A basis of the subspace that consists of all vectors perpendicular to both [1,0,5,-9] and [0,1,9,-7] is [-5, -9, 5].
To find a basis of the subspace that consists of all vectors perpendicular to both [1,0,5,-9] and [0,1,9,-7], we can use the concept of the cross product.
Let's consider the vectors [1,0,5,-9] and [0,1,9,-7] as vectors A and B, respectively.
We can find a vector C that is perpendicular to both A and B by taking the cross product of A and B.
C = A × B
To compute the cross product, we can use the following determinant formula:
C = [i, j, k]
[1, 0, 5]
[0, 1, 9]
Expanding the determinant, we have:
C = (0 × 9 - 1 × 5)i - (1 × 9 - 0 × 5)j + (1 × 5 - 0 × 1)k
= -5i - 9j + 5k
Therefore, we have found a vector C that is perpendicular to both [1,0,5,-9] and [0,1,9,-7], which is C = [-5, -9, 5].
To find a basis of the subspace, we can use this vector C as the basis vector. Since it is the only vector in the subspace, it forms a basis.
So, a basis of the subspace that consists of all vectors perpendicular to both [1,0,5,-9] and [0,1,9,-7] is [-5, -9, 5].
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In a lottery game, three winning numbers are chosen uniformly at random from {1...100}, sampling without replacement. Lottery tickets cost $1 and allow a player to pick 3 numbers. If a player matches the three winning numbers they win the jackpot prize of $1,000. For matching exactly two numbers, they win $15. For matching exactly one number they win $3.
Required:
Find the distribution of net winnings for a random lottery ticket. Show that the expected value of the game is -70.8 cents.
The sum of 9 and a number is less than 12. Which of the following inequalities expresses the solutions ?
Mike's scores on 5 quizzes he took are shown above. In which month was Mike's quiz score equal to the average of his 5 quizzes? Sept. 72, Oct. 83, Nov. 95, Dec. 77, Jan. 88
Answer:
Oct.
Step-by-step explanation:
average = (72 + 83 + 95 + 77 + 88)/5 = 83
Solve the quadratic equation x2 – 10x + 14 = –4 by completing the square.
Question 3 options:
A)
x = 5 ±
B)
x = –5 ±
C)
x = –7 ±
D)
x = 7 ±
Answer:
[tex] x = 5 \pm \sqrt{7} [/tex]
Step-by-step explanation:
x^2 - 10x + 14 = -4
Subtract 14 from both sides.
x^2 - 10x = -18
To complete the square, add the square of half of the x-term's coefficient.
x-term coefficient: -10
half of it: -5
squared: (-5)^2 = 25
Add 25 to both sides.
x^2 - 10x + 25 = -18 + 25
(x - 5)^2 = 7
Take square root of both sides. Be careful to include ± on the right side.
[tex] x - 5 = \pm \sqrt{7} [/tex]
Add 5 to both sides.
[tex] x = 5 \pm \sqrt{7} [/tex]
integrate by parts xInx
Answer:
[tex]\displaystyle \int {x \ln x} \, dx = \frac{x^2}{2} \bigg( \ln(x) - \frac{1}{2} \bigg) + C[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationIntegration
Integrals[Indefinite Integrals] Integration Constant CIntegration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration by Parts: [tex]\displaystyle \int {u} \, dv = uv - \int {v} \, du[/tex]
[IBP] LIPET: Logs, inverses, Polynomials, Exponentials, TrigStep-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \int {x \ln x} \, dx[/tex]
Step 2: Integrate Pt. 1
Identify variables for integration by parts using LIPET.
Set u: [tex]\displaystyle u = \ln x[/tex][u] Logarithmic Differentiation: [tex]\displaystyle du = \frac{1}{x} \ dx[/tex]Set dv: [tex]\displaystyle dv = x \ dx[/tex][dv] Integration Rule [Reverse Power Rule]: [tex]\displaystyle v = \frac{x^2}{2}[/tex]Step 3: Integrate Pt. 2
[Integral] Integration by Parts: [tex]\displaystyle \int {x \ln x} \, dx = \frac{x^2 \ln x}{2} - \int {\frac{x}{2}} \, dx[/tex][Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int {x \ln x} \, dx = \frac{x^2 \ln x}{2} - \frac{1}{2} \int {x} \, dx[/tex]Factor: [tex]\displaystyle \int {x \ln x} \, dx = \frac{1}{2} \bigg( x^2 \ln(x) - \int {x} \, dx \bigg)[/tex][Integral] Integration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x \ln x} \, dx = \frac{1}{2} \bigg( x^2 \ln(x) - \frac{x^2}{2} \bigg) + C[/tex]Factor: [tex]\displaystyle \int {x \ln x} \, dx = \frac{x^2}{2} \bigg( \ln(x) - \frac{1}{2} \bigg) + C[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Jody's team scored 21, 25, 36, 16, and 32 points at the last five football games. What is the mean number of points Jody's team scored? 20 points 21 points 25 points 26 points
Answer:
26 points
Step-by-step explanation:
Find the mean number of points by adding up all of the points and dividing it by 5
(21 + 25 + 36 + 16 + 32) / 5
130 / 5
= 26
So, the mean number of points is 26 points
Jody's team scored 21, 25, 36, 16 and 32 points at the last five football games. What is the mean number of points Jody's team scored ?
Solution:-To find the mean, first of all we have to add up all the given points and then divide by how many number of points there are. So, there are total 5 points. Hence, we have to divide all the given points by 5.
So, Mean = [tex] \bf \frac{21 \: + \: 25 \: + \: 36 \: + \: 16 \: + \: 32}{5} [/tex]
Mean = [tex] \bf \frac{130}{5} [/tex]
Mean = [tex] \bf 26 [/tex]
The mean number of points Jody's team scored is 26. [Answer]The length of the arc which subtends an angle 60° at
the centre of a circle of radius 3 cm is approximately
Answer:
π cm
Step-by-step explanation:
The formula for arc length (s) as a function of radius (r) and central angle Ф (in radians) is s = rФ.
In this problem r = 3 cm and Ф = 60°, and so the arc length subtended is
s = (3 cm)(π/3) = π cm
2(5+xi)-21+5i=3yi^2-3yi
Answer:
x = -8, y = 11/3
Step-by-step explanation:
HELP! PLEASE.............
9514 1404 393
Answer:
B. negative trend
Step-by-step explanation:
The sign of the slope of the best-fit line is the sign of the "trend". A line that slopes downward has a negative slope. Such a best-fit line indicates a negative trend.
Which postulate or theorem proves △SQY∼△PTY?
A. SAS Similarity Theorem
B. SSS Similarity Theorem
C. AA Similarity Postulate
Check the picture below.
[tex]\stackrel{ \textit{\LARGE S} }{\cfrac{8}{4}}~~ = ~~\stackrel{ \textit{\LARGE S} }{\cfrac{12}{6}}~~ = ~~\stackrel{ \textit{\LARGE S} }{\cfrac{4}{2}}\implies \text{\LARGE 2}\qquad \textit{similar triangles by SSS}[/tex]
Least common denominator in 1/30 + 1/24
Answer:
The LCD in 1/30 + 1/24 is 90.
The following amount was assigned to each. A penguin was $9, an octopus was $36, and ant was $27. Based on this information, how much will be given to a pig?
Answer:
$14
Step-by-step explanation:
Answer:
Is there options because this question not that in depth
Step-by-step explanation:
What is the measure of x?
A. 8
B. 9
C. 10
D. 11
Answer:
A
Step-by-step explanation:
71 is 10% of what number?
52 is 97% of what Number?
Explain steps.
Answer:
71 is 10% of 710
52 is 97% of 5200/97
Step-by-step explanation:
Let’s start with 71 is 10% of what number.
basically, what this is saying, is that 71 = 10% times and unknown valu. We can set this as x.
so, 71=0.1x
divide on both sides,
710=x
now the second one.
repeat the same process.
52=0.97x
divide
5200/97 =x
LAST ONEEE YAYYYYYYY
Answer:
80
Step-by-step explanation:
180 - 100 = 80. 180º is required for a straight line, and 100º have already been shown from the other angles. x = 80
wae21q42rwe2q4q2rwe3rq244e2eq2q22q
find sin(b) in the triangle
Answer:
We need the triangle, please
Explanation:
Can't find anything about a triangle without the triangle
Answer:
0
Step-by-step explanation:
Sin(undefined) reports 0.
If the value is not undefined, please provide the triangle.
whats the answer to this
A gym knows that each member, on average, spends 70 minutes at the gym per week, with a standard deviation of 20 minutes. Assume the amount of time each customer spends at the gym is normally distributed. Suppose the gym surveys a random sample of 49 members about the amount of time they spend at the gym each week. What are the expected value and standard deviation (standard error) of the sample mean of the time spent at the gym
Answer:
the expected value and the standard deviation of the sample mean is 70 and 2.86 respectively
Step-by-step explanation:
The computation of the expected value and the standard deviation of the sample mean is shown below:
The mean is 70
And, the standard deviation is
= 20 ÷ √49
= 20 ÷ 7
= 2.86
Hence, the expected value and the standard deviation of the sample mean is 70 and 2.86 respectively
Tammy writes the equation -1 / 8 = -1/8. Is she correct? Explain.
79%
3rd
Her monthly salary is twice the sum of her husband's salary and four. Her monthly
salary is also equal to four more than four times his salary. How much does the
husband make a month? Note the husband's monthly salary is in terms of thousand
dollars.
9514 1404 393
Answer:
0
Step-by-step explanation:
The two expressions for her salary can be equated:
2h +4 = 4 +4h
0 = 2h . . . . . . . . subtract 2h+4 from both sides
h = 0 . . . the husband's salary is zero dollars per month
Answer:
$2000
Step-by-step explanation:
The difference between the squares of two numbers is 35. Twice the square of
the first number increased by the square of the second number is 73. Find the
numbers.
Answer:
Los números son
7 y 8
Explicación paso a paso:
Si el número menor es "x" , el mayor es "x + 1"
entonces
( x + 1 )² - x² = 15
x² + 2x + 1 -x² = 15
2x + 1 = 15
2x = 15 - 1
2x = 14
x = 14/2
x = 7 ( número menor )
x + 1 = 7 + 1
x + 1 = 8 ( número mayor )
40 points help me please
Answer:
x=60
Step-by-step explanation:
(1/6)(x+6)=11
Multiply both sides by six:
(6)(1/6)(x+6)=11(6)
x+6=66
Take six from both sides:
x+6-6=66-6
x=60
Find the trigonometric ratios as simplified fractions and as decimals to the nearest thousandths (3 decimal places)
16 34
HElp me plssss ;-;
Please help me please
Answer:
486 square inches
Step-by-step explanation:
What is the volume of the composite figure? ASAP PLEASE!!!!
Answer:
74ft³
Step-by-step explanation:
Okay, so it's basically 3 rectangular figures smashed together so:
We'll do the 2 biggest one's first:
the formula for the volume of a rectangular figure is base x height so we first have to find the base:
4 x 3 = 12
So then we just plug our stuff in here:
12 x 3 = 36
Now there's 2 of these rectangles though so:
36 x 2 = 72
Now we're going to do the one in the middle:
1 x 2 = 2
2 x 1 = 2
Now we add that all together:
72 + 2 = 74
So, the volume of the composite figure is 74ft³
hope this helps:)
PLEASE HELP
what is an expression equivalent to (x4y3y)2 in the form xmyn.
Answer:
x^8 y^8
did you mean (x^4 y^3 y)2 or just (x4y3y)2
Sorry did you submitted it yet?
If the given expression is (x⁴y³y)², the expression equivalent to the given expression in form of xmyn is, x⁸y⁸.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
It is given that the expression is,
(x⁴y³y)²
Keep the base constant and add the exponents when multiplying similar bases. Maintaining the same base while multiplying the exponents will raise a base with power to another power. When dividing two bases with similar exponents, keep the exponents of the numerator and denominator constant.
We have to represent the given expression in the form of [tex]\rm x^m y^n[/tex].
We use the expression identity as,
[tex]x^m \times x^n = x^{m+n}[/tex]
[tex]\rm = (x^m)^n \\\\ = x^{mn}[/tex]
=(x⁴y³y)²
First, solve the term present in the bracket as,
=(x⁴y⁴)²
Open the bracket we get,
=(x⁴)²(y⁴)²
=x⁸y⁸
Thus, if the given expression is (x⁴y³y)², the expression equivalent to the given expression in form of [tex]\rm x^m y^n[/tex] is, x⁸y⁸.
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The length of a rectangular garden is 12 ft longer than the width, w. If the garden has a perimeter of 76 ft. Determine the length and width of the garden.
Step-by-step explanation:
length = l
width = w
perimeter of garden = 76 ft
perimeter = 2l + 2w
2l + 2w = 76 (eqn 1)
l - w = 12 (eqn 2)
(eqn 1) ÷ 2
l + w = 38 (eqn 3)
(eqn 2) + (eqn 3)
2l = 50
2l/2 = 50/2
l = 25
The length of the garden is 25 ft.
Substitute l = 25 into (eqn 3)
l + w = 38
25 + w = 38
w = 38 - 25
w = 13
The width of the garden is 13 ft.
The logging company would like to use its sample to provide convincing statistical evidence that over 50 percent of the trees in the forest are spruce trees. The logging company has decided to use a chi-square goodness-of-fit test to justify its claim. Why is the chi-square goodness-of-fit test not an appropriate procedure for the logging company to use
Answer:
The chi-square goodness-of-fit test is best used with categorical variables. The trees in the forest are not categorical variables but numerical.
Step-by-step explanation:
The chi-square goodness-of-fit test determines whether the distribution of cases in a single categorical variable follows a known distribution. The chi-square goodness-of-fit test data deal with data frequencies, levels, or counts of cases rather than percentages or other data transformations. Lastly, the categories of the variables are mutually exclusive because they assume the form of either or.
Answer:
A chi-square goodness-of-fit test would be used to show that the entire distribution of trees in the forest is different than what the forester reported, not necessarily the individual proportion representing the spruce trees.
Step-by-step explanation:
The answer is the explanation. Got it from CollegeBoard.org
A lie detector is known to be 4/5 reliable when the person is guilty and 9/10 reliable when the person is innocent. If a suspect is chosen from a group of suspects of which only 1/100 have ever committed a crime, and the test indicates that the person is guilty, what is the probability that he is guilty?
Answer:
0.0748 = 7.48% probability that he is guilty
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Tests indicates guilty
Event B: Person is guilty
Probability that the test indicates that the person is guilty:
4/5 = 0.8 of 1/100 = 0.01(person is guilty)
1 - 0.9 = 0.1 of 1 - 0.99(person is not guilty). So
[tex]P(A) = 0.8*0.01 + 0.1*0.99 = 0.107[/tex]
Test indicates guilty and the person is guilty;
0.01 of 0.8. So
[tex]P(A \cap B) = 0.01*0.8 = 0.008[/tex]
What is the probability that he is guilty?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.008}{0.107} = 0.0748[/tex]
0.0748 = 7.48% probability that he is guilty
The required value is [tex]\simeq0.925 \ or \ 92.5[/tex]%.
Probability:Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are to happen, using it.
Let [tex]T_G[/tex] and [tex]T_I[/tex] denote the test result being guilty or innocent respectively.
And, [tex]G[/tex] and [tex]I[/tex] denote that the person is guilty or innocent respectively.
Given that: [tex]P\left ( T_G\mid I \right )=\frac{4}{5}[/tex]
[tex]P\left ( T_I\mid I \right )=\frac{9}{10}\Rightarrow P\left ( T_G\mid I \right )=1-\frac{9}{10}=\frac{1}{10}[/tex]
[tex]P(G)=\frac{1}{100} \\ \therefore P(I)=1-P(G) \\ =1-\frac{1}{100} \\ =\frac{99}{100}[/tex]
Now, the required probability is,
[tex]P(I\mid T_G)=\frac{P\left ( T_G\mid I \right )\times P(I)}{P(T_G\mid I)\times P(I)+P\left ( T_G\mid G \right )\times P(G)}[/tex]
[tex]=\frac{\frac{1}{10}\times\frac{99}{100}}{\left ( \frac{1}{10}\times \frac{99}{100}\right )+\left ( \frac{4}{5}\times\frac{1}{100} \right )} \\ =\frac{0.099}{0.099+0.008} \\ =\frac{0.099}{0.107} \\ =0.92523 \\ \simeq 0.925 \\ or \ 92.5%[/tex]
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