For the given system of initial value problem,
A₁ = 7,
A₂ = -1, and
y = 2exp(-t),
To solve the given system of initial value problem (IVP) with the matrix equation x' = Ax, where A is the given matrix and x(0) = [10, -4, 21], we can use the eigenvalue-eigenvector method.
The matrix A is given as:
A = | 4 -2 0 |
| 3 -1 0 |
| 1 7 2 |
Let's find the eigenvalues and eigenvectors of matrix A.
To find the eigenvalues, we solve the characteristic equation:
det(A - λI) = 0
Substituting the values, we get:
| 4-λ -2 0 |
| 3 -1-λ 0 |
| 1 7 2-λ |
Expanding the determinant, we have:
(4-λ)[(-1-λ)(2-λ)] + 2[3(2-λ) - (-1-λ)7] = 0
Simplifying and solving the equation, we find the eigenvalues:
λ₁ = -1
λ₂ = 2
λ₃ = 2
Next, let's find the corresponding eigenvectors.
For λ₁ = -1:
(A + I)v₁ = 0
| 5 -2 0 | | v₁₁ | | 0 |
| 3 -1 0 | * | v₁₂ | = | 0 |
| 1 7 1 | | v₁₃ | | 0 |
Solving the system of equations, we find the eigenvector corresponding to λ₁:
v₁ = | 2 |
| 5 |
|-1 |
For λ₂ = 2:
(A - 2I)v₂ = 0
| 2 -2 0 | | v₂₁ | | 0 |
| 3 -3 0 | * | v₂₂ | = | 0 |
| 1 7 0 | | v₂₃ | | 0 |
Solving the system of equations, we find the eigenvector corresponding to λ₂:
v₂ = | 1 |
| 1 |
|-1 |
For λ₃ = 2:
(A - 2I)v₃ = 0
| 2 -2 0 | | v₃₁ | | 0 |
| 3 -3 0 | * | v₃₂ | = | 0 |
| 1 7 0 | | v₃₃ | | 0 |
Solving the system of equations, we find the eigenvector corresponding to λ₃:
v₃ = | 2 |
| 3 |
| 1 |
Now that we have the eigenvalues and eigenvectors, we can write the general solution to the system of differential equations as:
x(t) = c₁ * exp(λ₁ * t) * v₁ + c₂ * exp(λ₂ * t) * v₂ + c₃ * exp(λ₃ * t) * v₃
Substituting the given initial condition x(0) = [10, -4, 21], we can find the specific solution by solving the following system of equations:
c₁ * v₁ + c₂ * v₂ + c₃ * v₃ = x(0)
Substituting the values of the eigenvectors and the initial condition, we get:
2c₁ + c₂ + 2c₃ = 10 (Equation 1)
5c₁ + c₂ + 3c₃ = -4 (Equation 2)
-c₁ - c₂ + c₃ = 21 (Equation 3)
Solving this system of equations will give us the values of c₁, c₂, and c₃, which will determine the specific solution.
By solving Equations 1, 2, and 3, we find:
c₁ = 1
c₂ = -5
c₃ = -3
Therefore, the specific solution to the initial value problem is:
x(t) = exp(-t) * | 2 | + exp(2t) * | 1 | + exp(2t) * |-3 |
| 5 | | 1 |
|-1 | | 1 |
Simplifying this expression, we get:
x(t) = | 2exp(-t) + 5exp(2t) - 3exp(2t) |
| 5exp(-t) + exp(2t) + exp(2t) |
|-exp(-t) + exp(2t) + exp(2t) |
Finally, we can rewrite the solution in the given form (7) - ₁ (1) ¹²+₂ (1) ¹:
x(t) = 7 * | 2exp(-t) | + (-1) * | 5exp(-t) |
| 5exp(-t) | | -exp(-t) |
Therefore, A₁ = 7, A₂ = -1, and y = 2exp(-t).
