Question 3 (4 marks) Name and find the critical values of x? 2 n14 a = 0.005 x² n=8 a = 0.01 x2 n=18 a = 0.02
Answers
The critical values of x are 31.319, 18.475, and 28.869 for each case respectively.
To find the critical values of x (x₂), we'll use the chi-square distribution table. The critical values depend on the degrees of freedom (df) and the significance level (α).
1. For n=14 and α=0.005:
Degrees of freedom (df) = n - 1 = 14 - 1 = 13
From the chi-square table, x₂ (13, 0.005) ≈ 31.319
2. For n=8 and α=0.01:
Degrees of freedom (df) = n - 1 = 8 - 1 = 7
From the chi-square table, x₂ (7, 0.01) ≈ 18.475
3. For n=18 and α=0.02:
Degrees of freedom (df) = n - 1 = 18 - 1 = 17
From the chi-square table, x₂ (17, 0.02) ≈ 28.869
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Related Questions
In 12 years I will be five times as old as it was 32 years ago. Write an equation and define your variable.
Answers
The expression for the word problem can be written as x + 12 = 5 ( x - 32).
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that in 12 years I will be five times as old as I was 32 years ago. The expression in the mathematical form will be calculated as:-
x + 12 = 5 ( x - 32 )
Here, x will be the present age.
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Breast-feeding mothers secrete calcium into their milk. Some of the calcium may come from their bones, so mothers may lose bone mineral. Researchers measured the percent change in mineral content of the spines of 47 mothers during three months of breast-feeding.6Here are the data:
Blend Images/Superstock
(a)
The researchers are willing to consider these 47 women as an SRS from the population of all nursing mothers. Suppose that the percent change in this population has standard deviation ? = 2.5%. Make a stemplot of the data to verify that the data follow a Normal distribution quite closely. (Don
Answers
To create a stemplot, we first need to separate the data into "stems" and "leaves." Each stem represents the first digit(s) of each data point, while each leaf represents the last digit(s). For example, if the data point is 12.3, the stem would be 12 and the leaf would be 3.
To make a stemplot, the data should be arranged in increasing order, and then separated into stems and leaves.
STEMPLOT OF THE DATAHowever, you can use the data given and arrange it in increasing order and separate it into stems and leaves to make a stemplot. A stemplot is a good way to check if the data follow a normal distribution quite closely, the more the data is spread out and the more symmetric it is, the more likely it is to follow a normal distribution.
Also, it is important to mention that from the given data, it is not possible to conclude if the percent change in this population has standard deviation of 2.5%. This parameter can only be estimated from a sample if it follows a normal distribution which is not clear from the given data.
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Rewrite the function f(x) = -2(x+2)²-11 in the form f(x) = ax²+bx+c.
X
S
Answers
Answer:
\(\displaystyle{f(x)=-2x^2-8x-19}\)
Step-by-step explanation:
Given the vertex equation:
\(\displaystyle{f(x)=-2(x+2)^2-11}\)
First, apply the perfect square formula, expanding to standard form:
\(\displaystyle{f(x)=-2(x^2+4x+4)-11}\)
Expand -2 in:
\(\displaystyle{f(x)=-2x^2-8x-8-11}\)
Evaluate or simplify:
\(\displaystyle{f(x)=-2x^2-8x-19}\)
Hence,
\(\displaystyle{f(x)=-2x^2-8x-19}\)
Answer:
\(\huge\boxed{\sf f(x) = -2x\² - 8x - 19}\)
Step-by-step explanation:
Given function:f(x) = -2(x + 2)² - 11
Using formula: (a + b)² = a² + 2ab + b²f(x) = -2[(x)² + 2(x)(2) + (2)²] - 11
f(x) = -2(x² + 4x + 4) - 11
Distribute
f(x) = -2x² - 8x - 8 - 11
f(x) = -2x² - 8x - 19\(\rule[225]{225}{2}\)
What property is this?(n+13) + 4 = n + (13+4) Associative Property Commutative Property Additive Identity O Distributive Property
Answers
Answer:associative property?
Step-by-step explanation: because you adding
Please help with number 3 the whole thing please 28 points to the right one
Answers
In one year, a school uses 12,370 pieces of white paper, 5,670 fewer pieces of blue paper than white paper, and 3,500 fewer pieces of yellow paper than blue paper. How many pieces of paper does the school use in all?
