The water level at a pier is modeled by the function y= 2.5 cos(2pi/12.5) +12, where y represents the water level measured in meters, and x represents the number of hours since the last high tide. After how many hours is the water first expected to reach a depth of 12 meters? Round to the nearest tenth of an hour.
ANSWER CHOICES
1.6 hours
3.1 hours
14.4 hours
19.6 hours
Answer: 3.1 hours
Step-by-step explanation: Just took the quiz on edg.
Water will reach a depth of 12 meters after 3.1 hours approximately.
Function representing the level of water by 'y' and number of hours by 'x' is,
[tex]y=2.5\text{cos}(\frac{2\pi x}{12.5})+12[/tex]For y = 12 meters, (Substitute the value of y)
[tex]12=2.5\text{cos}(\frac{2\pi x}{12.5})+12[/tex]
[tex]12-12=2.5\text{cos}(\frac{2\pi x}{12.5})[/tex]
[tex]\text{cos}(\frac{2\pi x}{12.5})=0[/tex]
[tex]\frac{2\pi x}{12.5}=\frac{\pi }{2}[/tex] (Since, [tex]\text{cos}(\frac{\pi }{2})=0[/tex])
[tex]\frac{\pi x}{12.5}=\frac{\pi }{4}[/tex]
[tex]x=\frac{\pi }{4}\times \frac{12.5}{\pi}[/tex]
[tex]x=3.125[/tex]
[tex]x\approx3.1[/tex] hours
Therefore, water will reach a depth of 12 meters after 3.1 hours approximately.
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Which is a statistical question?
Question 1 options:
How many even numbers are there between 10 and 20?
How many letters are in the word "octopus"?
How many minutes does it take to travel to school?
Answer:
How many minutes does it take to travel to school?
Step-by-step explanation:
A statistical question means you expect variability in the responses.
For instance, if you look at the first question, there's only 1 answer, so there's no variability. If you look at the second question, there's also only 1 answer.
How many minutes does it take to travel to school?
======================================================
Explanation:
Choice A is not a statistical question because we don't need to use statistics to find the answer. We simply count out the number of even numbers between 10 and 20. There's no need to draw a random sample of elements and do statistical analysis.
The same goes for choice B as well. There are 7 letters in this word and this value does not fluctuate/change.
Therefore we rule out choices A and B.
Choice C on the other hand has its answer vary depending on which person you ask. If you ask enough people, then you can find the average number of minutes, which is one tool to do statistics. This variable is considered a random variable (RV).
Given that f(x) = x2 + 12x + 35 and g(x) = x + 7, find (f:g)(x) and express
the result in standard form.
Answer:
x^3+19x^2+119x+245
Step-by-step explanation:
The required value of function (f:g)(x) would be (x + 5) which is the ratio of function f(x) and g(x).
What is a quadratic equation?The quadratic equation is defined as a function containing the highest power of a variable is two.
Given that f(x) = x² + 12x + 35 and g(x) = x + 7
As per the question,
⇒ (f:g)(x) = (x² + 12x + 35) : (x + 7)
⇒ (f:g)(x) = (x² + 12x + 35) / (x + 7)
Solve the above quadratic equation, and we get
⇒ (f:g)(x) = (x² + 5x + 7x + 35) / (x + 7)
⇒ (f:g)(x) = x(x + 5) + 7(x + 5) / (x + 7)
⇒ (f:g)(x) = (x + 5)(x + 7) / (x + 7)
⇒ (f:g)(x) = (x + 5)
Therefore, the required value of function (f:g)(x) would be (x + 5).
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James is running around a square field. He starts at point A, then runs around the perimeter, passing through points B, C, and D, until he gets back to point A. Then he cuts across the diagonal to point C. In total, he covers 271 m. If AB¯¯¯¯¯¯¯¯ is 50 m long, what is the length of the diagonal AC¯¯¯¯¯¯¯¯?
Answer:
i dont know can someone help me out im dying over here
On the drawing for a house plan, the master bedroom is rectangular and has dimensions of 2.25 inches by 2.5 inches. If the scale of the drawing is 1/8 inch = 1 foot, what is the actual area of the master bedroom? Make sure to label your answer.
4pounds of tomatoes for 6 dollars what was the cost per pound of tomatoes
Answer:
$1.50
Step-by-step explanation:
Answer:
x = $1.50; The cost per pound of tomatoes is $1.50
Step-by-step explanation:
We can the cross method.
4 pounds = $6
1 pound = x
4x = 6*1
4x=6
4x/4 = 6/4
x= 1 1/2 or $1.50
x = $1.50
The cost per pound of tomatoes is $1.50
Hope this helps!
help please!
The graph shows two accounts with the same principal and annual interest rate. Use the graph to estimate the answer to each question.
About how much more compound interest than simple interest is earned after 35 years? Remember to show your work.
About how much more compound interest than simple interest is earned after 45 years?
Remember to show your work.
After 35 years the simple interest is $600 while the compound interest is $860, while after 45 years the simple interest is $700 while the compound interest is $1160
What is interest?
Interest is the amount of money made from investing a particular amount of time over a certain period of time. Interest can either be simple or compound.
From the graph given below:
After 35 years the simple interest is $600 while the compound interest is $860, while after 45 years the simple interest is $700 while the compound interest is $1160
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Assume that when adults with smartphones are randomly selected,41 % use them in meetings or classes. If 5 adult smartphone users are randomly selected, find the probability that exactly 2 of them use their smartphones in meetings or classes.
Answer:
0.345
Step-by-step explanation:
Use binomial probability:
P = nCr pʳ qⁿ⁻ʳ
where n is the number of trials,
r is the number of successes,
p is the probability of success,
and q is the probability of failure (1−p).
n = 5, r = 2, p = 0.41, and q = 0.59.
P = ₅C₂ (0.41)² (0.59)⁵⁻²
P = 0.345
Amy and Zach each have 24 feet of fencing for their rectangular gardens. Amy makes her fence 6 feet long. Zach makes his fence 8 feet long. Whose garden has the greater area? How much greater?
Answer:
Amy by 4 feet
Step-by-step explanation:
Look above for explanation
Please help ASAP PLEASE I NEED HELP
Answer:
4/9
Step-by-step explanation:
find common denominator which is 9
1/9 + 3/9 (I change the numerator because since we multiplied the bottom you do the top)
now add
1/9 + 3/9 = 4/9
hope that helps and makes since
Answer: 4/9
Step-by-step explanation: 1/9 + 1/3(which is 3/9) = 4/9.
When a hammer falls from a work bench, __________.
a
the kinetic energy of the hammer increases, while the potential energy increases
b
the kinetic energy of the hammer decreases while its potential energy increases
c
The kinetic energy of the hammer increases while the potential energy decreases
d
the kinetic energy of the hammer decreases, while it's potential energy decreases
Answer:
b
Step-by-step explanation:
so u have to read careful
Suppose a dilation of ΔUVW by scale factor of 1 4 , centered at the origin. Which new vertices are correct? A) U′(−2, −1) B) U′(−1, −2) C) V′(1, −1) D) V′(−1, 1) E) W′(−2, 2)
Answer:
you probably already have it. the answer is : A,C,E
Step-by-step explanation:
Trust me-
find the x and y intercept of the graph of -9x+3y=12
Step-by-step explanation:
by graph method
x = -b/2a
b = 3, a = -9
x = -3/-18
x = 1/6
back to the equation to substitute
-9x + 3y = 12
-9(1/6) + 3y = 12
- 3/2 + 3y = 12
-3 + 6y = 24
6y = 27
y = 9/2
x = 1/6, y = 9/2
1,4,5,9,14,23 what a situation
Answer:
If you are asking for the median, it's 9.
explanation:
Find the middle number and round it up. That is how to find median.
Jennifer had to finish 3 assignments during the week.
She completed the first assignment in 3 1/2 hours. The
second assignment took 1/2 hours lesser while the third
assignment took 2 1/2 hours more than the first. How
much time did it take her to complete the
assignments.
Answer:
6 1/2 hours
Step-by-step explanation:
3 1/2 + 1/2 + 2 1/2
4 + 2 1/2
6 1/2
First add the 3 1/2 and the 1/2 together to get 4. Then you add the 2 1/2 to the 4 to get 6 1/2. :)
Hope this helped!
Have an amazing day!!
PLEASE RATE!!
Answer: 12hrs 30mins
Step-by-step explanation: 3hrs 30mins + 3hrs + 6hrs = 12hrs 30mins
Hope that helps!
Jack has 24 game cards. He divides them between his brother, his sister, and himself in the ratio 2:1:5.
How many cards does each get?
Answer:
brother gets 6 cards
sister gets 3 cards
he gets 15 cards
Step-by-step explanation:
this can be rewritten as
2x + x + 5x = 24
combine like terms
8x = 24
divide both sides by 8
x = 24/8
x = 3
now, multiply x by each part of the ratio.
his brother = 2 * 3 = 6
his sister = 1 * 3 = 3
himself = 5 * 3 = 15
There are 30 flowers 2/5 are daisies 1/6 are roses the rest are carnations may many carnations are in the vase
Answer:
14
Step-by-step explanation:
If you add 2/5 of 30 (12) to 1/6 of 30 (5) you get 16. You then subtract 30-16! I hope this helps, and have a great day!
Which graph represents -3x+5y=-15?
Answer:
It's a straight line
Step-by-step explanation:
The line has a slope of 3/5 and a y-axis crossing of -3
need help with geometry problem
Answer:
D, B, C
Step-by-step explanation:
Because even though this is not a right triangle, it's super close. Therefore we can call side DC the SL, meaning angle C is larger. Angle D is largest, then B, then C.
1/7of21 what is answer
3
Step-by-step explanation:
1/7 of 21
=1/7 ×21
=1×3
= 3Please mark my answer the brainliest and rate me 5 star and follow me.please please please please please please
What is the volume I need some help
your answer is 64cm
thats it
The denominator for the improper fraction represented by the shaded area is .....
Answer:
4/3 is the fraction / the denomonator would then be 3
Step-by-step explanation:
4 shaded on the top and 3 shaded on the bottom. The numerator is on the top and the denomonator is on the bottom.
A cube made out of lead has a mass of 12 grams. A side of the cube has length 1 cm. What would be the mass of the cube whose sides have length 1.5 cm?
Answer:
The mass of a lead cube whose side have length 1.5 cm is 40.5 gramsStep-by-step explanation:
1. Let's review the information given to
1. Let's review the information given tous to answer the question correctly:
1. Let's review the information given tous to answer the question correctly:Mass of the cube made out of lead = 12
= 12grams
Side of the cube = 1 cm
2. What would be the mass of a lead
What would be the mass of a leadcube whose sides have length 1.5 cm?
What would be the mass of a leadcube whose sides have length 1.5 cm?For answering the question, let's
What would be the mass of a leadcube whose sides have length 1.5 cm?For answering the question, let'scalculate the volume of the cube and
What would be the mass of a leadcube whose sides have length 1.5 cm?For answering the question, let'scalculate the volume of the cube andthen its density, this way:
Volume = Height* Width * LengthVolume=1*1*1Volume =1 cmLet's recall the formula of the density:
Density Mass/Volume, therefore:
Density of the lead = 12/1= 12 gr/cm
Now, let's calculate the volume of the
Now, let's calculate the volume of thesecond cube:
Volume = Height Width LengthVolume = Height Width LengthVolume 1.5 * 1.5 1.5Volume = Height Width LengthVolume 1.5 * 1.5 1.5Volume =3.375 cm3Finally, let's calculate the mass, using
Finally, let's calculate the mass, usingthe density of the lead we already
Finally, let's calculate the mass, usingthe density of the lead we alreadyknow:
Density = Mass/Volume12 Mass/3.37512 Mass/3.375Mass 12 *3.37512 Mass/3.375Mass 12 *3.375Mass = 40.5 gramss3 people share 7 brownies how many brownies should each person get? Pls show your work
=> 3 people share 7 brownies
=> 7 ÷ 3
=> 2.3333333
=> 2.3
Therefore, each person takes 2 1/3
Answer:
2 ⅓
Step-by-step explanation:
division is the same as a fraction
the dividend is the numerator and the divisor is the denominator
7÷3 is the same as 7/3
change 7/3 into a mixed number which is 2 ⅓
What is 5 x 9 the answer
Answer:
5 x 9 is 45
Step-by-step explanation:
just is loll
Anita earned a 74, 85, and 84 on her first three biology exams. What is the minimum score she needs to get on the fourth test in order for her average exam score to be 82?
Answer:
85
Step-by-step explanation:
82×4=328
328=74+85+84+x
x=328-74-85-84
x=85
Solve 6x<90. Graph the solution
Answer:
image is attached (shaded area is where x could be)
Step-by-step explanation:
[tex]6x < 90[/tex]
divide both sides by 6
[tex]x < 15[/tex]
this means x is strictly less than 15
consider the line y=7-7x what is the slope of a line parallel to this line
Answer:
Step-by-step explanation:
Slope of the given line = -7
parallel: slope = -7
perpendiculr: slope = -1/(-7) = 1/7
Find the product 3 2/5 and 5/8. Express answer in simplest form
Answer:
2 1/8
Step-by-step explanation:
Hope this helps!!
Answer: 2.125
Step-by-step explanation: 3.4 x 5/8 = 2.125
Frederick, Josiah, and Shawnda each had 2 rolls of raffle tickets with 12 tickets in each roll.
Josiah hands out half of his tickets and Shawnda hands out one fourth of her tickets.
How many tickets do they have left altogether?
Answer:
they all have 52 left altogether
Step-by-step explanation:
they all have 2 rolls with 12 so that means they all have 24 if josiah hands out half of his tickets he would have 12 tickets left
If shawnda hands out 1 fourth of her tickets she will have 18 tickets
24 + 12 + 18 =54