Hermite polynomials, denoted by H(n, x), are a family of orthogonal polynomials with important applications in mathematical physics and probability theory. They are defined recursively, with base cases H(0, x) = 1 and H(1, x) = 2x. For n > 1, the recursive relation is given by H(n, x) = 2xH(n-1, x) - 2(n-1)H(n-2, x).
To implement a recursive function H that calculates the n-th Hermite polynomial at x using memoization, you can use a dictionary to store previously computed values of the polynomial. This will help in avoiding redundant computations and improve the efficiency of the algorithm.
Here's a Python implementation:
```python
def H(n, x, memo={}):
if n == 0:
return 1
elif n == 1:
return 2 * x
else:
if (n, x) not in memo:
memo[(n, x)] = 2 * x * H(n - 1, x) - 2 * (n - 1) * H(n - 2, x)
return memo[(n, x)]
```
This function takes an integer n and a double x as input and returns a double representing the value of the n-th Hermite polynomial at x. The function uses memoization to optimize performance, storing previously computed values in a dictionary called memo. This way, when encountering the same inputs again, the function can return the already computed value instead of performing the calculations anew.
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helppp i don’t get this
[tex]f(x)=-3x+4 \\\\[-0.35em] ~\dotfill\\\\ f(3)=-3(3)+4\implies f(3)=-9+4\implies \boxed{f(3)=-5} \\\\[-0.35em] ~\dotfill\\\\ f(-4)=-3(-4)+4\implies f(-4)=+12+4\implies \boxed{f(-4)=16} \\\\[-0.35em] ~\dotfill\\\\ 2f(3)~~ + ~~f(-4)\implies 2(-5)~~ + ~~16\implies -10+16\implies \text{\LARGE 6}[/tex]
Write the number for eight million one thousand .
Answer:
8,001,000
Step-by-step explanation:
It is known that 2x-3/x = x + 1 What is the value of x^2 -x + 3
The value of the equation x² - x + 3 is 37/9.
We have,
We can start by multiplying both sides of the equation by x:
2x - 3/x = x + 1
2x - 3 = x^2 + x
Rearranging and simplifying, we get:
x^2 - x + 3 = (2x - 3) + x^2
x^2 - x + 3 = x^2 + 2x - 3
-x + 3 = 2x - 3
5 = 3x
x = 5/3
Now we can substitute x into the equation x^2 - x + 3:
x^2 - x + 3 = (5/3)^2 - 5/3 + 3
x^2 - x + 3 = 25/9 - 15/9 + 27/9
x^2 - x + 3 = 37/9
Therefore,
The value of x² - x + 3 is 37/9.
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Provided by the code calling the method:
a. argument
b. variable
c. formal parameter
d. constant
e. expression
An argument is a value or reference passed to a method or function when it is called. It is provided by the code that calls the method and is used as input for the method's operation.
The term that best fits the description "Provided by the code calling the method" is "argument".
An argument is a value or reference that is passed to a method or function when it is called. The argument is provided by the code that calls the method and is used as input for the method's operation.
In contrast, a variable is a named storage location that holds a value, a formal parameter is a variable declared in the method's signature that receives an argument, a constant is a fixed value that does not change during program execution, and an expression is a combination of values, variables and operators that can be evaluated to a single value.
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What sample size is needed to obtain a 95 percent confidence interval for the proportion of fat in meat that is within 3 percent of the true value?
A sample size of at least 1068 to obtain a 95% confidence interval for the proportion of fat in meat that is within 3% of the true value.
