A ball is thrown vertically in the air with a velocity of 95 ft/s. The ball is at a height of 120 ft.
Answers
Answer:
The ball is at a height of 120 feet after 1.8 and 4.1 seconds.
Step-by-step explanation:
The statement is incomplete. The complete statement is perhaps the following "A ball is thrown vertically in the air with a velocity of 95 ft/s. What time in seconds is the ball at a height of 120ft. Round to the nearest tenth of a second."
Since the ball is launched upwards, gravity decelerates it up to rest and moves downwards. The position of the ball can be determined as a function of time by using this expression:
\(y = y_{o} + v_{o}\cdot t +\frac{1}{2}\cdot g \cdot t^{2}\)
Where:
\(y_{o}\) - Initial height of the ball, measured in feet.
\(v_{o}\) - Initial speed of the ball, measured in feet per second.
\(g\) - Gravitational constant, equal to \(-32.174\,\frac{ft}{s^{2}}\).
\(t\) - Time, measured in seconds.
Given that \(y_{o} = 0\,ft\), \(v_{o} = 95\,\frac{ft}{s}\), \(g = -32.174\,\frac{ft}{s^{2}}\) and \(y = 120\,ft\), the following second-order polynomial is found:
\(120\,ft = 0\,ft + \left(95\,\frac{ft}{s} \right)\cdot t +\frac{1}{2}\cdot \left(-32.174\,\frac{ft}{s^{2}} \right) \cdot t^{2}\)
\(-16.087\cdot t^{2} + 95\cdot t -120 =0\)
The roots of this polynomial are, respectively:
\(t_{1} \approx 4.075\,s\) and \(t_{2} \approx 1.831\,s\).
Both roots solutions are physically reasonable, since \(t_{1}\) represents the instant when the ball reaches a height of 120 ft before reaching maximum height, whereas \(t_{2}\) represents the instant when the ball the same height after reaching maximum height.
In nutshell, the ball is at a height of 120 feet after 1.8 and 4.1 seconds.
Related Questions
Find the value of x.
6x 1
5x + 2
Answers
Answer: 3
Step-by-step explanation:
6x plus 1 plus 5x plus 2 subtract 5 from 6 and five on both sides you will end up with 1x or xthe just add 1 plus to and get that x=3 . from how your problem is set up.
use the spinner below to answer the question. assume that it is equally probable that the pointer will land on any one of the five numbered spaces. if the pointer lands on a borderline, spin again.
Answers
The probability that the arrow will land on 2 or 3 is given by the following option:
2/5.
How to obtain the probability?A probability is calculated by the division of the number of desired outcomes by the number of total outcomes.
From the spinner given by the image shown at the end of the answer, we have that:
The total number of outcomes is given by the five regions of the spinner.The desired number of outcomes is given by 2, as there are two outcomes, 2 and 3, considering that all regions are equally as likely.Then the probability that the arrow will land on 2 or 3 is calculated as follows:
p = 2/5.
Meaning that the third option is correct.
Missing InformationThe complete problem, along with the options, is given by the image presented at the end of the answer.
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The weights for a group of 18-month- old girls are normally distributed with a mean of 24.5 pounds and a standard deviation of 2.8 pounds. Use the given table to find the percentage of 18 -month-old girls who weigh more than 27.3 pounds. _ % of 18-month-old girls in the sample weigh more than 27.3 pounds.
Answers
Remember that
z =(x - μ)/σ
where
μ=24.5 pounds
σ=2.8 pounds
so
For x=27.3 pounds
Find out the value of z
z=(27.3-24.5)/2.8
z=1
Looking at the given tables
The probability is equal to (100-84.13)=15.87
therefore
The answer is 15.87%In circle Q with m/PQR = 30 and PQ = 9 units, find the length of arc PR.
Round to the nearest hundredth.
