r --> radius of cylinder
h --> height of cylinder
π --> math special constant
We have an open cylinder with the following dimensions,
Radius of cylinder, r = 8 cm
Curved surface area of cylinder, A = 1000 cm². We have to calculate the height of this open cylinder. Let the height of an open cylinder be 'h cm' . Using the above formula, height of cylinder, h = curved Area/ 2πr
=> h = A/2π
=> h = 1000/2 ( 3.14)
=> h = 1000/6.28
=> h = 159.24
Hence, required value of height is 159.24 cm.
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Here is a scale drawing of a garden. Tom wants to plant a tree in the garden according to the following rules: It must be 4 m from A and 2 m from CD. Place a cross where Tom can plant the tree. D 2.5 cm A 4 cm C B 1 cm represents 2m
Answer:
the cross is the blue color
B=6,c=7.5 what is A in Pythagorean therom
Answer: 4.5
Step-by-step explanation:
A^2 +B^2 =C^2
A^2 + 6^2 =7.5^2
A^2 + 36= 56.25
A^2= 20.25
A= square root of 20.25
A= 4.5
Over 9 days Jaison jogged ----- 10m, 6m, 6m, 7m, 5m, 7m, 5m, 8m, 9m
Find the mean distance Jaison jogged
The mean distance Jaison jogged over 9 days is 7 meters per day. This was calculated by adding up all the distances he jogged and dividing by 9.
To calculate the average distance that Jaison jogged over the 9 days, we used the formula for mean, which involves summing up all the distances he jogged and dividing by the total number of days. After adding up the distances, we found that the total distance Jaison jogged was 63 meters. Dividing this by the 9 days gives us an average distance of 7 meters per day. Therefore, Jaison jogged an average of 7 meters each day over the 9-day period.
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Prove that sum of measure of three angles of triangle is 180
Proved that the sum of measure of three angles of triangle is 180 using the Polygon Angle Sum Theorem
To prove that the sum of the measures of three angles of a triangle is 180 degrees, we can use the Polygon Angle Sum Theorem, which states that the sum of the measures of the interior angles of a polygon with n sides is equal to (n-2) times 180 degrees.
A triangle is a polygon with three sides, so we can apply the Polygon Angle Sum Theorem to a triangle to find the sum of its interior angles. Using n=3, we have:
Sum of measures of interior angles of triangle = (n-2) × 180 degrees
= (3-2) × 180 degrees [since we are dealing with a triangle]
= 1 × 180 degrees
= 180 degrees
Therefore, the sum of the measures of the interior angles of a triangle is 180 degrees. This means that the sum of the measures of the three angles in a triangle is always 180 degrees, regardless of the size or shape of the triangle.
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a man allow 12% discount in a computer having marked price RS 32000. If he make Rs.1160 profit on it , Find the cost price of computer
Answer:
CP of computer = 27000 rs.
Step-by-step explanation:
D% = Dis/MP*100
12*32000/100 = Dis Dis = 3840 rs.We know, Dis = MP-SP
32000 - 3840 = SP28160 = SPGiven Profit= 1160 rs.
SP-CP = 1160CP = 28160-1160 = 27000So,CP = 27000 rs.
how can i slove this??
Answer:
[tex]5x {}^{3} - x + 5x + 2[/tex]
Step-by-step explanation:
Greetings!!!
So to find the sum of (f+g)(x) just simply add these two functions
f(x)+g(x)3x²+5x-2+(5x³-4x²+4)Add like terms together
5x³-x²+5x+2If you have any questions tag it on comments
Hope it helps!!!
Please help me answer!
As a result, the percentage of adults who selected math is different from the percentage of kids who did.
what is percentage ?As a number out of 100, a percentage is a method to express a proportion or a fraction. It is symbolized by the number %. If there are 25 boys in a class of 100 pupils, for instance, then there are 25% of boys in the class. It is a helpful method to compare quantities and to express changes in values over time.
given
120 80
Total 200
Women Overall Party A Party B
70 60
Overall 130
Therefore, there are 130 ladies in the group.
b) The chart indicates that 70 women plan to support Party A.
Thus, the percentage of adults who selected English was 40% of 48, which is equal to 0.4 times 48 and 19.2 when rounded to the closest whole number.
b) Reeshma is not accurate. The percentage of adults who selected math is 35%, while for children it is 40%, according to the pie chart.
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The complete question is:- complete the two-way table, which shows the voting intentions of a group of men and women. a How many women are in the group?
Men
Party A Party B 120
Total 200
Women 130
Total 380
b How many women intend to vote for Party A?
