Step-by-step explanation:
F(n)=|sin(n)|+|sin(n+1)|
then
F(n+π)=|sin(n+π)|+|sin(n+π+1)|=|sin(n)|+|sin(n+1)|=F(n)
and
F(π−n)=|sin(π−n)|+|sin(π−n+1)|=|sinn|+|sin(n−1)|≠F(n)
so we must prove when n∈(0,π), have
F(n)>2sin12
when n∈(0,π−1),then
F(n)=sinn+sin(n+1)=sinn(1+cos1)+sin1cosn
and n∈(π−1,π),then
F(n)=sinn−sin(n+1)
How prove it this two case have F(n)>2sin12? Thank you
and I know this well know inequality
|sinx|+|sin(x+1)|+|sin(x−1)|≥2sin1,x∈R
A(3, 7), B(5, 7), C(3-7), D(5, -7)
what is the area ?
Answer:
28 square units.
Step-by-step explanation:
This is a rectangle with sides (7 - (-7) and (5 - 3)
= 14 by 2
= 28 unit^2.
Determine the point estimate of the population proportion and the margin of error for the following confidence interval.Lower boundequals0.212,upper boundequals0.758,nequals1200The point estimate of the population proportion is . 485.(Round to the nearest thousandth as needed.)The margin of error is 0.273.(Round to the nearest thousandth as needed.)
Answer: The point estimate of the population proportion is . 485.
The margin of error is 0.273.
Step-by-step explanation:
Confidence interval for population proportion(p):
sample proportion ± Margin of error
Given: Lower bound of confidence interval = 0.212
Upper bound = 0.758
⇒sample proportion - Margin of error=0.212 (i)
sample proportion + Margin of error= 0.758 (ii)
Adding (i) and (ii) , we get
2(sample proportion) =0.970
⇒ sample proportion = 0.970÷2= 0.485
Since sample proportion is the point estimate of the population proportion.
So, the point estimate of the population proportion= 0.485
Now put sample proportion =0.485 in (ii), we get
0.485+ Margin of error= 0.758
⇒ Margin of error= 0.758 - 0.485 =0.273
i.e. The margin of error is 0.273.
I will give a brainliest and 20pts to the person that can use the Pythagorean theorem to solve for x. Please help. I went over it several times and the answer I got doesn't match up with what the box says
Answer:
x = 48
Step-by-step explanation:
Pythagorean thm:
a² + b² = c²
Given:
a = x
b = 36
c = 60
Work:
a² + b² = c²
x² + 36² = 60²
x² + 1296 = 3600
x² = 3600 - 1296
x² = 2304
√x² = √2304
x = 48
How many multiples of 4, that are smaller than 1,000, do not contain any of the digits 6, 7, 8, 9 or 0? I really need a answer.
Answer:
Step-by-step explanation:
We could start by listing multiples of 4 and looking for patterns. Do
you know what a multiple of a number is? It's that number multiplied
by another number. So the first multiple of 4 is 4x1, the second
multiple of 4 is 4x2=8, the third multiple of 4 is 4x3=12, etc.
Let's make a table of multiples of 4 from 1 to 100, with columns A-E
across the top and rows 1-5 down the left-hand side:
A B C D E
1 4 8 12 16 20
2 24 28 32 36 40
3 44 48 52 56 60
4 64 68 72 76 80
5 84 88 92 96 100
Now let's look at these multiples, remembering that there will be nine
more tables like this one from 101-1000.
Let's look for 6,7,8,9, and 0 in the columns first. Aha! We can erase
all of columns B, D, and E because there's a 6 or an 8 or a 0 in each
number in those columns. Now we're left with just:
A C
1 4 12
2 24 32
3 44 52
4 64 72
5 84 92
Now let's look at the rows. Wow! We can eliminate rows 4 and 5 because
they have 6, 7, 8, or 9, leaving:
A C
1 4 12
2 24 32
3 44 52
Just 6 numbers left!
So if from 1-100 there are 6 multiples of four that do not contain any
of the digits 6, 7, 8, 9, or 0, how many multiples of four like this
are there from 1-1000?