Answers
The length of the arc PR of the circle comes out to be 5.71 units
Arc refers to a part of the circumference or the perimeter of a circle
Given:
m ∠PQR = 30
PQ = 9 units
PQ is the radius of the circle as it originates from the center and end lies on the circumference of the circle
Thus, r = 9 units
Length of arc = (θ ÷ 360) * 2πr
where θ is the measure of the angle subtended by the arc
r is the radius
Thus,
PR = (30 ÷ 360) * 2π9
= 1/12 * 2 * 3.14 * 9
= 1.57 * 3
= 5.71 units
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On a coordinate plane, a curved line with minimum values of (negative 1.56, negative 6) and (3, 0), and a maximum value of (1.2, 2.9), crosses the x-axis at (negative 2.5, 0), (0, 0), and (3, 0), and crosses the y-axis at (0, 0). Which interval for the graphed function has a local minimum of 0? [–3, –2] [–2, 0] [1, 2] [
Answers
Question:
On a coordinate plane, a curved line with
minimum values
o (negative 1.56, negative 6)
o (3, 0),
maximum value
o (1.2, 2.9),
crosses the x-axis
o (negative 2.5, 0),
o (0, 0),
o (3, 0),
crosses the y-axis
o (0, 0).
Which interval for the graphed function has a local minimum of 0?
[–3, –2]
[–2, 0]
[1, 2]
[2,3]
Step-by-step explanation:
From the given information, it 'crosses' the x-axis at (3,0), and this is also a minimum. Thus the local minimum is at (3,0), so the answer choice for the interval is [2,3] (not indicated in the posted question, so double check).
The graphed function has a local minimum of 0 at [2, 4]
What is function?A special relationship where each input has a single output. It is often written as "f(x)" where x is the input value.
Given that, On a coordinate plane, a curved line with minimum values of (-1.56, -6) and (3, 0), and a maximum value of (1.2, 2.9), crosses the x-axis at (-2.5, 0), (0, 0), and (3, 0), and crosses the y-axis at (0, 0).
This means,
When x = -1.56, the minimum value of the function is y(min) = -6
And,
When x = 3, the minimum value of the function is y(min) = 0
Therefore, the graphed function has a local minimum of 0, when x = 3
That means, the interval which contains this value of x is [2, 4] because, x = 3 ∈ [2, 4]
Hence, the graphed function has a local minimum of 0 at [2, 4]
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True or False: The U.S. Bureau of the Census provides information that is useful for defining the denominator in rates.
Answers
Answer:
True
Step-by-step explanation:
please help!
For each sentence, drag a word that will make the statement true.
Words may be used once or more than once.
Equilateral triangles are ___
acute triangles.
Scalene triangles are ___
acute triangles.
Right triangles are ___
acute triangles.
Obtuse triangles are ___
isosceles triangles.
Answers
Answer:
Equilateral triangles are sometimes
acute triangles.
Scalene triangles are never
acute triangles.
Right triangles are never
acute triangles.
Obtuse triangles are always
isosceles triangles.
Answer pls
Maths questions
Attached paper question (Answer pls)
Answers
Answer:
25 wanted ice cream 10 wanted coffee 3/5 wanted ice teahola me pueden ayudar porfis aunque sea el punto 1 del el cuadro, solo necesito el cuadro porfa es que no entiendo, se los pido
Answers
Answer:
Si supiera te diría amigo perdón
Given the equation y = 3(2)x
Answers
Regarding the exponential function y = 3(2)^x, we have that:
We know that the graph has a y-intercept at (0,3), because the a-value is of 3.We know that the graph models exponential growth, because the b-value is of 2.The numeric value of the function at x = 3 is given as follows: 24.What is the exponential function?An exponential function is defined as follows:
y = ab^(x/n).
In which the parameters are defined as follows:
a is the initial value.b is the rate of change.n is the time needed for the rate of change.The function for this problem is given as follows:
y = 3(2)^x.
