Answer:
Step-by-step explanation:
cos(3x)=cos (3x+2π)=cos (3x+360)
period for 3x=360°
period=360/3=120°
Final answer:
The period of the function y = cos(3x) is π/3 or 120 degrees, since the coefficient '3' in the function's argument compresses the usual period of cos(x) by a factor of three.
Explanation:
The period of a trigonometric function represents the length of one complete cycle of the function. For the function y = cos(3x), we are dealing with a cosine function that has been horizontally compressed by a factor of 3. The standard period of the cosine function is 2π radians. However, the presence of the 3 within the argument of the cosine function means that the period is reduced by a factor of 3, because the function completes its cycle 3 times faster than the standard cosine function.
To find the period of the given function, we divide the standard period of the cosine function by the coefficient of the x variable inside the function:
Standard period of cos(x) = 2πPeriod of cos(3x) = ÷ 3Calculated period = 2π / 3Therefore, the period of y = cos(3x) is π/3 or approximately 120 degrees.
Erica drew the parallelogram below. Which expression can Erica use to find
the area of the parallelogram? *
HELPP
Area of the parallelogram = (base length) x (height)
Step-by-step explanation:
The parallelogram has 2 different sides.
To find:
The expression to calculate the area of parallelogram.
Base of the parallelogram= 5(1/4) in.
Height of the parallelogram= 4(1/5) in.
Area of the parallelogram= base x height
= 5(1/4) x 4(1/5) = 1 square inches.
So, the expression to calculate the area of the parallelogram is,
Area = (base length) x (height)
A manufacturer makes conical funnels for professional painters. The
funnels are formed from plastic with an 8-inch diameter base and height
of 9 inches. After the cones cool, a machine cuts off 1 inch of the tip to
leave a 1-inch diameter hole in the end. What is the volume of the funnel?
Round your answer to the nearest tenth and do NOT include units.
Answer: 151
Step-by-step explanation:
In this situation we have two cones, the big cone with volume [tex]V_{big}[/tex] and the small cone with volume [tex]V_{small}[/tex].
Now, if we want to know the total volume [tex]V_{T}[/tex] we have to substract [tex]V_{small}[/tex] from [tex]V_{big}[/tex], but first we have to calculate each volume:
For the big cone:
[tex]V_{big}=\frac{\pi R^{2} H}{3}[/tex]
Where:
[tex]R=\frac{Diameter}{2}=\frac{8 in}{2}=4 in[/tex]
[tex]H=9 in[/tex]
Then:
[tex]V_{big}=\frac{\pi (4 in)^{2} 9 in}{3}[/tex]
[tex]V_{big}=150.79 in^{3}[/tex] Volume of big cone
For the small cone:
[tex]V_{small}=\frac{\pi r^{2} h}{3}[/tex]
Where:
[tex]r=\frac{diameter}{2}=\frac{1 in}{2}=0.5 in[/tex]
[tex]h=1 in[/tex]
Then:
[tex]V_{small}=\frac{\pi (0.5 in)^{2} 1 in}{3}[/tex]
[tex]V_{small}=0.261 in^{3}[/tex] Volume of small cone
Calculating the total volume:
[tex]V_{T}=V_{big}-V_{small}[/tex]
[tex]V_{T}=150.79 in^{3}-0.261 in^{3}[/tex]
Finally:
[tex]V_{T}=150.52 in^{3} \approx 151 in^{3}[/tex]
Answer:
151 in^3
Step-by-step explanation:
Find the volume of the cones the subtract them to get your final answer
Which choice could be used in proving that the given triangles are similar?
The nth term of a sequence is n-4
a) Work out the first three terms of the sequence.
b) Work out the tenth term of the sequence.
Answer:
Step-by-step explanation:
nth term = n - 4
A) 1st term = 1 - 4 = -3
2nd term = 2 - 4 = -2
3rd term = 3 - 4 = -1
First three terms are: -3, -2, -1
b) tenth term = 10 - 4 = 6
a) The first three terms of the sequence are -3, -2, and -1.
b) The tenth term of the sequence is 6.
a) To find the first three terms of the sequence with the nth term given as n - 4, we can substitute the values of n from 1 to 3 into the formula:For n = 1:nth term = n - 4 = 1 - 4 = -3For n = 2:nth term = n - 4 = 2 - 4 = -2For n = 3:nth term = n - 4 = 3 - 4 = -1So, the first three terms of the sequence are: -3, -2, -1.b) To find the tenth term of the sequence, we can again use the formula with n = 10:nth term = n - 4 = 10 - 4 = 6So, the tenth term of the sequence is 6.For more questions on sequence -
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If the chance of rain is 80%, what is the likelihood of it raining?
Answer:
More likely
Step-by-step explanation: It wouldn't be likely because that is 100% of that happening
Answer:
It would be raining but not raining cats and dog and then goes away like 15-20 minutes. But the weather can change how much it is going to rain like if its hot and sunny at a high number it is 50 chance to not rain but if its like a low weather then its likely to rain.
I really hope this helps! But if it doesn't I'm sorry. (OwO)Use the X method to find the solutions of
6.x2 + 2x - 20 = 0.
X =
X=
Of 80 people attending a dance 28 dance with their hands touching the floor. If four people at the dance are selected at random, determine the probability that each of the 4 dance with their hands touching the floor.
`PLEASE HURRY ITS A QUIZ
Answer: The probability is 0.013
Step-by-step explanation:
Out of 80 people, 28 of them dance with the hands touching the ground.
Then, the probability of selecting at random someone that dances with the hands touching the floor is equal to the number of persons that dance in that way, divided by the total number of persons.
For the first selection, this is p1 = 28/80
now, the probability in the second selection will be 27/79, because we have selected 1 out of the 28 (and also 1 out of the 80)
for the third and the fourth we have:
p3 = 26/78
p4 = 25/77
Then the probability of the fourth events is equal to the product of the four probabilities:
P = (28/80)*(27/79)/(26/78)/(25/77) = 0.013
Answer:
The probability that each of the 4 dance with their hands touching the floor is 0.0129.
Step-by-step explanation:
There are a total of 80 people and out of them, 28 dance with their hands touching the floor. The probability of selecting a person who has their hands touching the floor while dancing can be computed as 28/80.
We are asked to computed the probability that four people are selected at random and all four of them dance with their hands touching the floor. The probability for selecting the first person is 28/80. For the second person, the total no. of people are now 79 and the people who can dance with their hands touching the floor are 27. So, the probability is 27/79. Similarly, for the third person, the probability is 26/78 and for the fourth person, the probability is 25/77.
So, the probability that all four people selected dance with their hands touching the floor is:
28/80 * 27/79 * 26/78 * 25/77 = 0.0129
A cereal box is 6 1/2 inches long ,3 1/2 inches wide , and 12 inches high .What is the volume of the box?
Answer:
273
Step-by-step explanation:
base (l times w) times height
Answer:
273 inch³
Step-by-step explanation:
v = l*h*w
v= 6 1/2 * 3 1/2 * 12
v= 13/2 * 7/2 * 12
v= 273
Amanda made the following figure by combining 1 cubic foot cubes.What is the volume of her figure?
Answer:
100
Step-by-step explanation:
I counted
What is the answer to this?
There are 6 faces on a cube. Each face is equal to the area of one square.
Area of one square = 2.5 x 2.5 = 6.25 units^2
Surface area = 6.25 x 6 = 37.5 units^2
Hope this helps!! :)
Answer:
37.5
Step-by-step explanation:
Since it is a cube, all edges are 2.5. To find one side, you do 2.5x2.5. That gives you 6.25. And you have 6 sides. So 6.25x6 = 37.5.
In a lab, a substance was heated by 6 °C each hour for 60 hours. What was the total change
in temperature?
Final answer:
The total change in temperature when a substance is consistently heated by 6 °C each hour for 60 hours is 360 °C, calculated by multiplying the hourly temperature increase by the number of hours.
Explanation:
To calculate the total change in temperature when a substance is heated by a consistent amount over a period of time, you simply multiply the rate of temperature change per hour by the total number of hours. In this case, the substance was heated by 6 °C each hour for 60 hours. So, the calculation will be 6 °C/hour * 60 hours.
The total change in temperature is therefore 6 °C/hour * 60 hours = 360 °C. This calculation shows the cumulative effect of consistent heating over a certain period.
Explain your answer, please.
Answer:
median =55
Step-by-step explanation:
The median is the middle number. It will fall exactly between those two numbers. Take the average
(51+59)/2 = 110/2 =55
The median is the middle number of a data set. We can find the median using two by the following.
51 + 59 = 110
110 / 2 = 55
The median is 55!
Best of Luck!
[ 5,-8,2,y] - [x,7,11,4]=[-2,z,13,13] solve for x y and z
Answer:
[x, y, z] = [7, 17, -15]
Step-by-step explanation:
The list equation resolves to four equations involving corresponding list elements:
5 -x = -2 ⇒ x = 7
-8 -7 = z ⇒ z = -15
2 -11 = 13 ⇒ looks like a wrong sign somewhere; this is FALSE
y -4 = 13 ⇒ y = 17
_____
Comment on the question
Since one of the equations turns out to be false, it makes us suspect there may be typos in the others as well. YMMV
A dilation has center (0,0). Find the image of the point L (- 4,0) for the scale factor 2
D2(L)=L’[ ]
Will award 20 points and brainliest for correct answer
Answer:
(-8,0)
Step-by-step explanation:
(-4×2 + 0, 0×2 + 0)
(-8,0)
Final answer:
The image of point L (-4,0) after a dilation with a scale factor of 2 from the center (0,0) is L' (-8,0).
Explanation:
To find the image of the point L (-4,0) after a dilation with a scale factor of 2 from the center (0,0), you multiply the coordinates of the point by the scale factor. Therefore, the coordinates of point L after dilation (L') would be (-4 × 2, 0 × 2) = (-8, 0).
The image of point L after the dilation is L' with coordinates (-8, 0).
The measure of angle M is_degrees.
Answer:
m=37
Step-by-step explanation:
The 2 angles are complementary, or add to 90 degrees. Wee know this because of the little square in the corner that indicates a right angle, which is equal to 90 degrees.
m+53=90
Solve for m by getting m by itself. To do this, subtract 53 from both sides to "reverse" the addition being done to m.
m+53-53=90-53
The 53s on the left cancel, and we are left with:
m=37
Answer:
M = 37°
Step-by-step explanation:
M + 53° = 90°
M = 90° - 53°
M = 37°
Which inequality statement is TRUE?
Answer:
A is true.
Step-by-step explanation:
The square root of 65 is approximately 8.06226. This means that 8 is less than [tex]\sqrt{65}[/tex] but [tex]\sqrt{65}[/tex] is less than 9.
Let me know if you need anymore help
Solve for k
3.1+k=5.67
Answer:
k =2.57
Step-by-step explanation:
3.1+k=5.67
Subtract 3.1 from each side
3.1-3.1+k=5.67-3.1
k =2.57
Answer:
k=2.57
Step-by-step explanation:
Okay so first things first we have to eliminate 3.1 so we can get the variable k by itself.
3.1+k=5.67
-3.1 -3.1
k=2.57
Just in case if you're confused we have to isolate thats why we were subtracting both sides by 3.1
(Hope you find this helpful ;w;)
what is x? please answer
Answer:
130º
Step-by-step explanation:
use the conveyor xd
The table shows the results of rolling a die 100 times. What was the average value per roll?
What Is the slope of the line on the graph?
Answer:
1/2 or 0.5 either way they're both right
Step-by-step explanation:
The slope of the line is 1/2
The formula for calculating the slope of the line is expressed as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
From the graph, using the coordinate points (0, 2) and (-4, 0)
Get the slope using the coordinate;
[tex]m=\frac{0-2}{-4-0}\\m=\frac{-2}{-4}\\m=\frac{1}{2}[/tex]
Hence the slope of the line is 1/2
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On March 12, Medical Waste Services provides services on account to Grace Hospital for $11,000, terms 2/10, n/30. Grace pays for those services on March 20.
Required:
For Medical Waste Services, record the service on account on March 12 and the collection of cash on March 20. (If no entry is required for a transaction/event, select "No journal entry required" in the first account field.)
Answer and Step-by-step explanation:
The journal entries are shown below:
On March 12
Account receivable A/c Dr $11,000
To Sales $11,000
(Being the goods are sold on credit)
On March 11
Cash $10,780
Sales discount ($11,000 × 2%) $220
To Account receivable $11,000
(Being the cash received is recorded)
Only these two entries are recorded
Since the payment is made within 10 days so Grace hospital is eligible for the discount
Please help!!! I would really appreciate it!!
Answer:
3. Terms
4. Like terms
5. Coefficient
Step-by-step explanation:
Please keep in mind that Brainly shouldn't be used to cheat on tests or exams.
What is three and fourteen hundredths as a decimal number.
Answer:
3.14
Step-by-step explanation:
Complete the sentence below with less than,
greater than or equal to.
The sum of the first 100 even natural numbers is
the sum of the first 101 odd
natural numbers.
Answer: The Answer is "less than"
Step-by-step explanation:
To find the sum of a series, you find the difference between the first and last term, multiply that by the number of terms, then divide by 2.
For the even numbers, 2 is the first term and 200 is the 100th term (because 2+(100-1)2 is equal to 200). So, (100(2+202)/2 = 10100.
For the odd numbers, 1 is the first term and 201 is the 101th term (because 1+(101-1)2 is equal to 201). So, (101(1+202))/2 = 10251.5.
10100<10251.5 so the sum of the first 100 even numbers is less than the sum of the first odd 101 numbers.
The sum of the first 100 even natural numbers is smaller than the sum of the first 101 odd natural numbers.
What is an even number?A number that is divisible by two into two equal whole numbers is called an even number. Even numbers are those that end in 0, 2, 4, 6, and 8.
The problem can be solved using the arithmetic sequence. The sum of the first 100 even numbers will be,
[tex]\text{Sum of first 100 even numbers} = \dfrac{100}{2} \times [2(2) +(100-1)2]=10,100[/tex]
The sum of the first 101 odd numbers will be,
[tex]\text{Sum of first 101 odd numbers} = \dfrac{101}{2} \times [2(1) +(101-1)2]=10,201[/tex]
Hence, the sum of the first 100 even natural numbers is smaller than the sum of the first 101 odd natural numbers.
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I really need help with 15 and 16 please
Answer:
15. 50 kg
16a. 5 kg
16b. 3.75 kg
Step-by-step explanation:
The formula relating force, mass, and acceleration can be solved for mass. This formula will apply to both problems. We'll use m for both "mass" and "meters". We presume you can avoid getting mixed up by understanding that meters is used in the context of acceleration: m/s².
F = ma
m = F/a . . . . . divide by a
__
15. m = (250 N)/(5 m/s²) = 50 kg
__
16a. m = (15 N)/(3 m/s²) = 5 kg
16b. m = (15 N)/(4 m/s²) = 3.75 kg
_____
Comment on units
Especially for physics problems, I like to keep the units with the numbers. It is helpful to remember that Newtons are equivalent to kg·m/s². So, dividing Newtons by acceleration in m/s² will give mass in kg. Since you're familiar with F=ma, it's not too hard to remember that the units of force (N) are the product of the units of mass (kg) and acceleration (m/s²).
g(a)=2a-3
h(a)=-3a+1
Find g(h(a)) =
Answer:
g(h(a)) = 6a-1
Step-by-step explanation:
They are trying to confuse you for no reason.
it migt be easier if you think of g(a) instead as g(x)=2x-3
So h(a)=3a+1, and we pu it info g(x), which would make it 3a+1=x, so g(3a+1) = 2(3a+1)-3=6a+2-3=6a-1
Abel is 43 years old, and he owns his car, which he uses to get to work. His
collision deductible is $250, and he does not have comprehensive coverage.
If his car's safety rating is 22, how much does he pay each month for car
insurance?
I think it's 11.40
Step-by-step explanation:
hope it's right
Answer:
216.67
Step-by-step explanation:
what is ( ⅚ -(⅓ )²)x ½
in a fraction please
Answer: 7/9
I hope that helps. That’s the answer I got.
Answer:
Step-by-step explanation:
[tex][ \frac{5}{6}-(\frac{1}{3})^{2}]*\frac{1}{2}=[\frac{5}{6}-\frac{1}{9}]*\frac{1}{2}\\\\=[\frac{5*3}{6*3}-\frac{1*2}{9*2}]*\frac{1}{2}\\\\=[\frac{15}{18}-\frac{2}{18}]*\frac{1}{2}\\\\=[\frac{15-2}{18}]*\frac{1}{2}\\\\=\frac{13}{18}*\frac{1}{2}\\\\=\frac{13}{36}[/tex]
What is the opposite of the opposite of -7.5? Thank you
Answer: 7.5
Step-by-step explanation: It's negative, so the opposite would be positive.
Answer:
7.5
Step-by-step explanation
They are both matching integers
mark me brainliest if I helped:D
Which is equivalent to log1/2462
A log1/2462/log4621/2
B log462/log1/2
C log 1/2 / log462
Answer:
B
Step-by-step explanation:
Given the expression:
[tex]log_{1/2} 462 [/tex]
we want to find an equivalent expression.
Change of base formula:
[tex]log_{a} b = \frac{log b}{log a} [/tex]
where log means logarithm with base 10, also known as common logarithm.
Then, the expression of the problem is transformed into:
[tex]log_{1/2} 462 = \frac{log 462}{log (1/2)} [/tex]