For the quadratic equations -
1) f(x) = x² - 16x + 3 → Vertex form is y = 3(x - 8)² - 61 and vertex is (8,-61).
2) f(x) = 4x² + 24x - 7 → Vertex form is y = 4(x + 3)² - 43 and vertex is (-3,-43).
3) f(x) = -2x² - 8x + 9 → Vertex form is y = -2(x + 2)² + 17 and vertex is (-2,17).
What is a quadratic function?
A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree.
The quadratic equation is written in the form ax² + bx + c = 0.
The vertex form of a quadratic equation is -
y = a(x - h)² + k
The first equation is - f(x) = x² - 16x + 3.
Here, a = 1, b = -16 and c = 3
The formula for h is -
h = -b/2a
h = -(-16)/2(1)
h = 16/2
h = 8
The formula for k is -
k = c - (b²/4a)
k = 3 - [(-16)²/4(1)]
k = 3 - (256/4)
k = 3 - 64
k = -61
So, the vertex form is -
y = a(x - h)² + k
y = 3(x - 8)² - 61
The vertex is written as (h,k).
The vertex is (8,-61).
Therefore, the vertex form and vertex is y = 3(x - 8)² - 61 and (8,-61) respectively.
The second equation is - f(x) = 4x² + 24x - 7.
Here, a = 4, b = 24 and c = -7
The formula for h is -
h = -b/2a
h = -(24)/2(4)
h = -24/8
h = -3
The formula for k is -
k = c - (b²/4a)
k = -7 - [(24)²/4(4)]
k = -7 - (576/16)
k = -7 - 36
k = -43
So, the vertex form is -
y = a(x - h)² + k
y = 4(x + 3)² - 43
The vertex is written as (h,k).
The vertex is (-3,-43).
Therefore, the vertex form and vertex is y = 4(x + 3)² - 43 and (-3,-43) respectively.
The third equation is - f(x) = -2x² - 8x + 9.
Here, a = -2, b = -8 and c = 9
The formula for h is -
h = -b/2a
h = -(-8)/2(-2)
h = 8/-4
h = -2
The formula for k is -
k = c - (b²/4a)
k = 9 - [(-8)²/4(-2)]
k = 9 - (64/-8)
k = 9 + 8
k = 17
So, the vertex form is -
y = a(x - h)² + k
y = -2(x + 2)² + 17
The vertex is written as (h,k).
The vertex is (-2,17).
Therefore, the vertex form and vertex is y = -2(x + 2)² + 17 and (-2,17) respectively.
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Ayuda por favorrr, necesito hallar los valores, bueno, con uno me conformo...
The measure of {x} in the figure is 14.
What is a Parallelogram?In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.
Given is a parallelogram as shown in the image.
Opposite sides of a parallelogram are equal. So, we can write -
9x - 77 = 3x + 7
9x - 3x = 7 + 77
6x = 84
x = 14
Therefore, the measure of {x} in the figure is 14.
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{Question in english -
Help please, I need to find the values, well, I'll settle for one...}
Can someone help please. Use the domain you obtained from part 1b to determine the equation for the line of best fit for the linear model. (To calculate slope, use the points within the domain that are the farthest left and farthest right on the scatterplot)
Answer:
I don't
Step-by-step explanation:
Find a possible formula for the trigonometric function whose values are in the following table.
Answer:
y = -3cos(πx/4) +3
Step-by-step explanation:
You want a possible trig function that describes the values in the given table.
ObservationLooking at the table, we find the minimum y-value is 0, and it corresponds to x=0 and x=8. This means the period (P) of the function is 8.
The maximum y-value is 6. This means the midline (M) of the function is 3, the average of the minimum and maximum: (0 +6)/2 = 3.
The amplitude (A) of the function is the difference between the maximum value and the midline value: 6 -3 = 3.
Trig functionsThe sine and cosine functions both oscillate back and forth between a value of -1 and a value of +1. The cosine function has its maximum at x=0, but the function needed here will have a minimum at x=0. We can use the cosine function, but it needs to be reflected over the x-axis (or midline).
In general the trig function we're looking for will have the form ...
y = Acos(2πx/P) +M
As discussed above, the value of A will need to be negative to reflect the function over its midline. For A=-3, M=3, P=8, the function is ...
y = -3cos(2πx/8) +3
y = -3cos(πx/4) +3
__
Additional comment
In the case where the extreme values (cosine) or the midline values (sine) are not at x=0, there is a "phase shift" involved. That is, the trig function will need to be translated horizontally to match values in the table. That translation is accomplished by adding or subtracting a value from x. Translation of the cosine function is not needed in this case.
Neal buys a board game. He pays for the board game and pays \$1.54$1.54dollar sign, 1, point, 54 in sales tax. The sales tax rate is 5.5\%5.5%5, point, 5, percent.
What is the original price of the board game, before tax?
The original price of the board game for which Neal pays $1.54, which includes a sales tax on the original price of 5.5% (5.5 percent) is about $1.46
What is a percentage?A percentage is a proportion or rate of an item within a set of items per one hundred (100) units of the set of items.
Percentages indicates the proportion of an item to be selected or received, such that percentage of each item within a set of items can be easily calculated.
The amount Neal pays for the board game = $1.54
The sales tax rate for the purchase = 5.5%
The sales tax is the percentage amount of an original price, each buyer pays when purchasing an item, and which is collected for the government agency by the seller of the item.
The original price of the board game can be found as follows;
Let x represent the original price of the board game, we get;
Therefore, we get;
x + 5.5% of x = 1.54
(1 + 0.055) × x = 1.54
1.055 × x = 1.54
x = 1.54/1.055 ≈ 1.46
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F(x)=x²-1/x+1
F'(x)= Lim h=0 (x+h) -f(x)/h
Answer:
So the derivative of the function F(x) = x^2 - 1/x + 1 is F'(x) = 2x - (x - 1)/x^2.
Step-by-step explanation:
The derivative of the function F(x) = x^2 - 1/x + 1 can be found by using the limit definition of the derivative. The derivative is the rate of change of the function at a given point and it is calculated as:
F'(x) = Lim h=0 (x + h)^2 - 1/(x + h) + 1 - (x^2 - 1/x + 1)/h
Expanding the expression inside the limit and simplifying, we get:
F'(x) = Lim h=0 2xh + h^2 - (1 - hx)/(x + h)^2
Using L'Hopital's Rule, we get:
F'(x) = Lim h=0 2x + 2h - (x - 1)/(x + h)^2
As h approaches 0, the limit becomes:
F'(x) = 2x + 2(0) - (x - 1)/x^2 = 2x - (x - 1)/x^2
So the derivative of the function F(x) = x^2 - 1/x + 1 is F'(x) = 2x - (x - 1)/x^2.
what is a1 in a geometric series for which Sn=21825, an=125, r=15.
The value of a1 in a geometric series for which Sn=21825, an=125, r=15 will be 5/9.
How to calculate fora termThe formula for the nth term in a geometric series is given by:
an = a1 * r^(n-1)
Where a1 is the first term, r is the common ratio, and n is the number of terms.
We are given Sn, an and r, and we can use the formula for the sum of a geometric series to solve for n:
Sn = a1 * (1 - r^n) / (1 - r)
Substituting the given values, we get:
21825 = a1 * (1 - 15^n) / (-14)
Multiplying both sides by -14, we get:
-304350 = a1 * (1 - 15^n)
Since we are given that an = 125, we can substitute this into the formula for an and solve for n:
125 = a1 * 15^(n-1)
Substituting a1 = -304350 / (1 - 15^n) from the equation above, we get:
125 = -304350 / (1 - 15^n) * 15^(n-1)
Dividing both sides by 15^(n-1), we get:
125 * 15^(1-n) = -304350 / (1 - 15^n)
Multiplying both sides by (1 - 15^n), we get:
125 * 15^(1-n) * (1 - 15^n) = -304350
Expanding the right-hand side, we get:
125 * (15 - 15^n) = -304350
Dividing both sides by 125, we get:
15 - 15^n = -2434.8
Adding 15^n to both sides, we get:
15^n = 15 - (-2434.8) = 2449.8
Taking the natural logarithm of both sides, we get:
n * log(15) = log(2449.8)
Dividing both sides by log(15), we get:
n = log(2449.8) / log(15)
Since n is the number of terms, it must be a positive integer. The closest positive integer to this value is 3, so n = 3.
Finally, we can use the formula for an to find a1:
an = a1 * r^(n-1)
Substituting the given values and n = 3, we get:
125 = a1 * 15^(3-1)
Dividing both sides by 15^(3-1), we get:
125 / 15^2 = a1
Calculating, we get:
a1 = 125 / 15^2
= 125 / 225
= 5/9.
