A ball is thrown straight up into the air by three different people, Alberto, Ben and Carrie. Below are different representations of their throws. Alberto’s throw can be described by the equation height=−16(time)^2+32(time)+4 Ben's throw can be described by the following table:
Answers
For given data, Carrie threw the ball highest = 35ft and ball stayed in the air longest = 3s for Carrie as well.
How does projectile motion work?Any object that is fired into the air and travels in that direction is referred to as a projectile. Gravitation, however, is another force that an object experiences after the first force that pushes it.
Three distinct individuals, Alberto, Ben, and Carrie, each toss a ball straight up into the air.
Following equation may be used to explain Alberto's throw.
[tex]H = -16t^2 + 32t + 4[/tex]
Now , to find the maximum height, we solve for first derivative w.r.t.t,
[tex]-32t + 32 = 0[/tex]
[tex]32t=32\\t = 1s[/tex]
Using t=1, we can find maximum height as
[tex]H =-16(1)^2 + 32(1) + 4\\\\H=(-16)+32+4[/tex]
[tex]H= 20[/tex] ft
Thus, when Alberto threw ball, maximum height attained= 20 ft and total time duration ball was in air = 1s.
From the given table( refer to attached image),
Fom given table,
we can drive the function for maximum height as,
[tex]H=at^2+bt+c[/tex]
now, putting values of t, to get values of H,
from table, for t=0,H=6
6=[tex]a(0)+b(0)+c[/tex]
[tex]c=6[/tex]
[tex]H=at^2+bt+6[/tex]
for t=1,H=14
[tex]14=a(1)^2+b.1+6\\\\8=a+b............(1)[/tex]
similarly,for t=2,H=14
[tex]14=a(2)^2+b.2+6\\\\8=4a+2b........(2)[/tex]
solving equation 1 and 2,
a=(-4) and b=12
∴[tex]H=-4t^2+12t+6[/tex]
we know, [tex]t=\frac{-b}{2a}\\\\t=\frac{-12}{-8}=3/2=1.5s[/tex]
When Ben threw ball, the maximum height ball attained was 14 ft and total time duration for which ball was in air was 1.5 seconds.
From the given graph(refer to attached image),When Carrie threw the ball Maximum Height attained = 35ft and Time duration ball was afloat is 3s
Thus,When Carrie threw the ball attained Maximum Height 35ft and ball stayed in the air longest.
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Complete Question: A ball is thrown straight up into the air by three different people, Alberto, Ben and Carrie. Below are different representations of their throws. Alberto’s throw can be described by the equation height=−16(time)^2+32(time)+4 Ben's throw can be described by the following table(refer to attached image).Who threw the ball highest and for whom the ball was in air for the longest?
Related Questions
pls help me in this The number of non square numbers between 12square and 13square are
Answers
Answer: 24
Step-by-step explanation:
n = 12^2
n + 1 = 13^2
2n = 12
Transpose the 2 on the other side, you get -
n = 12*2
Therefore, n = 24
Find the value of a in quadrilateral ABCD.
C
(11x + 140)*
D (13x + 143)
(4x +98)
(11z +135)
A
B
Answers
The value of x for the angles of the quadrilateral is: x = -4
How to find the angles in a quadrilateral?We know that the sum of angles in a quadrilateral is 360 degrees.
The angles are given as:
(11x + 140)°
(13x + 143)°
(4x + 98)°
(11x + 135)°
Thus:
(11x + 140)° + (13x + 143)° + (4x + 98)° + (11x + 135)° = 360°
Thus:
39x + 516 = 360
39x = 360 - 516
39x = -156
x = -156/39
x = -4
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Warning MEGA HARD question
What’s 9999999999999999x99999999999999
Answers
Answer:
1E+30
Step-by-step explanation:
sam is a regular at joe's diner. according to the waitress, the probability that sam will order ham is 0.8 and the probability that he will order coffee is 0.65. what is the probability that he will order neither ham nor coffee?
Answers
For an event based on order by sam for ham and coffee with different probabilities, then the probability that he will order neither ham nor coffee is equals to the 0.07.
We have sam is a regular customer at joe's diner. Let us consider two events be defined as A: sam will order ham
B: sam will order coffee
Now, the probability that sam will order ham, P( A) = 0.8
The probability that sam will order coffee, P( B) = 0.65
We have to determine the probability that he will order neither ham nor coffee.
Probability is chances of occurrence of an event. It is calculated by dividing the favourable response to total possible outcomes. Probability value always lies between 0 to 1. Apply probability law P( will order ham ) + P( will not order ham) = 1
=> Probability that sam will not order ham
[tex]P( \bar A ) [/tex] = 1 - 0.8 = 0.2
Probability that sam will not order coffee,
[tex]P( \bar A ) [/tex]= 1 - 0.65 = 0.35
Now, as we see both events A and B are independent events so, there corresponding also independent. Therefore, Probability that he will order neither ham nor coffee, [tex] P( \bar A ∩ \bar B) [/tex]
[tex]= P( \bar A) P(\bar B) [/tex]
= 0.2 × 0.35 = 0.07
Hence, required probability is 0.07.
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2 ft 3 in =______ in
Answers
Answer:
27 inches
Step-by-step explanation:
1 ft = 12 inches, therefore 2 ft = 24 inches because (12)(2)=24. Then you need to add the other 3 inches to 24, and 24 + 3 = 27 in.
find the volume of the prism below
Answers
The volume of the prism with given dimensions in the figure is equal to 612√3 cubic millimeter.
The dimensions of the triangular prism are,
Base of the triangle 'B' = 12mm
let us consider 'h' be the height of the triangle base.
Which intersect base at midpoint
height of the triangle 'h' = √ 12² - 6²
= √108
= 6√3mm
Side length of the prism 'l' = 17mm
Volume of the triangular prism
= ( 1/2 ) × Base × height × length of the side
= ( 1/2 ) × B × h × l
Now , substitute the values we have,
⇒ Volume of the triangular prism = (1/2) × 12 × 17 × 6√3
⇒ Volume of the triangular prism = 612√3 cubic millimeter.
Therefore, the volume of the triangular prism is equal to 612√3 cubic millimeter.
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in one day a 20 pound dog eats 3 cups of food. How much would a 50 pound dog eat
Answers
Let x be the amount of food (in cups) that a 50 pound dog eats in one day.
Since the amount of food eaten is directly proportional to the weight of the dog, we can set up the following proportion:
20 pounds / 3 cups = 50 pounds / x cups
To solve for x, we can cross-multiply:
20 pounds * x cups = 3 cups * 50 pounds
20x = 150
x = 7.5
Therefore, a 50 pound dog would eat approximately 7.5 cups of food in one day, assuming that the amount of food eaten is directly proportional to the weight of the dog.
If a cylinder has a volume of 2908.33 in^3 and a radius of 11.5 in. What is the height of the cylinder
*
5 in
6 in
7 in
8 in
Answers
If a cylinder has a volume of 2908.33 in³ and a radius of 11.5 in, the height of the cylinder include the following: C. 7 inches.
How to calculate the volume of a cylinder?In Mathematics and Geometry, the volume of a cylinder can be calculated by using this formula:
Volume of a cylinder, V = πr²h
Where:
V represents the volume of a cylinder.h represents the height of a cylinder.r represents the radius of a cylinder.By substituting the parameters, we have the following:
2908.33 = 3.14 × 11.5² × h
Height, h = 7.00 inches.
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2. Find the volume. Show work, and round to 2 decimal places
*triangle based prism*
Answers
answer
as we all know volume is equal to length times width times height therefore to get you answer you have to multiply all the three giving measurements the answer that you get you are supposed to round it to the nearest to decimal places when you say around it off to the nearest two decimal places it means that they need to be too this two numbers after the coma
Michelle was instructed to write two equivalent expressions for 6x + 15.
Her work is shown.
