Answer: [tex]\dfrac{1}{12}[/tex]
Step-by-step explanation:
Given: Emily has a box with 4 different colored tiles: one red, one green, one blue and one yellow.
We assume that repetition is not allowed
Total number of ways to draw two tiles = [tex]^4P_2=\dfrac{4!}{(4-2)!}[/tex] [By permuattaions]
[tex]=\dfrac{4\times3\times2}{2}=12[/tex]
Favourable outcome = First green then red (only one way)
So, the probability of drawing the green before the red [tex]=\dfrac{\text{favorable outcomes}}{\text{Total outcomes}}[/tex]
[tex]=\dfrac{1}{12}[/tex]
hence, the required probability =[tex]\dfrac{1}{12}[/tex]
Line d is parallel to line c in the figure below. Parallel lines d and c are intersected by lines q and p to form 2 triangles. At lines d and p, the angle is 2, at d and q, the angle is 1, and at q and p the angle is 3. At lines c and q, the angle is 4, at p and c, the angle is 5, and the third angle is 6. Which statements about the figure are true? Select three options. Vertical angles prove that Angle 2 is congruent to angle 5. In the two similar triangles, Angle 1 and Angle 4 are alternate interior angles. Vertical angles prove that Angle 3 is congruent to angle 6. The triangles are similar because alternate interior angles are congruent. In the two similar triangles, Angle 2 and Angle 4 are corresponding angles. The triangles are similar because corresponding sides are congruent.
Answer:
A B C
Step-by-step explanation:
Answer:
abc or 123
Step-by-step explanation:
A function f is defined by f(x) = 1 + 6x + x2 + 6x3 + x4 + ⋯ that is, its coefficients are c2n = 1 and c2n + 1 = 6 for all n ≥ 0. Find the interval of convergence of the series. Find an explicit formula for f(x).
From the odd-degree terms, take out one copy and rewrite the series as
[tex]1+6x+x^2+6x^3+\cdots=(1+x+x^2+x^3+\cdots)+5x+5x^3+\cdots[/tex]
[tex]1+6x+x^2+6x^3+\cdots=(1+x+x^2+x^3+\cdots)+5x(1+x^2+\cdots)[/tex]
Then if |x| < 1, we can condense this to
[tex]\displaystyle\sum_{n=0}^\infty x^n+5x\sum_{n=0}^\infty x^{2n}=\frac1{1-x}+\frac{5x}{1-x^2}=\frac{1+6x}{1-x^2}[/tex]
Since the series we invoked here converge on -1 < x < 1, so does this one.
The explicit formula of the function f(x) is [tex]f(x) = \frac{1 + x + 5x}{1-x^2}[/tex]
How to determine the explicit formula?The function definition is given as:
[tex]f(x) = 1 + 6x + x^2 + 6x^3 + x^4 + ...[/tex]
Expand the terms of the expression
[tex]f(x) = 1 + 5x + x + x^2 + 5x^3 + x^3 + x^4 + ...[/tex]
Split
[tex]f(x) = (1 + x + x^2 +x^3 + .....) + 5x + 5x^3 + .. ...[/tex]
Factor out 5x
[tex]f(x) = (1 + x + x^2 +x^3 + .....) + 5x(1 + x^2) + .. ...[/tex]
Express 1 as x^0
[tex]f(x) = (x^0 + x + x^2 +x^3 + .....) + 5x(1 + x^2) + .. ...[/tex]
Express x as x^1
[tex]f(x) = (x^0 + x^1 + x^2 +x^3 + .....) + 5x(1 + x^2) + .. ...[/tex]
Also, we have:
[tex]f(x) = (x^0 + x^1 + x^2 +x^3 + .....) + 5x(x^0 + x^2) + .. ...[/tex]
Rewrite the series using the summation symbol
[tex]f(x) = \sum\limits^{\infty}_{n=0}x^n+ 5x\sum\limits^{\infty}_{n=0}x^{2n}[/tex]
The sum to infinity of a geometric progression is:
[tex]S_{\infty} = \frac{a}{1- r}[/tex]
Where:
a represents the first term, and r represents the common ratio
Using the above formula, we have:
[tex]\sum\limits^{\infty}_{n=0}x^n = \frac{1}{1 - x}[/tex]
[tex]5x\sum\limits^{\infty}_{n=0}x^{2n} = 5x * \frac{1}{1 - x^2} = \frac{5x}{1-x^2}[/tex]
So, we have:
[tex]f(x) = \frac{1}{1-x}+ \frac{5x}{1-x^2}[/tex]
Take the LCM
[tex]f(x) = \frac{1 + x + 5x}{1-x^2}[/tex]
Evaluate the like terms
[tex]f(x) = \frac{1 + 6x}{1-x^2}[/tex]
Hence, the explicit formula of the function f(x) is [tex]f(x) = \frac{1 + x + 5x}{1-x^2}[/tex]
Read more about geometric series at:
https://brainly.com/question/12563588
Find the value of x, rounded to the nearest tenth.
Answer:
x = 8.9 units
Step-by-step explanation:
We will use the theorem of intersecting tangent and secant segments.
"If secant and tangent are drawn to a circle from an external point, the product of lengths of the secant and its external segment will equal the square of the length of tangent."
8(8 + 2) = x²
x² = 80
x = √80
x = 8.944
x ≈ 8.9 units
Therefore, length of the tangent = 8.9 units
8.43 An advertising executive wants to estimate the mean amount of time that consumers spend with digital media daily. From past studies, the standard deviation is estimated as 45 minutes. a. What sample size is needed if the executive wants to be 90% confident of being correct to within {5 minutes
Answer:
a
The sample size is [tex]n = 219.2[/tex]
b
The sample size is [tex]n = 537.5[/tex]
Step-by-step explanation:
From the question we are told that
The standard deviation is [tex]\sigma = 45 \minutes[/tex]
The Margin of Error is [tex]E = \pm 5 \ minutes[/tex]
Generally the margin of error is mathematically represented as
[tex]E = z * \frac{\sigma }{\sqrt{n} }[/tex]
Where n is the sample size
So
[tex]n = [\frac{z * \sigma }{E} ]^2[/tex]
Now at 90% confidence level the z value for the z-table is
z = 1.645
So
[tex]n = [\frac{1.645 * 45 }{5} ]^2[/tex]
[tex]n = 219.2[/tex]
The z-value at 99% confidence level is
[tex]z = 2.576[/tex]
This is obtained from the z-table
So the sample size is
[tex]n = [\frac{2.576 * 45 }{5} ]^2[/tex]
[tex]n = 537.5[/tex]
For the 90% confidence interval, the sample size is 219.2 and for the 99% confidence interval, the sample size is 537.5 and this can be determined by using the formula of margin of error.
Given :
An advertising executive wants to estimate the mean amount of time that consumers spend with digital media daily.From past studies, the standard deviation is estimated as 45 minutes.The formula of the margin of error can be used in order to determine the sample size is needed if the executive wants to be 90% confident of being correct to within 5 minutes.
[tex]\rm ME = z\times \dfrac{\sigma}{\sqrt{n} }[/tex]
For the 90% confidence interval, the value of z is 1.645.
Now, substitute the values of all the known terms in the above formula.
[tex]\rm n=\left(\dfrac{z\times \sigma}{ME}\right)^2[/tex] --- (1)
[tex]\rm n=\left(\dfrac{1.645\times 45}{5}\right)^2[/tex]
n = 219.2
Now, for 99% confidence interval, the value of z is 2.576.
Again, substitute the values of all the known terms in the expression (1).
[tex]\rm n=\left(\dfrac{2.576\times 45}{5}\right)^2[/tex]
n = 537.5
For more information, refer to the link given below:
https://brainly.com/question/6979326
Convert to a mixed number 8/5
Answer:
The improper fraction 8/5 can be changed to the mixed number 1 3/5 by dividing the numerator (8) by the denominator (5). This gives a quotient of 1 and a remainder of 3.
Step-by-step explanation:
what is the constant of proportionality for 4y=16
Answer:
Step-by-step explanation:
y=4x
You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately p ∗ = 22 % . You would like to be 95% confident that your esimate is within 1% of the true population proportion. How large of a sample size is required?
Answer:
The large of a sample size is required is 6,592
Step-by-step explanation:
In order to calculate large of a sample size is required we would have to calculate the following formula:
large of a sample size is required=(Z∝I2/E)∧2* P(1-P)
According to the given data we have the following:
E= margin of error= 1%=0.01
95% confident that your esimate is within 1% of the true population proportion, therefore, level of significance=∝=1-0.95=0.05
Z value for the 95% confident is 1.960, therefore, Z∝I2=1.960
Therefore, large of a sample size is required=(1.960/0.01)∧2* (0.22)(1-0.22)
large of a sample size is required=6,592
The large of a sample size is required is 6,592
HELP ASAP ALL THREE PLEASE 1. if a cyclic alkene has 12 carbon atoms, how many hydrogen atoms does it have 2.if a cyclic alkene has 12 hydrogen atoms, how many carbon atoms 3. is it possible to have an odd number of hydrogen atoms
Answer:
1. 24
2. 6
3. No
Step-by-step explanation:
The formula for cyclic alkene is [tex]C^{n} H^{2n}[/tex], so if it has 12 carbon atoms, it will have double the amount of hydrogen atoms, therefore, 24 hydrogen atoms.
The same works in reverse. If we have 12 hydrogen atoms in this, then there will be half the amount of carbon atoms, therefore 6.
Since the relationship between Carbon and Hydrogen here is double and half, odd numbers can't be divided by 2 and end up with a whole number, so an odd number of hydrogen atoms is not possible.
Hope this helped!
The ages of the members of a legislature from a particular state are listed below. Find the mean, median, and mode of the data set, if possible. If any measure cannot be found or does not represent the center of the data, explain why. 68 41 36 43 51 43 32 52 48
Answer:
Mean: 46
Median: 43
Mode: 43
Step-by-step explanation:
I hope this helped. I am sorry if you get this wrong.
What is the answer of 4=y-4
Answer:
y = 8Step-by-step explanation:
4 = y - 4
Group the constants at the left side of the equation
That's
4 + 4 = y
Add the constants
y = 8Hope this helps you
Answer:
y=8
Step-by-step explanation:
To solve this equation, we need to find out what y is.
4= y-4
Therefore, we must get y by itself on one side of the equation.
4 is being subtracted from y. The inverse of subtraction is addition. Add 4 to both sides of the equation.
4+4=y-4+4
4+4=y
8=y
y=8
Let's check our solution. Plug 8 back in for y.
4= y-4
4= 8-4
4=4
The equation above is true, so we know our answer is correct.
A candy store called "Sugar" built a giant hollow sugar cube out of wood to hang above the entrance to their store. It took 13.5\text{ m}^213.5 m 2 13, point, 5, start text, space, m, end text, squared of material to build the cube. What is the volume inside the giant sugar cube?
Answer:
3.375
Step-by-step explanation:
Answer:
3.375
Step-by-step explanation:
Had it on Khan
The test statistic of z=1.92 is obtained when testing the claim that p≠0.767. a. Identify the hypothesis test as being two-tailed, left-tailed, or right-tailed. b. Find the P-value. c. Using a significance level of α=0.10, should we reject H0 or should we fail to reject H0?
Answer:
it is a two tailed test
The p - value for z=1.92 is 0.9726
Using a significance level of α=0.10, We fail to reject H0. The calculated z value lies out side the Zα value.
Step-by-step explanation:
For p≠0.767
Taking null hypothesis as p≠0.767 and alternate hypothesis as p =0.767
H0 :p≠0.767 Ha :p≠0.767 it is a two tailed test
The p - value for z=1.92 is 0.9726 from the table.
Using a significance level of α=0.10
z value for 0.10 for two tailed test is ± 1.645
Z >zα
1.92> ± 1.645
Using a significance level of α=0.10, We fail to reject H0. The calculated z value lies out side the Zα value.
A Car Salesman sold $450000.00 in cars for the month of July.
He is paid a monthly salary of $6000.00 and 5% commission on
total sales. How much did he earn in July?
Answer:
$28,500
Step-by-step explanation:
$6,000 + 5% of $450,000 =
= $6,000 + 0.05 * $450,000
= $6,000 + $22,500
= $28,500
What are the vertices of the square below?
Answer:
The vertices are (7,6), (-7,6), (-7,-7) and (7,-7).
Step-by-step explanation:
The vertices are the coordinates of each corner of the square.
In this drawing, we have one vertex in each quadrant.
The vertex in the first quadrant has a x-coordinate of 7 and a y-coordinate of 6, so let's call this vertex A = (7,6).
The vertex in the second quadrant has a x-coordinate of -7 and a y-coordinate of 6, so let's call this vertex B = (-7,6).
The vertex in the third quadrant has a x-coordinate of -7 and a y-coordinate of -7, so let's call this vertex C = (-7,-7).
The vertex in the fourth quadrant has a x-coordinate of 7 and a y-coordinate of -7, so let's call this vertex D = (7,-7).
So the vertices are (7,6), (-7,6), (-7,-7) and (7,-7).
evaluate sin^-1(sin5)
−π2≤sin−1x≤π2
3π2≤5≤2π
−π2≤5−2π≤0≤π2
sin(5–2π)=sin5
Thus, sin−1(sin5)=5−2π
Sketch the region that corresponds to the given inequality. HINT [See Example 1.] 2x + y ≤ 10 Say whether the region is bounded or unbounded. The region is bounded. The region is unbounded. Find the coordinates of all corner points (if any). (If an answer does not exist, enter DNE.)
Answer:
See the attachment for sketch
Thr region is unbounded
DNE
Step-by-step explanation:
y≤ -2x + 10
The inequality is a straight line and region marked by the inequality. It has no boundaries. The boundaries extend to infinity. So the region is unbounded. Unbounded region has no corner points.
Mrs Wong bought a rice cooker for $126 after a discount of 30%.
(a) What was the price of the rice cooker before discount? (b) She paid $40 for a toaster. The total discount for the rice cooker and the toaster was $64. What was the percentage discount given for the
toaster?
Answer:
(a) $180
(b) 25%
Step-by-step explanation:
(a) $126 = 30% of x; x is the total
so from this, you get an equation: 126 = 0.3x
solve the equation: x = 180; so the amount before
discount is $180
(b) You know the price of discount for the rice cooker is
180-126 which is $54
Then you subtract 54 from 64 to get the discount amount for the toaster
10/40 is 1/4 or 25%
please answer this for me. i have no idea :( please please please, i am desperate.
================================================
Explanation:
Whenever the angle theta is between 0 and 90, the reference angle is exactly that value.
It's only when you get to other quadrants is when things get a bit tricky. Right now we're in quadrant 1, often written as Q1.
-------------------
Extra info:
If theta is between 90 and 180, then the reference angle is 180-theta. This region is Q2If theta is in quadrant 3, between 180 and 270, then the reference angle is theta-180. The order of subtraction is important since x-y is the not the same as y-x.Lastly, if theta is between 270 and 360 (in Q4), then the reference angle is 360-theta.As you can see, we have four quadrants starting with Q1 in the upper right corner. Then we move counterclockwise to get Q2,Q3 and Q4.Answer:
60 degrees
Step-by-step explanation:
In Quadrant 1, the reference angle is the same as theta.
So,
Reference Angle = 60 degrees
Actividad 1.1<br />Investigue sobre el tema de diferenciabilidad en un punto para encontrar los valores de "a" y "b" tales que<br />la función<br />definida a continuación sea diferenciable en t = 2, luego construya su gráfica.<br />at +b, sit < 2<br />f(t) = {2t2 – 1, si 2 st<br />1
Answer:
a = 8
b = -8
Step-by-step explanation:
You have the following function:
[tex]f(x)\\\\=at+b;\ \ t<2\\\\2t^2-1;\ \ 2\leq t[/tex]
A function is differentiable at a point c, if the derivative of the function in such a point exists. That is, f'(c) exists.
In this case, you need that the function is differentiable for t=2, then, you have:
[tex]f'(t)=a;\ \ \ \ t<2 \\\\f'(t)=4t;\ \ \ 2\leq t[/tex]
If the derivative exists for t=2, it is necessary that the previous derivatives are equal:
[tex]f'(2)=a=4(2)\\\\a=8[/tex]
Furthermore it is necessary that for t=2, both parts of the function are equal:
[tex]8(2)+b=2(2)^2-1\\\\16+b=8-1\\\\b=-8[/tex]
Then, a = 8, b = -8
subtract the following .1/2 from 3/5
Answer:
1/10
Step-by-step explanation:
1/2= 5/10 - make it an equivalent fraction with the same denominator as the other fraction.
3/5= 6/10
5/10-6/10- subtract
=1/10
Find the value of x in the isosceles triangle shown below.
Answer:
x=10.
Step-by-step explanation:
Please answer this without making mistakes
Answer:
14.16 miles further.
Step-by-step explanation:
Campbell to Summerfield
9.52mi + 4.62 mi + 10.08 mi = 24.24 mi
Princeton to summerfield
is 10.08 mi
Therefore difference is 24.24mi - 10.08mi = 14.16 mi
Hope this helps.
A nut-raisin mix costs $5.26 a pound. Rashid buys 15.5 pounds of the mix for a party. Rashid’s estimated cost of the nut-raisin mix is A.$16 B.$22 C.$61 D.$80
Answer:
D.$80
Step-by-step explanation:
$5.26 x 15.5= $81.53
The closest amount to $81.53 is D.$80
Question Help
During the morning rush, entering travelers can fill a station in 30 minutes. Fortunately, departing trains can empty it in 40 minutes.
rush-hour pace, how long will it take for the station to fill with travelers?
Answer:
One hour ten minutes
Step-by-step explanation:
departing trains can empty it in 40 minutes.
entering travelers can fill a station in 30 minutes.
Time it will take travellers to fill the train
= Time for departing train + time for filling a station
= 40 minutes+ 30 minutes
= 70 minutes
= One hour ten minutes
Tosh. Inc.'s bonds currently sell for $980 and have a par value of $1,000. They pay a $95 annual coupon and have a 12-year maturity, but they can be called in 3 years at $1,150. What is their yield to call (YTC)?
Answer:
14.24%
Step-by-step explanation:
We have found that the yield to call (YTC) formula is:
YTC = [C + (F-P) / N] / [(F + P) / 2]
Where:
C = Periodic coupon amount = 95
P = Current Price = 980
F = Redemption amount = 1150
N = time left to redemption = 3
We replace:
YTC = [95 + (1150-980) / 3] / [(1150 + 980) / 2]
YTC = 0.1424
In other words, the yield to call (YTC) is equal to 14.24%
What is 36/100 added with 4/10
Answer:
0.76 or 19/25
Step-by-step explanation:
Convert 4/10 so that it has a common denominator with 36/100.
4/10 x 10/10 = 40/100
Now that the denominator is the same, just add the top values.
40/100 + 36/100 = 76/100
We can also simplify the answer to be 19/25 by dividing the top and bottom by 4.
Answer:
19/25Step-by-step explanation:
[tex]\frac{36}{100}+\frac{4}{10}\\Let\: first\: deal\: with\: ;\frac{36}{100}\\\mathrm{Cancel\:the\:common\:factor:}\:4\\=\frac{9}{25}\\\\=\frac{9}{25}+\frac{4}{10}\\Now \:lets \:deal \:with ; \frac{4}{10}\\\mathrm{Cancel\:the\:common\:factor:}\:2\\=\frac{2}{5}\\=\frac{9}{25}+\frac{2}{5}\\\mathrm{Prime\:factorization\:of\:}25:\quad 5\times\:5\\\mathrm{Prime\:factorization\:of\:}5:\quad 5\\\mathrm{Multiply\:each\:factor\:the\:greatest\:number\:of\:times\:it\:occurs\:in\:either\:}25\mathrm{\:or\:}5\\[/tex]
[tex]\lim_{n \to \infty} a_n =5\cdot \:5\\\\\mathrm{Multiply\:the\:numbers:}\:5\cdot \:5=25\\=25\\\mathrm{Multiply\:each\:numerator\:by\:the\:same\:amount\:needed\:to\:multiply\:its}\\\mathrm{corresponding\:denominator\:to\:turn\:it\:into\:the\:LCM}\:25\\\mathrm{For}\:\frac{2}{5}:\:\mathrm{multiply\:the\:denominator\:and\:numerator\:by\:}5\\\frac{2}{5}=\frac{2\times \:5}{5\times \:5}=\frac{10}{25}\\=\frac{9}{25}+\frac{10}{25}\\[/tex]
[tex]\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}\\=\frac{9+10}{25}\\\\=\frac{19}{25}[/tex]
Determine the points of intersection of the equation circumference x² + (y-3) ² = 25 with the coordinate axes.
Answer:
[tex] x^2 +(y-3)^2 = 25[/tex]
And we want to find the coordinate axes so then we can do the following:
If x=0 we have:
[tex] 0^2 +(y-3)^2 = 25[/tex]
[tex] (y-3)^2= 25[/tex]
[tex] y-3= \pm 5[/tex]
[tex] y_1 = 5+3=8[/tex]
[tex] y_2 = -5+3=-2[/tex]
Now of y =0 we have:
[tex] x^2 +9 = 25[/tex]
[tex] x^2 = 16[/tex]
[tex] x= \pm 4[/tex]
And then the coordinate axes are:
(4,0) (-4,0), (0,8), (0,-2)
Step-by-step explanation:
For this cae we have the following functon given:
[tex] x^2 +(y-3)^2 = 25[/tex]
And we want to find the coordinate axes so then we can do the following:
If x=0 we have:
[tex] 0^2 +(y-3)^2 = 25[/tex]
[tex] (y-3)^2= 25[/tex]
[tex] y-3= \pm 5[/tex]
[tex] y_1 = 5+3=8[/tex]
[tex] y_2 = -5+3=-2[/tex]
Now of y =0 we have:
[tex] x^2 +9 = 25[/tex]
[tex] x^2 = 16[/tex]
[tex] x= \pm 4[/tex]
And then the coordinate axes are:
(4,0) (-4,0), (0,8), (0,-2)
For the functions f(x)=2x^2+3x+9 and g(x)=−3x+10 find (f⋅g)(x) and (f⋅g)(1)
Step-by-step explanation:
f(x)=2x²+3x+9
g(x) = - 3x + 10
In order to find (f⋅g)(1) first find (f⋅g)(x)
To find (f⋅g)(x) substitute g(x) into f(x) , that's for every x in f (x) replace it by g (x)
We have
(f⋅g)(x) = 2( - 3x + 10)² + 3(- 3x + 10) + 9
Expand
(f⋅g)(x) = 2( 9x² - 60x + 100) - 9x + 30 + 9
= 18x² - 120x + 200 - 9x + 30 + 9
Group like terms
(f⋅g)(x) = 18x² - 120x - 9x + 200 + 30 + 9
(f⋅g)(x) = 18x² - 129x + 239
To find (f⋅g)(1) substitute 1 into (f⋅g)(x)
That's
(f⋅g)(1) = 18(1)² - 129(1) + 239
= 18 - 129 + 239
We have the final answer as
(f⋅g)(1) = 128Hope this helps you
What is the relationship between angle a and angle b A) Vertical Angles B) Complementary Angles C) Supplementary Angles D) None of the above
Answer:
C. Supplementary
Step-by-step explanation:
Angle a and angle b are on the line CZA.
We can assume that line CZA is a straight line, which is equal to 180 degrees.
Since angle a and b are on the straight line together, they must add to 180 degrees. Therefore, they are supplementary angles.
So, choice C. Supplementary angles is correct.
A living room is two times as long and one and one-half times as wide as a bedroom. The amount of
carpet needed for the living room is how many times greater than the amount of carpet needed for the
bedroom?
1 1/2
2
3
3 1/2
Answer:
3
Step-by-step explanation:
let's call X the length of the bedroom, Y the wide of the bedroom, A the length of the living room and B the wide of the living room
A living room is two times as long as the bedroom, so:
A = 2X
A living room is one and one-half times as wide as a bedroom, so:
B = 1.5Y
The amount of carpet needed for the living room is A*B and the amount of carpet needed by the bedroom is X*Y
So, AB in terms of XY is:
A*B = (2X)*(1.5Y) = 3(X*Y)
It means that the amount of c arpet needed for the living room is 3 times greater than the amount of carpet needed for the bedroom.