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Ella invests £7000 for 2 years in an account paying compound interest.
In the first year, the rate of interest is 3%
In the second year, the rate of interest is 1.5%
Work out the value of Ella's investment at the end of 2 years.
Answer:
The formula for the future value of a single sum is:
F = P * (1 + r/n)^(nt)
Where:
F is the future value
P is the principal (the initial deposit)
r is the annual interest rate
n is the number of compounding periods per year
t is the number of years
For our calculation, we have:
P = £7000
r1 = 3% = 0.03
r2 = 1.5% = 0.015
n = 1 (annual compounding)
t1 = 1 (first year)
t2 = 1 (second year)
So, the future value of Ella's investment at the end of the first year is:
F1 = £7000 * (1 + 0.03/1)^(1 * 1) = £7000 * (1.03)^1 = £7,210
And the future value of Ella's investment at the end of the second year is:
F2 = £7,210 * (1 + 0.015/1)^(1 * 1) = £7,210 * (1.015)^1 = £7,333.15
So, at the end of 2 years, the value of Ella's investment is £7,333.15.
Step-by-step explanation:
Kweku drives about 18,000 miles a year. How much would he save in a year buying electricity for the Desla electric compared to buying gas for the deswagon?
Kweku would save $180 in a year buying electricity for the Desla electric compared to buying gas for the Deswagon, To make up for the higher sale price, it will take him more than 66 years.
What is subtraction?Subtraction is a mathematical operation. Which is used to remove terms or objects in the expression.
Given:
Deselectric costs $11900 more than the Deswagon.
Unit cost:
Deselectric: $0.11 per mile.
Deswagon: $0.12 per mile.
Kweku drives about 18,000 miles a year.
That means
The cost for each car;
Deselectric: 18000 x 0.11 = $1980
Deswagon: 18000 x 0.12 = $2160
The more cost is,
= $2160 - $1980
= $180 of savings in a year.
Now, the make-up for the higher sale price,
= 11900/180
= 66.11 in years.
Hence, it will take him more than 66 years.
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2. A student receives test scores of 62, 83, and 91. The student's term project score is 88 and her homework score
is 76. Each test is worth 20% of the final grade, the term project is 25% of the final grade, and the homework
grade is 15% of the final grade. What is the student's mean score in the class?
3. The median for the given set of six ordered data values is 27.5. What is the missing value? ______
5 12 23 ______ 41 51
4. For the following data, approximate the mean number of emails received per day.
2. The mean score is 80.6
3.The missing term is 32.
What is Mean?The arithmetic mean is found by adding the numbers and dividing the sum by the number of numbers in the list.
Given:
2. A student receives test scores of 62, 83, and 91.
Test A is 0.20 of the total and scores 62.
Test B is 0.20 of the total and scores 83.
Test C is 0.20 of the total and scores 91.
Test F is 0.25 of the total and scores 88.
Work H is 0.15 of the total and scores 76.
Now, Multiply the scores:
= 0.2 x 62 = 12.4
= 0.2 x 83 = 16.6
= 0.2 x 91 = 18.2
= 0.25 x 88 = 22
= 0.15 x 76 = 11.4
Now, add the scores to get the
= 12.4 + 16.6 + 18.2 + 22 + 11.4
= 80.6
3. let the missing term or 4th term be x.
So, The median is sum of 3rd and 4th term.
27.5 = 23 + x/ 2
55 = 23+ x
x= 32
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Find the total surface area of a cylindrical tank of height 2.1m and diameter 0.7 m. Also find the cost of painting at the rate of $9.5 per sq metre.
$51.21
Step-by-step explanationTotal surface area of cylindrical tank:
height = h = 2.1m
diameter = 0.7m
radius= diameter +2
r = 0.7 +2=0.35 m
Formula[tex](2\pi r{}^{2} ) + (\pi dh)[/tex]
[tex](2 \times 3.14 \times {0.35}^{2} ) + (3.14 \times 0.7 \times 2.1) [/tex]
[tex]2 \times 3.14 \times 0.35 {}^{2} = 0.77 [/tex]
[tex]3.14 \times 0.7 \times 2.1 = 4.62[/tex]
[tex]0.77 + 4.62 = 5.39m {}^{2} [/tex]
To find the cost of painting the surface area of tank, multiply the cost of painting per square meter by the total surface area of tank.
Cost of painting[tex]5.39 \times 9.50[/tex]
= $51.21
Judith's vegetable patch is 21 feet wide and 25 feet long. Judith wants to build a fence around the vegetable patch. The fencing material costs $1.00 per foot. How much would it cost in total to build the fence?
The length of the fencing will be 92 feet. And the total cost of the fencing will be $92.
What is the perimeter of the rectangle?Let W be the rectangle's width and L its length.
The perimeter of the rectangle will be defined as the total length of all of its sides. So the rectangle's perimeter will be
Perimeter of the rectangle = 2(L + W) units
Judith's vegetable patch is 21 feet wide and 25 feet long. Judith wants to build a fence around the vegetable patch. The length of fencing is given as,
P = 2(21 + 25)
P = 2 x 46
P = 92 feet
The fencing material costs $1.00 per foot. Then the total cost of the fencing is given as,
Total cost = $1 x 92
Total cost = $92
The length of the fencing will be 92 feet. And the total cost of the fencing will be $92.
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I need to know the answer for this question. Which por portion could be used to find the value of x
Answer:
[tex]\dfrac{9}{6}=\dfrac{8}{v}[/tex]
Step-by-step explanation:Similar polygons:Similar polygons are two polygons with same shape and different size.
In similar polygons
Corresponding angles are congruent.Corresponding sides are proportional.To find the value f 'x'
[tex]\dfrac{ED}{E'D'} = \dfrac{CD}{C'D'}\\\\\dfrac{9}{6}=\dfrac{8}{v}[/tex]
6x+5-2x=4+4x+1 how many solutions
determine the distance around the track if the straight away measures 200 meters and the diameter of the semicircles are 50 meters. use 3.14 for pi to determine the disrance to the nearest meter.
Answer:
2yfhyfjcxdddzònbɓchgghhhhhbbv xfbv xxg
In the figure below, m<2=35 and m
Answer:
36 Degrees
Step-by-step explanation:
First the entire angle of BAC is 71 degrees, so all you have to do is subtract the known angle (2) by the entire angle. 71-35= 36. So that means the measure of angle 1 is 36 degrees.
v=πh(R+r)t make R the subject of formula
Answer:
Step-by-step explanation:
Given the formula for the volume of a torus (v = πh(R + r)), you can isolate R by dividing both sides of the equation by πh(R + r), as follows:
v / (πh(R + r)) = R
πh(R + r) * R = v
R^2 = v / (πh(R + r))
R = √(v / (πh(R + r)))
So, R is the square root of the volume divided by πh(R + r).
A new hybrid car sold in the United States reports a fuel usage of 54mpg Write the equivalent rate in kilometers per liter. Round your answer to the nearest hundredth, if necessary.
Answer: To convert miles per gallon to kilometers per liter, we can use the conversion factor 1 mile = 1.60934 kilometers and 1 gallon = 3.78541 liters.
54 miles per gallon is equivalent to:
54 * 1.60934 km/mile / (1 gallon * 3.78541 liters/gallon) = 21.63 km/liter.
Rounding to the nearest hundredth, the equivalent rate is 21.63 km/liter.
Step-by-step explanation:
Enter the interval equivalent to
2
<
x
≤
5
or
x
>
7
The interval equivalent to each range is given below
x = 3 - 5
x' = 7,8,9
What exactly is interval notation?
Which section of the number line, from left to right, is included in the answer can be determined using interval notation (i.e., which part of the number line is shaded).
Endpoints not included in the solution are denoted by parentheses, whereas endpoints that are included are denoted by brackets.
We have that
The interval equivalent to each range is given below
x = 3 -5
x' = 7,8,9
From the Question we are told that
2 < x ≤ 5 or x >7
Generally the interval equivalent is given as follow from the number line
(...-1,0,1...)
For 2 < x ≤ 5
Here this means x is less than 2 and less than or equal to 5
Therefore
A range of numbers
x = 3 - 5
For x >7
Here x is greater than 7 i.e
x' = 7,8,9
in conclusion
The interval equivalent to each range is given below
x = 3 - 5
x' = 7,8,9
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-3a<-5,if a=2 please help I do not know the answer to the question.
