Answer:
To solve the quadratic equation 2x^2 + x - 3 = 0 by factoring, we follow these steps:
Step 1: Write the equation in standard quadratic form, which is ax^2 + bx + c = 0. In this case, the equation is already in standard form: 2x^2 + x - 3 = 0.
Step 2: Factor the quadratic expression on the left-hand side of the equation. We look for two numbers that multiply to give us the constant term (c) and add to give us the coefficient of the linear term (b). In this case, c = -3 and b = 1.
The two numbers that satisfy these conditions are -3 and 1, as -3 * 1 = -3 and -3 + 1 = -2.
Step 3: Use the factored form to set each factor equal to zero and solve for x.
2x^2 + x - 3 = 0
(2x - 3)(x + 1) = 0 (factored form)
Setting each factor equal to zero:
2x - 3 = 0
2x = 3
x = 3/2
x + 1 = 0
x = -1
So the solutions to the equation are x = 3/2 and x = -1.
A national survey of heads of households showed the percentage of those who asked for a raise and the percentage who got one. According to the survey, of the women interviewed, 24% had asked for a raise, and of those women who had asked for a raise, 45% received the raise. If a woman is selected at random from the survey population of women, find the following probabilities.
(a) P(woman asked for a raise) = _____.
(b) P(woman received raise, given she asked for one) = _____.
(c) P(woman asked for raise and received raise) = _____.
Probability
The following probabilities are found under the condition that a certain national survey of heads of households P(woman asked for a promotion) = 24%, P(woman received promotion, given she asked for one) = 45%, P(woman asked for promotion and received raise) = (24% x 45%) = 10.8%
Now,
Regarding a national survey concerning the head od households, only 24% of women interviewed had requested for a promotion and of those women who had asked for a promotion, 45% received the raise.
Therefore,
(a) P(woman asked for a promotion) = 24%
(b) P(woman received promotion, given she asked for one) = 45%
(c) P(woman asked for promotion and received raise) = (24% x 45%) = 10.8%
Probability refers to the percentage of an event taking place in a required time frame, in a specified place. It is considered a great aid in the fields of science and mathematics.
To learn more about probability,
https://brainly.com/question/30390037
#SPJ4
14 km
1. What is the circumference of the circle above?
Answer:
The Circumference of the circle shown in the picture is 87.96
Step-by-step explanation:
The formula in order to find the circumference is C=2πr.
r in this example is 14
so C= 2 * π * 14
π is always a constant value so all you have to do is add it to the calculator to get your answer.
Hope this helps!
C
A
2. A point C is on the line
segment AB such that A =
(4,3), B (14,7) and AC: CB =
2:3. Find the coordinate of C.
Answer:
Step-by-step explanation:
What is 2 X 2 X 8 + 25?
Answer:
57
Step-by-step explanation:
2 X 2 = 4
4 X 8 = 32
32 + 25 = 57
what is the correct alternative hypothesis for the wilcoxon rank sum test? group of answer choices ha: the two samples come from the same distribution. ha: the population slope coefficient is not equal to zero. ha: one distribution is shifted in location higher or lower than the other. ha: the population means are equal.
The correct alternative hypothesis for the Wilcoxon rank sum test is: ha: one distribution is shifted in a location higher or lower than the other. Option C is the answer.
This means that the test is designed to determine if there is a significant difference between the medians of two independent groups, rather than testing for a difference in means.
The null hypothesis for the test is that there is no significant difference between the two groups, while the alternative hypothesis states that there is a significant difference.
The Wilcoxon rank sum test is a nonparametric test and is used when the assumptions of the t-test are not met, such as non-normality or unequal variances.
Learn more about the alternative hypothesis at
https://brainly.com/question/27335001
#SPJ4
Use point-slope form to write the equation of a line that passes through the point (16,−14) with slope 1.
The equation of the line that passes through the point (16, -14) with slope 1 is y = x - 30.
What is meant by equation?
An equation is a mathematical statement that shows that two expressions are equal. It contains an equals sign and can include variables, constants, and mathematical operations. Equations are used to represent relationships between quantities and to solve problems in mathematics and science.
What is meant by slope?
Slope refers to the measure of the steepness of a line. It is calculated by dividing the change in the y-coordinate (vertical distance) by the change in the x-coordinate (horizontal distance) between two points on the line.
According to the given information
The point-slope form of the equation of a line is given by:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line and m is the slope of the line.
In this case, the line passes through the point (16, -14) and has a slope of 1. Plugging these values into the point-slope form, we get:
y - (-14) = 1(x - 16) y + 14 = x - 16 y = x - 30
So, the equation of the line that passes through the point (16, -14) with slope 1 is y = x - 30.
To know more about equation visit
brainly.com/question/10413253
#SPJ1
plsssssssss heelppp ...............
Answer:
hi i can help you if you want just text
ou and your friend join a new yoga studio that requires a one-time joining fee and monthly payments. (4.5 pts) a. if your friend stays with this studio for 15 months and pays $645 while you stay for 24 months and pay $852, write a linear function that describes the cost of studio membership, c, in terms of the number of months, m. (2.5 pts) a. what is the cost per month and what is the joining fee? (1 pt) b. determine the maximum number of months one can stay with this gym for $1500.
4⁄5 x + 15 = 3⁄10 x + 21
Answer:
x = 12
Step-by-step explanation:
If you're bored of solving equations the normal way, why not try this fun and easy method? Just follow these simple steps:
Subtract 3/10 x from both sides to eliminate the x term on the right side. This is like getting rid of the annoying person who always sits next to you in class.
4/5 x - 3/10 x + 15 = 21
Simplify the left side by finding the common denominator and combining the fractions. This is like putting all your candy in one bag and eating it faster.
(8/10 - 3/10) x + 15 = 21
5/10 x + 15 = 21
Subtract 15 from both sides to isolate the x term on the left side. This is like taking away your allowance and making you do chores.
5/10 x = 21 - 15
5/10 x = 6
Multiply both sides by 10/5 to solve for x. This is like giving you a magic wand that makes everything easier.
(10/5) (5/10) x = (10/5) (6)
x = 12
This is the solution of the equation. You can check it by plugging it back into the original equation and verifying that both sides are equal. Or you can just trust me
✧☆*: .｡. That's all folks, have fun with math! (✧ω✧) .｡.:*☆✧
How many significant digits are in the time measurement 0.0036 second?
Count the significant digits in the number.
Since there are no captive zeros or trailing zeros, only the two non-zero digits (3 and 6) are significant.
The time measurement 0.0036 seconds has 2 significant digits.
Significant digits in the time measurement 0.0036 seconds, let's first define what significant digits are and then determine the number of significant digits in the given measurement.
Significant digits are the meaningful digits in a number that contribute to its precision.
These digits help to reduce any ambiguity when reporting measurements.
To determine the significant digits in the number 0.0036 seconds:
Identify non-zero digits.
All non-zero digits (1-9) are always considered significant.
The non-zero digits are 3 and 6.
Identify leading zeros.
Leading zeros are the zeros that appear before the first non-zero digit.
These zeros are not considered significant.
The leading zeros are the three zeros before the 3.
Identify trailing zeros.
Trailing zeros are the zeros that appear after the last non-zero digit.
If the number has a decimal point, these zeros are considered significant.
There are no trailing zeros.
Identify captive zeros.
Captive zeros are the zeros that appear between non-zero digits.
These zeros are always considered significant.
There are no captive zeros.
Count the significant digits in the number.
Since there are no captive zeros or trailing zeros, only the two non-zero digits (3 and 6) are significant. So, the time measurement 0.0036 seconds has 2 significant digits.
For similar questions on significant digits
https://brainly.com/question/28052368
#SPJ11
Lea has two number cubes. The faces of each number cube are numbered from 1 to 6. Lea rolled the number cubes and recorded the number showing on the top face of each number cube. The results are shown in the table.
Based on these results, what is the experimental probability that the next time Lea rolls the number cubes, they will land with a 1 showing on the top face of one number cube and a 5 showing on the top face of the other number cube?
*
1 point
Captionless Image
Your answer
We can deduce here that the experimental probability that the next time Lea rolls the number cubes, they will land with a 1 showing on the top face of one number cube and a 5 showing on the top face of the other number cube is: 1/36.
What is probability?Probability is a measure for determining the possibility or chance that a specific event will take place. It is typically stated as a number between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty.
We can see that there is only one roll where one number cube that shows a 1 and the other number cube shows a 5. Therefore, the number of successful outcomes is 1.
The total number of rolls seen are: 36 rolls = 6 possible outcomes on the first number cube × 6 possible outcomes on the second number cube.
We can then see here that the probability will be = 1/36.
Learn more about probability on https://brainly.com/question/24756209
#SPJ1
If the reentry angle is 6.5°, what is x?
WORTH A LOt OF POINTS !!
Given the above conditions in the word problem above, x is also equal to 6.5°.
What is the explanation for the above response?
The angle x is the angle between this perpendicular line and the Earth's surface. It is also equal to the angle between the tangent line and the horizontal axis.
Since the reentry angle is 6.5°, we know that the tangent line makes an angle of 6.5° with the horizontal axis. We also know that the tangent line and the perpendicular line form a right angle, so the angle between the perpendicular line and the horizontal axis is 90° - 6.5° = 83.5°.
Finally, we can subtract this angle from 90° to find x:
x = 90° - 83.5° = 6.5°
Therefore, x is also equal to 6.5°.
Learn more about word problem at:
https://brainly.com/question/29203255?
#SPJ1
Carbon 14 has a half-life of 5,600 years. If a fossil contains 3 g of radioactive carbon 14, how many grams did it contain 11,200 years ago
Carbon 14 has a half-life of 5,600 years, which means that after 5,600 years, half of the initial amount of Carbon 14 will decay. Therefore, we can use the following formula to find the amount of Carbon 14 that was present 11,200 years ago:
A = A0 * (1/2)^(t/T)
where:
A0 = initial amount of Carbon 14
A = amount of Carbon 14 remaining after time t
t = time elapsed since the initial amount was present
T = half-life of Carbon 14
How many grams did it contain 11,200 years ago?We know that the fossil contains 3 g of Carbon 14, which is the amount remaining after 11,200 years. We want to find the initial amount, A0.
Let's plug in the values we have into the formula and solve for A0:
3 g = A0 * (1/2)^(11,200/5,600)
3 g = A0 * (1/2)^2
3 g = A0 * 1/4
A0 = 4 * 3 g
A0 = 12 g
Therefore, the fossil contained 12 g of Carbon 14 11,200 years ago.
Learn more about half-life from
https://brainly.com/question/28561047
#SPJ1
9x9x9x9x9x9x9x9x9x9x9x9xx99x9x9x999999xx99x
Answer: 2.2197307e+25
Step-by-step explanation: I just times it
Where is the turning point for f(x+4)+5
The answer of the given question based on the function is , the turning point of the function f(x+4)+5 is at the point (-4, -5).
What is Function?In mathematics, a function is a rule that assigns each input value (or argument) in a set to a unique output value in another set. In other words, it is a relationship between two sets of numbers, where each input value produces exactly one output value. Functions are usually represented using function notation, where the name of the function is followed by the input value in parentheses.
To find the turning point of the function f(x+4)+5, we need to first rewrite the function in vertex form, which is given by:
f(x) = a(x-h)² + k
where (h, k) is vertex of parabola.