Evaluate 2/3 + 1/3 + 1/6 + … THIS IS CONTINUOUS. It is NOT as simple as 2/3 + 1/3 + 1/6.
[tex]a=\dfrac{2}{3}\\r=\dfrac{1}{2}[/tex]
The sum exists if [tex]|r|<1[/tex]
[tex]\left|\dfrac{1}{2}\right|<1[/tex] therefore the sum exists
[tex]\displaystyle\\\sum_{k=0}^{\infty}ar^k=\dfrac{a}{1-r}[/tex]
[tex]\dfrac{2}{3}+\dfrac{1}{3}+\dfrac{1}{6}+\ldots=\dfrac{\dfrac{2}{3}}{1-\dfrac{1}{2}}=\dfrac{\dfrac{2}{3}}{\dfrac{1}{2}}=\dfrac{2}{3}\cdot 2=\dfrac{4}{3}[/tex]
Which property of equality was used to solve this equation?
X-5 = -14
X-5 + 5 = -14 + 5
x= -9
OA. addition property of equality
OB. subtraction property of equality
OC. multiplication property of equality
OD.division property of equality
Answer:
OA. addition property of equality
Step-by-step explanation:
In the second step of the problem, you can see they add 5 to both sides of the equation. So, it is the addition property of equality.
Answer:
addition property of equality
Step-by-step explanation:
X-5 = -14
Add 5 to each side using the addition property of equality
X-5 + 5 = -14 + 5
x= -9
Little bit more math hw
Answer:
[tex]x=-2[/tex]
Step-by-step explanation:
For these kind of problems, simply take the denominator and compare it to zero. Then solve the equation.
[tex]x+2=0\\\\\Rightarrow x=-2[/tex] By subtracting 2 from both sides!
Best Regards!
Reason Can you subtract a positive integer from a positive integer
and get a negive result? Explain your answer.
Answer:
No
Step-by-step explanation:
No matter the situation, when you multiply a negative by a negativeyou get a positive and a positive by a positive you get a positive. but if its two different like a negative and a positive then its NEGITIVE.
let's say you have 23 and you're multiplying by 2.
It's always increasing so it doesnt ever reach the negitive numbers.
_Thirty-two holes are drilled in rows on a metal block. The number of rows is more than the number of holes in each
row. Find the number of row. (a)7 (b)25(c)67
(d)4 (e) 12
_
Answer:
D
Step-by-step explanation:
Let the number of rows be x
And the numbers of holes in each be y
xy = 32
x and y must be factors of 32
From options stated
4 is the only factor of 32
Hence option D is correct
A model rocket is launched with an intitial upupward velocity of 202 ft/s. The rocket’s height h (in feet) after seconds is given by the following.
H=202t-16t^2
Given that the height of a object thrown within a gravitational field is given as a quadratic equation in time, t, the time at which the object is at a specified height can be found by the quadratic formula
The values of, t, for which the height of the rocket is 82 feet are;
t = 12.21 seconds or t = 0.42 seconds
Question: Parts of the question that appear missing but can be found online are (i) To find the values of the time, t, when the rocket's height is 82 feet and round answers to the nearest hundredth
The known parameters of the rocket are;
The initial upward velocity of the rocket, v = 202 ft./s
The given function representing the height, h, (in feet) after t seconds is presented as follows;
H = 202·t - 16·t²
The unknown;
The time for which the height of the rocket is 82 feet
Method;
Substitute H = 82 feet in the height function equation and solve for t as follows;
When H = 82, we get;
82 = 202·t - 16·t²
Therefore;
16·t² - 202·t + 82 = 0
Dividing the above equation by 2 gives;
(16·t² - 202·t + 82)/2 = 0/2
8·t² - 101·t + 41 = 0
By using the quadratic formula, we get;
[tex]\mathbf{t = \dfrac{101 \pm \sqrt{(-101)^2 - 4 \times 8 \times 41} }{2 \times 8} = \dfrac{101 \pm \sqrt{8889} }{16}}[/tex]
Therefore, the values of t given by rounding off to the nearest hundredth are;
t = 12.21 or t = 0.42
The values of the time, t, at which the height of the rocket is 82 feet are t = 12.21 seconds or t = 0.42 seconds
Learn more about equation models of height as a function of time here;
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which operation should you perform first when evaluating the expression 3²+ 2
Answer:
You should calculate 3² first.
Step-by-step explanation:
In PEMDAS, E (which stands for exponents) comes before A (which stands for addition) so therefore you should calculate 3² first.
Explanation:
The acronym PEMDAS helps determine the order of operations
P = parenthesis
E = exponents
M = multiplication
D = division
A = addition
S = subtraction
With the expression [tex]3^2+2[/tex] we have two operations going on here: exponents and addition.
Since exponents comes before addition (E comes before A in PEMDAS), this means we evaluate [tex]3^2[/tex] first, then add later.
Malia measures the longer side of a dollar bill using a ruler at school. Which of the following is most likely the quantity she measured?
Answer:
6.14 inches
Step-by-step explanation:
The one side of the dollar bill is 6.14 inch. The 6.14 inches of the dollar approximates the 156.1 mm. When Malia measures the longer side of a dollar bill from her rule it will be approximately 6.14 inches in length. The ruler normally has inches and cm sides. Very few rulers have mm scales. The most probable scale that malia would have measure is in inches.
look at the question below in the image
Answer:
117.8
Step-by-step explanation:
Surface area of a cone = πrl+πr², where r = radius and l = slant height
πrl
= π×3×9.5+π×3²
= 75π/2
= 117.8 (rounded to the nearest tenth)
Transform the given parametric equations into rectangular form. Then identify the conic. x= -3cos(t) y= 4sin(t)
Answer:
Solution : Option D
Step-by-step explanation:
The first thing we want to do here is isolate the cos(t) and sin(t) for both the equations --- ( 1 )
x = - 3cos(t) ⇒ x / - 3 = cos(t)
y = 4sin(t) ⇒ y / 4 = sin(t)
Let's square both equations now. Remember that cos²t + sin²t = 1. Therefore, we can now add both equations after squaring them --- ( 2 )
( x / - 3 )² = cos²(t)
+ ( y / 4 )² = sin²(t)
_____________
x² / 9 + y² / 16 = 1
Remember that addition indicates that the conic will be an ellipse. Therefore your solution is option d.
When Asia was young, her father marked her height on the door frame every month. He noticed that between the ages of one and three, he could predict her height (in inches) by taking her age in months, adding 75 inches, and multiplying the result by one-third.
Create an equation linking her predicted height, h, with her age in months, m.
[tex]The \: text \: tells \: us \: that \: we \: can \\ predict \: her \: height \: by \: taking \\ her \: age \: in \: months, \: adding \: 75, \\ and \: multiplying \: by \: \frac{1}{3} . \: So \: our \\ equation \: is [/tex]
[tex]h = (m + 75). \frac{1}{3} [/tex]
(or)
[tex]h = \frac{1}{3} (m + 75)[/tex]
b) Determine her predicted height on her second birthday
To predict Asia’s height on her second birthday, we substitute m=24
into our equation (because 2 years is 24 months) and solve for h.
[tex]h = \frac{1}{3} (24 + 75)[/tex]
[tex]h = \frac{1}{3} (99)[/tex]
[tex]h = 33[/tex]
Asia’s height on her second birthday was predicted to be 33 inches.
HELPP PLEASEE ��2222 is the diameter of a circle. The coordinates are �(−2, −3) and �(−12, −5). At what coordinate is the center of the circle located? A. (5, 1) B. (−5, −1) C. (−4, −7) D. (−7, −4)
Answer:
(-7, -4) which is your answer D in the list of options
Step-by-step explanation:
The center of the circle should be located half way in between the given points on the plane.
Then the center ahs to be located half way for the x coordinates of both points:
half way between -12 and -2 (notice that there is a difference of 10 units between them), therefore half way would be at 5 units to the right from the furthest point, that is -12 + 5 = -7
Similarly, for the y coordinate, we see that the difference is between -5 and -3 (a difference of two units) therefore the center point will be located half way (that is one unit) up from the lowest y coordinate: -5 + 1 = -4
Then the center of the circle is located at (-7, -4)
Simplify: (-2)^-3
a) 8
b) 1/8
c) -8
d) -1/8
Answer:
-1/8
Step-by-step explanation:
(-2)^-3
We know that a^-b = 1/a^b
1/(-2)^3
We know (-2)^3 = -8
1/(-8)
-1/8
how many feet are in 53 yards, 2 feet? enter only the number. Do not include units
There are 161 feet are in 53 yards, 2 feet.
What is unit conversion?
Unit conversion is the process of changing a quantity's measurement between various units, frequently using multiplicative conversion factors.
As we know that;
1 yard = 3 feet
53 yards = 3 ×53 feet
53 yards = 159 feet
53 yards, 2 feet = 159 feet + 2 feet
53 yards, 2 feet = 161 feet
Hence, there are 161 feet in 53 yards, 2 feet.
To learn more about the unit conversion, refer;
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#SPJ2
Evaluate the equation
Answer:
3 +4 i
Step-by-step explanation:
x + sqrt(yz)
Let x = 3 y=2 and z = -8
3 + sqrt(2*-8)
3+ sqrt(-16)
3 + sqrt(16) sqrt(-1)
We know sqrt(-1) = i
3 +4 i
At a sale, dresses were sold for $39 each. This price was 65% of a dress's original price. How much did a dress originally cost?
Answer:
Hey there!
We can write the equation:
0.65x=39
x=60
The dress originally sold for 60 dollars.
Hope this helps :)
which is the graph of the function fx=x^2+2x+3
Answer:
see below
Step-by-step explanation:
fx=x^2+2x+3
This is a parabola that opens upward
f(x) = (x^2 +2x)+3
= (x^2+2x+1) +3-1
= (x+1)^2 +2
This is in vertex form y =a(x-h)^2 +h where the vertex is (h,k)
This has a vertex as (-1,2)
And has a y intercept at (0,3)
this does not cross the x axis
2. mrs nepali draws rs 19800 as her monthly salary in a wholesale cosmetic shop and certain commission is given as per the monthly sales. if the sales of a month is rs 1200000 and her total income of the month including commission is rs 31800 find the rate of commission. * O 1% 4% 3% 2%
Answer 9 and 11 with explanation on how you solved it.
Answer:
(9). Range; {8, 5, 2, -1, -4}
(10). Range; {-15, -7, 1, 9, 17}
Step-by-step explanation:
Domain of a function is (x-values) determined by the input values and Range of a function is determined by the (y-values) output values of the function.
(9). For the given function,
f(x) = -3x + 2
If the Domain of this function is a set of values,
{-2, -1, 0, 1, 2}
For Range,
x -2 -1 0 1 2
f(x) 8 5 2 -1 -4
Therefore, Range of the function 'f' will be; {8, 5, 2, -1, -4}
(11). f(x) = 4x + 1
Domain is {-4, -2, 0, 2, 4}
Table for input-output values will be,
x -4 -2 0 2 4
f(x) -15 -7 1 9 17
Therefore, Range of the function will be {-15, -7, 1, 9, 17}
Which of the following is the solution set of the given equation? (x - 3) - 2(x + 6) = -5 a) {-4} b) {8} c) {-10}
Answer:
x = -10
Step-by-step explanation:
(x - 3) - 2(x + 6) = -5
Distribute
x-3 -2x-12 = -5
Combine like terms
-x -15 = -5
Add 15 to each side
-x-15+15 = -5+15
-x=10
Multiply each side by -1
x= -10
Answer:
c
Step-by-step explanation:
At α = 0.001, is the overall model significant?Group of answer choicesNo, F* < FcThe test is inconclusive because 0.001 < p < 0.10Yes, F* < Fc, and p < 0.05.Yes, F* > Fc, and p < 0.001.Yes, F* > Fc, and p > 0.05.
Answer:
No, F* < Fc
Step-by-step explanation:
Significance level or alpha level is the probability of rejecting the null hypothesis when null hypothesis is true. It is considered as a probability of making a wrong decision. It is a statistical test which determines probability of type I error. If the obtained probability is equal of less than critical probability value then reject the null hypothesis .
How do you find x when knowing the probability?
Answer:
x
Step-by-step explanation:
probability is the branch of mathematics concerning numeral descriptions of how likely an event is to occur or how likely it is that a proposition is true
which function represents the area of the triangle h(x)=1/2f(x)g(x)
Answer:
h=1/2fg
Step-by-step explanation:
Solve for x, h=1/2fg
It is true for all x; h=1/2fg
h=1/2fg
Both sides are equal
It is true for all x; h=1/2fg
Find the point(s) on the ellipse x = 3 cost, y = sin t, 0 less than or equal to t less than or equal to 2pi closest to the point(4/3,0) (Hint: Minimize the square of the distance as a function of t.) The point(s) on the ellipse closest to the given point is(are) . (Type ordered pairs. Use a comma to separate answers as needed.)
Answer and Step-by-step explanation:
The computation of points on the ellipse is shown below:-
Distance between any point on the ellipse
[tex](3 cos t, sin t) and (\frac{4}{3},0) is\\\\ d = \sqrt{(3 cos\ t - \frac{4}{3}^2) } + (sin\ t - 0)^2\\\\ d^2 = (3 cos\ t - \frac{4}{3})^2 + sin^2 t[/tex]
To minimize
[tex]d^2, set\ f' (t) = 0\\\\2(3cos\ t - \frac{x=4}{3} ).3(-sin\ t) + 2sin\ t\ cos\ t = 0\\\\ 8 sin\ t - 16 sin\ t\ cos\ t = 0\\\\ 8 sin\ t (1 - 2 cos\ t) = 0\\\\ sin\ t = 0, cos\ t = \frac{1}{2} \\\\ t= 0, \ 0, \pi,2\pi,\frac{\pi}{3} , \frac{5\pi}{3}[/tex]
Now we create a table by applying the critical points which are shown below:
t [tex]d^{2} = (3\ cos t - \frac{4}{3})^{2} + sin^{2}t[/tex]
0 [tex]\frac{25}{9}[/tex]
[tex]\pi[/tex] [tex]\frac{169}{9}[/tex]
[tex]2\pi[/tex] [tex]\frac{25}{9}[/tex]
[tex]\frac{\pi}{3}[/tex] [tex]\frac{7}{9}[/tex]
[tex]\frac{5\pi}{3}[/tex] [tex]\frac{7}{9}[/tex]
When t = [tex]\frac{\pi}{3}[/tex], x is [tex]\frac{3}{2}[/tex] and y is [tex]\frac{\sqrt{3} }{2}[/tex]. So, the required points are [tex](\frac{3}{2},\frac{\sqrt{3} }{2})[/tex]
When t = [tex]\frac{5\pi}{3}[/tex], x is [tex]\frac{3}{2}[/tex] and y is [tex]\frac{-\sqrt{3} }{2}[/tex]. So, the required points are [tex](\frac{3}{2},\frac{-\sqrt{3} }{2})[/tex]
2. You are going to produce tennis shoes
that come in 3 different colors. In order to
decide how many to make in each color,
you conduct a survey. Of the 300 people
you survey, 75 said that they would
purchase the yellow shoes. If you are
going to make 10,000 pairs of shoes, how
many should be yellow?
Please help thank you
Answer:
Hey there!
[tex]\frac{75}{300}[/tex]=[tex]\frac{x}{10000}[/tex]
750000=300x
x=2500
They should make 2500 yellow shoes.
Hope this helps :)
I need help with this!
Answer:
i) [tex]\frac38\pi[/tex]
ii) n = 33
Step-by-step explanation:
For this question you can actually focus on the sine, and forget about the e power. The x-coordinates of the extremes of the curve will be the same as for y=sin(4x)
i) equivalent to solving sin(4x) = -1, so 4x = 3/2 pi, x=3/8 pi
ii) The Tn values are at x = (n·π - π/2)/4
solving (n·π - π/2)/4 > 25 gives:
n > 1/2 + 100/π, so n > 32.331, but n must be integer, so we get n=33