The three planes intersect at a single point with coordinates (-3, -1, 0). Geometrically, this means that the three planes intersect at a specific point in three-dimensional space. The corresponding linear system of equations has a unique solution.
To determine the intersection of the three planes, we can first find the normal vectors of each plane. The normal vectors are obtained by taking the coefficients of x, y, and z in the equation of each plane.
The normal vectors for the three planes are:
Plane 1: (1, -1, 1)
Plane 2: (2, -1, -2)
Plane 3: (3, 1, -1)
Since the planes intersect, their normal vectors must be linearly independent. We can check this by forming a 3x3 matrix with the normal vectors as rows and computing its determinant. If the determinant is non-zero, the vectors are linearly independent. The determinant of the matrix [ (1, -1, 1), (2, -1, -2), (3, 1, -1) ] is 6, which is non-zero. Therefore, the normal vectors are linearly independent, and the three planes intersect at a single point. To find the coordinates of the intersection point, we can solve the corresponding linear system of equations formed by the three plane equations:
x - y + z = -2
2x - y - 2z = -9
3x + y - z = -2
Solving this system, we find that x = -3, y = -1, and z = 0. Therefore, the three planes intersect at the point (-3, -1, 0). Geometrically, this means that the three planes intersect at a specific point in three-dimensional space. The vector equation of the line formed by the intersection of the planes is r = (-3, -1, 0) + t(0, 0, 0), where t is a parameter representing any real number. Since there is only one point of intersection, the linear system of equations has a unique solution.
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A town has a population of 14000 and grows at 3% every year. What will be the population after 6 years, to the nearest whole number?
Answer:
Step-by-step explanation:
3x6= 18 then 14000 x 18 = 252,000
No image, Find the volume of a garden
seat in the shape of a
triangular prism with a height
of 30 inches and a base area
of 72 in^2 *Hint* Base
area means
they have
already
calculated
the area of
the base for
you!
Answer:
volume = 720 in³
Step-by-step explanation:
volume = 1/3Bh = 1/3 x 72 x 30 = 720 in³
Is it possible or impossible for a graph to have exactly one vertex of odd degree. If so, describe the graph by giving its degree sequence. If not, explain why not.
It is impossible for a graph to have exactly one vertex of odd degree.
What is a vertex?Vertex is described as a point on a polygon where the sides or edges of the object meet or where two rays or line segments meet.
The total of all vertices' degrees in any graph is always even. This is so because each edge adds two degrees—one for each endpoint—to the overall number of degrees.
The total number of degrees at all vertices must therefore be an even number.
If a graph had exactly one vertex of odd degree, the sum of the degrees of all other vertices would be even.
if we add an odd degree to an even sum, the result would be in an odd total degree count, which contradicts the fact that the sum of all degrees in a graph is always even.
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mary says the pen for her horse is an acute right triangle. Is this possible?
Given f(x)=3x^2+kx+9, and the remainder when f(x) is divided by x-3 is 6, then what is the value of k?
Answer:
k = - 10
Step-by-step explanation:
6=9+3(k+9)
3(k+9)=-3
k+9= -1
k= -10
The value of k is -10.
What is Division?Division is one of the operation in mathematics where number is divided into equal parts as that of a definite number.
Given a function 3x² + kx + 9.
Divide the function with x - 3.
Do the long division process.
After doing the long division,
(3x² + kx + 9) / (x - 3), we get the quotient as 3x + (k + 9) and the remainder as 9 + 3(k + 9).
9 + 3(k + 9) = 6
3(k + 9) = -3
k + 9 = -1
k = -1 - 9
k = -10
Hence the number k has the value -10.
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PLEASE PLEASE PLEASE HELP
Answer:
so so so sorry I usually don't do this but you know
Step-by-step explanation:
should have never be a
A cone has a volume of 100[tex]\pi[/tex] Cubic units and a diameter of 10 units. What is the height of the cone?
Answer:
12 units
Step-by-step explanation:
The formula for the volume of a cone is given as:
πr²h/3
The volume = 100π cubic units
Diameter = 10 units.
