A wooden roller coaster contains a run in the shape of a sinusoidal curve, with a series of hills. The crest of each hill is 108 feet above the ground. If it takes a car 1.9 seconds to go from the top of a hill to the bottom (4 feet off the ground), find a sinusoidal function of the form y = A sin(ωt - Φ) + B that models the motion of the coaster train during this run starting at the top of a hill.
Answer:
[tex]y(t)=52sin(3.3t+\pi/2)+56[/tex]
Step-by-step explanation:
We are given that
Height of crest, h=108 feet
Time for one cycle, T=1.9 s
We have to find a sinusoidal function of the form y = A sin(ωt - Φ) + B that models the motion of the coaster train during this run starting at the top of a hill.
We are given
[tex]y=Asin(\omega t-\phi)+B[/tex]
Amplitude,[tex]A=\frac{108-4}{2}=52 feet[/tex]
[tex]B=A+4=52+4=56 feet[/tex]
[tex]\omega=\frac{2\pi}{T}[/tex]
Using the formula
[tex]\omega=\frac{2\pi}{1.9}=3.3/s[/tex]
We assume,
Horizontal shift [tex]\phi=-\frac{\pi}{2}[/tex]
Substitute the values
[tex]y(t)=52sin(3.3t+\pi/2)+56[/tex]
Hence, the sinusoidal function that models the motion of the coaster train during this run starting at the top of a hill is given by
[tex]y(t)=52sin(3.3t+\pi/2)+56[/tex]
A family is driving 550 miles to their grandmother's house. They have already driven 350 miles.
Which equation shows the rate, r, in miles per hour, the family must drive to reach their
grandmother's house in 4 hours?
4r + 350 = 550
550 + 350 = 4r
4++ 350 = 550
T
550 - 350
Answer:
i tink is b
Step-by-step explanation:
The equation that represents the situation will be 4r + 350 = 550. Then the correct option is A.
What is speed?Speed is defined as the length traveled by a particle or entity in an hour. It is a scale parameter. It is the ratio of length to duration.
We know that the speed formula
Speed = Distance/Time
A family is driving 550 miles to their grandmother's house. They have already driven 350 miles.
Let 'r' be the speed of the car in miles per hour. The family must drive to reach their grandmother's house in 4 hours. Then the equation is given as,
4r + 350 = 550
The equation that represents the situation will be 4r + 350 = 550. Then the correct option is A.
More about the speed link is given below.
https://brainly.com/question/7359669
#SPJ5
Does anyone know wha this could be
The side lengths of a triangle are (5x + 1), (6x - 10), and (6x + 2). Write an expression in simplest
form fok the perimeter of the triangle.
A. 17x - 7
В. 17x+13
C. 10x
D. 30x
Answer:
A
Step-by-step explanation:
so the perimeter is the sum of all the sides which would be
(5x+1)+(6x-10)+(6x+2)
= 5x+1+6x-10+6x+2
=17x-7
which is A
if my answer helps please mark as brainliest.
A subway car travels at a rate of 32 meters per second. How far does it travel in 16 seconds? The subway travels _________. Please make sure to label the answer.
1.5 miles bc if you add them up and multiply you get 1.5 miles.
Answer:
512 meters per second
Step-by-step explanation:
32 x 16 = 512
Find the Area of this figure.
Answer:
158 m²
Step-by-step explanation:
I made this into 3 rectangles.
Figure 1:
9•8=72
The 9 is from the 13 m side, but I've taken 4 m off from the overlapping square.
Figure 2:
6•7=42
The 7 is from the 10 m side, but I've taken 4m off from the overlapping square again.
Remaining Area:
If you extend the lines into figures 1 and 2 from the top left corner and bottom right corner vertically, you will get a rectangle that is (11 m) x (4 m). This is not yet accounted for.
11•4=44
Add together: 72 + 42 + 44 = 158
*Note: You could also find the area of the squares a much easier way by subtracting the overlapping part after finding the area of both figures , but this is how I did it*
10 POINTS!
Samir will use 7 cups of apples to make 4 batches of applesauce. Decide whether each expression shows the number of cups of apples in one batch.
a. 7 divided by 4 Yes or no
b. 4 divided by 4 yes or no
c. 7/4 Yes or no
d. 4/7 yes or no
e. 7 times 1/4 yes or no
f. The answer is 1 3/4 yes or no
Answer:
A = yes
B = no
C = yes
D = no
E = yes
F = yes
Hope I helped!!!
a = (5)
b = (3)
Work out 4a + b
Step-by-step explanation:
IF A=5, B=3
4*5+3=20+3
=23
THE ANSWER IS 23
Frozen Taste ice cream factory wants to analyze if the customers like its new flavor, peanut butter chocolate chip. The probability that a customer likes the new flavor is .83. If a customer is asked to taste the flavor twice within 4 hours, then what is the probability that a customer likes this flavor the first time and the second time
Answer:
0.6889 = 68.89% probability that a customer likes this flavor the first time and the second time
Step-by-step explanation:
For each time the customer is asked, there are only two possible outcomes. Either they like the flavor, or they do not. Each event is 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 probability that a customer likes the new flavor is .83.
This means that [tex]p = 0.83[/tex]
What is the probability that a customer likes this flavor the first time and the second time
This is P(X = 2) when n = 2. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{2,2}.(0.83)^{2}.(0.17)^{0} = 0.6889[/tex]
0.6889 = 68.89% probability that a customer likes this flavor the first time and the second time
Add 3/10+ 33/100+ 1+ 7/10 ( in fraction form) (this is 4th grade not middle school) please help
Step-by-step explanation:
Please refer to the attachment
HELP guys i need extra to pass in my school and i am still failing by three points please i cant get it up on my own Madison has $6.50. Potatoes are $0.50 per pound. How many pounds of potatoes can Madison afford to buy?
In two or more complete sentences write and solve an inequality for this situation. Explain how you would solve this inequality.
Answer:
0.5p < 6.50
p < 13
Step-by-step explanation:
The inequality would be p < 13. Since Madison can't spend more than 6.50, the cost of potatoes would need to be less than 6.50. To solve the inequality, you would have to divide both sides by 0.5, giving you p < 13.
Answer:
Madison can buy 13 pounds of patatoes.
Step-by-step explanation:
You have to divide 6.50 by 0.50, but in order to do that you have to move the decimal on both sides two times to the right then you can divide. Then to double check you muliply 13 by 50.
PLEASE HELP!!!
Greta currently works 45 hours per week and earns a weekly salary of $729. She
will soon be starting a new job where her salary will be increased by 10% and her hours reduced by 10%.
How much more will she be earning per hour at her new job?
Answer:
$7.29 per hour at her new job.
Step-by-step explanation:
Answer:
$3.60
Step-by-step explanation:
Her hourly wage at her old job is 729/45 or $16.20 per hour. If her salary is increased by 10% then her wage weekly is $801.90. If her hours are reduced by 10% then she has to work 40.5 hours per week. This means you have to do 801.90/40.5 to get $19.80 per hour. So according to my math here she will make $3.60 more per hour at her new job. (Double check to make sure I'm correct)
Hopper Middle School wants to buy 40 t-shirts for the soccer team. They look at two stores to see which will give them the better deal. Store A charges $6.96 per shirt. Store B said the total cost for all 40 shirts would be $325, but they will give the school a 20% discount. Which store has the better deal?
How much will the shirts cost from store A?
How much will the shirts cost from store B?
How much does one shirt cost from store B?
Answer:
store A is 278.4 and store B is 260 and the cost for one shirt from store b is 8.125
Step-by-step explanation
6.96 x 40 gives you 278.4
325 - 20% gives you 260
325 divided by 40 gives you 8.125
then to check your answer you multiply 40 and 8.125 and it gives you 325
in a box of colored light, 1/2 of the light are red, 1/3 of the light are blue, and 1/6 lf the lights are green. the number of lights in the box is greater than 10. what ia the smallest number of lights that could be in the box?
Answer:
Step-by-step explanation:
Complete the following sentence.
The slope of the graph of y = x is
Answer:
The slope of y=x is 1
Step-by-step explanation:
Slope = 1
-7r2 + 7r + 2 = 2
Find Discriminant
Answer:
r = 1 , 0
Step-by-step explanation:
-7[tex]r^{2}[/tex] + 7r + 2 = 2
-7r(r-1)=2-2
-7r(r-1)=0
r-1=0
r=1
Kelly wants to buy cupcakes for her family. The radius of the cupcake is 12
inches, what is the distance around the cupcake? *
Your answer
Answer:
75.4 inches
Step-by-step explanation:
circumference = 2πr = 24π ≅ 75.4 inches
It's really more of a tubcake than a cupcake.
Carter is famous for his taco soup. His soup requires 2 cans of black beans for every 2 3/4 jars of salsa
His sister calls him and says she wants to make his taco soup. She says, "I put in 11 jars of salsa. How many cans of black
beans do I need to put in the soup to make it taste just like yours?"
How many cans of black beans does Carter's sister need to use?
A. 5 1/2 cans
B. 4 cans
C. 8 cans
D. 1 3/8 cans
Answer: The answer is 8 cans. Hope I helped :)
Step-by-step explanation:
How do I solve Y=2/3x-1 and y=3
Answer:
Step-by-step explanation:
Put the y value where it belongs-
3=2/3x-1 Now add like terms (if you add one to negative one it cancels out)
+1 +1
4=2/3x Divide (I used a calculator)
x=6
What is the solution to this equation?
x + 14 = -6
Answer:
x = -20
Step-by-step explanation:
i need help due tonight
Answer:
Y=6
Step-by-step explanation:
5(6)+1=31
30+1=31
Answer:
y=6
Step-by-step explanation:
5y+1=31
simplify
5y=30
divide both sides by 5
y=6
If n + 7 = 10, evaluate 2n - 2
7. (ASV, Exercise 2.20 ) - 3 points. A fair die is rolled repeatedly. Use precise notation of probabilities of events and random variables for the solutions to the questions below. (a) Write down a precise sum expression for the probability that the first five rolls give a three at most two times. (b) Calculate the probability that the first three does not appear before the fifth roll. (c) Calculate the probability that the first three appears before the twentieth roll but not before the fifth roll.
Answer:
0.9646 ; 0.5685
Step-by-step explanation:
Given that :
P(obtaining 3 on a die roll) = 1/6 = 0.1667
Obtaining 3 at most 2 times in five trials
Using binomial distribution formula :
P(x =x) = nCx * p^x * (1 - p)^(n - x)
n = 5 ;, p = 0.1667
P(x ≤ 2) = P(x = 0) + P(x =1) + P(x = 2)
Using the binomial probability :
P(x ≤ 2) = 0.4019 + 0.4019 + 0.1608
P(x ≤ 2) = 0.9646
B.) using geometric distribution :
(1 - p)^x-1 * p
P ≥ 5) = 1 - P(x ≤ 4) = 1 - p(x = 0) + p(x = 1) + p(x =2) + p(x = 3)
1 - (0.1667 + 0.1157+0.0965+0.0804)
= 0.5685
Pizza Guy pizza delivery time for a pizza is
approximately normally distributed with a
mean of 22 minutes and a standard deviation
of 5. Pizza Guy guarantees delivery within 30
minutes or the pizza is free. What percent of
customers will get a free pizza?
a) 3.5% b) 4.5% c) 5.0% d) 5.5% e) 6.5%
Answer:
5.5%
Step-by-step explanation:
the pizza is free 5.5 so he need to deliver the pizza on time
What is M? Enter only value in response.
Answer:
x=23
Step-by-step explanation:
132+128+4x+2+5x-11+4x-10=540
13x+241=540
13x=540-241
13x=299
x=23
What is 2 3/4 miles +3 1/3 miles?
Answer:
6 1/12
Step-by-step explanation:
You first convert 2 3/4 into 2 9/12. And then you convert 3 1/3 into 3 4/12. Now both of these have the same denominator so you can add. When you add your answer should be 6 1/12
A family eats at a restaurant. The bill is $42. The family leaves a tip and spends $49.77.
How much was the tip in dollars?
Round your answer to the nearest hundredth (second) decimal place.
The tip was $7.77
I hope this helped! please mark brainliest and vote 5 stars >:)
Answer:about 8 dollars
Step-by-step explanation:
0.7k − 1.6 ÷ 2 − 5.2 = 1.7 − 0.7
your answer is k=10 the step by step is kn the picture
what does 6 × 7/10 equal?
8. What is the DEGREE of the following binomial:
2x 5
Step-by-step explanation:
I'm thinking you are showing 2X^5 where 5 is the exponent. if so then it's the 5th degree