kam
An object oscillates as it moves along
the x-axis. Its displacement varies with
time according to the equation
x = 3 cos(6pi t + pi/2)
where t is in seconds
What is the frequency of this motion?
The frequency of this motion is 3 Hz
The standard equation of an oscillation is given by:
x = A cos(ωt + Ф)
Where x is displacement, A is amplitude, ω is angular frequency = 2πf and Ф is phase difference.
Given the equation:
x = 3 cos(6πt + π/2)
Hence;
ω = 6π
2πf = 6π
f = 3 Hz
The frequency of this motion is 3 Hz
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The lengths of 3-inch nails manufactured on a machine are normally distributed with a mean of 3.0 inches and a standard deviation of .009 inch. The nails that are either shorter than 2.98 inches or longer are than 3.02 inches are unusable. What percentage of all the nails produced by this machine are unusable?
Using the normal distribution, it is found that 2.64% of all the nails produced by this machine are unusable.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.In this problem:
The mean is of 3 inches, hence [tex]\mu = 3[/tex].The standard deviation is of 0.009 inches, hence [tex]\sigma = 0.009[/tex].Nails that are more than 0.02 inches from the mean are unusable, hence:
[tex]Z = \frac{0.02}{\sigma}[/tex]
[tex]Z = \frac{0.02}{0.009}[/tex]
[tex]Z = 2.22[/tex]
The proportion is P(|Z| > 2.22), which is 2 multiplied by the p-value of Z = -2.22.
Z = -2.22 has a p-value of 0.0132.
2 x 0.0132 = 0.0264
0.0264 x 100% = 2.64%
2.64% of all the nails produced by this machine are unusable.
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what color is my shirt?? PLEASE HELP I FORGOT
Answer:
um
Step-by-step explanation:
Answer:
Its white! atleast i think its white because your pfp has white clothes on
4. The original price of a pair of shoes is $80 and they are on sale for $48. What is the percent of discount?
O A 32%
O B. 40%
OC. 60%
O D. 66.7%
Answer:
c
Step-by-step explanation:
80 × percent = 48
percent = 48/80
= 0.6
= 60%
Solve for x in the equation x2 + 4x-4=8.
O x = -6 or x = 2
X=-2+2/2
O x = -2 or x = 6
O x=2+2V5
[tex] {x}^{2} + 4x - 4 = 8 \\ = > {x}^{2} + 4x - 4 - 8 = 0 \\ = > {x}^{2} + 4x - 12 = 0 \\ = > {x}^{2} + 6x - 2x - 12 = 0 \\ = > x(x + 6) - 2(x + 6) = 0 \\ = > (x - 2)(x + 6) = 0 \\ = > x = 2 \: \: \: or \: \: \: x = - 6 [/tex]
Answer:
x = -6 or x = 2
Hope you could get an idea from here.
Doubt clarification - use comment section.
A rental car company charges $35 per day to rent a car and $0.15 for every mile driven. Enola wants to rent a car, knowing that:
She plans to drive 450 miles.
She has at most $260 to spend.
Write and solve an inequality which can be used to determine xx, the number of days Enola can afford to rent while staying within her budget.
Answer:
260≤67.5+35x
Step-by-step explanation:
the ps/ms soccor team purchased uniforms and equipment for a total cost of 692. the equiptment cost 422 and the uniforms cost 30 each. how many unifroms were ordered
Answer:
The answer is 9 uniforms.
Step-by-step explanation:
You can set up the equation like this
Total Cost = Total Cost of Equipment + Total Cost of Uniforms
So the equation would be:
692 = 422 + 30 * (# of Uniforms)
So minus both sides by 422 and you get
692-422 = 30 * (# of Uniforms)
270 = 30 * (# of Uniforms)
Then divide both sides by 30 and you get
9 = # of Uniforms
So therefore, the answer is 9 Uniforms
Solve the system of equations
2x - 9y =14
x= -6y + 7
Answer: x=
6
7
=1
6
1
≈1.166666667
y=−
9
14
=−1
9
5
≈−1.555555556
Step-by-step explanation:
Which of the values shown are potential roots of f(x) = 3x3 â€"" 13x2 â€"" 3x 45? Select all that apply.
The potential roots of the function are, [tex]\pm1, \ \pm3, \ \pm5, \ \pm9,\ \pm15, \ \pm45,\ \pm \dfrac{1}{3},\ \pm \dfrac{5}{3}[/tex]
And the accurate root is 3 it can be determined by using rules of the rational root equation.
Given that,Function; [tex]\rm f(x) = 3x^3 - 13x^2 -3x + 45[/tex]
We have to determine,Which of the values shown are potential roots of the given equation?
According to the question,Potential roots of the polynomial are all possible roots of f(x).
[tex]\rm f(x) = 3x^3 - 13x^2 -3x + 45[/tex]
Using rational root theorem test. We will find all the possible or potential roots of the polynomial.
[tex]\rm p=\dfrac{All\ the \ positive}{Negative\ factors \ of\ 45}[/tex]
[tex]\rm q=\dfrac{All\ the \ positive}{Negative\ factors \ of\ 3}[/tex]
The factor of the term 45 are,
[tex]\pm1, \ \pm3, \ \pm5, \ \pm9,\ \pm15, \ \pm45[/tex]
And The factor of 3 are,
[tex]\pm1, \ \pm3[/tex]
All the possible roots are,
[tex]\dfrac{p}{q} = \pm1, \ \pm3, \ \pm5, \ \pm9,\ \pm15, \ \pm45,\ \pm \dfrac{1}{3},\ \pm \dfrac{5}{3}[/tex]
Now check for all the rational roots which are possible for the given function,
[tex]\rm f(x) = 3x^3 - 13x^2 -3x + 45\\\\ f(1) = 3(1)^3 - 13(1)^2 -3(1) + 45 = 3-13-3+45 = 32\neq 0\\\\ f(-1) = 3(-1)^3 - 13(-1)^2 -3(-1) + 45 =- 3-13+3+45 = 32\neq 0\\\\ f(3) = 3(3)^3 - 13(3)^2 -3(3) + 45 = 81-117-9+45 =0\\\\ f(-3) = 3(-3)^3 - 13(-3)^2 -3(-3) + 45 = -81+117+9+45 =-144\neq 0[/tex]
Therefore, x = 3 is the potential root of the given function.
Hence, The potential roots of the function are, [tex]\pm1, \ \pm3, \ \pm5, \ \pm9,\ \pm15, \ \pm45,\ \pm \dfrac{1}{3},\ \pm \dfrac{5}{3}[/tex].
For more details about Potential roots refer to the link given below.
https://brainly.com/question/25873992
Answer: ALL OF THEM
Step-by-step explanation:
Given the Data Points : (9, 72) (4, 32) (7, 56) What is the constant of variation?
The constant of variation of the data point is 8.
An equation is an expression that shows the relationship between two or more variables and numbers.
If two variables are proportional, they can be represented by:
y ∝ x
y = kx
k is the constant of variation.
For the point (9, 72):
72 = 9k
k = 8
For the point (4, 32):
32 = 4k
k = 8
For the point (7, 56):
56 = 7k
k = 8
The constant of variation of the data point is 8.
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Sally wants to buy themselves a beautiful, scrumptious, delightful cake but they don't know how money works. If Sally has $50.00, and the cake is $54.99, how much more do they need? literally just made this question off the top of my mind xD
Answer:
$4.99
Step-by-step explanation:
$54.99-$50.00=$4.99
Answer:
Step-by-step explanation:
cake: $54.99
sally money: $50.00
54.99-50= $4.99 lol
Fiona and her sisters grew over the past three months. She records the change in heights of her and her sisters in the table below. Height (in.) Height (in.) Height (in.) Month 1 Month 2 Month 3 Fiona 4 8 12 Alicia 4 5 6 Emilia 5 10 15 Which sister grew at a proportional rate? A.) Fiona only B.) Alicia only C.) Alicia and Emilia D.) Fiona and Emilia
Answer:
Open this doc for full answers and steps
Step-by-step explanation:
open the link!
blink.org
A shop charges $4.95 for a large 9-ounce frozen
yogurt.
What is the cost per ounce of the frozen yogurt?
Answer: $0.55
Step-by-step explanation:
$4.95/9=$0.55 ( 1 ounce frozen yogurt)
A shop charges $4.95 for 9 ounces frozen yogurt, then the cost of per ounce yogurt is $0.55.
What is an arithmetic operation?Addition, subtraction, multiplication, and division of two or even more integers are the four basic mathematical operations. Included among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.
As per the given data in the question,
Price of 9 ounce yogurt = $4.95
Then,
The cost of per ounce of yogurt = 4.95/9 = $0.55.
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Write the equation of the line that passes through the points (-1, 2) and (6, 3) in slope-intercept form.
Answer:
Step-by-step explanation:
Given:
x1 = -1
x2 = 6
y1 = 2
y2 = 3
Solution:
m = ( y2 - y1 ) / ( x2 - x1 )
m = ( 3 - 2 ) / ( 6 - -1 )
m = 1 / ( 6 + 1 )
m = 1/7
Then,
y - y1 = m ( x - x1 )
y - 2 = 1/7 ( x - -1)
y - 2 = 1/7 ( x + 1 )
y - 2 = 1/7x + 1/7
y = 1/7x + 1/7 + 2
y = 1/7x + 15/7
Sara has a cell phone plan that charges $2 per minute for her long distance calls to Italy. She also has a pay a flat fee of $10 each month to have this plan, no matter how many minutes she talks on the phone. If Sara talks for 20 minutes long distance this month, how much money does she have to pay in total? Show work that supports your response.
Answer:
50
Step-by-step explanation:
she pays 10 in a flat fees and 2 dollars a minute so you multiply the 2 by 20 and add 10
For a field trip 20 students rode in cars and the rest filled 5 buses. How many students were in each bus if no more than 250 students went on the trip?
Answer:
46 bc 250 -20 =230 and 230÷5= 46
PLEASE HELP ME!!!!!!!
Answer:
The answer is B
Step-by-step explanation:
The answer would be B because the domain of a function is always all real numbers.
How many points are on this plane?
Answer:
5
Step-by-step explanation:
A,B and C would be the inside of the plane not outside.
Please find the range of these numbers
Answer:
91 - 74 = 17
Step-by-step explanation:
The range is the difference between the highest and lowest values in a set of numbers.
Help please, 9th grade math.
Answer:
table k
Step-by-step explanation:
4:3 ratio
I need help with this question
Answer:
Option D
Step-by-step explanation:
a^2 + b^2 = c^2
5^2+b^2=9^2
25+b^2=81
b^2=56
b=2√14
The first three terms of a sequence are given. Round to the nearest thousandth (if
necessary).
158, 155, 152, ...
Find the 34th term
The 34th term of the sequence 158, 155, 152 ...... is 59
The sequence is as follows:
158, 155, 152 ......
let
a = first term = 158
d = common difference = 155 - 158 = -3
Using Arithmetic progression formula, let's find the 34th term as follows:
aₙ = a + (n - 1)d
a₃₄ = 158 + (34 - 1)-3
a₃₄ = 158 + (33)(-3)
a₃₄ = 158 - 99
a₃₄ = 59
Therefore, the 34th term of the sequence is 59.
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PLEASE HELP QUESTION IN PIC.
Answer:
Perimeter= 40
Area= 120.7
Step-by-step explanation:
Which sign makes this number sentence true?
|-56|___ 1561
A)>
B)<
C)=
D) X
The absolute value of -56 is 56
the new sentence is 56____1561
A is not true because 56 is not bigger then 1561 if you count and put on number line
B is very true if you look at A. 56 is smaller than 1516
So, the answer is a
I hope this helped if it's wrong, plz blame me.