Thr solution to the inequality - 3a < -5 is -6 < -5. This can be written as negative 6 less than negative 5
How to solve inequality?- 3a < -5
if a = 2
- 3a < -5
substitute into the inequality
= -3(2) < -5
= -6 < -5
Hence, the solution to the given inequality when a = 2 is negative 6 less than negative 5
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Question 2 2.1. Rewrite 92 and 146 as products of their prime factors. 2.2. Write down the LCM and HCF of 92 and 146. 2.3. 2.4. 2.7. The price of petrol is increased from R12,58 per litre to R13,28 per litre. Determine the percentage increase in the price. [1 Divide 240g in the ratio 5 : 3: 4. Thoriso can either walk to school at 5 km/h or ride her bicycle at 15 km/h. If she rides her bicycle, it takes her 10 minutes to get to school. 2.4.1. How long will it take her if she walks to school? (2) 2.4.2. Is this direct or indirect proportion? Give a reason for your answer. (2) 2.5. Brian wants to exchange South-African rand for British pound. If R1 is worth 0,075199 pound, how many pounds will he get for R2 100 if he must pay an agent commission of 1,5%? 2.8. (2 (2 (3 (3) (2) A motor car drives at an average speed of 106 km/h for 2 hours 45 minutes. At which constant speed must the car drive to travel the same distance in 2 hours 35 minutes? (4 [20
Answer:
2.1. 92 = 2 x 2 x 23, 146 = 2 x 73
2.2. LCM = 1148, HCF = 2
2.7. Percentage increase = 6.11%
2.4.1. It will take her 18 minutes to walk to school.
2.4.2. This is an indirect proportion as the time taken is inversely proportional to the speed.
2.5. He will get £157.63 if he pays the agent commission.
2.8. The car must drive at 120 km/h to travel the same distance in 2 hours 35 minutes.
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Chloe has already read 50 pages of a book and reads 40 additional pages per hour. Write the equation of the line that represents the number of pages read y in x hours. Plus sign Minus sign Multiplication sign Division sign Big fraction Superscript (Ctrl+Up) Square root Root Equals sign Not equal to Less-than sign Greater-than sign Less-than or equal to Greater-than or equal to Parentheses Pi
The necessary equation in the case at hand will be 40x + 50 = P, where P represents the total number of pages read and x represents the number of hours read.
What is an equation?A mathematical equation compares two numbers or values to a meaningful word, for instance, 6 x 4 = 12 x 2.
An equation is employed when more than one factor needs to be considered in order to fully understand or describe a situation.
So, to answer the question:
Chole has read the first fifty pages of the book.
Every hour, he reads forty pages.
For more than x hours, he reads.
The equation will then be as follows:
40x + 50 = P
P is the total number of pages read, while x denotes the number of hours spent reading.
Therefore, the necessary equation in the case at hand will be 40x + 50 = P, where P represents the total number of pages read and x represents the number of hours read.
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Carson ordered a set of beads. He received 48 beads in all. 24 of the beads were blue. What percentage of the beads were blue?
Answer:
Step-by-step explanation:
50%. 24 is half of 48. So, 50% of 48 if 24.
You want to buy a pet hamster that costs $42. You already have $15 and plan to save $8 per week. If w represents the number of weeks until you have enough money to buy the hamster, what equation represents your plan to afford the hamster.
I need help I can't think of what the equation would be!
Here the relation between number of weeks and Cost can be formulated as 42 = 15+ 8x. By simplifying the equation we get x= 3.375. So you need to save for 4 weeks to get enough money to buy the hamster.
Here you are saving money to buy a hamster. We have to formulate an equation to find out the number of weeks you should save to obtain the money.
The cost of the hamster = $42
Amount you have with you = $15
Amount you can save a week = $8.
Let the number of weeks is x
Then, the equation is
42 = 15 + 8x
8x = 42 -15
8x = 27
x = 27/8 = 3.375
Since it is the number of weeks, we could take only whole numbers. Here x is greater than 3. So the number of weeks to save the money to reach the target would be 4.
So by saving $8 for 4 weeks, you could buy the hamster.
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Identify the percent of change from 2/5 to 1/3 as an increase or a decrease. Then find the percent of change. Round to the nearest tenth of a percent
The percent of change is -1/15 which represent a decrease. percentage of change is 6.7%
What is percentage change?
Percentage change is the difference coming after subtracting the old value from the new value and then divide by the old value and the final answer will be multiplied by 100 to show it as a percentage. Generally, to convert a fraction into a percent, we multiply it by 100.
