Answers
Answer: a12 = 1/5120
Step-by-step explanation:
geometric sequence formula: an = a1*r^(n-1)
a1 = 2/5, r= 1/2, n= 12
a12 = 2/5*r^11
a12 = 2/5*1/2048
a12 = 1/5120
Related Questions
the teacher has a small class with only 7 students. the teacher grades their homework and reports scores of: 10, 7, 8, 12, 9, 11, and 13. what is the median?
Answers
Answer:
10
Step-by-step explanation:
To find the median in a set of data, organize the data from least to greatest.
Here, our data is the homework scores, those being:
10, 7, 8, 12, 9, 11, 13
Let's organize them in ascending order, like so:
7, 8, 9, 10, 11, 12, 13
The next step in finding the median is figuring out which number is in the middle. Since the amount of data we have is an odd number (7), there will be only one number in the middle.
We can find that the number in the middle is 10.
Thus, the median of the scores is 10.
Question 3 Let X1, X2,..., Xn be independent random variables, each having a uniform distri- bution over (0,1). Let M = maximum (X₁, X₂,..., Xn). Show that the distribution function of M, FM(-), is given by FM(x)=x, 0≤x≤1 What is the probability density function of M?
Answers
The distribution function of M, FM(-), is given by FM(x) = x, 0 ≤ x ≤ 1.
The probability density function of M is\(fM(x) = n * x^(^n^-^1^)\), 0 ≤ x ≤ 1.
In order to understand the distribution function of M, we need to consider the probability that M is less than or equal to a given value x. Since each Xi is uniformly distributed over (0,1), the probability that Xi is less than or equal to x is x.
For M to be less than or equal to x, all of the random variables Xi must be less than or equal to x. Since these variables are independent, their joint probability is the product of their individual probabilities. Therefore, the probability that M is less than or equal to x can be expressed as the product of n x's: P(M ≤ x) = x * x * ... * x = \(x^n\).
The distribution function FM(x) is defined as the probability that M is less than or equal to x. Therefore, FM(x) = P(M ≤ x) = \(x^n\).
To find the probability density function (PDF) of M, we differentiate the distribution function FM(x) with respect to x. Taking the derivative of \(x^n\)with respect to x gives us \(n * x^(^n^-^1^)\). Since the range of M is (0,1), the PDF is defined only within this range.
The distribution function of M is FM(x) = x, 0 ≤ x ≤ 1, and the probability density function of M is \(fM(x) = n * x^(^n^-^1^)\), 0 ≤ x ≤ 1.
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i need help with what is x 4x=20
Answers
Answer:
5
Step-by-step explanation:
You are looking for x so what you are really looking for is what times 4 =20 and that is 5.
5x4=20
Answer:
Divide each term in 4x = 20 by 4 and simplify.
X=5
4 units to the left of -4 is
Answers
Answer:
-8
Step-by-step explanation:
If you were to do integer operations, then this question algebraically would mean -4-4=-8 because going to the left on a number line is meaning subtraction/negative and going to the right is addition/positve!
Therefore, the answer is -8 :)
You purchase an 11 3/8s february $10,000 par treasury note at 103:11 and hold it for exactly one year at which time you sell it. what is your rate of return if your selling price is 100:13?
Answers
Based on the fact that you bought the treasury note at 103.11 and sold it for 100.13, your rate of return is -2.89%
What is the rate of return?The rate of return on the treasury note can be found as:
= (Selling price - Buying price) / Buying price x 100%
Solving gives:
= (100.13 - 103.11) / 103.11 x 100%
= -2.98/ 103.11 x 100%
= -2.89%
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use the laplace transform to solve the given integral equation. f(t) + t (t − τ)f(τ)dτ 0 = t
Answers
f(t) = L^(-1){1 / (s^2 + s)} Inverse Laplace transform tables or techniques, determine the time-domain function f(t) that satisfies the given integral equation.
The Laplace transform is a powerful mathematical tool that can be used to solve complex integral equations, like the one you've provided: f(t) + t * ∫(t - τ)f(τ)dτ = t.
To solve this equation using the Laplace transform, follow these steps:
1. Apply the Laplace transform to both sides of the equation. The Laplace transform of f(t) is F(s), and the Laplace transform of t is 1/s^2. The integral equation becomes:
L{f(t)} + L{t * ∫(t - τ)f(τ)dτ} = L{t}
F(s) + L{t * ∫(t - τ)f(τ)dτ} = 1/s^2
2. Next, apply the convolution theorem to the integral term. The convolution theorem states that L{f(t) * g(t)} = F(s) * G(s). In this case, f(t) = t and g(t) = (t - τ)f(τ):
F(s) + L{t} * L{(t - τ)f(τ)} = 1/s^2
3. Now, substitute the known Laplace transforms for t and f(t):
F(s) + (1/s^2) * F(s) = 1/s^2
4. Combine the terms containing F(s):
F(s) * (1 + 1/s^2) = 1/s^2
5. Isolate F(s) by dividing both sides of the equation by (1 + 1/s^2):
F(s) = (1/s^2) / (1 + 1/s^2)
6. Simplify the expression for F(s):
F(s) = 1 / (s^2 + s)
7. Finally, apply the inverse Laplace transform to F(s) to obtain the solution for f(t):
f(t) = L^(-1){1 / (s^2 + s)}
Using inverse Laplace transform tables or techniques, you can determine the time-domain function f(t) that satisfies the given integral equation.
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Jose earned 45 points in a video game. He lost 40 points, earned 80 points, then lost 25 more points. Enter and evaluate an expression to find his final score in the video game.
im confused any help?
Answers
Answer:
60 points
Step-by-step explanation:
Every time he earns points we add.
Every time he loses points we subtract.
We can write an equation to resemble the problem and simplify.
45 - 40 + 80 - 25
5 + 80 - 25
85 - 25
60
Best of Luck!
discriminate of 2x2 – 9x + 2 = –1
Answers
Answer:
The discriminant is less than 0, so there are two complex roots.
Step-by-step explanation: i think
Let X
=
A
.
¯¯¯¯¯¯
B
C
. Evaluate X for
(a) A
=
1
,
B
=
0
,
C
=
1
, (b) A = B = C = 1 and ( c) A = B = C = 0.
Answers
The given expressions, when A=1, B=0, and C=1, X evaluates to 1.001; when A=B=C=1, X evaluates to 1.111; and when A=B=C=0, X evaluates to 0.000. These evaluations are based on the given values of A, B, and C, and the notation ¯¯¯¯¯¯BC represents the complement of BC.
To evaluate the expression X = A.¯¯¯¯¯¯BC, we substitute the given values of A, B, and C into the expression.
(a) For A = 1, B = 0, and C = 1:
X = 1.¯¯¯¯¯¯01
To find the complement of BC, we replace B = 0 and C = 1 with their complements:
X = 1.¯¯¯¯¯¯01 = 1.¯¯¯¯¯¯00 = 1.001
(b) For A = B = C = 1:
X = 1.¯¯¯¯¯¯11
Similarly, we find the complement of BC by replacing B = 1 and C = 1 with their complements:
X = 1.¯¯¯¯¯¯11 = 1.¯¯¯¯¯¯00 = 1.111
(c) For A = B = C = 0:
X = 0.¯¯¯¯¯¯00
Again, we find the complement of BC by replacing B = 0 and C = 0 with their complements:
X = 0.¯¯¯¯¯¯00 = 0.¯¯¯¯¯¯11 = 0.000
In conclusion, when A = 1, B = 0, and C = 1, X evaluates to 1.001. When A = B = C = 1, X evaluates to 1.111. And when A = B = C = 0, X evaluates to 0.000. The evaluation of X is based on substituting the given values into the expression A.¯¯¯¯¯¯BC and finding the complement of BC in each case.
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an airplane descends 2.2 miles to an elevation of 5.95 miles. find the elevation of the plane before its descent.
Answers
Answer:
8.15 miles
Step-by-step explanation:
5.95+2.2=8.15
For the equation 5x+4y=20, (a) write it in slope-intercept form, (b) give the slope of the line, (c) give the y-intercept, and (d) graph the line. (c) The y-intercept is (Type an ordered pair, using integers or fractions.)
Answers
Considering the definition of a line, the slope-intercept form of the line is y= -5/4x + 5, where the slope is -5/4, the y-intercept is 5 and the graph is attached.
Definition of a linear equationA linear equation o line can be expressed in the slope-intercept form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin or y-intercept and represents the coordinate of the point where the line crosses the y axis.Line in this caseIn this case, the line is 5x+4y=20. Expressed in the slope-intercept form, you get:
4y=20 - 5x
y= (-5x +20)÷ 4
y= -5/4x + 5
where:
The slope is -5/4.The y-intercept is 5.The graph of the line is attached.
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What is the difference between the area of the larger circle in the area of the smaller circle leave your answer in terms of pi
Answers
Answer:
Area= π(R^2-r^2)
Step-by-step explanation:
Although I can't find the attached file
Let the radius of the large circle be R
And the radius of the small circle be r
Area of large circle is
Area= πR^2
Area of small circle is
Area= πr^2
The difference is
Area= πR^2- πr^2
Area= π(R^2-r^2)
Find the DISTANCE between (-4,5) and (3,-9) to the nearest TENTH.
Answers
Answer:
The answer is 15.7.
Step-by-step explanation:
The growth of a new strain of bacteria is represented by y = 79.31(1.48),
where x represents the number of days and y represents the number of
bacteria. Which is the best prediction for the number of bacteria on day 6?
O A. 833 bacteria
O B. 647 bacteria
O C. 117 bacteria
O D. 704 bacteria
Answers
Answer:
A
Step-by-step explanation:
y = 79.31(1.48)^6
y=833.84
Suppose you buy five boxes of cereal. In each box is a picture of a famous athlete. 20% of the cereal boxes contain Michael Phelps, 30% Lamar Jackson, and the rest Elena Delle Donne. Estimate the probability that you end up with a complete set of the pictures. a. Explain how you would use randomly generated numbers to model the likelihood that you end up with a complete set of pictures. (2 po
Answers
Estimate the probability of obtaining a complete set of pictures, randomly generated numbers can be used to simulate the process of selecting cereal boxes. By repeating this simulation multiple times, we can calculate the proportion of times a complete set is obtained and use it as an estimate of the probability.
To model the likelihood of obtaining a complete set of pictures, we can create a simulation using randomly generated numbers. In this simulation, we repeat the process of selecting cereal boxes multiple times, mimicking the real-world scenario.
For each simulation, we randomly select five cereal boxes and check if they contain a complete set of pictures. We keep track of the number of simulations where a complete set is obtained. By dividing this count by the total number of simulations, we can estimate the probability of ending up with a complete set of pictures.
By running this simulation thousands or even millions of times, we can obtain a more accurate estimate of the probability. The more simulations we run, the closer our estimate will be to the true probability.
This approach allows us to account for the randomness involved in selecting the cereal boxes and provides an estimate of the probability based on the simulated outcomes.
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Please help in answering matching these. I had already asked, but the past answer was wrong. I give the brainliest to whoever answers correctly. Thank you!
Answers
Answer:
y-axis : B) (-4, -3)
y = 1 : E) (4, 5)
y = x : C) (-3, 4)
y = -x : D) (3, -4)
x-axis : A) (4, 3)
Step-by-step explanation:
y-axis : B) (-4, -3)
y = 1 : E) (4, 5)
y = x : C) (-3, 4)
y = -x : D) (3, -4)
x-axis : A) (4, 3)
Reflect in y-axis: change sign of x-coordinate only
Reflect in x-axis: change sign of y-coordinate only
Reflect in y = 1 : change sign of y-coordinate and add 2 units
Reflect in y = x : swap numerical values of x and y coordinates AND change signs
Reflect in y = -x : swap numerical values of x and y coordinates (keep original +/- signs)
A farmer wants to plant 3,456 tomato plants. If he can put 5 plants in each row,
about how many rows will he need to make?
Answers
Answer:
691,2
Step-by-step explanation:
i found that
is it true ?
i hope it helps ! ?
\((m{}^{2})(m {}^{?}) = m {}^{5} \)
What is the answer for - ?
