Answer: 1,953,125
This is one single value and it is just a bit under 2 million.
Or more accurately, it's a bit over 1.9 million.
===========================================================
Explanation:
a = 5 = first termr = -5 = common ratioNote that dividing any term by its previous term gets us the common ratio
r = term2/term1 = -25/5 = -5r = term3/term2 = 125/(-5) = -5The r value must stay the same the entire time, or else the sequence isn't geometric.
The nth term of any geometric sequence is a*(r)^(n-1). With the 'a' and 'r' values we found, we update that to 5(-5)^(n-1)
-----------------
To verify that is the correct nth term expression, plug in various values of n to compare it with the given sequence.
If we tried n = 2 for instance, then we find the 2nd term is
5(-5)^(n-1) = 5(-5)^(2-1) = -25
which matches what your teacher gave you. I'll let you verify the other terms.
-----------------
The last thing we need to do is plug in n = 9 and simplify
5(-5)^(n-1)
5(-5)^(9-1)
5(-5)^8
5(390625)
1,953,125 this is one single value (rather than 3 separate values)
round off to the nearest two decimal places
a) 32,369
b) 99,004
Answer:
a = 32,37
b=99
Step-by-step explanation:
a = 32,369
The third decimal place is greater (or equal) than 5, so we need to add one unit to the second place.
= 32,37
b = 99,004
The third decimal place is lesser than 5, so we can simply delete it.
= 99,00
Since only zero in every decimal places are not relevant, we can remove them:
= 99
Anyone help please ):
Answer:
1.(a) 25.3
(b) 3.49
(c) 14.44
2.(a) 86.64
(b) 59.85
(c) 27.92
3. 5.92
4.(a) 13.96
(b) 43.32
(c) 101.12
5.(a) 59.85
(b) 10.47
(c) 50.6
6. 5.56
I need help it’s confusing to me.Someone pls help
Answer:
cylinder volume= 1005.30965cm²
rectangular prism volume= 384cm²
total volume: 1005.30965+384= 1389.31cm²
Calculate the gradient of the line 2y =8x+4
Answer:
m=4
2y/2=y
8x/2=4x
4/2=2
so
y=4x+4
I need HELP PLZZZZZ!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
7 C
Step-by-step explanation:
We want to find the y value for an x value of -9
The y value for the x value of -9 is 7
Find the surface area of the rectangular prism to the nearest hundredth.
Answer:
340
Step-by-step explanation:
2(10*8)=160
2(8*5)=80
2(5*10)=100
160+80+100=340
If the integral of the product of x squared and e raised to the negative 4 times x power, dx equals the product of negative 1 over 64 times e raised to the negative 4 times x power and the quantity A times x squared plus B times x plus E, plus C , then the value of A B E is
Answer:
[tex]A + B + E = 32[/tex]
Step-by-step explanation:
Given
[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{1}{64}e^{-4x}[Ax^2 + Bx + E]C[/tex]
Required
Find [tex]A +B + E[/tex]
We have:
[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{1}{64}e^{-4x}[Ax^2 + Bx + E]C[/tex]
Using integration by parts
[tex]\int {u} \, dv = uv - \int vdu[/tex]
Where
[tex]u = x^2[/tex] and [tex]dv = e^{-4x}dx[/tex]
Solve for du (differentiate u)
[tex]du = 2x\ dx[/tex]
Solve for v (integrate dv)
[tex]v = -\frac{1}{4}e^{-4x}[/tex]
So, we have:
[tex]\int {u} \, dv = uv - \int vdu[/tex]
[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = x^2 *-\frac{1}{4}e^{-4x} - \int -\frac{1}{4}e^{-4x} 2xdx[/tex]
[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{x^2}{4}e^{-4x} - \int -\frac{1}{2}e^{-4x} xdx[/tex]
[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{x^2}{4}e^{-4x} +\frac{1}{2} \int xe^{-4x} dx[/tex]
-----------------------------------------------------------------------
Solving
[tex]\int xe^{-4x} dx[/tex]
Integration by parts
[tex]u = x[/tex] ---- [tex]du = dx[/tex]
[tex]dv = e^{-4x}dx[/tex] ---------- [tex]v = -\frac{1}{4}e^{-4x}[/tex]
So:
[tex]\int xe^{-4x} dx = -\frac{x}{4}e^{-4x} - \int -\frac{1}{4}e^{-4x}\ dx[/tex]
[tex]\int xe^{-4x} dx = -\frac{x}{4}e^{-4x} + \int e^{-4x}\ dx[/tex]
[tex]\int xe^{-4x} dx = -\frac{x}{4}e^{-4x} -\frac{1}{4}e^{-4x}[/tex]
So, we have:
[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{x^2}{4}e^{-4x} +\frac{1}{2} \int xe^{-4x} dx[/tex]
[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{x^2}{4}e^{-4x} +\frac{1}{2} [ -\frac{x}{4}e^{-4x} -\frac{1}{4}e^{-4x}][/tex]
Open bracket
[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{x^2}{4}e^{-4x} -\frac{x}{8}e^{-4x} -\frac{1}{8}e^{-4x}[/tex]
Factor out [tex]e^{-4x}[/tex]
[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = [-\frac{x^2}{4} -\frac{x}{8} -\frac{1}{8}]e^{-4x}[/tex]
Rewrite as:
[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = [-\frac{1}{4}x^2 -\frac{1}{8}x -\frac{1}{8}]e^{-4x}[/tex]
Recall that:
[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{1}{64}e^{-4x}[Ax^2 + Bx + E]C[/tex]
[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = [-\frac{1}{64}Ax^2 -\frac{1}{64} Bx -\frac{1}{64} E]Ce^{-4x}[/tex]
By comparison:
[tex]-\frac{1}{4}x^2 = -\frac{1}{64}Ax^2[/tex]
[tex]-\frac{1}{8}x = -\frac{1}{64}Bx[/tex]
[tex]-\frac{1}{8} = -\frac{1}{64}E[/tex]
Solve A, B and C
[tex]-\frac{1}{4}x^2 = -\frac{1}{64}Ax^2[/tex]
Divide by [tex]-x^2[/tex]
[tex]\frac{1}{4} = \frac{1}{64}A[/tex]
Multiply by 64
[tex]64 * \frac{1}{4} = A[/tex]
[tex]A =16[/tex]
[tex]-\frac{1}{8}x = -\frac{1}{64}Bx[/tex]
Divide by [tex]-x[/tex]
[tex]\frac{1}{8} = \frac{1}{64}B[/tex]
Multiply by 64
[tex]64 * \frac{1}{8} = \frac{1}{64}B*64[/tex]
[tex]B = 8[/tex]
[tex]-\frac{1}{8} = -\frac{1}{64}E[/tex]
Multiply by -64
[tex]-64 * -\frac{1}{8} = -\frac{1}{64}E * -64[/tex]
[tex]E = 8[/tex]
So:
[tex]A + B + E = 16 +8+8[/tex]
[tex]A + B + E = 32[/tex]
A toy manufacturer wants to know how many new toys children buy each year. A sample of 686686 children was taken to study their purchasing habits. Construct the 85%85% confidence interval for the mean number of toys purchased each year if the sample mean was found to be 6.86.8. Assume that the population standard deviation is 2.12.1. Round your answers to one decimal place.
Answer:
The 85% confidence interval for the mean number of toys purchased each year is (6.7, 6.9).
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.85}{2} = 0.075[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.075 = 0.925[/tex], so Z = 1.44.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.44\frac{2.1}{\sqrt{686}} = 0.1[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 6.8 - 0.1 = 6.7
The upper end of the interval is the sample mean added to M. So it is 6.8 + 0.1 = 6.9
The 85% confidence interval for the mean number of toys purchased each year is (6.7, 6.9).
If you rolled two dice, what is the probability
that you would roll a sum of 11?
Give your answer as a simplified fraction. Enter
the number that belongs in the green box.
second
first
1 2 3 4 5 6
1 1,1 1,2 1,3 1,4 1,5 1,6
22,1 2,2 2,3 2,4 2,5 2,6
33,1 3,2 3,3 3,4 3,5 3,6
4 4,1 4,2 4,3 4,4 4,5 4,6
55,1 5,2 5,3 5,4 5,5 5,6
6 6,1 6,2 6,3 6,4 6,5 6,6
Enter
Answer:
2/36 or 1/18 simplified
Step-by-step explanation:
you have all the combinations listed which is good.
probability = number of successful events / number of total events
look for the sums that are 11 and count them (there are 2 - 5,6 and 6,5).total the number of all events (36)so you then get the 2/36there are
Find the value of X. Please help!!!
Answer:
x = 9
Step-by-step explanation:
The triangle given is an isosceles triangle because it has two equal sides. By implication, the two base angles that are opposite the two equal sides are equal to each other.
Therefore,
80° + 2(m<2) = 180° (sum of triangle theorem)
80 + 2(5x + 5) = 180
80 + 10x + 10 = 180
Add like terms
90 + 10x = 180
90 + 10x - 90 = 180 - 90 (substraction property of equality)
10x = 90
10x/10 = 90/10 (division property of equality)
x = 9
In each figure below find m∠1 and m∠2, if a||b. Show your work with statements.
m<1=130°[alternate angle are equal again]
m<1+m<2180°[linear pair]
m<2=180°-130°
====================================
If you have any questions feel free to ask me^^
Have a nice and great day!
Cayler#PilipinasAngBayanKo
Find the area please
Answer:
[tex]area = \frac{1}{2} \times 11 \times 18 \\ = 99 \: {ft}^{2} [/tex]
Find the volume of this solid figure. Use π = 3.14.
WITH SOLUTION PLEASE AND NO LINKS!
Answer:
180
Step-by-step explanation:
volume= (6*5)/2*12 =180 in
How to find the value of x round to the nearest tenth for a triangle if one side is 15ft and the other is 13ft
Answer:
C = 19.9 ft
Step-by-step explanation:
Your question isn't properly constructed. However, I'll attempt in providing a possible way of finding one of the sides of a given triangle.
Generally, the Pythagorean theorem is used to find the side of a triangle when two of its sides are known or provided.
Assuming the following data;
Let the length of sides of the triangle be;
Opposite side = a = 15 ft
Adjacent side = b = 13 ft
Hypotenuse side = c
From Pythagorean theorem;
Mathematically, Pythagorean theorem is given by the formula;
C² = a² + b²
C² = 15² + 13²
C² = 225 + 169
C² = 394
Taking the square root of both sides, we have;
C = √394
C = 19.9 ft
I’m confused. Can someone help? Please and thank you so much!
Answer:
Root of 65
Step-by-step explanation:
8^2 is equal to 64, so the sqrt of 64 would equal 8 exactly. The question is asking for which of the sqrts would be closest to 8, so sqrt of 65 is the number that is closest to 64, so it is the answer.
Answer:
[tex] \sqrt{65} [/tex]
as
[tex] \sqrt{64} = 8[/tex]
so it's the closest value to 8
and also
[tex] \sqrt{65} = 8.06[/tex]
via calculator
Bill Board is "lording" his SAT score over his friend, Rhoda Dendron, who took the ACT. "You only got a 25 in math," he chortled, "while I got a 300 in math." Given that the SAT has a μ of 500 and a σ of 100, and the ACT has a μ of 20 and a σ of 5, what is wrong with Bill’s logic (give the answer in both z scores and percentile ranks).
Answer:
Rhoda, whose ACT has a z-score of 1, scored in the 84th percentile in the ACT, compared to Bill, whose SAT has a z-score of -2, who scored in the 2nd percentile on the SAT. Due to the higher percentile(higher z-score) on her test, Rhoda did better on her respective test than Bill, and thus, his logic is wrong.
Step-by-step explanation:
Z-score:
In a set 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]
The Z-score 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. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Bill:
Scored 300, so [tex]X = 300[/tex]
SAT has a μ of 500 and a σ of 100.
His z-score is:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{300 - 500}{100}[/tex]
[tex]Z = -2[/tex]
[tex]Z = -2[/tex] has a p-value of 0.02.
This means that Bill, whose SAT score has Z = -2, scored in the 2nd percentile.
Rhoda
Scored 25, so [tex]X = 25[/tex].
ACT has a μ of 20 and a σ of 5
Her z-score:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{25 - 20}{5}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a p-value of 0.84
This means that Rhoda, whose ACT score has Z = 1, scored in the 84th percentile.
What is wrong with Bill’s logic ?
Rhoda, whose ACT has a z-score of 1, scored in the 84th percentile in the ACT, compared to Bill, whose SAT has a z-score of -2, who scored in the 2nd percentile on the SAT. Due to the higher percentile(higher z-score) on her test, Rhoda did better on her respective test than Bill, and thus, his logic is wrong.
Mary makes trail mix with bulk nuts and dried fruit. She spends $4.50 on the dried fruit. Mixed nuts cost $2.50 per pound. She has a total of $12 to spend. What are the possible number of pounds of nuts she can buy?
Answer: 3 pounds
Step-by-step explanation: 12 - 4.50 = 7.50 7.50/2.50=3
Find the length of side y.
y=_ft
Answer:
x= 0.22947
Step-by-step explanation:
Step-by-step explanation:
x=0 22 im not sure though ok
Which of the following statements is equivalent to 28 + 16?
Answer:
You need to show the statements or I can't help.
Someone please help me
Answer:
48
Step-by-step explanation: 1 foot is 12 inches. Since the feet are going up by ones, you can say 1=12, 2=24 (+12), 3=36(+12), 4=48(+12)
Hope this helps
Answer and Step-by-step explanation:
The answer is 48.
Each value of y is a multiple of 12, so for when there is 4 feet, you multiply 12 by 4 to get 48.
For when it is 1 foot, you multiply 12 by 1 to get 12.
For when it is 2 feet, you multiply 12 by 2 to get 24.
For when it is 3 feet, you multiply 12 by 3 to get 36
For when it is 5 feet, you multiply 12 by 5 to get 60.
If you were to continue, the y-values (aka the inches) will always be a multiple of 12.
#teamtrees #PAW (Plant And Water)
Cuale es la distancia entre dos puntos (6,-7)(-2,8)
Answer:
17
Step-by-step explanation:
Use the distance formula to determine the distance between the two points.
[tex]d = \sqrt{(x_{2} -x_{1})^{2} + (y_{2} - x_{1})^{2} }[/tex]
d = distance
[tex](x_{1}, y_{1})[/tex] = coordinates of the first point
[tex](x_{2}, y_{2})[/tex] = coordinates of the second point
Answer: The distance between the points (6,-7)(-2,8) is 17.
Step-by-step explanation:
To calculate the distance between two points, we apply the following formula:
[tex]\boldsymbol{\sf{d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2 } }}[/tex]
The points are:
(x₁, y₁) = 6, -7(x₂, y₂) = -2. 8We substitute in the formula and solve:
[tex]\boldsymbol{\sf{d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2 } }}\\ \\ \boldsymbol{\sf{d=\sqrt{(-2-6)^2+(8-(-7))^2 } }}\\ \\ \boldsymbol{\sf{d=\sqrt{(-8)^2+15^2}=\sqrt{64+225 } }}\\ \\ \boldsymbol{\sf{d=\sqrt{289}=17 }}[/tex]
The distance between the points (6,-7)(-2,8) is 17.
Sarah jogged 4.8 miles each day for 22 days last month. How many miles did Sarah jog in total?
Answer:
105.6
hope this helps
have a good day :)
Step-by-step explanation:
Which graph is a function of x?
Answer:
A vertical line through the origin
Step-by-step explanation:
Find the range of the data.
Answer:
7.3
Step-by-step explanation:
Biggest value = 8.9
smallest value = 1.6
range = 8.9-1.6 = 7.3
Step-by-step explanation:
range=highest number - lowest number
= 8.9 - 1.6
=7.3
A boy is flying two kites at the same time. He has 450 ft of line out to one kite and 390 ft to the other. He estimates the angle between the two lines to be 34 degrees. Approximate the distance between the kites.
Answer:
[tex]C=252.2ft[/tex]
Step-by-step explanation:
From the question we are told that:
First Kite Distance [tex]A=450ft[/tex]
Second Kite Distance [tex]B=390ft[/tex]
Angle [tex]\theta=34\textdegree[/tex]
Generally the equation for Distance X between the kites is mathematically given by
Using Cosine Rule
[tex]C^2=A^2+B^2-2abCos \theta[/tex]
Therefore
[tex]C^2=(450)^2+(390)^2-2(450)(390)Cos 34[/tex]
[tex]C^2=63607.81[/tex]
[tex]C=\sqrt(63607.81)[/tex]
[tex]C=252.2ft[/tex]
I need the answer or work this either pass or fail please !
Step-by-step explanation:
DAG = DG
120=120°
DHG + DG =360°
DHG +120° =360°
DHG+120°-120°=360°-120°
DHG°=240°
Instructor Vallejo is trying to figure out the percentage of students that still listen to The Doors. Instructor Vallejo
is pretty out of touch, so he doesn't have a prior percentage of students who listen to The Doors that he can use.
How many students should instructor Vallejo sample if he wants to be within 11% of the actual percentage of
students who listen to The Doors with a 82% confidence level.
Answer:
N=115
Step-by-step explanation:
n=.25(2.5715/.12)^2 =114.8 so round up to 115. Hope that help you
help pleaseee geometryyy
Step-by-step explanation:
angle ABE=angle EBC
2x+20=4x-620+6=4x-2xx=26/2X=13stay safe healthy and happy.Plz help me well mark brainliest if correct........????
Answer:
A) John
stay safe healthy and happy...Answer:
john
Step-by-step explanation:
4(-8x + 5) = -32.x - 26
solve the equation
Answer:
-46
Step-by-step explanation:
4(-8x + 5) = -32x - 26
-32x + 20 = -32x - 26
-32x + 32x = -26 - 20
x = -46
Answer:
-32x+20=-32x-26
20=-26
so unequal or undefined
hope this helps
have a good day :)
Step-by-step explanation: