Answer:
581
Step-by-step explanation:
find the coordinate vector of a =[ 2 3 4 5] with respect to the basis = [e22, e21, e12, e11 ] of m22.
The coordinate vector of vector a = [2, 3, 4, 5] with respect to the basis B = [e22, e21, e12, e11] of M22 is [3, 4, 5, 2].
To find the coordinate vector, we need to express vector a as a linear combination of the basis vectors. The given basis B represents the standard basis for a 2x2 matrix.
Let's break down the process step by step:
Start with the basis vectors: e22, e21, e12, e11.
Express vector a as a linear combination of the basis vectors:
a = 2 * e22 + 3 * e21 + 4 * e12 + 5 * e11
The coefficients in front of each basis vector represent the coordinates of a with respect to the basis B.
Therefore, the coordinate vector of a with respect to B is [2, 3, 4, 5].
However, it's important to note that the given basis B is not the standard basis for a 2x2 matrix. The standard basis for a 2x2 matrix consists of the following vectors: e11 = [1, 0, 0, 0], e12 = [0, 1, 0, 0], e21 = [0, 0, 1, 0], e22 = [0, 0, 0, 1].
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Consider sample of 47 football games, where at of them were won by the bomo tam. Use a 0.01 significance level to test the claim that the probability that the home team wins is greater than one half. Identify the null and alternative hypothes for this test.
The null hypothesis for this test is that the probability that the home team wins is equal to or less than one half. The alternative hypothesis is that the probability that the home team wins is greater than one half.
1. Identify the null hypothesis (H0): The null hypothesis for this test is that the probability that the home team wins is equal to or less than one half (P ≤ 0.5).
2. Identify the alternative hypothesis (Ha): The alternative hypothesis is that the probability that the home team wins is greater than one half (P > 0.5).
3. Determine the significance level (α): The significance level, also known as the alpha level, is set at 0.01. This means that we are willing to accept a 1% chance of rejecting the null hypothesis when it is actually true.
4. Collect the sample data: In this case, we have a sample of 47 football games, where "at" of them were won by the home team (let's assume "at" to be a specific number).
5. Calculate the test statistic: To test the claim, we need to calculate the test statistic based on the sample data. Since we are comparing a proportion (probability), we can use the z-test. The test statistic formula is given by:
z = (p - P) / √(P * (1 - P) / n)
Where:
p is the proportion of games won by the home team in the sample,
P is the claimed probability that the home team wins (in this case, P = 0.5),
n is the sample size.
6. Determine the critical value: Since we have a one-tailed test (alternative hypothesis is directional), we need to find the critical value corresponding to the significance level of 0.01 in the standard normal distribution (z-distribution). Using a z-table or a statistical software, the critical value for a 0.01 significance level is approximately 2.33.
7. Compute the test statistic: Plug in the values from the sample data into the test statistic formula calculated in Step 5 to obtain the z-value.
8. Compare the test statistic with the critical value: If the test statistic is greater than the critical value, we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.
9. Make a decision: If the test statistic is greater than the critical value, we reject the null hypothesis, indicating that there is sufficient evidence to support the claim that the probability that the home team wins is greater than one half. If the test statistic is less than or equal to the critical value, we fail to reject the null hypothesis, indicating that there is not enough evidence to support the claim.
10. Provide a conclusion: Based on the decision made in Step 9, state the conclusion in the context of the problem. For example, if we reject the null hypothesis, we can conclude that there is significant evidence to suggest that the home team has a greater than 50% chance of winning in these football games.
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the compound inequality
Find two negative consecutive integers such that the square of the first is five more than the second. Find the integers.
Answer:
the two consecutive negative integers are -2 and -1.
Step-by-step explanation:
Represent these negative integers by m and n.
Then (because the integers are consecutive) n = m + 1, and m^2 = n + 5.
Substituting m + 1 for n in the second equation, we get:
m^2 = m + 1 + 5, or
m^2 - m - 6 = 0
This factors into (m - 3)(m + 2) = 0. The only negative root is -2.
Thus, the two consecutive negative integers are -2 and -1.
Check: Is the square of the first five more than the second?
Is (-2)^2 = -1 + 5? YES
The integers aer -2 and -1.
Complete the equation
Divide and answer in simplest form: 5 ÷35
Step-by-step explanation:
Reduce 5/35 to lowest terms
The simplest form of 535 is 17.
Answer:
1/7
Step-by-step explanation:
divide both sides by 5
verify that the following equation is an identity. (sinx cosx)^2=sin2x 1
The equation [tex](sin(x)cos(x))^2 = sin(2x)[/tex] is verified to be an identity.
Simplify LHS and RHS?
To verify whether the equation [tex](sin(x)cos(x))^2 = sin(2x)[/tex] is an identity, we can simplify both sides of the equation and see if they are equivalent.
Starting with the left side of the equation:
[tex](sin(x)cos(x))^2 = (sin(x))^2(cos(x))^2[/tex]
Now, we can use the trigonometric identity [tex]sin(2x) = 2sin(x)cos(x)[/tex] to rewrite the right side of the equation:
[tex]sin(2x) = 2sin(x)cos(x)[/tex]
Substituting this into the equation, we have:
[tex](sin(x))^2(cos(x))^2 = (2sin(x)cos(x))[/tex]
Next, we can simplify the left side of the equation:
[tex](sin(x))^2(cos(x))^2 = (sin(x))^2(cos(x))^2[/tex]
Since both sides of the equation are identical, we can conclude that the given equation is indeed an identity:
[tex](sin(x)cos(x))^2 = sin(2x)[/tex]
Hence, the equation [tex](sin(x)cos(x))^2 = sin(2x)[/tex] is verified to be an identity.
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let y=f(x) be the particular solution to the differential equation dydx=ex−1ey with the initial condition f(1)=0 . what is the value of f(−2) ?
To find the value of f(-2) given the differential equation dy/dx = e^(x-1) * e^y with the initial condition f(1) = 0, we can use separation of variables and solve the differential equation.
Starting with the given differential equation:
dy/dx = e^(x-1) * e^y
Separating variables by multiplying both sides by dx and e^(-y):
e^(-y) dy = e^(x-1) dx
Now, we can integrate both sides of the equation:
∫ e^(-y) dy = ∫ e^(x-1) dx
Integrating the left side with respect to y and the right side with respect to x:
e^(-y) = e^(x-1) + C
Applying the initial condition f(1) = 0, where x = 1 and f(1) = 0:
e^(-0) = e^(1-1) + C
1 = 1 + C
C = -2
Substituting the value of C back into the equation:
e^(-y) = e^(x-1) - 2
Now, we can find the value of f(-2) by substituting x = -2 into the equation:
e^(-y) = e^(-2-1) - 2
e^(-y) = e^(-3) - 2
To find the value of f(-2), we need to solve for y:
e^(-y) = 2 - e^(-3)
y = -ln(2 - e^(-3))
Therefore, the value of f(-2) is f(-2) = -ln(2 - e^(-3)).
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Two spheres A and B of mass 7.5 kg and 6.3 kg respectively are separated by a distance of 0.59 m. Calculate the magnitude of the gravitational force A exerts on B and B exerts on A. force A exerts on B force B exerts on A If the force between the spheres is now 3.50 times 10-9 N, how far apart are their centers?
To calculate the magnitude of the gravitational force A exerts on B and B exerts on A, we can use Newton's law of universal gravitation:
[tex]F = (G * m1 * m2) / r^2[/tex]
where F is the gravitational force, G is the gravitational constant (approximately [tex]6.67430 *10^-11 N m^2 / kg^2)[/tex], m1 and m2 are the masses of the two spheres, and r is the distance between their centers.
For the force A exerts on B:
[tex]F_AB = (G * m_A * m_B) / r^2[/tex]
Substituting the given values: m_A = 7.5 kg, m_B = 6.3 kg, and r = 0.59 m:
F_AB = (6.67430 × 10^-11 N m^2 / kg^2) * (7.5 kg) * (6.3 kg) / (0.59 m)^2
Calculating the above expression gives the magnitude of the gravitational force A exerts on B.
For the force B exerts on A, we use the same formula:
[tex]F_BA = (G * m_A * m_B) / r^2[/tex]
Substituting the given values: m_A = 7.5 kg, m_B = 6.3 kg, and r = 0.59 m:
[tex]F_BA = (6.67430 * 10^-11 N m^2 / kg^2) * (6.3 kg) * (7.5 kg) / (0.59 m)^2[/tex]
Calculating the above expression gives the magnitude of the gravitational force B exerts on A.
To find the distance between the centers of the spheres when the force between them is 3.50 times 10^-9 N, we rearrange the formula to solve for r:
r = √((G * m_A * m_B) / F)
Substituting the given values: m_A = 7.5 kg, m_B = 6.3 kg, and F = 3.50 × 10^-9 N:
r = √[tex]((6.67430 * 10^-11 N m^2 / kg^2) * (7.5 kg) * (6.3 kg) / (3.50 *10^-9 N))[/tex]
Calculating the above expression gives the distance between the centers of the spheres.
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"Suppose X --> N(20,5)
(a) Find: (i) P(X> 18)
(ii) P(7 < X < 15)
(b) Find the value a such that P(20-a < X < 20+ a) = 0.99
(c) Find the value b such that P(20-b< X < 20+ b) = 0.95
a) i)P(X > 18)= 0.65542
ii)P(7 < X < 15)=0.154
b)The value of a using the standard normal table or a calculator is 12.875
c)the value of b using the standard normal table or a calculator is 9.8
a) Let X be the normal random variable with mean μ = 20 and standard deviation σ = 5. We have to find P(X > 18) and P(7 < X < 15).
(i) P(X > 18)
This can be calculated using the standard normal table or a calculator as follows:
z = (18 - μ)/σ
= (18 - 20)/5
= -0.4
P(X > 18) = P(Z > -0.4)
= 1 - P(Z ≤ -0.4).
Using the standard normal table or a calculator, P(Z ≤ -0.4) = 0.34458
Therefore, P(X > 18) = 1 - 0.34458 = 0.65542
(ii) P(7 < X < 15). This can be calculated using the standard normal table or a calculator as follows:
z₁ = (7 - μ)/σ
(7 - 20)/5 = -2.6z₂
(15 - μ)/σ = (15 - 20)/5
= -1
P(7 < X < 15) = P(-2.6 < Z < -1)
= P(Z < -1) - P(Z < -2.6)
Using the standard normal table or a calculator,
P(Z < -1) = 0.15866P(Z < -2.6) = 0.00466
Therefore, P(7 < X < 15) = 0.15866 - 0.00466 = 0.154
b) We have to find the value of a such that
P(20 - a < X < 20 + a) = 0.99.
This can be calculated as follows:
z₁ = (20 - a - μ)/σ
= (20 - a - 20)/5
= -a/5z₂ = (20 + a - μ)/σ
= (20 + a - 20)/5 = a/5
We need to find a such that
P(z₁ < Z < z₂) = 0.99
Using the standard normal table or a calculator,
P(Z < z₂) - P(Z < z₁) = 0.99P(Z < a/5) - P(Z < -a/5) = 0.99
This can be rewritten as
P(Z < a/5) - [1 - P(Z < a/5)] = 0.99P(Z < a/5) - P(Z < -a/5) = 0.995
From the standard normal table or a calculator,
P(Z < 2.575) = 0.995P(Z < -2.575) = 0.005
Therefore,
2.575 = a/5 or -2.575 = -a/5a = 12.875
Therefore, the value of a is 12.875.
c) We have to find the value of b such that P(20 - b < X < 20 + b) = 0.95.
This can be calculated as follows:
z₁ = (20 - b - μ)/σ
= (20 - b - 20)/5
= -b/5z₂
= (20 + b - μ)/σ
= (20 + b - 20)/5 = b/5
We need to find b such that
P(z₁ < Z < z₂) = 0.95
Using the standard normal table or a calculator,
P(Z < z₂) - P(Z < z₁) = 0.95P(Z < b/5) - P(Z < -b/5) = 0.95
This can be rewritten as
P(Z < b/5) - [1 - P(Z < b/5)] = 0.95P(Z < b/5) - P(Z < -b/5) = 0.975
From the standard normal table or a calculator,
P(Z < 1.96) = 0.975P(Z < -1.96) = 0.025
Therefore,1.96 = b/5 or -1.96 = -b/5b = 9.8
Therefore, the value of b is 9.8.
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Your reading teacher
has
20 students in his elos. If
he uses popnicle sticks to
randomly call on
students during class,
what is the probability
your name will
be
called
Answer:
5%
Step-by-step explanation:
20= 100%
1 x100 = 100
100/20= 5
what is the scale factor in the dilation?
PLEASE HURRY!!!
Answer: 1/3
Step-by-step explanation:
2.5:7.5
3:9
just simplify
I really need help please and thank you
Answer:
117 Degrees
Step-by-step explanation:
plz give brailiest, the 1 and 117 are the exact same angle
Francesca makes and sells jewelry. She uses the equation p = "285 + 45n to model the situation, where p is the amount of profit she
makes and n is the number of necklaces she sells. What does the y-intercept
The y-intercept for the given equation p = 285+45n is 285.
What is Y intercept?The Y-intercept is the point where the graph intersects the y-axis.
Y-intercept formulaTo find the y-intercept of a function y = f(x), substitute x=0 and solve for y.
According to the given question
we have an equation p = 285+45n
where,
p is the amount of profit
and, n is the number of necklaces
Let, p = y and n = x
then the given equation becomes y=285+45x
substitute, x = 0 in equation y = 285+45x
⇒ y = 285
Hence, the y-intercept of the equation p=285+45n is 285.
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Find the Surface area of the following figure below
Answer:
495
Step-by-step explanation:
Base area = 11*11 = 121
Lateral area = (11*4)*17/2 = 11*2*17 = 374
121+374=495
kam
A company's stock was selling at
$28 a share. A month later, it was
selling at $21 a share. What is the
percent loss?
[?]%
Answer:Im pretty sure it's 25% percent loss
Step-by-step explanation:
sorry if im wrong
A certain reality TV show lost a total of 9,000 viewers over the past 3 months. It lost the same number of
viewers each month.
The following equation describes this situation.
-9,000 = 3 = -3,000
What does -3,000 tell us?
Answer:
Step-by-step explanation:
- 3, 000 tells the number of views loss in each month.
Which scenario would most likely show a negative association between the variables? A. the height of a tree and the amount of time it takes to climb to the top of the tree
B. the number of people in the mall and the number of cars in the parking lot
C. miles traveled in a car and the amount of gasoline used
D. time spent reading a book and the number of pages left to read
Answer: i would say B because it makes the most sence
Step-by-step explanation:
Pls help me plz either sdys
Answer:
44
Step-by-step explanation:
14x3.14 is 43.96 and that after being rounded to the nearest tenth becomes 44
Which pair of equations below is a result of constructing the altitude, h, in triangle ABC?
Answer:
the answer is A:
sinA=h/c
sinC=h/a
Step-by-step explanation:
edge 2020
The pair of equations is sinA=h/a cosC=h/a
What is trigonometry?
Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms.
When a altitude is drawn from the base of the triangle
we can write
sinA=height/ a where a, is the side length of AB
also,cos C=height/a where a, is the side length of AB
Therefore,The pair of equations is where a, is the side length of AB
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x=-2
Identify what's the slope and what's the y-intercept
Answer:
There is no slope and no y-intercept.This is a line that is parallel to Y-axis
Three companies, A, B and C, make computer hard drives. The proportion of hard drives that fail within one year is 0.001 for company A, 0.002 for company B and 0.005 for company C. A computer manufacturer gets 50% of their hard drives from company A, 30% from company B and 20% from company C. The computer manufacturer installs one hard drive into each computer.
(a) What is the probability that a randomly chosen computer purchased from this manufacturer will experience a hard drive failure within one year? [4 marks]
(b) I buy a computer that does experience a hard drive failure within one year. What is the probability that the hard drive was manufactured by company C? [4 marks]
(a) The probability of the chosen hard drive to fail within one year is 0.005.
(b) The probability that the hard drive was manufactured by company C is 3.95%.
(a) The probability that a randomly chosen computer purchased from this manufacturer will experience a hard drive failure within one year is:
Probability of choosing hard drive from company A and failure within one year + Probability of choosing hard drive from company B and failure within one year + Probability of choosing hard drive from company C and failure within one year
P(A and F) = P(A) x P(F|A) = 0.5 x 0.001 = 0.0005
P(B and F) = P(B) x P(F|B) = 0.3 x 0.002 = 0.0006
P(C and F) = P(C) x P(F|C) = 0.2 x 0.005 = 0.0010
The probability that a randomly chosen computer purchased from this manufacturer will experience a hard drive failure within one year is:
0.0005 + 0.0006 + 0.0010 = 0.0021 (or 0.21%)
(b) Let F be the event that the hard drive fails within one year and C be the event that the hard drive is manufactured by company C.
We want to calculate P(C|F), the probability that the hard drive was manufactured by company C, given that it failed within one year;
P(C|F) = P(C and F) / P(F) = [P(C) x P(F|C)] / [P(A) x P(F|A) + P(B) x P(F|B) + P(C) x P(F|C)]
P(C|F) = (0.2 x 0.005) / (0.5 x 0.001 + 0.3 x 0.002 + 0.2 x 0.005)
P(C|F) = 0.083 / 0.0021 = 0.0395 (or 3.95%)
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The probability that the hard drive in my computer is manufactured by company C given that my computer experiences a hard drive failure within one year is approximately 0.74.
(a) Let the random variable X denote the number of hard drives in the computer manufacturer's hard drives that fail within one year. The probability distribution of X can be found as follows:
[tex]P(X = 0) = 0.5(1 - 0.001) + 0.3(1 - 0.002) + 0.2(1 - 0.005) = 0.9957[/tex]
[tex]P(X = 1) = 0.5(0.001) + 0.3(0.002) + 0.2(0.005) = 0.0016[/tex]
Thus, the probability that a randomly chosen computer purchased from this manufacturer will experience a hard drive failure within one year is 0.0016.
(b) Let the event H denote that the computer I buy experiences a hard drive failure within one year. Let the event Ci denote that the hard drive in my computer is manufactured by company
i. Then, using Bayes' theorem, we have:
[tex]P(C3 | H) = P(H | C3)P(C3) / P(H)[/tex]
We can find the values of the three probabilities in the above formula as follows:
P(H | C1) = 0.001
P(H | C2) = 0.002
P(H | C3) = 0.005
P(C1) = 0.5
P(C2) = 0.3
P(C3) = 0.2
[tex]P(H) = P(H | C1)P(C1) + P(H | C2)P(C2) + P(H | C3)P(C3)≈ 0.00135[/tex]
Thus, P(C3 | H) = 0.005(0.2) / 0.00135 ≈ 0.74
Therefore, the probability that the hard drive in my computer is manufactured by company C given that my computer experiences a hard drive failure within one year is approximately 0.74.
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What is the volume of a sphere with a radius of 6.3 cm, rounded to the nearest tenth of a cubic centimeter?
Answer:
1047.4 cm^3
Step-by-step explanation:
Answer:1047.4
Step-by-step explanation:
.
whats 10k - 90 = -10
Answer:
k = 8
Step-by-step explanation:
10*8 - 90 = -10
:/
Please solve as soon as possible thank you I appreciate it!
What is the value of s?
_____units
Answer:
17
Step-by-step explanation:
by Pythagoras
[tex]8 {}^{2} + 15 {}^{2} = {x}^{2} [/tex]
x=17
-6,-5,-4,-3,...rule
What is answer
Answer:
[tex]a_{n}[/tex] = n - 7
Step-by-step explanation:
There is a common difference between consecutive terms in the sequence
d = - 5 - (- 6) = - 4 - (- 5) = - 3 - (- 4) = 1
This indicates the sequence is arithmetic with nth term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = - 6 and d = 1 , then
[tex]a_{n}[/tex] = - 6 + 1 (n - 1) = - 6 + n - 1 = n - 7
How to write 0.00080 as a power of 10?
Answer:
8 × 10⁻⁴
Step-by-step explanation:
Bill needs to read 3 novels each month.
Let N be the number of novels Bill needs to read in M months.
Write an equation relating N to M. Then use this equation to find the number of novels Bill needs to read in 19 months.
Write the equation?
Number of the novels in 19 months: _ novels
Answer:
Each month Bill reads 3 novels so you get
N = 3m
If you plug in 6 for m we get
N = 3(6) = 18
Bill needs to read 18 novels in 19 months
Step-by-step explanation:
Can someone explain pls I don’t understand how to do it lol
Find the volume of the
rectangular prism.
3 cm
9 cm
7 cm
V = [?] cm3
Answer:
189cm^3
Step-by-step explanation:
First, we need to find the formula of "how to find the volume of any prism":
length * width *height
* = multiply
So that means we need to do:
7cm * 9cm * 3cm
= 189cm^3
^ = exponent
Hope this helped :)