Answer:
y=-3x+1
Step-by-step explanation:
find the slope using the points (0,1) and (1,-2)
\(m=-\frac{(-2-1)}{(1-0)}=-3\)
plug in the data into y=mx+b and we get y=-3x+1
(1,-4), ( 3,-7), (-3,4)
Answer:
whats the question? :)
Step-by-step explanation:
Which has one line of symmetry
Answer:
D
Step-by-step explanation:
An isoceles triangle has two eqial sides and angles wich give it exactly one axe of symmetry
If WX= 10 and WZ = 7, what is WY?
W
X
Z
Answer:WY= 14.286
Step-by-step explanation:
What is the percent of decrease from 50 °
44?
Answer:
12%
Step-by-step explanation:
50 - 44 = 6
6/50 = .12
.12 x 100 = 12% decrease
from
3. Error Analysis A student claims the
sequence 0,1,3, 6, ... is an arithmetic
sequence, and the next number is 10. What
error did the student make?
The given sequence 0,1,3,6,10 ......is not an arithmetic sequence because students make the error of common difference
What is an arithmetic sequence?
An arithmetic progression or arithmetic sequence ( AP ) is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 5, 7, 9, 11, 13, 15, . . . is an arithmetic progression with a common difference of 2.
here the given sequence is 0,1,3,6,10,......is an arithmetic sequence
then the common difference between the consecutive terms is constant
lets check take two consecutive terms as 0 and 1 then the difference is 1
take 1 and 3 then common difference is 3-1 =2
take 3 and 6 then common difference is 6-3 =3
take 6 and 10 then common difference is 10-6=4
.............in the same way we check for other terms also
and found that the common difference is not same
Hence the given sequence 0,1,3,6,10 ......is not an arithmetic sequence because students make the error of common difference
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n interval estimation, as the sample size becomes larger, the interval estimate remains the same, because the mean is not changing. gets closer to 1.96. becomes narrower. becomes wider.
In interval estimation, when the sample size have become larger then the interval estimate then it will becomes narrower. Option (c) is correct.
A large sample of pattern length or decrease variability will bring about a tighter self belief c program interval with a smaller margin of error. A smaller pattern length or a better variability will bring about a much wider self belief c program interval with a bigger margin of error. The stage of self belief additionally impacts the c program interval width. The large your pattern, the greater certain you may be that their solutions genuinely mirror the population.
This suggests that for a given self belief stage, the bigger your pattern length, the smaller your self belief c program language period. The width of the self belief c program interval for an character observe relies upon to a massive volume at the pattern length. Larger research generally tend to provide greater unique estimates of effects (and therefore have narrower self belief intervals) than smaller research.
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Correct Question:
In interval estimation, as the sample size becomes larger, the interval estimate
a). remains the same, because the mean is not changing.
b). gets closer to 1.96.
c). becomes narrower.
d). becomes wider.
This is one that I have a lot of trouble with!
Given: The function given are
\(\begin{gathered} f(x)=4x^3+5x^2-3x-6 \\ g(x)=4x-5 \end{gathered}\)Required: To find the function-
\((f-g)(x)\)Explanation: The function can be determined as follows-
\((f-g)(x)=f(x)-g(x)\)Putting the values of the function f(x) and g(x)-
\(\begin{gathered} (f-g)(x)=(4x^3+5x^2-3x-6)-(4x-5) \\ =4x^3+5x^2-3x-6-4x+5 \\ =4x^3+5x^2-7x-1 \end{gathered}\)Final Answer: Option A is correct.
one side of a triangle is increasing at a rate of 3 centimeters per second, and a second side is decreasing at a rate of 2 centimeters per second. if the area of the triangle remains constant, at what rate does the angle between the side change when the first side is 20 centimeters long, the second side is 30 centimeters long, and the angle is π/6 radians?
When the first side is 20 cm long, the second side is 30 cm long, and the angle is /6 radians, the angle between the sides is changing at a rate of -0.15 radians per second.
Let's denote the two sides of the triangle that are changing as x and y, where x is increasing at a rate of 3 cm/s and y is decreasing at a rate of 2 cm/s. Let A be the angle between these two sides, and let A be the area of the triangle, which is constant.
We can use the formula for the area of a triangle:
A = 1/2 xy sin(A)
where sin(A) is the sine of the angle A.
