Answer:
We can use the cosine double angle formula to find cos(2π/3):
cos(2θ) = cos^2(θ) - sin^2(θ)
Letting θ = π/3, we get:
cos(2π/3) = cos^2(π/3) - sin^2(π/3)
Using the values of cosine and sine of π/3 (which are known), we have:
cos(2π/3) = (1/2)^2 - (√3/2)^2
Simplifying, we get:
cos(2π/3) = 1/4 - 3/4
cos(2π/3) = -1/2
Therefore, cos(2π/3) is equal to -1/2.
Answer:
cos(2π/3) = cos(π/3 + π/3)
= cos²(π/3) - sin²(π/3)
= (1/2)² - (√3/2)²
= 1/4 - 3/4
= -2/4
= -1/2
Step-by-step explanation:
here are the steps:
Convert 2π/3 to degrees: 2π/3 * (180/π) = 120°Use the double angle formula for cosine: cos(2θ) = cos²(θ) - sin²(θ)Substitute π/3 for θ: cos(2π/3) = cos²(π/3) - sin²(π/3)Use the values of cosine and sine of π/3 from the unit circle: cos(π/3) = 1/2 and sin(π/3) = √3/2Substitute these values into the formula: cos(2π/3) = (1/2)² - (√3/2)²Simplify the expression inside the parentheses: cos(2π/3) = 1/4 - 3/4Combine like terms: cos(2π/3) = -2/4Simplify the fraction: cos(2π/3) = -1/2Therefore, cos(2π/3) = -1/2
Find the margin of error for a survey that has a sample size of 6400.
The margin of error for a survey with a sample size of 6400 and a 95% confidence level is approximately 1.6%.
What is confidence level?Confidence level is a statistical concept that measures the degree of certainty or reliability associated with an estimate, such as the mean, proportion, or regression coefficient, derived from a sample of data.
According to question:The margin of error (ME) for a survey depends on several factors, including the size of the sample, the level of confidence desired, and the population size (if applicable). Assuming a 95% confidence level, a sample size of 6400, and no information about the population size, the formula for calculating the margin of error is:
ME = 1.96 × √[(p × q) / n]
where:
1.96 is the z-score associated with a 95% confidence level
p is the estimated proportion of the population that has the characteristic of interest (this is usually unknown and is typically replaced with 0.5 to get the maximum possible margin of error)
q is 1 - p
n is the sample size
Assuming a conservative estimate of p = 0.5, we have:
ME = 1.96 × √[(0.5 × 0.5) / 6400]
≈ 0.016 or 1.6%
Therefore, the margin of error for a survey with a sample size of 6400 and a 95% confidence level is approximately 1.6%. This means that if the survey were conducted multiple times using the same sample size and methodology, the results would likely differ by no more than 1.6% in either direction (plus or minus) from the true population value.
To know more confidence level visit:
https://brainly.com/question/30229866
#SPJ1
50 Points! Multiple choice algebra question. Determine which pair of functions are inverse functions. Photo attached. Thank you!
The pair of the functions that are inverse is
A. f(x) = x - 4; g(x) = (x + 4)How to find the inverse of the functionThe inverse of the function is solved by the operations as follows
f(x) = x - 4 let y = f(x)
y = x - 4
solving for x
x = y + 4
interchanging the variables
y = x + 4 (this is the inverse)
the inverse x + 4 is equal to g(x) hence they are inverse functions
Learn more about inverse functions
https://brainly.com/question/3831584
#SPJ1
Draw and label a rectangular prism that has a surface area of 96 square meters
There are 2 sides.
First side is 12 by 2 so you would multiply them together which is 24 and since there is another side the same length multiply by 2 which is 48.
Second side small side is 2 by 4 so multiply them together which is 8 and since there is another side the same demension multiply 8 by 2 which is 16.
The last side is 12 by 4 so again multiply them together which is 48. Multiply it by two since there is another side with same dimension which is 96.
Now do 48 + 16 + 96 (the answer gotten after finding the areas for each sides and their identicals) which is 160 ft²
The label for rectangular prism that has a surface area of 96 square meters is in the attached image.
An individual depositing in a non-IRA account has to pay income taxes on the funds deposited and on interest earned in each year but does not have to pay taxes on withdrawals from the account.
Sarah, who is five years from retirement, receives a $10,000 bonus at work. She is trying to decide whether to save this extra income in an IRA account or in a regular savings account. Both accounts earn 8 percent nominal interest, and Sarah is in the 30 percent tax bracket in every year (including her retirement year)
If Sarah invests in the normal savings account, her net value (after taxes) five years from now will be?:
After five years, her IRA account's net worth (after taxes) will indeed be $14,322.88 ($10,000 + $4,322.88).
What do you mean by interest earned?Sarah will be required to file taxes just on interest received each year if she places the $10,000 inside a standard savings account, which will lower her net worth.
She will have earned $800 in pre-tax interest every year, assuming she receives nominal interest of 8% annually.
She will, however, be liable for $240 in taxes just on interest generated each year (30% of $800) since she falls into the 30% tax bracket.
Her pre-tax interest earnings after five years will total $4,000 ($800 x five years). She will still have paid $1,200 in total in taxes just on interest generated ($240 x 5)
She will therefore have a net worth of $12,800 ($10,000 + $4,000 - $1,200) in the normal savings account after five years (after taxes).
Sarah won't have to pay taxable income on the $10,000 invested in such an IRA account or the interest accrued until she starts taking distributions in retirement.
She will have earned $800 in pre-tax interest every year, assuming she receives nominal interest of 8% annually.
She will have the whole $800 to reinvest & compound each year, though, as she is not subject to income taxation on the interest gained each year.
She will have earned $4,322.88 in pre-tax interest after five years, and she won't have to pay any taxes until she starts taking withdrawals in retirement.
To know more about taxation visit:
https://brainly.com/question/28170783
#SPJ1
Find the area
Round to nearest tenth
The total surface area to paint is 22000 sq. ft.
What is surface area?Surface area is the measurement of the outer surface of an object. It is often used to calculate the area of a three-dimensional object, such as a cube, cylinder, or sphere, and is also used to calculate the area of the faces of a solid object. Surface area is measured in square units such as square centimeters (cm2), square meters (m2), or square inches (in2).
Surface Area = 2(lw + lh + wh)
Surface Area = 2((100' x 50') + (100' x 40') + (50' x 40'))
Surface Area = 2(5000' + 4000' + 2000')
Surface Area = 2(11000')
Surface Area = 22000 sq. ft.
Answer: The total surface area to paint is 22000 sq. ft.
To know more about surface area click-
http://brainly.com/question/16519513
#SPJ1
If October 15 falls on a Wednesday, then November 11 of that same year falls on which day of the week? (October has 31 days)
Answer:
There are 31 days in October, so there are 31 - 15 = 16 days left in October after October 15.
16 days is equivalent to 2 weeks and 2 days (since there are 7 days in a week), so November 11 is 2 weeks and 2 days after October 15.
Therefore, November 11 falls on a Wednesday + 2 weeks + 2 days = Friday.
So November 11 of that same year falls on a Friday.
The circumference of a circle is 20 cm. What is the
area, in square centimeters? Express your answer in terms
of TT.
The circumference of a circle whose area is 20π cm² in terms of pi is 8.94π centimeters.
What is the circumference of the circle?A circle is simply a closed 2-dimensional curved shape with no corners or edges.
The area of a circle is expressed mathematically as;
[tex]\text{A} = \pi \text{r}^2[/tex]
The circumference of a circle is expressed mathematically as;
[tex]\text{C} = 2\pi \text{r}[/tex]
Given that the area of the circle is 20π cm², we determine the radius of the circle.
[tex]\text{A} = \pi \text{r}^2[/tex]
[tex]20\pi \ \text{cm}^2 = \pi \times \text{r}^2[/tex]
[tex]\text{r}^2= \dfrac{ 20\pi \ \text{cm}^2}{\pi }[/tex]
[tex]\text{r}^2 = 20 \ \text{cm}^2[/tex]
[tex]\text{r} = \sqrt{20 \ \text{cm}^2}[/tex]
[tex]\text{r} = 4.47 \ \text{cm}[/tex]
Now, we determine the circumference of the circle.
[tex]\text{C} = 2\pi \text{r}[/tex]
[tex]\text{C} = 2 \times \pi \times 4.47 \ \text{cm}[/tex]
[tex]\text{C} = 8.94 \ \text{cm}\times\pi[/tex]
[tex]\text{C} = 8.94\pi[/tex]
Therefore, the circumference of the circle is 8.94π centimeters.
Learn more about circles here: brainly.com/question/11952845
Let a =⟨–7, 3⟩ and b =⟨–2, –12⟩, and c = a + b. What is the magnitude and direction angle of c?
Answer: direction angle of c is pi/4.
Step-by-step explanation: We can find c by adding the corresponding components of a and b:
c = a + b = ⟨–7, 3⟩ + ⟨–2, –12⟩ = ⟨–9, –9⟩
To find the magnitude of c, we can use the formula:
|c| = sqrt(c1^2 + c2^2)
where c1 and c2 are the x- and y-components of c, respectively. In this case, we have:
|c| = sqrt((-9)^2 + (-9)^2) = sqrt(162) = 9sqrt(2)
To find the direction angle of c, we can use the formula:
theta = atan(c2 / c1)
where theta is the angle between the positive x-axis and the vector c. In this case, we have:
theta = atan((-9) / (-9)) = atan(1) = pi/4
So the direction angle of c is pi/4.
Therefore, the magnitude of c is 9sqrt(2) and the direction angle of c is pi/4.
Many fences in a rectangular area for his dog to play in the backyard. The area measures 35 yards by 45 yards .What is the length of fence that Manny uses a) 1,575 yards b) 160 yards c) 80 yards d) 35 yards
On solving the provided question we can say that Manny would thus require 160 yards of fencing to surround the rectangular plot.
What is perimeter?A boundary is a closed route that embraces, encircles, or delimits a two-dimensional form or length in one dimension. The perimeter of a circle or an ellipse is its outermost section. The perimeter calculation is used in a variety of real-world situations. The perimeter of a form is the radius of its edge. Discover how to calculate the perimeter by adding the lengths of the sides of various shapes. The perimeter of a shape may always be calculated by multiplying the lengths of its sides. The perimeter of a thing is the region that surrounds it. At your house, one example is an enclosed garden. The distance around anything is referred to as its perimeter. A 200-foot fence will be required for a 50-foot-by-50-foot yard.
P = 2(l + w), where l is the length and w is the width, gives the perimeter of a rectangle.
The length in this example is 35 yards, while the breadth is 45 yards. So,
[tex]P = 2(35 + 45)\\= 2(80)\\= 160 yards\\[/tex]
Manny would thus require 160 yards of fencing to surround the rectangular plot.
As a result, option (b) 160 yards is the right answer.
To know more about perimeter visit:
https://brainly.com/question/6465134
#SPJ1
A recipe that uses 1/2 pound of almonds makes 5/6 cup of almond butter.
Which is a reasonable estimate for the amount of almond butter the recipe makes per pound of almonds?
a) less than 1 1/2 cup of almond butter
b) between 1 1/2 and 2 cups of almond butter
c) more than 2 cups of almond butter
Answer: C
Step-by-step explanation:
1/2 pound of almonds = 5/6 cup of almond butter
To find out how much almond butter 1 pound of almonds will make, we need to multiply both sides of the equation by 2:
1 pound of almonds = (2 × 1/2) pounds of almonds = 2 × 5/6 cups of almond butter
Simplifying, we get:
1 pound of almonds = 5/3 cups of almond butter
So, a reasonable estimate for the amount of almond butter the recipe makes per pound of almonds is more than 2 cups of almond butter. Therefore, the answer is (c) more than 2 cups of almond butter.
Answer: b) between 1 1/2 and 2 cups of almond butter
Step-by-step explanation:
We can create a proportion to help us solve this question.
[tex]\displaystyle \frac{\frac{1}{2} lbs\;almonds}{\frac{5}{6}lbs\;butter } =\frac{1lbs\;almonds}{xlbs\;butter}[/tex]
Now we can cross multiply.
[tex]\displaystyle \frac{1}{2} *x=\frac{5}{6} *1[/tex]
[tex]\displaystyle \frac{1}{2}x =\frac{5}{6}[/tex]
Next, we will divide both sides of the equation by one-half.
[tex]\displaystyle x =\frac{5}{6}\div \frac{1}{2}[/tex]
[tex]\displaystyle x =\frac{5}{6}* \frac{2}{1}[/tex]
[tex]\displaystyle x =\frac{10}{6}[/tex]
Lastly, we will find which answer option this falls under by creating an improper fraction. This leads us to answer optoin b, b) between 1 1/2 and 2 cups of almond butter.
[tex]\displaystyle 10-6=4\text{, so } 1\frac{4}{6} =1\frac{2}{3}[/tex]
Drag each tile to the correct box.
A scientist is studying the growth rates of three samples of bacteria in different conditions. The following three functions represent the number of bacteria in the three samples after x hours.
Sample A Sample B Sample C
x g(x)
0 60
1 120
2 240
3 480
Sample C starts
with 600 bacteria and
increases at a
rate of 20%.
f(x)=200(3/2)x^
Order the samples by their average growth rate over the interval [1, 3], from least to greatest.
Sample C
Sample A
Sample B
pleaseeee help thank youuu
we can see that the growth rate increases as x increases. However, since we are only interested in the average growth rate over the interval [1, 3], we can calculate it using the formula mentioned above.
How to solve the question?
To determine the average growth rate of each sample over the interval [1, 3], we need to calculate the ratio of the change in bacteria population to the change in time for each sample, and then take the average of these ratios over the given interval.
For Sample A, the change in bacteria population over the interval [1, 3] is 480 - 120 = 360, and the change in time is 3 - 1 = 2. So the average growth rate of Sample A over this interval is 360/2 = 180 bacteria per hour.
For Sample B, the change in bacteria population over the interval [1, 3] is 480 - 240 = 240, and the change in time is 3 - 1 = 2. So the average growth rate of Sample B over this interval is 240/2 = 120 bacteria per hour.
For Sample C, the change in bacteria population over the interval [1, 3] is (1.2600)(1.2*1.2 - 1) = 345.6, and the change in time is 3 - 1 = 2. So the average growth rate of Sample C over this interval is 345.6/2 = 172.8 bacteria per hour.
For Sample A, the growth rate is the highest, followed by Sample C and then Sample B. Therefore, the order of the samples by their average growth rate over the interval [1, 3] from least to greatest is Sample C, Sample A, and Sample B.
It's important to note that the growth rate of Sample C is not constant but increases over time due to the 20% increase in the initial bacteria population. The exponential function f(x) = 200(3/2)in power x represents this growth, and we can see that the growth rate increases as x increases. However, since we are only interested in the average growth rate over the interval [1, 3], we can calculate it using the formula mentioned above.
To know more about interval visit :-
https://brainly.com/question/479532
#SPJ1
Your complete question is :-A scientist is studying the growth rates of three samples of bacteria in different conditions. The following three functions represent the number of bacteria in the three samples after x hours.
Sample A Sample B Sample C
x g(x)
0 60
1 120
2 240
3 480
Vivian Thomas is going to put insecticide on her lawn to control grubworms.
The lawn is a rectangle measuring 123.8 feet by 80 feet. The amount of insecticide required is 0.02 ounces per square foot. Find how much insecticide Vivian needs to purchase.
The amount of insecticide that Vivian needs to purchase
for the control of pest in the lawn would be = 198.08 ounces
How to calculate the area of the rectangular lawn?To calculate the area of the rectangular lawn, the formula for the area of rectangle should be used. That is ;
Area = Length× width
Length = 123.8 feet
width = 80feet
Area = 123.8× 80 = 9,904ft²
But 0.02 ounces of insecticide = 1 ft²
X ounces = 9,904ft²
Make X the subject of formula;
X = 9904×0.02
= 198.08 ounces.
Learn more about area here:
https://brainly.com/question/28470545
#SPJ1
1. Which expression is equal to 4^0x4²?
A. 0
B. 1
C. 16
D. 64
• Concept: Exponents
• Solution:
You want to simplify the expression 4⁰×4².
We will use basic exponent properties for this.
First bear in mind that anything to the power of 0 is 1.
So that means that 4⁰ = 1.
We're not done yet because we still need to simplify the other part:
4².
Don't forget that:
4² ≠ 4×2Because
4² = 4×4 which is 16
So we have 1 times 16 or just 16.
Answer: choice "c": 16
Please help answer this with good explication and I'll give Thanks , five stars and maybe even brainly.
Andy has X pence. Kelly ha s 7 pence more than Andy . Georgia had a pence less than Andy. Total amount of money they have is 1.48
A) form an equation in terms of x and solve th equation
Let's call the amount of money Andy has "x".
According to the problem, Kelly has 7 pence more than Andy, so Kelly has x + 7 pence.
Georgia has a penny less than Andy, so Georgia has x - 1 pence.
The total amount of money they have is 1.48, which we can write as 148 pence.
So we can set up the equation:
x + (x + 7) + (x - 1) = 148
Simplifying and solving for x:
3x + 6 = 148
3x = 142
x = 47.33
Since we're dealing with pence, we'll round down to the nearest whole number:
x = 47
So Andy has 47 pence, Kelly has 54 pence (47 + 7), and Georgia has 46 pence (47 - 1).
How do you write 843,400 in scientific notation
Answer:
Scientific notation = 8.434 × 10^5
Scientific e notation = 8.434e5
Engineering notation = 843.4 × 10^3 ---> (thousand; prefix kilo- (k) )
Standard form = 8.434 × 10^5
please help studying my next grade:
12+6÷(82-33)x66
Answer:
3246
Step-by-step explanation:
To calculate this equation, we need to follow the order of operations, also known as PEMDAS. First, we evaluate anything inside parentheses, which in this case is (82-33), giving us 49. Next, we perform division, so we have 6 ÷ 49. Then, we multiply 49 and 66, resulting in 3234. Finally, we add 12 to 3234, leading to the final answer of 3246. Therefore, the value of the expression 12+6÷(82-33)x66 is 3246.
Answer:
3246
Step-by-step explanation:
2+7•(-3)^2
Help me
How do I solve. ?
Answer:
To solve the expression 2 + 7 • (-3)^2, we follow the order of operations, also known as PEMDAS/BODMAS, which stands for Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
First, we evaluate the exponent: (-3)^2 = 9 (because squaring a number means multiplying it by itself).
Next, we perform multiplication: 7 • 9 = 63.
Finally, we perform addition: 2 + 63 = 65.
So, the value of the expression 2 + 7 • (-3)^2 is 65.
HURRY DUE TONIGHT
Danielle was completing her science project and mixed saline solutions A and B. Brand A was a six gallon 18% saline solution and she ended up with an 18 gallon 8% saline solution mixture. Find the percent of saline solution in brand B.
A. 21%
B. 3%
Brand B contains 3% saline solution by volume.
The correct option is B.
We have,
Brand A was a six gallon 18% saline solution.
Final, she 18 gallon 8% saline solution mixture.
let the percentage of saline solution in brand B be x.
So, volume of saline solution
= 18% of 6 gallons + x% of (18 - 6) gallons
Then the equation is given as,
0.18(6) + 0.01x(18 - 6) = 0.08(18)
1.08 + 0.12x = 1.44
0.12x = 0.36
x = 3
Thus, the percentage of saline solution in brand B is 3%.
Learn more about the percentage here:
brainly.com/question/8011401
#SPJ1
According to government data, 20% of employed women have never been married. Assume an SRS of seven employed women are selected and asked if they have ever been married.
a. What is the random variable X of interest here? Define X.
b. Out of the 7 employed women selected at random, what is the probability that exactly 2 have never been married? (Show your work below) _________
c. Out of the 7 employed women selected at random, what is the probability that 2 or fewer have never been married? ___________
d. What are the mean and standard deviation of X?
Mean:_________ Standard Deviation _________
a. The total quantity of employed women among the sample of 7 who are not married yet is the random variable X of interest in this situation. b) Probability = 0.2749.
What is binomial distribution?The number of successes in a defined number of independent trials with two possible outcomes (success or failure) and a constant probability of success are described by a discrete probability distribution called a binomial distribution. The number of trials (n) and the likelihood that a trial will succeed (p) serve as the two parameters that define the binomial distribution.
a. The total quantity of employed women among the sample of 7 who are not married yet is the random variable X of interest in this situation.
b) The probability of 2 women who have never been married is:
P(X = 2) = (7 choose 2) * (0.2)² * (0.8)⁵
P(X = 2) = 21 * 0.04 * 0.32768
P(X = 2) = 0.2749
c) For 2 or fewer have never been married:
P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)
P(X ≤ 2) = (7 choose 0) * (0.2)⁰ * (0.8)⁷ + (7 choose 1) * (0.2)¹ * (0.8)⁶ + (7 choose 2) * (0.2)² * (0.8)⁵
P(X ≤ 2) = 0.0577 + 0.2013 + 0.2749
P(X ≤ 2) = 0.5339
d) The mean is given as:
μ = np
Substitute n = 7 and p = 0.2:
7 * 0.2 = 1.4
Now, the standard deviation is given as:
σ = √(np(1-p)) = √(7 * 0.2 * 0.8) = 1.0198
Learn more about binomial distribution here:
https://brainly.com/question/31197941
#SPJ1
Find the surface area
Round to the nearest tenth
There are [tex]144 + 336 = 480[/tex] square units of surface area overall. The shape has a surface area of 480.0 square units, rounded to the closest tenth.
what is surface area ?The dimensions and shape of the object are taken into account while calculating surface area. The volume of water of a cube, for instance, can be computed by adding the areas of the all six of its equal-sized faces. The surface temperature of something like a sphere, while on the other hand, must be calculated using mathematical methods that take into consideration its radius. The concept of surface area is crucial to many branches of mathematics, science, & engineering.
given
The area of each of the two triangles is [tex](1/2) * 3 * 8 = 12[/tex] square units since each triangle has a base of 3 and a height of 8, respectively.
The trapezium features an 8-inch height, a 6-inch top base, a 12-inch bottom base, and a 10-inch slant height.
two rectangles, each measuring 72 square units: 144 square units (2 x 72)
Four trapezoidal sides, each with a surface area of 12 + 72 = 84 square units 336 square units (4 x 84)
There are [tex]144 + 336 = 480[/tex] square units of surface area overall. The shape has a surface area of 480.0 square units, rounded to the closest tenth.
To know more about surface area visit:
https://brainly.com/question/2835293
#SPJ1
Can someone help proving these three distributions？How to get them
The proof of the three distributions as required as shown in the explanation part.
What are the proof of the three distributions?For x² distribution:
Let's start with the sample variance, which is defined as:
s^2 = ∑(y_i - y_bar)² / (n-1)
where;
y_i is the i-th observation in the sample, y_bar is the sample mean, and n is the sample size.We can rewrite this formula as:
s^2 = (∑y_i² - n*y_bar²) / (n-1)
Multiplying both sides by (n-1)/σ², we get:
s^2 / σ² = (∑y_i² - ny_bar²) / (σ²(n-1))
Now, let's define a new variable:
x² = ∑y_i² / σ²
Substituting x² into the above equation, we get:
s^2 / σ² = (x² - n*y_bar²/σ²) / (n-1)
Notice that n*y_bar²/σ² is just the sample mean squared in units of variance. We can rewrite it as:
n*y_bar²/σ² = (y_bar - μ)² / (σ²/n)
where;
μ is the population mean.Substituting this into the above equation, we get:
s^2 / σ² = (x² - (y_bar - μ)² / (σ²/n)) / (n-1)
Now, let's define a new variable:
ss = ∑(y_i - y_bar)² / σ²
Substituting ss into the above equation, we get:
s^2 / σ² = (x² - ss/(n-1)) / n
This is the desired result. We have shown that s²/σ² follows a x² distribution with n-1 degrees of freedom.
For t distribution:
Let's start with the sample mean, which is defined as:
y_bar = ∑y_i / n
We can rewrite this formula as:
y_bar - μ = (∑y_i - n*μ) / n
Now, let's define a new variable:
t = (y_bar - μ) / (s/√n)
where;
s is the sample standard deviation.Substituting y_bar - μ and s into the above equation, we get:
t = (∑y_i - nμ) / (s√n)
This is the desired result. We have shown that t follows a t distribution with n-1 degrees of freedom.
For F distribution:
Let's start with the sample variances, which are defined as:
s₁² = ∑(y_i - y₁)² / (n₁-1)
s₂² = ∑(y_i - y₂)² / (n₂-1)
where;
y₁ and y₂ are the sample means, and n₁ and n₂ are the sample sizes.We can rewrite these formulas as:
s₁² = (ss₁ - n₁*(y₁-μ)²) / (n₁-1)
s₂² = (ss₂ - n₂*(y₂-μ)²) / (n₂-1)
where;
μ is the population mean, and ss₁ and ss₂ are the sum of squares within each sample:ss₁ = ∑(y_i - y₁)²
ss₂ = ∑(y_i - y₂)²
Dividing these equations, we get:
s₁² / s₂² = (ss₁ / (n₁-1)) / (ss₂ / (n₂-1))
Now, let's define a new variable:
F = s₁² / s₂
Substituting s₁² / s₂² into the above equation, we get:
F = (ss₁ / (n₁-1)) / (ss₂ / (n₂-1))
This is the desired result. We have shown that F follows an F distribution with (n₁-1) and (n₂-1) degrees of freedom.
It's worth noting that the F distribution is only defined for positive values. Therefore, if s₁² / s₂² is less than 1, we need to take the reciprocal of the above equation to ensure that F is positive:
F = (ss₂ / (n₂-1)) / (ss₁ / (n₁-1))
Learn more about proof of distributions here: https://brainly.com/question/29184279
#SPJ1
Write and simplify this numerical expression. Forty-two divided by seven plus the quantity three divided by six
Therefore , the solution of the given problem of expression comes out to be 6.5 is the abbreviated numerical expression.
What is an expression?Shifting numbers, which can be expanding, variable diminishing, or blocking, should be used instead of random estimations. Only through exchanging goods like tools, expertise, or answers to problems could they assist one another. The explanation on the reality equation may include the justifications, elements, or mathematical claims for tactics like increased argumentation, falsification, and blending.
Here,
The mathematical expression is expressed as follows:
=> 42 / 7 + (3 / 6)
We can use the division operations to make the expression simpler:
=> 7 /42 = 6
=> 6 / 3 = 0.5.
The statement is thus more easily expressed as follows
=> 6 + 0.5
When we add the two numbers, we get:
=> 6.5
Therefore, 6.5 is the abbreviated numerical expression.
To know more about expression, visit:-
https://brainly.com/question/20927246
#SPJ1
What is tan(A)?
Remember to rationalize the denominator.
(Please Help)
Answer:
[tex]\frac{2 \sqrt{5}}{5}[/tex]
Step-by-step explanation:
As given by SOH-CAH-TOA
tan is equal to opposite/adjacent.
therefore for A, the opposite would be equal to 2, and adjacent would be equal to [tex]\sqrt{5}[/tex] as the hypotenuse is never referred to as an adjacent side. so the answer would be tan(A) = [tex]\frac{2}{\sqrt{5}}[/tex] however, to rationalize the denominator you must multiply the fraction by [tex]\frac{\sqrt{5} }{\sqrt{5} }[/tex] .
[tex]\frac{2}{\sqrt{5}} *\frac{\sqrt{5}}{\sqrt{5}} = \frac{2 * \sqrt{5}}{\sqrt{5} *\sqrt{5}}[/tex]
then simplify
[tex]\frac{2 \sqrt{5}}{5}[/tex]
Which of the following graphs is decreasing when x > 3?
PLEASE HELP ASAP! EXTRA POINTS!! I BEG HELP ME‼️‼️ (please click the picture and pick one GRAPH) PLEASE
Answer:
A. X
Step-by-step explanation:
You want to know which graph is decreasing for x > 3.
DecreasingA graph is decreasing when it slopes down to the right. The only graph in the group that has any decreasing portion is graph X. The decreasing part of that graph is to the right of x = 3, where x > 3.
Graph X is the one you want.
__
Additional comment
All the other graphs are increasing everywhere, so aren't even worth any consideration.
If something is going 70 km/sec per mpc and its recessional velocity is 49000 km/sec then what is its distance
Step-by-step explanation:
always and you come across a question that needs you to find the time or the distance or the speed the first thing that you need to think of is a triangle based formula so this is what you do you're right DStv in a triangle but you won't include the V therefore it will be DST and you just look at mainly at the formulas and try to identify the one that you're looking for and the way forward for example distance I have already drawn my small triangle and it's revealing that distance is equal to speed times time and speed is equal to a distance divided by time and time is equal to distance divided by speed in this case we're looking for the distance therefore I supposed to say speed time so was supposed to say 70 * 49,000 to get your answer
if a sample of 32 runners is taken from a population of 201 what is the mean
If a sample of 32 runners is taken from a population of 201, the mean is equal to 201.
What is a population?In Statistics and science, a population can be defined as a set of similar items or events that comprises every member of a group and from which a researcher, scientist, or experimenter, obtains or generates data for a statistical study.
What is a sample?In Statistics and science, a sample can be defined as a set of data that is collected from a population based on a well-defined sampling procedure.
In this context, we can reasonably infer and logically deduce that the mean (μ) could be equal to 201 runners because it represent the average.
Read more on population here: brainly.com/question/267132
#SPJ1
Given the following Confidence Interval for the population mean μ : ( 168.685, 177.315),
find the sample mean used to obtain it
according to the question the sample mean used to obtain the confidence interval was 173.
What is mean?The arithmetic means (in contrast to the geometrical mean) of a dataset is the average of all values split by the total amount of values. The most popular way to measure central tendency is with the "mean," which is widely utilised. This is obtained by dividing the number of values in the dataset by the total number of all the values. Either raw information or information that has been included in frequency tables can be used for calculations. The average of a number is known as the average. Simple math can be used to determine: After summing up all the digits, divide by the number of digits. the sum divided by the number.
given,
The confidence interval's midpoint is determined by the sample mean. Therefore, to find the sample mean, we add the lower and upper bounds of the confidence interval and divide by 2:
Sample mean = (Lower bound + Upper bound)/2
Sample mean = (168.685 + 177.315)/2
Sample mean = 173
Therefore, the sample mean used to obtain the confidence interval was 173.
To know more about mean visit:
https://brainly.com/question/30094057
#SPJ1
What is the value of the expression −38 − 16 − (−23)?
Answer:
-31
Step-by-step explanation:
100 POINTS + BRAINLIEST
A teacher hires a coach for a school trip. The cost is worked out using the
formula C =
m
3 + 40, where C is the cost in pounds and m is the number of
miles the coach travels.
(a) Calculate how much it would cost to hire the coach to travel a distance of
42 miles.
b) If the cost of the hire is £75,how many miles does the coach travel?
Answer:
(a) To calculate how much it would cost to hire the coach to travel a distance of 42 miles, we can substitute m = 42 into the formula and solve for C:
C = (42/3) + 40
C = 14 + 40
C = 54
Therefore, it would cost £54 to hire a coach to travel 42 miles.
(b) To find how many miles the coach travels if the cost of the hire is £75, we can set the formula equal to 75 and solve for m:
75 = (m/3) + 40
35 = m/3
m = 105
Therefore, the coach travels 105 miles if the cost of the hire is £75.
Match the appropriate list with the definition
a. reflexive, symmetric, and transitive only
b. congruence and midpoint.
A segment proof is a type of proof that shows the steps used to establish the congruence or equality of two line segments. The goal of a segment proof is to provide a clear and logical argument that demonstrates why the two segments are equal or congruent.
Segment proofs typically involve using a combination of definitions, postulates, and theorems to justify each step of the argument. For example, to prove that two line segments are congruent, one might use the segment addition postulate, the definition of congruence, and the reflexive, symmetric, and transitive properties of congruence.
The appropriate matching is:
1. Segment proofs include the following definitions as justifications/reasons: ⇔ reflexive, symmetric, and transitive only
2. Segment proofs include the following as congruence of segments: ⇔ congruence and midpoint.
To know more about Segment proofs, visit:
https://brainly.com/question/28337391
#SPJ1