Step-by-step explanation:
you cannot just put the actual numbers in and calculate ?
and you can't provide the correct problem statement, as it seems.
I assume you mean
an = 3n² - 1
a sequence starts with a1, so, n>=1
a1 = 3×1² - 1 = 3-1 = 2
a2 = 3×2² -1 = 3×4 - 1 = 12 - 1 = 11
a3 = 3×3² - 1 = 3×9 - 1 = 27 - 1 = 26
a4 = 3×4² - 1 = 3×16 - 1 = 48 - 1 = 47
a5 = 3×5² - 1 = 3×25 - 1 = 75 - 1 = 74
there, that is all there is to it. you really needed help with that ?
[tex]-3x^{2} -4y^{2} -z^{2}+6xy-6x+4z[/tex]
Based on a random sample of 50, a 95% confidence interval for the population proportion was computed. Holding everything else constant, which of the following will reduce the length of the confidence interval by half? (CHECK ALL THAT APPLY): A. Quadruple the sample size. B. Change the confidence level to 68%. C. Double the sample size. D. Change the confidence level to 99.7%. E. Decrease the sample proportion by half.
The length of the confidence interval is the margin of error, which is the ratio of the standard deviation and the square root of sample size. Hence, to reduce the length of confidence interval by half, Quadruple the sample size.
Recall :
Margin of Error = σ/√nEvaluating an hypothetical scenario :
Let standard deviation, σ = 2
Sample size = 50
Margin of Error = 2/√50 = 0.554
Using Quadruple of the sample size : (50 × 4) = 200 samples
Margin of Error = 2/√200 = 0.277(0.227 ÷ 0.554) = 0.5
Therefore, increasing the sample size, reduces the margin of error. Hence, using quadruple the sample size, will reduce the margin of error by half.
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it would take 15 men 8 days to dig a trench 240 m long find how many days less it would take 18 men to dig a trench 360m long working at the same rate
Answer:
24 men will take 3 days to dig a 72 meter trench.
Step-by-step explanation:
If 16 workers dig an 80-meter long trench in five days, how long will it take 24 workers to dig a 72-meter long trench?
If 16 workers take 5 days to dig an 80 meter long trench,
24 workers will definitely take lesser time to dig a 72 meter long trench as both the length of the trench and the number of workers is more
Lets write these values down in order: Number of Workers, Length of Trench, Number of Days:
16 80 5
24 72 ?
Lets represent the ? as x:
We know that Ratio of Trench length to men = 80/16 : 72/24 or 5 : 3
Which means that the first set (16 men) will take 5 days to dig a trench of 80 meters.
And therefore from the above ratio (5: 3), 24 men will take 3 days to dig a 72 meter trench.
HOPE IT WILL DEFINITELY HELP YOU
Suppose that 25% of people own dogs If you pick three people at random, what
is the probability that they all three own a dog? (Let me add that we don’t know the
populations size so calculate the probability as if the population is infinite.)
Answer:
1/64
Step-by-step explanation:
25% own a dog, so picking one person has a probability of 1/4 (0.25) for that person to own a dog.
picking 3 people means combining (multiplying) the probabilities of the non-overlapping and non-depending events.
picking the third person has 1/4 chance of owning a dog (as the population is "infinite") combined with the chance that also the second pick owned a dog, which has to be combined with the chance of the first pick owning a dog.
so,
1/4 × 1/4 × 1/4 = 1/4³ = 1/64 = 0.015625
CAN YOU GUYS PLEASE HELP ME? THANK YOU!
Answer:
60
step by step explanitation
Help!!????
Please!!!????
Answer:
true
mark me brainist if it comes out to be true
Answer:
The answer is TRUE.
Step-by-step explanation:
Please Help!
What is the locus of the midpoints of all chords that can be drawn from a given point on a circle with a radius of 6.
The locus of the midpoints of all chords that can be drawn from a given fixed point [tex](a,b)[/tex] on a circle with a radius of 6 units, is a circle of radius 3 units with center at a point whose x & y coordinates are shifted from the center of the given circle by [tex]\frac{a}{2}[/tex] and [tex]\frac{b}{2}[/tex] respectively.
Given: A circle of radius 6 units
To find: The locus of the midpoint of all chords that can be drawn from a given point on the circle.
To find the required locus, we need to know the following:
Locus of a moving point is the trajectory of that point. It is the geometrical figure represented by the equation which is satisfied by the coordinates of the moving point.A chord of a circle is a line segment joining any points of a circle.Equation of a circle with center at origin and radius of [tex]r[/tex] units is [tex]x^{2} +y^{2} =r^{2}[/tex] According to the midpoint formula, the coordinates of the midpoint of the line segment joining the points [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] is [tex](\frac{x_{1}+x_{2} }{2} ,\frac{y_{1}+y_{2} }{2} )[/tex]Let, without loss of generality, the given circle be centered at the origin. Even if it is not, we can shift the origin to the center of the given circle with coordinate transformation.
Then, the equation of the given circle is [tex]x^{2}+y^{2} =6^{2}[/tex], that is, [tex]x^{2}+y^{2} = 36[/tex]
Let the coordinates of the given fixed point be [tex](a,b)[/tex]
Let the coordinates of any point on the circle be [tex](p,q)[/tex] and let the coordinates of the midpoint of the chord joining the points [tex](a,b)[/tex] and [tex](p,q)[/tex] be [tex](h,k)[/tex]
We have to find the locus of [tex](h,k)[/tex]
Then, using the midpoint formula,
[tex](h,k)=(\frac{a+p}{2} ,\frac{b+q}{2})[/tex]
On solving, we get,
[tex]p=2h-a,q=2k-b[/tex]
Since [tex](a,b)[/tex] and [tex](p,q)[/tex] are both points on the given circle, they satisfy the equation of the circle, [tex]x^{2}+y^{2} = 36[/tex]
Then,
[tex]a^{2} +b^{2} =36[/tex]
[tex]p^{2} +q^{2} =36[/tex]
Substituting [tex]p=2h-a,q=2k-b[/tex] in [tex]p^{2} +q^{2} =36[/tex], we have,
[tex](2h-a)^{2} +(2k-b)^{2} =36[/tex]
[tex](2(h-\frac{a}{2}) )^{2} +(2(k-\frac{b}{2}))^{2} =36[/tex]
[tex]4(h-\frac{a}{2})^{2} +4(k-\frac{b}{2})^{2} =36[/tex]
[tex](h-\frac{a}{2})^{2} +(k-\frac{b}{2})^{2} =\frac{36}{4}[/tex]
[tex](h-\frac{a}{2})^{2} +(k-\frac{b}{2})^{2} =9[/tex]
[tex](h-\frac{a}{2})^{2} +(k-\frac{b}{2})^{2} =3^{2}[/tex]
This is the locus of the point [tex](h,k)[/tex]
Replace [tex](h,k)=(x,y)[/tex] to get,
[tex](x-\frac{a}{2})^{2} +(y-\frac{b}{2})^{2} =3^{2}[/tex]
This is the equation of a circle with center at [tex](\frac{a}{2} ,\frac{b}{2} )[/tex] and radius 3 units.
Thus, we can conclude that the locus of the midpoints of all chords that can be drawn from a given fixed point [tex](a,b)[/tex] on a circle with a radius of 6 units, is a circle of radius 3 units with center at a point whose x & y coordinates are shifted from the center of the given circle by [tex]\frac{a}{2}[/tex] and [tex]\frac{b}{2}[/tex] respectively.
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Find the area of the shaded part !
Answer:
Step-by-step explanation:
Semicircle:
Shaded area of semicircle = area of outer semicircle - area of inner semicircle
Outer semicircle:
d = 40 m r = 40/2 = 20m
Area of outer semicircle = πr²
= 3.14*20*20
= 1256 m²
Inner semicircle:
d = 30 m r = 30/2 = 15 m
Area of outer semicircle = πr²
= 3.14*15*15
= 706.5 m²
Shaded area of semicircle = 1256 - 706.5 = 549.5 m²
Shaded area of semicircle in both sides = 2 * 549.5 = 1099 m²
Rectangle on both sides:
Length = 50 m
width = 30 m
Area of shaded rectangles on both sides = 2* (length *width)
= 2* 50 * 30
= 3000 m²
Shaded area = 1099 + 3000 = 4099 m²
A clothing manufacturer purchased 50 yd of cotton and 80 yd of wool for a total cost of $1,330. Another purchase, at the same prices, included 75 yd of cotton and 20 yd of wool for a total cost of $895. Find the cost per yard of the cotton and of the wool.
Answer:
The cotton is $9 per yard and the wool is $11 per yard
Step-by-step explanation:
Create a system of equations where c is the cost per yard for the cotton and w is the cost per yard for the wool.
50c + 80w = 1330
75c + 20w = 895
Solve by elimination by multiplying the bottom equation by -4:
50c + 80w = 1330
-300c - 80w = -3580
Add these together and solve for c:
-250c = -2250
c = 9
Plug in 9 as c into one of the equations, and solve for w:
50c + 80w = 1330
50(9) + 80w = 1330
450 + 80w = 1330
80w = 880
w = 11
The cotton is $9 per yard and the wool is $11 per yard.
The equation of a parabola in standard form is
y = mx + b
y = mx2 + b
y = ax2 + bx + c
y = a(x - h)2 +k
Answer: y = ax2 + bx + c
looks like a slightly trick question...
y = ax2 + bx + c is the standard form...
y = a(x - h)2 +k is the graphing form
Step-by-step explanation:
Angle Sum Theorem Acellus
20 120 y = ?
We know
Sum of two interior angles=exterior angle
[tex]\\ \sf\longmapsto 20°+120°=<y[/tex]
[tex]\\ \sf\longmapsto <y=20°+120°[/tex]
[tex]\\ \sf\longmapsto <y=140°[/tex]
Hope it helps
I'm not sure how to do this
Answer:
1 and 5 sevenths of a bag
Step-by-step explanation:
2/7 males half to it takes 4/7 to make a full one multiply 4 by 3 and you get 12/7 so that makes 1 and 5/7
An equal number of juniors and seniors are trying out for six spots in this year's decathlon
team. If the team must consist of four seniors and two juniors, then how many different
possible decathlon teams could result if five juniors try out?
50
55
75
100
There are 50 different possible debating teams that could be selected as obtained using COMBINATION.
Since there are EQUAL number of juniors and seniors ;
Then we have 5 of each.
Here, the order of arrangement DOES NOT matter, Hence, we use COMBINATION
since the team MUST contain 4 SENIORS and 2 JUNIORS
4 Seniors from 5 = 5C4 = 5
2 Juniors from 5 = 5C2 = 10
Hence, (5C4 * 5C2) = 5 * 10 = 50
Hence, there are 50 different possible debating teams that could be selected.
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My friend needs help on this sorry!
A group of 6 children and 6 adults are going to the zoo. Child tickets cost $10, and adult tickets cost $14. How much will the zoo tickets cost in all?
9514 1404 393
Answer:
$144
Step-by-step explanation:
Multiplication is used to simplify repeated addition. To find the total cost, add up the costs of each of the tickets.
6 child tickets will cost $10 +10 +10 +10 +10 +10 = 6×$10 = $60
6 adult tickets will cost $14 +14 +14 +14 +14 +14 = 6×$14 = $84
Then the total cost of all of these tickets will be ...
$60 +84 = $144 . . . . cost of zoo tickets in all
Complete the table. Round your entries to the
nearest thousandth.
a
b
C
dz
ex
ASAP
a=2,5937
b=2,7048
c=2,7181
d=2,7183
e=2,7183
If total sales are $54000 your food service total is 42% of your total sales what is your dollar target for food service
Answer:
Your dollar target for food service is $22,680
Step-by-step explanation:
It is given in the question that total sales are = $54,000
your food service is 42% of your total sales = 42% × $54,000
= × 54,000
= 0.42 × 54,000
= $22,680
Hi friends,
Please assist with my question below.
In a right angle triangle, an angle of 30 degrees has an adjacent side which measures 17 cm. what is the length of its hypotenuse?
Answer : 19.6cm
I hope this helps you! Have a good day!
Identify the most relevant source of bias in this situation: A study seeks to investigate whether a new pain medication is safe to market to the public. They test by randomly selecting 300 men from a set of volunteers.
Answer:
The bias is they only picked men to test the new medication on to see if it was ready for the general public to use.
Step-by-step explanation:
in how many ways 6 gentleman and 4 ladies can be choosen out of 10 gentleman and 8 ladies?
Answer:
5880 ways
Step-by-step explanation:
For selections like this, we solve using the combination theory. Recall that
nCr = n!/(n-r)!r!
Hence given to find the number of ways 6 gentleman and 4 ladies can be choosen out of 10 gentleman and 8 ladies,
= 10C6 * 8C4
= 10!/(10-6)!6! * 8!/(8-6)!6!
= 10 * 9 * 8 * 7 * 6!/4 *3 *2 * 6! * 8 * 7 * 6!/2 * 6!
= 210 * 28
= 5880 ways
The arrangement can be done in 5880 ways
$26,876 is invested, part at 9% and the rest at 5%. If the interest earned from the amount invested at 9% exceeds the interest earned from the amount invested at 5% by $720.78, how much is invested at each rate? (Round to two decimal places if necessary.)
9514 1404 393
Answer:
$14,747 at 9%$12,129 at 5%Step-by-step explanation:
Let x represent the amount invested at 9%. Then the difference in interest amounts is ...
(9%)x -(5%)(26876 -x) = 720.78 . . . . . assuming a 1-year investment
0.14x -1343.80 = 720.78 . . . . . . . . . simplify
0.14x = 2064.58 . . . . . . . . . . . . . . add 1343.80
x = 14,747 . . . . . . . . . . . . . . . . divide by 0.14
$14,747 is invested at 9%; $12,129 is invested at 5%.
Please help.........
Answer:
a
Step-by-step explanation:
The sum of 3 times a number and 7 is equal to 2. Turn into an equation
Write the English phrase as an algebraic expression. Then simplify the expression. Let x represent the number. Six times the sun of 4 and a number
Answer:
6x + 24
Step-by-step explanation:
6 * (4 + x) = 6 * 4 + 6 * x = 6x + 24
A few more problems and then I’m done
Answer:
((c)).g(x) = 3 × 2^x +2..
help everyone!!!!!!..........
Answer:
a-648²
b-4.2²
Step-by-step explanation:
least 108*48 = 648²
Tìm vi phân toàn phần của các hàm số sau:
ln(x+√(x^2+y^2 ) ) ln(sin(y/x))
Let f = ln(x + √(x ² + y ²)) ln(sin(y/x)).
Then the total differential is
[tex]\mathrm df = \dfrac{\mathrm d\left(x+\sqrt{x^2+y^2}\right)}{x+\sqrt{x^2+y^2}}\ln\left(\sin\left(\dfrac yx\right)\right) + \ln\left(x+\sqrt{x^2+y^2}\right)\dfrac{\mathrm d\left(\sin\left(\frac yx\right)\right)}{\sin\left(\frac yx\right)}[/tex]
[tex]\mathrm df = \dfrac{\mathrm dx + \frac{\mathrm d(x^2+y^2)}{\sqrt{x^2+y^2}}}{x+\sqrt{x^2+y^2}}\ln\left(\sin\left(\dfrac yx\right)\right) + \ln\left(x+\sqrt{x^2+y^2}\right)\dfrac{\cos\left(\frac yx\right)\,\mathrm d\left(\frac yx\right)}{\sin\left(\frac yx\right)}[/tex]
[tex]\mathrm df = \dfrac{\mathrm dx + \frac{2x\,\mathrm dx+2y\,\mathrm dy}{\sqrt{x^2+y^2}}}{x+\sqrt{x^2+y^2}\right)\ln\left(\sin\left(\dfrac yx\right)\right) + \ln\left(x+\sqrt{x^2+y^2}}\right)\dfrac{\cos\left(\frac yx\right)\frac{x\,\mathrm dy-y\,\mathrm dx}{x^2}}{\sin\left(\frac yx\right)}[/tex]
[tex]\mathrm df = \dfrac{\left(2x+\sqrt{x^2+y^2}\right)\,\mathrm dx +2y\,\mathrm dy}{x\sqrt{x^2+y^2}+x^2+y^2\right)\ln\left(\sin\left(\dfrac yx\right)\right) \\\\ \indent + \dfrac1{x^2}\cot\left(\dfrac yx\right)\ln\left(x+\sqrt{x^2+y^2}}\right)(x\,\mathrm dy-y\,\mathrm dx)[/tex]
[tex]\mathrm df = \left(\left(\dfrac{2x+\sqrt{x^2+y^2}}{x\sqrt{x^2+y^2}+x^2+y^2}\right)\ln\left(\sin\left(\dfrac yx\right)\right) - \dfrac y{x^2}\cot\left(\dfrac yx\right)\ln\left(x+\sqrt{x^2+y^2}\right)\right)\,\mathrm dx \\\\ \indent + \left(\dfrac{2y}{x\sqrt{x^2+y^2}+x^2+y^2}\ln\left(\sin\left(\dfrac yx\right)\right)+\dfrac1x\cot\left(\dfrac yx\right)\ln\left(x+\sqrt{x^2+y^2}\right)\right)\,\mathrm dy[/tex]
Find the missing segment in the image below
Answer:
x = 42
Step-by-step explanation:
24+8 = 32
[tex]\frac{x}{24}[/tex] = [tex]\frac{x+14}{32}[/tex]
32x = 24(x+14)
32x = 24x+336
8x = 336
x = 42
If you were asked to measure the success of a campaign to fight for human rights, what criteria would you use?
Step-by-step explanation:
Many factors would be used to assess the effectiveness of a human rights campaign, including the following:
Social Influence. Direct Interpersonal Reach. Participant Observation. Reputation. Volume of Search & Interest. Website Traffic.
National Research.
In the graph above, which vertical line (V) and horizontal line (H) can be used to graph point A?
A)
V: x = 1; H: y = 4
B)
V: x = 4; H: y = 1
C)
V: y = 4; H: x = 1
D)
V: x = 1; H: y = –4
Answer:
V: x = 1; H: y = 4
Step-by-step explanation:
Point A is at x = 1 and y = 4
A vertical line at x=1 and a horizontal line at y = 4
SCALCET8 4.7.011. Consider the following problem: A farmer with 950 ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle. What is the largest possible total area of the four pens
Answer:
For any rectangle, the one with the largest area will be the one whose dimensions are as close to a square as possible.
However, the dividers change the process to find this maximum somewhat.
Letting x represent two sides of the rectangle and the 3 parallel dividers, we have 2x+3x = 5x.
Letting y represent the other two sides of the rectangle, we have 2y.
We know that 2y + 5x = 750.
Solving for y, we first subtract 5x from each side:
2y + 5x - 5x = 750 - 5x
2y = - 5x + 750
Next we divide both sides by 2:
2y/2 = - 5x/2 + 750/2
y = - 2.5x + 375
We know that the area of a rectangle is given by
A = lw, where l is the length and w is the width. In this rectangle, one dimension is x and the other is y, making the area
A = xy
Substituting the expression for y we just found above, we have
A = x (-2.5x+375)
A = - 2.5x² + 375x
This is a quadratic equation, with values a = - 2.5, b = 375 and c = 0.
To find the maximum, we will find the vertex. First we find the axis of symmetry, using the equation
x = - b/2a
x = - 375/2 (-2.5) = - 375/-5 = 75
Substituting this back in place of every x in our area equation, we have
A = - 2.5x² + 375x
A = - 2.5 (75) ² + 375 (75) = - 2.5 (5625) + 28125 = - 14062.5 + 28125 = 14062.5
Step-by-step explanation:
