Answer:
The model is [tex]V(t)=2239+249\sin(\frac{\pi}{2}t)[/tex].
Step-by-step explanation:
Consider the given information.
The volume of air inside the lungs increases or decreases so for this we will use the basic sine function [tex]B(t)=d+a\sin[b(t+ \frac{c}{a})][/tex] as our parent function.
Let us assume that the phase shift is 0 it means [tex]\frac{c}{b}=0[/tex].
The air that moves into and out of the lungs is about 498 mL.
It means the amplitude of the function will vary by 249(half of 498).
The reserve and residual volumes of air that remains in the lungs occupy about 1990 mL which is the minimum air in the lungs.
So, the max air will be: 1990+498 =2488 mL
And the average will be d=1990+249=2239 ml
The horizontal stretch will be [tex]b=\frac{2\pi}{4}=\frac{\pi}{2}[/tex] as we know that period of [tex]y=\sin t[/tex] is [tex]2\pi[/tex] and respiratory cycle for an average human takes about 4 seconds.
Hence, the model is [tex]V(t)=2239+249\sin(\frac{\pi}{2}t)[/tex].
Jackle works as a server at a local restaurant. She makes $8 per hour. She worked 34 hours last week. She made $250 in tips. What was her gross pay?
Answer:
522
Step-by-step explanation:
8x34=272+tips=522
Can someone help me asap.
Answer:
[tex] - \frac{1}{5 \sqrt{y} } [/tex]
Answer:
option 1
Step-by-step explanation:
[tex]\sqrt{y} =y^{\frac{1}{2}}\\\\(\frac{1}{\sqrt{y} })^{\frac{-1}{5}} =(\frac{1}{y^{\frac{1}{2}}})^{\frac{-1}{5}}\\\\= (y^{\frac{-1}{2}})^{\frac{-1}{5}}\\\\=y^{\frac{-1}{2}*\frac{-1}{5}}\\\\= y^{\frac{1}{10}}\\\\=\sqrt[10]{y}[/tex]
Passing through (4,5) and PARALLEL to y=2x-4
A PARALLEL line has the same angular coeficient, so:
[tex]f(x) = 2x+b[/tex]
[tex]f(4) = 5[/tex]
[tex]5 = 2\cdot 4 +b[/tex]
[tex]b = 5-8[/tex]
[tex]b = -3[/tex]
The line asked is:
[tex]f(x) = 2x-3[/tex]
Answer:
-2x+y=-3
Step-by-step explanation:
Choose a point (4,5) that the parallel line will pass through.
Find the slope m=2
To find an equation that is parallel to y=2x-4 the slopes must be equal. Using the slope of the equation, find the parallel line using the point-slope formula.
y-y1=m(x-x1) if m=2 and x1=4 and y1=5
y-5=2(x-4)
y-5=2x-8
Solve for y --- > y=2x-3
-2x+y=-3
(-2x+y=-3)*-1
2x-y=3
The function f(x) = –0.5x2 + 16x – 96 can be used to trace the path of a rocket, where the x-axis represents the ground and the y-axis measures the height of the rocket. The mathematical domain of the function is all real numbers.
The reasonable domain of the function is when 8 ≤ x ≤ x greater than or equal to eight but less than or equal to what value?
Answer:
24
Step-by-step explanation:
Put it in Desmos, and it’ll show you
The reasonable domain of the function is 8 ≤ x ≤ 24.7.
What is a function?A function has an input and an output.
A function can be one-to-one or onto one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
f(x) = -0.5x² + 16x – 96
The function represents the height of a rocket as a function of its horizontal position.
It is reasonable to assume that the rocket is launched from the ground
(x = 0) and that it has some minimum height (above ground level) before it is launched.
Now,
We can find this minimum height by finding the vertex of the parabola, which is given by.
x = -b / (2a)
where a = -0.5 and b = 16.
Plugging in these values, we get.
x = -16 / (2(-0.5))
x = 16
Now,
The vertex occurs at x = 16.
To find the minimum height, we can plug this value into the function.
f(16) = -0.5(16)² + 16(16) - 96
= 128
Therefore,
The rocket has a minimum height of 128 feet above ground level before it is launched.
To find the reasonable domain of the function.
Since the rocket is launched from the ground at x = 0 and has a minimum height of 128 feet, it is reasonable to assume that the rocket will remain above ground level for all values of x greater than or equal to 8, since the rocket must clear a height of 128 feet by the time it reaches x = 8.
Now,
We can find the x-value where the rocket reaches ground level
(i.e., its height is zero) by setting f(x) = 0.
Solving for x.
-0.5x² + 16x - 96 = 0
Using the quadratic formula.
x = ( -16 ± √(16² - 4(-0.5)(-96)) ) / (2(-0.5))
x = ( -16 ± √(1216) ) / (-1)
x ≈ 24.7 or x ≈ 7.3
Since the rocket is launched from the ground at x = 0, it is not reasonable to consider values of x less than 0.
Therefore,
The reasonable domain of the function is 8 ≤ x ≤ 24.7
This means,
The rocket will remain above ground level for all values of x between 8 and approximately 24.7.
Thus,
The reasonable domain of the function is 8 ≤ x ≤ 24.7.
Learn more about functions here:
https://brainly.com/question/28533782
#SPJ7
the dot is in the middle
5) What exponent matches the expression? *
1/8 . 1/8
[tex]\dfrac{1}{8}\cdot \dfrac{1}{8} = \dfrac{1}{8^2} = \left(\dfrac{1}{8}\right)^2 = \left(\dfrac{1}{8}\cdot 1\right)^2 = \left(\dfrac{1}{8}\cdot \dfrac{2}{2}\right)^2 = \left(\dfrac{2}{16}\right)^2[/tex]
What is the solution set for this inequality?
15 < -3m -9
Answer:
15= -3m-9
15+9 = -3m
24 = -3m
-8= m
Therefore the m value is -8
Simplify 6e - 9 + 10e
Answer:1
6
−
9
Step-by-step explanation:there you go
-2y + 6 = -12
what is y?
Answer:
y=3
Step-by-step explanation:
-12+6=-6
-6/-2=3
102 is 126% of what number
128.52
≈ 8.10
≈ 80.95
12.85
Step-by-step explanation:
102*100=10200
10200÷126=80.95
So the third one is correct
If Rick buys a remote control car for $29.00, what is his selling price?
Answer:
31
Step-by-step explanation:
31
The speed with which utility companies can resolve problems is very important. GTC, the Georgetown Telephone Company, reports it can resolve customer problems the same day they are reported in 80% of the cases. Suppose the 13 cases reported today are representative of all complaints.
Required:
a. How many of the problems would you expect to be resolved today? What is the standard deviation?
b. What is the probability 10 of the problems can be resolved today?
c. What is the probability 10 or 11 of the problems can be resolved today?
d. What is the probability more than 10 of the problems can be resolved today?
Answer:
a. 10.4 problems are expected to be resolved today, with a standard deviation of 1.44 problems.
b. 0.2457 = 24.57% probability 10 of the problems can be resolved today
c. 0.5137 = 51.37% probability 10 or 11 of the problems can be resolved today
d. 0.5017 = 50.17% probability more than 10 of the problems can be resolved today
Step-by-step explanation:
For each case, there are only two possible outcomes. Either they are solved, or they are not. Cases are independent of each other. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
It can resolve customer problems the same day they are reported in 80% of the cases.
This means that [tex]p = 0.8[/tex]
Sample of 13 cases:
This means that [tex]n = 13[/tex]
a. How many of the problems would you expect to be resolved today? What is the standard deviation?
Expected:
[tex]E(X) = np = 13*0.8 = 10.4[/tex]
Standard deviation:
[tex]\sqrt{V(X)} = \sqrt{13*0.8*0.2} = 1.44[/tex]
10.4 problems are expected to be resolved today, with a standard deviation of 1.44 problems.
b. What is the probability 10 of the problems can be resolved today?
This is [tex]P(X = 10)[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 10) = C_{13,10}.(0.8)^{10}.(0.2)^{3} = 0.2457[/tex]
0.2457 = 24.57% probability 10 of the problems can be resolved today.
c. What is the probability 10 or 11 of the problems can be resolved today?
This is [tex]p = P(X = 10) + P(X = 11)[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 10) = C_{13,10}.(0.8)^{10}.(0.2)^{3} = 0.2457[/tex]
[tex]P(X = 11) = C_{13,11}.(0.8)^{11}.(0.2)^{2} = 0.2680[/tex]
[tex]p = P(X = 10) + P(X = 11) = 0.2457 + 0.2680 = 0.5137[/tex]
0.5137 = 51.37% probability 10 or 11 of the problems can be resolved today.
d. What is the probability more than 10 of the problems can be resolved today?
This is
[tex]P(X > 10) = P(X = 11) + P(X = 12) + P(X = 13)[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 11) = C_{13,11}.(0.8)^{11}.(0.2)^{2} = 0.2680[/tex]
[tex]P(X = 12) = C_{13,12}.(0.8)^{12}.(0.2)^{1} = 0.1787[/tex]
[tex]P(X = 13) = C_{13,13}.(0.8)^{13}.(0.2)^{0} = 0.0550[/tex]
[tex]P(X > 10) = P(X = 11) + P(X = 12) + P(X = 13) = 0.2680 + 0.1787 + 0.0550 = 0.5017[/tex]
0.5017 = 50.17% probability more than 10 of the problems can be resolved today
Which chart belong with the graph at the right?
Answer:
Chart nº 2
Step-by-step explanation:
Just match each points you will see which one is actually on the diagram!
What is the value of g?
580
g
Your answer
Answer:
32 degrees
Step-by-step explanation:
The total angle formed is 90 degrees because there is a right angle.
So, 90 - 58 = g
32 degrees = g
1 cm equals 10 mm how many millimeters does 2.5 cm equal label your answer
Which of the following measurements form a right triangle? Select all that apply.
A. 7in., 24 in., & 25 in.
B. 18ft., 23 ft., & 29 ft.
C. 10 in., 24 in., & 26 in.
Pls answer asap. Ty :)
Answer:
B C
Step-by-step explanation:
because imagine that you have a huge doll house and you're wondering if you can get it in your room but you aren't sure what will happen if you try and push it through your door
18.
(01.04 MC)
What is 83,734.21 written in expanded form?
8 x 10,000 + 3 x 1,000 + 7 x 100 + 2 x 0.1 + 1 x 0.01
8 x 10,000 + 3 x 1,000 + 7 x 100 + 4 x 10 + 3 x 1 + 1 x 0.1 + 2 x 0.01
8 x 10,000 + 3 x 1,000 + 7 x 100 + 3 x 10 + 4 x 1 + 2 x 0.1 + 1 x 0.01
8 x 100,000 + 2 x 10,000 + 7 x 1,000 + 3 x 100 + 4 x 10 + 3 x 0.1 + 1 x 0.01
Answer:
(C) 8 x 10,000 + 3 x 1,000 + 7 x 100 + 3 x 10 + 4 x 1 + 2 x 0.1 + 1 x 0.01
Step-by-step explanation:
8 x 10,000 + 3 x 1,000 + 7 x 100 + 3 x 10 + 4 x 1 + 2 x 0.1 + 1 x 0.01=
80,000 + 3,000 + 700 + 30 + 4 + 0.2 + 0.01=
83,734.21.
I hope this helps!
1/4x+2=-4 how do you do this step by step?
Answer:
6.25 is the answer, I really dfon't know how to figure out which would be the procedure becuase I'm a little oxidated
The average age of a group of teachers and professors is 40. If the teachers and average 35 years and the professors 50 years, then what is the ratio of the number of teachers to professors. Accounting and finance uni
Answer:
2:1
Step-by-step explanation:
average age of both = 40
average age of teachers = 35
average age of professors = 50
35 + 35 + 50 = 120
120 / 3 = 40
Some one has to make two guitars and it took them 8 week now they have an order of 7 guitars how long will it take to finish the 7 guitars
Answer:
28 Weeks
Step-by-step explanation:
8÷2=4
4×7=28
28 Weeks
Shelby keeps all her vacation pictures in 2 photo albums. One of the photo albums is 2/3 full and the other is 5/6 full. How much of the photo albums are full?
Answer: 1 1/2
Step-by-step explanation:
Write a possible third degree polynomial with integer coefficient that have zeros: 1 2i, -4. Assume the leading coefficient to be 1
Answer:
The polynomial is:
[tex]p(x) = x^3 + 2x^2 - 3x + 20[/tex]
Step-by-step explanation:
A third degree polynomial can be written in function of it's zeros [tex]x_1, x_2, x_3[/tex] the following way:
[tex]p(x) = a(x - x_1)(x - x_2)(x - x_3)[/tex]
In which a is the leading coefficient.
Integer coefficient that have zeros: 1+2i, 1-2i, -4
Leading coefficient: 1
So
[tex]p(x) = 1(x - (1+2i))(x - (1-2i))(x - (-4))[/tex]
[tex]p(x) = (x - 1 -2i)(x - 1 + 2i)(x + 4)[/tex]
[tex]p(x) = ((x-1)^2 - (2i)^2)(x + 4)[/tex]
[tex]p(x) = (x^2 - 2x + 1 - 4i^2)(x + 4)[/tex]
Since [tex]i^2 = -1[/tex]
[tex]p(x) = (x^2 - 2x + 1 + 4)(x + 4)[/tex]
[tex]p(x) = (x^2 - 2x + 5)(x + 4)[/tex]
[tex]p(x) = x^3 + 4x^2 - 2x^2 - 8x + 5x + 20[/tex]
[tex]p(x) = x^3 + 2x^2 - 3x + 20[/tex]
HELPPP look at the figure.
What is the slope of the graph?
Answer:
-5
Step-by-step explanation:
becuses look at where the slope intersecs the y axis. Its -5
EZ
Answer:
its
3.6
Step-by-step explanation:
trust me
estimate the sum 1.37+0.9. betwen answers like bettwen 3
Is 5x-1=9 always, sometimes, or never true? And why?
Answer:
never
Step-by-step explanation:
first ral correct answer gets brainliest
What expression is equivalent to (-18) - 64n?
Answer:-2(9+32n)
Step-by-step explanation:
Which of the following points is a solution of the inequality y < -Ixl?
(1, 0)
(1, -1)
(1, -2)
Answer:
(1, -2)
Easy Question for me
3) Sandra drove 126 miles in 2 hours at a constant speed. Use a proportion to find how long it
will take her to drive 189 miles at the same speed.
The equation 3s=21 can be used to find the number of students s in each can on a field trip. How Many students are in each Van? Please Hlep Me With This ASAP
Do you agree with Amur? Explain why.
would would my grade go down to if i got a 78% on a test? it’s a summative so it’s 60% of my grade. i have a 98 in that class.
Answer:
yes it would go down a little bit but not much, so it nothing to worry about to much
Step-by-step explanation: