Answer:
20 teachers
Step-by-step explanation:
Because if you take 100 and minus it by 29, 23, 4 and 24 you get 20.
Arrange the functions for which the result is a non-infinite value and the limit exists in ascending order of their limit values as x tends to infinity. Please see picture attached.
Answer:
see attached
Step-by-step explanation:
The limit as x gets large is the ratio of the highest-degree terms. In most cases, the limit can be found by evaluating that ratio. Where an absolute value is involved, the absolute value of the highest-degree term is used.
If the ratio gives x to a positive power, the limit does not exist. If the ratio gives x to a negative power, the limit is zero.
The arrangement of functions according to the given condition
[tex]m(x)=\frac{4x^{2}-6 }{1-4x^{2} }[/tex]
[tex]h(x)=\frac{x^{3} -x^{2} +4}{1-3x^{2} }[/tex]
[tex]k(x)=\frac{5x+1000}{x^{2} }[/tex]
[tex]i(x)=\frac{x-1}{|1-4x| }[/tex]
[tex]g(x)=\frac{|4x-1|}{x-4}[/tex]
[tex]l(x)=\frac{5x^{2} -4}{x^{2} +1}[/tex]
[tex]f(x)=\frac{x^{2} -1000}{x-5}[/tex]
[tex]j(x)=\frac{x^{2}-1 }{|7x-1|}[/tex]
What is limit?A limit is the value that a function approaches as the input approaches some value.
According to the given question
[tex]l(x)=\frac{5x^{2} -4}{x^{2} +1}[/tex]
⇒[tex]\lim_{nx\to \infty} \frac{5x^{2} -1}{x^{2} +1}[/tex]
⇒[tex]\lim_{x \to \infty} \frac{x^{2} }{x^{2} } \frac{5-\frac{1}{x^{2} } }{1+\frac{1}{x^{2} } }[/tex]
= 5 ([tex]\frac{1}{x^{2} } = 0[/tex] ,as x tends to infinity [tex]\frac{1}{x^{2} }[/tex] tends to 0)
[tex]i(x)=\frac{x-1}{|1-4x|}[/tex]
⇒[tex]\lim_{x \to \infty} \frac{x-1}{|1-4x|}[/tex] = [tex]\lim_{x \to \infty} \frac{x}{x} \frac{1-\frac{1}{x} }{|\frac{-1}{4}+\frac{1}{x} | }[/tex] =[tex]\frac{1}{\frac{1}{4} }[/tex] =[tex]\frac{1}{4}[/tex]
As x tends to infinity 1/x tends to 0, and |[tex]\frac{-1}{4}[/tex]| gives 1/4
[tex]f(x)= \frac{x^{2} -1000}{x--5}[/tex]
⇒[tex]\lim_{x \to \infty} \frac{x^{2} -1000}{x-5}[/tex]= [tex]\lim_{x \to \infty} \frac{x^{2} }{x} \frac{1-\frac{1000}{x^{2} } }{1-\frac{5}{x} }[/tex]= [tex]\lim_{x \to \infty} x\frac{1-\frac{1000}{x^{2} } }{1-\frac{5}{x} }[/tex] ⇒ limit doesn't exist.
[tex]m(x)=\frac{4x^{2}-6 }{1-4x^{2} }[/tex]
⇒[tex]\lim_{x\to \infty} \frac{4x^{2} -6}{1-4x^{2} }[/tex]=[tex]\lim_{x\to \infty} \frac{x^{2} }{x^{2} } \frac{4-\frac{6}{x^{2} } }{\frac{1}{x^{2} } -4}[/tex] [tex]= \lim_{n \to \infty} \frac{4}{-4}[/tex] = -1
As x tends to infinity [tex]\frac{1}{x^{2} }[/tex] tends to 0.
[tex]g(x)=\frac{|4x-1|}{x-4}[/tex]
⇒[tex]\lim_{x\to \infty} \frac{|4x-1|}{x-4}[/tex] = [tex]\lim_{x \to \infty} \frac{|x|}{x} \frac{4-\frac{1}{x} }{1 -\frac{4}{x} } }[/tex] = 4
as x tends to infinity 1/x tends to 0
and |x|=x ⇒[tex]\frac{|x|}{x}=1[/tex]
[tex]h(x)=\frac{x^{3}-x^{2} +4 }{1-3x^{3} }[/tex][tex]\lim_{x \to \infty} \frac{x^{3} -x^{2} +4}{1-3x^{3} }[/tex][tex]= \lim_{x \to \infty} \frac{x^{3} }{x^{3} } \frac{1-\frac{1}{x}+\frac{4}{x^{3} } }{\frac{1}{x^{3} -3} }[/tex] = [tex]\frac{1}{-3}[/tex] =[tex]-\frac{1}{3}[/tex]
[tex]k(x)=\frac{5x+1000}{x^{2} }[/tex]
[tex]\lim_{x \to \infty} \frac{5x+1000}{x^{2} }[/tex] = [tex]\lim_{x \to \infty} \frac{x}{x} \frac{5+\frac{1000}{x} }{x}[/tex] =0
As x tends to infinity 1/x tends to 0
[tex]j(x)= \frac{x^{2}-1 }{|7x-1|}[/tex]
[tex]\lim_{x \to \infty} \frac{x^{2}-1 }{|7x-1|}[/tex] = [tex]\lim_{x \to \infty} \frac{x}{|x|}\frac{x-\frac{1}{x} }{|7-\frac{1}{x}| }[/tex] = [tex]\lim_{x \to \infty} 7x[/tex] = limit doesn't exist.
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Find the value of c such that the three points (5,5), (-3,1), and (6,c) lie on the same line. Note: Three points are on the same line if the slope of the line through any two points is always the same.
Answer:
c = 5.5
Step-by-step explanation:
We can find the slope of the line using the given points (5,5) and (-3,1) using rise over run:
-4/-8 = 1/2
Now, we can plug in the slope and a point into the equation y = mx + b to find b:
5 = 1/2(5) + b
5 = 2.5 + b
2.5 = b
Then, we can plug in 6 in the point (6,c) to find c:
y = (1/2)(6) + 2.5
y = 3 + 2.5
y = 5.5
c = 5.5
Answer:
c = 5.5
Step-by-step explanation:
Find the slope with two points
m = (y2-y1)/(x2-x1)
m = (1-5)/(-3-5)
= -4/-8
= 1/2
If all the points are on the same line, then they have the same slope
m = (y2-y1)/(x2-x1)
Using the first and third points
1/2 = (c-5)/(6-5)
1/2 = (c-5)/1
1/2 = c-5
Add 5 to each side
5+1/2 = c
5.5 =c
A cylinder fits inside a square prism as shown. For every
cross section the ratio of the area of the circle to the
area of the square is on
since the area of the circle is the area of the square,
the volume of the cylinder equals
Cross section
o
o
o
o
the volume of the prism or (20(h) or turh.
the volume of the prism or (47)(h) or 2nuh.
the volume of the prism or (20)(h) or Ph.
the volume of the prism or (47)(h) or iPh.
kl *
Answer:
Volume of cylinder = π/4 (the volume of the prism) or π/4 (4r²)(h) or πr²h (D)
The complete question related to this found on brainly (ID: 4049983 and 4265826) is stated below:
A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is or πr^2 or π/4. Since the area of the circle is π/4 the area of the square, the volume of the cylinder equals
A) π/2(the volume of the prism) or π/2 (2r)(h) or πrh.
B) π/2 (the volume of the prism) or π/2 (4r2)(h) or 2πrh.
C) π/4(the volume of the prism) or π/4 (2r)(h) or π/4(r2h).
D) π/4(the volume of the prism) or π/4 (4r2)(h) or πr2h.
See attachment for diagram
Step-by-step explanation:
Area of the cross section in the cylinder
Area of circle = πr²
Area of the cross section in the square prism
Area of square = (side length)²
Here the side length = diameter
Diameter = 2×radius = 2r
Area of square = (2r)² = 4r²
Ratio of area of circle to area of square = πr²/4r² = π/4
Area of circle/area of square = π/4
Area of circle = π/4 × area of square
Area of circle = π/4 × 4r²
Volume of cylinder = area of circle × height
Volume = πr² ×h = πr²h
Volume of square prism = area of square × height = (2r)²h = 4r²h
Ratio of volume of cylinder to volume of square prism = πr²h/4r²h = π/4
Volume of cylinder/volume of square prism = π/4
Volume of cylinder = π/4 × volume of square prism = π/4 × 4r²h
= πr²h
Therefore Volume of cylinder = π/4 (the volume of the prism) or π/4 (4r²)(h) or πr²h (D)
20. The profit of a company increased steadily over a ten-year span. The following ordered pairs show the number of units sold in hundreds and the profit in thousands of units over the ten-year span, (number of units sold, profit) for specific recorded years: (46,250), (48, 305), (50,350), (52, 390), (54, 410) a) Use linear regression to determine a function y, where profit in thousands of dollars depends on the number of units sold in hundreds. b) Predict when the profit will exceed one million dollars.
Answer:
20
Step-by-step explanation:
The linear function represents the number of units sold y in terms of profit x is y = 27.5x - 1015.
What is a linear function?
A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant slope.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
As per the given pair of (number of units sold y, profit x)
Linear equation slope and y-intercept
A linear equation or function is given as ;
y = mx + c
Here, c is the y-intercept and m is the slope.
The slope associated with two points (x₁, y₁) and (x₂, y₂) is given by
Slope m = (y₂ - y₁)/(x₂ - x₁)
Therefore slope of (46,250), (48, 305)
m = (305 - 250)/(48 - 46) = 27.5
Put, m = 27.5 and (46,250)
250 = 27.5(46) + c
c = -1015
y = 27.5x - 1015
Hence "The linear function represents the number of units sold y in terms of profit x is y = 27.5x - 1015".
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Please answer this correctly
Answer:
The second question
Step-by-step explanation:
The orca starts at -25 meters. She goes up 25 meters.
up 25 = +25
-25+25=0
Answer:
Option 2
Step-by-step explanation:
The orca swims at the elevation of -25 meters. The orca swims up 25 meters higher than before.
-25 + 25 = 0
www.g A survey of athletes at a high school is conducted, and the following facts are discovered: 19% of the athletes are football players, 79% are basketball players, and 14% of the athletes play both football and basketball. An athlete is chosen at random from the high school: what is the probability that they are either a football player or a basketball player
Answer:
84%
Step-by-step explanation:
The probability that the selected player is a football player, P(F)=19%
The probability that the selected player is a basketball player, P(B)=79%
The probability that the selected player play both football and basketball,
[tex]P(B \cap F)=14\%[/tex]
We want to determine the probability that a randomly chosen athlete is either a football player or a basketball player, [tex]P(B \cup F)[/tex]
In probability theory
[tex]P(B \cup F)=P(B)+P(F)-P(B \cap F)\\=79\%+19\%-14\%\\=84\%[/tex]
The probability that a randomly chosen athlete is either a football player or a basketball player is 84%.
To get from North to East, you walk 12 meters south and 16 meters east, as shown
in the diagram below. If you wanted to walk straight from North to East, what would
the distance be? Solve for x
Answer:
ur pito is to small
Step-by-step explanation:
it to little
forex is the name of the U.S. stock exchange.
-true
-false
Answer:
false
Step-by-step explanation:
hello
this is false
FOREX means Foreign Exchange
it refers to the foreign exchange market
hope this helps
Answer:
true, forex trading is a profitable than staking cryptocurrency. forex trading is the best thing I will refer someone I love because learning never stops and no on is above blowing accounts when beginning Forex
Determine if the matrix below is invertible. Use as few calculations as possible. Justify your answer. 3 0 -4 2 0 6 -3 0 8
a. The matrix is invertible. The columns of the given matrix span R^3.
b. The matrix is not invertible. If the given matrix is A, the columns of A do not form a linearly independent set.
c. The matrix is invertible. The given matrix has 2 pivot positions.
d. The matrix is not invertible. If the given matrix is A, the equation Ax = 0 has only the trivial solution.
Answer:
b. The matrix is not invertible. If the given matrix is A, the columns of A do not form a linearly independent set.
Step-by-step explanation:
A square matrix is said to be invertible if the product of the matrix and its inverse result into an identity matrix.
3 0 -4
2 0 6
-3 0 8
Since the second column elements are all zero, the determinant of the matrix is zero ad this implies that the inverse of the matrix does not exist(i.e it is not invertible )
A square matrix is said to be invertible if it has an inverse.
The matrix is not invertible. If the given matrix is A, the columns of A do not form a linearly independent set.
The matrix is given as:
[tex]\left[\begin{array}{ccc}3&0&-4\\2&0&6\\-3&0&8\end{array}\right][/tex]
Calculate the determinant
The determinant of the matrix calculate as:
[tex]|A| = 3 \times(0 \times 8- 6 \times 0) - 0(2 \times 8 - 6 \times -3) -4(2 \times 0 - 0 \times -3)[/tex]
[tex]|A| = 3 \times(0) - 0(34) -4(0)[/tex]
[tex]|A| = 0 - 0 -0[/tex]
[tex]|A| = 0[/tex]
When a matrix has its determinant to be 0, then
It is not invertibleIt does not form a linear independent set.Hence, the correct option is (b)
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Nine balls, each marked with a number from 1 to 9, are placed in a bag and one
Ball is taken out at random. What is the probability that the number on the ball is:
(a) odd, (b) a multiple of 3, (c) 5, (d) not a 7
Answer:
a =5/9 b=1/3 c=1/9 d=8/9
Step-by-step explanation:
there are total 9 numbers
in a
there are 5 odd numbers
in b
there are 3 multiplier of 3
in c
there is only one 5
in d
there are 8 numbers except 7
a) 5/9 b) 1/3 c) 1/9 d) 8/9
Step-by-step explanation:
a) odd numbers between 1 to 9 are 1,3,5,7,9. so there are 5 odd numbers.
total balls are 9
=> probability is 5/9
b) multiples of 3 = 3, 6,9 there are 3 numbers.
=> probability is = 3/9 = 1/3
c) 5. only one 5 is there between 1 to 9 numbers.
=> probability is 1/9
d) not a 7.
removing 7. there will 8 numbers.
=> probability is 8/9
The price of a vase was increased by 10% to £22.What was the price before the increase
Answer: £20.
Step-by-step explanation:
Let the old price = £x
Percent increase. = 10%
Increment. = 10% of £x
= 10x/100
Now new price = £22
To determine the old price we have
x + 10x/100. = 22
We now multiply everything by 100 to make it a linear expression
100x + 10x = 2200
110x = 2200, therefore
x. = 2200/110
= £20
Therefore, the price before the increase. = £20.
Find the product of all positive integer values of $c$ such that $3x^2+7x+c=0$ has two real roots. I will award a lot of points
Answer: 24
Step-by-step explanation:
Let's find one solution:
3x² + 7x + c = 0
a=3 b=7 c=c
First, let's find c so that it has REAL ROOTS.
⇒ Discriminant (b² - 4ac) ≥ 0
7² - 4(3)c ≥ 0
49 - 12c ≥ 0
-12c ≥ -49
[tex]c\leq\dfrac{-49}{-12}\quad \rightarrow c\leq \dfrac{49}{12}[/tex]
Since c must be a positive integer, 1 ≤ c ≤ 4
Example: c = 4
3x² + 7x + 4 = 0
(3x + 4)(x + 1) = 0
x = -4/3, x = -1 Real Roots!
You need to use Quadratic Formula to solve for c = {1, 2, 3}
Valid solutions for c are: {1, 2, 3, 4)
Their product is: 1 x 2 x 3 x 4 = 24
Answer:
$3x^2+7x+c=0$
comparing above equation with ax²+bx+c
a=3
b=7
c=1
using quadratic equation formula
[tex]x = \frac{ - b + - \sqrt{b {}^{2} - 4ac} }{ 2a} [/tex]
x=(-7+-√(7²-4×3×1))/(2×3)
x=(-7+-√13)/6
taking positive
x=(-7+√13)/6=
taking negative
x=(-7-√13)/6=
A rookie quarterback is negotiating his first NFL contract.His opportunity cost is 10%. He has been offered three possible 4-year contracts. Payments are guaranteed, and they would be made at the end of each year. Terms of each contract are as follows:________.
1 2 3 4
Contract 1 $3,000,000 $3,000,000 $3,000,000 $3,000,000
Contract 2 $2,000,000 $3,000,000 $4,000,000 $5,000,000
Contract 3 $7,000,000 $1,000,000 $1,000,000 $1,000,000
As his advisor, which contract would you recommend that he accept?
Answer:
He should accept contract 2 because it has a higher present value.
Step-by-step explanation:
we need to find the present value of each contract:
Contract 1 = $3,000,000/1.1 + $3,000,000/1.1² + $3,000,000/1.1³ + $3,000,000/1.1⁴ = $2,727,273 + $2,479,339 + $2,253,944 + $2,049,040 = $9,509,596
Contract 2 $2,000,000/1.1 + $3,000,000/1.1² $4,000,000/1.1³ + $5,000,000 /1.1⁴ = $1,818,182 + $2,479,339 + $3,005,259 + $3,415,067 = $10,717,847
Contract 3 $7,000,000/1.1 + $1,000,000/1.1² + $1,000,000/1.1³ + $1,000,000/1.1⁴ = $6,363,636 + $826,446 + $751,315 + $683,013 = $8,624,410
If f(x)=2x−1, show that f(f(x))=4x−3. Find f(f(f(x))).
Answer: f(f(f(x)))=8x-7
Step-by-step explanation:
Since we were given f(x) and f(f(x)), We plug that into f(x) again to get f(f(f(x))).
2(4x-3)-1 [distribute]
8x-6-1 [combine like terms]
8x-7
The total area under the standard normal curve to the left of zequalsnegative 1 or to the right of zequals1 is
Answer:
0.3174
Step-by-step explanation:
Z-score:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the area under the normal curve to the left of Z. Subtracting 1 by the pvalue, we find the area under the normal curve to the right of Z.
Left of z = -1
z = -1 has a pvalue of 0.1587
So the area under the standard normal curve to the left of z = -1 is 0.1587
Right of z = 1
z = 1 has a pvalue of 0.8413
1 - 0.8413 = 0.1587
So the area under the standard normal curve to the right of z = 1 is 0.1587
Left of z = -1 or right of z = 1
0.1587 + 0.1587 = 0.3174
The area is 0.3174
(0, 3) and (-2, -1)
Write an equation in slope intercept from of the line that passes through the given points.
Answer:
y = 2x + 3
Step-by-step explanation:
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Slope-Intercept Form: y = mx + b
Step 1: Find slope m
m = (-1 - 3)/(-2 - 0)
m = -4/-2
m = 2
y = 2x + b
Step 2: Rewrite equation
y = 2x + 3
*You are given y-intercept (0, 3), so simply add it to your equation.
If the 2412 leaves are not a random sample, but the researchers treated the 2412 leaves as a random sample, this most likely made the data more:_____________.1. accurate, but not precise2. precise, but not accurate3. neither4. both accurate and precise
Answer:
2. Precise but not accurate
Step-by-step explanation:
In a high precision, low accuracy case study, the measurements are all close to each other (high agreement between the measurements) but not near/or close to the center of the distribution (how close a measurement is to the correct value for that measurement)
What number must you add to complete the square?
X^2 + 8x= 11
A. 12
B. 16
c. 8
D. 4
Answer:
16
Step-by-step explanation:
X^2 + 8x= 11
Take the coefficient of x
8
Divide by 2
8/2 =4
Square it
4^2 = 16
Add 16 to each side
F (X) = x² - 2x and 6(x) = 3x+1
A) Find F(g(-4))
B) Find F(g(x)) simply
C) find g^-1 (x)
Part A
g(x) = 3x+1
g(-4) = 3(-4)+1 ... every x replaced with -4
g(-4) = -12+1
g(-4) = -11
Plug this into the f(x) function
f(x) = x^2 - 2x
f( g(-4) ) = (g(-4))^2 - 2( g(-4) )
f( g(-4) ) = (-11)^2 - 2(-11)
f( g(-4) ) = 121 + 22
f( g(-4) ) = 143 is the answer====================================================
Part B
Plug the g(x) function into the f(x) function
f(x) = x^2 - 2x
f( g(x) ) = ( g(x) )^2 - 2( g(x) ) ... replace every x with g(x)
f( g(x) ) = (3x+1)^2 - 2(3x+1)
f( g(x) ) = (9x^2+6x+1) + (-6x-2)
f( g(x) ) = 9x^2+6x+1-6x-2
f( g(x) ) = 9x^2-1 is the answerNote that we can plug x = -4 into this result and we would get
f( g(x) ) = 9x^2-1
f( g(-4) ) = 9(-4)^2-1
f( g(-4) ) = 9(16)-1
f( g(-4) ) = 144-1
f( g(-4) ) = 143 which was the result from part A
====================================================
Part C
Replace g(x) with y. Then swap x and y. Afterward, solve for y to get the inverse.
[tex]g(x) = 3x+1\\\\y = 3x+1\\\\x = 3y+1\\\\3y+1 = x\\\\3y = x-1\\\\y = \frac{1}{3}(x-1)\\\\y = \frac{1}{3}x-\frac{1}{3}\\\\g^{-1}(x) = \frac{1}{3}x-\frac{1}{3}\\\\[/tex]
Want Brainliest? Get this correct Which of the following is the product of the rational expressions shown below?
We multiply the numerators together to get x*2x = 2x^2 as the numerator for the answer.
The denominators pair up and multiply to get (x-5)(x+4) = x^2+4x-5x-20 = x^2-x-20. You can use the distributive property, FOIL, or the box method to expand out (x-5)(x+4)
So that's how we end up with (2x^2) all over (x^2-x-20) as the answer.
1. Lisa is a regional manager for a restaurant chain that has locations in the towns of Berwick, Milton, and Leesburg. She would like to investigate if a difference exists in the proportion of customers who rate their experience as satisfactory or better between the three locations. The following data represent the number of customers who indicated they were satisfied from random samples taken at each location.
Berwick Milton Leesburg
Number Satisfied 80 85 60
Sample Size 100 120 80
The expected frequency of satisfied customers from the Berwick sample is________.
a. 60
b. 75
c. 80
d. 90
2. Lisa is a regional manager for a restaurant chain that has locations in the towns of Berwick, Milton, and Leesburg. She would like to investigate if a difference exists in the proportion of customers who rate their experience as satisfactory or better between the three locations. The following data represent the number of customers who indicated they were satisfied from random samples taken at each location.
Berwick Milton Leesburg
Number Satisfied 80 85 60
Sample Size 100 120 80
The expected frequency of satisfied customers from the Milton sample is________.
a. 60
b. 75
c. 80
d. 90
3. Lisa is a regional manager for a restaurant chain that has locations in the towns of Berwick, Milton, and Leesburg. She would like to investigate if a difference exists in the proportion of customers who rate their experience as satisfactory or better between the three locations. The following data represent the number of customers who indicated they were satisfied from random samples taken at each location.
Berwick Milton Leesburg
Number Satisfied 80 85 60
Sample Size 100 120 80
The expected frequency of satisfied customers from the Leesburg sample is________.
a. 60
b. 75
c. 80
d. 90
4. Lisa is a regional manager for a restaurant chain that has locations in the towns of Berwick, Milton, and Leesburg. She would like to investigate if a difference exists in the proportion of customers who rate their experience as satisfactory or better between the three locations. The following data represent the number of customers who indicated they were satisfied from random samples taken at each location.
Berwick Milton Leesburg
Number Satisfied 80 85 60
Sample Size 100 120 80
The chi-square test statistic for these samples is_______.
a. 1.49
b. 2.44
c. 4.15
d. 5.33
5. Lisa is a regional manager for a restaurant chain that has locations in the towns of Berwick, Milton, and Leesburg. She would like to investigate if a difference exists in the proportion of customers who rate their experience as satisfactory or better between the three locations. The following data represent the number of customers who indicated they were satisfied from random samples taken at each location.
Berwick Milton Leesburg
Number Satisfied 80 85 60
Sample Size 100 120 80
The degrees of freedom for the chi-square critical value is_______.
a. 1
b. 2
c. 3
d. 4
6. Lisa is a regional manager for a restaurant chain that has locations in the towns of Berwick, Milton, and Leesburg. She would like to investigate if a difference exists in the proportion of customers who rate their experience as satisfactory or better between the three locations. The following data represent the number of customers who indicated they were satisfied from random samples taken at each location.
Berwick Milton Leesburg
Number Satisfied 80 85 60
Sample Size 100 120 80
The chi-square critical value using alpha = 0.05 is_______.
a. 2.706
b. 3.841
c. 5.991
d. 7.815
7. Lisa is a regional manager for a restaurant chain that has locations in the towns of Berwick, Milton, and Leesburg. She would like to investigate if a difference exists in the proportion of customers who rate their experience as satisfactory or better between the three locations. The following data represent the number of customers who indicated they were satisfied from random samples taken at each location.
Berwick Milton Leesburg
Number Satisfied 80 85 60
Sample Size 100 120 80
Using alpha = 0.05, the conclusion for this chi-square test would be that because the test statistic is
A. More than the critical value, we can reject the null hypothesis and conclude that there is a difference in proportion of satisfied customers between these three locations.
B. Less than the critical value, we can reject the null hypothesis and conclude that there is a difference in proportion of satisfied customers between these three locations.
C. More than the critical value, we fail to reject the null hypothesis and conclude that there is no difference in proportion of satisfied customers between these three locations.
D. Less than the critical value, we fail to reject the null hypothesis and conclude that there is no difference in proportion of satisfied customers between these three locations.
Answer:
1) Option B is correct.
Expected frequency of satisfied customers from the Berwick sample = 75
2) Option D is correct.
Expected frequency of satisfied customers from the Milton sample = 90
3) Option A is correct.
Expected frequency of satisfied customers from the Leesburg sample = 60
4) Option B is correct.
The chi-square test statistic for these samples = 2.44
5) Option B is correct.
The degrees of freedom for the chi-square critical value = 2
6) Option C is correct.
The chi-square critical value using alpha = 0.05 is 5.991
7) Option D is correct.
The conclusion for this chi-square test would be that because the test statistic is less than the critical value, we fail to reject the null hypothesis and conclude that there is no difference in proportion of satisfied customers between these three locations.
Step-by-step explanation:
Berwick Milton Leesburg
Number Satisfied 80 85 60
Unsatisfied 20 35 20
Sample Size 100 120 80
Since this is a chi test that aims to check if there are differences in the proportion of expected number of customers for each location, we state the null and alternative hypothesis first.
The null hypothesis usually counters the claim we hope to test and would be that there is no difference between the proportion of expected frequency of satisfied customers at the three locations.
The alternative hypothesis confirms the claim we want to test and is that there is a significant difference between the proportion of expected frequency of satisfied customers at the three locations.
So, the total proportion of satisfied customers is used to calculate the expected number of satisfied customers for each of the three locations.
80+85+60= 225
Total number of customers = 100 + 120 + 80 = 300
Proportion of satisfied customers = (225/300) = 0.75
1) Expected frequency of satisfied customers from the Berwick sample = np = 100 × 0.75 = 75
2) Expected frequency of satisfied customers from the Milton sample = np = 120 × 0.75 = 90
3) Expected frequency of satisfied customers from the Leesburg sample = np = 80 × 0.75 = 60
4) Berwick Milton Leesburg
Number Satisfied 80 85 60
Unsatisfied 20 35 20
Sample Size 100 120 80
Proportion for unsatisfied ccustomers = 0.25
So, expected number of unsatisfied customers for the three branches are 25, 30 and 20 respectively.
Chi square test statistic is a sum of the square of deviations from the each expected value divided by the expected value.
χ² = [(X₁ - ε₁)²/ε₁] + [(X₂ - ε₂)²/ε₂] + [(X₃ - ε₃)²/ε₃] + [(X₄ - ε₄)²/ε₄] + [(X₅ - ε₅)²/ε₅] + [(X₆ - ε₆)²/ε₆]
X₁ = 80, ε₁ = 75
X₂ = 85, ε₂ = 90
X₃ = 60, ε₃ = 60
X₄ = 20, ε₄ = 25
X₅ = 35, ε₅ = 30
X₆ = 20, ε₆ = 20
χ² = [(80 - 75)²/75] + [(85 - 90)²/90] + [(60 - 60)²/60] + [(20 - 25)²/25] + [(35 - 30)²/30] + [(20 - 20)²/20]
χ² = 0.3333 + 0.2778 + 0 + 1 + 0.8333 + 0 = 2.4444 = 2.44
5) The degree of freedom for a chi-square test is
(number of rows - 1) × (number of columns - 1)
= (2 - 1) × (3 - 1) = 1 × 2 = 2
6) Using the Chi-square critical value calculator for a degree of freedom of 2 and a significance level of 0.05, the chi-square critical value is 5.991.
7) Interpretation of results.
If the Chi-square test statistic is less than the critical value, we fail to reject the null hypothesis.
If the Chi-square test statistic is unusually large and is greater than the critical value, we reject the null hypothesis.
For this question,
Chi-square test statistic = 2.44
Critical value = 5.991
2.44 < 5.991
test statistic < critical value
The test statistic is Less than the critical value, we fail to reject the null hypothesis and conclude that there is no difference in proportion of satisfied customers between these three locations.
Hope this Helps!!!
please i need this answer right now !!!! Dx
Answer: the answer is d sin30degrees equal 5/x because sin is opposite over hyponuese
[PLEASE HELP] Each of these statements describe a transformation of a graph of y = x, The which of the statements correctly describe the graph of y =x + 7???
Answer:
B
Step-by-step explanation:
Adding the 7 to the input (x) will increase the output (y) by 7. Therefore, the graph is translated 7 units up.
Answer:
The answer is B
Step-by-step explanation:
well the equation of a line is : y = mx + b
in this question the equation is y = x
so the line y = x +7 will be 7 units up than y = x
How do you determine whether the sign of a trigonometric function (sine, cosine, tangent) is positive or negative when dealing with half angles? Explain your reasoning and cite examples. Why do you think the half-angle identities include positive and negative options but the other identities don't seem to have this option built in?
Answer:
This question is about:
sin(A/2) and cos(A/2)
First, how we know when we need to use the positive or negative signs?
Ok, this part is kinda intuitive:
First, you need to know the negative/positve regions for the sine and cosine function.
Cos(x) is positive between 270 and 90, and negative between 90 and 270.
sin(x) is positive between 0 and 180, and negative between 180 and 360.
Then we need to see at the half-angle and see in which region it lies.
If the half-angle is larger than 360°, then you subtract 360° enough times such that the angle lies in the range between (0° and 360°)
and: Tan(A/2) = Sin(A/2)/Cos(A/2)
So using that you can infer the sign of the Tan(A/2)
Now, why these relationships use the two signs?
Well... this is because of the square root in the construction of the relationships.
This happens because:
(-√x)*(-√x) = (-1)*(-1)*(√x*√x) = (√x*√x)
For any value of x.
so both -√x and √x are possible solutions of these type of equations, but for the periodic nature of the sine and cosine functions, we can only select one of them.
So we should include the two possible signs, and we select the correct one based on the reasoning above.
Suppose that the scores of bowlers in particular league follow a normal distribution such that the standard deviation of the population is 6. Find the 95% confidence interval of the mean score for all bowlers in this league, using the accompanying data set of 10 random scores. Round your answers to two decimal places and use ascending order. Score 86 86 93 88 98 107 93 75 89
Answer:
A 95% confidence interval for the population mean score for all bowlers in this league is [86.64, 94.48].
Step-by-step explanation:
Since in the question only 9 random scores are given, so I am performing the calculation using 9 random scores.
We are given that the scores of bowlers in particular league follow a normal distribution such that the standard deviation of the population is 6.
The accompanying data set of 9 random scores in ascending order is given as; 75, 86, 86, 88, 89, 93, 93, 98, 107
Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;
P.Q. = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\bar X[/tex] = sample mean score = [tex]\frac{\sum X}{n}[/tex] = [tex]\frac{815}{9}[/tex] = 90.56
[tex]\sigma[/tex] = population standard deviation = 6
n = sample of random scores = 9
[tex]\mu[/tex] = population mean score for all bowlers
Here for constructing a 95% confidence interval we have used a One-sample z-test statistics because we know about population standard deviation.
So, 95% confidence interval for the population mean, [tex]\mu[/tex] is ;
P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5% level
of significance are -1.96 & 1.96}
P(-1.96 < [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < 1.96) = 0.95
P( [tex]-1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\bar X-\mu}[/tex] < [tex]1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ) = 0.95
P( [tex]\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ) = 0.95
95% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] , [tex]\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ]
= [ [tex]90.56-1.96 \times {\frac{6}{\sqrt{9} } }[/tex] , [tex]90.56+1.96 \times {\frac{6}{\sqrt{9} } }[/tex] ]
= [86.64 , 94.48]
Therefore, a 95% confidence interval for the population mean score for all bowlers in this league is [86.64, 94.48].
Phil Nelson deposited $35,000 at Wachovia Bank at 3.5% interest
compounded quarterly. How much money will be in this account at
the end of the year?
Answer:
$36,241.20
Step-by-step explanation:
Compounded Interest Rate Formula: A = P(1 + r/n)^nt
Since we are given P, r, n, and t, simply plug it into the formula:
A = 35000(1 + 0.035/4)⁴⁽¹⁾
A = 35000(1 + 0.00875)⁴
A = 35000(1.00875)⁴
A = 35000(1.03546)
A = 36241.2
Researchers wanted to know whether it is better to give the diphtheria, tetanus and pertussis (DTaP) vaccine in the thigh or the arm. They collect data on severe reactions to this vaccine in children aged 3 to 6 years old. What would be the best statistical test for them to utilize?
A. One-sample chi-square
B. Linear regression
C. T-test
D. Two-sample chi-square
Answer:
D. Two-sample chi-square
Step-by-step explanation:
A chi-square test is a test used to compare the data that is observed, from the data that is expected.
In a two-sample chi-square test the observed data should be similar to the expected data if the two data samples are from the same distribution.
The hypotheses of the two-sample chi-square test is given as:
H0: The two samples come from a common distribution.
Ha: The two samples do not come from a common distribution
Therefore, in this case, the best statistical test to utilize is the two-sample chi-square test.
PLS HELP ASAP!!!!........
Answer:
aaaaha pues
Step-by-step explanation:
Answer:
what happened
Step-by-step explanation:
I don't know what to do.
Answer:
104.93 in
Step-by-step explanation:
When we draw out a picture of our triangle, we should see that we need to use sin∅ to solve:
sin23° = 41/x
xsin23° = 41
x = 41/sin23°
x = 104.931
Solve the system of equations for the variables: x+2y-z=3 x+y-2z= -1
Answer:
z=0
x= -5
y=4
Step-by-step explanation:
Check the attachment please
Hope this helps :)
Step-by-step explanation:
x + 2y − z = 3
x + y − 2z = -1
There are three variables but only two equations, so this system of equations is undefined. We cannot solve for the variables, but we can eliminate one of them and reduce this to a single equation.
Double the first equation:
2x + 4y − 2z = 6
Subtract the second equation.
(2x + 4y − 2z) − (x + y − 2z) = (6) − (-1)
2x + 4y − 2z − x − y + 2z = 7
x + 3y = 7