The equation of the new function after shifting 6 units right and 4 units down is f(x) = (x + 6)² - 4.
If we are to apply the changes below to the quadratic parent function, F(x) = x², what is the equation of the new function, given that we are to shift 6 units to the right and 4 units down? We will approach this question by following the steps outlined below.
Step 1: Identify the parent function F(x) = x² and its transformations
Step 2: Write the equation of the new function
Step 3: Simplify the new equation of the function.Step 1: Identify the parent function F(x) = x² and its transformations
Here, we are given the quadratic parent function F(x) = x² and two transformations: shift 6 units right and shift 4 units down.
The general equation for the horizontal and vertical shifts of a quadratic function is given by:f(x) = a(x - h)² + k, where a, h, and k are constants.
The value of a determines the direction of opening of the parabola, while (h, k) represents the vertex of the parabola.
If a > 0, the parabola opens upwards, while a < 0, the parabola opens downwards. If the values of (h, k) are positive, the parabola is shifted right and up, respectively. On the other hand, if the values of (h, k) are negative, the parabola is shifted left and down, respectively.
Therefore, given the quadratic parent function F(x) = x² and two transformations: shift 6 units right and shift 4 units down, we can represent these changes by the following:
a = 1 (since the parabola opens upwards)h = -6 (since we are shifting the parabola 6 units to the right)k = -4 (since we are shifting the parabola 4 units down)
Step 2: Write the equation of the new function Now that we have identified the constants a, h, and k, we can write the equation of the new function as follows:f(x) = a(x - h)² + kf(x) = 1(x - (-6))² + (-4)Replacing the constants a, h, and k in the equation, we have:f(x) = (x + 6)² - 4
Step 3: Simplify the new equation of the function.f(x) = (x + 6)² - 4= (x + 6)(x + 6) - 4= x² + 12x + 36 - 4= x² + 12x + 32Therefore, the equation of the new function after shifting 6 units right and 4 units down is f(x) = x² + 12x + 32.
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What is the sum of the series?
Pls help I need this answer
Answer:
B , D , A
Step-by-step explanation:
(4x³ - 4 + 7x) - (2x³ - x - 8)
distribute the first parenthesis by 1 and the second by - 1
= 4x³ - 4 + 7x - 2x³ + x + 8 ← collect like terms
= 2x³ + 8x + 4 ← equivalent to expression B
---------------------------------------------------------------
(- 3x² + [tex]x^{4}[/tex] + x) + (2[tex]x^{4}[/tex] - 7 + 4x) ← remove parenthesis
= - 3x² + [tex]x^{4}[/tex] + x + 2[tex]x^{4}[/tex] - 7 + 4x ← collect like terms
= 3[tex]x^{4}[/tex] - 3x² + 5x - 7 ← equivalent to expression D
------------------------------------------------------------------
(x² - 2x)(2x + 3)
each term in the second factor is multiplied by each term in the first factor, that is
x²(2x + 3) - 2x(2x + 3) ← distribute parenthesis
= 2x³ + 3x² - 4x² - 6x ← collect like terms
= 2x³ - x² - 6x ← equivalent to expression A
Describe the given translation: T(0, 7)
Answer:
ok t means some thing but zero and seven should be solved
Si 3,390 kg de plomo ocupan un volumen de 0.3m3. Encuentra la densidad del plomo.
The density of lead is 11,300 kg/[tex]m^3[/tex], which means that lead is a dense material with a significant mass per unit volume.
To find the density of lead, we can use the formula:
Density = Mass / Volume
Given that the mass of lead is 3,390 kg and the volume is 0.3 [tex]m^3[/tex], we can substitute these values into the formula:
Density = 3,390 kg / 0.3[tex]m^3[/tex]
To simplify the calculation, we divide the mass by the volume:
Density = 11,300 kg/[tex]m^3[/tex]
Therefore, the density of lead is 11,300 kg/[tex]m^3[/tex].
Density is a physical property of a substance that describes how much mass is packed into a given volume. In this case, the density of lead tells us that for every cubic meter of lead, there are 11,300 kilograms of mass.
It is important to note that the density of lead is a characteristic property and remains constant regardless of the size or shape of the sample. It is a useful parameter in various scientific and industrial applications.
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The question probable may be:
If 3,390 kg of lead occupy a volume of 0.3 m^3, find the density of lead.
Please answer ASAP I will brainlist
The system has no solution. Option C is correct.
To solve the given system of equations using row operations, we can write the augmented matrix and perform Gaussian elimination. The augmented matrix for the system is:
1 1 -1 | 6
3 -1 1 | 2
1 4 2 | -34
We'll use row operations to transform the augmented matrix into row-echelon form or reduced row-echelon form. Let's proceed with the row operations:
R2 = R2 - 3R1:
1 1 -1 | 6
0 -4 4 | -16
1 4 2 | -34
R3 = R3 - R1:
1 1 -1 | 6
0 -4 4 | -16
0 3 3 | -40
R3 = R3 + (4/3)R2:
1 1 -1 | 6
0 -4 4 | -16
0 0 0 | -4
Now, we can rewrite the augmented matrix in equation form:
x + y - z = 6
-4y + 4z = -16
0 = -4
From the last equation, we can see that it leads to a contradiction (0 = -4), which means the system is inconsistent. Therefore, the system has no solution.
The correct answer is (C) This system has no solution.
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If the expenditure of a person is 75% of his income and his income tax which is 13% of his income is $585. What is his expenditure?
The person's expenditure is $1,755. (30 words)
To find the expenditure, we need to determine the person's income first. Since the income tax is 13% of the income and is given as $585, we can calculate the income. Dividing the income tax by the tax rate gives us the income. So, $585 divided by 0.13 equals $4,500, which is the person's income.
Now, we can calculate the expenditure. Given that the expenditure is 75% of the income, we can multiply the income by 0.75 to find the expenditure. So, $4,500 multiplied by 0.75 equals $3,375. Therefore, the person's expenditure is $3,375. (120 words)
In summary, the person's expenditure is $3,375. To find this, we first determined the person's income by dividing the given income tax of $585 by the tax rate of 13%, resulting in an income of $4,500.
Then, we calculated the expenditure by multiplying the income by 0.75 since the expenditure is stated to be 75% of the income. Thus, the person's expenditure is $3,375.
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Suppose for 40 observations, the variance is 50. If all the observations are increased by 20, the variance of these increased observation will be
Select one:
a. 50
b. 70
c. 50/20
d. 40
e. 50-20=30
Note: Answer D is NOT the correct answer. Please find the correct answer. Any answer without justification will be rejected automatically.
Answer:
a) 50
Step-by-step explanation:
The variance will not change as all the observations are increased uniformly.
Proof:
Variance formula:
[tex]s^{2} = \frac{\sum x_i^{2} }{n} -\frac{(\sum x_i)^{2} }{n^{2} }[/tex]
When the obervations are inc by 20,
[tex]s_1^{2} = \frac{\sum (x_i + 20)^{2} }{n} -\frac{(\sum (x_i + 20))^{2} }{n^{2} }\\\\=\frac{\sum(x_i^{2} + 2*20*x_i + 20^{2} )}{n} - \frac{(\sum x_i +20n)^{2} }{n^{2} } \\\\=\frac{\sum x_i^{2} + 40\sum x_i + 20^{2}n }{n} - \frac{(\sum x_i)^{2} +2*20n\sum x_i + 20^{2} n^{2} }{n^{2} } \\\\= \frac{\sum x_i^{2}}{n} - \frac{(\sum x_i)^{2}}{n^{2} } +\frac{40\sum x_i}{n} + 20^{2} - \frac{40\sum x_i}{n} - 20^{2}\\\\s_1^{2}= \frac{\sum x_i^{2}}{n} - \frac{(\sum x_i)^{2}}{n^{2} }\\\\=s^{2}[/tex]
Therefore variance doesn't change
y= -x^2 + x+ 12 in intercept form
Answer:
y = x + 12
Step-by-step explanation:
y = -x² + x + 12
y intercept form is, y = mx + c
where m = -b / a
the general quadratic equation is,
y = ax² + bx + c
thus, according to the question
m = -1 / -1 = 1
constant, c = 12
thus, the intercept form of the equation would be,
y = x + 12
HELP DUE IN 3 DAYS!!!!! Which symbol should go in the box to make the equation true, and why? (1 point) the fraction two fourths followed by a box followed by the fraction four eighths a >, because the fraction two fourths is equal to the fraction eight eighths. b >, because the fraction two fourths is equal to the fraction six eighths. c =, because the fraction four eighths is equal to the fraction two fourths. d =, because the fraction four eighths is equal to the fraction two halves.
The correct answer is c) =, because the fraction four eighths is equal to the fraction two fourths.
To determine which symbol should go in the box to make the equation true, let's analyze the fractions given and compare their values.
The fraction "two fourths" can be simplified to "one-half" since both the numerator and denominator can be divided by 2. Therefore, "two fourths" is equal to "one-half."
Now, let's look at the fraction "four eighths." We can simplify this fraction by dividing both the numerator and denominator by 4, which gives us "one-half" as well. So, "four eighths" is also equal to "one-half."
Now, based on the given fractions, we have the equation:
(one-half) [BOX] (one-half)
We need to determine the correct symbol to fill in the box.
Looking at the values of the fractions, we see that both "two fourths" and "four eighths" are equivalent to "one-half." Therefore, the correct symbol to make the equation true is the equality symbol (=).
Hence, the correct answer is:
c) =, because the fraction four eighths is equal to the fraction two fourths.
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Find the center and radius of the circle represented by the equation below.
Answer:
centre = (5, - 6 ) , radius = 7
Step-by-step explanation:
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r is the radius
given
x² + y² - 10x + 12y + 12 = 0 ( subtract 12 from both sides )
x² + y² - 10x + 12y = - 12 ( collect terms in x/ y )
x² - 10x + y² + 12y = - 12
using the method of completing the square
add ( half the coefficient of the x/ y terms )² to both sides
x² + 2(- 5)x + 25 + y² + 2(6)y + 36 = - 12 + 25 + 36
(x - 5)² + (y + 6)² = 49 = 7² ← in standard form
with centre (5, - 6 ) and radius = 7
Answer:
Center = (5, -6)
Radius = 7
Step-by-step explanation:
To find the center and the radius of the circle represented by the given equation, rewrite the equation in standard form by completing the square.
To complete the square, begin by moving the constant to the right side of the equation and collecting like terms on the left side of the equation:
[tex]x^2-10x+y^2+12y=-12[/tex]
Add the square of half the coefficient of the term in x and the term in y to both sides of the equation:
[tex]x^2-10x+\left(\dfrac{-10}{2}\right)^2+y^2+12y+\left(\dfrac{12}{2}\right)^2=-12+\left(\dfrac{-10}{2}\right)^2+\left(\dfrac{12}{2}\right)^2[/tex]
Simplify:
[tex]x^2-10x+(-5)^2+y^2+12y+(6)^2=-12+(-5)^2+(6)^2[/tex]
[tex]x^2-10x+25+y^2+12y+36=-12+25+36[/tex]
[tex]x^2-10x+25+y^2+12y+36=49[/tex]
Factor the perfect square trinomials on the left side:
[tex](x-5)^2+(y+6)^2=49[/tex]
The standard equation of a circle is:
[tex]\boxed{(x-h)^2+(y-k)^2=r^2}[/tex]
where:
(h, k) is the center.r is the radius.Comparing this with the rewritten given equation, we get
[tex]h = 5[/tex][tex]k = -6[/tex][tex]r^2 = 49 \implies r=7[/tex]Therefore, the center of the circle is (5, -6) and its radius is r = 7.
Scores on the Wechsler Adult Intelligence Scale for the 20 to 34 age group are approximately Normally distributed with mean 110 and standard deviation 15. How high must a person score to be in the top 4% of all scores? (Round your answer to the nearest whole number, if necessary.)
Answer:
The person must score 136 to be in the top 5% of all scores in wechsler adult intelligence scale.
Step-by-step explanation:
What is defined as the normal distribution?
A normal distribution is a data set arrangement in which the majority of values cluster inside the center of the range and the remainder taper off symmetrically toward any extreme.
A histogram inside a normal distribution curve is sometimes used to design the curve.
The formula for the normal distribution is;
z = (x - μ)/σ
where,
z = z- score, taken fro table
Mean μ = 110
Standard deviation σ = 15
Sample mean x.
If we want to be in the top 5%, we must outperform 95% of the remaining scores. So we must investigate.
In with us standard normal probability table, look up 0.95 and get the Z score that corresponds to that.
z = 1.7
Put the value in formula ad find x.
1. 7 = (x - 110)/15
x = 25.5 + 110
x = 135.5
x = 136 (whole number)
Thus, the person must score 136 to be in the top 5% of all scores in wechsler adult intelligence scale.
Use the side lengths to prove which triangles form a right triangle.
Select all the triangles that form a right triangle
The side length that prove a right angle triangle is √2, √3 and √5.
How to find the side of a right triangle?A right angle triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.
Therefore, a right angle triangle can be proved by using the Pythagoras's theorem as follows:
Hence,
c² = a² + b²
where
c = hypotenuse sidea and b are the other legsTherefore,
(√2)² + (√3)² = (√5)²
Hence, the right angle triangle is the triangle with sides √2, √3 and √5.
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If two opposite sides of a square are increased by 13 meters and the other sides are decreased by 7 meters, the area of the rectangle that is formed is 69 square meters. Find the area of the original square.
Answer:
(x + 13)(x - 7) = 69
x² + 6x - 91 = 69
x² + 6x - 160 = 0
(x + 16)(x - 10) = 0
x = 10, so the area of the original square is 100 m².
Two models R1 and R2 are given for revenue (in millions of dollars) for a corporation. Both models are estimates of revenues from 2030 through 2035, with t = 0 corresponding to 2030.
R1 = 7.23 + 0.25t + 0.03t^2
R2 = 7.23 + 0.1t + 0.01t^2
How much more total revenue (in millions of dollars) does that model project over the six-year period ending at t = 5? (Round your answer to three decimal places.)
Step-by-step explanation:
To find the difference in total revenue projected by the two models over the six-year period ending at t = 5, we need to calculate the revenue for each model from t = 0 to t = 5 and subtract the results.
For R1:
R1 = 7.23 + 0.25t + 0.03t^2
Substituting t = 5:
R1(5) = 7.23 + 0.25(5) + 0.03(5^2)
R1(5) = 7.23 + 1.25 + 0.75
R1(5) = 9.23 + 0.75
R1(5) = 9.98 million dollars
For R2:
R2 = 7.23 + 0.1t + 0.01t^2
Substituting t = 5:
R2(5) = 7.23 + 0.1(5) + 0.01(5^2)
R2(5) = 7.23 + 0.5 + 0.25
R2(5) = 7.73 + 0.25
R2(5) = 7.98 million dollars
To find the difference, we subtract R2(5) from R1(5):
Difference = R1(5) - R2(5)
Difference = 9.98 - 7.98
Difference = 2 million dollars
Therefore, the model R1 projects 2 million dollars more in total revenue than R2 over the six-year period ending at t = 5.
The area of the figure is square units.
3 units, 8 units, 3 units, 9 units, 3 units, 21 units
The area of the figure is 114 square units.
To determine the area of the figure, we need to identify its shape.
From the given dimensions, it appears that we have three rectangular sections.
The first section has a length of 3 units and a width of 8 units, giving us an area of 3 [tex]\times[/tex] 8 = 24 square units.
The second section has a length of 3 units and a width of 9 units, resulting in an area of 3 [tex]\times[/tex] 9 = 27 square units
The third section has a length of 3 units and a width of 21 units, yielding an area of 3 [tex]\times[/tex] 21 = 63 square units.
To find the total area of the figure, we need to sum up the areas of the individual sections:
Total area = 24 + 27 + 63 = 114 square units.
Therefore, the area of the figure is 114 square units.
It's important to note that without a clear description or diagram of the figure, it's challenging to provide an accurate interpretation.
The given dimensions could represent various arrangements, and the resulting area would vary accordingly.
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I can't really see the graph clearly but I think that the x-intercepts should be (-16/7, 0) and (32/7, 0).
Answer:
x-intercepts: -2, 4
Step-by-step explanation:
The given graph shows a parabola that opens downwards.
The y-intercept is the point at which the curve crosses the y-axis, so when x = 0. From inspection of the given graph, we can see that the parabola crosses the y-axis when y = 8. Therefore, the y-intercept is (0, 8).
The x-intercepts are the points at which the curve crosses the x-axis, so when y = 0. From inspection of the given graph, we can see that the parabola crosses the x-axis when x = -2 and x = 4. Therefore, the x-intercepts are (-2, 0) and (4, 0).
Let X_1,…,X_n be a random sample. For S(X_1,…,X_n )=1/(1/n ∑_(i=1)^n▒〖(x_i-c)〗^2 ) , find its asymptotic distribution where EX^k=α_k.
The asymptotic distribution of the estimator S(X₁, ..., Xₙ) is a standard normal distribution, denoted as N(0, 1).
To find the asymptotic distribution of the estimator S(X₁, ..., Xₙ), we can use the Central Limit Theorem (CLT). However, we need some additional assumptions to apply the CLT, such as the finite variance of the random variables.
Given that E(Xᵢ^k) = αₖ for all k, we can assume that the random variables Xᵢ have a finite variance. Let's denote the variance of Xᵢ as Var(Xᵢ) = σ².
First, let's simplify the estimator S(X₁, ..., Xₙ):
S(X₁, ..., Xₙ) = 1 / (1/n ∑ᵢ (Xᵢ - c)²)
Notice that the numerator is a constant and doesn't affect the asymptotic distribution. So, we can focus on analyzing the denominator.
Let's calculate the expected value and variance of the denominator:
E[1/n ∑ᵢ (Xᵢ - c)²] = 1/n ∑ᵢ E[(Xᵢ - c)²] = 1/n ∑ᵢ (Var(Xᵢ) + E[Xᵢ]² - 2cE[Xᵢ] + c²)
= 1/n (nσ² + α₁ - 2cα₁ + c²) (using the fact that E[Xᵢ] = α₁ for all i)
Var[1/n ∑ᵢ (Xᵢ - c)²] = 1/n² ∑ᵢ Var[(Xᵢ - c)²] = 1/n² ∑ᵢ (Var(Xᵢ - c)²) = 1/n² ∑ᵢ (Var(Xᵢ))
= 1/n² (nσ²) = σ²/n
Now, let's apply the CLT. According to the CLT, if we have a sequence of independent and identically distributed random variables with a finite mean (μ) and a finite variance (σ²), the sample mean (in this case, our denominator) converges in distribution to a standard normal distribution as the sample size approaches infinity.
Therefore, as n approaches infinity, the asymptotic distribution of S(X₁, ..., Xₙ) will follow a standard normal distribution.
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Which is equivalent to 4/9 1/2x*?
92x
9 1/8x
Answer:
B. [tex] 9^{\frac{1}{8}x} [/tex]
Step-by-step explanation:
[tex] \sqrt[4]{9}^{\frac{1}{2}x} = [/tex]
[tex] = ({9}^{\frac{1}{4}})^{\frac{1}{2}x} [/tex]
[tex] = 9^{\frac{1}{4} \times \frac{1}{2}x} [/tex]
[tex] = 9^{\frac{1}{8}x} [/tex]
prove that the lim x→−3 (10 − 2x) = 16
Answer:
Proving that the limit of the equation 10 - 2x as x approaches -3 is 16 involves using the definition of a limit.
Here's how you would approach it:
Let epsilon be a small positive number. We want to find a value of delta such that if x is within a distance of delta from -3, then 10 - 2x is within a distance of epsilon from 16.
So, we start with:
|10 - 2x - 16| < epsilon
Simplifying,
|-2x - 6| < epsilon
And using the reverse triangle inequality,
|2x + 6| > ||2x| - |6||
Now, we can choose a value for delta such that if x is within delta of -3, then |2x + 6| is within delta + 6 of |-6| = 6.
So,
||2x| - |6|| < epsilon
and therefore:
|2x - 6| < epsilon
Choosing delta = epsilon/2, we can prove that:
0 < |x + 3| < delta -> |2x - 6| < epsilon
Therefore, we have proved that the limit of 10 - 2x as x approaches -3 is 16 using the definition of a limit.
Step-by-step explanation:
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help please its due in 2 hrs
Answer:
Step-by-step explanation:
. Mira bought $300 of Freerange Wireless stock in
January of 1998. The value of the stock is expected
to increase by 7.5% per year. Use a graph to predict
the year the value of Mira's stock will reach $650.
29.4.3 Quiz: Parabolas with Vertices at the Origin
Question 5 of 10
The equation below describes a parabola. If a is negative, which way does the
parabola open?
y=ax²2²
O A. Right
B. Down
OC. Up
OD. Left
SUBMIT
The equation of a parabola with its vertex at the origin includes a negative coefficient 'a', the parabola opens downward. option B.
The equation y = ax² represents a parabola with its vertex at the origin. In this case, if the coefficient 'a' is negative, it determines the direction in which the parabola opens.
When 'a' is negative, the parabola opens downward. This means that the vertex, which is at the origin (0, 0), represents the highest point on the graph, and the parabola curves downward on both sides.
To understand this concept, let's consider the basic equation y = x², which represents a standard upward-opening parabola. As 'a' increases, the parabola becomes narrower. Conversely, when 'a' becomes negative, it flips the parabola upside down, resulting in a downward-opening parabola.
For example, if we have the equation y = -x², the negative coefficient causes the parabola to open downward. The vertex remains at the origin, but the shape of the parabola is now inverted.
In summary, when the equation of a parabola with its vertex at the origin includes a negative coefficient 'a', the parabola opens downward. This can be visually represented as a U-shape curving downward from the origin. So Optyion B is correct.
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. Initially 100 milligrams of a radioactive substance was present.
After 6 hours the mass had decreased by 3%. If the rate of
decay is proportional to the amount of the substance present at
time t, nd the amount remaining after 24 hours.
Answer:
Incomplete Question
v2=v02+2ax ; solve for x.
To solve for x in the equation v2 = v0^2 + 2ax, we can rearrange the equation to isolate x:
x = (v2 - v0^2) / (2a)
In this equation, v2 represents the final velocity, v0 is the initial velocity, a is the acceleration, and x is the displacement. By substituting the given values of v2, v0, and a into the equation, we can calculate the value of x.
The equation v2 = v0^2 + 2ax is derived from the kinematic equation that relates displacement, velocity, acceleration, and time. By isolating x, we can determine the displacement.
The equation represents the final velocity (v2) as the sum of the square of the initial velocity (v0^2) and the product of twice the acceleration (2a) and displacement (x).
To solve for x, we subtract v0^2 from v2 to obtain (v2 - v0^2), and then divide this difference by 2a. This yields the value of x, which represents the displacement.
By substituting the provided values of v2, v0, and a, we can evaluate the expression and calculate the value of x. This equation is commonly used in physics and mechanics to determine the displacement of an object given its initial and final velocities and acceleration.
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Evaluate the given expression for x=5
x² + 3x - 2
(5)² + 3 × 5- 2
25 + 15 - 2
40 - 2
38...
12. Write the coordinates of Triangle ABC.
A. 2 B.5 C. 6
13. Translate the Triangle (-2, 5). Draw the new image on the grid above.
14. Each coordinate will move how many on the x-axis? 8
Direction right
I
15. Each coordinate will move how many on the y-axis?
ordinates to the translated triangle image.
Given the following diagram: We need to find the coordinates of triangle ABC, translate the triangle (-2, 5) and draw the new image on the grid above, and determine the amount each coordinate will move on the x-axis and y-axis during translation.
1. Coordinates of triangle ABC:A = (2, 6)B = (5, 8)C = (6, 3)2. Translation of triangle (-2, 5)The translation of a triangle can be done by adding or subtracting a constant value from the x-coordinates and y-coordinates of each vertex of the original triangle.
For example, if we want to translate a triangle by 3 units to the right and 2 units up, we would add 3 to the x-coordinates and add 2 to the y-coordinates of each vertex of the original triangle. Using this method, we can translate the triangle (-2, 5) as follows:
New coordinates of A = (2 + (-2), 6 + 5) = (0, 11)New coordinates of B = (5 + (-2), 8 + 5) = (3, 13)New coordinates of C = (6 + (-2), 3 + 5) = (4, 8)3. New image of triangle (-2, 5)The new image of the triangle (-2, 5) is shown in the following diagram:4. Amount each coordinate moves on x-axis During translation, each coordinate moves 2 units to the right (from -2 to 0).5. Amount each coordinate moves on y-axis During translation, each coordinate moves 6 units up (from 5 to 11).
Therefore, the coordinates of the translated triangle image are (0, 11), (3, 13), and (4, 8).
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What is the probability that you will be in district 12 with Katniss & Peeta?
Answer:
0
Step-by-step explanation:
theres only 2 people each district
Solve 4563÷257 using long division method show the steps
2 5 7 ÷ 4 5 6 3
- 2 5 7
1993
- 1 7 9 9
Answer:
194
Which is the graph of the linear inequality 1/2x – 2y > –6? On a coordinate plane, a solid straight line has a positive slope and goes through (negative 4, 2) and (4, 4). Everything above and to the left of the line is shaded. On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 4, 2) and (4, 4). Everything above and to the left of the line is shaded. On a coordinate plane, a solid straight line has a positive slope and goes through (negative 4, 2) and (4, 4). Everything below and to the right of the line is shaded. On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 4, 2) and (4, 4). Everything below and to the right of the line is shaded.
The correct graph of the linear inequality 1/2x - 2y > -6 is the one where a solid straight line has a positive slope and goes through (negative 4, 2) and (4, 4), and everything below and to the right of the line is shaded.
A sample consists of the following N = 7 scores: 5, 0, 4, 5, 1, 2 and 4.
a. Compute the mean and standard deviation for the sample
Mean =
Standard deviation=
b. Find the z-score for each score in the sample
X= 5, z=
X= 0, z=
X= 4, z=
X= 5, z=
X= 1, z=
X= 2, z=
X= 4, z=
a. Mean = 3
Standard deviation = 2
b. The z-scores for each score in the sample are: 1, -1.5, 0.5, 1, -1, -0.5, 0.5.
a. To compute the mean and standard deviation for the sample, we follow these steps:
Calculate the mean (average)
Mean = (sum of all scores) / (number of scores)
Mean = (5 + 0 + 4 + 5 + 1 + 2 + 4) / 7
Mean = 21 / 7
Mean = 3
The mean of the sample is 3.
Calculate the standard deviation
The formula for standard deviation for a sample is given by:
Standard deviation = sqrt((sum of squared differences from the mean) / (number of scores - 1))
First, calculate the squared differences from the mean for each score:
(5 - 3)^2 = 4
(0 - 3)^2 = 9
(4 - 3)^2 = 1
(5 - 3)^2 = 4
(1 - 3)^2 = 4
(2 - 3)^2 = 1
(4 - 3)^2 = 1
Next, sum up these squared differences:
4 + 9 + 1 + 4 + 4 + 1 + 1 = 24
Now, divide this sum by (number of scores - 1):
24 / (7 - 1) = 24 / 6 = 4
Finally, take the square root of this result:
Standard deviation = sqrt(4) = 2
The standard deviation of the sample is 2.
b. To find the z-score for each score in the sample, we use the formula:
z = (X - Mean) / Standard deviation
For each score, we substitute the values into the formula:
X = 5, z = (5 - 3) / 2 = 2 / 2 = 1
X = 0, z = (0 - 3) / 2 = -3 / 2 = -1.5
X = 4, z = (4 - 3) / 2 = 1 / 2 = 0.5
X = 5, z = (5 - 3) / 2 = 2 / 2 = 1
X = 1, z = (1 - 3) / 2 = -2 / 2 = -1
X = 2, z = (2 - 3) / 2 = -1 / 2 = -0.5
X = 4, z = (4 - 3) / 2 = 1 / 2 = 0.5
The z-scores for each score in the sample are:
z = 1, z = -1.5, z = 0.5, z = 1, z = -1, z = -0.5, z = 0.5
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