2 A group of 48 adults are asked what their favourite subject was at school. They can choose from
maths, English and science.
A group of 32 school children are asked the
same question.
Jose and his children went into a grocery store where they sell apples for $2.25 each and mangos for $1.25 each. Jose has $20 to spend and must buy at least 9 apples and mangos altogether. Also, he must buy at least 3 apples and at most 9 mangos. If � x represents the number of apples purchased and � y represents the number of mangos purchased, write and solve a system of inequalities graphically and determine one possible solution.
Answer: $15.25
Step-by-step explanation:
Let x be the number of apples purchased and y be the number of mangos purchased. Then we have the following constraints:
2.25x + 1.25y ≤ 20 (Jose has $20 to spend)
x + y ≥ 9 (Jose must buy at least 9 apples and mangos altogether)
x ≥ 3 (Jose must buy at least 3 apples)
y ≤ 9 (Jose can buy at most 9 mangos)
To solve this system of inequalities graphically, we can plot the relevant lines and shade the feasible region.
First, we graph the line 2.25x + 1.25y = 20 by finding its intercepts:
When x = 0, we have 1.25y = 20, so y = 16.
When y = 0, we have 2.25x = 20, so x = 8.89 (rounded to two decimal places).
Plotting these intercepts and connecting them with a line, we get:
| *
16 | *
|
| /
| /
|/
0 *--------*
0 8.89
Next, we graph the line x + y = 9 by finding its intercepts:
When x = 0, we have y = 9.
When y = 0, we have x = 9.
Plotting these intercepts and connecting them with a line, we get:
|
9 | *
|
| /
| /
|/
0 *--------*
0 9
Finally, we shade the feasible region by considering the remaining constraints:
x ≥ 3: This means we shade to the right of the line x = 3.
y ≤ 9: This means we shade below the line y = 9.
Shading these regions and finding their intersection, we get:
| *
16 | * |
| |
| / |
| / |
|/ |
9 *--------*---
| | /
| |/
| *
0 *--------*
3 8.89
The feasible region is the shaded triangle bounded by the lines 2.25x + 1.25y = 20, x + y = 9, and x = 3.
To find one possible solution, we can pick any point within the feasible region. For example, the point (4, 5) satisfies all the constraints and represents buying 4 apples and 5 mangos, which costs 4(2.25) + 5(1.25) = $15.25.
Im a trapezoid measuring 8cm, 10cm, 16 cm and 10cm on its sides. What is my Perimeter? 1-5 po lhat
Answer:
See Below.
Step-by-step explanation:
To find the perimeter of a trapezoid, you simply add up the lengths of all four sides.
In this case, the trapezoid has sides of 8 cm, 10 cm, 16 cm, and 10 cm.
Perimeter = 8 cm + 10 cm + 16 cm + 10 cm
Perimeter = 44 cm
Therefore, the perimeter of the trapezoid is 44 cm.
Simplify.
Remove all perfect squares from inside the square root. Assume x is positive.
20x8 =
The simplified form of the given expression as required to be determined in the task content is; 2x⁴√5.
What is the simplified form of the given expression?It follows from the task content that the Simon form of the given expression √20x⁸ is required to be determined from the task content.
On this note, since the given expression is; √20x⁸.
We have that; = √ (4 × 5 × x⁸)
Therefore, since 4 and x⁸ are perfect squares; it follows that we have;
= 2x⁴ √5.
Ultimately, the simplified form of the given expression as required to be determined is; 2x⁴ √5.
Complete question; The correct expression is; √20x⁸.
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Write a quadratic function in standard form to represent the data in the table.
Ordered pairs arranged in a table. From left to right the pairs are: 2, 3, and 4, 1, and 6, 3, and 8, 9, and 10, 19.
y = x2 − x +
PLEASE HELP MARKING BRAINLEIST JUST ANSWER ASAP AND BE CORRECT
The perimeter of the figure is 16p + 10.
What is perimeter?The whole length of a two-dimensional or three-dimensional shape's sides or edges is known as its perimeter. It is frequently referred to as the shape's perimeter or circumference. It is possible to determine the perimeter of many geometric forms with accuracy. The perimeter is a key idea in geometry and has several practical uses, such as determining the radius of a circular racetrack or determining the length of fencing required for a certain property.
The perimeter of a figure is the sum of the lengths of all its sides.
Thus,
Perimeter = (p - 9) + (7p + 5) + (p - 9) + (7p + 5)
Perimeter = 2p + 2(7p) + 2(5)
Perimeter = 16p + 10
Hence, the perimeter of the figure is 16p + 10.
