The power series representation for f(x) = 1/(1-x) centered at x=0 is:
1 + x + x^2 + x^3 + ...
To find a power series representation for a function, we can use the formula:
f(x) = ∑(n=0 to infinity) [an(x-a)^n]
where a is the center of the series and an is the coefficient of the (x-a)^n term.
For example, let's find a power series representation for the function f(x) = 1/(1-x) centered at x=0:
Using the formula, we have:
f(x) = ∑(n=0 to infinity) [an(x-0)^n]
To find the coefficients an, we can use the formula for the geometric series:
1/(1-x) = 1 + x + x^2 + x^3 + ...
So, we have:
an = [x^n]/n!
Substituting this into the power series formula, we get:
f(x) = ∑(n=0 to infinity) [(x^n)/(n!)](x-0)^n
Simplifying, we get:
f(x) = ∑(n=0 to infinity) [(x^n)/(n!)]
Therefore, the power series representation for f(x) = 1/(1-x) centered at x=0 is:
1 + x + x^2 + x^3 + ...
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The school park has a circular pond with a diameter of 8 yards. What is the pond's droumference? Use 3.14 for x. If necessary, round your answer to the nearest hundredth
Answer:
The circumference is 8π yards, or about 25.13 yards. Since we need to use 3.14 for π, the circumference of the pond is about 8 × 3.14 = 25.12 yards.
A statistically significant F test means that at least one variable in the model is statistically significant, but that does not mean that all of the variables in the model are statistically significant.
Select one: True False
A high p value (greater than alpha) indicates a significant predictor in the regression.
Select one:True False
1) A statistically significant F test means that at least one variable in the model is statistically significant, but that does not mean that all of the variables in the model are statistically significant.
Select one: True
2) A high p-value (greater than alpha) indicates a significant predictor in the regression.
Select one: False
In statistics, a process known as test static is used to determine the significance of the observed result. A hypothesis test is also used for this test. Everywhere in statistical analysis, the P-value or probability value notion is applied. It establishes the statistical significance and significance testing measure. Let's go into detail about the P-value's definition, calculation, table, interpretation, and how to utilise it to determine the significance level, among other things, in this post.
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A zombie infection in Duluth High School grows by 15% per hour. The initial group of
zombies was a group of 4 freshmen. How many zombies are there after 6 hours?
Growth or decay situation?
What is the rate of growth or decay?
What is the growth or decay factor?
Initial amount?
What is the equation?
How many zombies are there after 6 hours?
Find a 3Ã3 matrix with exactly one (real) eigenvalue -4, such that the -4-eigenspace is a line.
The solution to this system is `x = [1, 1/4, 1/16]`, which is a nonzero vector in the -4-eigenspace.
One possible solution is the following matrix:
```
A = [[-4, 0, 0],
[1, -4, 0],
[0, 1, -4]]
```
We can verify that the eigenvalue -4 has algebraic multiplicity 3 by computing the characteristic polynomial:
```
det(A - lambda*I) = (-4 - lambda) * (-4 - lambda) * (-4 - lambda)
```
where `I` is the 3x3 identity matrix. Therefore, the eigenvalue -4 has geometric multiplicity 1, since the -4-eigenspace is a line.
To find the eigenvector associated with this eigenvalue, we solve the equation `(A - (-4)*I)x = 0`, or equivalently, `Ax = (-4)x`. This gives us the following system of equations:
```
-4x1 = 0
x1 - 4x2 = 0
x2 - 4x3 = 0
```
The solution to this system is `x = [1, 1/4, 1/16]`, which is a nonzero vector in the -4-eigenspace.
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If the series is convergent, use the alternating series estimation theorem to determine how many terms we need to add in order to find the sum with an error less than 0.00005.
To answer your question, let's start with a quick review of the alternating series estimation theorem. So, we need to find the smallest integer value of n that is greater than log(B/0.00005) - 1.
This theorem states that if we have an alternating series and the absolute value of the terms decrease in size as we move through the series, then the error of approximating the sum of the series with the nth partial sum is less than or equal to the absolute value of the (n+1)th term.
In other words, if we add up the first n terms of an alternating series and call that partial sum S_n, then the true sum S is somewhere between S_n and S_n+1, and the error in approximating S with S_n is at most |a_n+1|, where a_n+1 is the (n+1)th term in the series.
Now, to apply this to your question, we need to know a few more things. Specifically, we need to know what the alternating series in question looks like, and what the terms of the series are. We also need to know what it means for the series to be convergent.
So, let's say that the alternating series in question is of the form:
a_1 - a_2 + a_3 - a_4 + ...
According to the alternating series estimation theorem, we need to find the smallest value of n such that |a_n+1| < 0.00005. That is, we need to find the smallest value of n such that:
|(-1)^(n+2)b_n+1| < 0.00005
Since b_n decreases as n gets larger, we know that b_n+1 < b_n, so we can simplify this inequality to:
(-1)^(n+2)b_n+1 < 0.00005
Now, we could solve this inequality explicitly, but since we don't know what the b_n values are, it's easier to approximate the answer. Since we want the error to be less than 0.00005, we know that the (n+1)th term must be smaller than 0.00005. So, we can set up an inequality like this:
b_n+1 < 0.00005
we can use the largest value of b_n that we know of (let's call it B) to get an upper bound on n. That is:
B < b_n for all n
So, we can solve for n as follows:
b_n+1 < 0.00005
B < b_n for all n
B < b_n+1 for all n (since b_n decreases as n gets larger)
B < 0.00005
n+1 > log(B/0.00005)
n > log(B/0.00005) - 1
So, we need to find the smallest integer value of n that is greater than log(B/0.00005) - 1. This will give us the number of terms we need to add up in order to approximate the sum of the series to within an error of 0.00005.
To determine how many terms we need to add in a convergent alternating series to find the sum with an error less than 0.00005, we will use the Alternating Series Estimation Theorem. The theorem states that if we have a converging alternating series, the absolute error in the approximation by the sum of the first n terms is less than or equal to the absolute value of the (n+1)-th term.
Here's a step-by-step explanation:
1. Identify the series as an alternating series, which means it should have the form (-1)^n * a_n, where a_n is a sequence of positive numbers.
2. Make sure the series is convergent by checking that a_n is decreasing and approaches zero as n approaches infinity.
3. Apply the Alternating Series Estimation Theorem by setting the (n+1)-th term less than the desired error, which in this case is 0.00005: |(-1)^(n+1) * a_(n+1)| < 0.00005.
4. Solve for n in the inequality above to determine the minimum number of terms needed to achieve the desired error.
By following these steps, you will find the number of terms you need to add in the convergent alternating series to obtain a sum with an error less than 0.00005.
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(Chapter 12) If u = and v =, then u*v = .
Therefore, the vector product of u and v is [-4, 7, -4].
The vector product, also known as the cross product, of two vectors u and v is defined as a vector that is perpendicular to both u and v. Its magnitude is equal to the area of the parallelogram formed by the two vectors, and its direction is given by the right-hand rule.
To calculate the vector product of two vectors u and v using the formula u x v = [u2v3 - u3v2, u3v1 - u1v3, u1v2 - u2v1], we need to take the second and third components of u and v, and cross multiply them. Then, we subtract the result of the third component of u multiplied by the second component of v from the second component of u multiplied by the third component of v. This gives the first component of the resulting vector. Similarly, we can calculate the second and third components of the resulting vector.
In this problem, the vectors u and v are given as:
u = [2, 3, 1]
v = [1, -2, -2]
Substituting these values into the formula for the vector product, we get:
u x v = [u2v3 - u3v2, u3v1 - u1v3, u1v2 - u2v1]
u x v = [(2)(-2) - (3)(-2), (3)(1) - (2)(-2), (1)(-2) - (2)(1)]
u x v = [-4 + 6, 3 + 4, -2 - 2]
u x v = [2, 7, -4]
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14 ft NET OF ΤΟΥ BOX 12 ft 15 ft What is the surface area, in square feet, of the toy box?
The surface area, in square feet, of the toy box is 1116
What is the surface area, in square feet, of the toy box?From the question, we have the following parameters that can be used in our computation:
Dimensions 14 ft, 12 ft and 15 ft
The surface area, in square feet, of the toy box is calculated as
Surface area = 2 * (lw + lh + wh)
substitute the known values in the above equation, so, we have the following representation
Surface area = 2 * (14 * 12 + 14 * 15 + 12 * 15)
Evaluate
Surface area = 1116
Hence, the surgface area is 1116
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What is the distance, in units, between the points (−3, 1) and (2, −1)?
\sqrt{x} 3\\
\\
\sqrt{x} 5\\
\sqrt{x} 21\\
\\
\sqrt{x} 29
Answer:
[tex] \sqrt{ { (- 3 - 2)}^{2} + {(1 - ( - 1))}^{2} } [/tex]
[tex] \sqrt{ {( - 5)}^{2} + {2}^{2} } [/tex]
[tex] \sqrt{25 + 4} = \sqrt{29} [/tex]
mary is shipping out her makeup kits, which come in 1/2 ft cube boxes. if she is using a shipping box that is 1 1/2 ft wide, 3 feet long and 2 feet in height, how many make up kit boxes can be shipped in each box?
Mary is shipping her makeup kits in boxes with dimensions of 1/2 ft x 1/2 ft x 1/2 ft. The shipping box dimensions are 1 1/2 ft wide, 3 ft long, and 2 ft high.
To determine how many makeup kit boxes can fit in each shipping box, we need to find the volume of both boxes and divide the volume of the shipping box by the volume of the makeup kit box.
First, we'll find the volume of the makeup kit box:
[tex]Volume = length × width × height = (1/2 ft) × (1/2 ft) × (1/2 ft) = 1/8 cubic feet[/tex]
Next, we'll find the volume of the shipping box:
[tex]Volume = length × width × height[/tex]
= (3 ft) × (1 1/2 ft) × (2 ft) = 3 ft × 3/2 ft × 2 ft = 9 cubic feet
Now, we'll divide the volume of the shipping box by the volume of the makeup kit box:
[tex]Number of makeup kit boxes = Volume of shipping box ÷ Volume of makeup kit box[/tex]
= 9 cubic feet ÷ 1/8 cubic feet = 72
Therefore, Mary can ship 72 makeup kit boxes in each shipping box.
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This is not my math book cause I'm not grade 4... Pls help
Answer:
2, 2
Step-by-step explanation:
As the diagram number goes up by 1, it looks like the number of tiles goes up by 2; 4 + 2 = 6, 6 + 2 = 8, etc. This means that the growth, or slope, is 2; the number of tiles is 2 times the diagram number. But, we can't stop there, because 1 times 2 is 2, not 4, and 2 times 2 is 4, not 6. Well, what is 4 - 2, and what is 6 - 4? The answer to both of these expressions is 2. This tells us that we also have to add 2.
Here's me checking my work on all of the values in the table:
1 × 2 = 2 and 2 + 2 = 4
2 × 2 = 4 and 4 + 2 = 6
3 × 2 = 6 and 6 + 2 = 8
4 × 2 = 8 and 8 + 2 = 10
If you need more help with that, let me know. :)
Question 14 3 pts A sample of n = 9 scores has SS = 72. The variance for this sample is s2 = 9. True O False
72 = (9-1) * s^2
s^2 = 9
The variance for this sample is s^2 = 9, which matches the given value. Hence, the statement is true.
To determine whether the statement is true or false, we need to calculate the variance using the given information.
Terms:
- Sample: A subset of a population, in this case, n = 9 scores.
- Variance: A measure of how much the scores in the sample vary, denoted as s².
- Scores: The individual data points in the sample.
To calculate the variance (s²) for a sample, use the following formula:
s² = SS / (n - 1)
Where:
- SS = 72 (sum of squared deviations)
- n = 9 (number of scores in the sample)
Now, let's calculate the Variance:
s² = 72 / (9 - 1)
s² = 72 / 8
s² = 9
The calculated variance is 9, which matches the given variance in the statement. Therefore, the statement is True.
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An online pet store offers the hamster house shown in the figure below.
Choose all of the expressions that could be used to find the volume of the hamster house.
