Answer:
Hi
Step-by-step explanation:
Use Cramer's vale to solve the following system of equation: J2X1 - X2-3 = 0 ./) X1 + 3X2-7= 0 3X1 + 2X2-1=0 4X1 + 5X2 = 14
Using Cramer's rule the solutions to the system of equations are:
X1 = 21 / (-J2 - 9)
X2 = -12 / (-J2 - 9)
Using Cramer's rule, we can solve the system of equations:
J2X1 - X2 - 3 = 0
X1 + 3X2 - 7 = 0
3X1 + 2X2 - 1 = 0
4X1 + 5X2 = 14
The values of X1 and X2, we'll calculate the determinants.
Let D be the determinant of the coefficient matrix:
D = |J2 -1 0| = J2(-1) - 3(3) = -J2 - 9
D1 is the determinant obtained by replacing the first column of the coefficient matrix with the constants:
D1 = |0 -1 0| = 0(-1) - (-7)(3) = 21
D2 is the determinant obtained by replacing the second column of the coefficient matrix with the constants:
D2 = |J2 0 0| = J2(0) - 3(4) = -12
Now, we can calculate the values of X1 and X2 using the determinants:
X1 = D1 / D = 21 / (-J2 - 9)
X2 = D2 / D = -12 / (-J2 - 9)
Therefore, the solutions to the system of equations are:
X1 = 21 / (-J2 - 9)
X2 = -12 / (-J2 - 9)
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A polynomial of degree 3 is multiplied by a polynomial of degree 5. What is the degree of the product?
Answer:
8
Step-by-step explanation:
The degree of a polynomial refers to the term with the highest exponent. Thus the highest exponent in a degree 3 polynomial is x3; for a degree 5 polynomial, it's x5. When you multiply
x3*x5 = x3+5 = x8.
So the product of a degree 3 polynomial and a degree 5 polynomial is a degree 8 polynomial.
Your leading term will result from the 3-degree term of the first polynomial, and the 5-degree term of the second. So you'll have something like ax3 * bx5. That will result in x3*x5=x8, so your product will have degree 8.
Korey kept track of the number of miles he ran each week for five weeks. The median number of miles he ran during the five weeks was 20, and the mean was 21. Which list could show the number of miles Korey ran each of the five weeks?
Options:
A. 18, 20, 20, 22, 25
B. 20, 20, 20, 25, 25
C. 16, 19, 21, 22, 22
D. 20, 20, 21, 22, 22
Answer:
A. 18, 20, 20, 22, 25
Step-by-step explanation:
Required
Which list has a mean of 21 and median of 20
Each of the list have 5 numbers and they've all been sorted.
The median is the number at the 3rd position (i.e. the middle number)
So, list C and D are out because they do not have a median of 20.
Next, calculate the mean of lists A and B
[tex]\bar x = \frac{\sum x}{n}[/tex]
A. 18, 20, 20, 22, 25
[tex]\bar x = \frac{18 + 20 + 20 + 22 + 25}{5}[/tex]
[tex]\bar x = \frac{105}{5}[/tex]
[tex]\bar x = 21[/tex]
B. 20, 20, 20, 25, 25
[tex]\bar x = \frac{20 + 20 + 20 + 25 + 25}{5}[/tex]
[tex]\bar x = \frac{110}{5}[/tex]
[tex]\bar x = 22[/tex]
Only list A has a median value of 20 and a mean value of 21
let f(x) = x2/3 + 4x, then by the Fundamental Theorem of Calculus where F(x) = ∫f(x) then F'(x) = f(x) so we are looking for the function F whose derivative is x2/3 + 4x.
By the power rule, the function F (whose derivative is x2/3 + 4x) would have to be an x3 and an x2 function since the power rule reduces the exponent by 1. But notice that if it was just x3 and x2 then the derivative of that would be 3x2 and 2x while f(x) is x2/3 + 4x. That means F(x) must be composed of x3/9 and 2x2 so the derivative turns out right.
The Fundamental Theorem of Calculus also states that 0∫b f(x)dx = F(b) - F(0) therefore we can say 0∫b f(x)dx = (b3/9 + 2b2) - (03/9 + 2(0)2) which is just b3/9 + 2b2
By the Fundamental Theorem of Calculus where F(x) = ∫f(x) then F'(x) = f(x).
We are looking for the function F whose derivative is x^(2/3) + 4x.
By the power rule, the function F (whose derivative is x^(2/3) + 4x) would have to be an x³ and an x² function since the power rule reduces the exponent by 1.
The derivative of x^3 is 3x² and the derivative of 2x² is 4x. As F'(x) = x^(2/3) + 4x.
But notice that if it was just x^3 and x^2 then the derivative of that would be 3x² and 2x while f(x) is x^(2/3) + 4x.
That means F(x) must be composed of x^(2/3+1)/(2/3+1) and 2x^1/(1+1) so the derivative turns out right.Hence, the function F(x) = 3x^(5/3)/5 + 2x^2/2 = 3x^(5/3)/5 + x^2.
The Fundamental Theorem of Calculus also states that ∫(from 0 to b) f(x)dx = F(b) - F(0).
Therefore we can say 0∫b f(x)dx = (b^(3/9) + 2b²) - (0^(3/9) + 2(0)²) which is just b^(3/9) + 2b².
Hence, the answer is b^(3/9) + 2b².
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IO. Write an
an equation
m=4
(0,0)
y=-
Please don’t use those link things they don’t work for me please just answer the question, brainliest for the first
2. Including the outlier, what is the Q1, Q3, and IQR of the data set?
id
A.Q1 = 29; Q3 = 29; IQR = 2
B.Q1 = 27; Q3 = 29; IQR = 28
C.Q1 = 28; Q3 = 27; IQR = 1
D.Q1 = 27; Q3 = 29; IQR = 2
2 hot
the annual
The present population of
of a town is 66550. If the annual population growth
rate is 10% what was
the Population growth of town 3 years ago ?
Answer:
Population (t=-3)= 50,000
Step-by-step explanation:
Giving the following information:
Annual growth rate (g)= 10%
Number of periods (n)= 3 years
Present Value (PV)= 66,550 people
To calculate the population three years ago, we need to use the following formula:
Population (t=-3)= PV / (1 + g)^n
Population (t=-3)= 66,550 / (1.1^3)
Population (t=-3)= 50,000
How many solutions does the equation 3(x-5)-7=-3x8 have
Answer:
not really good at maths. 15.33
Step-by-step explanation:
3(x-5)-7=3×8
3x-15-7=24
3x =24+15+7
3x = 46
Three will divide it's self to give you one and divide 46 to give you 15.333
(correct me if i'm wrong)
You read that a nationwide survey found that the preferences for ice cream (people had to
choose ONE) are: chocolate: 31%; vanilla: 25%; strawberry: 4%; cookie dough: 17%; and "other":
23%. You live in Berryville, where growing strawberries is a major industry. You suspect that
this may affect the distribution of preferences in your area. You get a sample of 500 Berryville
residents and have them make a choice.
a. State the null hypothesis in words. b. State the alternative hypothesis in words
Answer : Null Hypothesis (H0) The proportion of people choosing strawberry as their preferred flavor of ice cream in Berryville is equal to or greater than the national average of 4%.”
Alternative Hypothesis (Ha) The proportion of people choosing strawberry as their preferred flavor of ice cream in Berryville is significantly lower than the national average of 4%.”
Explanation :
a. Null Hypothesis (H0) is a statement which suggests that there is no significant difference between two populations or samples in the study. In this scenario, the null hypothesis can be stated as follows:“The proportion of people choosing strawberry as their preferred flavor of ice cream in Berryville is equal to or greater than the national average of 4%.”
b. Alternative Hypothesis (Ha) is a statement that counters the null hypothesis by suggesting that there is a significant difference between two populations or samples in the study. In this scenario, the alternative hypothesis can be stated as follows:“The proportion of people choosing strawberry as their preferred flavor of ice cream in Berryville is significantly lower than the national average of 4%.”
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On a coordinate plane, a triangle is located at (3, 4), and a square is located at
(10, 4). What is the distance between the square and triangle?
Answer:
7
Step-by-step explanation:
Answer:
7 units north
Step-by-step explanation:
Count from 3,4 to 10,4 and there are seven units
The equations of two lines are:
2x-y=4 and y=-2x+8.
What is the value of x in the solution for this system?
Answer:
x = 3
Step-by-step explanation:
2x - y = 4
y = -2x + 8
-y = -2x + 4
y = -2x + 8
0 = -4x + 12
-4x = -12
x = 3
Let X = {a, b, c) and A = {4, X, {a}, {b,c}}, Ag = {4, X, {b}, {a, c}} be two o-algebras over X. Then a. An.A, is not a o-algebra over X. b. An A, is a o-algebra over X and A, UA, is not a g-algebra over X. c. A, UA, is a o-algebra over X. d. None of the above. O O b. e. O d. a Let (X, 4) be a measurable space and let f, g: X → R be two mea- surable functions. Which of the following statements is false? a. 52 . 108>1] + \S1g
An A is a -algebra over X and A ∪ Ag is not a -algebra over X.