6x + 15 = x + x + x + x + x + x + 15
6x + 15 = 6(x + 15)
Part A: Explain which one of Michelle’s equations is true for all values of x and which one of Michelle’s equations is false for all values of x. (2 pts.)
Part B: Write another equivalent expression for 6x + 15.
Answers
Michelle’s equations that is true for all values of x is 6x + 15 = x + x + x + x + x + x + 15.
Michelle’s equations that is false for all values of x is 6x + 15 = 6(x + 15).
Another equivalent expression for 6x + 15 is 3(2x + 5).
What is an expression?In Mathematics and Geometry, an expression simply refers to a type of mathematical equation which is typically used for illustrating the relationship that exist between two (2) or more variables and numerical quantities (number), without an equal to sign (symbol).
Michelle’s equations can be written for all values of x as follows;
6x + 15 = x + x + x + x + x + x + 15.
However, Michelle’s equations is false for all values of x when it is written as 6(x + 15).
Another equivalent expression is given by;
6x + 15 = 3(2x + 5).
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Answer:
Part A: The equation 6x + 15 = 6(x + 15) is true for all values of x because it distributes the 6 to both terms inside the parentheses and simplifies to the original expression. However, the equation 6x + 15 = x + x + x + x + x + x + 15 is false for all values of x. While it may be true for specific values of x, such as x = 1 or x = 2, it is not true for all values of x because the number of x terms changes depending on the value of x.
Part B: Another equivalent expression for 6x + 15 could be 3(2x + 5), which also simplifies to the original expression. This is because we can factor out a common factor of 3 from both terms and simplify to 3(2x + 5) = 6x + 15.
Step-by-step explanation:
example of writing a linear approximation and approximating the value of a functionIf y = 2x2 + x - 4, find the equation of the tangent when x = 1.
Answers
The equation of the tangent line to the function y = 2x^2 + x - 4 at the point x = 1 is y + 1 = 5(x - 1).
To find the equation of the tangent line to the function y = 2x^2 + x - 4 at the point x = 1,
we will follow these steps:
Evaluate the function at x = 1 to find the point (1, y):
[tex]y = 2(1)^2 + 1 - 4[/tex]
y = 2 + 1 - 4
y = -1
So, the point is (1, -1).
Find the derivative of the function to get the slope of the tangent line:
[tex]dy/dx = d(2x^2 + x - 4)/dx[/tex]
dy/dx = 4x + 1
Evaluate the derivative at x = 1 to find the slope of the tangent line:
m = 4(1) + 1
m = 5
Use the point-slope form to find the equation of the tangent line:
y - y1 = m(x - x1)
y - (-1) = 5(x - 1).
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on tuesday, a local gas station had 135 135135 customers. the table above summarizes whether or not the customers on tuesday purchased gasoline, a beverage, both, or neither. based on the data in the table, what is the probability that a gas station customer selected at random on that day did not purchase gasoline?
Answers
The probability that a randomly selected gas station customer on that day did not purchase gasoline is 10/27.
We know that, the probability of any event is the ratio of the number of favorable case to that event to the total number of cases.
The total number of customers in that Gas Station on that day = 135
According to the data table,
Number of customers did not purchase gas but purchased beverage = 35
Number of customers neither purchase gas nor beverage = 15
So total number of customers did not purchase gas = 35 + 15 = 50
Here number of favorable cases = 50
So the probability that a randomly selected gas station customer on that day did not purchase gasoline = 50/135 = 10/27.
Hence the required probability is 10/27.
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The given question is incomplete. The complete question is -
"On Tuesday, a local gas station had 135 customers. The table above summarizes whether or not the customers on Tuesday purchased gasoline, a beverage, both, or neither. Based on the data in the table, what is the probability that a gas station customer selected at random on that day did not purchase gasoline?
Customer Purchases at a Gas Station"
The angle of elevation from object A to object B is always
the,(__________) the angle of depression from object B to object A.
A. Greater Than
B. Less Than
C. Equal to
D. Unrelated to
Answers
Angle of elevation = angle depression
I draw two cards from a well-shuffled deck, without replacement. What is the probability that I will draw two aces?
Answers
The probability of drawing two aces from a well-shuffled deck of 52 cards without replacement is 0.45%.
The probability of drawing two aces from a well-shuffled deck of 52 cards without replacement can be calculated as follows:
First, we calculate the probability of drawing an ace on the first draw. Since there are four aces in the deck and 52 cards in total, the probability of drawing an ace on the first draw is:
P(Ace on first draw) = 4/52 = 1/13
Next, we need to calculate the probability of drawing an ace on the second draw, given that an ace was already drawn on the first draw. Since there are now only three aces remaining in the deck and 51 cards in total, the probability of drawing an ace on the second draw is:
P(Ace on second draw given an ace on first draw) = 3/51
To calculate the probability of drawing two aces, we multiply the probability of drawing an ace on the first draw by the probability of drawing an ace on the second draw, given that an ace was already drawn on the first draw:
P(Drawing two aces) = P(Ace on first draw) x P(Ace on second draw given an ace on first draw)
P(Drawing two aces) = (1/13) x (3/51)
P(Drawing two aces) = 0.0045 or approximately 0.45%.
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At Bob's Auto Plaza there are currently 15 new cars, 7 used cars, 9 new trucks, and 6 used trucks. Bob is going to choose one of these vehicles at random to be the Deal of the Month. What is the probability that the vehicle that Bob chooses is new or is a car
Answers
The probability that the vehicle Bob chooses is new or is a car is [tex]\frac{31}{37}[/tex]
To determine the probability that the vehicle Bob chooses is new or is a car at Bob's Auto Plaza, follow these steps:
1. Calculate the total number of vehicles:
15 new cars + 7 used cars + 9 new trucks + 6 used trucks = 37 vehicles
2. Calculate the number of new vehicles:
15 new cars + 9 new trucks = 24 new vehicles
3. Calculate the number of cars (both new and used):
15 new cars + 7 used cars = 22 cars
4. Since we have already counted the new cars in both categories, we need to subtract the number of new cars once to avoid double counting:
24 new vehicles + 22 cars - 15 new cars = 31 vehicles that are either new or cars
5. Finally, calculate the probability:
Probability = (number of vehicles that are new or cars) / (total number of vehicles)
[tex]Probability = \frac{31}{37}[/tex]
So, the probability that the vehicle Bob chooses is new or is a car is [tex]\frac{31}{37}[/tex] .
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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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[Part A] Which is the ratio for sin A, written as a fraction in simplest form?
Answers
The ratio for sin A, written as a fraction in simplest form, is 3 / (2√3).
The sine function is a mathematical function that takes an angle as its input and returns the ratio of the length of the side opposite to the angle to the length of the hypotenuse in a right triangle
In a right triangle, the sine of an angle A is defined as the ratio of the length of the side opposite to angle A to the length of the hypotenuse. Therefore, we have:
sin A = Opposite / Hypotenuse
Substituting the given values, we get
sin A = CB / AB = 8√3 / 16 = √3 / 2
To simplify this fraction further, we can multiply both the numerator and denominator by √3:
sin A = (√3 / 2) × (√3 / √3) = 3 / (2√3)
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The given question is incomplete, the complete question is:
Which is the ratio for sin A, written as a fraction in simplest form?
The
perimeter of a rectangle is 75
ft and the length is 27 ft. What is
the area of the rectangle?
Answers
Warm Up (4/13) 1 of 21 of 2 Items Question POSSIBLE POINTS: 1 Responses A A B B C C D D Skip to navigation
Answers
Answer:
Since line segment PQ is the result of reflecting line segment AB across the x-axis, we know that the y-coordinates of corresponding points on AB and PQ are the same but have opposite signs.
So if P has coordinates (2,-2) on PQ, then its corresponding point on AB must have coordinates (2, 2). Similarly, if Q has coordinates (8,-2) on PQ, then its corresponding point on AB must have coordinates (8, 2).