Hence the parameters are given as follows:
a = 3 -> y-intercept at (0,3).b = 2 > 1, hence exponential growth.At x = 3, the numeric value of the function is obtained as follows:
y = 3 x 2^3
y = 3 x 8
y = 24.
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solve pls brainliest
Answers
B.) 147 members
Answer:
A. -10
B. 147
Step-by-step explanation:
I hope this helps!
-90/9 = -10
7 * 21 = 147
we have n distinguishable objects and are selecting k from them. match the selection type with the number of ways the selection can happen. group of answer choices ordered selections with repetition [ choose ] ordered selection without repetition [ choose ] unordered selection without repetition [ choose ] unordered selection with repetition
Answers
With the help of permutation and combination we conclude that the correct matches are:
Ordered selections with repetition: [choose]
Ordered selection without repetition: [choose]
Unordered selection without repetition: [choose]
Unordered selection with repetition: [choose]
What is permutation?
In mathematics and combinatorics, a permutation refers to an arrangement or ordering of objects. It is a way of selecting and arranging a set of items in a specific order.
Here's how the selection types correspond to the number of ways the selection can happen:
Ordered selections with repetition: [choose]
In this selection type, the order of selection matters, and repetition is allowed. This means that an object can be selected multiple times. The number of ways to make the selection is denoted by \(n^k\), where n represents the number of available objects and k represents the number of objects to be selected.
Ordered selection without repetition: [choose]
In this selection type, the order of selection matters, but repetition is not allowed. Each object can be selected only once. The number of ways to make the selection is denoted by P(n, k), which represents the number of permutations of k objects chosen from n distinct objects. The formula for P(n, k) is n! / (n - k)!
Unordered selection without repetition: [choose]
In this selection type, the order of selection does not matter, and repetition is not allowed. Each object can be selected only once. The number of ways to make the selection is denoted by C(n, k) or n choose k, which represents the number of combinations of k objects chosen from n distinct objects. The formula for C(n, k) is n! / (k! * (n - k)!).
Unordered selection with repetition: [choose]
In this selection type, the order of selection does not matter, and repetition is allowed. Each object can be selected multiple times. The number of ways to make the selection is denoted by C(n + k - 1, k) or (n + k - 1) choose k, which represents the number of combinations of k objects chosen from n distinct objects when repetition is allowed. The formula for C(n + k - 1, k) is (n + k - 1)! / (k! * (n - 1)!).
So, the correct matches are:
Ordered selections with repetition: [choose]
Ordered selection without repetition: [choose]
Unordered selection without repetition: [choose]
Unordered selection with repetition: [choose]
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In the two diagrams, all the triangles weigh the same and all the squares weigh the same.
For each diagram, come up with...
1. One thing that "must" be true
2. One thing that "could" be true
3. One thing that "cannot possibly" be true
Answers
Answer:
1. A triangle weighs more than a square.
2. A triangle could weigh more than a circle.
3. A triangle cannot possibly weigh more than 4 squares and a circle.
A number of tourist were interviewed on their
choice of
means
of travell Two-thirds said
they had travel by road, 13 by air. 4
the by
both
air and road. If
20 tourist had not travel
road
Represent the information on
on a Vena
diagram:
by either
air
or road. Represent the information on a venn diagram
Answers
Answer:
A number of tourists were interviewed on their choice of means of travel. Two- thirds said that they travelled by road, 1330 by air and 415 by both air and road. If 20 tourists did not travel by either air or road ; (i) represent the information on a Venn diagram ; (ii) how many tourists (1) were interviewed ; (2) travelled by air only?
