A child shot a toy rocket into the air from their playhouse which stood 5 ft above the ground. The rocket rose to 50 ft above the ground and landed on the ground 3.4 seconds later. The path of the toy rocket could be modeled by a quadratic function, h(t), where h is the height of the toy rocket in feet after t seconds.
(1) What is the practical domain of the function?
(2) What is the practical range of the function?
(3) How would the theoretical domain and range of the function differ from the practical domain and range of the situation?
Answers
Answer:
Part A)
All real numbers between 0 and 3.4 (including 0 and 3.4).
Part B)
All real numbers between 5 and 50 (including 5 and 50).
Part C)
See below.
Step-by-step explanation:
We know that the rocket rose to a maximum of 50 feet and was in the air for 3.4 seconds. The rocket started at a height of 5 feet.
Part A)
The practical domain of a function is the domain with the context. Here, our domain is the number of seconds that had passed. Time can't be negative, so our domain must be greater than or equal to 0. Also, since we know that our rocket landed after 3.4 seconds, this means that our practical domain is all real numbers between 0 and 3.4 including 0 and 3.4.
Part B)
The practical range of a function is the range with the context. Here, our range is the height the rocket reaches. We know that the rocket started at a height of 5 feet, so our practical range should be greater than or equal to 5. We also know that the maximum height the rocket reached was 50 feet. So, our practical range is all real numbers between 5 and 50 including 5 and 50.
Part C)
The theoretical domain and range differs from the practical domain and range in that the theoretical counterparts don't consider the context. For the theoretical domain and range, we will analyze this as a normal quadratic. Since it's a quadratic, the theoretical domain is all real numbers. Since our maximum value is y=50, our theoretical range is all numbers less than or equal to 50.
However, this can't be used since negative time (e.g. height after -2 seconds) is inapplicable and negative height doesn't make sense in this context either (well, technically negative height can indicate that the rocket goes underground, but this is not mentioned here).
So, it is important to determine when to use practical domain/range and theoretical domain/range!
Related Questions
HELPPP MEE BEST ANSWER GET THE BRAINLIEST!!
Answers
Answer:
The correct answer is 1/2 = ?/100
Step-by-step
The circle is divided into 2 halves and the angle is 100 degrees
Multiply (3x-7)(2x^2-8x+3)
Answers
Answer:
6x^3-38x^2+65x-21
Step-by-step explanation:
I need help on this question please
Answers
Answer:
Its 3
Step-by-step explanation:
Add them all together and divide by 6
The perpetrator is either one or the other of the two persons X and Y. Both persons are on the run from the authorities, and after an initial investigation, both fugitives appear equally likely to be the perpetrator. Further investigation reveals that the actual perpetrator has blood type A. 10% of the population has blood type A; you may assume that the innocent one of persons X and Y has a 10% chance of having blood type A. In the investigation, you find two samples of blood; the first sample belongs to person X, and the second sample belongs to person Y. In the process of testing the blood, the sample belonging to person Y was accidentally destroyed (you may assume that the destruction was random). The sample belonging to person X was determined to be blood type A. In light of this new information, find the probability that person X is the perpetrator
Answers
Answer:
The probability is [tex]P(X | B) = 0.91[/tex]
Step-by-step explanation:
Generally the probability of the perpetrator being X is equal to the probability of the perpetrator being Y (given that both fugitives appear equally likely to be the perpetrator )
This can be mathematically represented as
[tex]P(X) = P(Y) = \frac{1}{2}[/tex]
Let G represent the event that the blood type of the sample is type A
Generally if X has a blood type A then it is almost certain that the perpetrator is X compared to Y
This can be mathematically represented as
[tex]P(G | X) = 1[/tex]
( Here this means the probability of the sample being of type A given that the X has a blood type A )
Given that the sample belonging to Y accidentally destroyed
Then the probability that Y is innocent given that the blood type of Y is of type A
This can be mathematically represented as
[tex]P(G | Y) = 10\%[/tex]
[tex]P(G | Y) = 0.10[/tex]
Generally according to Bayes rule the probability that person X is the perpetrator mathematically as
[tex]P(X | G) = \frac{P(G|X) * P(X)}{ P(G|X) * P(X) + P(G | Y ) * P(Y)}[/tex]
[tex]P(X | B) = \frac{1 * 0.5 }{ 1 * 0.5 + 0.10 * 0.5}[/tex]
[tex]P(X | B) = 0.91[/tex]
Find the slope of the line that passes through (1, 4) and (10, 9). Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answers
Answer:
The answer is
[tex] \frac{5}{9} \\ [/tex]
Step-by-step explanation:
The slope of a line given two points can be found by using the formula
[tex]m = \frac{ y_2 - y _ 1}{x_ 2 - x_ 1} \\ [/tex]
where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
(1, 4) and (10, 9)
The slope is
[tex]m = \frac{9 - 4}{10 - 1} = \frac{5}{9} \\ [/tex]
We have the final answer as
[tex] \frac{5}{9} \\ [/tex]
Hope this helps you
Answer:
5/9
Step-by-step explanation:
Slope formula
y2-y1/x2-x1
Solution
9-4/10-1
5/9
Best of Luck!
a sin^3theta+b cos^3theta=sintheta costheta and a sintheta-b costheta=0 then prove a^2+b^2=1
Answers
Answer:
Proof in explanation
Step-by-step explanation:
Trigonometric Identities
The basic trigonometric identity is:
[tex]\sin^2\theta+\cos^2\theta=1[/tex]
We'll use it and some basic algebra to prove that, given:
[tex]a sin^3\theta+b cos^3\theta=sin\theta cos\theta[/tex]
And
[tex]a\sin\theta-b\cos\theta=0[/tex]
Then
[tex]a^2+b^2=1[/tex]
From the equation:
[tex]a\sin\theta-b\cos\theta=0[/tex]
We have:
[tex]a\sin\theta=b\cos\theta\qquad [1][/tex]
The equation
[tex]a sin^3\theta+b cos^3\theta=sin\theta cos\theta[/tex]
Can be rewritten as
[tex]a\sin\theta \sin^2\theta+b \cos^3\theta=\sin\theta \cos\theta[/tex]
Replacing [1]:
[tex]b\cos\theta \sin^2\theta+b \cos^3\theta=\sin\theta \cos\theta[/tex]
Taking the common factor:
[tex]b\cos\theta (\sin^2\theta+ \cos^2\theta)=\sin\theta \cos\theta[/tex]
The expression in parentheses is 1, thus:
[tex]b\cos\theta =\sin\theta \cos\theta[/tex]
Dividing by [tex]\cos\theta[/tex]
[tex]b=\sin\theta[/tex]
Replacing in
[tex]a\sin\theta=b\cos\theta[/tex]
We have
[tex]a\sin\theta=\sin\theta\cos\theta[/tex]
Dividing by [tex]\sin\theta[/tex]
[tex]a=\cos\theta[/tex]
Now:
[tex]a^2+b^2=(\cos\theta)^2+(\sin\theta)^2[/tex]
This expression is 1, thus it's proven:
[tex]\boxed{a^2+b^2=1}[/tex]
A certain restaurant always overbooks. If possible. At 7:00 pm the restaurant can seat 50 parties, but takes reservations for 53. If the probability of a party not showing up is 0.04, assuming independence, what is the probability that the restaurant can coommodate all the customers who do show up? You must show all of your work including the correct formulas for calculation to receive full credit of this answer
Answers
Answer:
The probability that the restaurant can accommodate all the customers who do show up is 0.3564.
Step-by-step explanation:
The information provided are:
At 7:00 pm the restaurant can seat 50 parties, but takes reservations for 53. If the probability of a party not showing up is 0.04. Assuming independence.Let X denote the number of parties that showed up.
