A ball is thrown into the air by a baby alien on a planet in the system of Alpha Centauri with a velocity of 43 ft/s. Its height in feet after t seconds is given by y=43t-23t^{2}.
A. Find the average velocity for the time period beginning when t=1 and lasting
.01 s: -0.20202020
.005 s: 0.020100
.002 s: 0.010020
.001 s:
NOTE: For the above answers, you may have to enter 6 or 7 significant digits if you are using a calculator.
B. Estimate the instanteneous velocity when t=1.
Answers
The average velocity for the time period = (2.508977e-03) / (0.001) = 2.508977 ft/s
To find the average velocity for the given time periods, we can use the formula:
average velocity = (change in position) / (change in time)
For the time period beginning when t = 1 and lasting 0.01 s:
y(1.01) - y(1) = (43(1.01) - 23\((1.01)^{2}\)) - (43(1) - 23\((1)^{2}\))
= -0.2020202
average velocity = (-0.2020202) / (0.01) = -20.20202 ft/s
For the time period beginning when t = 1 and lasting 0.005 s:
y(1.005) - y(1) = (43(1.005) - 23(1.005\()^{2} )\)) - (43(1) - 23(1\()^{2}\))
= 0.020100
average velocity = (0.020100) / (0.005) = 4.02 ft/s
For the time period beginning when t = 1 and lasting 0.002 s:
y(1.002) - y(1) = (43(1.002) - 23(1.002)\()^{2}\)) - (43(1) - 23(1\()^{2}\))
= 0.010020
average velocity = (0.010020) / (0.002) = 5.01 ft/s
For the time period beginning when t = 1 and lasting 0.001 s:
y(1.001) - y(1) = (43(1.001) - 23(1.001\()^{2}\)2) - (43(1) - 23(1\()^{2}\))
= 2.508977e-03
average velocity = (2.508977e-03) / (0.001) = 2.508977 ft/s
The estimated instantaneous velocity when t = 1 is -3 ft/s.
To estimate the instantaneous velocity when t = 1, we can find the derivative of y with respect to t, and evaluate it at t = 1:
y(t) = 43t - 23\(t^{2}\)2
y'(t) = 43 - 46t
y'(1) = 43 - 46(1) = -3
Therefore, the estimated instantaneous velocity when t = 1 is -3 ft/s.
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Related Questions
POPULATION One of the world's smallest countries. Vatican City, has a population less than 10 people. About how many people live in this country?
Answers
Answer:
Population of Vatican city is 825
Step-by-step explanation:
Have a nice Day , Hope this helped you I would appreciate it if you could mark my answer brainliest
Answer:
No. of people in Vatican City < 10
Step-by-step explanation:
Since there are less than 10 people, we use the inequality sign <.
< means less than.
No. of people in Vatican City < 10
the independent groups t test may be used to analyze the relationship between two variables when:
Answers
In this case, the independent groups t-test helps determine if there is a significant difference in the means of the dependent variable between the two independent groups.
The independent groups t-test may be used to analyze the relationship between two variables when:
1. The two variables consist of one continuous dependent variable and one categorical independent variable with two independent groups (levels).
2. The independent groups are not related or matched in any way, meaning that the data in one group does not influence the data in the other group.
3. The assumption of normality and homogeneity of variances for the continuous dependent variable are met within each group.
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In this case, the independent groups t-test helps determine if there is a significant difference in the means of the dependent variable between the two independent groups.
The independent groups t-test may be used to analyze the relationship between two variables when:
1. The two variables consist of one continuous dependent variable and one categorical independent variable with two independent groups (levels).
2. The independent groups are not related or matched in any way, meaning that the data in one group does not influence the data in the other group.
3. The assumption of normality and homogeneity of variances for the continuous dependent variable are met within each group.
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Find the largest six digits number which is divisible by 120 exactly.
