Most Algebra 1 Formulas for needed for CST
Answers
The below would be most important Algebra 1 Formulas for CST.
Linear Equation:
\(Ax + By + C = 0\)
Equation of Straight Line or Slope:
\(y = mx+b\)
Point-slope form:
\(y-y_{1} = m(x-x_1)\)
Slope when 2 points are given:
\(m = \frac{(y_2 - y_1)}{(x_2-x_1)}\)
Quadratic Equation:
\(Ax^2 + Bx +C = 0\)
When lines are parallel:
Slope of both lines are equal. \(m_1 = m_2\)
When lines are perpendicular:
Slope of perpendicular lines are opposite reciprocals, meaning if the slope of a line \(l_1\) is \(\frac{1}{2}\). The line \(l_2\) perpendicular to \(l_1\) is \(-\frac{2}{1}\).
Work Formula:
Total Work Done = Number of Days \(\times\) Efficiency
where Efficiency is inversely proportional to Time Taken.
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Related Questions
5. This prism has a right triangle for a base. The volume of the prism is 54 cubic units.
What is the value of h?
units
4
A
C
5
h
D
B
Answers
If the volume is 54 cubic units, then the value of h must be 9 units.
What is the value of h?The volume of the triangular prism will be:
V = A*h
Where A is the area of the triangle face, we know that for a triangle of base B and height H is:
A = B*H/2
Looking at the image we can see that the base is 4 units and the hypotenuse is 5 units, then the height is:
height = √(5² - 4²) = 3
Then the area is:
A = 4*3/2 = 6 square units.
We know that the volume of the prism is 54 cubic units, then:
54 cubic units = (6 square units)*h
(54 cubic units)/(6 square units) = h
9 units = h
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When we multiply a number by a positive power of 10, we move the decimal point to which direction?
A. left
B. right
C. either
D. we don't move the decimal point
Answers
Answer:
C
Step-by-step explanation:
It goes to the left when multiplied with positive 10
someone designed a game that attracts children. in case of the child won they will get a gift otherwise the child will lose their money. There is a box filled with n balls
• The child along with the game owner switch turns such that in each turn a player
could draw k balls at once at two conditions:
√k ∈ Z ∧ 1 ≤ k ≤ n
• The child draws first.
• The player who draws the last ball, wins
I am trying to design a recursive algorithm in Python programming language that takes
input N
output: true if the child won otherwise false
Answers
The algorithm is designed to find out whether the child wins or loses in a game where two players take turns to pick balls. The algorithm takes the number of balls remaining in the box as input and returns True if the child wins, otherwise False.
The algorithm assumes that both players play optimally. The algorithm works by recursively picking balls from the box and checking whether the child or the game owner wins the game.
This is a recursive problem where each player plays optimally. There are two players in the game. The child will pick the balls first and then the game owner takes turns. Both will pick the balls optimally in order to win.
In each turn, k balls can be picked from the box. The winner is the one who picks the last ball. If the child picks the last ball, they win otherwise the game owner wins.
The algorithm is as follows:
Algorithm - Pick Balls
1. Define a recursive function called PickBalls(n). The function takes one parameter as input, which is the number of balls remaining in the box.
2. Check if the number of balls remaining is less than or equal to k. If yes, then return True as the game has ended and the child has won.
3. If the number of balls is greater than k, then pick k balls from the box.
4. If the child picks the last ball, then return True.
5. If the child does not pick the last ball, then the game owner picks the balls recursively.
6. If the game owner picks the last ball, then return False. Otherwise, return True.
Explanation: We are designing a recursive algorithm to find out whether the child will win or lose in a game where two players take turns to pick balls. The algorithm takes the number of balls remaining in the box as input and returns True if the child wins, otherwise False. We are assuming that both players play optimally. The algorithm works as follows:
If the number of balls remaining in the box is less than or equal to k, then the child can pick all the balls and win the game. Therefore, the function returns True.
If the number of balls remaining in the box is greater than k, then the child picks k balls from the box. If the child picks the last ball, then they win the game. Therefore, the function returns True.
If the child does not pick the last ball, then the game owner picks the balls recursively. If the game owner picks the last ball, then they win the game. Therefore, the function returns False. If the game owner does not pick the last ball, then the child picks again and the process repeats itself. If the child eventually picks the last ball, then they win the game. Therefore, the function returns True.
Conclusion: The algorithm is designed to find out whether the child wins or loses in a game where two players take turns to pick balls. The algorithm takes the number of balls remaining in the box as input and returns True if the child wins, otherwise False. The algorithm assumes that both players play optimally. The algorithm works by recursively picking balls from the box and checking whether the child or the game owner wins the game.
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a rectangle with an area if 32 sqaure units and a perimter of 36 sqaure units
Answers
Let X be a random variable with cumulative distribution function (cdf) given by Fx (x) = {1 - e^(-bx^2), x > 0 0, x < 0
where b>0 is a known constant. (i) Find the pdf of the random variable X.
(ii) Find the pdf of the random variable Y = X2.
Answers
(i) The pdf of random variable X is:
\(fx(x) = {2bx e^{(-bx^2)}\), x > 0
0, x < 0
(ii) The pdf of Y is:
\(fy(y) = b\sqrt y / e^{(by)} , y > 0\)
0, y ≤ 0
(i) To find the probability density function (pdf) of X, we need to take the derivative of the cumulative distribution function (cdf) with respect to x.
For x > 0, we have:
\(Fx(x) = 1 - e^{(-bx^2)}\)
Differentiating both sides with respect to x gives:
fx(x) = d/dx Fx(x) = \(d/dx [1 - e^{(-bx^2)}] = 2bx e^{(-bx^2)}\)
For x < 0, we have:
Fx(x) = 0
Differentiating both sides with respect to x gives:
fx(x) = d/dx Fx(x) = d/dx [0] = 0
Therefore, the pdf of X is:
\(fx(x) = {2bx e^{(-bx^2)}\), x > 0
{0, x < 0
How to find the pdf of \(Y = X^2\)?(ii) To find the pdf of \(Y = X^2\), we can use the transformation method. The transformation function is \(g(x) = x^2\).
We have:
Fy(y) = P(Y ≤ y) = P(\(X^2\) ≤ y) = P(-√y ≤ X ≤ √y) = Fx(√y) - Fx(-√y)
Differentiating both sides with respect to y gives:
fy(y) = d/dy Fy(y) = d/dy [Fx(√y) - Fx(-√y)]
= (1/2y) fx(√y) - (-1/2y) fx(-√y)
\(= (1/2y) 2b\sqrt y e^{(-by)}\)
= \(b\sqrt y / e^{(by)}\)
Therefore, the pdf of Y is:
\(fy(y) = b\sqrt y / e^{(by)} , y > 0\)
0, y ≤ 0
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Can someone help me with this math please?
Answers
Answer: x = 30
Step-by-step explanation:
Since the triangles are similar, line EF corresponds to line JK
EF is 2.5 times bigger than JK
So the sides in the first triangle are 2.5 times bigger than the second triangle
Line FG corresponds to line KL so line FG / the value of X is 30 (12 * 2.5)
Write equation- \(\frac{12.5}{5} = \frac{x}{12}\)
Divide- \(2.5 = \frac{x}{12}\)
Multiply by 12- \(2.5(12) = \frac{x}{12}(12)\)
Answer- \(30 = x\)
so x = 30
can someone help I need an inequality that shows how much I can spend on brochures I have $1900 to spend and brochures cost $0.40 each
Answers
Answer:
0.40x=1900
Step-by-step explanation:
A= (a, b}
B = {1,2,3}
Select the expression that is an element of AxBxB.
a. (1,2,3)
b. (a, a,1)
c. (b,2^2)
d. (2.1.1)
Answers
The expression that is an element of AxBxB is (1,2,3)
The given data is A= (a, b}, B = {1,2,3}
The product of two matrices A and B is defined if the number of columns of A is equal to the number of rows of B. If both A and B are square matrices of the same order, then both AB and BA are defined.
\(& \ A \times B=\left\{\begin{array}{c}(a, 1),(a, 2),(a, 3),(b, 1) \\(b, 2),(b, 3)\end{array}\right. \\\)
\(& A \times B \times B=\left\{\begin{array}{l}(a, 1,1),(a, 1,2),(a, 1,3), \\(a, 2,1),(a, 2,2),(a, 2,3),\end{array}\right. \\& (a, 3,1),(a, 3,2),(a, 3,3) \\ & (b, 1,1),(b, 1,2),(b, 1,3) \\& \left.\begin{array}{l}(b, 2,1),(b, 2,2),(b, 2,3) \\(b, 3,1),(b, 2),(b, 3,3)\end{array}\right\} \\\)
\(& \therefore(b, 2,3) \in D \times B \times B \\\\& (a, a, 1) \notin A \times B \times B \\\\& \left(b, 2^2\right) \quad \forall A \times B \times B \\\\& (2,1,1) \notin A \times B \times B \\\\&=(b, 2,3) \in \cap \times B \times B \\&\end{aligned}\)
The union of two sets X and Y is equal to the set of elements that are present in set X, in set Y, or in both the sets X and Y.