Radius = Diameter/2
= 10 units/2 = 5 units
Hence:
Formula to find the height of a cone
h = 3V/πr²
We substitute
h = 3 × 100π/π × 5²
h = 300π/25π
h = 12 units
The height = 12 units
find the mean median mode, round to the neaerest tenth. 60,70,75,78,80,80,83,85,87,90.90,90,90,93,95,95,98,100.
Answer:
Mean: 84.6
median:85
mode:90,80
range:40
minimum:60
maximum:100
Step-by-step explanation:
Answer:
mean = 85.5
median = 88.5
mode = 90
Step-by-step explanation:
Okay, so the mean is the sum of the terms divided by the total number of term so basically:
60 + 70 + 75 + 78 + 80 + 80 + 83 + 85 + 87 + 90 + 90 + 90 + 90 + 93 + 95 + 95 + 98 + 100 = 1,539
1,539 ÷ 17 = 85.5
Now, the median is just the number in the middle so we already have our numbers in order so the middle numbers are 87 and 90, so we just have to add them together and then divide by 2:
87 + 90 ÷ 2 = 88.5
and the mode is just the number that's repeated most, and that number is 90
hope this helps:)
Help me PLZZ it’s worth 20 points
Answer: uhhhhhhhhhhhhhhhhhhh whats the question?
Step-by-step explanation:
Let A = {1, 2, 3, 4} and B = {5, 6, 7}.
a). Give an example of an onto function f: A→B, or explain why this is impossible. (You can draw a graph, make a table, or list ordered pairs.)
b). Give an example of a one-to-one function g: A→B, or explain why this is impossible. (You can draw a graph, make a table, or list ordered pairs.)
c). Give an example of an equivalence relation on A, or explain why this is impossible. (You can draw a graph or list ordered pairs.)
The relation ‘equal to’ is an equivalence relation on A.
a) To give an example of an onto function f: A → B, we need to ensure that every element in set B is mapped to from set A. Since set B has three elements (5, 6, 7) and set A has four elements (1, 2, 3, 4), it is impossible to have an onto function from A to B.
This is because there are more elements in A than in B, so at least one element in B will not have a corresponding element in A.
b) A function g: A → B is a one-to-one function if each element of set A is paired with a distinct element in set B. Let us create a table to get the one-to-one function g.
Table of one-to-one function gA1234B5677The function g: A → B can be defined by g(1) = 5, g(2) = 6, g(3) = 7 and g(4) = 7.
Hence, this is a one-to-one function.
c) An equivalence relation is a relation that is reflexive, symmetric, and transitive.
We can define an equivalence relation on set A using the relation ‘equal to’. Every element of set A is equal to itself, i.e., ∀ a ∈ A, a = a.
Hence, this is a reflexive relation on A. Also, if a and b are two elements of A such that a = b, then b = a.
Hence, this is a symmetric relation on A. Also, if a, b, and c are three elements of A such that a = b and b = c, then a = c. Hence, this is a transitive relation on A.
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Anna owns a small business selling used books. She knows that in the last week 29 customers paid cash, 26 customers used a debit card, and 62 customers used a credit card.
Based on these results, express the probability that the next customer will pay with cash as a percent to the nearest whole number.
The probability that the next customer will pay with cash, expressed as a percent to the nearest whole number, is 25%.
To calculate the probability that the next customer will pay with cash, we need to use the total number of customers in the last week (29 + 26 + 62 = 117) and the number of customers who paid with cash (29).
The probability that the next customer will pay with cash can be expressed as: P(cash) = 29/117
To express this probability as a percentage, we can multiply by 100:
P(cash) = 29/117 × 100 ≈ 24.79%
Therefore, the probability that the next customer will pay with cash is approximately 24.79%. To round this to the nearest whole number, we need to look at the decimal part of the percentage. If it's less than 0.5, we round down, and if it's 0.5 or greater, we round up. In this case, the decimal part is 0.79, which is greater than 0.5, so we round up:
P(cash) ≈ 25%
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Jeremiah and his children went into a bakery and he bought $20 worth of cupcakes and cookies. Each cupcake costs $5 and each cookie costs $1.25. He bought 4 times as many cookies as cupcakes. Graphically solve a system of equations in order to determine the number of cupcakes, x,x, and the number of cookies, y,y, that Jeremiah bought.