Ps.Brainlist would help a lot
Answer:
B
Step-by-step explanation:
The | | around -56 means absolute value or the total of the number, which in this case is 56, therefore 56 is less than 1561.
What is the HCF of 62 and 24 ?
Answer: As you can see when you list out the factors of each number, 2 is the greatest number that 24 and 62 divides into.
Step-by-step explanation:
Who wants to help with a math discussion?
The distance between two points, a and b, on a number line is expressed as
|a – b|, where a and b are rational numbers. Think about locating a point halfway between a and b on a number line. How can you find the coordinate for such a point? Develop a formula in terms of a and b that you can use to find the coordinate. Your formula must work for positive and negative values of a and b. Does absolute value play a role in your formula? Why or why not? Under what circumstances might your formula be used in the real world? Explain.
Discuss how you can find the coordinate of a point located other fractional distances from a to b (or from b to a). For example, locate a point three-fourths of the distance from a to b. What kind of calculation is involved?
The distance between two points is the number of units between them.
Halfway points (a) and (b)
To locate a point halfway points (a) and (b), we use the following steps
Calculate the absolute difference between both pointsDivide the absolute difference by 2Add the quotient to the smaller point.Assume the smaller value is (a), the point (P) halfway points (a) and (b) would be
[tex]P = a + \frac{|a - b|}{2}[/tex]
Take for instance, a = 5, and b = 10.
The halfway point would be:
[tex]P = 5 + \frac{|5 - 10|}{2}[/tex]
[tex]P = 5 + \frac{5}{2}[/tex]
[tex]P = 5 + 2.5[/tex]
[tex]P = 7.5[/tex]
The halfway point between 5 and 10 is 7.5
The formula works for negative values, and absolute values are used to return the actual difference between both points
Real world circumstance
The formula can be used to calculate the halfway distance between a school gate and the school library (as an instance)
Fractional distance
To determine the fractional distance, we simply replace the 1/2 in the original formula with the appropriate fraction.
Take for instance, three-fourths from (a) to (b) would be:
[tex]P = a + \frac{3|a - b|}{4}[/tex]
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Alg 2 the problem is below please help !!!
if the nth term of a sequence is n^2-5 what are the first three terms and the 10th term
Answer:
-4, -1, 4
95
Step-by-step explanation:
when n is 1
n² - 5 = 1² - 5
1 - 5 = -4
when n is 2
n² - 5 = 2² - 5
4 - 5 = -1
when n is 3
n² -5 = 3² - 5
9 - 5 = 4
10th term, when n is 10
n² - 5 = 10² - 5
100 - 5 = 95
The ratio of the radii of two circles is 2:3. Find the ratio of their areas. If the area of the bigger circle is 3123 sq. cm, find the area of the smaller circle.
Answer:
Your answer .
Step-by-step explanation:
Find the area between f(x) = 3x and f(x) = x2 on the interval (0,3]
Answer:
[tex]A=4.5[/tex]
Step-by-step explanation:
The area between two curves over the interval [tex][a,b][/tex] is [tex]A=\int\limits^b_a {f(x)-g(x)} \, dx[/tex] where [tex]f(x)[/tex] is the upper function and [tex]g(x)[/tex] is the lower function.
Therefore:
[tex]A=\int\limits^3_0 {3x-x^2} \, dx[/tex]
[tex]A=\frac{3}{2}x^2-\frac{x^3}{3}\Big|_0^3[/tex]
[tex]A=[\frac{3}{2}(3)^2-\frac{(3)^3}{3}]-[\frac{3}{2}(0)^2-\frac{(0)^3}{3}][/tex]
[tex]A=\frac{3}{2}(9)-\frac{27}{3}[/tex]
[tex]A=\frac{27}{2}-\frac{27}{3}[/tex]
[tex]A=\frac{9}{2}[/tex]
[tex]A=4.5[/tex]
So, the area between [tex]f(x)=3x[/tex] and [tex]g(x)=x^2[/tex] on the interval [tex](0,3][/tex] is [tex]4.5[/tex] square units.