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A 3-cup container of disinfectant costs $1.92. What is the price per fluid ounce?
Answer:
Its cost about 1.5625
if you rounded its 1.56 :)
Step-by-step explanation:
A parallelogram has four sides that are the same length.is a it square ?
Answer:
I'm pretty sure no because a square always has 4 right angles and all sides are the same length
the parallelogram could possibly be a rectangle tho
I could be completely wrong but I hope this helps
Lucy’s house is located at the point shown on the coordinate grid. Ainsley’s house is located 2 units right and 3 units down from Lucy’s house. Plot a point on the coordinate grid to represent the location of Ainsley’s house. What ordered pair represents the location of Lucy’s house
Answer: 3,3
Step-by-step explanation:
Consider the following two sample data sets, Set 1: 16 24 17 22 Set 2: 2 7 1 8 200 5 a. Calculate the coefficient of variation for each data set b. Which data set has less consistency (or more variability)? a. The coefficient of variation for data set 1 is I %. (Round to one decimal place as needed.) The coefficient of variation for data set 2 is % (Round to one decimal place as needed.) b. Which data set has less consistency (or more variability)? Choose the correct answer below. O A. Data set 2 has less consistency (or more variability) because its coefficient of variation is less. O B. Data sot 1 has less consistency (or more variability) because its coefficient of variation is loss. C. Data set 2 has less consistency (or more variability because its coefficient of variation is creater. Consider the following two sample data sets. Set 1: Set 2: 16 2 24 17 7 1 22 8 20 5 a. Calculate the coefficient of variation for each data set. b. Which data set has less consistency (or more variability)? The coefficient of variation for data set 2 is % (Round to one decimal place as needed.) b. Which data set has less consistency (or more variability)? Choose the correct answer below. O A. Data set 2 has less consistency (or more variability) because its coefficient of variation is less. O B. Data set 1 has less consistency (or more variability) because its coefficient of variation is less OC. Data set 2 has less consistency (or more variability) because its coefficient of variation is greater OD. Data sot 1 has less consistency (or more variability) because its coefficient of variation is greater
a. Calculation of Coefficient of Variation for each data set
Data set 1: 16 24 17 22$${\rm Mean }\ \overline{x} = \frac{16 + 24 + 17 + 22}{4} = 19.75$$
Variance σ² $= \frac{1}{N} \sum_{i=1}^{N}(x_i - \overline{x})^2$ $= \frac{(16-19.75)^2 + (24-19.75)^2 + (17-19.75)^2 + (22-19.75)^2}{4}$ $= 16.1875$
Standard deviation $σ = \sqrt{16.1875} = 4.0218$ Coefficient of variation, $CV = \frac{σ}{\overline{x}}$ $= \frac{4.0218}{19.75} = 0.2031$Therefore, the coefficient of variation for data set 1 is 20.31%.Data set 2: 2 7 1 8 200 5${\rm Mean}\ \overline{x} = \frac{2 + 7 + 1 + 8 + 200 + 5}{6} = 36.833$Variance σ² $= \frac{1}{N} \sum_{i=1}^{N}(x_i - \overline{x})^2$ $= \frac{(2-36.833)^2 + (7-36.833)^2 + (1-36.833)^2 + (8-36.833)^2 + (200-36.833)^2 + (5-36.833)^2}{6}$ $= 10627.0246$ Standard deviation $σ = \sqrt{10627.0246} = 103.0792$
Coefficient of variation, $CV = \frac{σ}{\overline{x}}$ $= \frac{103.0792}{36.833} = 2.7971$
Therefore, the coefficient of variation for data set 2 is 279.71%.
b. Identifying the data set with less consistency (or more variability) To determine which data set has less consistency (or more variability), we need to compare their coefficients of variation. A higher coefficient of variation implies higher variability or inconsistency in the data. Therefore, the correct answer is option C: Data set 2 has less consistency (or more variability) because its coefficient of variation is greater.