Use cosine to find the missing value round to 2 decimal places #trigonometry
Answers
Answer:
1. 17.27 cm
2. 19.32 cm
3. 24.07°
4. 36.87°
Step-by-step explanation:
1. Determination of the value of x.
Angle θ = 46°
Adjacent = 12 cm
Hypothenus = x
Using cosine ratio, the value of x can be obtained as follow:
Cos θ = Adjacent /Hypothenus
Cos 46 = 12/x
Cross multiply
x × Cos 46 = 12
Divide both side by Cos 46
x = 12/Cos 46
x = 17.27 cm
2. Determination of the value of x.
Angle θ = 42°
Adjacent = x
Hypothenus = 26 cm
Using cosine ratio, the value of x can be obtained as follow:
Cos θ = Adjacent /Hypothenus
Cos 42 = x/26
Cross multiply
x = 26 × Cos 42
x = 19.32 cm
3. Determination of angle θ
Adjacent = 21 cm
Hypothenus = 23 cm
Angle θ =?
Using cosine ratio, the value of θ can be obtained as follow:
Cos θ = Adjacent /Hypothenus
Cos θ = 21/23
Take the inverse of Cos
θ = Cos¯¹(21/23)
θ = 24.07°
4. Determination of angle θ
Adjacent = 12 cm
Hypothenus = 15cm
Angle θ =?
Using cosine ratio, the value of θ can be obtained as follow:
Cos θ = Adjacent /Hypothenus
Cos θ = 12/15
Take the inverse of Cos
θ = Cos¯¹(12/15)
θ = 36.87°
PLEASE Find the scale factor that was used
Will give brainliest!!
Check provided photo.
Answers
Answer:
1/4
Step-by-step explanation:
Scale factor = 3/12 = 1/4
Melissa read 250 pages of a book last weekend. This weekend she reads 240 pages of a book. What is the percent of change in the number of pages she read last weekend to the number of pages she read this weekend?
Answers
Answer:
there is a 4% decrease in the number of pages read by Melissa
Step-by-step explanation:
Percentage change = (books read this week - books read last week) / books read last week x 100
(240 - 250) / 250 x 100
= -10/250 x 100 = -4%
In 1895, the first a sporting event was held. The winners prize money was 150. In 2007, the winners check was 1,163,000. (Do not round your intermediate calculations.)
What was the percentage increase per year in the winners check over this period?
If the winners prize increases at the same rate, what will it be in 2040?
Answers
The estimated winners' prize in 2040, assuming the same rate of increase per year, is approximately $54,680,580,063,400.
The initial value is $150, and the final value is $1,163,000. The number of years between 1895 and 2007 is 2007 - 1895 = 112 years.
Using the formula for percentage increase:
Percentage Increase = [(Final Value - Initial Value) / Initial Value] * 100
= [(1,163,000 - 150) / 150] * 100
= (1,162,850 / 150) * 100
= 775,233.33%
Therefore, the winners' check increased by approximately 775,233.33% over the period from 1895 to 2007.
To estimate the winners' prize in 2040, we assume the same rate of increase per year. We can use the formula:
Future Value = Initial Value * (1 + Percentage Increase)^Number of Years
Since the initial value is $1,163,000, the percentage increase per year is 775,233.33%, and the number of years is 2040 - 2007 = 33 years, we can calculate the future value:
Calculating this expression:
Future Value = 1,163,000 * (1 + 775,233.33%)^33
Using a calculator or computer software, we can evaluate this expression to find the future value. Here's the result:
Future Value ≈ $1,163,000 * (1 + 77.523333)^33 ≈ $1,163,000 * 47,051,979.42 ≈ $54,680,580,063,400
Therefore, based on the assumed rate of increase per year, the estimated winners' prize in 2040 would be approximately $54,680,580,063,400.
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Find the sales tax. Sales Tax Selling Price Rate of Sales Tax Sales Tax $90.00 7% ? The sales tax is $
Fast please
Answers
The total cost with sales tax would be $ 96.30
Sally is now 10 years older than Suki. 5 years ago, the sum of their age was 40. How old are they now?
Answers
Answer:
Sally is 30 and Suki is 20
Step-by-step explanation:
x = Sally's age
y = Suki's age
x = 10 + y
(x - 5) + (y - 5) = 40
x = 30, y = 20
what is the value of the expressionwhat is the value of the expression (3.2+0.2)2+12
Answers
Given the expression: (3.2+0.2)2+12
To get the value of the expression, do the following:
1. add 3.2 and 0.2
\(3.2+0.2=3.4\)2. multiply 3.4 by 2
\(3.4\cdot2=6.8\)3. add 6.8 and 12
\(6.8+12=18.8\)So, the value of the expression = 18.8
what value of x makes 1/2 (3x+ 4) = 1/2 x true
Answers
The value of x which makes the given expression 1/2(3x+4) = 1/2x true is -2
We have to simplify the given expression to find the value of x
1/2(3x + 4) = 1/2x
Cancel 1/2 from both sides
⇒ 3x + 4 = x
⇒ 2x = -4
⇒ x = -2
Hence, the value of x is -2 which makes the given expression true.
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What is the slope of a line perpendicular to the line whose equation is 3x + y = -4.
Fully reduce your answer.
Answers
Answer:
1/3
Step-by-step explanation:
When the equation of a line is in standard form:
ax +by = c
We can find its slope by solving for y:
by = -ax +c
y = -a/bx +c/b
The slope is the coefficient of x. The slope is -a/b.
__
A perpendicular line has a slope that is the negative reciprocal of this:
slope of perpendicular line = -1/(-a/b) = b/a
In the given equation, a=3, b=1, so the slope of the perpendicular line is ...
b/a = 1/3
Point Q is on a circle and located at (-4, 5). Point R is the radius of the circle and located at (1, -2). What is the length of the diameter to the nearest tenth?
Answers
According to the solving the length of the diameter to the nearest tenth
= 8.9.
What is meant by the term radius?The distance between any two points on a circle's perimeter and its center appears to be its radius. Usually, it is denoted by the letters "R" or "r." This number is significant in almost all calculations using circles. The radius of a circle determines both its surface area and circumference.
What do radius and diameter mean?The radius of a circle stretches from the center to the edge, whereas the diameter cuts through the center. The circumference of a circle divides it in half.
According to the given information:
(-4,-2) is a single point.
(-8,-10) another point is at the center is not on the circle.
Now let us begin.
r²=(1 - -4)²+(-2 - 5)²
r²=(5)²+(-7)²
r² = 25 + 49
r² = 74
r=√74 ≃ 8.6
The radius is about 8.9.
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ok so i have 2 questions in math but whoever is savage enough to do them i will award brainliest so ya. PLZ DO THEM BOTH!
Answers
Answer:
Step-by-step explanation:
2x > -7
x > -7/2
if x > -7/2 2x+7
if x = -7/2 0
if x< -7/2 -2x-7
x-4+7>0
x+3 > 0
x > -3
If x > -3 (x-4)+7
if x = -3 0
if x< -3 (-x+4)-7
find the slope of a line tangent to f(x)=x3 at the point (x,f(x)).
Answers
the slope of the tangent line to f(x) = x³ at any point (x, f(x)) is 3x².
The derivative of f(x) = x³ can be found using the power rule of differentiation. According to the power rule, the derivative of xⁿ is \(nx^(n-1).\)
Applying the power rule to f(x) = x³, we get:
f'(x) = \(3x^(3-1)\)
f'(x) = 3x²
Now, to find the slope of the tangent line at a specific point (x, f(x)), we substitute the x-coordinate of the point into the derivative function f'(x).
So, the slope of the tangent line to f(x) = x³ at the point (x, f(x)) is given by:
slope = f'(x) = 3x²
Therefore, the slope of the tangent line to f(x) = x³ at any point (x, f(x)) is 3x².
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a certain dj takes requests for songs at a party. assume that there are 120 people at the party, each of whom makes exactly one request for a song. all of their requests are made independently. assume that each person asks for a pop song with probability 0.37, a rock song with probability 0.2, or a rap song with probability 0.43. what is the probability that 50 or more requests are made for pop songs?
Answers
the probability that 50 or more requests are made for pop songs is 0.0967, or about 9.67%.
Define binomial distributionThe binomial distribution is a probability distribution that describes the number of successes in a fixed number of independent trials, where each trial has the same probability of success.
We can use the binomial distribution to model this situation, where the number of trials is 120 (the number of people at the party), and the probability of success (making a request for a pop song) is 0.37. Let X be the number of requests for pop songs. Then:
The mean of X is μ = np = 120 x 0.37 = 44.4
The standard deviation of X is σ = sqrt(np(1-p)) = sqrt(120 x 0.37 x 0.63) = 4.32
To find the probability that 50 or more requests are made for pop songs, we can use the normal approximation to the binomial distribution, which applies when np >= 10 and n(1-p) >= 10.
Let Z be a standard normal random variable, then:
P(X >= 50) = P((X - μ)/σ >= (50 - μ)/σ)
= P(Z >= (50 - 44.4)/4.32)
= P(Z >= 1.2963)
= 1 - P(Z < 1.2963)
= 1 - 0.9033
= 0.0967
Therefore, the probability that 50 or more requests are made for pop songs is approximately 0.0967, or about 9.67%.
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Does anyone knows how to solve this?
Answers
Answer:
This is the answer do it fast. Ok
Answer:
see explanation
Step-by-step explanation:
Given a parabola in standard form
y = ax² + bx + c ( a ≠ 0 )
Then the x- coordinate of the vertex is
\(x_{vertex}\) = - \(\frac{b}{2a}\)
y = x² - 8x + 13 ← is in standard form
with a = 1 and b = - 8 , then
\(x_{vertex}\) = - \(\frac{-8}{2}\) = 4
Substitute x = 4 into the equation for corresponding value of y
y = 4² - 8(4) + 13 = 16 - 32 + 13 = - 3
Vertex = (4, - 3 )
The axis of symmetry is a vertical line passing through the vertex with equation
x = 4 ← equation of axis of symmetry
To determine direction of opening
• If a > 0 then graph opens up
• If a < 0 then graph opens down
Here a = 1, thus graph opens up
(b) The monthly salary of a staff working in a doll shop is Rs. 7,500. She sold the dolls of Rs. 1,20,000 in a month. If she earned Rs. 13,500 in a month, find the rate of commission? Please help and i will give you the brainleist
Answers
Answer:
5%Step-by-step explanation:
Let the rate of commission is x%.
Total earning is:
7500 + 120000*x/100 = 135001200x = 13500 - 75001200x = 6000x = 6000/1200x = 5Answer:
Let the rate of the commission be x%
Now, according to the given problem
The total monthly earning is
\( \frac{120000x}{100} + 7500 = 13500 \\ 1200x = 13500 - 7500 \\ 1200x = 6000 \\ x = \frac{6000}{1200} \\ \boxed{x = 5}\)
Therefore, the rate of commission is 5%
5% is the right answer.Field X is functionally dependent on field Y if the value of field X depends on the value of field Y. true or false
Answers
True, Field X is a dependent function on Field Y if the value of Field X depends on the value of Field Y.
In relational database theory, a dependent function is a constraint between two sets of objects related to a database. In other words, the dependency function is the boundary of two behaviors in a relationship. FD: The productivity function X → Y is called trivial if Y is part of X. In other words, the FD:X → Y dependency means that the value of Y is determined by the value of X. Two bunches of X values that share the same thing must have the same Y value where Z = U - XY is the residue. In simple terms, if the values of the X attributes are known (assuming they are x), then the values of the Y attributes corresponding to x can be determined by looking at them in an R tuple containing x. Usually, X is called the determinant set and Y is called the correlation set. The efficient function FD: X → Y is said to be trivial if Y is part of X.
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