The random variable X follows a Binomial distribution with parameters n = 53 and p = 0.96.
As there are only 50 sets available, the restaurant can accommodate all the customers who do show up if and only if 50 or less customers showed up.
Compute the probability that the restaurant can accommodate all the customers who do show up as follows:
[tex]P(X\leq 50)=1-P(X>50)\\=1-P(X=51)-P(X=52)-P(X=53)\\=1-[{53\choose 51}(0.96)^{51}(0.04)^{53-51}]-[{53\choose 52}(0.96)^{52}(0.04)^{53-52}]\\-[{53\choose 53}(0.96)^{53}(0.04)^{53-53}]\\=1-0.27492-0.25377-0.11491\\=0.3564[/tex]
Thus, the probability that the restaurant can accommodate all the customers who do show up is 0.3564.
To earn a fitness reward, your average heart rate while walking must be between 80 and 89 beats per minute, inclusive. Suppose you recorded 85, 81, and 87 beats per minute on your first three recordings. What are the possible heart rates you can have on the fourth and final recording in order to earn a fitness reward?
Answers
Answer:
Between 67 and 103 beats per minute
Step-by-step explanation:
The minimum would be 80. That means that the minimum sum would have to be 320 among the four numbers.
85+81+87=253
320-253=67 so 67 will be the minimum
now, we should see the maximum. It will be 89 so the sum of the four numbers cannot be anymore than 89*4 which is 356
So, 356-253=103
yay savvas, my favorite
A. between 67 and 103 beats per minute inclusive
Step-by-step explanation:
What I did was I just started from the top and tried out the mean with 69 and saw that that was 80, so that was right. Then I tried 103, and that was 89, so that's obviously the max. So it was pretty simple. I do not know the way you are supposed to do it. That's what I came on here for, but none of the answers anyone but was right..
8r-9r+11r what is the answer
Answers
Answer:
10r
Step-by-step explanation:
8r - 9r +11r
-r +11r
10r
How many ounces are in 2 ounces
Answers
Answer:
2 ounces are in 2 ounces
Step-by-step explanation:
Answer:2
Step-by-step explanation:
Divide.
(6x² +36x+33) + (x+5)
Your answer should give the quotient and the remainder.
Quotient: 0
Remainder: 0
?
Answers
Answer: Evaluation : 6x^2 +37x+38 Factor: 6(x − - √ 457-37/12 )(x− √ 457-37/12)
Step-by-step explanation: Evaluation: (6x ^2 +36x+33)+(x+5)
Combine 36x and x to get 37x.
6x ^2 +37x+33+5
Add 33 and 5 to get 38.
6x ^2 +37x+38
Factor: Its pretty long
You have 120 followers you purchase 1,000 fake followers for $18 what percentage of followers are real
Answers
Answer:
12%
Explanation:
The $18 don't matter in this problem.
120/1000 is not a lot so it would be predicted to be 12% due to the amount.
What is a complimentary angle
Answers
Answer:
Step-by-step explanation:
it is an angle that adds up to 90 degrees.
Answer:
Complementary angles are two angles that, when their measurements are added together, add up to be 90°.
Step-by-step explanation:
For example, two angles that measure 31° and 59° respectively would be complementary angles.
Hope this helps!
20 POINTS!! ASAP, PLS SHOW WORK TYY
Answers
Answer:
[tex]\sin(\theta)=-\sqrt5/5\text{ and } \csc(\theta)=-\sqrt5\\\cos(\theta)=2\sqrt5/5\text{ and } \sec(\theta)=\sqrt5/2\\\tan(\theta)=-1/2\text{ and } \cot(\theta)=-2[/tex]
Step-by-step explanation:
First, let's determine which quadrant our angle θ lies in.
Remember ASTC, where:
Everything is positive in QI,
Only sine (and cosecant) is positive in QII,
Only tangent (and cotangent) is positive in QIII,
And only cosine (and secant) is positive in QIV.
Since our tangent is negative, and our cosine is positive, this means that our θ must be in QIV.
In QIV, sine is negative, tangent is negative, and cosine is positive.
With that, let's figure out the remaining trig ratios.
We know that:
[tex]\tan(\theta)=-1/2[/tex]
Remember that tangent is the ratio of the opposite side to the adjacent side.
Let's figure out our hypotenuse using the Pythagorean Theorem:
[tex]a^2+b^2=c^2[/tex]
Substitute 1 for a and 2 for b (we can ignore the negative since we're squaring anyways). This yields:
[tex](1)^2+(2)^2=c^2[/tex]
Square:
[tex]1+4=c^2[/tex]
Add:
[tex]c^2=5[/tex]
Take the square root:
[tex]c=\sqrt{5}[/tex]
So, our square root is √5.
So, our three sides are: Opposite=1, Adjacent=2, and Hypotenuse=√5.
Sine and Cosecant:
Remember that:
[tex]\sin(\theta)=opp/hyp[/tex]
Substitute 1 for the opposite and √5 for the hypotenuse. This yields:
[tex]\sin(\theta)=1/\sqrt5[/tex]
Rationalize:
[tex]\sin(\theta)=\sqrt5/5[/tex]
And since our angle is in QIV, we add a negative:
[tex]\sin(\theta)=-\sqrt5/5[/tex]
Cosecant is simply the reciprocal of sine. So:
[tex]\csc(\theta)=-\sqrt5[/tex]
Cosine and Secant:
Remember that:
[tex]\cos(\theta)=adj/hyp[/tex]
Substitute 2 for the adjacent and √5 for the hypotenuse. This yields:
[tex]\cos(\theta)=2/\sqrt5[/tex]
Rationalize:
[tex]\cos(\theta)=2\sqrt5/5[/tex]
Since our angle is in QIV, cosine stays positive.
Secant is the reciprocal of cosine. So:
[tex]\sec(\theta)=\sqrt5/2[/tex]
Tangent and Cotangent:
We were given that:
[tex]\tan(\theta)=-1/2[/tex]
To find cotangent, flip:
[tex]\cot(\theta)=-2[/tex]
And we're done!
What is the volume of the following figure ?
Answers
The required volume of the given figure is 7 cubic units.
What is volume?Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
The volume of the given 1 cube is 1 cubic unit,
Now,
In the figure,
There are 7 cubes,
So the volume is given as = 1 × 7 = 7 cubic units.
Thus, the required volume of the given figure is 7 cubic units.
Learn more about Volume here:
https://brainly.com/question/1578538
#SPJ5
Can anyone help? I’m having trouble.
Answers
Answer:
The square root of fifty is 7.10 rounded
Step-by-step explanation:
It would be around 7 on the number line. Hope this helps!!
Write the equation of the line that it is parallel to 2X = 1−3Y and passes through (-5,7) .
Answers
Answer:
3y=1-2x....
y=1/3-2/3x.....m=-2/3
y=-2/3x+b replacement(-5,7)
b=11/3
y=-2/3x+11/3
Step-by-step explanation:
Anthony Tedesco sold his used mountain bike and accessories for $306. If he
received 8 times as much money for the bike as he did for the accessories, find
how much money he received for the bike.
He received $
for the bike.
Answers
Professor Cramer determines a final grade based on attendance, two papers, three major tests, and a final exam. Each of these activities has a total of 100 possible points. However, the activities carry different weights. Attendance is worth 3%, each paper is worth 9%, each test is worth 17%, and the final is worth 28%. (a) What is the average for a student with 81 on attendance, 90 on the first paper, 92 on the second paper, 86 on test 1, 71 on test 2, 93 on test 3, and 62 on the final exam
Answers
Answer:
78.67
Step-by-step explanation:
The computation of the average for a student is shown below:
= Different Weights × different activities
= (3% × 81) + (9% × 90) + (9% × 92) + (17% × 86) + (17% × 71) + (17% × 93) + (28% × 62)
= 2.43 + 8.1 + 8.28 + 14.62 + 12.07 + 15.81 + 17.36
= 78.67
Hence, the average of the student is 78.67
We simply applied the above formula
one possible combination of homeroom groups is 18 groups of 10 students and 5 groups of 12 students. which equation uses the x = 10 students and y=12 students, combination to represent the situation in point- slope form? is the answer y-18 =-5/6 (× - 5) ,y- 5 = - 5/6 (× -18) ,y +5 =-5/6 (× +18) or y+18= -5/6 (× +5)
Answers
Answer: y - 5 = -5/6 (x - 18)
Step-by-step explanation:
The point-slope form of a linear equation is written using the slope of the line and one point in the line. From part A, the slope of the line representing this situation is m = -5/6.
Since x represents the number of 10-student groups and y represents the number of 12-student groups, the combination of 18 groups of 10 students and 5 groups of 12 students is represented by the point (18,5).
Answer:
Step-by-step explanation:
Y=-(x-4)^2+9 what’s the domain
Answers
Answer:
y=−x2+8x−7
Step-by-step explanation:
F=epd solve for e..........
Answers
This a simple literal equation all you have to do is divide (ph) from e and repeat on the other side
Solve for y.
A. 11
B. 21
C. 24
D. 42
Answers
Answer:
A. 11
Step-by-step explanation:
Since the measure of (4x- 6) is 90°, you would first solve the equation for x
4x - 6 = 90
4x - 6 + 6 = 90 + 6
4x = 96
x = 24°
-------------------------------------------------------------------------------------
Since (4x - 6) was a right angle, (x + 6y) is also a right angle. Therefore, you would do:
x + 6y = 90
24 + 6y = 90
24 + 6y - 24 = 90 -24
6y = 66
y = 11°
---------------------------------------------------------------------------------------
Hope this was helpful!!!
Suppose an employee is suspected of having used an illegal drug and is given two tests that operate independently of each other. Test A has probability 0.91 of being positive if the illegal drug has been used. Test B has probability 0.88 of being positive if the illegal drug has been used. The company requires that an employee, Al Capone, take and pass both tests to keep his job. Assume that Al has, in fact, been using the illegal drug. What is the probability that neither test is positive (and thus Al gets to keep his job)
Answers
Answer:
The probability that neither test is positive
P(A⁻ ∩ B⁻ ) = 0.0108
Step-by-step explanation:
Step(i) :-
Given the two tests are independently
Test A has probability 0.91 of being positive if the illegal drug has been used
P(A) = 0.91
Test B has probability 0.88 of being positive if the illegal drug has been used
P(B) = 0.88
If events are independently then ,
[tex]P(A n B) = P(A) P(B)[/tex]
Step(ii):-
The probability that neither test is positive (and thus Al gets to keep his job)
[tex]P(A^{-} n B^{-} ) = P(A^{-} ) P(B^{-} )[/tex]
P(A⁻ ∩ B⁻ ) = P(A⁻ ) P(B⁻ )
= ( 1- P(A) ) ( 1 - P(B))
= (1 - 0.91 ) ( 1 - 0.88 )
= (0.09) (0.12)
= 0.0108
The probability that neither test is positive
P(A⁻ ∩ B⁻ ) = 0.0108
Which has a value greater than 600 but less than 6,000?
A. 6.1 x 10^3
B. 5.9 x 10^4
C. 5.26 x 10^3
D. 7.87 x 10^3
(look at the picture)
Answers
Answer:
c
Step-by-step explanation:
5.26×10³=5260 which is less than 6000 and greater than 600
Suppose Đ1 and Đ2 are known to be complementary. If mÐ1 = 20, then mÐ2 =
0 20
O 70
0 340
0 160
Answers
Answer:
70
Step-by-step explanation:
complementary angles are 2 angles that add up to 90, the first angle is already 20 so just subtract 90-20 to find other angle
Luna rented a car for $83.00 a week plus $0.20 for each mile the car is driven. What is
the greatest number of miles Luna can drive the car in one week if she wishes to spend at
most $100.00
Answers
Answer:
135 miles
Step-by-step explanation:
So first we have to find the difference of 83 and 100. So 100-83=27. So for miles, she can spend 27 dollars. Now, since per mile it costs 20 cents or 1/5 of a dollar, every time she drives 5 miles she'll have to pay one more dollar. So One dollar = 5 miles. Then we do the total amount of money she can spend on miles (27) and multiply that by the amount of miles per dollar (5) and we get 135 miles. So she can drive 135 miles.
For one English test, sandy had to answer 15 questions. Of these questions, she answered 80 percent of them correctly. How many questions did sandy correctly answer on her test?
Answers
Answer:
12
Step-by-step explanation:
15×0.8= 12
you're multiplying the total number of questions with the score as a decimal
The National Center for Health Statistics, housed within the U.S. Centers for Disease Control and Prevention (CDC), tracks the number of adults in the United States who have health insurance. According to this agency, the uninsured rates for Americans in 2018 are as follows: 5.1% of those under the age of 18, 12.4% of those ages 18–64, and 1.1% of those 65 and older do not have health insurance (CDC website). Approximately 22.8% of Americans are under age 18, and 61.4% of Americans are ages 18–64.a. What is the probability that a randomly selected person in the United States is 65 or older?b. Given that the person is an uninsured American, what is the probability that the person is 65 or older?
Answers
Answer:
a. 0.158
b. 0.01942
Step-by-step explanation:
For part a we define probability that the randomly selected person is if 65 years or more than that
a.
Probability of under age = 22.8% = 0.228
Probability of those from age 18 to 64 = 61.4% = 0.614
1-0.228-0.614
= 0.158
b.
P(uninsured) = p(those not up to 18) * p(those uninsured or under 18) + p(those age 18-64) * p(uninsured or under 18) + p(being 64plus) x P(uninsured or 64 plus)
= 0.228 x 0.051 + 0.614 x 0.124 + 0.158 x 0.011
= 0.011628 + 0.076136 + 0.001738
=0.089502
P(65 of older|uninsured) = p(64+) x P(uninsured or 64 plus)
= 0.157 x 0.011/0.089502
= 0.001738/0.089502
= 0.01942
a. The probability that a randomly selected person in the United States is 65 or older is 0.158
b. In the case when the person is an uninsured American so the probability is 0.01942
Calculation of probabilities:a.
Since
Probability of under age = 22.8% = 0.228
And,
Probability of those from age 18 to 64 = 61.4% = 0.614
So, the probabilities of 65 or older is
= 1 - 0.228-0.614
= 0.158
b.
Now
P(uninsured) = p(those not up to 18) × p(those uninsured or under 18) + p(those age 18-64) × p(uninsured or under 18) + p(being 64plus) × P(uninsured or 64 plus)
= 0.228 × 0.051 + 0.614 × 0.124 + 0.158 × 0.011
= 0.011628 + 0.076136 + 0.001738
=0.089502
So,
P(65 of older|uninsured) = p(64+) × P(uninsured or 64 plus)
= 0.157 × 0.011 ÷ 0.089502
= 0.001738 ÷ 0.089502
= 0.01942
learn more about the probability here: https://brainly.com/question/16096170
Find the sum.
7/30 + 9/20 PLS
Answers
Answer:
41/60
Step-by-step explanation:
Convert the fractions into like denominators: 7/30 = 140/600, 9/20 = 270/600
Add: 140/600+270/600 = 410/600
Divide into a smaller fraction: 41/60
Answer:
it is your a ss 344543534543543543e53
Step-by-step explanation:
no capion needed
