Sin function goes up and down, standard amplitude is 1 unit. The sin function modelling the given situation is [tex]f(x) = 30\sin(\dfrac{\pi x}{5}) + 90[/tex]
How does sine function works?Suppose that we've got
[tex]f(x) = a\sin(bx + c) + d[/tex]
It has got
Amplitude or maximum height from average motion horizontal axis = a+dAnd thus, the minimum low from horizontal axis is -a (sin ranges from -1 to 1, and multiplying a to it make it range from -a + d to a).Period of wave: [tex]\dfrac{2\pi}{b}[/tex]Phase shift (horizontal left shift) = c/bHorizontal line around which wave moves is: y = dThe situation given has:
Maximum blood pressure as 120 mm/Hg = a + d
Minimum blood pressure as 60 mm/Hg = -a + d
Thus, adding both will give:
[tex](a+d) + (-a + d) = 120 + 60\\2d = 180\\d = 90[/tex]
Thus, as a + d = 120, thus, a = 120-d = 120 - 90 = 30
Now, The period is given to be 10 minutes, or we get:
[tex]\dfrac{2\pi}{b} = 10\\\\b = \dfrac{\pi}{5}[/tex]
Since count started from 0, thus, c= 0
Therefore, the sine function modelling the given situation is:
[tex]f(x) = a\sin(bx + c) + d \\\\f(x) = 30\sin(\dfrac{\pi x}{5}) + 90[/tex]
Here x is the number of minutes passed.
Learn more about sine function modelling the situation here:
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Answer:
A
Step-by-step explanation:
Special right triangle 30-60-90 degrees lesson 3 homework
please help ASAPPPP SOMEONE :(
Answer:
rip
Step-by-step explanation:
Pls help (giving brainliest to first answer)
Answer:
(0, -7) and (5, 0)
Step-by-step explanation:
y-intercept is when x = 0, therefore (0, -7)
x-intercept is when y = 0, therefore (5, 0)
Answer:
X intercept: (5,0) Y intercept: (0,-7)
Step-by-step explanation:
So you want to look at where you have an x value (input) and it's output (y) is 0 for x intercept, and you want to look at the y value (output) and it's input (x) to be 0 for the y intercept, so on the left we see that 5 = 0, and on the right we see that -7 = 0, and then write them as is, so (5,0) and (0,-7)
Hope that made sense and this helps!
The _____ is a point estimate of the population mean for the variable of interest. a. sample mean b. geometric mean c. median d. sample
There are different ways to estimate a variable. The sample mean is a point estimate of the population mean for the variable of interest.
What is a point estimate of the population mean?A point estimate is known to be the value of a sample statistic that is often applied as one estimate of a specific population parameter.
The sample mean is defined simply as a form of average value seen in a sample. A sample is known to be the little portion of a whole.
Learn more about sample mean from
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Is what's below a complete sentence or a fragment?
Iris West is very happy today.
Answer:
complete sentence
Step-by-step explanation:
it has a subject and a verb
Answer:
I would say sentence.
Step-by-step explanation:
It has punctuation, a subject, and a verb, so I would say it's a sentence.
I need help!!!!!!!!!
Answer:
Greatest- 2 × 4/9
Then- 1 2/3 × 4/9
Then- 7/7 × 4/9
Lest- 3/4 × 4/9
Step-by-step explanation:
The right hand fraction you are timing by is the same whilst on the left they grow so you order them and dont focus on the times aspect of the question
Given the function f(x)=4x2−3x+4f(x)=4x2-3x+4. Calculate the following values:
f(−2)=f(-2)=
f(−1)=f(-1)=
f(0)=f(0)=
f(1)=f(1)=
f(2)=f(2)=
Answer:
26, 11, 4, 5, 14
Step-by-step explanation:
To find the value of the function, replace the variable with the number and do the arithmetic.
f(-2) = 4(-2)² -3(-2) +4 = 16 +6 +4 = 26
For doing repetitive calculations, it is convenient to write the formula into a calculator or spreadsheet and let it work from the list of values. That is what we did in the attached. It shows a table of x and f(x) for the values of x you are interested in.
The function values are ...
f(-2) = 26f(-1) = 11f(0) = 4f(1) = 5f(2) = 14_____
Additional comment
For evaluating polynomials, either by hand or machine, it is often convenient to rewrite the polynomial in Horner Form. The total number of math operations tends to be reduced. When doing this by hand, the arithmetic tends to be easier.
f(x) = (4x -3)x +4
That is, the powers of x accumulate as each layer in parentheses is multiplied by x and the next coefficient added to the result.
Using this form, ...
f(-1) = (4(-1) -3)(-1) +4
f(-1) = (-7)(-1) +4 = 11
PLEASE HELP: find the minimum and maximum values for the function with the given domain interval
Answer:
I think that it's the third one.
Step-by-step explanation:
Answer:
minimum value = 0.001
maximum value = 10
Step-by-step explanation:
To find the minimum and maximum values for the function, substitute the endpoints of the domain into the function:
when x = -3:
[tex]\implies k(-3)=10^{-3}=0.001[/tex]
when x = 1:
[tex]\implies k(1)=10^{1}=10[/tex]
Therefore,
minimum value = 0.001
maximum value = 10
One equation in a system of equations is y=2x+10. Which equation below would have to be the second equation so that the system has infinitely many solutions?
Answer:
D
Step-by-step explanation:
y = 2x + 10 is the same thing as y = 2(x + 5) because 2 x x = 2x and 2 x 5 = 10
Simplify Option D
y=2(x+5)y=2x+2(5)y=2x+10As everything is same
i.e
A1/A2=B1/B2=C1/C2Hence infinitely many solutions are present
A robot can complete 7 tasks in
2
3 hour. Each task takes the same amount of time.
a. How long does it take the robot to complete one task?
b. How many tasks can the robot complete in one hour?
the answer is fourteen (14)
I need help please! There are only 3 answer choices.
A cat climbed up a 6.5 ft ladder. If the ladder is placed at a 75 degree angle of elevation, then how far up the tree is the top of the ladder?
A) 5.9 feet
B) 6.3 feet
C) 6.7 feet
Answer:
B) 6.3 feet
Step-by-step explanation:
sin Θ = opp/hyp
sin 75° = h/6.5
h = 6.5 sin 75°
h = 6.3
Answer: B) 6.3 feet
Jake is buying a sweater with a price of $30 shown on the tag. The store is having a sale that will reduce the price by 30%. Sales tax of 5% will be added to the final purchase price. What is Jake’s total cost for the sweater? (I ALREADY KNOW THE ANSWER. BUT I NEED THE WORK FOR THE ANSWER TO SHOW MY TEACHER) (the answer is $22.05)
Reducing
30-30*0.3=
21
21+21*0.05=22.05
Ok I need help please?
Answer:
Step-by-step explanation:
1. 4/1
2. 5/1
3. 1/8
4. 2/3
5. 3/4
6. 4/12 = 1/3, 8/12 = 2/3
7. 2/5, 3/5
The table shows the purchases of two customers at a concession stand at the basketball game. Hamburgers Drinks Total Cost Customer 1 2 $13.00 Customer 2 3 7 $21.00 You want to buy 8 drinks and 9 hamburgers for you and your friends. How much do you expect to pay?
[tex]\bold{\huge{\blue{\underline{Solution}}}}[/tex]
[tex]\bold{\underline{ Given :- }}[/tex]
Customer 1 bought 2 hamburgers and 4 drinks at a cost of $13.00Customer 2 bought 3 hamburgers and 7 drinks at a cost of $21.00[tex]\bold{\underline{ To \: Find :- }}[/tex]
We have to find the total cost of 8 drinks and 9 hamburgers[tex]\bold{\underline{ Let's \: Begin :- }}[/tex]
Let the cost of hamburgers and drinks be x and y
According to the question,
[tex]\sf{ 2x + 4y = 13.00 ...eq( 1 ) }[/tex]
[tex]\sf{ 3x + 7y = 21.00 ...eq(2) }[/tex]
Solving eq( 1 ) we get :-
[tex]\sf{ 2x + 4y = 13 }[/tex]
[tex]\sf{ 2x = 13 - 4y }[/tex]
[tex]\sf{ x = (13 - 4y)/2 ...eq(3)}[/tex]
Subsituting eq(3) in eq( 2 ) :-
[tex]\sf{ 3( 13 - 4y)/2 + 7y = 21 }[/tex]
[tex]\sf{ 39 - 12y/2 + 7y = 21 }[/tex]
[tex]\sf{ 39 - 12y + 14y = 42}[/tex]
[tex]\sf{ 2y = 42 - 39 }[/tex]
[tex]\sf{ 2y = 3 }[/tex]
[tex]\sf{ y = 3/2 }[/tex]
Subsituting value of y in eq(3) :-
[tex]\sf{ x = 13 - 4(3/2)/2}[/tex]
[tex]\sf{ x = 13 - 2(3)/2}[/tex]
[tex]\sf{ x = 13 - 6/2}[/tex]
[tex]\sf{ x = 7/2 }[/tex]
Therefore,
[tex]\sf{ Cost\: of \:8 \:drinks}[/tex]
[tex]\sf{ = 8 * 3/2 }[/tex]
[tex]\sf{ = 4 * 3 }[/tex]
[tex]\sf{ = 12.00 dollars}[/tex]
And
[tex]\sf{ Cost\: of \:9 \:hamburgers }[/tex]
[tex]\sf{ = 9 * 7/2 }[/tex]
[tex]\sf{ = 63/2}[/tex]
[tex]\sf{ = 31.50 dollars}[/tex]
Total cost of the 8 drinks and 9 hamburgers
[tex]\sf{ 12.00 + 31.50}[/tex]
[tex]\sf{\red { = 43.50 \:dollars}}[/tex]
Hence, The total cost paid by you for 8 drinks and 9 hamburgers is $43.50 .
cot 75= 2 - square root 3
Answer:
The value of cot 75° is 2 - √3 or 0.2679(approx).
Step-by-step explanation:
I hope it helps!
Muffin<3
HELP PLEASE
A 180-ounce bag weighs more than an 11-pound bag. True or false?
True
False
Answer:
True
Step-by-step explanation:
Just a tip, there are 16 ounces in a pound, and just searching 180 ounces into pounds can help with this stuff to if you don't want to do math yourself
Answer: False
Step-by-step explanation: Pound weighs more in ounce.
Help me pls
1. In a two-digit number, the sun of the two digits is 10. If the two digits are reversed, the original number is less than the new number by 36. Find the original number.
2. In a two-digit number, twice the tens digit is less than the units digit by 3. If the two digits are reversed, the new number is greater than twice the original number by 18. Find the original number
1) The pairs of numbers are:
19 and 91, which do not satisfy the condition
28 and 82, which do not satisfy the condition
37 and 73, which satisfy the condition
45 and 54, which do not satisfy the condition
The number is 37.
Another method:
10x+y+36 = 10y+x, or
9x+36 = 9y, or
x+4= y …(1)
x+y = 10, or
y = 10-x …(2)
Equate (1) and (2)
x+4 = 10-x
2x = 10–4 = 6, or x = 3 so y = 10–3 = 7.
So the number is 37
( Sorry I can answer number 1 i'm in a rush and I don't really use my brain it's useful but also not. I hope someone answer your question number 2 'ᴗ' Good luck! I also hope my answer is useful. )
Business A charter bus service charges a $125 transportation fee plus
$8.50 per passenger. This is represented by the function c = 8.5p + 125,
where c is the total cost based on p passengers. What is the total cost of
transportation for the following numbers of passengers: 50, 100, 150, 200,
and 250?
Life Science Tyrannosaurus rer was one of the largest
non
Answer:
550, 975, 1400, 1825, and 2250
Step-by-step explanation:
If r = 12.5 and s = |−13|, which of the following inequalities is not true?
r ≠ s
r < s
r ≥ s
r ≤ s
Answer:
C is not true
Step-by-step explanation:
r is not larger than or equal to s
help me please i don't uderstand
Answer:
(a) d = 2.1 (b) a = 8.7
Step-by-step explanation:
[tex]d^{2}+d^{2} = 3^{2}[/tex]
[tex]2d^{2} = 9\\d = \sqrt[2]{9/2} = 2.1[/tex]
The hypotenuse = 5*2 = 10
[tex]5^{2} + a^{2} = 10^{2}\\a^{2} = 100 - 25 = 75\\a = \sqrt{75} = 8.7[/tex]
Will someone please help me with this?!? It’s simple but my answer isn’t correct. I would appreciate it so much
Answer:
(2x + 1)(3x - 2)
Step-by-step explanation:
f(x) = 6x² - x - 2
consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 6 × - 2 = - 12 and sum = - 1
the factors are + 3 and - 4
use these factors to split the x- term
6x² + 3x - 4x - 2 ( factor the first/second and third/fourth terms )
= 3x(2x + 1) - 2(2x + 1) ← factor out (2x + 1) from each term
= (2x + 1)(3x - 2) , then
f(x) = (2x + 1)(3x - 2) ← in factored form
Question shown below within image.
Answer:
m∠x = 119°
m∠y = 61°
m∠z = 119°
Step-by-step explanation:
Angle x:
m∠x = 180° - 61° (sum of angles in a straight line)m∠x = 119°Angle y:
m∠y = 61° (Alternate interior angles)
Angle z:
m∠z = 119° (Sum of angles in a line, corresponding angles)
-Chetan K
helpppppp pleaseeeeeee
Joe will rent a car for the weekend. He can choose one of two plans. The first plan has an initial fee of $51.98 and costs an
additional $0.17 per mile driven. The second plan has an initial fee of $59.98 and costs an additional $0.13 per mile driven. How
many miles would Joe need to drive for the two plans to cost the same?
Answer:
200
Step-by-step explanation:
This problem is about linear equations. We assume Joe drive X miles, and the total cost is $Y, then we can get:
Plan I: Y=51.98+0.17X
Plan II: Y=59.98+0.13X
When both plans cost the same, 51.98+0.17X=59.98+0.13X. We will get X = 200
Directions: Solve the following inequalities. Be sure to follow the rules for operations with signed numbers.
1. -4x + 2 > 0
2. +5x > x + 4
3. 3x + 4 < 10
4. -10x + 5 -4 > 4x + 3
5. 6x + 3 < 7x - 10
6. 2x - 4 < 8x + 2
7. -3s + 3 > 3
8. 4s + 2s > 6
9. 6t < 12
10. 11x < 121
11. 3x > 36
12. 25x < 500
13. 16r < 8 (10)
14. 6s > 216
15. 8x < 64
Celia has some cakes.
2/3
of the cakes are chocolate cake and
6/7
of the remaining cakes are cheesecakes. The rest of the cakes are carrot cakes.
What fraction of the cakes are carrot cakes?
Leave your answer as a fraction in the simplest form.
The carrot cakes are the fraction of the cake given by [tex]1 - \frac{6}{7}[/tex] multiplied by [tex]\frac{1}{3}[/tex]
The fraction of the cakes that are carrot cakes is [tex]\underline {\dfrac{1}{21}}[/tex]How are the cakes evaluated as fractions?The fraction of the cake that are chocolate cake = [tex]\dfrac{2}{3}[/tex]
The fraction of the remaining cake that cheesecakes = [tex]\dfrac{6}{7}[/tex]
The rest of the cakes = carrot cakes
Required:
The fraction of the cake that are carrot cakes
Solution:
The fraction of the cakes that are not chocolate cake = [tex]1 - \dfrac{2}{3} = \mathbf{ \dfrac{1}{3}}[/tex]
The fraction of the remaining cakes that are cheesecake = [tex]\dfrac{6}{7} \times \dfrac{1}{3} = \mathbf{ \dfrac{6}{21}}[/tex]
The fraction of the cake that are carrot cake = [tex]\dfrac{1}{3} - \dfrac{6}{7} \times \dfrac{1}{3} = \mathbf{\dfrac{1}{21}}[/tex]
The fraction of the cakes that are carrot cake is [tex]\underline{\dfrac{1}{21}}[/tex]Learn more about fractions here:
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Just an answer and a simple explanation are needed. Please and thank you!
Answer:
KL = 51
Step-by-step explanation:
1: Make an equation
[tex]10x -2 = 5x-8 + 7x -12[/tex]
the 10x is the JL line which is the whole line segment
2: start solving by getting all x to be on one side
[tex]10x-5x-7x = -8 -12 +2[/tex]
3: simplify
[tex]-2x = -18[/tex]
4: solve for x
[tex]x=9[/tex]
5: plug x back into KL
[tex]7(9)-12 = 51[/tex]
(56x + 16y) × 0,4/x = 32
what is x and y?
Answer:
112x + 32y
----------------
5x
Step-by-step explanation:
x and y are variables
1- Convert the expression
2- Simplify the expression
3- Calculate
How do i solve this???
please please please help
Answer:
32
4 cups
Step-by-step explanation:
Answer:
ratio
Step-by-step explanation:
0 to 100
i dont know the second one srry