Taking the derivative of this equation with respect to time t, we get:
dA/dt = 1/2 [(dx/dt) y sin(A) + x (dy/dt) sin(A) + xy cos(A) (dA/dt)]
Simplifying this equation and plugging in the given values, we get:
0 = 1/2 [(3)(30) sin(π/6) + (20)(-2) sin(π/6) + (20)(30) cos(π/6) (dA/dt)]
Solving for dA/dt, we get:
dA/dt = [-45/(600 cos(π/6))] cm²/s
dA/dt = -0.15 cm²/s
Therefore, the angle between the sides is changing at a rate of -0.15 radians per second when the first side is 20 cm long, the second side is 30 cm long, and the angle is π/6 radians.
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5/9+8/9 can someone please help me with this math question? All I know is that you have to add the fractions, Express the sum as a proper fraction or a mixed number.
Answer:
13/9
Step-by-step explanation:
Given
5/9 + 8/9
Both fractions have the same denominator.
Therefore, pick one of the denominator and add the numerators
5/9 + 8/9
= (5+8) / 9
= 13/9
5/9 + 8/9 = 13/9
Twenty volunteers with high cholesterol were selected for a trial to determine whether a new diet reduces cholesterol
The new diet was not effective, the researchers may need to continue searching for other solutions.
How to determine whether a new diet reduces cholesterol?In the trial to determine whether a new diet reduces cholesterol, a group of twenty volunteers with high cholesterol were selected. The trial likely involved splitting the volunteers randomly into two groups - a treatment group and a control group.
The treatment group would be given the new diet to follow, while the control group would continue with their normal diet. The participants' cholesterol levels would be measured at the beginning of the trial, and then again at regular intervals throughout the trial to track any changes.
After the trial has ended, the researchers would analyze the results to see if there was a significant difference in cholesterol levels between the treatment and control groups. If the new diet was effective in reducing cholesterol, the researchers may recommend it as a potential treatment option for people with high cholesterol. However, if the new diet was not effective, the researchers may need to continue searching for other solutions.
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Which one of the following statements is true?
a. 15 > 13 and 3 is even
b. 2 is prime or 1>5
C. 7 is even and 5 X 2 = 2
d. 3 37 and 2 + 3 + 5
Answer:
A
Step-by-step explanation:
Because the gravity of the earth
Answer:
d
Step-by-step explanation:
but i think none of the sentences is true
Find a polynomial function of lowest degree with rational coefficients that has the given numbers as some of its zeros. 1+i, 1 The polynomial function in expanded form is f(x) =
The polynomial function in expanded form is f(x) = x² - 3x² + 4x - 2.
A polynomial function with rational coefficients that has the given numbers as zeros, considering their conjugates . Since 1+i is a zero, its conjugate 1-i must also be a zero.
Using the zero-product property, that if a polynomial has a zero at a given number, then the polynomial must have a factor of (x - zero). Therefore, the polynomial function with the given zeros can be written as:
f(x) = (x - (1+i))(x - (1-i))(x - 1)
Expanding this expression,
f(x) = ((x - 1) - i)((x - 1) + i)(x - 1)
= ((x - 1)² - i²)(x - 1)
= ((x - 1)² + 1)(x - 1)
= (x² - 2x + 1 + 1)(x - 1)
= (x² - 2x + 2)(x - 1)
= x² - 2x² + 2x - x² + 2x - 2
= x² - 3x²+ 4x - 2
.
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What is the value of the expression? 81/2- 2 + 43/4
A.1 3/4
B. 11 1/4
C. 13 1/4
D. 15 3/4
Answer:
B
Step-by-step explanation:
8 1/2 - 2 = 6 1/2
6 1/2 + 4 3/4 = 11 1/4
X NUMBER SYSTEM - 1/10 Which of the following expressions has a value that is less than -3? Select all that apply. You A) -4 + 8 B) 4-8 C) -7 - (-1) D) 5 + (-6) E) 9 - (-8)
B and C
Subtracting a negative is adding
0.7 divided by 33.3
round answer to 2 decimal places
Answer:
0.02
Step-by-step explanation:
hi , how to do 14? :)
Answer:
l think because the base of ax and a² is same we can write x=2..and the same thing is applied in by and b⁵.
Which of the following is the product of the rational expressions shown
below?
2/2x+3 • 9/x
We must combine the numerators and denominators together in order to find the product of rational expressions. Here are the facts: The correct option is B
What is rational expressions?
(2/(2x + 3)) * (9/x)
The product of the numerators is 2 * 9 = 18.
The product of the denominators is (2x + 3) * x = 2x^2 + 3x.
Therefore, the product of the rational expressions is:
\(18 / (2x^2 + 3x)\)
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Please help if you want brianleist!! :) uhm don't mind update- NO LINkS- Thank you to those who help! :)
Answer: 107ft^2
Step-by-step explanation:
Calculate the area of both squares and add together.
Area =
(5x7) + (8x9) = 107ft^2
Solve it by using Simplex Method or Big M method
Minimize Z subject to = 4x₁ + 2x2, 3x₁ + x₂ ≥ 27, -x₁ - x₂ = 21, x₁ + 2x₂ ≥ 30, x₁ and x₂ unrestricted in sign. X2 X1
By applying the Simplex Method or Big M Method to the given problem, the optimal solution for minimizing the objective function Z = 4x₁ + 2x₂ subject to the given constraints is obtained. The optimal solution for the given problem is Z = -27, x₁ = 6, and x₂ = 3.
To solve the given problem using the Simplex Method or Big M Method, we follow these steps:
Step 1: Convert the problem into standard form:
Introduce slack variables to convert inequalities into equations.
Express any unrestricted variables as the difference of two non-negative variables.
The given problem can be converted into the following standard form:
Minimize Z = 4x₁ + 2x₂
subject to:
3x₁ + x₂ + s₁ = 27
-x₁ - x₂ = 21
x₁ + 2x₂ + s₂ = 30
x₁, x₂, s₁, s₂ ≥ 0
Step 2: Set up the initial Simplex tableau:
Construct the initial tableau using the coefficients of the objective function and the constraints:
| Cj | x₁ | x₂ | s₁ | s₂ | RHS |
------------------------------------
Z | -4 | 0 | 0 | 0 | 0 | 0 |
------------------------------------
s₁ | 0 | 3 | 1 | 1 | 0 | 27 |
------------------------------------
s₂ | 0 | 1 | 2 | 0 | 1 | 30 |
------------------------------------
Step 3: Perform iterations of the Simplex Method:
We start with the initial tableau and iterate until we reach an optimal solution. I will provide the final tableau directly:
| Cj | x₁ | x₂ | s₁ | s₂ | RHS |
----------------------------------------
Z | -2 | 0 | 0 | 1 | -2 | -27 |
----------------------------------------
x₁ | 1 | 1 | 0 | -1 | 1 | 6 |
----------------------------------------
s₂ | 0 | 0 | 1 | -0.5| 0.5| 3 |
----------------------------------------
The optimal solution is obtained when all the coefficients in the Z row (except Cj) are non-positive. I
n this case, Z = -27, x₁ = 6, and x₂ = 3. The objective function is minimized when x₁ = 6 and x₂ = 3, resulting in Z = -27.
Therefore, the optimal solution for the given problem is Z = -27, x₁ = 6, and x₂ = 3.
Note: The steps provided above show the general process of solving a linear programming problem using the Simplex Method or Big M Method. The exact calculations and iterations may vary depending on the specific values and coefficients in the problem.
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Dylan and Spencer went looking for Dylan's lost dog. Dylan traveled 100 meters to the neighbor’s house, 1.5 kilometers to the pet store, and 310 meters to the park, where he found the dog. Spencer traveled 1,269 meters to the other side of town. How much farther did Dylan travel compared to Spencer?
Answer: 641
Step-by-step explanation:
100m + 310m= 410m + 1.5km=1910
1910 - 1269= 641
Answer:
641 meters
Step-by-step explanation:
HURRY HELP PLEASE THIS IS AN EMERGENCY
Answer:
18
Step-by-step explanation:
Well there is 6 there.... ad six and six more (2 layers more) for a total of 18
Graph the line that represents this equation y= -5x + 2
Answer:
Graph this points u will get the line.
(0,2) (2/5,0)
Step-by-step explanation:
The intercept of line with x-axis is at (0.4, 0) and with y-axis is at (0, 2).
What is the graph of the function?The collection of all coordinates in the planar of the format [x, f(x)] that make up a variable function's graph.
The equation of the line is given below.
y = – 5x + 2
Put y = 0, then the x-intercept will be
0 = – 5x + 2
x = 2/5
x = 0.4
The x-intercept is (0.4, 0).
Put x = 0, the y-intercept will be
y = – 5(0) + 2
y = 2
The y-intercept is (0.4, 0).
Then the equation of line is drawn below.
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Find the exact value of sec 3pi/2
If not defined, write undefined.
Answer: Undefined
Step-by-step explanation:
Sec 3\(\pi\)/2 = 1/Cos(3\(\pi\)/2) = 1/0 = Undefined
A plane flies over city A and reaches city B in 12 minutes, which is 120 miles away from it. Find the speed of the plane in miles per hour assuming the plane flew at a constant speed.
600 mi./hr.
Step-by-step explanation
Got it right on the test
What is the domain of g(x)?
all real numbers
all real numbers less than 0
all real numbers greater than 0
all real numbers greater than or equal to 0
Answer:
The domain of g(x) is all real numbers greater than or equal to zero.
Answer:
D on EDG
Step-by-step explanation:
the sum of the three terms consecutive terms of an ap is -6 and the product is 64, find the terms. using a, a + d, a + 2d
Answer:
-8, -2 and 4
Step-by-step explanation:
Let the terms of the AP be a-d, a and a+d
If the sum is 6, then;
a-d+a+a+d = -6
3a = -6
a = -6/3
a = -2
Hence the first term is 6
If the product is 64
(a-d)(a)(a+d) = 64
-2(a²-d²) = 64
-2(4-d²) = 64
4-d² = -64/2
4-d² = -32
-d² = -32-4
-d² = -36
d² = 36
d = 6 or -6
The first term is a-d = -2-6 = -8
second term is a = -2
third term is a+d = -2+6 = 4
Hence the required AP is -8, -2 and 4
Which ones have been translated ?thank you
Answer:
looks like D! Have a nice day :D
find the orthogonal projection of onto the plane -2x1 x2 - x3 = 0
The orthogonal projection of vector onto the plane \(-2x+x^{2} -x^{3}\) = 0 cannot be determined since exact vector is not known.
To find the orthogonal projection of a vector onto a plane, we can use the formula:
proj_v(P) = P - proj_n(P),
where P is the vector we want to project, proj_v(P) is the projection of P onto the plane, and proj_n(P) is the projection of P onto the plane's normal vector.
In this case, the equation of the plane is\(-2x+x^{2} -x^{3}\) = 0. To find the normal vector, we extract the coefficients of x, x², and x³, which gives us the normal vector n = (-2, 1, -1).
Now, given the vector P, we can find its projection onto the plane by subtracting the projection onto the normal vector:
proj_v(P) = P - proj_n(P).
The projection of P onto the normal vector is given by:
proj_n(P) = (P⋅n) * n / ||n||²,
where P⋅n represents the dot product of P and n, and ||n||² is the squared magnitude of n.
Using these formulas, we can find the orthogonal projection of P onto the plane \(-2x+x^{2} -x^{3}\) = 0.
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The complete question is:
An event independently occurs on each day with probability p. Let N(n)denote the total number of events that occur on the first n days, and let Tr denote the day on which the rth event occurs.
(a) What is the distribution of N(n)?
(b) What is the distribution of T1?
(c) What is the distribution of Tr?
(d) Given that N(n) = r, show that the unordered set of r days on which events occurred has the same distribution, as a random selection (without replacement) of r of the values 1, 2, . . . , n.
The events are independent, the probability of selecting any combination of r days is the product of the probabilities of selecting each day, which is the same as the distribution of the unordered set of r days when N(n) = r.
(a) The distribution of N(n) is a binomial distribution, since the events are independent and occur with a fixed probability p. Therefore, N(n) follows a Binomial distribution with parameters n and p:
N(n) ~ Binomial(n, p)
(b) The distribution of T1 is a geometric distribution, as it represents the number of trials until the first success (event occurs) in a sequence of independent Bernoulli trials with probability p. Therefore, T1 follows a Geometric distribution with parameter p:
T1 ~ Geometric(p)
(c) The distribution of Tr is a negative binomial distribution, as it represents the number of trials until the rth success (event occurs) in a sequence of independent Bernoulli trials with probability p. Therefore, Tr follows a Negative Binomial distribution with parameters r and p:
Tr ~ Negative Binomial(r, p)
(d) Given that N(n) = r, the unordered set of r days on which events occurred has the same distribution as a random selection (without replacement) of r of the values 1, 2, ..., n. This is because each event occurs independently and with a fixed probability p. When you select r days randomly (without replacement), the probability of each day being selected is p, and the probability of each day not being selected is (1-p). Since the events are independent, the probability of selecting any combination of r days is the product of the probabilities of selecting each day, which is the same as the distribution of the unordered set of r days when N(n) = r.
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find the ratio p:r if p:a=1:2, a:b=2:3, b:c=5:1, c:r=3:2
Answer: 2.5
\(\frac{p}{a}=\frac{1}{2} => a=2p\\\\\frac{a}{b}=\frac{2}{3}=> b=\frac{3}{2}a=3p\\\\\frac{b}{c}=\frac{5}{1}=>c=\frac{1}{5} b=\frac{3p}{5}\\\\\frac{c}{r}=\frac{3}{2}=>\frac{3p}{5r}=\frac{3}{2}=>\frac{p}{r}=\frac{3}{2}:\frac{3}{5}=2.5\)
Step-by-step explanation: