a. the equation of the plane containing the points (-1, 3, 4), (-1, 9, 4), and (1, -1, 1) is 6x + 4z = 10.
b. An additional point on the plane is (0, y, 2.5),
How do we calculate?We find the following:
Vector v1 = (-1, 9, 4) - (-1, 3, 4) = (0, 6, 0)
Vector v2 = (1, -1, 1) - (-1, 3, 4) = (2, -4, -3)
Normal vector n = v1 × v2
cross product:
cross product = (0, 6, 0) × (2, -4, -3)
cross product = (0(0) - 6(-3), 0(2) - 0(-3), 6(2) - 0(-4))
cross product = (18, 0, 12)
The equation of the plane is in the form Ax + By + Cz = D:
18x + 0y + 12z = 18(-1) + 0(3) + 12(4)
18x + 12z = -18 + 0 + 48
18x + 12z = 30
6x + 4z = 10
b.
We say let x = 0
6(0) + 4z = 10
4z = 10
z = 10/4
z = 2.5
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Help me plz. I need this done TODAY.
The volume of a cube is 216 cubic feet. What is the length of each side of the cube?
side = ? ? ? feet
Answer:
find the cube root of 216 to get the length of one side as you get the volume of a cube by length x length x length
Step-by-step explanation:
the the cube root of 216 is 6
so the length of one side is 6 inches
Hope This Helps :)
Answer: I think it is 54 because there are four sides of a cube. So I just did 216/4 and got 54.
Step-by-step explanation:
Might be wrong but this is what I think the answer is.
A container in the shape of a cylinder has a volume of 60 cubic meters. Its base has an area of 15 square units. What is the height of the container?
options
3m
2m
4m
5m
The answer would be 4m
2
A = 2.5 km
b= 5 km
h =
Answer:
First of all, we have to make area km by multiplying 10 then solve, the answer is 5
Angle 1 is an alternate exterior to angle 8.
If angle 1 = 30 degrees, what is the measure of angle 8?
Answer:
If the two alternate exterior angles are from two parallel lines cut by a transversal, angle 8 would be 30 degrees.
Explanation:
Alternate exterior angles resulting from two parallel lines cut by a transversal are congruent.
Prove the The Argument principle for meromorphic functions i.e. calculate the integral 1 f' L 2πi where does not hit zeroes or poles of f.(meromorphic: locally a quotient of two holomorphic functions).
The Argument Principle for meromorphic functions states that the integral of the logarithmic derivative of a meromorphic function around a closed curve is equal to 2πi times the sum of the winding numbers of the curve around its zeros and poles. This result is derived using the Residue Theorem and the properties of zeros and poles.
To prove the Argument Principle for meromorphic functions, we start by considering a meromorphic function f(z) on a closed curve C, where f(z) is holomorphic except at a finite number of isolated singularities (poles and/or removable singularities) within the region enclosed by C. We assume that C is positively oriented.
The Argument Principle states that the integral of the logarithmic derivative of f(z) along the curve C is equal to 2πi times the sum of the winding numbers of the curve around the singularities of f(z) within the region enclosed by C. Mathematically, it can be expressed as:
∮C (f'(z)/f(z)) dz = 2πi (N - P)
where N is the sum of the winding numbers of C around the zeros of f(z) and P is the sum of the winding numbers of C around the poles of f(z).
To prove this, we can use the Residue Theorem. First, we write f(z) as a product of its zeros and poles:
f(z) = (z - z₁)^(n₁) (z - z₂)^(n₂) ... (z - z_N)^(n_N) / (z - w₁)^(m₁) (z - w₂)^(m₂) ... (z - w_P)^(m_P)
where z₁, z₂, ..., z_N are the zeros of f(z) with respective multiplicities n₁, n₂, ..., n_N, and w₁, w₂, ..., w_P are the poles of f(z) with respective multiplicities m₁, m₂, ..., m_P.
Taking the logarithmic derivative of f(z), we get:
(f'(z)/f(z)) = ∑ (n_j/(z - z_j)) - ∑ (m_k/(z - w_k))
Now, we consider the integral of (f'(z)/f(z)) dz along the closed curve C. By the Residue Theorem, this integral can be evaluated as the sum of the residues of the function (f'(z)/f(z)) at its isolated singularities within the region enclosed by C.
The residues at the zeros z_j of f(z) are given by n_j, and the residues at the poles w_k of f(z) are given by -m_k. Therefore, the integral becomes:
∮C (f'(z)/f(z)) dz = ∑ (n_j) - ∑ (m_k) = N - P
where N is the sum of the winding numbers of C around the zeros of f(z), and P is the sum of the winding numbers of C around the poles of f(z).
Finally, using the fact that the integral of (f'(z)/f(z)) dz is equal to 2πi times the sum of the residues, we arrive at:
∮C (f'(z)/f(z)) dz = 2πi (N - P)
which proves the Argument Principle for meromorphic functions.
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what what is the instantaneous velocity of the caterpillar at time t=6
a) 0 m/s
b) 3.0 m/s
c) 6.0 m/s
d) 0.33 m/s
The number of cellular phones in use in the United States is increasing exponentially The number, N, in millions, in use is given by the exponential function N(t) -0.05(1.32), where "q" is the number of years after 1990. (Source: Cellular Telecommunications and Internet Association) Find N(30) and explain its meaning in the context of the scenario, b. Find t when N(O) = 420 and explain its meaning in the context of the scenario, c. Explain the meaning of the value 1.32 (from the equation) in the context of the scenario. 4. Use your calculator's graphing feature to solve 3' = 4x+5. Explain how you used your calculator and reproduce any tables or graphs produced by your calculator. Include detailed graph for points too please.
The number of cellular phones in the US is projected to grow exponentially, reaching 5.071 million in 30 years and 420 million in 13.955 years. The growth factor is 1.32, which suggests that the number of cellular phones is increasing by approximately 32% each year.
a. To find N(30), we substitute t = 30 into the given exponential function:
[tex]\[N(t) = 0.05 * (1.32)^t\][/tex]
N(30) = 0.05 * (1.32)³⁰
You can calculate this value using a calculator or a computer software. The result is approximately 5.071 million.
In the context of the scenario, N(30) represents the estimated number of cellular phones in use in the United States, in millions, 30 years after 1990. It indicates the projected growth in the number of cellular phones over time based on the given exponential function.
b. To find t when N(0) = 420, we set N(t) equal to 420 and solve for t:
[tex]\[420 = 0.05 * (1.32)^t\][/tex]
Dividing both sides by 0.05:
[tex]\begin{equation}8400 = (1.32)^t[/tex]
To solve this equation for t, we can take the logarithm of both sides using the base 1.32:
log(8400) = t * log(1.32)
Now, solve for t by dividing both sides by log(1.32):
[tex]\begin{equation}t = \log(8400) / \log(1.32)[/tex]
You can calculate this value using a calculator or a computer software. The result is approximately 13.955 years.
In the context of the scenario, t represents the number of years after 1990 when the number of cellular phones in use in the United States reaches 420 million. It indicates the time it takes for the number of cellular phones to reach a specific value based on the given exponential function.
c. The value 1.32 in the equation N(t) = 0.05 * (1.32)^t represents the growth factor or the rate of exponential growth of the number of cellular phones. It indicates how much the number of cellular phones is multiplied by each unit of time (in this case, each year). In this scenario, the value 1.32 suggests that the number of cellular phones is increasing by approximately 32% each year.
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Can someone really help me!
lets take number one for example,
When subtracting negative numbers, the (-) in the number (-20) cancels out the original minus sign, therefore, to answer the equation:
10 - (-20)
you would need to turn the equation into an addition problem, getting the equation:
10 + 20
and from there you can get the simple answer of:
30
(brainliest please)
Starting a business is a risky, but sometimes very profitable decision. Last year, a financial analyst tracked business startups in the IT industry and found that 65% of these businesses generated a profit in their first year. The analyst decides to track 50 new IT businesses this year. Assuming a binomial distribution, a. What is the probability that exactly 32 of them will generate a profit in the next year? b. What is the probability that at most 30 will generate a profit in the next year? c. What is the probability that at least 35 of them will generate a profit in the next year?
(a) The probability of success is 65% or 0.65, and the number of trials is 50.
(b) The probability as follows:
P(X ≤ 30) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 30)
(C) The probability as follows:
P(X ≥ 35) = P(X = 35) + P(X = 36) + P(X = 37) + ... + P(X = 50)
a. The probability of exactly 32 of the 50 IT businesses generating a profit in the next year can be calculated using the binomial distribution formula. In this case, the probability of success (a business generating a profit) is 65% or 0.65, and the number of trials is 50. Using the formula, we can calculate the probability as follows:
P(X = 32) = C(50, 32) * (0.65)^32 * (1 - 0.65)^(50 - 32)
where C(n, k) represents the binomial coefficient, equal to n! / (k! * (n - k)!). Calculating this expression gives us the probability that exactly 32 businesses will generate a profit.
b. To calculate the probability that at most 30 businesses will generate a profit, we need to find the cumulative probability from 0 to 30. We can calculate the probability as follows:
P(X ≤ 30) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 30)
The problem involves determining the probability that at most 30 out of 50 IT businesses will generate a profit in their first year. We can use the binomial distribution formula to calculate this probability. The formula is given by:
P(X ≤ k) = Σ (nCk * p^k * q^(n-k))
Where:
P(X ≤ k) is the probability of having at most k successes,
n is the number of trials (50 businesses),
k is the number of successes (profitable businesses),
p is the probability of success (65% or 0.65),
q is the probability of failure (35% or 0.35),
nCk is the combination formula (n choose k).
To find the probability that at most 30 businesses will generate a profit, we need to calculate the cumulative probability from 0 to 30. Using the binomial distribution formula, we can find the probability of each possible outcome (0, 1, 2, ..., 30) and sum them up. The cumulative probability can be calculated using software or statistical tables.
c. To calculate the probability that at least 35 businesses will generate a profit, we need to find the cumulative probability from 35 to 50. We can calculate the probability as follows:
P(X ≥ 35) = P(X = 35) + P(X = 36) + P(X = 37) + ... + P(X = 50)
These calculations can be performed using a statistical software package, spreadsheet software, or using statistical tables for the binomial distribution.
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Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Answer:
y= 3
x= -2
Step-by-step explanation:
..,............
¿Cuál es el valor de X en la ecuación 6(4x+1)-3(2x-3)=3(4x-5)-6(x+1)?
Using mathematical operators, the value of x in the equation is -3
What is an equation?An equation is a mathematical statement that shows that two expressions are equal. There are different types of equations based on the degree. Linear equation, quadratic equation, and cubic equation are some of the common types of equations.
Linear equations have one degree, quadratic equations have two degrees, and cubic equations have three degrees. The degree of an equation is the highest power of the variable in the equation.
In the given problem, we can find the value of x by using mathematical operators.
6(4x + 1) - 3(2x - 3) = 3(4x - 5) - 6(x + 1)
Open the brackets;
24x + 6 - 6x + 9 = 12x - 15 - 6x - 6
Collect like terms
24x - 6x + 9 + 6 = 12x - 6x - 6 - 15
18x + 15 = 6x - 21
18x - 6x = -21 - 15
12x = -36
Divide both sides by the coefficient of x;
12x/12 = -36/12
x = -3
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Pls helpp
Fr
Algebra
Answer:((2x^3)^4)/1x^2
Step-by-step explanation:
(2x^3)^4)=((2x)^4)(^3 times ^4)=16x^12
16x^12/1x^2=(16x/1x)(x^12-2)
The Martins’ van can hold up to 8 passengers. Debbie writes the inequality p < 8, where p is the number of passengers that can fit in the van. Select the choice that provides the best explanation for Debbie’s error and the correct answer in this case. Debbie should have used 8p because 8 passengers can fit in the van. The correct inequality is 8p < 1. Debbie should have switched the inequality symbol to greater than. The correct inequality is p > 8. Debbie should have included 8 as a possible choice. The correct inequality is p < 9. Debbie should have used the not equals sign to compare the two sides of the inequality. The correct answer is p ≠ 8.
Answer:
Debbie should have included 8 as a possible choice. The correct inequality is p < 9.
Step-by-step explanation:
Given
Passengers = Up to 8
Required
Determine why [tex]p < 8[/tex] is incorrect and make corrections
The inequality [tex]p < 8[/tex] means that the van can hold less than 8 passengers.
To make correction, the digit 8 has to be included in the inequality.
This can be written as:
[tex]p <9[/tex] or[tex]p \le 8[/tex]
Base on the given options, option (c) best answered the question.
regalo puntos y me dan su ID en free fire o el nombre como sale
tengo 12 años
Answer:
Eso es loca
Step-by-step explanation:
brainliest please??
Answer:
OK
Step-by-step explanation:
Write in standard form:
v^2 = 81
Darren scored a mark of 57 on the Miller Analogies Test. This test has a mean of 50 and a standard deviation of 5. Jennifer scored 120 on the WISC Intelligence Test. This test has a mean of 100 and a standard deviation of 15. Comparing their scores, comment on who had a better score? Explain your answer
The performance scores (each score is an x-value) of three drivers were converted to standard scores. Comment on what each of the standard z-score indicates and determine the related implication
Z = 0.03
Z = 4.2
Z = -0.49
Darren had a better score than Jennifer based on their respective test scores.
To compare their scores, we need to consider their individual test scores in relation to the mean and standard deviation of each test.
For Darren's score of 57 on the Miller Analogies Test, we can calculate the z-score using the formula:
z = (x - μ) / σ
where x is the individual score, μ is the mean, and σ is the standard deviation. Plugging in the values, we have:
z = (57 - 50) / 5 = 1.4
For Jennifer's score of 120 on the WISC Intelligence Test, we can calculate the z-score using the same formula:
z = (120 - 100) / 15 = 1.33
Comparing the z-scores, we can see that Darren's z-score of 1.4 is higher than Jennifer's z-score of 1.33. A higher z-score indicates a score that is further above the mean relative to the standard deviation. Therefore, Darren's score of 57 on the Miller Analogies Test is relatively better than Jennifer's score of 120 on the WISC Intelligence Test in terms of their respective distributions.
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HELP PLZ WILL GIVE BRAINLIST
Answer:
V=141.3
Step-by-step explanation:
V=π*r2*h or V=B.h
V=3.14*(3*3)*5
V=3.14*9*5
V=141.3
refer to exhibit 34-1. the opportunity cost of one unit of y in country b is group of answer choices 1 unit of x. 0.5 units of x. 2 units of x. 20 units of x.
In Exhibit 34-1, the opportunity cost of one unit of Y in Country B is 2 units of X.
Opportunity cost refers to the value of the next best alternative that is forgone when making a choice. In this case, the opportunity cost of one unit of Y in Country B is being compared to the amount of X that could be produced instead.
The given information states that the opportunity cost of one unit of Y in Country B is 2 units of X. This means that for every unit of Y that Country B produces, it must give up the production of 2 units of X. In other words, the resources and efforts that could have been used to produce 2 units of X are instead allocated to producing one unit of Y.
This relationship indicates the relative trade-off between the production of X and Y in Country B. By sacrificing the production of 2 units of X, Country B can produce one unit of Y. The opportunity cost of producing Y is therefore 2 units of X.
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McKenzie spends $13.00 of the $20.00 in her wallet. Which decimal represents the fraction of the $20.00 McKenzie spent?
Answer:
0.65
Step-by-step explanation:
Just divide 13 by 20
Four years ago. Sherman bought 150 shares of Boca-Cola stock for $15 a share. He received a dividend of $0.30 per share each year. If the stock price has increased to $50 per share, what would be his total return?
Sherman's total return on his investment in Boca-Cola stock is $5,430.
The formula for the total return on an investment is as follows:
total return = capital gain + dividend yield
Initially, Sherman bought 150 shares of Boca-Cola stock for $15 a share.
Therefore, the initial investment (also known as the initial cost) is:
$15 x 150 = $2,250
Four years later, the stock price of Boca-Cola is $50 per share.
The capital gain is calculated as follows:
capital gain = final share price - initial share price
capital gain = $50 - $15
capital gain = $35
Therefore, the capital gain on Sherman's 150 shares is:
$35 x 150 = $5,250
Next, we need to calculate the total amount of dividends that Sherman received over the 4 years. The dividend per share is $0.30. Therefore, the total amount of dividends received is:
total dividends = dividend per share x number of shares x number of years
Sherman received dividends for 4 years, so:
total dividends = $0.30 x 150 x 4
total dividends = $180
The dividend yield is calculated as follows:
dividend yield = total dividends / initial cost
dividend yield = $180 / $2,250
dividend yield = 0.08 or 8%
Finally, we can calculate the total return:
total return = capital gain + dividend yield
total return = $5,250 + $180
total return = $5,430
Therefore, Sherman's total return on his investment in Boca-Cola stock is $5,430.
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A grain silo is shown below:
Grain silo formed by cylinder with radius 6 feet and height 168 feet and a half sphere on the top
What is the volume of grain that could completely fill this silo, rounded to the nearest whole number? Use 22 over 7 for pi.
Answer: 13750+262=14,012 ft^3
Step-by-step explanation:
Hello!!!
Find the volume of the bottom and top separately and then add them. Cylinder volume is the area of the bottom times the height (22/7)(5^2)•175=13750 ft^3
The volume of a sphere isV=(4/3)(22/7)r^3where r is the radius. also 5 since it fits on the cylinder. Also we only want half the sphere so useV=(2/3)(22/7)•5^3=261.9 ft^3 round upto 262. Now add together 13750+262=14,012 ft^3
Hope this helps~!!!!!