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Coordinate matrix for differentiation Let L :P2P be the linear transformation given by L(p(t)) = 5p"(t) + 1p' (t) + 3p(t) + 3tp(t). Let E = (C1, C2, C3) be the basis of P2 given by el(t) = 1, ez(t) = t, ez(t) = ť. and let F = (f1, 82, 83, fa) be the basis of P3 given by fi(t) = 1, fz(t) = t, fz(t) = {2, fa(t) = {'. Find the coordinate matrix LFE of L relative to the ordered bases & and F. LFE = Save & Grade 2 tries left Save only
The coordinate matrix LFE of L relative to the ordered bases E and F is given by:
LFE=12,3,0,12,3,0,0
LFE =
[[5, 1, 3, 3],
[0, 0, 3, 0],
[0, 0, 0, 0]]
This matrix can be obtained by computing the entries of LFE in terms of the components of L with respect to the basis E and then expressing those components with respect to the basis F. The elements of LFE are computed as follows:
LFE[1,1] = L(e1) = = 5 + 1 + 3 + 3 = 12
LFE[1,2] = L(e2) = = 0 + 0 + 3 + 0 = 3
LFE[1,3] = L(e3) = = 0 + 0 + 0 + 0 = 0
LFE[2,1] = L(f1) = = 5 + 1 + 3 + 3 = 12
LFE[2,2] = L(f2) = = 0 + 0 + 3 + 0 = 3
LFE[2,3] = L(f3) = = 0 + 0 + 0 + 0 = 0
LFE[3,1] = L(f4) = = 0 + 0 + 0 + 0 = 0
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Complete the sequence in the grids so that starting
of a 2x2 board turned off by pressing one at a time on each
grid we reach all the lit squares.
Another strategy is to start by pressing a square in the middle of the grid, and then pressing the squares adjacent to it. This should help you turn off the squares in a cross pattern.
What is sequence?In mathematics, a sequence is an ordered list of elements, typically numbers, which may be finite or infinite. Each element in the sequence is called a term. For example, the sequence {1, 2, 3, 4, 5} is a finite sequence of integers with five terms. Sequences can be represented in several ways, such as listing out the terms, using a formula to generate the terms, or using recursive rules. For example, the sequence of even numbers can be generated using the formula 2n, where n is a positive integer. So, the first five terms of the sequence are 2, 4, 6, 8, 10. Sequences are used in many areas of mathematics, including number theory, calculus, and statistics. They are also used in real-world applications, such as modeling population growth or predicting stock prices.
Here,
One common strategy is to start by pressing one of the corner squares, and then pressing the squares adjacent to it. Then, move to the adjacent corner square and repeat the process. This should help you turn off the squares in one diagonal line.
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A granola bar weighs 0.84 ounces. There are 8 bars in a box. What is the
total weight of the granola bars using the correct number of significant digits
it's not 6.72 i need the answer with significant digits
The total weight of the granola bars in the box is 6.7 ounces.
How to find the total weight of the granola barsTo calculate the total weight of the granola bars with the correct number of significant digits, we need to multiply the weight of a single bar by the number of bars in the box.
Given parameters:
Weight of a single bar = 0.84 ouncesNumber of bars in the box = 8Total weight of the granola bars
= Weight of a single bar x Number of bars in the box
= 0.84 ounces x 8
= 6.72 ounces
Since the weight of a single bar is given with two significant digits, and we have multiplied it by a whole number, the answer should be reported with two significant digits.
so we can say that, the total weight of the granola bars is 6.7 ounces.
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Create a Dataset Give a positive integer less than 100 as the last data value in each of the following datasets so that the resulting dataset satisfies the given condition (a) The mean of the numbers is substantially less than the median 51,52,53,54 (b) The mean of the numbers is substantially more than the median 2,3,4,5, (c) The mean and the median are equal. 2,3,4,5
(a) Dataset with mean substantially less than median:
9, 10, 11, 12, 90
The mean of this dataset is (9+10+11+12+90)/5 = 26.4, while the median is 11, which is substantially greater than the mean. The last data value is 90, which is a positive integer less than 100.
(b) Dataset with mean substantially more than median:
98, 99, 100, 101, 200
The mean of this dataset is (98+99+100+101+200)/5 = 119.6, while the median is 100, which is substantially less than the mean. The last data value is 200, which is a positive integer less than 100.
(c) Dataset with mean equal to median:
2, 3, 4, 4, 5
The mean of this dataset is (2+3+4+4+5)/5 = 3.6, which is equal to the median (the middle value of the dataset). The last data value is 5, which is a positive integer less than 100.
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