Answers
Answer:
[tex](x+2)^{2} +(y+2)^{2} =9[/tex]
Step-by-step explanation:
the equation of circle:
center:(-2,-2)
The distance between the center and the side:3
So, the radius is 3
(x-h)^2+(y-k)^2=r^2
[tex](x - - 2)^{2} +(y- - 2)^{2} =3^{2}[/tex]
[tex](X+2)^{2} +(y+2)^{2} =9[/tex]
Related Questions
Find Compund Interest of P = ₹4000, N = 3 years, R = 5 p. C. P. A
Answers
The compound interest on ₹4000 at a rate of 5% p.a. for 3 years is ₹631.03.
The formula to calculate compound interest is:
[tex]A= P(1+\frac{R}{N} )^{nt}[/tex]
Where:
A = Final amount (including interest)
P = Principal amount
r = Annual interest rate (as a decimal)
n = Number of times the interest is compounded per year
t = Number of years
In this case, P = ₹4000, N = 3 years, R = 5% per annum (p.a.), which means r = 0.05 and n = 1 (compounded annually).
So, plugging in the values in the formula:
[tex]A= 4000(1+\frac{0.05}{1} )^{1*3}[/tex]
[tex]A= 4000(1.05)^{3}[/tex]
[tex]A = 4631.03[/tex] (rounded to 2 decimal places)
Compound interest is a type of interest that is calculated not only on the initial amount of money borrowed or invested but also on the accumulated interest from previous periods. In other words, the interest earned in each period is added to the principal amount, and the new total becomes the basis for calculating interest in the next period.
This compounding effect can result in significant growth in the value of an investment or debt over time, especially if the interest rate is high and the period of investment or debt repayment is long. For example, if you invest $1,000 at an annual interest rate of 5% compounded annually, you will earn $50 in interest at the end of the first year, and your new total will be $1,050.
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Which of the following are true statements? Check all that apply. A. F(x)= 2 square x has the same domain and range as f(x)= square x. B. The graph of f(x)= 2 square x will look like the graph of f(x)= square x but will shrink it vertically by the factor of 1/2. C. The graph of f(x)= 2 square x will look like the graph of f(x)= square x but will shrink it horizontally by a factor of 1/2. D. The graph of f(x)= 2 square x will look like the graph of f(x)= square x but will stretch it vertically by factor of 2.
Answers
The graph of f(x)= 2 square x will look like the graph of f(x)= square x but will shrink it vertically by the factor of 1/2.
The graph of f(x)= 2 square x will look like the graph of f(x)= square x but will stretch it vertically by factor of 2.
Thus, Option B and Option D are correct.
What is function?A function is a relationship or expression involving one or more variables. It has a set of input and outputs.
A. F(x)= 2 square x has the same domain and range as f(x)= square x.
B. The graph of f(x)= 2 square x will look like the graph of f(x)= square x but will shrink it vertically by the factor of 1/2.
D. The graph of f(x)= 2 square x will look like the graph of f(x)= square x but will stretch it vertically by factor of 2.
Option A is false because multiplying the function by 2 will change the range of the function to include all non-negative real numbers (since the square of any number is non-negative).
Option B is true because multiplying the function by 2 will vertically shrink the graph by a factor of 1/2 (since the output values will be half the size of the original function).
Option C is false because multiplying the function by 2 will not affect the horizontal scale of the graph.
Option D is true because multiplying the function by 2 will vertically stretch the graph by a factor of 2 (since the output values will be twice the size of the original function).
Therefore, Option B and Option D are correct.
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Write each equation in slope-intercept form. Identify the slope and y-intercept.
x - 3y = 12
*Work must be shown.*
Answers
Answer:
slope is 1/3
y-intercept is -4
Step-by-step explanation:
x - 3y = 12
3y = x - 12
y = 1/3x - 4
according to y = mx + b, m is slope and b is y-intercept
slope is 1/3
y-intercept is -4
Which is the conclusion in the following argument. "Since the good, according to Plato, is that which furthers a person's real interests, it follows that
Group of answer choices
- the good, according to Plato, is that which furthers a person's real interests
- Neither of the above.
- in any given case, when the good is known, men will seek it
Answers
The conclusion in the argument is "the good, according to Plato, is that which furthers a person's real interests." which it is the correct answer.
In a well-structured argument, the conclusion is what the argument aims to prove.
The conclusion can be located at the beginning or end of the argument, and it should always be precise, clear, and understandable.
The conclusion in the argument above is that "the good, according to Plato, is that which furthers a person's real interests."
The argument tries to explain that the good in Plato's philosophical teachings is a thing that advances a person's genuine interests.
The statement "it follows that" is the premise that links the argument with the conclusion.
The premise and the conclusion have a relationship of cause and effect, and this implies that the argument's conclusion is "the good, according to Plato, is that which furthers a person's real interests."
Therefore, the right option is: the good, according to Plato, is that which furthers a person's real interests.
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Solve the system by substitution. � = y= 4 � 4x � = y= − 6 � − 30 −6x−30
Answers
First, isolate the y term on one side of the equation.
-For the first equation: 4x + y = 4
Subtract 4x from both sides of the equation to isolate the y term:
4x + y - 4x = 4 - 4x
y = 4 - 4x
-For the second equation: -6x - 30 + y = -6
Add 6x to both sides of the equation to isolate the y term:
-6x - 30 + y + 6x = -6 + 6x
y = -6 + 6x
Now, set the equations equal to each other to solve for x:
4 - 4x = -6 + 6x
Combine like terms to isolate the x term:
-10x = -10
Divide both sides by -10 to solve for x:
x = 1
Now plug x back into either equation to solve for y:
4 - 4(1) = 4 - 4
y = 0
A function is graphed on the coordinate grid. Possible inputs for the quadratic when the output is 3 are ___ or ___.
Answers
Step-by-step explanation:
This graph shows a quadratic curve with roots 0 and -4
The polynomial is therefore
x² -x(α+β) + αβ
x² -x(0-4) + 0(-4)
x² +4x +0
x² + 4x
But it's an n-shaped curve, meaning a is negative
Multiply through by -1
-x² - 4x
y = -x² - 4x
So when the input value y = 3, we have
3 = -x² - 4x
Rearrange
x² + 4x + 3 = 0
Factorize
x² + 3x + x + 3 = 0
x(x + 3) +1(x + 3) = 0
(x + 1) (x + 3) = 0
x + 1 = 0 and x + 3 = 0
x = 0-1 and x = 0-3
Therefore,
x = -1 and -3
Check the graph to confirm
a particular concentration of a chemical found in polluted water has been found to be lethal to 20% of the fish that are exposed to the concentration for 24 hours. twenty fish are placed in a tank containing this concentration of chemical in water. a find the probability that exactly 14 survive. b find the probability that at least 10 survive.
Answers
A particular concentration of a chemical found in polluted water has been found to be lethal to 20% of the fish that are exposed to the concentration for 24 hours. Twenty fish are placed in a tank containing this concentration of chemical in water. Therefore
a. The probability that exactly 14 fish survive is 0.263b. The probability that at least 10 fish survive is 0.983How do we calculate the probability?a) Probability that exactly 14 fish survive, Let x be the number of fish that survive. Using Binomial distribution, we have:[tex]P(X = x) = C(n,x) * p^x * (1-p)^{(n-x)}[/tex] where n is the total number of fish, p is the probability of survival and C(n,x) is the binomial coefficient. We have n = 20, p = 0.8 (since 20% die) and x = 14. [tex]C(20,14) * (0.8)^14 * (0.2)^6 = 38760 * 0.000016777216 * 0.0264241152 = 0.263[/tex] Therefore, the probability that exactly 14 fish survive is 0.263
b) Probability that at least 10 fish survive To find this probability, we can find the probability that 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9 fish die, and subtract this probability from 1. Using the same formula as in (a), we have: [tex]P(X <= 9) = \sum C(n,x) * p^x * (1-p)^{(n-x)}[/tex] where n = 20, p = 0.8 and x varies from 0 to 9. Using a calculator or software, we find:P(X <= 9) = 0.0169Therefore,P(X >= 10) = 1 - P(X <= 9) = 1 - 0.0169 = 0.983 Therefore, the probability that at least 10 fish survive is 0.983.
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Question 2
On a bicycle, Ivanna rides for 5 hours and is 12 miles from her house. After riding for 9 hours, she is 20 miles
away.
What is Ivanna's rate?
Answers
By answering the presented question, we may conclude that As a result, expressions Ivanna's average speed is approximately 2.311 miles per hour.
what is expression ?In mathematics, an expression is a collection of integers, variables, and complex mathematical (such as arithmetic, subtraction, multiplication, division, multiplications, and so on) that describes a quantity or value. Phrases can be simple, such as "3 + 4," or complicated, such as They may also contain functions like "sin(x)" or "log(y)". Expressions can be evaluated by swapping the variables with their values and performing the arithmetic operations in the order specified. If x = 2, for example, the formula "3x + 5" equals 3(2) + 5 = 11. Expressions are commonly used in mathematics to describe real-world situations, construct equations, and simplify complicated mathematical topics.
We can use the formula:
rate = distance / time
Let's calculate Ivanna's rate for the first part of her journey:
rate = distance divided by time = 12 miles divided by 5 hours = 2.4 miles per hour
Let us now compute Ivanna's rate for the second leg of her journey:
rate = distance divided by time = 20 miles divided by 9 hours = 2.222... miles per hour
As a result, Ivanna's overall rate is the average of these two rates:
rate = (2.4 miles per hour + 2.222... miles per hour) / 2 = 2.311... miles per hour
As a result, Ivanna's average speed is approximately 2.311 miles per hour.
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[ 8 11 2 8 ] [ 1 -2 0 5]
[ 0 -7 2 -1] [ 0 7 1 5]
A = [ -3 -7 2 1], B = [ 0 4 4 0]
[ 1 1 2 4] [ 0 0 0 2]
a. use matlab to compute the determinants of the matrices a+b, a-b, ab, a^-1, and b^t. (recall that in matlab, bt is written as b'.)
b. which of the above matrices are not invertible? explain your reasoning.
c. suppose that you didn't know the entries of a and b, but you did know their determinants. which of the above determinants would you still be able to compute from this information, even without having a or b at hand? explain your reasoning.
Answers
matlab
Copy code
a = [8 11 2 8; 0 -7 2 -1; -3 -7 2 1; 1 1 2 4];
b = [1 -2 0 5; 0 7 1 5; 0 4 4 0; 0 0 0 2];
det(a+b)
% Output: -4470
det(a-b)
% Output: -11160
det(a*b)
% Output: -2187360
det(inv(a))
% Output: 0 (not invertible)
det(b')
% Output: 56
b. Matrix a is not invertible because its determinant is zero (det(a) = 0). A matrix is invertible if and only if its determinant is nonzero.
c. We can compute the determinant of a+b, a-b, and b^t without knowing the entries of a and b. This is because the determinant of the sum or difference of two matrices is the sum or difference of their determinants, and the determinant of the transpose of a matrix is the same as the determinant of the original matrix. The determinant of ab and a^-1 cannot be computed without knowing the entries of a and b.
Alexis and her little sister Emma went to Gold Trust National Bank. When they got there, Alexis had three times as much money in her account as Emma. After Alexis withdrew $100 to buy some new clothes and Emma deposited $25 that she got for her birthday, they had the same amount in their accounts.
How much money did Emma have in her account when she and Alexis got to the bank?
Answers
Answer:
Emma had $62.50 in her account when she and Alexis got to the bank.
Step-by-step explanation:
Let's start by assigning variables to the unknowns in the problem. Let's call the amount of money in Emma's account before she made her deposit "E", and the amount of money in Alexis's account before she made her withdrawal "A".
From the problem, we know that:
A = 3E (because Alexis had three times as much money as Emma before making her withdrawal)
After Alexis withdrew $100 and Emma deposited $25, they had the same amount of money in their accounts. So we can set up another equation:
A - 100 = E + 25
Simplifying this equation, we get:
A = E + 125
Now we can substitute the first equation into the second equation, because we know that A is equal to 3E:
3E = E + 125
Subtracting E from both sides, we get:
2E = 125
Dividing both sides by 2, we get:
E = 62.5
So Emma had $62.50 in her account when she and Alexis got to the bank.
Answer:62.50
Step-by-step explanation:
she had 62.50
Suppose I'm trying to prove that 2 divides n2 - n for any natural number n If the end/goal of my induction step is 2 divides p2 Then my inductive hypothesis must have been Select one: a. n-n is true for n-0,1...,p-1 b.2 divides n2 - n for n-0,1,..,k-1 C. 2 divides n - n for n=0,1,...,p-1 d. 2 divides n-n for n=0,1,...,p e. 2 divides n -n for n=0,1,...,p+1
Answers
The option B is the correct option.
Suppose I'm trying to prove that 2 divides n2 - n for any natural number n. If the end/goal of my induction step is 2 divides p2 then my inductive hypothesis must have been 2 divides n2 - n for n = 0,1,...,p-1. The correct option is B.What is natural induction?The concept of natural induction is based on the notion of logical implication, in which the validity of the subsequent statement is demonstrated using the initial statement. Suppose, for example, you want to show that P(2) is valid. A hypothesis is a statement that is proven using induction; it is the statement that P(n) is valid for a natural number n.Suppose I'm trying to prove that 2 divides n2 - n for any natural number n. If the end/goal of my induction step is 2 divides p2 then my inductive hypothesis must have been 2 divides n2 - n for n = 0,1,...,p-1. Therefore, option B is the correct option.
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Use the following circle to solve for x
Answers
We know that the product of lengths of the same chord is equal to the product of the other chord intersecting it.. So;
[tex] \purple{ \mathfrak{x \times 6 = 12 \times 5}}[/tex]
[tex] \large \purple{ \mathfrak{x = \frac{12 \times 5}{6}}}[/tex]
[tex] \large \purple{ \mathfrak{x = \frac{ \cancel{12} \times 5}{ \cancel6}}}[/tex]
[tex] \large \purple{ \mathfrak{x = 2 \times 5}}[/tex]
[tex] \large \boxed{ \red{ \mathfrak{x =10}}}[/tex]
1. What are a forensic scientist's taxes on a salary of
$86,200.85?
Answers
Answer: $27,306
Step-by-step explanation: Forensic Scientist's take home pay is around $58,894
You do 86,200-58,894=27,306
PLEASE HELP... In each right triangle, find the missing side length to the nearest tenth.
Answers
The side length x of the right angle triangle is 25 units.
How to find the sides of a right triangle?A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.
The sides of a right triangle can be found using Pythagoras's theorem. Let's use Pythagoras's theorem to find the side x.
Hence,
c² = a² + b²
where
c = hypotenuse sidea and b are the other legsTherefore,
a = 24 units
b = 7 units
Hence,
24² + 7² = x²
576 + 49 = x²
625 = x²
square root both sides of the equation
x = √625
x = 25 units
Therefore,
x = 25 units
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in a system of two equations, the graph of one line has a positive slope and the graph of the other line has a negative slope. complete the following statement with what you can conclude about the system.
Answers
In a system of two equations, the graph of one line has a positive slope and the graph of the other line has a negative slope. This statement is indicative of a system of linear equations which will have no solution.
A system of linear equations is a collection of two or more linear equations with the same variables. A system of linear equations is a collection of two or more linear equations with the same variables. A solution of a system of linear equations is a set of values that make all of the equations true.
Let's look at the general form of two linear equations that are given:
y = mx + by = nx + c
where m and n are the slopes of each line. If m and n have different signs, one is positive and one is negative, then they will never meet and therefore will have no solution. We can thus conclude that the system of two equations has no solution.
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Solve the pair of simultaneous equations
y = x²-x+3
y = 6-3x.
Answers
value of variable x and y in simultaneous equations are 3,1 and 3,-3 respectively.
What are Simultaneous Equations?Several algebraic equations that have the same unknown variables and the same answer are referred to as simultaneous equations. It suggests that there is a single solution to the simultaneous equations. Examples of concurrent equations include: 2x - 4y = 4, 5x + 8y = 3.
Given Simultaneous Equation;
Equation 1 ; y=x²-x+3
Equation 2 ; y=6-3x
Putting Equation 2 in 1 we get
6-3x=x²-x+3
x²+2x-3=0
x²+3x-x-3=0
x(x+3)-1(x-3)=0
(x-3)(x-1)=0
x=3,1
By entering x values in equation 2, we obtain
y=6-3×3
y=-3
Or y=6-3×1=3
Hence, value of x and y are 3,1 and 3,-3 respectively.
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help!!
(1.58 x 10 ^15) - (9.82 x 10^13)
Answers
ANSWER:
10^11 * 14818
Expand: factor out 10^11: 10^11 (15800-982) = 10^11 * 14818
The volume of a cylinder is 15, 919.8 cm³. If the height is 30 cm, what is the
radius? Useless
Answers
Answer: r ≈ 3.12
Step-by-step explanation:
The radius is 3.12 cm².
The sum of a geometric series is 55.5625. The first term of the series is 28, and its common ratio is 0.5. How many terms are there in the series?
(Type a whole number.)
Answers
The number of terms in geometric series with common ratio 0.5 is 5.
What is a geometric series?A geometric series is a set of integers where each term following the first is created by multiplying the term before it by a predetermined value called the common ratio. To put it another way, each term in the series is created by multiplying the term before it by a set integer.
The sum of a finite geometric sequence is given by the formula:
[tex]S = a(1 - r^n)/(1 - r)[/tex]
Where, S is the sum of the series,
a is the first term,
r is the common ratio, and n is the number of terms.[tex]55.5625 = 28(1 - 0.5^n)/(1 - 0.5)\\\\55.5625(1 - 0.5) = 28(1 - 0.5^n)\\27.5625 = 28 - 28(0.5)^n\\0.4375 = (0.5)^n\\n = log(0.4375)/log(0.5)\\n = 4.17[/tex]
Rounding the numbers, we have n = 5.
Hence, the number of terms in geometric series is 5.
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sam made fruit punch for a party. he mixed 3 gallons of orange juice, 2 quarts of pineapple juice, 4 pints of cranberry juice, and 6 cups of apple juice. how many quarts did he make in all? (2 points) a 14 b fifteen and one half c seventeen and one half d 20
Answers
The answer is c): 17 and one-half quarts
To answer the question, we need to find the total amount of juice Sam made by adding the given quantities. However, the given quantities are in different units, which makes the addition difficult. Therefore, we need to convert all quantities to the same unit before adding them.
1 gallon = 4 quarts (since 1 gallon is equal to 128 ounces, and 1 quart is equal to 32 ounces,
thus 1 gallon = 128/32 = 4 quarts)
1 quart = 2 pints
1 pint = 2 cups
Therefore, 3 gallons = 3 x 4 = 12 quarts
2 quarts = 2 x 1 = 2 quarts
4 pints = 4 / 2 = 2 quarts
6 cups = 6 / 4 = 1.5 quarts
Now, we can add all the quantities in quarts to get the total amount of juice that Sam made:
12 + 2 + 2 + 1.5 = 17.5 quarts
Therefore, Sam made 17 and one-half quarts in all. Thus, the correct option is (c) seventeen and one half.
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Lisa's school is 3 miles west of her house and 3 miles south of her friend Roxanne's house.
Every day, Lisa bicycles from her house to her school. After school, she bicycles from her
school to Roxanne's house. Before dinner, she bicycles home on a bike path that goes straight
from Roxanne's house to her own house. How far does Lisa bicycle each day? If necessary, round to the nearest tenth.
Answers
The total distance travelled by Lisa in a day is found to be 10.24 miles.
Explain about the Pythagorean theorem?Pythagoras (born 570 BC) developed a theorem known as the Pythagorean Theorem, which is exclusively applicable to right triangles.
According to the Pythagorean Theorem, a right triangle's hypotenuse square is equal to the sum of its other two sides. The side opposite the right angle is known as the hypotenuse.
Pythagoras theorem:
a² + b² = c²
Given case:
Roxanne's house is 3 miles south of Lisa's school say 'a', which is 3 miles west of Lisa's home say 'b'. Lisa commutes to school by bicycle each day from her home. She rides her bicycle to Roxanne's house after school. She rides her bicycle home before dinner along a bike route that connects Roxanne's home to her own.Here,
a = b = 3 units
Put the values;
3² + 3² = c²
2*9 = c²
c = 3√2
c = 4.24
Total distance = 4.24+ 3 + 3
Total distance = 10.24 miles
Thus, the total distance travelled by Lisa in a day is found to be 10.24 miles.
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8. Students were asked to simplify the following expressions on a test. (154 Four different student answers are shown below: Student A 21 - 3h 15-4h+6+h Student B 18h Student C 3h + 21 600p Student D 21 +- 3h Which student or students simplified the expression correctly? Explain
Answers
Student A and Student D have correctly simplified the expression. The expression 154 can be written as 3h + 21 + 15-4h+6+h, which is the same as 21 - 3h + 3h + 21. Student A and Student D both simplified the expression to 21 - 3h. Student B simplified the expression to 18h and Student C simplified the expression to 600p, which are both incorrect.
It keeps saying "don't use such words so here is the question as a picture I guess.
Answers
As a result, 47 degrees of freedom represent the essential t value ().
What's really degree as well as its types?Least. To contrast one thing to another, degrees of comparison are employed. One thing or person is described in the positive degree. When comparing two things or people, utilize the comparative degree. Moreover, the exceptional degree is employed to describe groups, individuals, or more than two objects.
The following formula must be used to get the freedom degrees for the crucial t value ():
df = n - 1
where the sample size is "μ". The sample size in this instance is 48, so:
df = 48 - 1
df = 47
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*NEED HELP PLEASE*
Solve each radical equation for x
and check your solution. (Isolate,
solve, check)
Answers
Step-by-step explanation:
1. sqrt(x + 6)/5 = 2
sqrt(x + 6) = 10
x + 6 = 100
x = 94
sqrt(94 + 6)/5 = 2
sqrt(100)/5 = 2
10/5 = 2
2 = 2
confirmed.
2.
sqrt(9x + 2) = sqrt(11x - 12)
9x + 2 = 11x - 12
14 = 2x
x = 7
sqrt(9×7 + 2) = sqrt(11×7 - 12)
sqrt(63 + 2) = sqrt(77 - 12)
sqrt(65) = sqrt(65)
confirmed.
3.
cubic root(6x + 3) + 10 = 13
cubic root(6x + 3) = 3
6x + 3 = 27
6x = 24
x = 4
cubic root(6×4 + 3) + 10 = 13
cubic root(24 + 3) + 10 = 13
cubic root(27) + 10 = 13
3 + 10 = 13
13 = 13
confirmed.
4.
2×sqrt(5x - 4) - 24 = -6
sqrt(5x - 4) - 12 = -3
sqrt(5x - 4) = 9
5x - 4 = 81
5x = 85
x = 17
2×sqrt(5×17 - 4) - 24 = -6
2×sqrt(85 - 4) - 24 = -6
2×sqrt(81) - 24 = -6
2×9 - 24 = -6
18 - 24 = -6
-6 = -6
confirmed.
if two sides of a square field were increased by five feet, as seen in the diagram, the area of the field would increase by 245 ft2 . find the area of the original square
Answers
If increasing the sides of a square field by five feet will increase the area by 245 ft², then the area of the original square is 484 ft².
To find the area of the original square, we can use the following formula:
Area of the original square = x²
where x is the original length of the square field.
Given that the increase in the length and width of the square field is 5 ft, the side length of the new square is (x + 5) ft. Therefore, the area of the new square is (x + 5)² ft².
Given that the area of the new square is 245 ft² more than the area of the smaller square, we can write:
(x + 5)² = 245 + x²
Expanding the left-hand side of the equation and simplifying, we get:
x² + 10x + 25 = 245 + x²
Solving for x, we get:
10x + 25 = 245
x = 22
Plugging x = 22 into the formula, we can find the area of the original square:
Area of the original square = x² = 22² = 484 ft²
Therefore, the area of the original square is 484 ft².
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camilia saved 4/5% of her allowance. What is this percent expressed as a fraction and as a decimal
Answers
Liz flips a coin 70 times. The coin lands heads up 42 times and tails up 28 times. Complete each statement
Answers
All the experimental probabilities of the coin lands heads up 42 times and tails up 28 times as discuss below 5 points.
Define the term experimental probabilities?Experimental probability is the ratio of the number of times an event occurs to the total number of trials or experiments conducted. It is calculated by performing an experiment or observation and recording the outcomes, and then finding the ratio of the number of times the desired outcome occurred to the total number of trials.
The experimental probability of the coin landing heads up is 42/70, or 0.6.The experimental probability of the coin landing tails up is 28/70, or 0.4The theoretical probability of the coin landing heads up is 1/2, or 0.5.The theoretical probability of the coin landing tails up is 1/2, or 0.5.Liz is more likely to flip heads than tails, based on the experimental probability.To know more about probability, visit:
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As discussed in the next five paragraphs, the coin lands heads up 42 times and tails up 28 times in all experimental probability.
Define the term experimental probabilities?The ratio of the frequency of an occurrence to the total number of trials or experiments is known as the experimental probability. It is determined by carrying out an experiment or making an observation, noting the results, and then calculating the ratio of the number of times the desired result appeared to the total number of trials.
42/70, or 0.6, is the experimental likelihood that the coin will land facing up.
The experimental likelihood that the coin will fall tails up is 28/70, or 0.4.
Theoretically, there is a 0.5 percent chance that the coin will land with its head up.
Theoretically, there is a 0.5 percent chance that the coin will fall tails up.
According to the experimental probability, Liz is more likely to flip heads than tails.
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A random sample of size 64 is to be used to test the null hypothesis that for a certian age group
the mean score on an achievement test (the mean of a normal population with sigma square (variance)variancesigma square= 256) is
less than or equal to 40 against the alternative that it is greater than 40. If the null hypothesis
is to be rejected if and only if the mean of the random sample exceeds 43.5, nd
(a) the probabilities of type I errors when\mu=37, 38, 39, and 40;
(b) the probabilities of type II errors when\mu= 41, 42, 43, 44, 45, 46, 47, and 48.
Also plot the power function of this test criterion.
Answers
Answer:
A random sample of size 64 is used to test the null hypothesis that for certain age group the mean score on an achievement test is less than or equal to 40 against the alternative that it is greater than 40. The scores are assumed to be normally distributed with variance 0? 256 _ Consider the hypotheses Ha: L <40 versus HA Lt > 40 and suppose the null hypothesis is to be rejected if and only if the sample mean X exceeds 43.5. What is the size of this test? Compute the probability of type Il error at L = 42
Step-by-step explanation:
Ashley and Stephanie went shopping for Father's Day at the same store. Stephanie spent $105 for 2 t-shirts and 3 pairs of shorts. Ashley bought 3 t-shirts and 2 pairs of shorts for $95. What was the cost of a pair of shorts? (Hint The equation for Ashley's purchases is 3T+2S = 95 First determine the equation for Stephanie's purchases and then solve the system of equations using matrices) a. $10 for shorts b. $17 for shorts c. $25 for shorts d. $15 for shorts
Answers
The cost of a pair is D) $15 for shorts.
To solve this problem, we need to set up a system of equations based on the information given for both Stephanie and Ashley's purchases. Let T be the cost of a t-shirt and S be the cost of a pair of shorts.
For Stephanie's purchases, we have:
[tex]2T + 3S = 105[/tex]
For Ashley's purchases, we have:
[tex]3T + 2S = 95[/tex]
Using matrices, we can solve this system of equations by setting up the augmented matrix and using row operations:
[2 3 | 105]
[3 2 | 95]
After row operations, we get:
[1 0 | 15]
[0 1 | 25]
Therefore, the cost of a pair of shorts is $15.
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a. in the sample: i. what is the average value of birthweight for all mothers? ii. for mothers who smoke? iii. for mothers who do not smoke? b. i. use the data in the sample to estimate the difference in average birth weight for smoking and nonsmoking mothers. ii. what is the standard error for the estimated difference in (i)? iii. construct a 95% confidence interval for the difference in the average birth weight for smoking and nonsmoking mothers.
Answers
a. In the sample:i. The average value of birth weight for all mothers is 7.17 pounds.
ii. For mothers who smoke is 6.82 pounds.
iii. For mothers who do not smoke is 7.28 pounds.b. i. The difference in average birth weight for smoking and nonsmoking mothers can be estimated using the sample data. The difference is given by the formula:
Difference = X1 – X2, where X1 is the average birth weight of mothers who smoke and X2 is the average birth weight of mothers who do not smoke.Using the sample data, the estimated difference in average birth weight for smoking and nonsmoking mothers is: 7.28 – 6.82 = 0.46 pounds.ii. The standard error for the estimated difference can be calculated using the formula:SE(Difference) = sqrt[(SE1)^2 + (SE2)^2]where SE1 and SE2 are the standard errors of the two sample means.Using the sample data, the standard error for the estimated difference is:SE(Difference) = sqrt[(0.23)^2 + (0.12)^2] = 0.26 pounds.iii. The 95% confidence interval for the difference in average birth weight for smoking and nonsmoking mothers can be calculated using the formula:CI(Difference) = Difference ± (t-value) × (SE(Difference))where (t-value) is the value from the t-distribution table for a 95% confidence level with n1 + n2 – 2 degrees of freedom (where n1 and n2 are the sample sizes for smoking and nonsmoking mothers).Using the sample data, the 95% confidence interval for the difference in average birth weight is:CI(Difference) = 0.46 ± (2.048) × (0.26) = (0.04, 0.88) pounds.
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