A tub contained 80 gallons
of water. The water drained from
the tub at a rate of 5 gallons every 4
minutes. At this rate, how many
minutes did it take
for all the water to
drain from the tub?
Answer:
its 64 because 4x16= 64
Step-by-step explanation:
It costs $4.95 to professionally dryclean a pair of slacks. Marcie uses a product that allows her to dry-clean clothes in her own dryer. For about $12, she can dry-clean 16 garments. 1. How much would it cost to have the slacks professionally dry-cleaned 16 times? 2. How much would she save by doing the job herself?
If an item is on sale for 60% off, that means you actually PAY _____% of the price.
Answer:
40%
Step-by-step explanation:
100-60=40
find the surface area of the figure below
Answer:
64
Step-by-step explanation:
square= 16
triangle= 12
12*4 = 48+16 = 64
Answer:
64 m²
Step-by-step explanation:
Hello There!
The surface area is the total area of the figure
So in order to find the area we need to find the area of each shape
For the square:
the square has a length of 4 so we can simply find the area by squaring it
4 * 4 = 16
so the area of the square is 16 square meters
Now we need to find the area of the triangles
The formula for area of a triangle is
[tex]A=\frac{bh}{2}[/tex]
where b = base and h = height
The triangles dimensions are:
base - 4m
height - 6m
having found these dimensions we plug them in into the formula
[tex]A=\frac{4*6}{2} \\4*6=24\\\frac{24}{2} =12[/tex]
so the area of one of the triangles is 12 square meters
We want to find the total area of all of the triangles
To do so we multiply the area of one triangle by 4 (because there are four triangles)
12 * 4 = 48
So the total area of the four triangles is 48 square meters
Finally we add the two areas
48 + 16 = 64
so we can conclude that the total surface area of the pyramid is 64 m²
Express your answer in scientific notation. 6.4 * 10^5 + 36,000 =
Answer:
6.76x10^5
^ represents to the 5th power
Step-by-step explanation:
find the volume of the 2 dice if the length of the base of the cube is 4cm
A) 64cm cubed
B) 96cm cubed
C) 108cm cubed
D) 128cm cubed
Answer:
I think the answer is A 64cm cubed
Please help me!!!
Hhhhhhhhhhhhhh
Answer:
C: -|x| + 3
Step-by-step explanation:
From the graph, we see that when y = 2, x is either +1 or -1
Also,when y = 1, x = +2 or -2
Thus,we can say that;
y = (-x) + 3 or -(x - 3)
So, we can write this in absolute value form as; y = -|x| + 3
Find the equation of the sphere in standard form, one of whose diameters has (-5,2, 9) and (3, 6, 1) as ondpoints. (a) x2 + y2-2 + 2x + 8y - 10z +6=0 (b) x2 + y2 + 2 + 2x - 8y + 10z +6 = 0 (C) x2 + y2 + 2 + 2A-8y- 10z + 6 = 0 (d) x2 + y2 +7 + 2x + 8y - 10z-6 = 0
The equation of the sphere in standard form, one of whose diameters have (-5, 2, 9) and (3, 6, 1) as endpoints, is [tex]x^2 + y^2 + z^2 - 8x - 4y - 10z + 48 = 0[/tex]. Therefore, the correct option is (d) [tex]x^2 + y^2 + 7 + 2x + 8y - 10z - 6 = 0[/tex].
To find the equation, we start by finding the center of the sphere. The center of the sphere is the midpoint of the line segment connecting the given endpoints. Using the midpoint formula, we find the center to be [tex]((-5 + 3)/2,(2 + 6)/2,(9 + 1)/2) = (-1, 4, 5)[/tex].
Next, we find the radius of the sphere. The radius is half the length of the diameter, which is the distance between the two endpoints. Using the distance formula, we find the radius to be [tex]\sqrt{(-5 - 3)^2 + (2 - 6)^2 + (9 - 1)^2} = \sqrt{64 + 16 + 64} = \sqrt{144} = 12[/tex].
Finally, we substitute the center and radius into the equation of a sphere: [tex](x - h)^2 + (y - k)^2 + (z - l)^2 = r^2[/tex], where (h, k, l) is the center and r is the radius. Plugging in the values, we get [tex](x + 1)^2 + (y - 4)^2 + (z - 5)^2 = 12^2[/tex].
Expanding and simplifying, we arrive at the equation for sphere's standard form, [tex]x^2 + y^2 + z^2 - 8x - 4y - 10z + 48 = 0[/tex].
Therefore, the correct option is (d) [tex]x^2 + y^2 + 7 + 2x + 8y - 10z - 6 = 0[/tex].
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