Answer: (2,8)
Step-by-step explanation:
5x+1.25=20
y=4x
5x+1.25y=20 y=4x
1.25y=-5x+20
1.25y/1.25=-5x+20/1.25
y=-4x+16
9. a) Why does every pair of whole
a
numbers have a GCF of 1 or greater?
Answer:
A whole number is any positive integer greater than zero and is not a fraction or a decimal. Any whole number can be divided by itself and one so therefor all pairs of whole numbers have a GCF of one. However the bigger the number the more factors it can have so the GCF of a pair of whole numbers may have a greater GCF than 1.
Step-by-step explanation:
lily wants to put a bird food mix in her bird feeder.Her bird feeder can hold 8 cups of bird food.The bird food is a mix of 20% corn and the rest is sunflowers seeds how many cups of corn will lily need to fill the 8 cup bird feeder.If the rest of the mix is sunflower seed,what percent of the bird food is sunflower seed.
Answer:
80%
Step-by-step explanation:
100% is full so you do 100%-20%=80% so thats the answer
Need to help to find the slope pls helppp
Answer:
Step-by-step explanation:
easy
Answer:
it is 2
Step-by-step explanation:
rise over run
it goes up 2 points and
moves right 1 point
2/1 =2
Please help me on this question if you would want brianleist!! Tank yah!! ^^
Solve for n. c/d = d/c - 1/n
Answer:
Hi! The other answer is not correct to your question
The answer to your question is n= [tex]\frac{dc}{(c+d)(c-d)}[/tex]
Step-by-step explanation:
Solve the rational equation by combining expressions and isolating the variable n
※※※※※※※※※※※※※※※
⁅Brainliest is greatly appreciated!⁆
- Brooklynn Deka
Hope this helps!!
PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!
Answer:
a no b yes c no d no e yes
Step-by-step explanation:
Determine The Sum Of - -5-8-11--------269 b)1-3+9----243
Given expression are:
a) -5 - 8 - 11 -... - 269 = -11823.
b) 1 - 3 + 9 - ... + 243 = 364.
a) To find the sum of the given expressions, we first have to identify the type of the sequence.
The first expression is an arithmetic sequence with common difference -3.
Using the formula of the sum of arithmetic sequence, we can find the sum of the sequence.
Formula to find sum of n terms in an arithmetic sequence:
Sn = (n/2) [2a + (n-1)d]
where n is the number of terms in the sequence, a is the first term and d is the common difference)
To find the sum of the first expression, we need to calculate the number of terms in the sequence.
Given, First term, a = -5 Common difference, d = -3 Last term, l = -269
Using the formula for finding nth term in an arithmetic sequence:
l = a + (n-1)d-269
= -5 + (n-1) (-3)-269
= -5 -3n + 3-3n
= -267n = 89
Therefore, there are 89 terms in the sequence.
Now, using the formula of the sum of the arithmetic sequence:
Sn = (n/2) [2a + (n-1)d]S89
= (89/2) [2(-5) + (89-1) (-3)]S89
= (89/2) [-10 - 264]S89
= -11823
The sum of the
is -11823.
b)The second expression is a geometric sequence with common ratio 3.
Using the formula of the sum of geometric sequence, we can find the sum of the sequence.
Formula to find sum of n terms in a geometric sequence:
S = [a(1-r^n)] / [1-r]where n is the number of terms in the sequence, a is the first term and r is the common ratio
To find the sum of the second expression, we need to calculate the number of terms in the sequence.
Given, First term, a = 1 Common ratio, r = 3 Last term, l = 243
Using the formula for finding nth term in a geometric sequence:
l = ar^(n-1)243
= 1 x 3^(n-1)3^(n-1)
= 243n-1 = 5n = 6
Therefore, there are 6 terms in the sequence.
Now, using the formula of the sum of the geometric sequence:
S = [a(1-r^n)] / [1-r]S
= [1(1-3^6)] / [1-3]S
= [1-729] / (-2)S
= 364
The sum of the geometric sequence is 364.
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Question 10 of 10
What is the value of y?
10"
50
A. 30°
B. 40°
C. 50°
D. 60°
Answer:
i think ik it the aswer is c
1. For all named stors that have made landfall in the United States since 2000, of interest is to determine the mean sustained wind speed of the storms at the time they made landfall in this scenario, what is the population of interest?
2. Based on the information in question 1, what is the parameter of interest?
A. The average π sustained wind speed of the storms at the time they made landfall
B. The mean µ of sustained wind speed of the storms
C. The proportion µ of the wind speed of storm
D. The mean µ usustained wind speed of the storms at the time they made landfall
E. The proportion π of number of storms with high wind speed
1. The population of interest are all named storms that have made landfall in the United States since 2000.
2. The parameter of interest is the mean µ of sustained wind speed of the storms. Therefore, the correct answer is option B.
The other options are not correct as follows:
Option A. The average π sustained wind speed of the storms at the time they made landfall - The term "average" is equivalent to "mean." However, π is not applicable since it denotes the constant 3.14159....
Option C. The proportion µ of the wind speed of storm - Proportion refers to a fraction or percentage of a whole, so this answer is illogical because µ denotes the mean.
Option D. The mean µ of sustained wind speed of the storms - This answer is wrong because it is not the correct order.
Option E. The proportion π of the number of storms with high wind speed - This answer is incorrect since π denotes the constant 3.14159..., and it is not applicable in this context.
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The population of interest is all named storms that have made landfall in the United States since 2000. The parameter of interest would be the mean sustained wind speed of the storms at the time they made landfall, as you're seeking the average wind speed at the moment of landfall.
Explanation:The population of interest refers to the complete group of individuals or cases that a researcher is interested in studying. In this case, it would be all named storms that have made landfall in the United States since 2000.
The parameter of interest is a numerical measure that describes a characteristic of a population. Based on the information in question 1, the parameter of interest would be D. The mean µ sustained wind speed of the storms at the time they made landfall. This is because you're interested in knowing the average wind speed of the storms at the moment they hit the land, not the proportion of storms with high wind speed or any other aspect of the storms.
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The null hypothesis is that the laptop produced by HP can run on an average 120 minutes without recharge and the standard deviation is 25 minutes. In a sample of 60 laptops, the sample mean is 122 minutes. Test this hypothesis with the alternative hypothesis that average time is not equal to 120 minutes. What is the p-value?
The p-value can be calculated to test the null hypothesis that the average running time of HP laptops is 120 minutes against the alternative hypothesis that it is not equal to 120 minutes.
The p-value for testing the hypothesis that the average time for the HP laptops is not equal to 120 minutes can be calculated using a t-test. Given a sample mean of 122 minutes, a sample size of 60, a null hypothesis mean of 120 minutes, and a standard deviation of 25 minutes, we can calculate the t-value and find the corresponding p-value.
To calculate the t-value, we use the formula: t = (sample mean - null hypothesis mean) / (sample standard deviation / sqrt(sample size))
Plugging in the values, we get: t = (122 - 120) / (25 / sqrt(60))
Calculating the t-value, we find t ≈ 0.894
To find the p-value associated with this t-value, we can refer to a t-distribution table or use statistical software. The p-value represents the probability of observing a t-value as extreme as the one obtained, assuming the null hypothesis is true.
Since the p-value (0.757) is greater than the commonly used significance level of 0.05, we fail to reject the null hypothesis. This suggests that there is not enough evidence to conclude that the average running time of HP laptops is significantly different from 120 minutes.
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Consider the function f() = x ln (2+1). Interpolate f(T) by a second order polynomial on equidistant nodes on (0,1). Estimate the error if it is possible.
To interpolate the function f(x) = x ln(2+1) by a second-order polynomial on equidistant nodes on the interval (0,1), we can use the Lagrange interpolation formula.
To interpolate f(T) by a second-order polynomial on equidistant nodes on (0,1), we need three equidistant nodes. Let's denote these nodes as x₀, x₁, and x₂, with x₀ = 0, x₁ = h, and x₂ = 2h, where h = (1-0)/2 = 1/2.
We can construct the Lagrange polynomial P₂(x) of degree 2 that interpolates f(x) at these nodes. The Lagrange interpolation formula for P₂(x) is:
P₂(x) = f(x₀) × L₀(x) + f(x₁) × L₁(x) + f(x₂) × L₂(x)
where L₀(x), L₁(x), and L₂(x) are the Lagrange basis polynomials.
Using the given function f(x) = x ln(2+1), we can evaluate f(x₀), f(x₁), and f(x₂). Plugging these values into the Lagrange interpolation formula, we obtain the second-order polynomial interpolation for f(T).
To estimate the error, we can use the error formula for polynomial interpolation. The error term E(x) is given by:
E(x) = f(x) - P₂(x)
To calculate the error, we would need to evaluate the derivative of f(x) and find its maximum value on the interval (0,1). However, without knowing the interval (T), we cannot estimate the error.
In summary, we can interpolate f(T) by a second-order polynomial on equidistant nodes on (0,1) using the Lagrange interpolation formula. However, without specifying the interval (T), it is not possible to estimate the error.
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Helpoopooo please !!!!!!
Answer:
I believe the answer is 2/3
Step-by-step explanation:
Graph on a coordinate plane P(-3,-5)
Answer:
Answer is in the image below
Answer:
P is simply the mark or letter that the point will be called. In this case we have -3,-5. You will move left 3 spaces from the origin and down 5 places from the spot you marked -3. After that will be point P
Can a simple directed graph G = (V, E) with at least three vertices and the property that deg+(v) + deg¯(v) = 1, Vv € V exist or not? Show an example of such a graph if it exists or explain why it cannot exist.
No, such a simple directed graph with at least three vertices and the property that deg+(v) + deg¯(v) = 1 cannot exist.
The property deg+(v) + deg¯(v) = 1 implies that for every vertex v in the graph, the sum of its in-degree (deg¯(v)) and out-degree (deg+(v)) is equal to 1. In a directed graph, the in-degree of a vertex represents the number of incoming edges, while the out-degree represents the number of outgoing edges.
If we consider a graph with at least three vertices, let's say v1, v2, and v3, and apply the given property, we would have:
deg+(v1) + deg¯(v1) = 1
deg+(v2) + deg¯(v2) = 1
deg+(v3) + deg¯(v3) = 1
However, this leads to a contradiction. In a directed graph, the sum of in-degrees and out-degrees of all vertices is always equal. Therefore, if we sum up the equations above, we would get:
deg+(v1) + deg+(v2) + deg+(v3) + deg¯(v1) + deg¯(v2) + deg¯(v3) = 3
Since each term on the left-hand side of the equation is at least 1 (due to the property), the sum would be at least 6. This contradicts the fact that the sum should be equal to 3.
Hence, a simple directed graph with at least three vertices and the property deg+(v) + deg¯(v) = 1 cannot exist.
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Finish the song:
Good little girl....
Always picking a fight with me~
You know that I'm bad!
But you're spending the night with me....
What do you want from my world?
You're a good little girl♪♪♪
Answer:
Bad little boy
That's what you're acting like
I really don't buy
That you're that kind of guy
And if you are
Why do you want to hang out with me?
Step-by-step explanation:
i had to look in the internet hehe click the ❤️
please
Can someone help me with this. Will Mark brainliest.
Answer:
B (3, -4)
Step-by-step explanation:
A( -7, 2)
midpt ( -2, -1)
Equation:
(x + 5, y - 3)
Solve for B:
( -2, -1)
(x + 5, y - 3)
(3, -4)
Write an equation of the line that passes through point (-1, 5) and has the slope m = 4.
Answer:
y=4x+5
Step-by-step explanation:
y=mx+c
gradient =m
y intercept=c
m=4
c=5
so
y=4x+5
Answer:
y=4x+9
Step-by-step explanation:
y=mx+b
y=4x+b
5=4(-1)+b
5=-4+b
b=9
y=4x+9
what is 1 2/7- 3/4 equal to
9514 1404 393
Answer:
15/28
Step-by-step explanation:
We can rearrange the problem a bit and make it a little simpler.
1 2/7 - 3/4 = (1 -3/4) + 2/7 = 1/4 + 2/7
= (7+4·2)/(4·7) = 15/28
_____
The sum of fractions can always be found by ...
[tex]\dfrac{a}{b}+\dfrac{c}{d}=\dfrac{ad+bc}{bd}\\\\\dfrac{1}{4}+\dfrac{2}{7}=\dfrac{1\cdot7+4\cdot2}{4\cdot7}=\dfrac{7+8}{28}=\dfrac{15}{28}[/tex]