To do this, we can start by completing the square:
f(x+4) + 5 = a(x+4-h)² + k
f(x+4) = a(x+4-h)² + k - 5
To complete the square, we need to add and subtract (4-h)²/4a inside the parentheses:
f(x+4) = a(x+4-h)² + k - 5 + (4-h)²/4a - (4-h)²/4a
f(x+4) = a(x+4-h)² + (4-h)²/4a + (4a*k-20a)/4a
Now the function is in vertex form:
f(x+4) = a(x+4-h)² + (4-h)²/4a + (4a*k-20a)/4a
The vertex of the parabola is at (h, k), so in this case, the vertex is at (-4, -5).
Therefore, the turning point of the function f(x+4)+5 is at the point (-4, -5).
To know more about Vertex form visit:
https://brainly.com/question/30404804
#SPJ1
On Wednesday, Gavriel ran 5 miles. On Thrusday, he ran 3/4 as far. How far did he run on Thursday
He run on Thursday is 3.75 miles.
Algebra helps in converting a mathematical statement into an equation. We know if we have ‘more’ or ‘sum’ in the given sentence we use addition operation (+) . Similarly If we have ‘less’ or ‘difference’ we use subtraction (−) . If we have a ‘quotient’ we use division operation (÷) . To define more generalized terms; we use algebra. It is a very vast branch of mathematics and is used in all the branches of mathematics like polynomial, linear equations, graphs, etc. and in daily life too.
Now, Gavriel ran 5 miles on Wed
and, On Thursday, he ran 3/4 as far.
We have to find the how far did he run on Thursday.
On Thursday , The distance will be:
=> 5 × 3/4
=> 15/4
=> 3.75 miles
Learn more about Distance at:
https://brainly.com/question/15172156
#SPJ4
Alice used the following steps to solve the equation...
Look at the Screen Shot ∨∨∨∨∨∨∨∨∨∨∨∨∨∨∨∨∨∨∨∨∨∨∨∨∨∨∨∨∨∨∨∨
The solution to the linear equation is determined as 5.
What are the steps of solving the equation?
The equation to solve is:
3x - 8 = 7
To solve for x, you can follow these steps:
Step 1: Add 8 to both sides of the equation to isolate the term with x on one side:
3x - 8 + 8 = 7 + 8 (combine constants here)
This simplifies to:
3x = 15
Step 2: Divide both sides of the equation by 3 to solve for x:
3x/3 = 15/3
This simplifies to:
x = 5
Learn more about linear equation here: https://brainly.com/question/28732353
#SPJ1
the dimensions of a cylinder are shown in the diagram. five point eight centimeters. seven point six centimeters. which measurement is closest to the lateral surface area in square centimeters of the cylinder?
The measurement that is closest to the lateral surface area of the cylinder is 132.15 square centimeters.
To determine the lateral surface area of a cylinder, you can use the formula 2πrh, where "r" represents the radius of the circular base of the cylinder, and "h" represents the height of the cylinder. This formula calculates the total area of the curved part of the cylinder, excluding the top and bottom circular bases.
The height of the cylinder is 5.8 cm and the radius of the circular base is 7.6/2 = 3.8 cm.
So, the lateral surface area of the cylinder is approximately:
2π(3.8)(5.8) ≈ 132.15 cm²
The value that is nearest to the lateral surface area of the cylinder is 132.15 square centimeters.
Learn more about measurement
https://brainly.com/question/2107310
#SPJ4
HELLPPPPP PLS!!!! 20 POINTS
Using your calculator, graph these functions and find the solution to the system.
f(x)= x^2 + x - 6
g(x)= -2x^2 - 2x + 12
1- (-3, 0) and (2, 0)
2- (0, -6) and (0, 12)
3- No solution: They do not intersect.
4- (-6, 12)
The solutions to the system of equations f(x) = x² + x - 6 and g(x) = -2x² - 2x + 12 are (-3, 0) and (2, 0). So, correct option is 1.
To graph the functions f(x) and g(x) using a calculator, we can enter the equations into the calculator's graphing function and choose an appropriate window to display the graph. Once the graphs are displayed, we can look for the points of intersection to find the solution to the system of equations.
Using a graphing calculator, we can see that the graphs of f(x) and g(x) intersect at two points: (-3, 0) and (2, 0). These points represent the x-coordinates of the solutions to the system of equations.
To verify that these points are indeed the solutions, we can substitute each of them into both equations and check that they satisfy both equations simultaneously.
For point (-3, 0):
f(-3) = (-3)² + (-3) - 6 = 0
g(-3) = -2(-3)² - 2(-3) + 12 = 0
Therefore, (-3, 0) is a solution to the system of equations.
For point (2, 0):
f(2) = 2² + 2 - 6 = 0
g(2) = -2(2)² - 2(2) + 12 = 0
Therefore, (2, 0) is also a solution to the system of equations.
The point (0, -6) and (0, 12) are not the points of intersection and (-6, 12) is not a solution to the system of equations.
Therefore, the answer is option 1.
To learn more about equations click on,
https://brainly.com/question/29131268
#SPJ1
i need help please help me
The following are the correct vertical translation and you can use this information to fill the table in the picture:
sqrt{x+5} - shift down 5 units2 - sqrt{x-4} - shift up 2 unitssqrt{x+3} + 1 - shift up 1 unitsqrt{x+4} + 3 - shift up 3 unitssqrt{x-2} - 3 - shift down 3 units3sqrt{x} - 1 - no shiftsqrt{x} + 2 - shift up 2 unitssqrt{x} - 3 - shift down 3 units3sqrt{x-4} - no shiftsqrt{x+6} - no shiftWhat to know about Vertical TranslationA vertical translation refers to a type of transformation that moves a function or graph vertically up or down without changing its shape. Specifically, a vertical translation of distance c is given by the function:
f(x) + c
where f(x) is the original function and c is a constant that determines the amount and direction of the translation. If c is positive, the graph of the function is shifted upwards; if c is negative, the graph is shifted downwards.
For example, the function f(x) = x^2 has a graph that is a parabola opening upwards. If we apply a vertical translation of 2 units, the resulting function is:
f(x) + 2 = x^2 + 2
The graph of this function is also a parabola, but it has been shifted vertically upwards by 2 units. Similarly, a vertical translation of -3 units would give us the function f(x) - 3 = x^2 - 3, which is the same parabola shifted downwards by 3 units.
Learn more about Vertical Translation here:
https://brainly.com/question/14899490
#SPJ1
A group of friends wants to go to the amusement park. They have $214.50 to spend on parking and admission. Parking is $12, and tickets cost $33.75 per person, including tax. Which tape diagram could be used to represent the context if � p represents the number of people who can go to the amusement park?
The equation that can be used to represent number of people who can go to the amusement park is 12 + 33.75x = 215.50.
We have,
the total amount to spent on amusement park = $214.50
And the parking fees = $12
The ticket cost per person = $33.75
let the number of person be x.
Then, the equation can become as
12 + 33.75x = 215.50
Simplifying the equation we get
33.75x = 215.5 - 12
33.75x = 203.5
x= 6.02
Learn more about Equations here:
brainly.com/question/18109354
#SPJ1
A fifth grade teacher is designing a game based on one of her favorite children's books. While reading the book she counted the number of white cats, black cats, and brown cats that appear in the illustrations. The table below summarizes her data. (Use the data box in the picture :D)
The teacher wants to use a probability model to simulate the counting of cats. She wants the probability of counting a cat of a certain color to match the frequency of white, black and brown cats in the book.
Select all the probability *devices* that would best represent the observed probabilities from the table shown.
A)Spinner
B)Color Cube
C)Bags or Marble
D)Front View and Rear View
Please help :D
Answer:
color cube
Step-by-step explanation:
find the mean i’d the data in the dot plot below. make sure to show your work and explain the steps you took in solving the problem.
The mean of the data in the dot plot is approximately 5.33.
What does the calculation's mean mean?By dividing the sum of the numbers by the total number of numbers, the mean, or average, of the given numbers is determined. Mean is equal to (Sum of all Observations / Total Observations).
We must sum up all the values and divide by the total number of values to determine the mean of the data in the dot plot.
The first step is to count the dots for each value:
3 has 3 dots
4 has 5 dots
5 has 6 dots
6 has 8 dots
7 has 5 dots
8 has 3 dots
Then, multiplying each value by the quantity of dots associated with it, we must total up all the products:
(3 x 3) + (4 x 5) + (5 x 6) + (6 x 8) + (7 x 5) + (8 x 3) = 3 + 20 + 30 + 48 + 35 + 24 = 160
Last but not least, we must divide the entire number of values—i.e., dots—by the sum:
160 ÷ (3 + 5 + 6 + 8 + 5 + 3) = 160 ÷ 30 = 5.33
To know more about mean visit:-
https://brainly.com/question/31101410
#SPJ1
If m∠A = (4x − 2)° and m∠B = (6x − 20)°, what is the value of x?
A. 34
B. 20.2
C. 11.2
D.9
x has a value of 9. The correct response is (D).
Since the measures of angles A and B are equal, we can set them equal to each other and solve for x:
m∠A = m∠B
4x - 2 = 6x - 20
Subtracting 4x from both sides, we get:
-2 = 2x - 20
Adding 20 to both sides, we get:
18 = 2x
Dividing both sides by 2, we get:
x = 9
Therefore, the value of x is 9. Answer choice (D) is correct.
Learn more about algebraic Expression here:
https://brainly.com/question/953809
#SPJ1
What is the slope from (−4, 6) to (2, 2/3)
The slope from of (−4, 6) to (2, 2/3) can be written as -17/18
How can the slope be written?The slope of line can be represented as =slope whereby (x1, y1) = serves as the coordinates of first point in the line (x2, y2)serve as as the coordinates of second point in the line
From the question, x1 = -4, y1 = 6 , x2 = 2, y2 =2/3 then we can set up into the formula as
(y2 - y1) / (x2 - x1)
(y2 - y1) =(2/3 - 6) =-17/3
(x2 - x1) = (2 - (-4))= 6
Hence slope = -17/18
Learn more about slope at:
https://brainly.com/question/16949303
#SPJ1
Part B
The chess club started with 18 chess sets. The teachers ordered 3 cases of 15 chess sets. They will divide the total number of chess sets so that each teacher receives an equal number. Then they will give any extra sets to the school library.
What is the greatest number of chess sets each of the 4 teachers should get?
Enter your answer in the box.
In the fraction , the greatest number of chess sets each of the 4 teachers should get is 15.
What is fraction?
Part of a whole is a fraction. The quantity is written as a quotient in mathematics, where the numerator and denominator are divided. Each is an integer in a simple fraction. Whether it is in the numerator or denominator, a complex fraction contains a fraction. The numerator and denominator of a correct fraction are opposite each other.
Here the In starting number of chess sets = 18
Ordered number of chess set cases = 3
In each case number of chess sets= 15
Then total number of ordered chess sets = 3*15 = 45.
Now total number of chess set in chess club = 45+18 = 64.
The number of teacher = 4.
Then expression is ,
The number of chess sets each of the 4 teachers should get = 63/4 = 15 [tex]\frac{3}{4}[/tex]
Remaining set = 3.
Hence the greatest number of chess sets each of the 4 teachers should get is 15.
To learn more about fraction refer the below link
https://brainly.com/question/78672
#SPJ1
Randy is designing a circular garden that is 18 feet in diameter. He is buying plastic edging that costs $1. 50 per foot. He can only buy edging in whole-foot amounts. How much does it cost Randy to buy edging for his garden? Use 3. 14 for pie.
If the diameter of circular-garden is 18 feet, then it will cost Randy an amount of $85.50 to buy edges for his garden.
The "Circumference" of circle is defined as the "total-length" of the boundary or the outer edge of the circle.
The circumference formula is : Circumference = π × Diameter,
The "diameter" of garden is = 18-feet,
So, Circumference = 3.14 × 18 = 56.52 feet,
Since, Randy needs to buy plastic-edging to cover the entire circumference of garden, he needs to buy 56.52 feet of edging.
We know that, Randy can only buy edging in whole-foot amounts,
So, rounding up to the nearest whole foot, we get 57 feet,
The cost of edging is = $1.50 per foot,
So, "total-cost" for Randy to buy edging for his garden is,
⇒ Total Cost = (Cost per foot) × (Number of feet),
⇒ $1.50 × 57,
⇒ $85.50
Therefore, it will cost Randy $85.50 to buy edging for his circular garden.
Learn more about Circumference here
https://brainly.com/question/16125353
#SPJ4
Given P(A)=0.3, P(B)=0.57 and P(A and B)=0.251, find the value of P(B|A):, rounding to the nearest thousandth
The required value of probability P(B|A) is approximately 0.837.
As mentioned in the question,
P(A)=0.3, P(B)=0.57 and P(A and B)=0.251,
We can use the formula for conditional probability to find P(B|A):
P(B|A) = P(A and B) / P(A)
Substituting the given values, we get:
P(B|A) = 0.251 / 0.3 = 0.83667
Rounding to the nearest thousandth, we get:
P(B|A) ≈ 0.837
Therefore, the value of P(B|A) is approximately 0.837.
Learn more about conditional probability here:
https://brainly.com/question/30144287
#SPJ1
For the hypothesis test h0:μ=8 against h1:μ>8 with variance unknown and n=10, find the best approximation for the p-value for the test statistic t0=2. 155
The best approximation for the p-value for the test statistic t0 = 2.155 is 0.032.
To find the best approximation for the p-value for the hypothesis test with null hypothesis H0: μ=8 and alternative hypothesis H1: μ>8, with variance unknown and n=10, and a test statistic t0=2.155, we need to use the t-distribution with degrees of freedom (df) equal to n-1 = 10-1 = 9.
The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed one, assuming the null hypothesis is true. Since this is a one-tailed test with the alternative hypothesis in the form of μ>8, the p-value corresponds to the area in the right tail of the t-distribution.
Using a t-table or calculator with the t-distribution, we can find the probability of obtaining a t-value as large as 2.155 or larger with 9 degrees of freedom. This probability is approximately 0.032. Therefore, the best approximation for the p-value for this hypothesis test is 0.032.
We can interpret this result as follows: if the null hypothesis is true (i.e., if the population mean is 8), the probability of obtaining a sample mean as extreme or more extreme than the observed one (i.e., greater than 8.215) is 0.032. Since this probability is relatively small, we may reject the null hypothesis in favor of the alternative hypothesis at a significance level of 0.05 or smaller.
To learn more about test statistic here:
https://brainly.com/question/31744574
#SPJ4
Expanda 12. 907. 054 mostrando cada digito por el valor en su lugar
We can expand 12.907.054 as 1 × 10,000,000,000 + 2 × 1,000,000,000 + 9 × 100,000,000 + 0 × 10,000,000 + 7 × 1,000,000 + 0 × 100,000 + 5 × 10 + 4 × 1.
To expand a decimal number by showing each digit by value, we need to break it down into its place values. For example, in the number 12.907.054, the first digit to the left of the decimal point is in the billions place, the second digit is in the hundred millions place, and so on.
So, we can expand 12.907.054 as follows:
1 × 10,000,000,000 + 2 × 1,000,000,000 + 9 × 100,000,000 + 0 × 10,000,000 + 7 × 1,000,000 + 0 × 100,000 + 5 × 10 + 4 × 1
This means that 12.907.054 can be written as the sum of its place values. The first digit to the left of the decimal point is worth 10 billion, the second digit is worth 1 billion, and so on until we reach the ones place.
Expanding a decimal number by showing each digit by value is a way to better understand the place values of each digit and to break down the number into smaller parts for easier analysis.
To learn more about digit click on,
https://brainly.com/question/7042218
#SPJ4