A softball player tosses a ball straight up into the air as high as possible. The ball has an initial upward
velocity of 40 ft/sec. The function that gives the height, h feet, of the ball at any time, t seconds, after letting go
is:
Answers
The required function that gives the height, h feet, of the ball at any time, t seconds, after letting go is h(t) = 16t(2.5 - t).
Assuming that air resistance is negligible, the height of the ball as a function of time can be modeled by the following equation:
h(t) = -16t² + vt + h₀
In this case, the ball is tossed straight up into the air, so its initial velocity is 40 ft/sec in the upward direction, and its initial height is 0 feet (assuming that the ground is at the reference level). Therefore, the equation becomes:
h(t) = -16t² + 40t + 0
Simplifying the equation, we get:
h(t) = 16t(2.5 - t)
Therefore, the function that gives the height, h feet, of the ball at any time, t seconds, after letting go is:
h(t) = 16t(2.5 - t)
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Related Questions
time series data of a typical the gap store should show which of the following data patterns? multiple choice a. trend b. cyclical c. seasonal d. all of the options are correct. e. random
Answers
The time series data should show a. trend b. cyclical c. seasonal, so the correct answer is d. all of the options are correct.
What is time series data:
Time series data refers to a collection of data points that are measured over time at regular intervals. The time series data could refer to various metrics such as sales, revenue, foot traffic, website traffic, inventory levels, and other relevant business metrics that change over time.
By analyzing time series data, businesses can gain insights into trends, patterns, and other factors that can affect their operations.
Time series can be used for forecasting. By analyzing past trends and patterns, businesses can make predictions about future performance and take proactive measures to achieve their goals.
Since the time series will follow the trend, have multiple choices, and will be cyclical and it will analyze the patterns over time periods seasonally.
Therefore,
The time series data should show a. trend b. cyclical c. seasonal, so the correct answer is d. all of the options are correct.
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The rate constant for first-order degradation of a N2O2 in a solution (1.0 mg/ml) at 40°C
is 0.00351 hr-1, activation energy is 2000 cal/mol, and R = 1.987 cal/mol/degree.
Calculate
a. The rate constant for first-order degradation of N2O2 at room temperature (25°C).
Answers
The 0.0035 hr⁻¹ first-order degradation rate constant in the 40 °C, 1.0 mg/ml solution, where R = 1.987 cal/mol/degree and 2,000 cal/mol activation energy indicates;
a. The rate constant for first-order degradation of N₂O₂ at room temperature is approximately 4.12595 × 10⁻² hr⁻¹
What is a first-order reaction?A first order reaction is one that has a rate that varies linearly with the concentration of one reactant
The given parameters are;
Temperature of the solution = 40°C
T₁ = 40 °C + 273.15 = 313.15 K
The rate constant, K₁ = 0.00351 hr⁻¹
Concentration of the solution = 1.0 mg/ml
Activation energy, Eₐ = 2000 Cal/mol
R = 1.987 cal/mol/degree
The formula by which the rate constant can be found is presented as follows;
\(log\dfrac{k_2}{k_1} =\dfrac{E_a}{2.303\times R} \times \dfrac{T_2-T_1}{T_1\cdot T_2}\)
a. Room temperature = 25 °C
T₂ = 25 °C + 273.15 = 298.15 K
Therefore;
\(log\dfrac{k_2}{0.00351} =\dfrac{2000}{2.303\times 1.987} \times \dfrac{313.15-298.15}{313.15 \times 298.15}\)
\(k_2=0.00351 \times 10^{\left(\dfrac{2000}{2.303\times 1.987} \times \dfrac{313.15-298.15}{313.15 \times 298.15}\right)} \approx 4.12595\times 10^{-2}\)
The rate constant for first-order degradation of N₂O₂ at room temperature is k₂ ≈ 4.12595 × 10⁻² hr⁻¹Learn more about the rate constant for first-order degradation here:
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Lines l and m are parallel lines cut by the transversal line t. Which angle is congruent to ∠7?
Answers
Answer:
<3, <2 or <6
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
i had it in usatestprep
A worldwide organization of academics claims that the mean IQ score of its members is 118, with a standard deviation of 17. A randomly selected group of 40 members of this organization is tested, and the results reveal that the mean IQ score in this sample is 115.8. If the organization's claim is correct, what is the probability of having a sample mean of 115.8 or less for a random sample of this size
Answers
Answer:
0.2061 = 20.61% probability of having a sample mean of 115.8 or less for a random sample of this size
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
A worldwide organization of academics claims that the mean IQ score of its members is 118, with a standard deviation of 17.