Answers
Answer:
999,960
Step-by-step explanation:
let x be a multiple of 120
120x ≤ 999,999
999,999 / 120 = 8333.325
8333 ≤ x ≤ 8334
8333(120) = 999,960
8334(1200) = 1,000,080 this is a 7-digit number
Therefore, the largest 6-digit number that is exactly divisible by 120 is 999,960
Someone help me please
Answers
All the correct values that make the given inequality true are,
⇒ d = - 24, - 23, - 21, - 19, - 14
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
We have to given that;
The inequality is,
⇒ 3d ≥ - 72
Now, We can solve as;
⇒ 3d ≥ - 72
Divide by 3 both side,
⇒ d ≥ - 72/3
⇒ d ≥ - 24
Thus, All the correct values that make the given inequality true are,
⇒ d = - 24, - 23, - 21, - 19, - 14
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Bob is interested in examining the relationship between the number of bedrooms in a home and its selling price. After downloading a valid data set from the internet, he calculates the correlation. The correlation value he calculates is only 0.05What does Bob conclude? A)Bob gives up on his research becauser=.05 means there is no relationship of any kind between bedrooms and selling price. B) Bob continues his research because even though there is no linear relationship here, there could be a different relationship.
Answers
Bob continues his research because even though there is no linear equation relationship between the number of bedrooms and selling price, there could be another type of relationship.
Bob continues his research because even though the correlation value he calculated between the number of bedrooms and the selling price was only 0.05, this does not necessarily mean that there is no relationship of any kind between these two variables. It simply means that there is no linear relationship between the two. There could still be other types of relationships between the two variables, such as an exponential or quadratic relationship. It is possible that further analysis and exploration of the data set would reveal such a relationship and allow Bob to uncover the relationship between the two variables. Additionally, even if the correlation value is low, it does not necessarily mean that there is no relationship between the two variables. It simply means that the relationship is weak. Therefore, Bob should continue his research in order to uncover any potential relationships between the number of bedrooms and selling price.
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now consider that the penetrance of the disease is 75%. what is the probability that individual ii-2 exhibits this disease given this penetrance?
Answers
The probability that individual ii-2 exhibits the disease given a 75% penetrance is 0.75 or 75%.
Penetrance refers to the probability of an individual expressing a particular trait or disease given their genetic makeup. In this case, the penetrance of the disease is 75%, which means that there is a 75% chance that an individual with the genetic mutation for the disease will actually exhibit the disease. Therefore, the probability that individual ii-2 exhibits the disease given this penetrance is also 0.75 or 75%.
1. Penetrance is the probability that an individual with a specific genotype will express the associated phenotype or disease.
2. In this case, the penetrance of the disease is 75%, which means there is a 75% chance that an individual with the disease-associated genotype will exhibit the disease.
3. Given this penetrance, the probability that individual ii-2 exhibits the disease is 0.75 or 75%.
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PLs help answer ASAP
Answers
Answer:
The factors of the given equation are:
(11x−8)(11x+2)
Step-by-step explanation:
Since both terms are perfect squares,
Factorize using the difference of squares formula,
\(a^{2} -b^{2}\)\(=(a+b)(a-b)\)
where a=11x−3 and b=5.
=> (11x-3+5)(11x-3-5)
=> (11x+2)(11x−8)
=>\((11x-3)^{2}-25\)
Use the binomial theorem \((a-b)^{2}=a^{2} +b^{2} -2ab\) to expand\((11x-3)^{2}-25\)
=> \((11x^{2})+(3)^{2}- 2(11x)(3)-25\)
=>\(121x^{2} + 9 - 66x -25\)
=> \(121x^{2} -16+ 66x\)
By the splitting method,
=> (11x−8)(11x+2)
The factors of the equation are (11x−8)(11x+2).
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PLS HELP
A jewelry company purchases a necklace for $24. If they mark it up 36% to sell it at their store, what is the selling price of the necklace? (If necessary, round to the hundredths)
Answers
Answer:
I believe the answer would be 32.64
Step-by-step explanation:
$24 x 36% = 8.64
8.64 + 24 = $32.64
The mean time required to repair breakdowns of a certain copying machine is 93 minutes. The company which manufactures the machines claims that breakdowns of its newer model are easier to fix. To test this claim, a sample of 18 breakdowns of the new model were observed, resulting in a mean repair time of 86.8 minutes with a standard deviation of 14.6 minutes. Using a significance level of a = 0.10, determine if the new copy machines are faster to repair. State clearly what your null and alternative hypotheses are, show your work, and state your conclusion.
Answers
A significance level of 0.10, we have enough evidence to conclude that the new copy machines have a significantly faster mean repair time compared to the older model.
To test if the new copy machines are faster to repair, we can set up the following null and alternative hypotheses:
Null Hypothesis (H₀): The mean repair time for the new copy machines is the same as the mean repair time for the older model.
Alternative Hypothesis (H₁): The mean repair time for the new copy machines is less than the mean repair time for the older model.
Let's perform a one-sample t-test to test these hypotheses. The test statistic is calculated as:
t = (sample mean - population mean) / (sample standard deviation / √(sample size))
Given:
Population mean (μ) = 93 minutes
Sample mean (\(\bar x\)) = 86.8 minutes
Sample standard deviation (s) = 14.6 minutes
Sample size (n) = 18
Significance level (α) = 0.10
Calculating the test statistic:
t = (86.8 - 93) / (14.6 / sqrt(18))
t = -6.2 / (14.6 / 4.24264)
t ≈ -2.677
The degrees of freedom for this test is n - 1 = 18 - 1 = 17.
Now, we need to determine the critical value for the t-distribution with 17 degrees of freedom and a one-tailed test at a significance level of 0.10. Consulting a t-table or using statistical software, the critical value is approximately -1.333.
Since the test statistic (t = -2.677) is less than the critical value (-1.333), we reject the null hypothesis.
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HELP!
What is the missing term? What is the rule? 8 9/10, 7 7/10, 6 1/2 , _________
Answers
Answer:
5 3/10
Step-by-step explanation:
You subtract 1 1/5 from the number (n).
(In equation) x = n - 1 1/5
The rule is to subtract 1 2/10 each time
To figure this out, first look at the whole numbers
8, 7, 6, ___
You can see that your subtracting one to get to the next number.
Now look at the fractions.
9/10, 7/10, 1/2
To figure out the change you want all the fractions to have the same denominator.
1/2 = 5/10
9/10, 7/10, 5/10, ___
You can now also see that 2/10 is being subtracted each term.
Adding the two changes you get 1 + 2/10 = 1 2/10
An investment firm invested in two companies last year. They invested $8000 in Company A and made a profit of 11%. They invested $24,000 in Company B and made a profit of 13%. What was the investment firm's total profit?
Answers
Answer:
The investment firm's total profit is $4,000
Step-by-step explanation:
The Profit from Company A = 11% * $8,000
= 11 * $8,000/100
= $880
The Profit from Company B = 13% * $24,000
= 13 * $24,000/100
= $3,120
The total profit = $880 + $3120
= $4,000
Thus, the investment firm's total profit is $4,000
If f(x) and f^-1(x) are inverse functions of each other and f(x)=2x+5 what is f^-1(6)
Answers
The value of function f ⁻¹ (6) is,
⇒ f ⁻¹ (6) = 1/2
We have to given that;
f (x) and f⁻¹ (x) are inverse functions of each other and f(x) = 2x + 5.
Hence, The value of inverse of f (x) is,
f (x) = 2x + 5
y = 2x + 5
y - 5 = 2x
x = 1/2 (y - 5)
Hence, f ⁻¹ (x) = 1/2 (x - 5)
Plug x = 6;
f ⁻¹ (6) = 1/2 (6 - 5)
f ⁻¹ (6) = 1/2
Thus, The value of function f ⁻¹ (6) is,
⇒ f ⁻¹ (6) = 1/2
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what's
\( \sqrt{10 {}^{2} - 6 {}^{2} } \)
Answers
\( \sqrt{100 - 36} \\ \sqrt{64} \\ 8\)
hope it helps you ❣❣Mark me as brainliest
Answer:
8 is your answer
Step-by-step explanation:
hey there,
->
\( \sqrt{10{}^{2} - {6}^{2} } \)
->
\( \sqrt{100 - 36} \)
->
\( \sqrt{64} \)
->
\(8\)
Select the correct answer.
If a group of distinct objects can be arranged in 120 different ways, how many objects are there?
O
O
A. 3
O
B. 4
OC. 5
D. 6
Answers
Answer: C. 5
Step-by-step explanation:
Which of the following is
correct scientific notation?
7.032 x 1^4
7.032 x 100^4
7.032 x 10^4
70.32 x 10^4
Answers
Answer:
Third
Step-by-step explanation:
.................
The underlying statistical distribution for the x-bar chart is the.
Answers
The x-bar chart relies on the Normal Distribution due to the Central Limit Theorem, which states that the distribution of sample means will approach a normal distribution as the number of samples increases.
1. An x-bar chart is a type of control chart used to monitor the process mean of a continuous data set. It helps to determine whether a process is stable and under control.
2. The x-bar chart is based on the concept of sampling. In a process, multiple samples are taken, and their means (x-bar) are calculated.
3. According to the Central Limit Theorem, when a large number of samples are taken from a population, the distribution of the sample means will approach a normal distribution, regardless of the population's original distribution.
4. This is why the underlying statistical distribution for the x-bar chart is the Normal Distribution. The x-bar chart assumes that the sample means follow a normal distribution, allowing for the identification of process changes, shifts, or trends by monitoring the control limits and variation in the x-bar chart.
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Which of the following numbers can be expressed as repeating decimals?
3 over 7 , 2 over 5 , 3 over 4 , 2 over 9
Answers
Answer:
2 over 9 can be expressed as a repeating decimal.
Step-by-step explanation:
please help me i have 5 minutes left: )! ill give Brainliest thanks<3
Answers
Multiply.
17.22⋅(−2.4)
Enter your answer in the box.
Answers
HELP URGENTLY NEEDED STUCK ON THIS FOR 2 DAYS!!!!! LOTS OF POINTS FOR PERSON WHO HELPS!!!
Jada is three years older than twice her brother’s age. Select all the equations that correctly represent the relationship between Jada’s age j and her brother’s age b.
Multiple select question.
A) j=2b+3
B) j=2(b+3)
C) j=b2−3
D) b=2j+3
E) b=j−32
F) b=j2−3
Answers
Answer:
A
Step-by-step explanation:
2b meaning two times the age then add three like the question says.
In a school auditorium there are 33 seats in each row of seats. How many rows are needed for 528 students to each have a seat?
Record your answer and fill in the bubbles on your answer document. Be sure to use the correct place value.
Keypad
1 2 3
4 5 6
7 8 9
0 . -
/
CLEAR
Answers
All you have to do is divide
The graph of a quadratic function with vertex (1,-1) is shown in the figure below. Find the domain and the range. Write your answers as inequalities, using or as appropriate. Or, you may instead click on "Empty set" or "All reals" as the answer.
Answers
The domain of the function is all real numbers and range is y ≥ -1.
Since the vertex is at (1,-1), the axis of symmetry is x = 1.
This means that the domain of the function is all real numbers.
To find the range, we need to consider the y-values of the graph. Since the vertex is the lowest point of the graph, the range must be all y-values greater than or equal to -1.
However, since the parabola opens upwards, there is no upper bound on the y-values.
Therefore, the range is given by y ≥ -1.