Answers
Answer:
22270 pieces of paper
Step-by-step explanation:
White: 12370 [12,370 pieces of white paper]
Blue: 6700 (12370-5670). [5,670 fewer pieces of blue paper than white paper]
Yellow: 3200 (6700-3200). [3,500 fewer pieces of yellow paper than blue paper]
The sum is 22270 pieces of paper.
Which solution set is graphed on the number line?
4 -3 -2 -1
0 1
2
3
4
0x21
Ox>1
Ox<1
O XS1
Answers
(2.569
3
2. Stephanie has 3 bags of soil to put in her garden. Each bag of soil will cover 125 ft.
How many square feet will Stephanie be able to cover if she uses all these bags of soil?
(7.3A)
Answers
i cant understand your question define briefly
Mario buys tickets for either 47 or 57 dollars. He purchases 14 tickets and spends 738 dollars. How many tickets did he purchase at each price?
Answers
Answer:
6 tickets were purchased at $47
8 tickets were purchased at $57
Step-by-step explanation:
Let the tickets purchased at $47 be x
Let the tickets purchased at $57 be y
We can form an equation from the question given which will be:
x + y = 14 ....... i
47x + 57y = 738 ........ ii
From equation i
x = 14 - y ........ iii
Substitute iii into ii
47x + 57y = 738
47(14-y) + 57y = 738
658 - 47y + 57y = 738
Collect like terms
-47y + 57y = 738 - 658
10y = 80
y = 80/10
y = 8
8 tickets were purchased at $57
Note that from i
x + y = 14
x + 8 = 14
x = 14 - 8
x = 6
6 tickets were purchased at $47
.
Simplify by using the Distributive Property
4(4f-2g)
Answers
Answer:
the answer is 16f-8g
Answer:
16f - 8g
Step-by-step explanation:
You would multiply the terms in the middle by 4 so 4f*4 would be 16f since 4*4 is 16 and then 4*2g would be 8g since 4*2 is 8
Rapid rental car charges a $40 rental fee, $15 for gas, and $0.25 per mile driven. For the same car, Capital Cars charges $45 for rental and gas and $0.35 per mile. For how many miles is the rental cost at both companies the same
Answers
Answer:
The cost would be the same for 100 miles & Total cost would be $80.
what is 30 grams in ounces?
Answers
Answer:
1.05821886 ounces
Step-by-step explanation:
To convert 30 grams to ounces, use the conversion factor 1 ounce = 28.3495 grams.
How many even numbers less than 500 can be formed using 1,2 3 4 5?
Answers
28 different even numbers can be formed using 1,2,3,4 and 5 that are less than 500.
To form the even number from a combination of five different numbers 1 to 5 and the even number less that will be formed from such a combination are less than 500. Therefore, in this scenario, 28 different event numbers will be formed. The cases to formed the even number from 1,2,3,4 and 5 are given below:
Case 1: There is only one digit in the number.
The only even integers in this situation are 2 and 4, adding up to a total of 2.
Case 2: There are exactly two digits in the number.
In this instance, the first digit must be one of the other four permitted digits and the last digit must be either 2 or 4, for a sum of 2*4=8.
Case 3: There are exactly three digits in the number.
In this instance, the middle digit must be one of the other four permitted digits, and the last digit must either be 2 or 4.
The total will be 2*3*2=12 if the middle digit is not 5, which means the first digit must be one of two digits other than the final two digits and 5.
As a result, there exist 28 even numbers with the digits 1, 2, 3, and 5 that are less than 500.
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Algebra:
Kapil's age is m years. What is his grandfather's age if he is 10 years more than thrice Kapil's age?
Answers
The grandfather's age if he is 10 years more than thrice Kapil's age is
3x +10.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
Kapil's age is m years.
His Grandfather is 10 years more than thrice Kapil's age.
Thrice Kapil's age = 3x
and, 10 years more than thrice Kapil's age = 3x + 10
Then, the age of Grandfather is
= 3x+ 10
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I need help can I have how to do it and some work so I can do it.
Answers
3x-y=2....(i)
2x-y=3.....(ii)
now adding the eqn I and ii ,
3x-y=2
2x-y=3
+ + +
5x=5
x=1
Now substituting the value of x in eqn I
3×1-y=2
3-y=2
-y=-1
y=1
Simplify 3(5y + 6) -4
Answers
Given:
To simplify 3(5y+6)-4
\(\begin{gathered} 3(5y+6)-4 \\ 15y+18-4 \\ 15y+14 \end{gathered}\)Hence the simplified value os 15y+14.
give me a follow on isnta
Answers
Answer:
Step-by-step explanation:
ok
Answer:ok np
Step-by-step explanation:
26. In sentence 8 (reproduced below), the writer wants to provide evidence to clarify the previous sentence's point about what advocates fail to consider.
In many areas, purchasing or renting land for a tiny home requires compliance with local building codes.
Which of the following versions of the underlined text would best accomplish this goal?
(A) (as it is now)
(B) costs more than the home itself
(C) is an inconvenient and time-consuming process
(D) can be avoided if a friend is willing to share land
(E) may be unnecessary if the homeowner claims to be camping
Answers
The following versions of the underlined text would best accomplish this goal is an inconvenient and time-consuming process
This version of the underlined text best accomplishes the writer's goal of providing evidence to clarify the previous sentence's point about what advocates fail to consider. By mentioning that compliance with local building codes is an inconvenient and time-consuming process, it highlights a significant factor that advocates may overlook when promoting the idea of purchasing or renting land for a tiny home. This evidence emphasizes the challenges and potential barriers involved in the process, which helps to clarify the previous point and provide a more comprehensive understanding of the situation.
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Pls help me! I’ll help u if u do!!
Answers
Answer:
a) $160
b) $116.50
Step-by-step explanation:
a) Let the original price of the yellow bicycle be $x.
Since both has the same original price,
original price of yellow bicycle= 100% x
original price of green bicycle= 100% x
Discounted price of yellow bicycle
= (100% -25%) x
= 75% x
Discounted price of green bicycle
= (100% -30%) x
= 70% x
Difference in cost
= 75%x -70%x
= 5% x -----(1)
From 2nd paragraph:
Discounted price of yellow bicycle
= Kyreen's money +3.50
Discounted price of green bicycle
= Kyreen's money -4.50
Difference in cost
= (Kyreen's money +3.50) -(Kyreen's money -4.50)
= Kyreen's money +3.50 -Kyreen's money +4.50
= 3.50 +4.50
= 8.00 -----(2)
Equating (1) and (2) together:
5% x= 8.00
\( \frac{5}{100} x = 8\)
\(x = 8 \div \frac{5}{100} \)
\(x = 8 \times \frac{100}{5} \)
x= 8 ×20
x= 160
Thus, the original price of the yellow bicycle is $160.
_______
b) Amount Kyreen has at first
= discounted price of yellow bicycle -$3.50
= 75%($160) -$3.50
= $120 -$3.50
= $116.50
is (2,-3) a solution for the inequality y<2x-5?
Answers
Answer: no
Step-by-step explanation:
You have a mortagege of $275,000
after down payment with an interest
rate of 3% for 30 years.
What does P, r,n, and t are equal to?
Answers
Answer:
Our calculator limits your interest deduction to the interest payment that would be paid on a $1,000,000 mortgage. Interest rate: Annual interest rate for this
Step-by-step explanation:
describe the graph of the solution
Answers
First, we want to note two things:
We have a solid circle at -10, so -10 IS part of the solution.We have shading to the right of -10, meaning we also need to include numbers to the right of -10, or numbers greater than -10.
We can describe this with an inequality: x ≥ -10
Be sure you use ≥ and not >, since -10 is included.
We can describe this with interval notation: [ -10, infty )
Be sure you use [ and not ( on -10, since -10 is included.
You can also use set-builder notation: { x | x ≥ -10 }
1. an island is considering adding another character to their vehicle license plates in order to increase the
number of license plates available. currently, a license plate must have exactly four-character spaces. each
character space may be filled with any capital letter other than i, b, z, or o or any number between, and
including, 0 to 9. letters and numbers may repeat on the plates.
(a) how many different license plate numbers are available under the current structure of exactly four
characters per plate? show your calculations.
(a) if the state required all license plates to have exactly five characters instead of four, how many
different license plate numbers would be available with the additional character requirement? show
your calculations.
(a) how many times bigger is the set of license plate numbers with exactly five characters than that with
the set of four characters? show your calculations.
Answers
There are 26,884,736 different license plate numbers available with exactly four characters per plate.
What is the total number of available license plate numbers with four characters?To calculate permutations of available license plate numbers with four characters, we need to consider the number of options for each character space and account for repetition.
Since each character space can be filled with any capital letter other than i, b, z, or o, or any number between 0 to 9, there are 26 options for each space.
Therefore, the total number of possibilities is obtained by multiplying the number of options for each space together:
\(26 * 26 * 26 * 26 = 26^4 = 456,976.\)
If the state required all license plates to have exactly five characters, the calculation would be similar. Each character space can still be filled with the same options, and now we have five spaces to consider.
Therefore, the total number of possibilities for five characters is:
\(26 * 26 * 26 * 26 * 26 = 26^5 \ = 11,881,376.\)
To find how many times bigger the set of license plate numbers with exactly five characters is compared to four characters,
We can divide the total possibilities for five characters by the total possibilities for four characters: 11,881,376 / 456,976 ≈ 26.
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F(x)=3x+5
G(x)=4x^2-2
H(x)=x^2-3x+1
Find f(x) + g(x)-h(x)
A.6x^2+6x-1
B.5x^2+4
C.3x^2+2
D.3x^2+6x+2
Answers
The simplified form of f(x) + g(x)-h(x) is 3x² +6x+2
What is an expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a complete sentence. Any one of the following mathematical operations can be used. A sentence has the following structure: Number/variable, Math Operator, Number/Variable is an expression.
f(x) + g(x)-h(x)
= 3x+5 + 4x²-2 - (x²-3x+1)
Simplify paranthesis
= 3x+5 + 4x²-2 -x²+3x-1
Group like terms
= 4x² -x² +3x+3x+5-2-1
= 3x² +6x+2
The simplified form of f(x) + g(x)-h(x) is 3x² +6x+2
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Daily BER (kl/day) = 5.4 x 24 hours x body mass (kg) Mihir has a body mass of 65 kg. Calculate Mihir's daily basic energy requirement.
Answers
Mihir's daily basic energy requirement is 8424 (kl/day).
How to find BMI body mass index or BER from body mass?
As the formula to find daily BER is given below,
\(Daily\ BER\ = 5.4 \times 24 \times body\ mass\)
body mass = 65 kg
Therefore, put body mass, to find BER,
\(Daily\ BER\ = 5.4 \times 24 \times 65\\Daily\ BER\ = 8424\ (kl/day)\)
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Mihir's daily basic energy requirement is 7,776 kJ/day.
what is meaning of body mass?A person's BMI is calculated by dividing their weight in kilograms (or pounds) by their square of height in meters (or feet). A high BMI may indicate excessive body fat. BMI measures weight categories that could lead to health issues, but it does not assess a person's health or body fat percentage.
to calculate Mihir's daily basic energy requirement using the formula:
Daily BER (kl/day) = 5.4 x 24 hours x body mass (kg)
We can substitute the given values to get:
Daily BER (kl/day) = 5.4 x 24 hours x 65 kg
Daily BER (kl/day) = 7,776 kJ/day
Therefore, Mihir's daily basic energy requirement is 7,776 kJ/day.
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Which of these is parallel to y= 4x-2
y=5+4x
y=4-3x
y=4x+1
y=5-4x
y=4x-4
Answers
Answer:
y=4x+5(the first one)
y=4x+1
y=4x-4
Step-by-step explanation:
If the slope is the same, it is parallel
The equation for a linear equation is y=mx+b
mx is the slope
your original equation is y=4x-2, so the slope is 4.
To find which ones are parallel, you find the ones with the slope 4x(make sure it isn't -4x).
What is the value of x? What is the measure of angle 6? Show all of your work and/or explain your answer.
Answers
Answer:
1) 5 & 9
5=Corresponding Angle
9=Alternate Exterior Angle
2) 7 & 8
We know 4 is supplementary to 8. Since that is true, 7 & 8 are also.
8=Corresponing angle to 4
7=Verticle angle to 8
3) We know 1 and 3 equal 180
x-20+x+40=180
2x+20=180
2x=180-20
2x=160
x=80
<2=X+20
=80+20
=100
Angle 2 is the same as angles 5 and 6 added together.
We know angle 5 is the same as angle 1 (corresponding angles).
<1=X-20
=80-20
=60
Now that we know <2=100 and <5=60, we can figure out <6
100-60=40
<6=40°
Step-by-step explanation:
1) 5 & 9
5=Corresponding Angle
9=Alternate Exterior Angle
2) 7 & 8
We know 4 is supplementary to 8. Since that is true, 7 & 8 are also.
8=Corresponing angle to 4
7=Verticle angle to 8
3) We know 1 and 3 equal 180
x-20+x+40=180
2x+20=180
2x=180-20
2x=160
x=80
<2=X+20
=80+20
=100
Angle 2 is the same as angles 5 and 6 added together.
We know angle 5 is the same as angle 1 (corresponding angles).
<1=X-20
=80-20
=60
Now that we know <2=100 and <5=60, we can figure out <6
100-60=40
<6=40°
Write out the form of the partial fraction decomposition of the function appearing in the integral: 5 72 Determine the numerical values of the coefficients, A and B, where A B and -5x-72 2 5x - 66 denominator denominator B=
Answers
The numerical values of the coefficients A and B are:
A = -1/6
B = 1/6
To perform partial fraction decomposition, we need to break down the fraction into simpler terms.
The form of the partial fraction decomposition of the given function is:
5/(5x - 72) = A/(5x - 66) + B/(5x - 72)
Here, A and B are the coefficients we need to find. We can find them by cross-multiplying and equating the numerators of both sides of the equation:
5 = A(5x - 72) + B(5x - 66)
Now, we can substitute some values of x to get two equations in terms of A and B:
For x = 14:
5 = A(5(14) - 72) + B(5(14) - 66)
Simplifying and solving for A and B, we get:
A = 1/6
B = -1/6
For x = 12:
5 = A(5(12) - 72) + B(5(12) - 66)
Simplifying and solving for A and B again, we get:
A = -1/6
B = 1/6
Generally, for a function f(x) with a rational expression in the integral, we can use partial fraction decomposition to rewrite the expression as a sum of simpler fractions. This makes it easier to find the integral.
The coefficients A and B are constants in the simpler fractions, and their values can be determined by solving a system of linear equations.
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T/F There exists a function f such that f(x) > 0, f'(x) < 0, and f"(x) > 0 for all x.
Answers
True, there exists a function f such that f(x) > 0, f'(x) < 0, and f"(x) > 0 for all x.
An example of such a function is\(f(x) = e^(-x)\), where e is the base of the natural logarithm (approximately 2.718).
Let's verify the given conditions:
f(x) > 0:
Since e^(ax) is always positive for any real value of x and any constant a, \(e^(-x)\)is also always positive for any real value of x.
f'(x) < 0:
To find the first derivative, apply the chain rule: \(f'(x) = -e^(-x). As e^(-x)\) is always positive, the derivative
\(f'(x) = -e^(-x)\) is always negative for all x.
f"(x) > 0:
To find the second derivative, apply the chain rule again:
\(f"(x) = e^(-x). As e^(-x)\)is always positive, the second derivative\(f"(x) = e^(-x)\) is always positive for all x.
Thus, it is true that there exists a function f with the given conditions.
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The function \(f(x) = e^(-x)\) meets all the given conditions.
True. There exists a function f such that \(f(x) > 0, f'(x) < 0, and f"(x) > 0\) for all x. One example of such a function is \(f(x) = e^(-x)\).
True. There exists a function f(x) that satisfies the given conditions: f(x) > 0, f'(x) < 0, and f''(x) > 0 for all x.
Consider the function \(f(x) = e^(-x)\). This function has the following properties:
1. f(x) > 0 for all x because the exponential function is always positive.
2. \(f'(x) = -e^(-x)\)which is always negative because e^(-x) is always positive, and the negative sign in front makes the derivative negative.
3. \(f''(x) = e^(-x)\)which is always positive.
Thus, the function \(f(x) = e^(-x)\)meets all the given conditions.
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Ms. King goes to Kroger. She sees that Sprite costs $4 for a 12-pack of cans of $7.50 for a 24-pack of cans. Which is the better buy?
Answers
Answer:
7.50 for 24
Step-by-step explanation: