Answers
Cosine function has period of 2[tex] \pi [/tex] because the function value will be same for variable that 2[tex] \pi [/tex] appart. In the problem, cos [tex]- \pi /2[/tex] and cos [tex] 3 \pi /2 [/tex] difference would be 4[tex] \pi [/tex], which is 2 * [tex] 2 \pi [/tex]. That means they both should have same value.
Related Questions
Which of the following equations is of a parabola with a vertex at (0, 3)?
y = (x - 3) ^2
y = (x + 3) ^2
y = x ^2 - 3
y = x^ 2 + 3
Answers
The General Equation of Parabola having vertex at (0,0) and Focus(a,0) and (0,a) is
[tex]y^{2}= 4ax[/tex] or [tex]x^2 =4ay[/tex]
Now ,the Given equation of parabola having vertex at (0,3) is
x^2=y-3
It is 3 unit above y axis. So the parabola will open in the upward direction.
Out of all the options provided which are
1.y = (x - 3) ^2
2.y = (x + 3) ^2
3.y = x ^2 - 3
4.y = x^ 2 + 3
Option 4. y = x^ 2 + 3 is correct.
Answer:
y = x^ 2 + 3
Step-by-step explanation:
A classic counting problem is to determine the number of different ways that the letters of "personnel""personnel" can be arranged. find that number.
Answers
The number of different ways in which the letter of “PERSONNEL” can be arranged is [tex]\boxed{\bf 90,720}[/tex].
Further explanation:
A permutation is an arrangement of objects in their order in which we find number of ways that can occur in a period of time.
If all the letters are different then the number of arrangement can be written as follows:
[tex]\boxed{\begin{aligned}P(n)&=n!\\&=n\cdot (n-1)\cdot (n-2)...2\cdot 1\end{aligned}}[/tex]
The number of different permutation can be calculated as follows:
[tex]\boxed{p(n)=\dfrac{n(n-1)(n-2)...2\cdot 1}{n_{1}!\cdot n_{2}!}}[/tex]
Here, [tex]n_{1}[/tex] and [tex]n_{2}[/tex] are the different kind of object such that [tex]n_{1}+n_{2}+n_{3}+\cdot \cdot+n_{k}=n[/tex].
Given:
The given word is “PERSONNEL”.
Calculation:
Step 1:
First consider that all the letters are different i.e, repetition of letter is allowed.
The given word “PERSONNEL” has [tex]9[/tex] letters.
Therefore, the number of ways for arranging nine letters can be calculated as follows:
[tex]\begin{aligned}P(9)&=9\cdot (9-1)\cdot (9-2)\cdot \cdot 2\cdot 1\\&=9\cdot 8\cdot 7\cdot 6\cdot 5\cdot 4\cdot3 \cdot 2\cdot 1\\&=362,880\end{aligned}[/tex]
Therefore, the different arrangements of the given word is [tex]362,880[/tex].
Step 2:
Since, the letter N and E is repeated two times in given word “PERSONNEL” then the half of the arrangement is repeated of these two letters.
Use the formula for finding the number of distinguishable permutation. It can be calculated as follows:
[tex]\begin{aligned}\text{Number of permutation}&=\dfrac{362880}{2!\cdot 2!}\\&=\drac{362880}{4}\\&=90,720\end{aligned}[/tex]
The number of different ways that the letter of “PERSONNEL” can be arranged is [tex]90,720[/tex].
Thus, the number of different ways that the letter of “PERSONNEL” can be arranged is [tex]\boxed{\bf 90,720}[/tex].
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Answer details:
Grade: High school
Subject: Mathematics
Chapter: Permutation
Keywords: Permutation, combination, personnel, counting, arrangement, different ways, order, letters, different ways, repetition, arranged objects, distinguishable permutation, counting problem.
The number of different ways to arrange the letters of 'personnel' is calculated using combinatorics and permutation formulas, resulting in 151,200 unique arrangements.
To find the number of different ways to arrange the letters of the word "personnel", we must use the principles of combinatorics and permutations.
The word 'personnel' consists of 9 letters with repetitions: there are three E's, two N's, one P, one S, one O, and one L. To count the number of unique arrangements, we start with the total factorial of all letters, which is 9!, but then we need to account for repeated letters by dividing by the factorials of the frequency of each repeating letter.
This results in the following permutation formula:
N! / (n1!)n2!...nk!
Where N is the total number of letters, and n1, n2, ..., nk are the number of times each unique letter is repeated.
So for 'personnel': 9! / (3!)(2!) = 151,200
There are therefore 151,200 unique ways to arrange the letters in 'personnel'.
The table gives the probability distribution of the number of books sold in a day at a bookstore. What is the probability of 16 or more books being sold on a given day?
number of books sold in a day
0-5
6-10
11-15
16-20
21-25
probability
0.110
0.206
0.464
0.201
?
Answers
From the given table we can see that there are 2 such categories:
1) 16 - 20
2) 21 - 25
To find the probability of 16 or more books sold , we need to add the probability of both these categories. Probability of selling 16 - 20 books is 0.201 and probability of selling 21 - 25 books is unknown. The given distribution is a probability distribution. So sum of probabilities of all categories must be equal to 1. So, the probability of selling 21-25 books is 0.019 only then the probabilities sum up to 1.
Thus,
The probability that 16 or more books are sold on a give day = 0.201 + 0.019 = 0.220
The probability of 16 or more books being sold on a given day is 0.22 or 22%.
What is probability?Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.
The table gives the probability distribution of the number of books sold in a day at a bookstore.
The missing probability will be
We know that the sum of all the outcomes must be one.
0.110 + 0.206 + 0.464 + 0.201 + x = 1
On solving, we have
x = 0.019
The number of books sold in a day Probability
0-5 0.110
6-10 0.206
11-15 0.464
16-20 0.201
20-25 0.019
The probability of 16 or more books being sold on a given day will be
[tex]\rm P(x \geq 16) = 0.201 + 0.019 = 0.22[/tex]
The probability of 16 or more books being sold on a given day is 0.22 or 22%.
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Compute the requested average. Tim Worker receives the following income monthly from a second job. Jan. Feb. Mar. Apr. May June $200 $150 $250 $260 $285 $380 What is his average pay? (To the nearest hundredth.)
254.17255.37257.83259.85
Answers
200 + 150 + 250 + 260 + 285 + 380 + 200 + 225 + 200 + 250 + 220 + 150 = 2770
2770 divided by 12 =230.83 is the average
What are the approximate solutions of 4x2 + 3 = −12x to the nearest hundredth?
x ≈ −3.23 and x ≈ 0.23
x ≈ −2.72 and x ≈ −0.28
x ≈ 0.28 and x ≈ 2.72
x ≈ −0.23 and x ≈ 3.23
Answers
[tex] 4x^{2} + 12x + 3 = 0 [/tex]
determine if this equation were factorable, it's not for this one
so I use quadratic formula, try to search the formula online
[tex]x1 = \frac{-12 + \sqrt{(12)^{2} - 4*4*3} } {2*4} = \frac{-12 + 4\sqrt{6} }{8} = \frac{4(-3 + \sqrt{6}) }{8} = \frac{-3 + \sqrt{6}}{2} = - 0.28[/tex]
[tex]x2 = \frac{-12 - \sqrt{(12)^{2} - 4*4*3} } {2*4} = \frac{-12 - 4\sqrt{6} }{8} = \frac{4(-3 - \sqrt{6}) }{8} = \frac{-3 - \sqrt{6}}{2} = - 2.72[/tex]
x ≈ −2.72 and x ≈ −0.28 is the solution
Anton must pay a co-pay of $30 for an office visit. His insurance company will then pay 85% of the cost of the visit. How much will Anton pay for an office visit that costs $270? (Points : 1) $36.00 $40.50 $56.00 $70.50
Answers
Given:
Anton must pay a co-pay of $30 for an office visit.
His insurance company will then pay 85% of the cost of the visit.
Office visit costs $270
Solution:
[tex] co-pay \; =\; \$30 [/tex]
[tex] Insurance \; Company \; pay = 85\% \; of\; 270 = \frac{85}{100} \cdot 270 = \frac{22950}{100}=\$ 22950\\ \\ Anton \; Pay\; remaining \; of\; what\; Insurance\; Company\; pay.\\ \\ So, \; Anton \; Pay = \$270 - \$229.50=\$40.5\\ \\ [/tex]
Conclusion:
Anton totally Pay = Remaining amount for office visit + Co-pay for office visit
[tex] Anton \; pay \; for\; an \; office \; visit \; that\; costs \; \$270\; = \; \$30 \; + \; \$40.5\; =\; \$70.5 [/tex]
Given cos A = 0.25 find angle A in degrees. Round your answer to the nearest hundredth.
34.12°
123.98°
56.78°
75.52°
Answers
cos A=0.25
so
A=arc cos (0.25)-------> using a calculator----> A=75.5225°
Round to the nearest hundredth-----> A=75.52²
the answer is
the option 75.52°
the inverse of an exponential function is the quadratic function? true or false?
Answers
The inverse of an exponential function is a logarithmic function.
Hope this helps!
The measure of dispersion which is not measured in the same units as the original data is the
a. variance
b. standard deviation
c. median
d. coefficient determination
Answers
Variance is not expressed in the same units as the original data.
Variance is measured by:
Finding the difference between the mean of a data set and the variables in the data set Squaring this difference Summing up the squaresBecause variance is squared, it is no longer the same units as the rest of the data set. For instance, if the data set is in centimeters, the variance will be in centimeters².
In conclusion, the variance of a data set is not measured in the same unit as the data set.
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Final answer:
The measure of dispersion which is not measured in the same units as the original data is the variance.
Explanation:
The measure of dispersion which is not measured in the same units as the original data is the variance. The variance is a squared measure and does not have the same units as the data. On the other hand, the standard deviation is derived from the variance and it measures the spread in the same units as the data.
Then again, the standard deviation, which is the square foundation of the fluctuation, is estimated in similar units as the first information. It gives a proportion of the spread of the information that is all the more effectively interpretable. The middle is a proportion of focal inclination and doesn't give data about the scattering or spread of the information.
The coefficient of assurance, otherwise called R-squared, is a proportion of how well the relapse line fits the information and isn't straightforwardly connected with scattering.
What is the domain of the relation graphed below? GET 50 POINTS!
Answers
domain {-5, -4, -3, 1, 2, 5}
Explanation:
Domain is defined as the inputs to a certain function.
In other words, for a certain function f(x), the domain would be the x values for this function.
Now, the domain for the given graph would simply be all the x values which have a corresponding y-value on the graph which are: -5, -4, -3, 1, 2 and 5
Hope this helps :)
Answer:
Domain is the set of x values
so domain is {-5 , -4 , -3 , 1 , 2 , 5}
Just a quick math question.
When converting 18 quarts into gallons, I would have to divide by 4 to get the answer which is 4.5, but why am I dividing by 4? Where did 4 come from?
Answers
A circle is divided into 18 equal parts how many degrees is the angel measure for part?
Answers
To find out the number of degrees in each part take 360 and divide that value by 18.
That is the angle measure for each particular part.
Below is the graph of f ′(x), the derivative of f(x), and has x-intercepts at x = –3, x = 1 and x = 2. There are horizontal tangents at x = –1.5 and x = 1.5. Which of the following statements is true?
A) f has a relative minimum at x = 1.5
B) f has relative maximum at x = -1.5
C) f is decreasing on the interval from x = 1 to x = 2
D) none of these are true
https://seminole.flvs.net/webdav/assessment_images/educator_apcalcab_v14/08_01_04.gif
Answers
the derivitive is just the slope
minimum happens when the derivitive goes from negative to positive, imagine a slope of the function, the minimum is where the slope goes from neative to positive, and to get there, it has to pass through 0
max happens when the derivitive goes from positive to negative
increaseing is when the derivitive is positive
so, based on what you said, the slope of f(x) is 0 at x=-3, x=1 and x=2 since those are where the derivitive is 0 (derivitive is just the slope)
A and B are wrong because the derivitive isn't 0 at those points
C is correct because increasing means that the derivitive is positive, and so therefo since the only hoirontal place in between 1 and 2 is 1.5, it must remain positive throughout and not dip down, C is right
D is wrong then
answer is C
The only statement that is true as regards the graph of f ′(x) is;
C: f is decreasing on the interval from x = 1 to x = 2
We are told that the graph of f ′(x) has x-intercepts at x = –3, x = 1 and x = 2.Now, f'(x) is simply the derivative of f(x) and the derivative of f(x) is defined as the slope.
Since x-intercepts of the derivative are at x = –3, x = 1 and x = 2. It means that the values of x that will make the slope to be zero are x = –3, x = 1 and x = 2.Now, the minimum for the derivative graph usually happens when the the graph goes from negative to positive. This means that the graph is decreasing when the x-intercepts of the slope is positiveIn contrast the graph is increasing when the x-intercepts of the slope is negative.
Let us look at the options;
Option A; This is not correct because the derivative has to be zero at minimum point. Option B; This is not also correct because the derivative has to be zero at maximum point.Option C; This is correct because slope is positive when the graph is decreasing and from x = 1 to x = 2 is positive interval.Read more about graph of derivative of a function at; https://brainly.com/question/2284808
At a local department store, pants have been reduced to $26. this price is at 68.4% of the original price for pants. given this, what was the original price of the pants?
Answers
[tex]26 \div .684 = a[/tex]
Find two numbers their sum is −7 and their difference is 14
PLZ HELP FAST
Answers
Find the equation of the line with the given properties: slope of 2, contains the point ( 4, -3).
Answers
Answer:
y = 2x - 11
Step-by-step explanation:
We are given that a line has a slope of 2 and passes through the point (4, -3).
As the question doesn't specify, we can write the equation of the line in any format.
There are 3 ways to write the equation of the line. They are:
Slope-intercept form, which is y=mx+b, where m is the slope and b is the value of y at the y intercept.Standard form, which is ax+by=c, where a, b, and c are free integer coefficients, however a and b cannot be 0 and a cannot be negative. Point-slope form, which is [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1,y_1)[/tex] is a point.Although while all of these choices are valid, let's write the equation in slope-intercept form, as that is the most common way to write the equation of the line.
As we are already given the slope of the line, we can immediately plug it into the equation as m.
Replace m with 2.
y = 2x + b
Now we need to find b.
As the line contains the point (4, -3), we can use its values to help solve for b.
Substitute 4 as x and -3 as y.
-3 = 2(4) + b
Multiply.
-3 = 8 + b
Subtract 8 from both sides.
-11 = b
Substitute -11 as b in the equation.
y = 2x - 11
Topic: finding the equation of the line
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-r+8(-5r-2) what is the equivalent expression
Answers
-41r+16
Answer:
Step-by-step explanation:
On Monday, Amie rides her bike from home to school. After school, she bikes to work. After work, she bikes home. Based on the information in the diagram below, about how many miles does Amie bike on Monday?
Answers
The answer is D: 13.1 miles
The price of 6 pretzels is $5.10. Simon and Sofia bought 8 pretzels an shared the cost equally. How much did each person pay?
Answers
Answer:
$3.40
Step-by-step explanation:
To find out the amount each person paid, let's find the total cost of the pretzels first.
6 pretzels ----- $5.10
1 pretzel ----- $5.10 ÷6= $0.85
8 pretzels ----- 8($0.85)= $6.80
The total cost of 8 pretzels is thus $6.80.
Since the total cost was shared equally amongst two people, each person paid half of the total cost.
Amount each person paid
= $6.80 ÷2
= $3.40
By taking a quotient between the total cost and the number of people, we can see that each one pays $3.40
How much did each person pay?We know that the price of 6 pretzels is $5.10, then the price for each pretzel is given by the quotient:
$5.10/6 = $0.85
We know that Simon and Sofia bought 8 pretzels, so they pay:
P = 8*$0.85 = $6.80
And they divide that evenly between the two, so we can take the quotient:
p = $6.80/2 = $3.40
That is the amount that each person pays.
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A customer buys 3 bottles of water for ninety-nine cents each seven percent tax on each bottle what is the total bill
Answers
.. 3*$0.99 = $2.97
The tax is
.. 0.07*$2.97 = $0.2079 ≈ $0.21
The total bill, including tax is
.. $2.97 +0.21 = $3.18
______
This is how every bill is computed wherever you may shop. It is a good idea to figure this out.
Which values are solutions to the inequality below?
Check all that apply.
√x ≤ 11
a) 121
b) 120
c) 111
d) -10
e) 122
f) no solutions
Answers
The values that are solutions to the inequality √x ≤ 11 are 121, 120, and 111.
Explanation:To find the values that are solutions to the inequality √x ≤ 11, we first need to square both sides of the inequality. This gives us x ≤ 121. So any value of x that is less than or equal to 121 will be a solution.
Now let's check each option:
a) 121: 121 is equal to 121, so it is a solution.b) 120: 120 is less than 121, so it is a solution.c) 111: 111 is less than 121, so it is a solution.d) -10: Negative numbers do not have real square roots, so -10 is not a solution.e) 122: 122 is greater than 121, so it is not a solution.f) no solutions: This option is not a valid solution.In summary, the values that are solutions to the inequality √x ≤ 11 are: 121, 120, and 111.
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What is the smallest integer greater than -1/2 .
Answers
Add the reciprocal of 1 1/5 to the sum of the numbers (+1.25) and (−1 3/4 ).
Answers
The reciprocal is this number flipped, so 5/6.
To find the sum of 1.25 and -1 3/4, we will convert the decimal to a fraction. 0.25 is read as "twenty-five hundredths," so the fraction would be 25/100. This will simplify to 1/4, so 1.25 = 1 1/4.
1 1/4 + -1 3/4 = -2/4 = -1/2.
Now we add 5/6 + -1/2:
Find the least common denominator (LCD). 6 is the first number that both 6 and 2 will divide into evenly. This gives us 5/6 + -3/6 (we multiply 2 by 3 to get 6, so we multiply the numerator, -1, by 3 as well). This equals 2/6 which simplifies to 1/3.
The answer would be 1/3 after adding the reciprocal of 1 1/5 to the sum of the numbers (+1.25) and (−1 3/4 ).
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
It is given that:
The fraction is 1 1/5 = 6/5
The reciprocal of the above fraction = 5/6
= 1.25 - 1 3/4 + 5/6
= 1.25 - 7/4 + 5/6
= 1.25 - 11/12
= 4/12
= 1/3
Thus, the answer would be 1/3 after adding the reciprocal of 1 1/5 to the sum of the numbers (+1.25) and (−1 3/4 ).
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How would paying off the lowest outstanding balance credit card first be beneficial over paying off the one with the highest interest rate?
Answers
Paying off the lowest outstanding balance credit card first can be beneficial for motivation and momentum, even if it's not the most mathematically efficient approach.
Explanation:When paying off credit card debt, it can be beneficial to start by paying off the credit card with the lowest outstanding balance. This approach is called the Snowball Method and is popularized by financial expert Dave Ramsey. The Snowball Method focuses on tackling the smallest debt first, regardless of the interest rate, as it provides a psychological boost and motivates individuals to continue paying off their debts.
By paying off the smallest debt first, you can quickly eliminate one of your credit card balances. This can give you a sense of accomplishment and momentum to continue paying off your other debts. It's important to note that while the Snowball Method may not be the most mathematically efficient approach in terms of saving on interest payments, it can be effective in helping individuals stay motivated and committed to paying off their debts.
If a 16 in. by 24 in. window has a wooden frame 3 inches wide surrounding it, what is the total area of the window and frame?
Answers
24 + 3 = 27
19 * 27 = 513
Answer: 513 in squared
Hope this helped!
Answer:
The CORRECT answer is 660 sq inches
Step-by-step explanation:
This figure shows circle Z with chords AB and RS . mAR=55° mRB=66° AB=8 m RS=8 m What is mRS?
Answers
m RB = 66°
Like AB=8 m =RS →m RS = m AB
m AB = m AR + m RB
m AB = 55° + 66°
m AB = 121°
m RS = m AB
M RS = 121°
Answer: m RS is 121°
Answer:
The correct answer is, mRs = 121°
Step-by-step explanation:
From figure we get ,
mAR=55° mRB=66° AB=8 m RS=8 m
To find mRS
Using given information we can write,
mAB = mAR + mRB = 55 + 66 = 121°
Since AB=8 m RS=8 m,
AB = RS
⇒ mAB = mRS
mAB = 121°
Therefore mRS = 121°
The correct answer is given by,
mRS = 121°
All side lengths of ΔJKL equal 2 units. A transformation maps ΔJKL to ΔJ'K'L'. The length of side J'K' is 5 units. Is this a rigid transformation?
No, there is no one-to-one mapping of all the points of the pre-image to the image.
No, at least one segment length is not preserved, making this a nonrigid transformation.
Yes, the vertices of the pre-image map to the vertices of the image.
Yes, all of the side lengths of the pre-image are proportionate to the image.
Answers
rigid means everything stays the same, but orientation sometimes changes.
No, at least one segment length is not preserved, making this a nonrigid transformation. Option B is correct.
What is geometric transformation?It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.
It is given that, all side lengths of ΔJKL equal 2 units. A transformation maps ΔJKL to ΔJ'K'L'. The length of side J'K' is 5 units.
A transformation that leaves a geometric figure's size or shapes unchanged is known as a rigid transformation. It is a unique type of metamorphosis in which a figure's size or shape is left unchanged.
From the definition, it is obtained that there is no rigid transformation because at least one segment length is not preserved.
Thus, no at least one segment length is not preserved, making this a nonrigid transformation. Option B is correct.
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Use the chart above to determine the premium for 10-year term insurance. $10,000 policy for a 35-year-old male. Premium = _____?
6.11
61.10
611.00
6,110.00
Answers
Answer:
Option B 61.10
Step-by-step explanation:
Given is a chart giving the premium to be paid for 10 year term insurance for different age groups for an amount of 1000 policy.
We have to calculate the premium for a 35 year old man for 10 year term insurance for 10000 policy.
From the chart we find that for a 35 year old man premium = 6.11
This premium is for 1000 dollars.
Since here sum assured is 10000 dollars, we get the premium
=6.11(10) = 61.10 dollars
Option B is correct
Premium = 61.10 dollars
Help me ASAP
THANKS
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Answers
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Group of kids rode horses to canyon. 20 eyes 30 legs between them. How many horses
Answers
Final answer:
To solve this problem, we set up equations based on the total number of eyes and legs. By solving the system, we find that the group consists of 5 horses.
Explanation:
The question asks us to solve a problem involving a group of kids and horses by using the given information about the total number of eyes and legs. Since humans have two eyes and two legs, and horses have two eyes and four legs, we can set up a system of equations to find the solution.
Let's denote the number of kids as 'k' and the number of horses as 'h'. Since each human and horse has two eyes, the total number of eyes is given by the equation: 2k + 2h = 20. Similarly, the total number of legs is given by the equation: 2k + 4h = 30. Solving these equations will give us the number of kids and horses in the group.
Solving for 'k' from the first equation gives us k = 10 - h. Substituting this into the second equation gives us 2(10 - h) + 4h = 30. Simplifying this equation results in 20 - 2h + 4h = 30, which further simplifies to 2h = 10, and thus h = 5. Therefore, there are 5 horses in the group.