A solid shape is shown; two rectangular prisms are attached. The total length of the shape is 6 feet. One rectangular prism has a length of 1 foot, width of 3 feet and height of 4 feet. The second rectangular prism has a length as 6 feet, width as 3 feet and height as 2 feet.
A.
(
1
×
3
×
4
)
+
(
2
×
5
×
3
)
B.
(
1
×
3
)
+
(
4
×
2
)
+
(
5
×
3
)
C.
(
1
×
3
×
2
)
+
(
6
×
3
×
2
)
D.
3
×
(
1
+
4
)
+
2
×
(
5
+
3
)
E.
(
3
×
4
)
+
1
×
(
2
×
5
)
+
3
11 / 14
10 of 14 Answered
All the correct expressions that could be used to find the volume of the hamster house are,
⇒ (1 × 3 × 4) + (6 × 3 × 2)
How to solveGiven that;
One rectangular prism has a length of 1 foot, a width of 3 feet and a height of 4 feet.
And, The second rectangular prism has a length as 6 feet, a width as 3 feet, and a height of 2 feet.
Hence, the Volume of first rectangular prism is,
⇒ 1 × 3 × 4
And, Volume of a second rectangular prism is,
⇒ 6 × 3 × 2
Thus, All the correct expressions that could be used to find the volume of the hamster house are,
⇒ (1 × 3 × 4) + (6 × 3 × 2)
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Advance America is a payday loan company that offers quick, short-term loans using the borrower's future paychecks as collateral. Advance America charges $17 for each $100 loaned for a term of 14 days. Find the APR charged by Advance America.
The APR charged by Advance America is approximately 443.2%.
Convert the loan term of 14 days to a fraction of a year.
There are 365 days in a year, so the fraction of a year for a 14-day loan is 14/365.
Simple interest is calculated with the following formula:
S.I. = (P × APR × T)/100,
Here P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years.
As per the question, we have:
P = $100, S.I. = $17 and T = 14/365.
Substitute the values in the formula,
17 = (100 × APR × 14/365)/100
APR = (365 × 17)/14
APR = 443.2 %
Therefore, the APR is about 443.2%.
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The ratio of rookies to veterans in the camp was 2 to 7. Altogether there were 252 rookies and veterans in the camp.
How many of them were rookies?
Answer:
56 of them were rookies.
Step-by-step explanation:
Let x = the number of rookies; y = the number of veterans.
We have the total number of people:
x + y = 252 (1)
The ratio x/y = 2/7 is equal to:
7x = 2y, so x = 2y/7
Substituting x into (1):
2y/7 + y = 252
9y/7 = 252
y = 252 × 7/9 = 196
So substituting y into (1):
x + 196 = 252
x = 252 - 196 = 56.
There were 56 rookies in the camp.
To find the number of rookies in the camp, we will use the given ratio and the total number of people in the camp.
Step 1: Write down the ratio of rookies to veterans, which is 2:7.
Step 2: Add the two parts of the ratio together: 2 + 7 = 9 parts.
Step 3: Divide the total number of people in the camp by the total number of parts. In this case, there are 252 people and 9 parts: 252 / 9 = 28. This means each part represents 28 people.
Step 4: Multiply the number of people per part by the number of parts for rookies to find the total number of rookies: 2 parts (rookies) * 28 people per part = 56 rookies.
So, there were 56 rookies in the camp.
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if the coefficient of determination is 0.298, what percentage of the variation in the data about the regression line is unexplained? g
Therefore, approximately 70.2% of the variation in the data about the regression line is unexplained.
The coefficient of determination, denoted as R², is the proportion of the variation in the dependent variable that is explained by the independent variable(s). Therefore, the percentage of the variation in the data about the regression line that is unexplained can be found by subtracting the coefficient of determination from 1 and then multiplying the result by 100.
Percentage of variation unexplained = (1 - R^2) x 100%
Substituting R² = 0.298, we get:
Percentage of variation unexplained = (1 - 0.298) x 100%
Percentage of variation unexplained = 0.702 x 100%
Percentage of variation unexplained = 70.2%
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Multiply and simplify.
x-1
2-1
x2+2x+1 X+1
01
X + 1
X - 1
X-1
X + 1
(x - 1)²
(x + 1)²
Answer:
try to get am math tutor........
what concept does the mean of a discrete random variable generalize?
The mean of a discrete random variable generalizes the concept of an average value or expected value of the outcomes of a random experiment where the possible outcomes are discrete and random. A discrete random variable is a variable that can only take on specific, isolated values, and the mean of this variable represents the weighted average of all possible values, with each value being weighted by its probability of occurrence. Therefore, the mean of a discrete random variable provides a measure of central tendency that summarizes the distribution of the variable.
Hi! The mean of a discrete random variable generalizes the concept of an "expected value." In this context, "discrete" refers to a finite or countable number of distinct values, "random" indicates the variable's outcomes depend on chance, and "variable" represents a quantity that can vary.
The expected value is a weighted average of all possible values that a discrete random variable can take on, with each value being multiplied by its respective probability. It provides a measure of the "central tendency" or the long-term average outcome of the random variable.
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HELP PLS
For $8, you can buy one 8 inch pie or five 3 inch snack pies at a bakery. Which option provides more pie?
as alpha increases the exponential smoothing model group of answer choices produces sluggish forecasts. reacts quickly to changes in the data. reacts slowly to changes in the data. does not change.
Exponential smoothing is a popular forecasting technique used to predict future trends in time-series data. It works by assigning weights to historical data points, with more recent data points receiving higher weights. The level of smoothing is controlled by a smoothing parameter called alpha, which ranges between 0 and 1. As alpha increases, the influence of older data points decreases, and the model becomes more reactive to recent changes in the data.
When alpha is high, the exponential smoothing model group of answer choices tends to produce sluggish forecasts. This is because the model gives more weight to recent data points, which can cause it to overreact to short-term fluctuations in the data. As a result, the model may miss important trends or patterns in the data that would have been captured by a more balanced weighting scheme.
On the other hand, when alpha is low, the model tends to be more stable and less reactive to short-term changes in the data. This can be useful for predicting long-term trends or for smoothing out noisy data sets.
In summary, the choice of alpha in an exponential smoothing model depends on the characteristics of the data and the goals of the forecast. A high alpha value may be appropriate for short-term forecasting or for data sets with high volatility, while a low alpha value may be more suitable for long-term forecasting or for data sets with low volatility.
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let f be the function that satisfies the given differential equation (dy/dx = xy/2). write an equation for the tangent line to the curve y = f(x) through the point (1,1). then use your tangent line equation to estimate the value of f(1.2).
Our estimate for f(1.2) is 1.1 which satisfies differential equation.
To find the equation of the tangent line to the curve y = f(x) through the point (1,1), we first need to find the value of f(1) at x = 1. To do this, we can solve the differential equation given:
[tex]dy/dx = xy/2[/tex]
Separating the variables, we get:
[tex]dy/y = x/2 dx[/tex]
Integrating both sides, we get:
[tex]ln|y| = x^2/4 + C[/tex]
Where C is the constant of integration. To find the value of C, we can use the initial condition that f(1) = 1:
ln|1| = 1/4 + C
C = -1/4
So our equation for f(x) is:
[tex]ln|y| = x^2/4 - 1/4[/tex]
Simplifying, we get:
[tex]y = e^(x^2/4 - 1/4)[/tex]
To find the equation of the tangent line through the point (1,1), we need to find the slope of the tangent line at x = 1. To do this, we take the derivative of f(x) and evaluate it at x = 1:
[tex]f'(x) = (1/2)x e^(x^2/4 - 1/4)f'(1) = (1/2)(1) e^(1/4 - 1/4) = 1/2[/tex]
So the slope of the tangent line at x = 1 is 1/2. Using the point-slope form of a line, we get:
[tex]y - 1 = 1/2(x - 1)[/tex]
Simplifying, we get:
y = 1/2 x + 1/2
To estimate the value of f(1.2), we can use our tangent line equation. Plugging in x = 1.2, we get:
[tex]y = 1/2(1.2) + 1/2 = 1.1[/tex]
So our estimate for f(1.2) is 1.1.
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Which equation is modeled on the number line below?
A
B
C
D
-12-11-10
3 x 4 = 12
-3x (-4)=12
3x (-4)=-12
4x (-3)=-12
HHHH>
89101112
4
7:5
Answer: equation 3x (-4) = -12 has a solution of x = 1, which can be represented on the number line between -2 and -3.
Step-by-step explanation: Based on the number line and the answer choices provided, it appears that the equation modeled on the number line is:
C) 3x (-4) = -12
This equation can be interpreted as "what number multiplied by 3 and then multiplied by -4 will give a result of -12". Solving for x, we get:
3x (-4) = -12
-12x = -12
x = -12/-12
x = 1
Therefore, the equation 3x (-4) = -12 has a solution of x = 1, which can be represented on the number line between -2 and -3.
Help me please!!!!!!!!!!!!!!
The equation of the table of values is f(x) = 2x
Representing the equation of the tableFrom the question, we have the following parameters that can be used in our computation:
The table of values
On the table of values, we can see that
The x values are multiplied by 2 to get the y values
When represented as a function. we have
f(x) = 2 * x
Evaluate the product
f(x) = 2x
Hence, the function equation is f(x) = 2x
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Help with the two questions please!
The values of x and y are y = 27 and x = 18 & x = 3 and y = 12
The triangles are similar by SAS and SSS
Calculating the values of x and yGiven that the triangles are similar
So, we have
12/y = 4/9 and x/12 = 6/4
When evaluated, we have
4y = 12 * 9 and 4x = 12 * 6
Divide both sides by the coefficients of x and y
So, we have
y = 27 and x = 18
For the similar trapezoid, we have
(2x + 1)/3 = (4x + 9)/9 and 3/4 = 9/y
So, we have
6x + 3 = 4x + 9 and 3y = 4 * 9
Evaluate
2x = 6 and 3y = 36
So, we have
x = 3 and y = 12
The similarity of the trianglesFor the first pair of triangles, the triangles are similar by SAS because of the following corresponding sides and angles
QE corresponds to DC∠Q corresponds to ∠DQR corresponds to DRFor the second pair of triangles, the triangles are similar by SSS because the corresponding sides have the same scale factor of 1.5
i.e. RP/NM = 3/2 = 1.5, PN/LM = 6/4 = 1.5 and RN/LN = 9/6 = 1.5
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In the prime factorization of 109!, what is the exponent of 3?
The exponent of 3 in the prime factorization of 109! is 76.
To find the exponent of 3 in the prime factorization of 109!, we need to first determine how many factors of 3 there are in the prime factorization of each number from 1 to 109. We can do this by dividing each number by 3 and adding up the quotient (ignoring any remainder) until the quotient becomes less than 3. For example, for the number 27, we divide 27 by 3 to get 9, then divide 9 by 3 to get 3, then divide 3 by 3 to get 1. So the exponent of 3 in the prime factorization of 27 is 3.
Doing this for all the numbers from 1 to 109, we get:
- There are 36 numbers that have at least one factor of 3.
- There are 12 numbers that have at least two factors of 3.
- There are 4 numbers that have at least three factors of 3.
- There is 1 number (81) that has at least four factors of 3.
To find the exponent of 3 in the prime factorization of 109!, we need to add up the number of factors of 3 in each of these numbers:
- The 36 numbers with at least one factor of 3 contribute a total of 36 factors of 3.
- The 12 numbers with at least two factors of 3 contribute a total of 24 factors of 3 (since each one has 2 factors of 3).
- The 4 numbers with at least three factors of 3 contribute a total of 12 factors of 3 (since each one has 3 factors of 3).
- The 1 number with at least four factors of 3 contributes 4 factors of 3.
So the total number of factors of 3 in the prime factorization of 109! is 36 + 24 + 12 + 4 = 76. Therefore, the exponent of 3 in the prime factorization of 109! is 76.
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Which number sentence has a sum of 5? -8 + 3 3 + (-8) -3 + 8 8 + 3
Answer:
-3 + 8 = 5
Step-by-step explanation:
-8 + 3 = -5
3 + (-8) = -5
-3 + 8 = 5
8 + 3 = 11
Which expression represents the phrase 5+ the quotient of 12. 8 and 3. 2
Expression 5 + (12.8 ÷ 3.2) represents the phrase 5 + the quotient of 12. 8 and 3. 2 and option (a) is the correct answer.
Expressions refer to a phrase with at least two numbers or variables with any mathematical operations such as addition, exponents, etc. x - 6, 9 + 4y, and 6a are all examples of mathematical expressions.
Equations refer to a sentence when two expressions are equated with the help of '='. x - 6 = 6a is an example of an equation.
In phrase 5+ the quotient of 12. 8 and 3. 2
We divide the phrase into different mathematical operations.
The first operation is of addition with 5, we can write the beginning as 5 + ...
The next operation is division in the phrase the quotient of 12. 8 and 3. 2 which is added to the expression and we get 5 + (12.8 ÷ 3.2)
And we get our answer.
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The complete question might be :
Which expression represents the phrase 5+ the quotient of 12. 8 and 3. 2?
a. 5 + (12.8 ÷ 3.2)
b. 5 - (12.8 + 3.2)
c. 5 + (12.8 * 3.2)
d. none of the above
Geometry: Transformations
The point (-4, -1), is the bottom of a triangle. Which point would it map to if the triangle was translated right 5 units and reflected about the x-axis.
A) (2, 1)
B) (1, 1)
C) (-4, -4)
D) (-9, 1)
Answer: Ur answer will be A.
Once you solve for ONE of the variables in a system, then...
*
you must determine the inverse of the corresponding matrix.
you must see that it works for all equations of the system.
you must involuntarily lubricate your corneas.
you must substitute the value of that variable in an equation to solve for the remaining variable.
The complete sentence is,
Once you solve for ONE of the variables in a system, then you must substitute the value of that variable in an equation to solve for the remaining variable.
We have to given that;
To find the method after, Once you solve for ONE of the variables in a system,
Hence, We get;
The correct method is,
Once you solve for ONE of the variables in a system, then you must substitute the value of that variable in an equation to solve for the remaining variable.
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Simplify:
(-10x²) (-2x¹)
Find the value of the standard normal random variable z, called zo such that: (a) P(Z < zo) = 0.7819 = z0 = (b) P(-20 < x zo) = 0.4015 z0 =
(e) P(-20 < < 0) = 0.4659 z0 =
To find the value of the standard normal random variable z, called zo, we can use a standard normal distribution table or a calculator with a standard normal distribution function.
(a) P(Z < zo) = 0.7819
Looking at a standard normal distribution table, we can find the closest value to 0.7819, which is 0.78 in the table. The corresponding value of z is 0.80. Therefore, zo = 0.80.
(b) P(-20 < x < zo) = 0.4015
Since we are given a range of values for x, we need to convert this to a range of values for z using the formula z = (x - μ) / σ, where μ is the mean and σ is the standard deviation. For the standard normal distribution, μ = 0 and σ = 1.
P(-20 < x < zo) = P((-20 - 0) / 1 < (x - 0) / 1 < (zo - 0) / 1)
= P(-20 < z < zo)
Using a standard normal distribution table, we can find the probabilities corresponding to -20 and zo, which are 0.0000 and 0.6554, respectively. Then, we can subtract the probability of z < -20 from the probability of z < zo to get the probability of -20 < z < zo.
P(-20 < z < zo) = P(z < zo) - P(z < -20) = 0.6554 - 0.0000 = 0.6554
However, this is not equal to the given probability of 0.4015. Therefore, there must be an error in the question or in the given probability.
(e) P(-20 < z < 0) = 0.4659
Since we are given a range of values for z, we can look up the probabilities corresponding to -20 and 0 in a standard normal distribution table, which are 0.0000 and 0.5000, respectively. Then, we can subtract the probability of z < -20 from the probability of z < 0 to get the probability of -20 < z < 0.
P(-20 < z < 0) = P(z < 0) - P(z < -20) = 0.5000 - 0.0000 = 0.5000
Therefore, zo is not needed for this part of the question.
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