The intersection of sets can be denoted using the symbol ‘∩’. As defined above, the intersection of two sets A and B is the set of all those elements which are common to both A and B. Symbolically, we can represent the intersection of A and B as A ∩ B.
Therefore, the expression that is an element of AxBxB is (1,2,3).
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a motorist is pumping gas into his car at a rate of 5/12 of a gallon every 1/24 of a minute. At this rate how many gallons of gas will he have pumped into his car in 1/2 of a minute?
Answers
Answer:
5 gallons.
Step-by-step explanation:
5*12=60
60/12=5
A sterilization procedure yields a decimal reduction time of
0.65 minutes. Calculate the minimum sterilization time required to
yield 99.9% confidence of successfully sterilizing 50 L of medium
containing 10^6 contaminating organisms using this procedure.
Answers
The minimum sterilization time required to achieve a 99.9% confidence level in successfully sterilizing 50 L of medium containing 10^6 contaminating organisms is approximately 1.95 minutes.
To calculate the minimum sterilization time required to yield 99.9% confidence of successfully sterilizing 50 L of medium containing 10^6 contaminating organisms, we need to use the concept of decimal reduction time (D-value) and the number of organisms.
The D-value represents the time required to reduce the population of microorganisms by one log or 90%. In this case, the given D-value is 0.65 minutes.
To achieve a 99.9% confidence level, we need to reduce the population of microorganisms by three logs or 99.9%, which corresponds to a 10^-3 reduction.
To calculate the minimum sterilization time, we can use the following formula:
Minimum Sterilization Time = D-value × log10(N0/Nf)
Where:
D-value is the decimal reduction time (0.65 minutes).
N0 is the initial number of organisms (10^6).
Nf is the final number of organisms (10^6 × 10^-3).
Let's calculate it step by step:
Nf = N0 × 10^-3
= 10^6 × 10^-3
= 10^3
Minimum Sterilization Time = D-value × log10(N0/Nf)
= 0.65 minutes × log10(10^6/10^3)
= 0.65 minutes × log10(10^3)
= 0.65 minutes × 3
= 1.95 minutes
Therefore, the minimum sterilization time required to yield 99.9% confidence of successfully sterilizing 50 L of medium containing 10^6 contaminating organisms using this procedure is approximately 1.95 minutes
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consider discrete random variables x and y . let y = ( 1 with probability 1/8 2 with probability 7/8 and given y = y, x = ( 2y with probability 3/4 4y with probability 1/4
Answers
The probability distribution of x depends on the value of y. When y is 1, x has a higher probability of being 2, while when y is 2, x is more likely to be 8.
The given information defines the probability distributions of both x and y. The variable y is a discrete random variable with two possible outcomes, 1 and 2. The probabilities assigned to each outcome, 1/8 and 7/8, indicate the likelihood of y taking on those values. Given the value of y, the variable x is determined. When y is 1, x takes on the value of 2y, which is 2.
This occurs with a probability of 3/4. On the other hand, when y is 2, x becomes 4y, resulting in a value of 8. This happens with a probability of 1/4. We have a random variable y that can take on the values 1 and 2 with probabilities of 1/8 and 7/8, respectively. Based on the value of y, the random variable x is determined to be 2y with a probability of 3/4 and 4y with a probability of 1/4.
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Please answer correctly !!!! Will mark brainliest !!!!!!!!!!!!!!
Answers
Answer:
A. 2.2
Step-by-step explanation:
The average rate of change between 2 x values is the total change of the y values (output values) divided by the change in the x values.Slope is special situation of that.
point 1 (x₁,y₁) → ( 2,7.5)
point 2 (x₂,y₂) → ( 18,42.5)
slope = 42.5 -7.5/18-2 =35 / 16 = 2.1875 ≈ 2.2
Cine ma poate ajuta?
Answers
Answer:
u think its A if not sorry
Step-by-step explanation:
Katie wants to collect over 100100100 seashells. She already has 343434 seashells in her collection. Each day, she finds 121212 more seashells on the beach. Katie can use fractions of days to find seashells.
Answers
Answer:
Step-by-step explanation:
So far, Charlie has driven 9.3 miles. He needs to drive a total of 29 miles. How many more miles must Charlie drive?
Answers
Answer:
19.7 miles
Step-by-step explanation:
29-9.3=19.7
Charlie has a total of 19.7 miles left to drive to get to 29 miles distance.
Find the volume of a pyramid with a square base, where the area of the base is 16\text{ m}^216 m
2
and the height of the pyramid is 25.4\text{ m}25.4 m. Round your answer to the nearest tenth of a cubic meter.
Answers
The volume of the pyramid with a square base is 135.5 cubic m if the base area is 16 cubic m and the height is 25.4 m.
What is a square pyramid?In geometry, it is defined as the shape having a square base with equal sides length and all the vertex of the square's joints at the top, which is perpendicular to the centre of the square.
We know the volume of the square pyramid V;
V = Bh/2
B is the base area, B = 16 square m
h is the height of the pyramid, h = 25.4 m
V = (16×25.4)/3
V = 135.46 ≈ 135.5 cubic m
Thus, the volume of the pyramid with a square base is 135.5 cubic m if the base area is 16 cubic m and the height is 25.4 m.
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If the density of gasoline is approximately 6 pounds per gallon, approximately what is the density of gasoline in grams per cubic centimeter? (Note: 1 gallon= 3,785.4 cubic centimeters and 1 kilogram= 2.2 pounds, both to the nearest 0.1.) 0.003 0.72 3.5 10,323 49,962
Answers
To convert the density of gasoline from pounds per gallon to grams per cubic centimeter, we need to perform the following conversions:
1 pound = 0.4536 kilograms (to the nearest 0.1)
1 gallon = 3,785.4 cubic centimeters (to the nearest 0.1)
First, let's convert pounds to kilograms:
6 pounds * 0.4536 kilograms/pound = 2.7216 kilograms (approximately, rounded to the nearest 0.1)
Next, let's convert gallons to cubic centimeters:
1 gallon = 3,785.4 cubic centimeters
Now, we can calculate the density of gasoline in grams per cubic centimeter:
Density = (Mass in grams) / (Volume in cubic centimeters)
Density = (2.7216 kilograms * 1000 grams/kilogram) / (3,785.4 cubic centimeters)
Density ≈ 0.718 grams per cubic centimeter (approximately, rounded to the nearest 0.1)
Therefore, the density of gasoline in grams per cubic centimeter is approximately 0.72 grams per cubic centimeter.
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christine baked 55 with 11 scoups of flour, how many scoups of flour does christine need in order to bake 70 cookies
Answers
when changing a percent to a fraction, what will the denominator be for 37.5% once the decimal point has been removed and before you simplify the fraction?
Answers
The percentage of 37.5% when converted to fraction, the denominator will be 1000.
The percentage is 37.5% , to convert it to fraction we have to divide the number that is in percentage by 100.
Hence, 37.5% = 37.5 / 100
Again When we remove the decimal we get that we will divide the number again by 10.
Hence the number becomes 375 / 1000.
Therefore we have to divide it by 1000 .
By employing an unlimited series of digits following the decimal separator, the decimal system has been expanded to represent any real number in an infinite number of decimals (see decimal representation).
The decimal numerals in this context are frequently referred to as terminating decimals since they have a limited amount of non-zero digits after the decimal separator. A repeating decimal is an infinite decimal that, after a certain point, repeats the same set of digits indefinitely.
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What
is the image of (-5, 3) after a reflection over the x-axis?
Answers
Answer: (-5, -3)
Step-by-step explanation:
The equipment will cost $26,000. What lump sum should be invested today at 6%, compounded semiannually, to yield $26,000?a. $ 17,189.06 b. $ ...
Answers
To yield $26,000 in the future, compounded semiannually at an interest rate of 6%, a lump sum investment needs to be made today. The correct amount to invest can be calculated using the present value formula.
The present value formula can be used to calculate the amount that should be invested today to achieve a specific future value. The formula is given by:
PV = FV / (1 + r/n)^(n*t)
In this case, the future value (FV) is $26,000, the interest rate (r) is 6%, and the compounding is semiannually (n = 2). We need to solve for the present value (PV).
Using the formula and substituting the given values:
PV = 26,000 / \((1 + 0.06/2)^(2*1)\)
PV = 26,000 / \((1.03)^2\)
PV = 26,000 / 1.0609
PV ≈ $24,490.92
Therefore, the correct lump sum to invest today, at 6% compounded semiannually, to yield $26,000 in the future is approximately $24,490.92.
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I need help pls
ASAP
Answers
Answer:
look at the picture ..........
solve for the volume of the cylinders and sphere.
Answers
The volume of the cylinder with radius(r) 7 inches and height(h) 9 inches
is 1384.74 cubic inches.
What is a cylindrical shape?A cylinder is a three-dimensional solid object with two bases that are identically circular and are connected by a curving surface that is located at a specific height from the center.
Examples of cylinders are toilet paper rolls and cold beverage cans.
The volume of a cylinder is πr²h.
Curved surface area = 2πrh.
Total surface area = 2πr(h + r).
Given, a cylindrical shape of radius(r) 7 inches and height(h) 9 inches.
We know the volume of a cylinder is πr²h.
∴ The volume of this cylinder is
= π×(7)²×9 cubic inches.
= 441π cubic inches.
= 1384.74 cubic inches.
For the volume of a sphere, it is (4/3)πr³.
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PLS HELP ASAP THANKS ILL GIVE BRAINLKEST PLS THANKS
Answers
A house on the market was valued at 428,000 . After several years, the value decreased by 7%. By how much did the house's value decrease in dollars? What is the current value of the house?
Answers
The house's value decreases by $29,960. The current value of the house is $398,040. The solution has been obtained by using arithmetic operations.
What are arithmetic operations?
The four fundamental operations that can be used to express any real number are referred to as "arithmetic operations" in mathematics. The four operations that produce quotient, product, sum, and difference are division, multiplication, addition and subtraction, respectively.
We are given that a house on the market was valued at $428,000.
After several years, the value decreased by 7%.
So, the price decreases by
$428,000 * (0.07) = $29,960
Now, the current value of the house is
$428,000 - $29,960 = $398,040
Hence, the house's value decreases by $29,960 and the current value of the house is $398,040.
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im not sure how to do this (7th grade math)
Answers
Answer:
The answer is: A
Step-by-step explanation:
Answer:
a) q<0
Step-by-step explanation:
\( \frac{q}{r} < 0 \\ = r \times \frac{q}{r} < 0 \times r \\ = q < 0\)
Which graph represents a function with amplitude 4 and period π?
On a coordinate plane, a cosine function has a maximum of 4 and minimum of negative 4. It completes one period at 2 pi.
On a coordinate plane, a cosine function has a maximum of 2 and minimum of negative 2. It completes one period at pi.
On a coordinate plane, a cosine function has a maximum of 2 and minimum of negative 2. It completes one period at 2 pi.
On a coordinate plane, a cosine function has a maximum of 4 and minimum of negative 4. It completes one period at pi.
Answers
The correct option is On a coordinate plane, a cosine function has a maximum of 4 and minimum of negative 4. It completes one period at pi.
What is amplitude?The maximum displacement or distance moved by a point on a vibrating body or wave measured from its equilibrium position.
Given:
function with amplitude 4 and period π.
also, The period of a wave is the time for a particle on a medium to make one complete vibrational cycle.
so, the amplitude 4 means function has a maximum of 4 and minimum of negative 4.
Hence, On a coordinate plane, a cosine function has a maximum of 4 and minimum of negative 4. It completes one period at pi.
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Answer:
D
Step-by-step explanation:
just took it
Recall that a cycle in an undirected graph is a sequence of distinct vertices (V1, V2, ..., Vk) with k > 3 such that the edges {V1, V2}, {V2, V3},..., {Uk-1, Vk} and also {Uk, v1} all exist. (a) Design an algorithm which given an undirected connected graph determines whether the graph has a cycle. If the graph has |V| vertices and |E| edges, your algorithm should run in O([V] + El) time. (b) Justify the correctness and run-time of your algorithm.
Answers
The overall runtime of the algorithm is O(|V|+|E|). The DFS algorithm has a runtime of O(|V|+|E|), as does the main algorithm, which runs DFS for each vertex.Therefore, the algorithm has a total runtime of O(|V|+|E|).
a) Algorithm to determine if a graph has a cycle:The algorithm is implemented using DFS (Depth First Search) traversal, which starts from every vertex in the graph. During the DFS traversal, we maintain a set of vertices on the current path. We continue DFS traversal of each unvisited neighbor vertex, and if a neighbor is already on the path set, then we have found a cycle.
The algorithm to determine if a graph has a cycle is given below -Graph G(V, E)Start DFS from each vertex v in VIf DFS utility detects a cycle, then return true.
Else, return false.Let's take a look at the DFS algorithm below -DFS(vertex u)
1. Mark u as visited.
2. For every unvisited neighbor v of u, doDFS(v)
3. If v is already on the current path, return true to denote the existence of a cycle.
4. If there is no cycle, return false to denote that the graph does not contain a cycle.
The overall runtime of the algorithm is O(|V|+|E|).
The DFS algorithm has a runtime of O(|V|+|E|), as does the main algorithm, which runs DFS for each vertex.
b) Justification of the correctness and runtime of the algorithm:The algorithm provided uses a DFS traversal.
Therefore, the algorithm can detect a cycle in an undirected connected graph. If there is a cycle, then the algorithm will correctly detect it.
Since the algorithm starts DFS from each vertex, it will detect the cycle even if it starts from a vertex other than the one containing the cycle.
Therefore, it's correct.The overall runtime of the algorithm is O(|V|+|E|). The DFS algorithm has a runtime of O(|V|+|E|), as does the main algorithm, which runs DFS for each vertex.
Therefore, the algorithm has a total runtime of O(|V|+|E|).
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the rescue center has budgeted a total of 2581.8 for this 30-day month. how many dogs are at the rescue center math problem
Answers
11423 be the number of dogs are at the rescue center.
What is Expression?An expression is combination of variables, numbers and operators.
A pet rescue center is creating a monthly food budget.
The center currently has two-thirds as many dogs as cats.
Each animal is fed 2 cans of food a day.
Dog food costs $0.08 per can, cat food costs $0.05 per can
The rescue center has budgeted a total 2581.8 of for food for this .
2(0.08)x+2(0.05)y= 2581.8
Let x be the number of dogs.
cats be y.
2/3x =y
2(0.08)x+2(0.05)2/3x= 2581.8
0.16x+0.066x=2581.8
0.226x=2581.8
x=11423
Hence, 11423 be the number of dogs are at the rescue center.
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Consider the hypotheses shown below. Given that x
ˉ
=119,σ=27,n=46,α=0.10, complete parts a through c below. H 0
:μ=128
H A
⩽μ
=128
a. State the decision rule in terms of tho criteal value(s) of the test statistic: Reject the null hypothesis it the calculated value of the tost statistic, is otherwise, do not roject the null hypothesis. (Round to two decimal places as needed. Use a comma to separate answers as needed.) b. Stase the calculated value of the tost statistic. Tho best stasistic is (Round to toro decimal paces as needod.) c. State the conclusion. Beceuse the test statiski the null hypothesis and conclude the pepulation moan equal to 120 .
Answers
a. Decision rule: Reject the null hypothesis if the calculated z-value is less than or equal to -1.28. b. Calculated z-value: -1.8892. c. Conclusion: Reject the null hypothesis, indicating evidence that the population mean is less than 128.
To complete parts (a) through (c), we need to perform a hypothesis test for the given hypotheses
H0: μ = 128 (null hypothesis)
HA: μ ≤ 128 (alternative hypothesis)
Given: X= 119 (sample mean)
σ = 27 (population standard deviation)
n = 46 (sample size)
α = 0.10 (significance level)
a. The decision rule is to reject the null hypothesis if the calculated value of the test statistic is less than or equal to the critical value(s) of the test statistic. Since the alternative hypothesis is one-sided (μ ≤ 128), we will use a one-sample z-test and compare the calculated z-value with the critical z-value.
To find the critical z-value, we need to determine the z-value corresponding to the significance level α = 0.10. Looking up the critical value in the standard normal distribution table, we find that the critical z-value is -1.28 (rounded to two decimal places).
b. The calculated value of the test statistic, in this case, is the z-value. We can calculate the z-value using the formula
z = (X - μ) / (σ / √n)
Substituting the given values:
z = (119 - 128) / (27 / √46) ≈ -1.8892 (rounded to two decimal places)
c. The conclusion is based on comparing the calculated value of the test statistic with the critical value. Since the calculated z-value of -1.8892 is less than the critical z-value of -1.28, we have enough evidence to reject the null hypothesis. Therefore, we conclude that the population mean is less than 128.
The conclusion statement in part (c) is inconsistent with the given alternative hypothesis and should be revised accordingly.
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