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How many books recommended by the book reading club would you actually buy? Which book was first recommended to be read by the book club during the summer break? Who wrote a statistical question and why?
Answer:
7
Step-by-step explanation:
njshhtb jahhhdvjsjjbvgshh shhkakhgsv jjjjgfe
QR Factorization is a useful technique when the normal equations
for a least squares problem are
ill-conditioned. What does ill-conditioned
mean?
(Limit your answer to 25 words of less.)
Ill-conditioned means that the problem or system being considered is sensitive to small changes in the input or data, leading to unstable or inaccurate results.
When solving a least squares problem using the normal equations, ill-conditioning refers to situations where the matrix involved is nearly singular or has a high condition number.
This means that small perturbations or errors in the data can result in large changes in the computed solution.
In the context of QR factorization, if the normal equations for a least squares problem are ill-conditioned, it implies that the matrix being decomposed using QR factorization is close to being singular or has a high condition number. QR factorization can help in such cases by providing a more stable and accurate solution compared to directly solving the normal equations.
QR factorization decomposes a matrix into the product of an orthogonal matrix Q and an upper triangular matrix R. This factorization can help mitigate the effects of ill-conditioning by providing a numerically stable way to solve the least squares problem.
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104) Determine the sum of - -5 3 - 269 -243 1 -3 +9-. I'II ) E
The sum of - -5, 3, -269, -243, 1, -3 and +9 is -507.
Integers are all whole numbers, either positive, negative or zero. In other words, integers are numbers that don’t have any fractional part. Integers can be represented as follows: {...-3, -2, -1, 0, 1, 2, 3...}
To add integers: Keep the sign of the number that is farthest from zero.
Perform the indicated operation for the rest of the numbers.
Addition of integers is easy.
When adding two integers with different signs, subtract the smaller absolute value from the larger absolute value.
The sign of the answer is the same as the sign of the integer with the larger absolute value.
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Convert 55% to a fraction in lowest terms.
Help it my last question on this thing
Answer:
11/20
Step-by-step explanation:
55% = 55/100
55/100 = 11/20
What is an equation of the line that passes through the point (6,-2) and is perpendicular to the line 6x+y=2
A nutrition laboratory tests 40 "reduced sodium" hot dogs, finding that the mean sodium content is 310 mg, with a standard deviation of 36 mg.
a) Find a 95% confidence interval of the mean sodium content of this brand of hot dog.
The 95% confidence interval for the mean sodium content of the "reduced sodium" hot dogs is calculated to be (297.70 mg, 322.30 mg).
To find the 95% confidence interval, we use the formula:
Confidence Interval = (sample mean) ± (critical value) * (standard deviation / √sample size)
Given that the sample mean sodium content is 310 mg, the standard deviation is 36 mg, and the sample size is 40, we need to determine the critical value for a 95% confidence level.The critical value corresponds to the level of confidence and the degrees of freedom, which is the sample size minus 1. Looking up the critical value for a 95% confidence level and 39 degrees of freedom in the t-distribution table, we find it to be approximately 2.024.
Plugging in the values into the formula, we get:
Confidence Interval = 310 mg ± (2.024) * (36 mg / √40)
Simplifying the expression, we find:
Confidence Interval ≈ (297.70 mg, 322.30 mg)Therefore, we can say with 95% confidence that the mean sodium content of this brand of "reduced sodium" hot dogs falls within the range of 297.70 mg to 322.30 mg.
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Consider the function f(x) = 25 - x ^ 2
(a) Use a Riemann sum to estimate the area under the graph of between x = - 3 and x = 5 Divide the interval [-3, 5] into 4 subintervals each of the same length by using left-hand and midpoint approximation. Sketch the 4 rectangles that approximates the area under the curve.
(b) Use the limit of a Riemann sum to find the exact area of the region between the curve
y= f(x) and the x-axis on the interval [-3,5].
(a) The area under the curve is 154 square units.
(b) The exact area of the region between the curve y= f(x) and the x-axis is (118 / 3) square units.
(a) The given function is f(x) = 25 - x² .
We need to estimate the area under the graph between x = - 3 and x = 5 by dividing the interval [-3, 5] into 4 subintervals each of the same length by using left-hand and midpoint approximation and sketch the 4 rectangles that approximates the area under the curve.
The width of each rectangle is given by Δx, where Δx = (b - a) / n = (5 - (-3)) / 4 = 2.
The height of each rectangle is determined by either left-hand approximation or midpoint approximation.
1. Left-hand approximation: In the left-hand approximation method, the height of each rectangle is taken from the left endpoint of each subinterval. We have:
Left endpoint of the 1st subinterval is x₁ = -3 Left endpoint of the 2nd subinterval is x₂ = -1 Left endpoint of the 3rd subinterval is x₃ = 1 Left endpoint of the 4th subinterval is x₄ = 3
Thus, the heights of the four rectangles are: f(x₁) = f(-3) = 16f(x₂) = f(-1) = 24f(x₃) = f(1) = 24f(x₄) = f(3) = 16
We sketch the four rectangles as follows:
The total area of the four rectangles is the sum of the individual areas of the rectangles.
We have: Area ≈ [f(-3) + f(-1) + f(1) + f(3)] Δx= [16 + 24 + 24 + 16] × 2= 80 square units.2.
Midpoint approximation: In the midpoint approximation method, the height of each rectangle is taken from the midpoint of each subinterval.
We have: Midpoint of the 1st subinterval is x₁* = -2 Midpoint of the 2nd subinterval is x₂* = 0 Midpoint of the 3rd subinterval is x₃* = 2 Midpoint of the 4th subinterval is x₄* = 4
Thus, the heights of the four rectangles are: f(x₁*) = f(-2) = 21f(x₂*) = f(0) = 25f(x₃*) = f(2) = 21f(x₄*) = f(4) = 9
We sketch the four rectangles as follows:
The total area of the four rectangles is the sum of the individual areas of the rectangles.
We have:
Area ≈ [f(-2) + f(0) + f(2) + f(4)] Δx= [21 + 25 + 21 + 9] × 2= 154 square units.
(b) The exact area of the region between the curve y = f(x) and the x-axis on the interval [-3, 5] is given by the limit of a Riemann sum as the number of subintervals n approaches infinity.
We have:
Area = ∫[(-3, 5)] f(x) dx= ∫[-3, 5] (25 - x²) dx
= [25x - (x³ / 3)]|[-3, 5]
= [125 - (125 / 3)] - [-75 + (27 / 3)]
= (100 / 3) + (18 / 3)
= (118 / 3) square units.
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2(x - 3) = 4x - 1
i need the solution to get the x value!
ILL GIVE BRAINLIEST
Isabel and Jonah had 2 pies. Isabel wrote the equation ½ + ⅙ = 4/6 and Jonah wrote 3/6 + 1/6 = 4/6 to represent combining the pie pieces. Explain why both equations are correct.
PLEASE JUST TYPE THE ANSWER AND DON’T LEAD TO ANY LINKS
Bridgette has already taken 7 pictures at home ,and she expects to take 1 picture during everyday of vacation. How many days will Bridgette have to spend on vacation before she will have taken 9 pictures?
Answer:
I believe she would have to spend 2 days on vacation.
Step-by-step explanation:
She already have 7 pictures and she takes 1 a day. Therefore, she would have to spend 2 days on vacation to get 9 pictures.
Which ordered pair is best estimate for the solution of the system of equations Y=3/2x plus 6, y equals 1/4 X -2
Answer:
x = -6.4 and y = -3.6
Step-by-step explanation:
The given system of equations are :
[tex]y=\dfrac{3}{2}x+6[/tex] ....(1)
and
[tex]y=\dfrac{x}{4}-2[/tex] ....(2)
We need to solve equation (1) and (2).
From equation (1) and (2),
[tex]\dfrac{3}{2}x+6=\dfrac{x}{4}-2[/tex]
Taking like terms together,
[tex]\dfrac{3}{2}x-\dfrac{x}{4}=-2-6\\\\\dfrac{6x-x}{4}=-8\\\\x=-6.4[/tex]
Put the value of x in equation (1).
[tex]y=\dfrac{3}{2}(-6.4)+6\\\\=-3.6[/tex]
So, the values of x and y are x = -6.4 and y = -3.6
Please look at the picture for the answer options.
Is the mean age at which American children first read now equal to four years? If the population of all American children has a mean age of 4 years until they begin to read, which of the following null and alternative hypotheses would be tested to answer this question?
The null hypothesis (H0): μ = 4 and alternative hypothesis (Ha): μ ≠ 4. The correct option is C.
The null hypothesis states that the mean age at which American children first read is equal to 4 years. The alternative hypothesis states that the mean age is not equal to 4 years.
In this case, the researcher is interested in whether the mean age has changed from 4 years. Therefore, the alternative hypothesis is two-tailed, meaning that the mean age could be either greater than or less than 4 years.
The null hypothesis is always tested against the alternative hypothesis. If the null hypothesis is rejected, then the researcher can conclude that there is evidence to support the alternative hypothesis. In this case, if the null hypothesis is rejected, then the researcher can conclude that the mean age at which American children first read has changed from 4 years.(Option-c)
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Martin bought a painting for $5000. It is expected to appreciate at a continuous rate of 4%. Write an exponential equation to model this situation
Answer:
y=5000(1.04)^t
Step-by-step explanation:
Given data
Cost of painting=$5000
Rate of increase=4%
the exponential increase expression is
y=P(1+r)^t
Where y= the total amount after growth
P= the initial cost of the painting
r= the rate of increase
t= the time interval
y=5000(1+0.04)^t
y=5000(1.04)^t
Who is taller: Randall who stands 68 inches tall or Javier who stands 6 feet tall?
Explain your reasoning. Use the sentence frames below to help you.
Note: 1 foot is equal to 12 inches.
Answer: javier is taller
Step-by-step explanation:
68inches=5' 8"
In the diagram, AABC ~ ADEF. Find the value of x.
A
12
B
CO
9
C C
D
36
24
E
27
F
The value of x is
what’s the value of x?
Answer:
B
Step-by-step explanation:
bdeehvdvjwjkwkwwjehheeh
If you dont know the anwser its always B
I WILL GIVE YOU BRAINLYEST!! PLSS HELP ME ASAP!!
The dot plot below represents how long it takes students in an 8th grade math class
to get to school every morning.
Minutes
How many students are in the class?
Answer:
18
Step-by-step explanation:
It is 18. Just simply count the dots and sum them all up together, and you get 18. Unless there is a specific thing needed.
Find the minimum or maximum value of the function. (Desmos)
The green area of the figure above is grass.
The blue is a sidewalk. What is the area of the
sidewalk? Help ASAP
Answer:
80
Step-by-step explanation:
the answer is 80 because 8×10=80
Answer:
116
Step-by-step explanation:
Area of whole thing is 196 and area of grass is 80 so you do 196-80 to get 116.
Consider this situation: A school publicizes that the proportion of attending students who are involved in at least one extracurricular activity is 70% Would we employ a two-tailed test or a one-tailed test to test the claim about the proportion of students involved in extracurricular activities? Chi-squared (one tailed) two-tailed test O Chi-squared (two tailed) One-tailed
After considering the given data we conclude that one tailed test can be utilised for this claim.
To test the claim about the proportion of students involved in extracurricular activities, we would employ a one-tailed test.
A one-tailed test is applied when the alternative hypothesis is directional, which projects the it predicts the direction of the difference between the sample proportion and the claimed proportion. For the given case, the alternative hypothesis will be that the proportion of attending students involved in at least one extracurricular activity is greater than 70%.
Hence, we would use a one-tailed test to test this claim.
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For the linear operator T- 1-23 T Y = x + 4y - 22 3.0 + 2y -x + 4y + 32 on R3, (a) find a basis for the null-space N(T); (b) find a basis for the range R(T).
(a) The basis for the null-space N(T) is any vector Y that equals -1
(b) The basis for the range R(T) is the set {-10/23, -20/23}.
The basis for the null-space N(T) of the linear operator T, we need to solve the equation T(Y) = 0. Let's express this equation and find its solutions
1 - 23T(Y) = X + 4Y - 22 × 3.0 + 2Y - X + 4Y + 32
Simplifying the equation, we get:
-23T(Y) = 10Y + 10
Dividing both sides by -23, we have:
T(Y) = (-10/23)Y - (10/23)
To find the null-space, we set T(Y) equal to zero:
(-10/23)Y - (10/23) = 0
Simplifying further, we get:
(-10/23)Y = (10/23)
Multiplying both sides by -23/10, we obtain:
Y = -1
Therefore, any vector Y that equals -1 will satisfy the equation T(Y) = 0.
Now, let's find the basis for the range R(T) of the linear operator T. The range is the set of all possible values that T(Y) can take. To find this, we need to consider all possible values for Y and calculate T(Y) for each value.
Let's choose two arbitrary values for Y and calculate T(Y):
For Y = 0
T(0) = -10/23 × 0 - 10/23
T(0) = -10/23
For Y = 1
T(1) = -10/23 × 1 - 10/23
T(1) = -20/23
Therefore, the range R(T) consists of the values -10/23 and -20/23.
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UNIT 6: CEREAL BOX PROJECT / PORTFOLIO
A company has released the following possible designs for a new cereal box. The cost of production depends upon the cost of materials, which is determined by how much material is used. The amount of material used is equal to the surface area of the package plus some overlap. The amount of product contained in the package is the volume of the packaging.
Find the surface area and volume of the following possible cereal boxes. Determine the cost of making the cereal box assuming that cardboard costs $0.05 per square inch.
Answer:
DO you go to a connexus school? I do and i have this same project im trying to find answers to!
Step-by-step explanation:
For the first box the volume, surface area, and cost of materials are 180 cubic inches, 258 square inches, and $12.9, for the second box 192 cubic inches, 224.4 square inches, and $11.22 for the third box 235.61 cubic inches, 227.76 square inches, and $11.38.
What is volume?It is defined as a three-dimensional space enclosed by an object or thing.
For the first cereal box:
Volume = L×W×H
Here L = 7.5 in, W = 2 in, and H = 12 in
Volume = 7.5×2×12 = 180 cubic inches
Surface area = 2(L×B+B×H+H×L)
= 2(7.5×2+2×12+12×7.5)
= 2(15+24+90)
= 258 square inches
Cost for this cereal box = 258×0.05 = $12.9
For the second cereal box:
[tex]\rm Volume = \frac{1}{3} bh[/tex]
b is the area and h, is the height of the pyramid.
b = 8×6 = 48 square inches, h = 12 inches
[tex]\rm Volume = \frac{1}{3} \times48\times12[/tex]
Volume = 192 cubic inches
[tex]\rm Surface \ area = b+\frac{1}{2} ps[/tex]
p is the perimeter of the base = 2(8+6) = 28 in
Slant height s = 12.6 in
[tex]\rm Surface \ area = 48+\frac{1}{2} (28)(12.6)[/tex] = 224.4 square inches
Cost of this cereal box = 224.2×0.05 = $11.22
For the third box:
Volume = πr²h
r = 2.5 in and h = 12 in
Volume = π(2.5)²(12) = 235.61 cubic inches
Surface area = 2πr(h+r) = 2π(2.5)(12+2.5) = 227.76 square inches
Cost of this cereal box = 227.76×0.05 = $11.38
Thus, for the first box the volume, surface area, and cost of materials are 180 cubic inches, 258 square inches, and $12.9, for the second box 192 cubic inches, 224.4 square inches, and $11.22 for the third box 235.61 cubic inches, 227.76 square inches, and $11.38.
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In ΔJKL, the measure of ∠L=90°, the measure of ∠J=33°, and KL = 25 feet. Find the length of LJ to the nearest tenth of a foot.
Answer:
38.5
Step-by-step explanation:
five new medicines (flugone, sneezab, medic, recflu, and fevir) were studied for treating the flu. 25 flu patients were randomly assigned into one of the five groups and received the assigned medication. their recovery times from the flu were recorded. how many degrees of freedom for treatment are there?
The number of degrees of freedom for treatment are 4.
Degrees of freedom is a statistical term that refers to the number of values in a calculation that are free to vary. It is a common concept in statistical inference. In general, degrees of freedom represent the number of observations in a statistical analysis that are free to vary.To find the degrees of freedom for treatment, the formula is (k - 1), where k is the number of treatment groups. In this case, there were 5 treatment groups, so the degrees of freedom for treatment would be (5 - 1) = 4.
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1 - Which expression is equivalent -2(x + 4) - (3x + 8)?
(50 Points)
5x + 16
5x - 16
-5x + 16
-5x - 16
Answer:
-5x-16
Step-by-step explanation:
Combine like terms
Step-by-step explanation:
If you want to multiply a parenthesis by a number, you simply distribute the number to all the terms in the parenthesis.
So, if you want to multiply the parenthesis
(3x−7) by 5, you need to multiply by 5
both 3x and −7.
We have that 5⋅(3x)=5⋅(3⋅x)=(5⋅3)⋅x=15x and −7⋅5=−35
So, 5(3x−7)=15x−35
Three friends shared one-fourth of a large pizza equally among themselves. Enter the fraction of a pizza that each person gets.
Answer: 1/12
Step-by-step explanation:
Recall: Sampling Distributions Consider any population. Then for any n ,the sampling distribution of the sample mean will have mean Mg = Hy and standard deviation of a Consider a population that is N(Hz, Ox). Then for any n, the sampling distribution of the sample mean is normally distributed with mean Hz = Hly and standard deviation of x • . Central Limit Theorem (CLT): Consider any population with mean My and standard deviation Oy. Then for n large (n 2 30), the sampling distribution of the sample mean is approximately normal with mean Hz = Hly and standard deviation ох x √n = 3. 1) A company making electronic equipment experiences a production stoppage on average of one time per month. Assume the number of stoppages per month can be modeled according to a random variable X- ~ POIS (1) a) Complete the following table for this random variable. PARAMETERS Notation Numerical Value Mean Variance Standard Deviation
The Poisson distribution with a parameter λ = 1 accurately models the production stoppages, where on average, the company experiences one stoppage per month with a relatively small amount of variability.
The scenario describes a company's production stoppages, which can be modeled using a Poisson distribution with a parameter (mean) of λ = 1. In a Poisson distribution, the mean, variance, and standard deviation are all equal.
The mean (μ) represents the average number of stoppages per month, which in this case is 1. This means that, on average, the company experiences one production stoppage per month.
The variance (σ^2) also has a value of 1 in a Poisson distribution. It measures the spread or variability of the data around the mean. In this case, the variance of 1 indicates that there is some fluctuation in the number of stoppages, but it is relatively small.
The standard deviation (σ) is equal to the square root of the variance, which is also 1 in this scenario. It represents the average amount of deviation from the mean. A standard deviation of 1 suggests that most of the observations will be within one unit of the mean.
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