Therefore, the length of line segment AB is the distance between points (2, 2) and (8, 2) on the coordinate plane, which is:
AB = |8 - 2| = 6
So the answer is B) 6
How to do substitution
Answers
Step Two→ Substitute the expression from step one into the 2nd equation.
Step Three→ Solve the second equation for the given variable.
Step Four→ Plug you solution back into the first equation.
Step Five→ Write your solution as a point.
The angle of elevation to a nearby tree from a point on the ground is measured to be 32^{\circ}
∘
. How tall is the tree if the point on the ground is 71 feet from the tree? Round your answer to the nearest tenth of a foot if necessary.
Answers
The height of the tree is 44.4 feet.
What is height?Height is the vertical distance between two points.
To calculate the height of the tree, we use the formula below
Formula:
h = dtan∅.................... Equation 1Where:
h = height of the treed = Distance from the point on the ground to the tree∅ = Angle of elevationFrom the question,
Given:
d = 71 feet∅ = 32°Substitute these values into equation 1
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three or more lines that contain the same point are called?
Answers
Answer:
concurrent lines
Step-by-step explanation:
If there are more than 2 lines (or in this case, 3 lines) that meet at a singular and same point, then they are called concurrent lines.
suppose that the efficacy of a certain drug is . consider the sampling distribution (sample size ) for the proportion of patients cured by this drug. what is the mean of this distribution? what is the standard error of this distribution? round your answer to three decimal places.
Answers
Answer: Assuming that the proportion of patients cured by the drug is p = 0.6 and the sample size is n = 100, we can find the mean and standard error of the sampling distribution as follows:
Mean = p = 0.6
Standard error = sqrt[(p*(1-p))/n] = sqrt[(0.6*(1-0.6))/100] = 0.049
Rounding to three decimal places, the standard error is 0.049.
Step-by-step explanation:
Austin collected 30 9/10 kilograms of grass for recycling in exactly 2/3 of the class he collectible was the total amount in kilograms of blue grAss
Answers
Answer: Let's call the total amount of grass that Austin collected "G" in kilograms. We know that he collected 30 9/10 kilograms, which can be written as a mixed number or an improper fraction:
30 9/10 = 309/10
So, we have:
G = 309/10
We also know that 2/3 of the grass he collected was blue grass. So, let's call the amount of blue grass "B" in kilograms. We can set up an equation based on the information given:
B = (2/3)G
Substituting G = 309/10, we get:
B = (2/3)(309/10)
B = 206/5
B = 41 1/5
Therefore, the total amount of blue grass Austin collected was 41 1/5 kilograms.
Step-by-step explanation:
ΔABC has coordinates of A (–5, –7), B (6, –3), and C (2, 7). Find the coordinates of its image after a dilation centered at the origin with a scale factor of 2. A (–2.5, –3.5), B (3, –1.5), C (1, 3.5) A (–10, –7), B (12, –3), C (4, 7) A (–5, –7), B (6, –3), C (2, 7) A (–10, –14), B (12, –6), C (4, 14)
Answers
The coordinates of triangle A'B'C' after a dilation centered at the origin with a scale factor of 2 are:
A' (-10, -14).
B' (12, -6).
C' (4, 14).
What is a dilation?In Geometry, a dilation is a transformation that is typically used for changing the dimension (size) of a geometric figure, but not its shape.
In this scenario an exercise, we would dilate the coordinates of the pre-image by applying a scale factor of 2 that is centered at the origin as follows:
Ordered pair A (-5, -7) → Ordered pair A' (-5 × 2, -7 × 2) = Ordered pair A' (-10, -14).
Ordered pair B (6, -3) → Ordered pair B' (6 × 2, -3 × 2) = Ordered pair B' (12, -6).
Ordered pair C (2, 7) → Ordered pair C' (2 × 2, 7 × 2) = Ordered pair C' (4, 14).
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Please help me this is due tomorrow
Answers
Answer:
Step-by-step explanation:
4
7) suppose that the temperatures of healthy humans are approximately normally distributed with a mean of 98.6 degrees and a standard deviation of 0.8 degrees. if 130 healthy people are selected at random, the probability that the average temperature for these people is 98.25 degrees or higher is closest to
Answers
Answer: To solve this problem, we need to use the central limit theorem to find the distribution of the sample means. The central limit theorem states that if we take random samples of size n from a population with a mean μ and a standard deviation σ, the distribution of the sample means approaches a normal distribution with a mean of μ and a standard deviation of σ/√n, as n gets larger.
In this case, we have a population of healthy humans with a mean temperature of μ = 98.6 degrees and a standard deviation of σ = 0.8 degrees. We want to find the probability that the average temperature for a sample of 130 healthy people is 98.25 degrees or higher. The sample size is large enough to use the normal distribution to approximate the distribution of the sample means.
The z-score corresponding to a sample mean of 98.25 degrees is:
z = (98.25 - 98.6) / (0.8 / sqrt(130)) = -1.91
Using a standard normal distribution table or calculator, we can find the probability that a standard normal random variable is greater than -1.91:
P(Z > -1.91) = 0.9719
Therefore, the probability that the average temperature for a sample of 130 healthy people is 98.25 degrees or higher is approximately 0.9719 or 97.19%.
Step-by-step explanation:
A level 0. 95 confidence interval is: a range of values with margin of error ± 0. 95, which is also correct 95% of the time. Any interval with margin of error ± 0. 95. A range of values computed from sample data that will contain the true value of the parameter of interest 95% of the time. A range of values computed from sample data by a method that guarantees that the probability the interval computed contains the parameter of interest is 0. 95
Answers
A level 0.95 confidence interval is a range of values computed from sample data that will contain the true value of the parameter of interest 95% of the time. So, the correct answer is C).
A level 0.95 confidence interval is a statistical measure used to estimate the true value of a population parameter based on a sample of data. It provides a range of values that is likely to contain the true value of the parameter with a certain degree of confidence.
The level of confidence, in this case 0.95, means that if the same sampling method and data analysis were repeated multiple times, the resulting confidence intervals would contain the true population parameter in 95% of cases.
The width of the interval, or margin of error, is influenced by factors such as sample size, variability, and level of confidence. So, the correct option is C).
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PLEASE HELP MEEEE
Jessica has 400 cm^3 of material. She uses 35cm^3 to make a right triangular prism. She wants to make a second prism that is a dilation of the first prism with a scale factor of 2.5
How much more material does Jessica need in order to make the second prism?
(THE ANSWER IS NOT 52.8)
Answers
Answer:
Jessica has 400 cm^3 of material. She uses 35cm^3 to make a right triangular prism. She wants to make a second prism that is a dilation of the first prism with a scale factor of 2.5.
The volume of the first prism is 35 cm^3. Since the second prism is a dilation of the first prism with a scale factor of 2.5, its volume will be (2.5)^3 = 15.625 times greater than that of the first prism. Therefore, the volume of the second prism will be 35 x 15.625 = 546.875 cm^3.
To make the second prism, Jessica needs an additional material of 546.875 - 35 = 511.875 cm^3.
So Jessica needs an additional material of 511.875 cm^3 to make the second prism.
Step-by-step explanation:
What is the surface area?
6 yd
10 yd
5 yd
Answers
The surface area of the right rectangular prism 280 yd².
What is the surface area of the right rectangular prism?A rectangular prism is simply a three-dimensional solid shape which has six faces that are rectangles.
The surface area of a rectangular prism is expressed as;
S.A = 2( wl + hl + hw )
Where w is the width, h is height and l is length.
From the diagram:
Length l = 6 yd
Width w = 5 yd
Height = 10 yd
Plug the values into the above formula:
S.A = 2( wl + hl + hw )
S.A = 2( 5×6 + 10×6 + 10×5 )
S.A = 2( 30 + 60 + 50 )
S.A = 2( 90 + 50 )
S.A = 2( 140 )
S.A = 280 yd²
Therefore, the surface area is 280 square yards.
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