From the question,
The old amount is 2/5
The new amount is 1/3
We substract the new amount from the old amount
1/3 - 2/5
= -1/15
The percent of change is -1/15 which represent a decrease
To calculate the percentage change
1/15 x 100
= 6.7%
hence, the percentage of change is 6.7%
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A bread dough doubles in size every hour. You begin measuring the volume of the dough 1 hour after the dough is prepared. The volume y (in cubic inches) of the dough times hours after the dough is prepared is represented by y=35(2^x-1). When will the volume of the dough be 4200 cubic inches?
The volume of the dough will be 4200 cubic inches in about 7.9 hours later.
What is a function?A function can be defined as the outputs for a given set of inputs.
The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.
Given, A bread dough doubles in size every hour and is represented by the function y = 35(2ˣ⁻¹).
Now, The volume of the dough would be 4200 cubic inches when,
4200 = 35(2ˣ⁻¹).
2ˣ⁻¹ = 4200/35.
2ˣ⁻¹ = 120.
2ˣ/2 = 120.
2ˣ = 240.
[tex]log_22^x = log_2240[/tex].
[tex]x = 7.9[/tex].
So, About 7.9 hours later.
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Please help a friend out.
The value of the variable x is 125 degrees
How to determine the value of the angleIt is important to note that alternate angles are equal.
Also, angles at a point is 360 degrees
From the information given in the diagram, we have that;
70 degrees and and the angle tangent to C are equal, so we have;
70 degrees + x degrees + x degrees + 40 degrees = 360 degrees
Let's represent mathematically;
70 + x + x + 40 = 360
collect the like terms
70 + 2x + 40 + 360
2x = 360 - 110
Subtract the values
2x = 250
make 'x' the subject of formula
x = 250/2
divide the values
x = 125 degrees
Hence, the value is 125 degrees
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Brian’s earnings vary directly with the number of hours he works. Suppose that he worked 9 hours yesterday and earned $99. How much will he earn today if he works 8 hours?
Answer: $88
Step-by-step explanation:
$99/9= $11 per hour
If Brian works 8 hours:
8x11= 88
Please help!!! I’m really confused and need help
110 miles/hr is the interval with highest average speed. Option C is correct.
Rate of change of a graphThe given diagram is a graph with different rate of change. According to the graph, we are to determine which interval has the highest average speed.
Average speed = change in distance/time
Considering the change between t = 4 and t = 5;
Average speed = 270 - 160/5 - 4
Average speed= 110/1
Average speed = 110 miles/hr
Hence the interval that has the highest average speed is 110 miles/hr
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what happens when the sampling distribution is altered (e.g. filtering out all values below the mean) and how does it effect type 1 errors.
In other words, altering the sampling distribution in this way increases the likelihood of making a type 1 error.
What is mean?The arithmetic mean, arithmetic average, or simply the mean or average, is the sum of a collection of numbers divided by the number of numbers in the collection in mathematics and statistics. The collection is frequently a collection of results from an experiment, observational research, or survey.
Here,
The sampling distribution is a distribution of the values of a statistic (such as the mean or median) calculated from a set of sample data. It gives us information about how the statistic is likely to vary from sample to sample, and it is used in hypothesis testing to calculate the probability of observing certain results if the null hypothesis is true.
Filtering out all values below the mean has the effect of changing the shape, location, and spread of the sampling distribution. For example, if the original sampling distribution is normally distributed with a mean of 0 and a standard deviation of 1, filtering out all values below the mean would result in a new sampling distribution with a mean greater than 0 and a standard deviation smaller than 1.
When the sampling distribution is altered, for example by filtering out all values below the mean, it can have an effect on type 1 errors. Type 1 errors occur when we reject the null hypothesis when it is actually true.
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Each of three friends flips a coin 82 times. The results for each friend are shown in the tables. Find the relative frequency for the event "tails" for each friend. If the friends combine their results to get 114 heads and 132 tails, what is the relative. frequency for the event "tails"? Use pencil and paper. Suppose each friend flips a coin 820 times. Is there a value you would expect the relative frequency for the event "tails"
to be close to?
The relative frequency for the event tails is given as follows:
53.64%.
The expected relative frequency should be closed to the theoretical probability of 0.5.
How to obtain the relative frequency?The relative frequency is given by the division of the number of desired outcomes by the number of total outcomes.
The relative frequency for all the throws is obtained as follows:
132/(114 + 132) = 132/146 = 53.64%.
Considering a fair coin, it is equally as likely to come up heads or tails, hence increasing the number of trials, the relative frequency of each outcomes is expect to be closer to 50%.
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