This means that \(\mu = 118, \sigma = 17\)
A randomly selected group of 40 members
This means that \(n = 40, s = \frac{17}{\sqrt{40}} = 2.6879\)
What is the probability of having a sample mean of 115.8 or less for a random sample of this size?
This is the pvalue of Z when X = 115.8.
\(Z = \frac{X - \mu}{\sigma}\)
By the Central Limit Theorem
\(Z = \frac{X - \mu}{s}\)
\(Z = \frac{115.8 - 118}{2.6879}\)
\(Z = -0.82\)
\(Z = -0.82\) has a pvalue of 0.2061
0.2061 = 20.61% probability of having a sample mean of 115.8 or less for a random sample of this size
Question 3 of 5
What is the median of the data set?
7, 9, 11, 14, 18, 20, 30, 35
Answers
Answer:
16
Step-by-step explanation:
To find the median, we find the middle of the data set.
7, 9, 11, 14, 18, 20, 30, 35
There are 8 values
7, 9, 11, 14, 18, 20, 30, 35
The median is between the 4th and 5th numbers
We need to find the mean of the middle two numbers
(14+18)/2 =32/2= 16
Answer:
16
Step-by-step explanation:
Median means the middle term in a data set.Remember that, you have to arrange the data points from smallest to largest to find the median of a data set.The formula to find the median of a data set is:\(\sf (\frac{n+1}{2}\:)^ t^h \:data\)
Here,
n ⇒ number of terms
Let us find it now.
7, 9, 11, 14, 18, 20, 30, 35
\(\sf Median=\sf (\frac{n+1}{2}\:)^ t^h \:data\\\\\sf Median=\sf (\frac{8+1}{2}\:)^ t^h \:data\\\\\sf Median=\sf 4.5^ t^h \:data\)
In this case, add 4th and 5th data and divide it by 2.
\(\sf Median = \frac{14+18}{2}\\\\ \sf Median = \frac{32}{2}\\\\\sf Median = 16\)
Write the equation of the line in point-slope form that goes through the points (0, 1) and (2, 7)
Answers
Answer:
point - slope form
y - 1 = 3 (x-0)
Step-by-step explanation:
step(i):-
Given points are (0,1) and (2,7)
The slope of the line
\(m = \frac{y_{2}-y_{1} }{x_{2} -x_{1} }\)
\(m = \frac{y_{2}-y_{1} }{x_{2} -x_{1} } = \frac{7-1}{2-0} = \frac{6}{2} = 3\)
m =3
Step(ii):-
point -slope form
y - y₁ = m(x-x₁)
Equation of the straight line passing through the point (0,1) and having slope 'm' = 3
y - 1 = 3 (x-0)
y -1 = 3x
3x - y +1=0
Equation of the straight line passing through the point (0,1) and having slope 'm' = 3 is 3x -y +1=0
The number of measles cases decreased by 7% to 606 cases this year. What was the number of cases prior to the increase? Express your answer rounded correctly to the nearest whole number.
Answers
Answer:
652 cases
Step-by-step explanation:
The formula for percentage increase is 100 times the final-initial/final value. If we plug the numbers in and calculate, we get 652 cases. Have a great day!
The median weekly income for a student who drops out of high school is 451. Someone with a bachelor's degree from college earns 1053 in that same week. Calculate each person's yearly income and then the difference between them.
Answers
The difference between their yearly incomes is $31,304.
To calculate each person's yearly income, we need to multiply their weekly income by the number of weeks in a year. Assuming there are 52 weeks in a year, the yearly income can be calculated as follows:
For the student who drops out of high school:
Yearly Income = Weekly Income x Number of Weeks
= 451 x 52
= 23,452
For someone with a bachelor's degree:
Yearly Income = Weekly Income x Number of Weeks
= 1053 x 52
= 54,756
The difference between their yearly incomes can be found by subtracting the student's yearly income from the bachelor's degree holder's yearly income:
Difference = Bachelor's Yearly Income - Student's Yearly Income
= 54,756 - 23,452
= 31,304
Therefore, the difference between their yearly incomes is $31,304.
It is important to note that these calculations are based on the given information and assumptions. The actual yearly incomes may vary depending on factors such as work hours, additional income sources, deductions, and other financial considerations.
Additionally, it is worth considering that educational attainment is just one factor that can influence income, and there are other variables such as experience, job type, and market conditions that may also impact individuals' earnings.
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Please answer it I will wait to see for brainliest
Answers
Answer:
D
Step-by-step explanation:
Answer:
ok so the odd one out is A) the measure of <ahd is 30°
Step-by-step explanation:
external angle is equal to the sum of the two interior angles on the opposite side
3x= x +15 +x +15
3x=x+x+15+15
3x= 2x +30
3x-2x= 30
x = 30
For what value of A is the function, (x), continuous at x=0?
Answers
(i) \(\lim_{x \to \frac{\pi^-}{2}}\) h(x) = 3
(ii) \(\lim_{x \to \frac{\pi^+}{2}}\) h(x) = -1
(iii) h(0) = 1/7
The value of λ must be 7, for h(x) to be continuous at x = 0.
The given function is,
h(x) = 1/7, when x = 0
= 1 - 2 cos 2x, when x < π/2
= 1 + 2 cos 2x, when x > π/2
= x cos x/sin λx, when x < 0
Now,
(i) \(\lim_{x \to \frac{\pi^-}{2}}\) h(x) = \(\lim_{x \to \frac{\pi^-}{2}}\) (1 - 2 cos 2x) = 1 - 2 cos π = 1 + 2 = 3
(ii) \(\lim_{x \to \frac{\pi^+}{2}}\) h(x) = \(\lim_{x \to \frac{\pi^+}{2}}\) (1 + 2 cos 2x) = 1 + 2 cos π = 1 - 2 = -1
(iii) h(0) = 1/7
Since the function is continuous at x = 0, so
\(\lim_{x \to 0}\) h(x) = h(0)
\(\lim_{x \to 0}\) x cos x/sin λx = 1/7
\(\lim_{x \to 0}\) cos x.\(\lim_{x \to 0}\) 1/λ(sinλx/λx) = 1/7
1/λ = 1/7
λ = 7
Hence the value of λ must be 7.
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Name the rays in the figure to the right (options in picture)
Answers
The rays in the shown figure are QB, BQ and MB
What is a ray?A ray is any set of straight lines passing through one point. They are lines that project from one point to another with at arrow head.
From the given diagram, the rays are the vector QB, BQ (since can proceed in different direction) and the line MB
Hence the rays in the shown figure are QB, BQ and MB
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Country A has an exponential growth rate of 4.3% per year. The population is currently 4,079,000, and the land area of Country A is 19,000,000,000 square yards. Assuming this growth rate continues and is exponential, after how long will there be one person for every square yard of land?
Answers
The number of years it would it take for there to be one person for every square yard is 108,325.68 years.
How many years would it take for there to be one person for every square yard?When there is one person for every square yard, it means that the population and land area are equal in value.
Number of years = (In FV / PV) / r
FV = future populationPV = present populationr = rate of growth(In 19 billion / 4,079,000) / 0.043 = 108,325.68 years
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A boy walks 5km due north and then 4km due east. Find the bearing of his current position from the starting point, how far is the boy now from the starting point
Answers
You see applications of mathematics concepts in everyday life. Can you give at least two examples that you believe are relevant to this math course (calculus)?
Answers
Answer:
circiut analysis
second law of thermodynamics
Step-by-step explanation:
in RC and Ral circiut, first order differential equations is an appropriate approach to solving the circuits
Pls help!!
Find the area of the white region.
1500
7 cm
A=[?] cm2
Enter a decimal rounded to the nearest tenth.
Answers
Answer:
51.9 cm²
Step-by-step explanation:
From the diagram attached,
Area of the white region(segment)(A) = Area minor sector- area of the triangle
A = (πr²∅/360°)-(1/2r²sin∅)............... Equation 1
Where r = radius of the circle, Ф = reflex angle formed at the center of the circle, π = pie
From the question,
Given: r = 7 cm, Ф = 150°
Constant: π = 22/7
Substitute these values into equation 1
A = [(22/7)×7²×150/360]-[(1/2)×7²×sin150]
A = 64.17-12.25
A = 51.92
A = 51.9 cm²
![Pls help!!Find the area of the white region.15007 cmA=[?] cm2Enter a decimal rounded to the nearest tenth.](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/rl1BzT6mIYpekaLsQzcFyAVBICH4LK5N.png)
The coordinate grid represents the school playground. Which of the following accurately describes the location of a playground area? Select all that apply.
Answers
Answer:
the answer is the first one
Step-by-step explanation:
the slide is 2 under left and 4 units up from the soccer field
- How many "tenths" make one
Answers
Answer:
10 tenths make a one
Step-by-step explanation:
because it works like dimes making a dollar you need 10 of them to make a dollar, and they are in the tenths position.
Answer:
ten tenths
Step-by-step explanation:
10/10 = 1
Hope this helps
ILL MARK BRAINLIEST PLEASE HELP
A maximum can occur at the each of the following except
A. A vertex
B. An intersection of constants
C. A point outside the unbounded region
D. Within the bounded region
Answers
Solve for m.
m – 6.82 = 9.24
Answers
Explanation: m-6.82=9.24
+6.82= +6.82
————————
M= 16.06
Just add the inverse operation of 6.82 to both sides and you get 6.82.
Below is a position-time graph of the O'Connor Panthers in pursuit of a victory over the
Marshall Rams.
100
80
Position
(ds) 60-
40
201
A 10
20
30
40
50
60
Time (s)
Find the total yardage traveled from 0-120 seconds.
70
-9
90
100
110
120
Answers
According to the information we can infer that the total yardage traveled from 0 to 120 seconds is 140 yards.
How to calculate the total yardage traveled?To calculate the total yardage traveled we have to consider the movement of the O'Connor Panthers. In this case we have to consider that the movement in the y axis.
In this case we can conclude that the total yardage traveled was 140 yards because:
From 0 to 20 seconds they moved 30 yards. From 20 to 40 seconds they moved 10 yards.From 40 to 60 seconds they moved 40 yards.From 60 to 80 seconds they didn't move.From 80 to 90 seconds they moved 20 yards.From 90 to 120 secons they moved 40 yards.30 + 10 + 40 + 20 + 40 = 140Learn more about yards in: https://brainly.com/question/28062239
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10
Select the correct answer.
The given equation has been solved in the table.
Step
1
2
3₂
4
5
-
Statement
-7--7
7+7=-7+7
0
2
22-0
2=0
=
In which step was the subtraction property of equality applied?
O A. step 2
OB.
step 3
OC.
step 4
O D.
The subtraction property of equality was not applied to solve this equation.
Answers
The step in which the subtraction property of equality was applied to solve the equation is given as follows:
D. The subtraction property of equality was not applied to solve this equation.
What is the subtraction property of equality?The subtraction property of equality states that subtracting the same number from both sides of an equation does not affect the equality, and hence it is used to isolate a variable that is adding on a side of the expression.
For this problem, to remove the term -7, we add 7 to both sides of the expression, hence the addition property of equality was applied.
In the other step, the multiplication property was applied, hence option D is the correct option for this problem.
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HELP WILL MARK BRAINLEST
no files nd no pictures
Answers
Answer:
6xsquared +9x + 12Heather had 20 stickers. She bought 27 stickers from a store in the mall and got 6 stickers for her birthday. Then Heather gave 4 of the stickers to her sister and used 11 to decorate a greeting card. How many stickers does Heather have left?
Answers
Answer:
38 stickers
Step-by-step explanation:
20+27=47
47+6=53
53-4=49
49-11=38
20+27+6-(4+11)=38 stickers
Part A: A graph passes through the points (0, 2), (2, 6), and (3, 12). Does this graph represent a linear function or a non-linear function? Explain your answer in words.
Part B: Write one example of a linear function and one example of a non-linear function. (Use x and y as the variables) (10 points)
Answers
Answer:
Step-by-step explanation:
Part A: No. The line would have to be straight in order for the graph to be linear.
Part B:
Linear: y=2x-4.
Nonlinear: y=x^2-6.
What is the place value of 8in the following number
861250
Answers
Answer:
Hundred Thousands
Step-by-step explanation:
Standard Form:
861,250
Place Value:
From left to right for 861,250
Digit Place Value
8 hundred Thousands
6 Ten Thousands
1 Thousands
2 Hundreds
5 Tens
0 Ones
hundred thousand because 8 is under hundreds of thousands column
10. The width of a rectangle is doubled and the length is halved. This produces a square with perimeter of Pem. What is the perimeter (in cm) of the original rectangle? A) 2.5p B) 1.25P C) 0.5P D) 2P E) None of these
Answers
9514 1404 393
Answer:
B) 1.25P
Step-by-step explanation:
The perimeter of the square is P, so each side is 0.25P. That means the rectangle had sides of 2(0.25P) and 1/2(0.25P) = 0.5P and 0.125P.
The rectangle's perimeter is ...
perimeter = 2(L+W) = 2(0.5P +0.125P) = 2(0.625P)
perimeter = 1.25P . . . . matches choice B
Write a polynomial
f(x)
in general form that has the following characteristics.
• Degree 3
• Leading coefficient of 4
• One double root at
x = −6
• One root at
x = 5/2
Answers
The general form representation of the polynomial which is as described in the task content is; f(x) = 4x³ + 38x² + 24x - 360.
Polynomials in general form.It follows from the task content that the Polynomial in discuss has;
Degree 3.Leading coefficient of 4.One double root at, x = −6.One root at; x = 5/2.Therefore, the factored form of a polynomial can be written as follows;
P(x) = a (x - p) (x - q) (x - r) where p, q and r are the roots of the polynomial and a is the leading coefficient.
Since the factors of the polynomial f(x) are; (x + 6), (x + 6) and (x - 5/2).
Hence, the polynomial f(x) in discuss can be written as follows;
f(x) = 4 (x + 6) (x + 6) (x - 5/2)
f(x) = (x + 6) (x + 6) (4x - 10)
f(x) = 4x³ + 38x² + 24x - 360
Therefore, the required polynomial in standard form is; f(x) = 4x³ + 38x² + 24x - 360.
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4x - 5y = 6
- 8x +10y = -12
gausse elimination
Answers
Step-by-step explanation:
4x−5y=6
−8x+10y=−12
Isolate x for 4x –5y = 6: x=6-5y/4
Substitute x= 6+5y/4
[-8 (6-5y/4) +10y=-12]
Simplify
[-12= -12 ]
The solutions to the system of equations are:
x=6+5y/4
What is the value of y?
Answers
Answer:
The value of y in what equation, y can equal anything depending on the equation.
To pay for a home improvement project that totals $20,000, a homeowner is choosing between two different credit card loans with an interest rate of 9%. The first credit card compounds interest quarterly, while the second credit card compounds monthly. The homeowner plans to pay off the loan in 10 years.
Part A: Determine the total value of the loan with the quarterly compounded interest. Show all work and round your answer to the nearest hundredth. (4 points)
Part B: Determine the total value of the loan with the monthly compounded interest. Show all work and round your answer to the nearest hundredth. (4 points)
Part C: What is the difference between the total interest accrued on each loan? Explain your answer in complete sentences. (2 points)
Please only responded if you know how to do it, will give the brainiest to however answers it correctly
Answers
The total value of the loan with quarterly compounded interest is approximately $45,288.38, while the total value of the loan with monthly compounded interest is approximately $45,634.84. The difference in total interest accrued is approximately $346.46.
Part A: To determine the total value of the loan with quarterly compounded interest, we can use the formula for compound interest:
A = P(1 + r/n)^(nt),
where:
A is the total value of the loan,
P is the principal amount (initial loan amount),
r is the interest rate (in decimal form),
n is the number of times interest is compounded per year,
and t is the number of years.
Given:
P = $20,000,
r = 9% or 0.09,
n = 4 (quarterly compounding),
t = 10 years.
Substituting the values into the formula, we have:
A = 20000(1 + 0.09/4)^(4*10).
Calculating this value, we find:
A ≈ $45,288.38.
Therefore, the total value of the loan with quarterly compounded interest is approximately $45,288.38.
Part B: To determine the total value of the loan with monthly compounded interest, we follow the same formula but with a different value for n:
n = 12 (monthly compounding).
Substituting the values into the formula, we have:
A = 20000(1 + 0.09/12)^(12*10).
Calculating this value, we find:
A ≈ $45,634.84.
Therefore, the total value of the loan with monthly compounded interest is approximately $45,634.84.
Part C: The difference between the total interest accrued on each loan can be calculated by subtracting the principal amount from the total value of each loan.
For the loan with quarterly compounding:
Total interest = Total value - Principal
Total interest = $45,288.38 - $20,000
Total interest ≈ $25,288.38.
For the loan with monthly compounding:
Total interest = Total value - Principal
Total interest = $45,634.84 - $20,000
Total interest ≈ $25,634.84.
The difference between the total interest accrued on each loan is approximately $346.46.
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