Answers
Answer:
5/2
Step-by-step explanation:
\((m^{2})(m^{?}) = m^{5}\\ m^{2*?} = m^{5}\\m^{2*5/2} = m^{5}\\(m^{2})(m^{5/2}) = m^{5}\)
Fred spent $41.50 at a garden show. He bought a large pot for $29 and some plants for $2.50 each. how many plants did fred buy
Answers
the total money spent by fred is 41.50 $
the cost of the pot is 29 $
and he buys plants of the remaining money
so, remaining money is, 41.50 - 29 = 12.50$
it is given that the cost of a plant is 2.50$
so, in 12.50$ the number of plant he bought is,
12.50/2.50 = 5 plants
thus, he bought 5 plants.
The image of a trapezoid is shown.
What is the area of the trapezoid?
17.4 m2
20.3 m2
40.6 m2
69.6 m2
Answers
Answer:
C. \(40.6m^{2}\)
Step-by-step explanation:
= \(\frac{1}{2}\) x ( 11 + 3 ) x 5.8
= \(\frac{1}{2}\) x 7 x 5.8 =
\(40.6m^{2}\)
Which of the following is a way in which statistics are made to be misleading?
Answers
The statistics are made to be misleading in such a way that the scale is altered on the graph. So, option C is correct.
What are statistics?Statistics is the study of the discipline that concerns the organization, collection, analysis, and presentation of data.
A hasty generalization is fallacy in which a conclusion is reached before sufficient or unbiased evidence is gathered.
The statistics are made to be misleading in such a way that the scale is altered on the graph. So, option C is correct.
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The blue triangle is a dilation of the black triangle. What is the scale factor of the dilation?
Answers
The scale factor of the dilation is equivalent to 2.
What is triangle? What is scale factor?A triangle is a polygon with three edges and three vertices. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller). Mathematically -[k] = (final dimensions)/(original dimensions)
[k] = (A/B)
Given is that blue triangle is a dilation of the black triangle.
Since both the triangles are similar, we can write -
FG/MN = scale factor [k]
k = 4/2
k = 2
Therefore, the scale factor of the dilation is equivalent to 2.
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Answer:
the scale factor is 2 : 1 LM is 2.5 units
Step-by-step explanation:
A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size
the scale factor is 2 : 1 (FG : MN = 4 : 2 = 2 : 1)
therefore the LM side that the question asks is also in 2 : 1 scale
LM = EF : 2
LM = 5 : 2
= 2.5
In a certain chemical, the ratio of zinc to copper is 3 to 11. A jar of the chemical contains 385 grams of copper. How many grams of zinc does it contain?
Answers
Answer:
35 grams
Step-by-step explanation:
The ratio of zinc to copper is 3 to 11
A jar of chemical contains 385 grams if copper
Therefore the number of grams of zinc it contains can be calculated as follows
3/11= x/385
11x= 385
x= 385/11
= 35 grams
Hence the chemical contains 35 grams of zinc
Please help I’ll give Brainly
What did I do wrong??
Answers
Alternate Interior Angles: (MISSING ONE)
∠3 & ∠6
∠4 & ∠5
Alternate Exterior Angles: (MISSING ONE)
∠1 & ∠8
∠2 & ∠7
Same-Side Interior Angles: (ALL CORRECT)
∠4 & ∠6
∠3 & ∠5
Vertical Angles: (ALL CORRECT)
∠6 & ∠7
∠5 & ∠8
∠1 & ∠4
∠2 & ∠3
Corresponding Angles: (ALL CORRECT)
∠1 & ∠5
∠2 & ∠6
∠3 & ∠7
∠4 & ∠8
Supplementary Angles: (CONTAINS EXTRAS)
∠3 & ∠1
∠5 & ∠7
John has 48 square centimeter tiles he wants to use to create a mosaic. He wants the mosaic to be rectangular with a length that is 2 centimeters longer than the width.
Which equation could John solve to find w, the greatest width in centimeters he can use for the mosaic?
w(w – 2) = 48
w(w + 2) = 48
2w(w – 2) = 48
2w(w + 2) = 48
Answers
The equation that could John solve to find w, the greatest width in centimeters he can use for the mosaic is option B: w(w + 2) = 48.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
The mosaic to be formed is rectangular in shape.
Area of a rectangle = length x width
The length is longer than the width by 2,
So, length = w+2
Area of a rectangle = (w+2) x w
The correct equation is B: w(w + 2) = 48
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Answer: B
Step-by-step explanation:
Colette ha an exterminator viit regulary to control an ongoing cockroach 3,800 15% 3 year
Answers
If the initial population is 3800. The population of cockroaches after 3 years will be 1603.
Consider the function:
y = a(1 ± r)ⁿ
where n is the number of times growth/decay, a = initial amount, and r = fraction by which this growth/decay occurs.
If there is a plus sign, there is exponential growth happening by r fraction or r%.
If there is a minus sign, there is exponential decay happening by r fraction or r%.
If the population is currently 3,800 cockroaches.
The expression is given as
y = 3800(0.75)ⁿ
The population of cockroaches after 3 years will be
y = 3800(0.75)³
y = 3800 x 0.4218
y = 1603.125
y ≅ 1603
Hence, the population of cockroaches after 3 years will be 1603.
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The complete question is:
Colette has an exterminator visit regularly to control an ongoing cockroach problem. it's been working, and the population has declined by 15% every year. if the population is currently 3,800 cockroaches, how many will there be in 3 years? if necessary, round your answer to the nearest whole number.
Nicole runs 6 miles in 45 minutes. At the same rate, how many minutes would she take to run 4 miles?
Answers
Answer:
30 minutes
Step-by-step explanation:
6=45
4=x
6x2/3=4
45x2/3=30
x=30
Answer:
66 minutes
Step-by-step explanation:
HELP. GIVING BRAINLIST. BRAINLIST. DONT MESS AROUND PLEASE IM DESPERATE.
Answers
Answer:
make me brain list
thank u
Step-by-step explanation:
Which statement is true about the value of |-5|? It is the distance that -5 is form 0 on the number line. It is the distance that -5 from 5 on the number line. It is less than 5. It is greater than 5.
Answers
Answer: It is the distance that -5 is form 0 on the number line
Step-by-step explanation:
We can define the absolute value of any number:
IxI as:
"The distance between the point x and the origin in the coordinate axis"
If we are in one dimension, x is just a value, and the coordinate axis will be a number line.
Then we could rewrite this as:
"is the distance between the value x and the 0 in the number line"
So:
IxI = x if x > 0
IxI = -x if x < 0.
Then:
I -5 I
Is the distance between the number -5, and the 0 in the number line, and this is:
I - 5 I = 5.
The correct option is:
"It is the distance that -5 is form 0 on the number line"
Answer:
Answer: It is the distance that -5 is form 0 on the number line
Step-by-step explanation:
The diagram that is best at displaying data dispersion is a: Multiple Choice a. scatter diagram. b. stem-and-leaf display. c. skewness graph. d. box plot
Answers
The best diagram to use to display data dispersion is a box plot. A box plot is a diagram that shows how a dataset is distributed and helps to identify any outliers.
The diagram that is best at displaying data dispersion is a box plot. Here's the main answer:When there is a need to compare the distribution of data, a box plot is often the best method.
A box plot is a diagram that shows how a dataset is distributed. It shows how data is spread out and helps to identify any outliers. It is most effective for comparing data sets that have a large number of data points and when the data is not normal (not evenly distributed).
A box plot is a great way to summarize large amounts of data and it is also very easy to read and interpret. It shows a number of statistical values, including the median (the middle value of the data set), the quartiles (the values that divide the data set into four equal parts) and the range (the difference between the maximum and minimum values).
Additionally, it can identify any outliers in the data, which are values that are significantly different from the rest of the data.A box plot is created by drawing a rectangle between the first and third quartiles (the middle 50% of the data) with a line drawn inside it to show the median.
Lines are then drawn from the edges of the rectangle to the minimum and maximum values. Any outliers are marked with a point outside of the rectangle.
The box plot is a great way to compare data sets and to visualize the dispersion of the data
The best diagram to use to display data dispersion is a box plot. A box plot is a diagram that shows how a dataset is distributed and helps to identify any outliers. It is most effective for comparing data sets that have a large number of data points and when the data is not normal. A box plot is created by drawing a rectangle between the first and third quartiles with a line drawn inside it to show the median.
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