In this case, let's analyze the properties of the sets in question:
X = {a, b, c}
A = {4, X, {a}, {b, c}}
Ag = {4, X, {b}, {a, c}}
To determine if An A is a -algebra over X, we need to check if it satisfies the three conditions of a -algebra:
1. X ∈ An A: In this case, X = {a, b, c} ∈ An A, since X is a subset of itself.
2. An A is closed under complementation: For any set E ∈ An A, we need to ensure that its complement, X \ E, is also in An A. Let's check the sets in A:
- {4} ∈ An A: The complement is X \ {4} = {a, b, c}, which is not in An A.
- X ∈ An A: The complement is X \ X = ∅, which is in An A.
- {a} ∈ An A: The complement is X \ {a} = {b, c}, which is in An A.
- {b, c} ∈ An A: The complement is X \ {b, c} = {a}, which is in An A.
Since not all sets in A have complements in An A, An A is not closed under complementation and therefore not a -algebra over X.
Now let's analyze A ∪ Ag to determine if it is a -algebra over X:
1. X ∈ A ∪ Ag: Since X is a subset of itself, X ∈ A ∪ Ag.
2. A ∪ Ag is closed under complementation: For any set E ∈ A ∪ Ag, we need to ensure that its complement, X \ E, is also in A ∪ Ag. Let's check the sets in A and Ag:
- {4} ∈ A ∪ Ag: The complement is X \ {4} = {a, b, c}, which is in A ∪ Ag.
- X ∈ A ∪ Ag: The complement is X \ X = ∅, which is in A ∪ Ag.
- {a} ∈ A ∪ Ag: The complement is X \ {a} = {b, c}, which is in A ∪ Ag.
- {b, c} ∈ A ∪ Ag: The complement is X \ {b, c} = {a}, which is in A ∪ Ag.
Since all sets in A and Ag have complements in A ∪ Ag, A ∪ Ag is closed under complementation and is a -algebra over X.
In conclusion, option b is the correct answer: An A is a -algebra over X, and A ∪ Ag is not a -algebra over X.
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Find the value of x to the nearest tenth.
Answer:
2.8
Step-by-step explanation:
√(4² - 2²) = √12
=> √[(√12)² - 2²] = √8 ≈ 2.8
Find the surface area.
24 in.
40 in.
10 in.
26 in.
NEED HELP ASAP!!
Answer:
200
Step-by-step explanation:
The box part of the box plot contains all the values between whích numbers?
25
30
35
40
45
50
between 27 and 36 and between 37 and 40
between 32 and 36
between 32 and 37
between 27 and 32 and between 37 and 40
Answer:
between 32 and 37
Step-by-step explanation:
that's my answer
What is 1/4 of 32? Whoever answers first gets Brainliest.
Answer:
8
Step-by-step explanation:
it is
Answer:
8
Step-by-step explanation:
1/4 of 32
1/4 = 25%
25% of 32
32 × 25 ÷ 100
= 8
or
32 ÷ 4 =8
ill give brainliest
Write and solve the equation for the following situation:
Angles 1 and 2 are complementary. The measure of angle 1 is 16° larger than the measure of angle 2.
A. x + 16 = 90 x = 74
B. x + (x - 16) = 90 x = 53
C. 2x + 16 = 90 x = 37
D. x + 16 = 180 x = 164
2.
Is (x+2) a factor of r + 8x + 12
Answer:
no because it is not factorable
Step-by-step explanation:
What is the value of x?
Answer:
A
Step-by-step explanation:
the total angles can only add up to 180°, therefore 35 + 70 = 105, 180 - 105 = 75°. 75° = A.
What is a scatterplot?
a graph showing the relationship between two sets of data
a relationship between two variables
a data point that does not fit the general pattern in the data
a group of data points around a value
Answer:
a graph showing the relationship between two sets of data
Step-by-step explanation:
find Measure angle WZY QUICK PLEASE
Answer:
<WZY = 31°
Step-by-step explanation:
First, we can see that <XZW is equal to <WZY.
Given that, we know we can set the two equations equal to each other to find "x".
8x - 1 = 5x + 11
Now that the two equations are set equal to each other, all we have to do is simplify to find x.
Bring 5x over and subtract it from 8x.
3x - 1 = 11
Bring -1 over and add it to 11.
Since you're subtracting a negative, it becomes positive allowing you to add it to 11.
3x = 12
Now you need to get x by itself. Do do that, you need to divide three by itself, and whatever you do to one side, you must do to the other.
3x/3 = 12/3
Now you have:
x = 4
____________________________________________________
Now that you know the value of x, all you need to do is plug x back into the equation for <WZY
5(4) + 11
20 + 11
31.
And there is your answer - <WZY = 31°
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1
Problem 1.
The force system shown is to be replaced with an equivalent system consisting of a horizontal force applied at b and a vertical force applied to the horizontal leg.
1.1. What is the magnitude of the vertical force, in Newton, applied to the horizontal leg? (rounded-off to the nearest whole number; do not write the unit)
The magnitude of the vertical force applied to the horizontal leg in the equivalent force system.
To determine the magnitude of the vertical force applied to the horizontal leg, we need to find the vertical component of the given force system. Looking at the diagram, we observe that the force system consists of a vertical force at point A and a horizontal force at point B. We can use trigonometry to find the vertical component of the force at point A.
Let's denote the magnitude of the force at point A as F_A and the angle it makes with the horizontal leg as θ. The vertical component of the force can be calculated using the formula: Vertical component = F_A * sin(θ).
Since the vertical component of the force should be equal to the force we are trying to find, we can set up the equation: Vertical component = F_vertical.
Now, we can substitute the given values into the equation and solve for F_vertical. Once we have the value, we can round it off to the nearest whole number, as instructed.
Please note that without specific values or angles provided in the problem statement or accompanying diagram, it is not possible to provide a precise numerical answer.
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Catherine Destivelle was the first woman rock climber to complete a solo ascent in 1992. She is helping to design an inside rock-climbing wall on which other climbers can practice. She draws the figure
below on the coordinate grid to represent part of the wall. Each square represents one foot
Answer:
count the unit squares
Step-by-step explanation:
Answer:
8
Step-by-step explanation:
please help me ........
HELP ASAP! first one to answer gets brainliest and 15 points
No links or fake answers
5 questions attached
Answer:
1st: x-120
2nd: 0
3rd: x+12
4th: 120 + x
5th: x+12
im pretty sure that's right...?
I won't get brainliest lol
Bryce is testing whether school is more enjoyable when students are making high grades. He asked 100 students if they enjoyed school and whether their GPA was
above or below 3.0. He found that 33 of the 40 students with a GPA above 3.0 reported that they enjoyed school, and 5 of the 60 students with a GPA below 3.0
reported that they enjoyed school. What is the probability that a student with a GPA below 3.0 does not enjoy school?
Three angles of a quadrilateral measure 45°, 95°, and 111°. What is the measure of the fourth angle of the quadrilateral?
Answer:
109°
Step-by-step explanation:
sum of angles of a quadrilateral=360°
45+95+111+fourth angle=360
fourth angle=360-251=109°
I would love some help pls, if anyone could talk me through it, that would be phenomenal I have no clue what’s going on lol
Answer:
B) 7x - 3 = 4
Step-by-step explanation:
3x - 12 = -9
3x = 3
x = 1
A) NOPE
x - 5 = -6
x = -1
B) YES
7x - 3 = 4
7x = 7
x = 1
The speed of a garden snail is about 8.5×10−6 miles per second. If a garden snail moves at this speed in a straight line for 2×103 seconds, how far would the snail travel in standard notation and scientific notation.
Answer:
17*10^-3 miles
Step-by-step explanation:
Given data
Speed= 8.5×10^−6 miles per second
Time taken=2×10^3 seconds
We know that the expression for the speed is given as
speed= distance/time
distance= speed* time
substitute
distance= 8.5×10^−6* 2×10^3
distance= 8.5*2*(10^-6+3)
distance= 17*10^-3 miles
Question 10 of 10
In a unit circle, 0 = 3pi/2 radians. What is the terminal point?
A. (0,1)
B. (1,0)
C. (-1,0)
D. (0, -1)
The terminal point is (0, -1) if in a unit circle the angle is 3π/2 option (D) is correct.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)
We have:
In a unit circle, θ = 3π/2 radians.
r = 1
Angle θ = 3π/2
The terminal point is (rcosθ, rsinθ)
= (cos3π/2, sin3π/2)
= (0, -1)
Thus, the terminal point is (0, -1) if in a unit circle the angle is 3π/2 option (D) is correct.
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