Explain how you would find the highest point the rider achieved on this jump.
A. What would be the two quantities you would measure for x and y?
B. What would your equation possibly look like? Put the picture on a grid and show some possible points
C. What points could you use to find the maximum height? How would you use those points? Be specific
Answers
The maximum height achieved by the rider is given by the equation above. You can calculate this value using the given measurements and plug them into the equation to find the maximum height.
What is statistics?
Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data. It involves the use of methods and techniques to gather, summarize, and draw conclusions from data.
A. The two quantities you would measure for x and y are the time and height, respectively.
B. The equation that relates time and height for an object in projectile motion is given by:
y = y0 + v0y * t - (1/2) * g * t²
where:
y = vertical height at any time t
y0 = initial vertical height (in this case, the height of the ramp)
v0y = initial vertical velocity (in this case, the vertical velocity of the rider at the top of the ramp)
g = acceleration due to gravity (approx. 9.81 m/s²)
t = time elapsed since the rider left the ramp
To apply this equation to the given image, you can put the picture on a grid with the x-axis representing time and the y-axis representing height.
C. To find the maximum height, you need to determine the point at which the rider's height is greatest. From the plotted points, you can see that the maximum height occurs at the point where the curve reaches its apex. You can find this point by calculating the time at which the vertical velocity of the rider becomes zero (i.e., the highest point of the jump). This occurs at the peak of the curve, where the vertical velocity changes from positive to negative. To calculate this time, you can use the equation for vertical velocity in projectile motion:
v = v0y - g * t
where:
v = vertical velocity at any time t
v0y = initial vertical velocity (in this case, the vertical velocity of the rider at the top of the ramp)
g = acceleration due to gravity (approx. 9.81 m/s²)
t = time elapsed since the rider left the ramp
At the peak of the jump, the vertical velocity becomes zero, so we can set v = 0 and solve for t:
0 = v0y - g * t
t = v0y / g
Substituting this value of t into the equation for height, we can find the maximum height:
y = y0 + v0y * (v0y / g) - (1/2) * g * (v0y / g)²
y = y0 + (v0y² / 2g)
Therefore, the maximum height achieved by the rider is given by the equation above. You can calculate this value using the given measurements and plug them into the equation to find the maximum height.
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Once we have found the vertex, we can determine the maximum height achieved by the rider.
What is statistics?
Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data. It involves the use of methods and techniques to gather, summarize, and draw conclusions from data.
To find the highest point the rider achieved on a jump, we need to measure the rider's height at different points during the jump.
A. The two quantities we would measure for x and y would be:
x: the horizontal distance the rider travels during the jump
y: the vertical height of the rider at different points during the jump
B. The equation that describes the rider's motion during the jump would be a quadratic equation in the form of:
y = ax² + bx + c
Where:
a is the coefficient of the quadratic term and represents the acceleration due to gravity
b is the coefficient of the linear term and represents the initial velocity of the rider
c is the constant term and represents the initial height of the rider
C. To find the maximum height, we need to find the vertex of the parabola that represents the rider's motion.
The vertex is the highest point on the parabola and is located at the point (-b/2a, c - b²/4a).
To find the vertex, we need to measure the rider's height at least two different points during the jump.
The two points should be on either side of the vertex to ensure that we have captured the shape of the parabola correctly.
hence, Once we have measured the rider's height at these two points, we can plug the values into the equation and solve for the vertex. Once we have found the vertex, we can determine the maximum height achieved by the rider.
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Related Questions
solve the equation -75=y^3+50
Answers
Answer: y = -5
Step-by-step explanation:
We move the constants to one side to get y^3 = -125.
Then, we cube root both sides to get y = -5.
19. You are laying on the ground looking up at a building. The distance between your head and the top of the
building is 60 feet. You need to look up at an angle of elevation of 55° to see the top of the building.
(Hint: draw a picture.)
a. How tall is the building?
b. How far is your head from
the base of the building?
Answers
The building is approximately 74.8 feet tall, and your head is approximately 117.7 feet away from the base of the building.
We can use trigonometry to solve this problem. Let's call the height of the building "h" and the distance from your head to the base of the building "d".
Using the tangent function;
tan(55°) = h/d
We know that h + 60 = d, so we can substitute h with d - 60:
tan(55°) = (d - 60)/d
Simplifying this equation, we get;
d = (h + 60)/tan(55°)
Substituting this value of d in first equation, we have;
tan(55°) = h/[(h + 60)/tan(55°)]
Simplifying this equation, we get;
h = 60 tan(55°)
Using a calculator, we find that h ≈ 74.8 feet.
Therefore, the building is approximately 74.8 feet tall.
To find the distance from your head to the base of the building, we can use the Pythagorean theorem;
d² = h² + 60²
Substituting h with 60 tan(55°), we get;
d² = (60 tan(55°)² + 60²
Using a calculator, we find that d ≈ 117.7 feet.
Therefore, your head is approximately 117.7 feet away from the base of the building.
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Find D and write answer in simplest radical form
Answers
The length or value of d is 3m
What is meant by length?
Length is a measurement of how long something is, typically referring to the longest dimension of an object or space. It is a fundamental physical quantity and can be measured in various units, such as meters, feet, or inches. Length is important in many fields, including mathematics, science, and engineering.
According to the given information
In a right-angled triangle, the side opposite to the 90-degree angle is called the hypotenuse. The side opposite to the 60-degree angle is equal to the hypotenuse multiplied by the square root of 3 divided by 2. Since AC is the hypotenuse and its length is given as 2*(√(3))m, we can find the length of BC (d) as follows:
d = (AC * √(3)) / 2 d = (2 * √(3) * √(3)) / 2
d = 3m
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The value of houses in Livingston goes up by 7% each year. Ben owns a house in Livingston that is currently worth $281,320. How much will it be worth in 9 years?
Answers
Ben's house will be worth $490,523.96 in 9 years if the value continues to increase at a rate of 7% per year.
Formula for Compound InterestWe can use the formula for compound interest, which is:
A = P × (1 + r)ⁿ
Where:
A = final amount
P = principal (starting value)
r = annual interest rate (expressed as a decimal)
n = number of compounding periods
In this case, the principal is $281,320, the annual interest rate is 7% (or 0.07 as a decimal), and the number of compounding periods is 9 years. Plugging in these values, we get:
A = $281,320 × (1 + 0.07)⁹
A = $281,320 × 1.743
A = $490,523.96
Therefore, Ben's house will be worth approximately $490,523.96 in 9 years if the value continues to increase at a rate of 7% per year.
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Find the area of the shape
Answers
The area of the composite shape are
1. Orange
2. Light blue
3. Purple
4. Green
5. Red
6. Yellow
7. Light green
8. Yellow
9. Dark blue
10. Pink
How to find the area of the composite shapesThe area of the composite shapes are solved as follows
1. rectangles
= 7 * 3 + (15 - 7) * 1.5
= 21 + 12
= 33 square cm
2.
= 39 x 4 + 0.5(39 + 26) x (18 - 4)
= 156 + 455
= 611 square m
3.
= 12 * 15 + 0.5 x 15 x 10
= 180 + 75
= 255 square ft
4.
= 15 x 7 + 0.5 x π x 3.5 x 3.5
= 105 + 19.24
= 124.2 square cm
5.
= 0.5 x 10 x 22 - 0.5 x 6 x 12
= 110 - 36
= 74 square yd
6.
= 0.5 x π x 3 x 3 + 0.5 x 6 x 11
= 14.14 + 33
= 47.1 square m
7.
= 18 x 6 - 2 x π x 2 x 2
= 108 - 25.13
= 82.8 square m
8.
= 4 x 16 + 0.5 (16 + 10) x (8 - 4)
= 64 + 52
= 116 square cm
9.
= 18 x 8 - 4 * 0.5 x 4 x 4
= 144 - 32
= 112 square cm
10.
= [0.5 (7 + (9 + 3)) x (15 + 6 - 17)] + [(17 - 6) x (9 + 3)] + [6 x 9]
= 38 + 132 + 54
= 224 square cm
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An angle is two collinear rays with a common endpoint. Find an example that contradicts this definition. How would you change the definition to make it more accurate?
Answers
Opposite rays can be defined as a figure formed by two collinear rays with a common endpoint, since the two rays lie on the same line.
Mona loves making beaded necklaces. Today, she has a string that is 20 centimeters long. She leaves 2 centimeters on each end. Then, she fills the rest of the string with little beads that are 4 millimeters wide. How many little beads will she need?
Answers
Answer:
40 beads
Step-by-step explanation:
First, let's find the length of string that the beads will be on.
The string is originally 20 cm, but 2 cm is taken off each side.
So, the string that the beads will be on is only 16 cm now.
Each bead is 4 mm wide, so we have to convert the bead width to centimeters.
4/10=0.4
So each bead is 0.4 cm.
Now to find how many beads will fit, we have to divide the length by the width of the bead.
16/0.4=40
So, Mona will need 40 beads. Hope this helps ;)
The graph of line m is shown. What is the
equation of the line that is perpendicular to line
m and passes through the point (3,2)?
WRITE IN POINT SLOPE FORM
Answers
Answer:6
Step-by-step explanation:
PLS HELP I WILL GIVE 100 PTSSSSSSSSSSSSSSSSSSSS fool answers get reported good answers get brainiest
Answers
C) 36 yards 18*6=108
108ft to yards is 36
Answer:C
Step-by-step explanation:
Each jump rope is 6 feet long, so 18 jump ropes would require a total of:
18 x 6 = 108 feet of rope
Since there are 3 feet in a yard, we can convert 108 feet to yards by dividing by 3:
108 ÷ 3 = 36 yards
Therefore, the football coach should buy 36 yards of rope. The answer is (C).
PLEASE HELP! SHOW WORK AND EXPLAIN ON HOW YOU GOT THE ANSWER! I WILL MARK YOU BRAINLIEST IF YOU DO!
Answers
Katie's claim can be represented by the equation: a² ¢= 4(1/2ab) + b²
How to explain the equationKatie's claim can be represented by the equation:
Outer square area = Sum of areas of four triangles + Inner square area or mathematically, a² = 4(1/2ab) + b²
where "a" and "b" are the lengths of the legs of the right triangle and "a²" represents the area of the outer square, while "b²" represents the area of the inner square.
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A stained glass window is shaped like a semicircle. The bottom edge of the window is 4 feet long.
What is the area of the stained glass window?
Answers
Answer: 12.57
Step-by-step explanation:
the radius is 2 so you 2 times pi squared
The zoom feature on a camera lens allows you dilate what appears on the display. When you change from 100% to 400%, the new image on your screen is an enlargement of the previous image with a scale factor of 4. If the new image is 38 millimeters wide, what was the width of the previous image?
Answers
the width of the previous image is 9.5mm.
What is the width?The widthh can be defined as the horizontal measurement or distance measured from side to side.
In geometry, the shorter side of an object is frequently referred to as its "width". For instance, both of the given rectangles are identical rectangles, but one of them has been rotated to demonstrate that the shorter side of the rectangle is referred to as its width.
In the given problem,
if the width of the previous image is x,
4x=38
⇒x=9.5mm
So, the width of previous image is 9.5mm.
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A Ray's pizza party each pizza was cut into 8 slices. There were 7 groups of children. Each group ate 2\frac{1}{2} pizzas. How many pizzas were eaten at the party in all?
Answers
18 pizzas were eaten at the party in total.
What is total number?The term "total number" refers to the complete count or sum of a set of numbers or objects. It is the result of adding up all the individual numbers or objects in a set to get a final value that represents the entire set.
According to question:If each pizza was cut into 8 slices, then 2 and 1/2 pizzas is equivalent to 20 slices of pizza because:
2\frac{1}{2} \times 8 = 20
Since there were 7 groups of children, the total number of slices of pizza eaten at the party is:
20 slices/pizza x 7 groups = 140 slices
To convert this to the number of pizzas eaten, we divide the total number of slices by the number of slices per pizza:
140 slices ÷ 8 slices/pizza = 17.5 pizzas
Therefore, 17.5 pizzas were eaten at the party in total. However, since a pizza cannot be divided into fractions, we should round up to the nearest whole number, giving us a final answer of 18 pizzas.
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determine if each of the following statements is true or false. if a statement is false, explain which part of the statement is incorrect. a) skipped b) as the degree of freedom increases, the t distribution curve becomes more similar to the standard normal curve c) the two mean non-pooled test is used for 2 independent populations under the assumption that the two populations share the same standard deviation. d) the standard error is always equal to the sample standard deviation.
Answers
a) Given statement: skipped : I'm not sure what statement you're referring to, as there is no statement labeled "a" in question.
Hence answer provided.
b) As the degrees of freedom increase, the t distribution curve does become more similar to the standard normal curve.
True. Because the t distribution resembles the normal distribution when the degrees of freedom are high.
c) The two mean non-pooled test is used for 2 independent populations under the assumption that the two populations have different standard deviations.
False - Because the non-pooled t-test can be used to compare the means of the two populations when the assumption of equal variances is true.
d) The standard error is the standard deviation of the sampling distribution and is calculated by dividing the sample standard deviation by the square root of the sample size.
False - Because the standard error, which is determined as the sample standard deviation divided by the square root of the sample size, is a measure of the variability of the sample mean.
a) Given statement: skipped : I'm not sure what statement you're referring to, as there is no statement labeled "a" in question.
b) Given statement : As the degrees of freedom increase, the t distribution curve does become more similar to the standard normal curve.
The given statement is true.
Because, When the degrees of freedom are large, the t distribution approaches the standard normal distribution.
c) Given statement: The two mean non-pooled test is used for 2 independent populations under the assumption that the two populations share the same standard deviation.
The given statement is true.
Because, When the assumption of equal variances is met, the non-pooled t-test can be used to compare the means of the two populations.
d) Given statement: The standard error is not always equal to the sample standard deviation.
The given statement false.
Because, The standard error is a measure of the variability of the sample mean, and it is calculated as the sample standard deviation divided by the square root of the sample size.
The sample standard deviation is a measure of the variability within the sample itself.
The standard error tends to be smaller than the sample standard deviation because it accounts for the effect of the sample size on the variability of the sample mean.
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Maria claims that any fraction located between
1
5
5
1
and
1
7
7
1
on a number line must have a denominator of
6
6.
Enter a fraction that shows Maria's claim is incorrect.
Answers
However, 2/7 is not equivalent to any fraction with denominator 6. Therefore, Maria's claim is incorrect.
Fraction calculation.
A fraction is a way of representing a part of a whole or a ratio between two quantities. It consists of two numbers, the numerator (located above the fraction line) and the denominator (located below the fraction line), separated by a horizontal fraction bar. The numerator represents the number of parts of the whole or the ratio, while the denominator represents the total number of equal parts or the denominator of the ratio.
For example, the fraction 3/4 represents three out of four equal parts or three parts out of a total of four parts. It can also be interpreted as a ratio of three to four. Fractions can be simplified by dividing both the numerator and denominator by their greatest common factor. For instance, the fraction 6/8 can be simplified to 3/4 by dividing both the numerator and denominator by 2.
A counterexample to Maria's claim is the fraction 2/7.
To see this, note that 1/5 is equivalent to 14/70 and 1/7 is equivalent to 10/70. Therefore, any fraction between 1/5 and 1/7 can be expressed in the form n/70, where 10 < n < 14.
However, 2/7 is not equivalent to any fraction with denominator 6. Therefore, Maria's claim is incorrect.
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Consider a cone with a height of 9 in and a base diameter of
6 in.
Using a calculator, approximate the volume of the cone.
To do the approximation, do not round any intermediate
steps, and use the button on the calculator. Round your
answer to the nearest hundredth.
Make sure that you use the correct units in your answer.
Answers
A cone with a height of 9 in and a base diameter of 6 in has the volume 84.78 cubic inches.
The formula for the volume of a cone is:
V = (1/3)π[tex]r^{2}[/tex]h, where r is the radius of the base and h is the height.
In the question it is given height = 9 in and a base diameter = 6 in.
Radius = diameter/2
r = d/2 = 6/2 = 3 inches
Substituting the values in the formula:
V = (1/3)π[tex](3\ in)^2[/tex](9 in)
Simplifying the expression:
V ≈ 84.78 [tex]in^3[/tex]
Rounding to the nearest hundredth, we get:
V ≈ 84.78 [tex]in^3[/tex]
Therefore, the approximate volume of the cone is 84.78 cubic inches.
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Write an equation using the parent function y = √x that has a domain of 3≤x<∞ and a range of -2≤y<∞.
Answers
The equation using the parent function y = √x that has a domain of 3≤x<∞ and a range of -2≤y<∞ is y = √(x - 3) - 2.
What is equation?An equation is a mathematical statement that indicates the equality of two expressions. It typically contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Equations are used to solve problems in various fields of mathematics, science, engineering, and economics. They can be written in various forms, such as standard form, slope-intercept form, point-slope form, and more.
Here,
To shift the parent function y = √x to the right by 3 units and down by 2 units, we use the transformation:
y = √(x - 3) - 2
This equation has a domain of 3 ≤ x < ∞, since we subtract 3 from x inside the square root function. The range is -2 ≤ y < ∞, since we subtract 2 from the square root function.
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simply the following expression below.
(x^2 -3x+7)
Answers
The expression (x^2 -3x+7) cannot be simplified further because there are no like terms to combine or any other operations to perform. It is already in its simplest form.
Simplifying the given expression.The expression (x^2 -3x+7) is a quadratic expression, meaning it has a degree of 2. It cannot be simplified further because there are no like terms to combine, which is the only operation that can be performed to simplify polynomials.
To understand this, let's look at the individual terms of the expression. The term x^2 is the highest degree term, which means it has the greatest power of x.
The term -3x is the linear term, which means it has a degree of 1. And the constant term is 7, which means it has a degree of 0.
Since the terms have different degrees and there are no like terms, there is no way to simplify the expression any further.
Therefore, (x^2 -3x+7) is already in its simplest form.
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Can someone please help me ASAP? It’s due today!!
A. Method 1
B. Method 1 and 2
C. Method 2
D. Method 3
Answers
Based on the information, we can infer that the most accurate method would be method 3 because it randomly selects the participants without any preference.
What would be the most appropriate method for this survey?The most appropriate method for this survey would be method three (option D) because it will have a group of people who were chosen randomly. This means that people can have different ranges of age, gender, preferences, among others.
This is important because they will represent all the diversity of characteristics of the public, which will allow a study in this population to be more accurate.
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The perimeter of a rectangle is 80 inches. The
length of the rectangle is 12 inches.
Which equation could represent the width of the
rectangle, w?
Answers
Answer:
Step-by-step explanation:
Fill in the blanks. 8 x 12 = 8 x (10 + ?) = (8 x 10) + (8 x ?) = 80 + ? = ?
(i need help on the question marks)
Answers
8 x 12 = 8 x (10 + 2) = (8 x 10) + (8 x 2) = 80 + 16 = 96.
Using the following formula (rate/12)
principal x ----------------- = monthly payment
(1-(1+rate/12)-60
What is the monthly payment on a 24000 loan at 6% for 60 months?
Answers
For a loan of $24,000 at 6% interest over 60 months, the monthly payment is $466.47.
What is Monthly Payment?A monthly payment is the sum of money that is made towards a debt or loan on a regular basis; it normally consists of both the main and interest. It is a set sum that the borrower must consistently pay until the debt is repaid in full. Mortgages, auto loans, student loans, and personal loans all frequently include monthly installments. The loan amount, the interest rate, and the term of the loan all affect how much will be paid each month.
We can use the following calculation to determine a loan's monthly payment:
M = P * (r * (1 + r)ⁿ) / ((1 + r)ⁿ⁻¹)
where:
M = payment each month
P = Principal (the loaned amount)
r = (Divide the annual interest rate by 12 to get the monthly interest rate)
n = total payments (12 divided by the number of years)
By entering the specified values, we obtain:
P = 24000
r = 6% / 12 = 0.005
n = 60
M = 24000 * (0.005 * (1 + 0.005)⁶⁰) / ((1 + 0.005)^60 - 1)
M = $466.47 (rounded to the nearest cent)
So, $466.47 is the monthly payment for a $24,000 loan with a 6% interest rate over 60 months.
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i dont rlly understand this if someone wants to help
Answers
The value of one square in each sample is:
(a) 2
(b) 6
(c) 3
(d) 5
How to determine the value of one square in each sample?
Let x represent the value one square. Thus, the value of one square in each sample can be determined as follow.
(a) 2x + 1 = 5 (Left side is equal to right side)
2x = 5 - 1
2x = 4
x = 4/2
x = 2
(b) 10 = x + 2 + 2
10 = x + 4
x = 10 - 4
x = 6
(c) 5 + 1 + x = 9
6 + x = 9
x = 9 - 6
x = 3
(d) 25 = 5x
x = 25/5
x = 5
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please help me on this question
Answers
Andrew has $28, and Matthew has 5 times that amount, or $140.
What is amount?The term "amount" typically refers to a quantity or sum of something. It can refer to a physical quantity of something, such as the amount of water in a glass, or an abstract quantity, such as the amount of time it takes to complete a task.
According to given information:Let x be the amount of money that Andrew has.
Then, the amount of money that Matthew has is 5 times x, which is 5x.
Together, they have a total of $168, so we can write an equation:
x + 5x = 168
Simplifying, we get:
6x = 168
Dividing both sides by 6, we get:
x = 28
Therefore, Andrew has $28, and Matthew has 5 times that amount, or $140.
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Solve the quadratic equation 9x2 − 16 = 0
Answers
Answer:
x = ± [tex]\frac{4}{3}[/tex]
Step-by-step explanation:
9x² − 16 = 0
9x² = 16
x² = [tex]\frac{16}{9}[/tex]
x = ± √[tex]\frac{16}{9}[/tex]
x = ± [tex]\frac{4}{3}[/tex]
So, the answer is: x = [tex]\frac{4}{3}[/tex] , - [tex]\frac{4}{3}[/tex]
A bag contains pennies, nickels, dimes, and quarters. There are 50 coins in all. Of the coins,16% are pennies and 42% are dimes There are 6 more nickels than pennies. How much money does the bag contain?.
Answers
The bag contains 4.63 dollars.
To find :
Total amount of the coins bag contains.
Solution:
According to the given statement, a bag contains 50 coins.
Number of pennies = 16% of 50
= 0.16 × 50
= 8 pennies
Number of dimes = 42% of 50
= 0.42 × 50
= 21 dimes
Number of nickels = 6 more than pennies
= 8 + 6
= 14 nickels
Number of quarters = Rest of the coins
= 50 - (8 + 21 + 14)
= 50 - 43
= 7 quarters
Since,
1 penny = 0.01 dollar
8 pennies = 0.01 × 8 = 0.08 dollar
1 dime = 0.10 dollar
21 dimes = 0.10 × 21 = 2.1 dollar
1 nickel = 0.05 dollar
14 nickel = 0.05 × 14 = 0.70 dollar
1 quarter = 0.25 dollar
7 quarter = 0.25 × 7 = 1.75 dollars
Total value of the coins in the bag = 0.08 + 2.10 + 0.70 + 1.75
= 4.63 dollars
Hence, The bag contains 4.63 dollars.
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suppose the confidence interval (0.6358, 0.7532) represents the proportion of skyline college students who say math is their favorite subject. a. based on the confidence interval, is it likely 60% of skyline college students say math is their favorite subject?
Answers
Answer: No, it is not likely that 60% of Skyline College students say math is their favorite subject based on the given confidence interval of (0.6358, 0.7532).
The confidence interval tells us that we are 95% confident that the true proportion of Skyline College students who say math is their favorite subject lies between 0.6358 and 0.7532. This means that if we were to take many random samples from the population of Skyline College students and construct 95% confidence intervals for the proportion of students who say math is their favorite subject, 95% of those intervals would contain the true population proportion.
Since 0.60 is not within the interval (0.6358, 0.7532), it is unlikely that the true proportion of Skyline College students who say math is their favorite subject is 60%. However, we cannot make any definitive statements about the population proportion based on this one confidence interval alone.
Step-by-step explanation:
(CALC) The first derivative of the function f is given by f'(x)= cosx^2/ x -1/5. How many critical values does have on the open interval, (0,10) ?a) oneb) threec) fourd) fivee) seven
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The function f has only one critical value on the open interval (0,10), and the answer is (a) one.
To find the critical values of the function f(x) on the open interval (0,10), we need to find the values of x where f'(x) is equal to zero or undefined.
First, we need to find the values of x where f'(x) is undefined. Since f'(x) contains a term of x in the denominator, it will be undefined at x = 0. However, since the interval we are interested in is (0,10), we can exclude this value.
Next, we need to find the values of x where f'(x) is equal to zero. We can set the numerator of f'(x) equal to zero and solve for x
cos(x²) = 1/5
Taking the inverse cosine of both sides, we get
x² = arccos(1/5)
x = ±√(arccos(1/5))
However, since we are only interested in the interval (0,10), we can discard the negative root. Using a calculator, we can find that
√(arccos(1/5)) ≈ 2.6779
Therefore, the correct option is (a) one
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please explain every step clearly
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As a result, for the two schools, the measures of variability are:
Mountain View School:
Range = 4, Variance = 9.1733, Standard deviation = 3.029
Bay Side School:
Range = 10, Variance = 7.84, Standard deviation = 2.8.
How do you define standard deviation?The degree of variance or dispersion in a set of data values is measured by standard deviation. The degree to which the data values deviate or vary from the mean or average value of the data set is indicated by this statistical indicator.
We must ascertain the range, variance, and standard deviation for each dataset in order to determine the measures of variability for the two schools.
Mountain View School:
Range: The smallest class size is 5 and the largest is 9, so the range is 9-5 = 4.
Variance: To calculate the variance, we need to find the mean first.
Mean = (5+6+8+9+8+2+0+10+2+4+5+6+8)/15
= 5.6
Then, we can find the variance using the formula:
Variance = Σ(xi - μ)²/n
= [(5-5.6)² + (6-5.6)² + (8-5.6)² + (9-5.6)² + (8-5.6)² + (2-5.6)² + (0-5.6)² + (10-5.6)² + (2-5.6)² + (4-5.6)² + (5-5.6)² + (6-5.6)² + (8-5.6)²]/15
= 9.1733
Standard deviation = √(9.1733) = 3.029
Bay Side School:
Range: The smallest class size is 0 and the largest is 10, so the range is 10-0 = 10.
Variance: To calculate the variance, we need to find the mean first.
So,
Mean will be = (8+7+6+5+5+4+4+3+1+0+2+0+0+2+3+5)/15
= 3.6
Then, we can find the variance using the following formula:
Variance = Σ(xi - μ)²/n
= [(8-3.6)² + (7-3.6)² + (6-3.6)² + (5-3.6)² + (5-3.6)² + (4-3.6)² + (4-3.6)² + (3-3.6)² + (1-3.6)² + (0-3.6)² + (2-3.6)² + (0-3.6)² + (0-3.6)² + (2-3.6)² + (3-3.6)² + (5-3.6)²]/15
= 7.84
Standard deviation will be = √(7.84)
= 2.8
As a result, for the two schools, the measures of variability are:
Mountain View School:
Range = 4, Variance = 9.1733, Standard deviation = 3.029
Bay Side School:
Range = 10, Variance = 7.84, Standard deviation = 2.8
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rewrite the following standard form quadratic into vertex form: f(x) = -2(x + 1 )^2 + 8
Answers
Step-by-step explanation:
f(x) = - 2 (x+1)^2 + 8 is already in vertex form
quadratic form can be found by expanding it :
f(x) = -2 ( x^2 + 2x +1) + 8
f(x0 = -2x^2 -4x -2 + 8
f(x) = - 2x^2 - 4x + 6 <=====quadrtaic form