Hence, the domain of the function is all real numbers and range is y ≥ -1.
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You have now invested some money in your bank account with an interest rate of 5% every year. At year 3 , you will find out that you have $30,000 in your bank account. How much money will you have in your bank account at year 2?
a. $25,915.13
b. $27,210.88
c. $28,571.43
d. $30,000.00
e. None of the above
Answers
At year 2, you will have approximately $25,915.13 in your bank account, assuming an initial investment with a 5% interest rate compounded annually. The correct answer is (a).
To find out how much money you will have in your bank account at year 2, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = Final amount (in this case, $30,000)
P = Principal amount (initial investment)
R = Annual interest rate (5% or 0.05)
N = Number of times interest is compounded per year (assumed to be once per year)
T = Number of years (in this case, 3)
Let’s solve for P, the principal amount at year 0:
30,000 = P(1 + 0.05/1)^(1*3)
30,000 = P(1.05)^3
Dividing both sides of the equation by (1.05)^3:
P = 30,000 / (1.05)^3
P ≈ 25,915.13
Therefore, at year 2, you will have approximately $25,915.13 in your bank account.
The correct answer is (a) $25,915.13.
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Find PNFNM
answer choices below
Answers
Answer:
The answer is C. HOPE THIS HELPS!
Step-by-step explanation:
PLS GIVE ME BRAINILIEST IT WOULD REALLY REALLY HELP ME!
Determine the principal value for the trigonometric expression. Give an exact answer in degrees.
sin^-1 (-1)
Answers
The Principal value for the trigonometric expression sin^-1 (-1) will be \(\frac{-\pi }{2}\)
and \(-\frac{\pi }{2}\) will be (-90°) in degree.
What is sine inverse function?
The inverse of the sine function, also known as the arcsine function, returns the angle's value when the sine function's opposite side and hypotenuse ratio are equal.
Formula for sine inverse function:
Ф= \(sin^{-1} (\frac{Opposite\ side}{Hypotenuse} )\)
Given trigonometric expression is sin^-1 (-1)
Using arc sine formula or sine inverse function,
\(= sin^{-1}(-1)\\\\= -sin^{-1}(1)\\\\= -\frac{\pi }{2}\)
Hence, The Principal value for the trigonometric expression sin^-1 (-1) will be \(\frac{-\pi }{2}\)
and \(-\frac{\pi }{2}\) will be (-90°) in degree.
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plsss helppp i have 1hr left
What is the value of x in the equation *x - y = 30, when y = 15?
O 4
8
O 80
O 200
Answers
Answer:
Is there an option of 45
Step-by-step explanation:
x-15=30
so +15
x=45
The product of two consecutive even integers is 48.
Find the numbers.
Let x be the 1steven integer Let x+2 be the 2nd even integer
Equation: (__) ( __ + __)= ___
Answers
Answer:
x(x + 2) = 48
x^2 + 2x - 48 = 0
(x - 8)(x + 6) = 0
x = -8, so x + 2 = -6
x = 6, so x + 2 = 8
The numbers are -8 and -6, or 6 and 8.
Which equation represents the equation of the parabola with focus (-3, 3) and directrix y =7?
y =1/8 (x+3)^2- 5 y = 1/8(x -3)^2 + 5 y = -1/8 (x+3)^2 + 5
y=-l/8(x-3)^2 + 5
Answers
The given focus point is (−3,3), and the directrix equation is y=7.Let P(x,y) be any point on the parabola. The perpendicular distance of P from directrix is y-7. Similarly, distance between point P and the focus is PF.
See the diagram below, to understand the scenario:As the parabola is symmetric about the directrix, the distance between the point P and directrix is equal to the distance between the focus and the point P.So, the distance PF is equal to y−7. Using the distance formula, find PF:PF = [(x−(−3))^2 + (y−3)^2]^(1/2)PF^2 = (x+3)^2 + (y−3)^2
Next, use the definition of the parabola and substitute PF^2 = 4a(y−k),where (h,k) are the vertex and a is the distance between the vertex and focus. Thus, the vertex is (-3,5) (as the directrix is y=7), a = 2 (PF = 2), and the equation of the parabola can be expressed in the form y = a(x−h)^2 + k.y = 1/8(x+3)^2- 5Thus, the required equation of the parabola is y = 1/8(x+3)^2- 5.
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Write down any significant observations you may have while trying to match the graphs. Using the multi-coordinate tool (from Capstone) select 3 special and consecutive points A) Initial position (m1) B) Changing direction (m2) C) Final position (m3) Take a Snapshot of your graper with the multi-coerdinate tools for your report. Do not erase your data Analyze the Data Compute the average velocity of the cart going from: A) point m1 to m2 Think about what the sign in this average velocity means. Make annotations for your report. Before adding a velocity vs time graph to your capstone file. Make a prediction of how it will look like. Testing your ideas Add a new plot area to your graph to show velocity vs time graph in the same page. Compare the result with your prediction. If they are ditferent describe what those differences are. if your prediction was correct, describe what your thought process was. Add this to your report. Using high light range of points tool to select your velocity points between your m1 and m2 points (use your time values a reference). Once they are selected use the statistics tool to get the mean and record it. Do the same for your m2 to m3 range. Compute your percent difference between the mean value given by capstone and your calculations wsina data peints. ICaestone value - vour valuel/casstone value * 100 Analyze this differences and explain: A) Why is there a Percent Difference between your average value calculation and the mean value given by Capstone? B) What does this Percent difference represent? C) What is the highest the percent difference can be before it becomes significant/insignificant?.
Answers
Observations while trying to match the graphs:
- The position vs. time graph shows the initial position, a change in direction, and the final position.
- The initial position (m1) is a point on the graph where the position is zero or the starting position of the object.
- The changing direction (m2) is the point on the graph where the position changes from positive to negative or vice versa.
- The final position (m3) is the point on the graph where the position stabilizes or reaches its final value.
Average velocity of the cart going from m1 to m2:
To compute the average velocity, we need to find the displacement and the time interval between m1 and m2. The displacement is the difference between the positions at m2 and m1, and the time interval is the difference between the corresponding time values.
Prediction of velocity vs. time graph:
Based on the change in direction observed in the position vs. time graph, the velocity vs. time graph is expected to show a change in sign at the point corresponding to m2. The velocity will be positive before m2 and negative after m2.
Comparison of prediction with the actual result:
After adding the velocity vs. time graph to the Capstone file, it is compared with the prediction. If the prediction matches the actual result, it implies that the understanding of the relationship between position and velocity is correct. If there are differences, those differences are noted and analyzed.
Percent difference between average value calculation and Capstone mean value:
The mean value of velocity between m1 and m2 is obtained using Capstone's statistics tool, and a similar calculation is performed manually using the selected velocity points. The percent difference between these values is computed using the formula: (Capstone value - Your value) / Capstone value * 100.
Analysis of differences and explanations:
A) The percent difference between the average value calculation and the mean value given by Capstone can arise due to rounding errors or differences in calculation methods. Capstone may use a slightly different algorithm for computing the mean.
B) The percent difference represents the deviation between the manually calculated average value and the value provided by Capstone. It indicates the degree of variation between the two methods.
C) The significance of the percent difference depends on the context and the tolerance for error. A higher percent difference may be considered significant if it exceeds a predetermined threshold or if it affects the overall analysis or conclusions drawn from the data. Conversely, a lower percent difference may be considered insignificant if it falls within an acceptable range of error.
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how many years in two scores?brainliest best answer.
Answers
Answer:
40 years
Step-by-step explanation:
I think 1 score is 20 years
so 2 scores = 2 x 20 = 40 years
I may be wrong so someone check
-Chetan K