To calculate the sample size needed for a 95% confidence interval for the proportion of fat in meat that is within 3% of the true value, we can use the following formula:
[tex]n = (Z^2 \times p \times (1-p)) / E^2[/tex]
where:
n is the sample size
Z is the Z-score for the desired confidence level (1.96 for a 95% confidence interval)
p is the estimated proportion of fat in the population (we can use 0.5 as a conservative estimate)
E is the maximum allowable margin of error (0.03 in this case)
Substituting the values, we get:
[tex]n = (1.96^2 \times 0.5 \times (1-0.5)) / 0.03^2[/tex]
n = 1067.11
Rounding up to the nearest whole number, we get a sample size of 1068. Therefore, we need a sample size of at least 1068 to obtain a 95% confidence interval for the proportion of fat in meat that is within 3% of the true value.
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The following situations are either possible or impossible. Indicate all possible situations.
A is a 5x4 matrix whose columns are linearly dependent and span R5.
The linear transform TA=Ax : R2 → R4 is one-to-one
1. A is a 5x4 matrix whose columns are linearly dependent and span R5:
This situation is impossible.
A 5x4 matrix with linearly dependent columns cannot span R5.
2. The linear transform TA=Ax : R2 → R4 is one-to-one:
This situation is also impossible.
1. A is a 5x4 matrix whose columns are linearly dependent and span R5:
This situation is impossible.
A 5x4 matrix has 4 columns, and since they are linearly dependent, it means that at least one column can be expressed as a linear combination of the other columns. In order to span R5, you need a set of 5 linearly independent columns.
Therefore, a 5x4 matrix with linearly dependent columns cannot span R5.
2. The linear transform TA=Ax : R2 → R4 is one-to-one:
This situation is also impossible.
A one-to-one (injective) linear transformation requires that the dimension of the domain (R2) is less than or equal to the dimension of the codomain (R4).
However, for a linear transformation to be one-to-one, the number of linearly independent vectors in the domain must equal the number of linearly independent vectors in the codomain.
Since the dimension of R2 is 2 and the dimension of R4 is 4, it's impossible to have a one-to-one linear transformation from R2 to R4.
In conclusion, both situations are impossible.
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67) At a local fast food joint, cars arrive randomly at a rate of 12 every 30 minutes. Service times are random (exponential) and average 2 minutes per arrival. The average time in the queue for each arrival is
A) 2 minutes.
B) 4 minutes.
C) 6 minutes.
D) 8 minutes.
E) 10 minutes.
E) 10 minutes. At the local fast food joint, cars arrive randomly at a rate of 12 every 30 minutes, which is equivalent to a rate of 0.4 cars per minute (12 arrivals / 30 minutes). The service time for each car averages 2 minutes per arrival and follows an exponential distribution.
To find the average time in the queue for each arrival, we can use Little's Law. Little's Law states that the average number of customers in a system (L) is equal to the arrival rate (λ) multiplied by the average time a customer spends in the system (W). In other words, L = λW.
In this scenario, we are given the arrival rate (λ) and the service time (μ), but we want to find the average time a customer spends in the system (W). To do this, we can use the formula for the average time in an M/M/1 queue: W = 1 / (μ - λ).
Plugging in the values, we get W = 1 / (0.5 cars/minute - 0.4 cars/minute) = 1 / 0.1 cars/minute = 10 minutes. Thus, the average time in the queue for each arrival is 10 minutes.
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All F tests compare variances by ___________________.
a. dividing them
b. multiplying them
c. subtracting them
d. dividing, multiplying, AND dividing them.
All F test compare variances by dividing them.
How to perform F test?F tests compare the variances of two or more populations by dividing them. The F statistic is calculated as the ratio of the sample variances of the populations being compared.
This ratio represents the difference in variances between the populations and is used to determine whether the difference is statistically significant. F tests are commonly used in ANOVA to test.
if there is a significant difference between the means of multiple groups. Understanding F tests and their interpretation is important in many fields, including science, engineering, finance, and more.
Therefore, it is important to know that F tests compare variances by dividing them, and this forms the basis of hypothesis testing in many statistical analyses.
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9. Two equations are shown below. Which of the
statements best explains the relationship between the
equations?
y = 3x
y=x+3
A. In y = x + 3, the value of y is 3 more than the value of
y = 3x.
B. In y = 3x, the value of y is 3 times the value of y in the
equation y = x +3
C. In y = 3x, the value of y is three times the value of x,
and in y = x + 3 the value of y is three less the value of x.
D. In y = 3x, the value of y is three times the value of x,
and in y = x + 3, the value of y is three more than the
value of x.
The statements best explains the relationship is In y = 3x, the value of y is three times the value of x, and in y = x + 3, the value of y is three more than the value of x. So, the correct answer is D).
The equation y = 3x represents a linear function with a slope of 3 and a y-intercept of 0. This means that for every increase of 1 in the value of x, the value of y will increase by 3.
On the other hand, the equation y = x + 3 represents another linear function with a slope of 1 and a y-intercept of 3. This means that for every increase of 1 in the value of x, the value of y will increase by 1.
Therefore, the value of y in the equation y = 3x will always be three times the value of x, while the value of y in the equation y = x + 3 will always be three more than the value of x. So, the correct option is D).
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Z0=4 ; Zn=1/2 Zn-1+1
Answer:
Z_1 = 3
Z_2 = 2.5
Z_3 = 2.25
Step-by-step explanation:
To find the next three terms in the sequence defined by Z_0 = 4 and Z_n = (1/2) Z_(n-1) + 1, we can use the recursive formula to calculate each term.
First, we can calculate Z_1 by substituting n = 1 into the recursive formula:
Z_1 = (1/2) Z_0 + 1 = (1/2) (4) + 1 = 3
This means that the second term in the sequence is 3.
Next, we can calculate Z_2 by substituting n = 2 into the recursive formula:
Z_2 = (1/2) Z_1 + 1 = (1/2) (3) + 1 = 1.5 + 1 = 2.5
This means that the third term in the sequence is 2.5.
Finally, we can calculate Z_3 by substituting n = 3 into the recursive formula:
Z_3 = (1/2) Z_2 + 1 = (1/2) (2.5) + 1 = 1.25 + 1 = 2.25
This means that the fourth term in the sequence is 2.25.
Therefore, the next three terms in the sequence are 3, 2.5, and 2.25.
Each term in the sequence is calculated by taking half of the previous term and adding 1. The sequence starts at 4, so the second term is calculated by taking half of 4, which is 2, and adding 1, which gives 3. The third term is calculated by taking half of 3, which is 1.5, and adding 1, which gives 2.5. The fourth term is calculated by taking half of 2.5, which is 1.25, and adding 1, which gives 2.25. This pattern continues for each subsequent term in the sequence.
Write the solution of the logistic differential equation dP/dt = P(35.1-0.0015P) with initial condition P(0) = 936
Answer:
P(t) = 23400/(1 +e^(-35.1t))
Step-by-step explanation:
You want the solution of the logistic differential equation dP/dt = P(35.1-0.0015P) with initial condition P(0) = 936.
SolutionThe generic solution to p' = p(a -bp) with p(0) = c is ...
p = (a/b)/(1 +(a/(bc) -1)e^(-at))
For a = 35.1, b = 0.0015, c = 936, we have the coefficients ...
a/b = 35.1/0.0015 = 23400
a/(bc) -1 = 23400/936 -1 = 24
That means the solution equation is ...
P(t) = 23400/(1 +24e^(-35.1t))
P(t) = e^(35.1t - 0.00075P² + C). The logistic differential equation you provided is dP/dt = P(35.1 - 0.0015P) with an initial condition P(0) = 936. To solve this equation, we will use the method of separation of variables.
First, separate the variables P and t by dividing both sides by P(35.1 - 0.0015P):
(1/P) dP = (35.1 - 0.0015P) dt.
Now, integrate both sides with respect to their respective variables:
∫(1/P) dP = ∫(35.1 - 0.0015P) dt.
The left side is a simple integration, resulting in ln|P| + C₁. The right side requires integration by parts, which yields 35.1t - 0.00075P² + C₂. Combining the constants of integration, we get:
ln|P| = 35.1t - 0.00075P² + C.
Now, exponentiate both sides to remove the natural logarithm:
P = e^(35.1t - 0.00075P² + C).
To find the constant C, use the initial condition P(0) = 936:
936 = e^(35.1(0) - 0.00075(936)² + C).
Solve for C, and then plug it back into the equation:
P(t) = e^(35.1t - 0.00075P² + C).
This equation represents the solution to the given logistic differential equation with the specified initial condition. Note that the actual values for C and the final equation form may require further calculations based on the integration steps.
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1. a is__
X
-1
0
1
b is__
f(x)
3
6
12
y=___
The equation of the exponential table of values is y = 6(2)^x
Calculating the equation of the table of valuesFrom the question, we have the following parameters that can be used in our computation:
x y
-1 3
0 6
1 12
In the above table of values, we can see that
As x increases by 1The function value doublesThis means that the function is an exponential function
As a general rule, an exponential function is represented as
y = ab^x
Where
a = y when x = 0
So, we have
y = 6b^x
Also, the function value doubles
This mean that
b = 2 i.e. the rate
So, we have
y = 6(2)^x
Hence, the equation of the table of values is y = 6(2)^x
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what is the equation of the line containing
A (3,7) B(0,23) ?
The equation of the line passing through points A and B is: y = (-16/3)x + 59.
To find the equation of the line passing through two given points, we need to use the slope-intercept form of the equation of a line, which is y = mx + b, where m is the slope of the line and b is the y-intercept.
First, we need to find the slope of the line. We can use the formula:
m = (y2 - y1)/(x2 - x1)
where (x1, y1) = A(3,7) and (x2, y2) = B(0,23). Substituting the values, we get:
m = (23 - 7)/(0 - 3) = -16/3
Next, we need to find the y-intercept, b. We can use the point-slope form of the equation of a line:
y - y1 = m(x - x1)
Using the point A(3,7), we get:
y - 7 = (-16/3)(x - 3)
Simplifying, we get:
y = (-16/3)x + 59
Therefore, the equation of the line passing through points A and B is:
y = (-16/3)x + 59.
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Find the value of the expression 5x7-4x4
Giving brainliest
the temperature T, in degrees Fahrenheit, during the day can be modeled by the equation T(x)=-0.07x^2, where x is the number of hours after 6 a.m. At what time is the temperature a maximum? What is the maximun temperature?
Answer: To find the time at which the temperature is maximum, we need to find the vertex of the quadratic function T(x) = -0.07x^2. Recall that the x-coordinate of the vertex of a quadratic function f(x) = ax^2 + bx + c is given by -b/2a. In this case, a = -0.07 and b = 0 (since there is no linear term), so the x-coordinate of the vertex is x = -b/2a = -0/(-0.14) = 0.
Since x is the number of hours after 6 a.m., the time corresponding to x = 0 is 6 a.m. Therefore, the temperature is a maximum at 6 a.m.
To find the maximum temperature, we evaluate T(0) = -0.07(0)^2 = 0. Therefore, the maximum temperature is 0 degrees Fahrenheit. Note that this result makes sense, since the quadratic function T(x) = -0.07x^2 is a downward-facing parabola, which means that the temperature decreases as the number of hours after 6 a.m. increases.
Step-by-step explanation:
Answer: Answer: To find the time at which the temperature is maximum, we need to find the vertex of the quadratic function T(x) = -0.07x^2. Recall that the x-coordinate of the vertex of a quadratic function f(x) = ax^2 + bx + c is given by -b/2a. In this case, a = -0.07 and b = 0 (since there is no linear term), so the x-coordinate of the vertex is x = -b/2a = -0/(-0.14) = 0.
Step-by-step explanation:
If f(x)=square root of x +3/square root of x, then f'4=
f'(4) = 5/32. This means that at x = 4, the slope of the tangent line to the curve y = f(x) is 5/32.
To find f'(4), we first need to find the derivative of the given function f(x). We can use the quotient rule to do this:
f(x) = sqrt(x) + 3/sqrt(x)
[tex]f'(x) = (1/2)x^(-1/2) - 3/2x^(-3/2)[/tex]
Now we can substitute x = 4 to find f'(4):
[tex]f'(4) = (1/2)4^(-1/2) - 3/24^(-3/2)[/tex]
f'(4) = (1/2)(1/2) - 3/2(1/16)
f'(4) = 1/4 - 3/32
f'(4) = 5/32
Therefore, This also means that the rate of change of f(x) at x = 4 is 5/32, which is the instantaneous rate of change or the derivative of the function at that point.
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Question 4 of 10
Using the graphing function on your calculator, find the solution to the system
of equations shown below.
OA. More than 1 solution
OB. No solution
C. x= 3, y = 4
OD. x = 4, y = 3
y-2x = -2
y-x= 1
The solution to the system of equations is x = 3, y = 4, option C is correct.
To solve the system of equations using a graphing calculator, we first need to rewrite the equations in slope-intercept form:
y - 2x = -2 can be rewritten as y = 2x - 2
y - x = 1 can be rewritten as y = x + 1
From the graph, we can see that the lines intersect at the point (3, 4). Therefore, the solution to the system of equations is x = 3, y = 4
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Almost every year, there is some incidence of volcanic activity on the island of Japan. In 2005 there were 5 volcanine episodes, defined as either eruptions or sizable seismic activity. Suppose the expected number of episodes is 2.4 per year. Let X be the number of episodes in the 2-year period 2008-2009.
(a) What model might you use to model X? Why? Justify the appropriateness of this model for this problem. Provide the parameter values for the model chosen.
(b) Using the model calculate the probability that there will be no episodes in this period?
(c) Using the model, calculate the probability that there are more than three episodes in this period.
a. The appropriate model for this problem is the Poisson distribution because it's model the number of rare events occurring in a fixed interval of time or space.
b. Using the model the probability that there will be no episodes in this period is 0.82%.
c. Using the model, the probability that there are more than three episodes in this period is 70.57%.
(a) The appropriate model for this problem is the Poisson distribution, which models the number of rare events occurring in a fixed interval of time or space. The conditions for a Poisson distribution are:
The events are rare or random.The events are independent of each other.The average rate of events is constant over time or space.In this case, we are interested in the number of volcanic episodes occurring in a 2-year period, which is a fixed interval of time. The events are rare and independent of each other, and the average rate of events is given as 2.4 per year. Therefore, the Poisson distribution is appropriate for modeling X.
The parameter value for the Poisson distribution is λ, the average rate of events per unit of time or space. In this case, λ = 2.4 x 2 = 4.8 for the 2-year period.
(b) The probability that there will be no episodes in this period is given by the Poisson probability mass function:
P(X = 0) = e^(-λ) * λ^0 / 0! = e^(-4.8) * 4.8^0 / 0! = 0.0082 (rounded to four decimal places)
Therefore, the probability that there will be no episodes in the 2008-2009 period is approximately 0.0082, or 0.82%.
(c) The probability that there are more than three episodes in this period is given by the complement of the probability that there are three or fewer episodes:
P(X > 3) = 1 - P(X ≤ 3)
We can use the Poisson cumulative distribution function to calculate P(X ≤ 3):
P(X ≤ 3) = Σ(e^(-λ) * λ^k / k!) for k = 0 to 3
P(X ≤ 3) = e^(-4.8) * (4.8^0 / 0! + 4.8^1 / 1! + 4.8^2 / 2! + 4.8^3 / 3!)
P(X ≤ 3) = 0.2943 (rounded to four decimal places)
Therefore, P(X > 3) = 1 - P(X ≤ 3) = 1 - 0.2943 = 0.7057 (rounded to four decimal places)
Therefore, the probability that there are more than three episodes in the 2008-2009 period is approximately 0.7057, or 70.57%.
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One third of a cake is divided amung 6 people at a party what fraction does each person get
Select the correct answer.
Which pair of statements correctly compares the two data sets?
:
●
+1
0
+2
0 1 2 3 4 5 6
O C.
O D.
00
3
●●
4 5 6
●
7
●
7
8
9
10
11
8 9
H
13
11 12
10 11 12 13
OA. The difference of the means is 1. This value is less than half of the mean absolute deviation of either data set.
OB. The difference of the means is 1. This value is more than half of the mean absolute deviation of either data set.
The difference of the means is 1. This value is 1 times the mean absolute deviation of either data set.
The difference of the means is 1. This value is 2 times the mean absolute deviation of either data set.
The pair of statements that correctly compares the two data sets are A. The difference of the means is 1. This value is less than half of the mean absolute deviation (MAD) of either data set.
How to determine the mean absolute deviation of either data set?To calculate the mean absolute deviation (MAD) of each data set, we have:
First data set:
Mean = (1+0+2+0+1+2+3)/7 = 9/7
MAD = [(1-9/7) + (0-9/7) + (2-9/7) + (0-9/7) + (1-9/7) + (2-9/7) + (3-9/7)]/7
= [2/7 + (-9/7) + 5/7 + (-9/7) + 2/7 + 5/7 + 6/7]/7
= 12/49
Second data set:
Mean = (4+5+6+7+7+8+9+10+11+12+13)/11 = 85/11
MAD = [(4-85/11) + (5-85/11) + (6-85/11) + (7-85/11) + (7-85/11) + (8-85/11) + (9-85/11)
+ (10-85/11) + (11-85/11) + (12-85/11) + (13-85/11)]/11
= [(-61/11) + (-56/11) + (-49/11) + (-42/11) + (-42/11) + (-29/11) + (-16/11) + (-5/11)
+ (6/11) + (17/11) + (28/11)]/11
= 408/121
Therefore, the MAD of the first data set is 12/49, and half of the MAD of the first data set is 6/49, which is less than 1,
Also, the MAD of the second data set is 408/121, and half of the MAD of the second data set is 204/121, which is greater than 1.
Hence, the correct statement is A. The difference of the means is 1. This value is less than half of the mean absolute deviation of either data set.
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show the coordinates
Answer:
A' = (-5,4)
B' = (-4,4)
C' = (-4,5)
D' = (-1,2)
E' = (-2,1)
Step-by-step explanation:
For the 90 degrees counterclockwise rotation (x,y) will be (-y,x) so just switch places and put the negative sign.
Cathy bought a new bicycle for $150. She paid an additional $12 in sales tax. At that rate, how much would she pay for a bycicle helmet that costs $39 before tax?
Cathy would pay $42.12 for a bicycle helmet that costs $39 before tax.
To find out how much Cathy would pay for a bicycle helmet, we need to calculate the sales tax on the helmet and add it to the original price.
The sales tax rate remains the same, so Cathy would pay the same percentage of sales tax on the helmet as she did on the bicycle.
Sales tax on the bicycle = $12
Price of the bicycle = $150
Tax rate = Sales tax / Price of the bicycle = $12 / $150
To calculate the sales tax on the helmet, we multiply the tax rate by the price of the helmet:
Sales tax on the helmet = Tax rate * Price of the helmet = ($12 / $150) * $39
Now we can calculate the total cost of the helmet:
Total cost of the helmet = Price of the helmet + Sales tax on the helmet = $39 + ($12 / $150) * $39
To simplify the calculation, let's first evaluate ($12 / $150):
($12 / $150) = 0.08
Now we can calculate the total cost of the helmet:
Total cost of the helmet = $39 + (0.08 * $39)
Total cost of the helmet = $39 + $3.12
Total cost of the helmet = $42.12
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jeff's golf score was 5 strokes less than mikes golf score. mikes score was 2 strokes more than sams. if sams score relatives to par was 2, what was jeff's golf score
Jeff's golf score was 1 stroke under par.
Let's first find out what was Mike's golf score.
We know that Mike's score was 2 strokes more than Sam's score, so if Sam's score was 2 over par, then Mike's score must have been:
2 + 2 = 4 over par
We also know that Jeff's score was 5 strokes less than Mike's score. Therefore, Jeff's score relative to par would be:
4 + (-5) = -1 over par
So Jeff's golf score was 1 stroke under par.
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Which equations have the same value of x as Three-fifths (30 x minus 15) = 72? Select three options. 18 x minus 15 = 72 50 x minus 25 = 72 18 x minus 9 = 72 3 (6 x minus 3) = 72 x = 4.5
The equations have the same value of x as Three-fifths (30 x minus 15) = 72 are 8 x minus 9 = 72, 3 (6 x minus 3) = 72, x = 4.5. Option C, D and E
What are algebraic expressions?Algebraic expressions are defined as mathematical expressions that are composed of coefficients, constants, variables, terms and factors.
Also, algebraic expressions are known to consist of arithmetic operations.
These operations are;
AdditionBracketParenthesesSubtractionDivisionMultiplicationFrom the information given, we have that;
Three-fifths (30 x minus 15) = 72
This is represented as;
3/5(30x - 15) = 72
divide the values
3(6x - 3) = 72
Now, expand the bracket, we get;
18x - 9 = 72
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Two forces, with magnitudes 100 N and 150 N, act on an object at 90° to one
another. Determine the magnitude of the resultant force acting on the object.
Answer:
345
Step-by-step explanation:
just add them all up thats how i got the answer
The expanded form of a number is given.(6×10,000)+(5×1,000) (7×1(3×1100(6×10,000)+(5×1,000)+(7×1)+(3× 1001 )
What is the number in decimal form?
The value of the given numerical expression will be 8,010.000047.
Given that:
(6 × 10,000) + (5 × 1,000) + (5 × 1,000) + (7 × 1) + (3 × 1001)
[7 × 1 × {3 × 1100 × (6 × 10,000)}]
Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The value of the expression is calculated as,
(6 × 10,000) + (5 × 1,000) + (5 × 1,000) + (7 × 1) + (3 × 1001)
[7 × 1 × {3 × 1100 × (6 × 10,000)}]
(65000 / 1386000000) + 5000 + 7 + 3003
0.000046898 + 5000 + 7 + 3003
8010.000047
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If the median of a set of data is equal to the mean, then
(a) The data are Normally distributed.
(b) The data are approximately Normally distributed.
(c) The distribution is skewed.
(d) The distribution is symmetric.
(e) One can't say anything about the shape of the distribution without any certainty.
If the median of a set of data is equal to the mean, then it implies that the data has a symmetric distribution. The correct answer is option d.
This is because the mean is sensitive to extreme values and tends to be pulled in the direction of the skewness of the distribution. On the other hand, the median is not sensitive to extreme values and only depends on the order of values in the data set.
Thus, if the median and mean are equal, it suggests that the distribution is symmetric and does not have any skewness. However, one cannot infer anything about whether the distribution is normal or approximately normal based solely on the equality of the median and mean.
The correct answer is option d.
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You are planning an end of the year party for your math class. Your teacher needs help deciding which products are the better buy.
Determine the unit rate for each brand and determine what is the best purchase item.
a) What is the cost per bottle of 18 Gatorades?
b) What is the cost per bottle of 24 Gatorades?
c) Which is the better buy?
Step-by-step explanation:
The cost per bottle of 24 Gatorades would be:
• For Gatorade Zero Thirst Quencher Bottles: $0.63 x (24/18) = $0.84
• For Gatorade Thirst Quencher Sports Drink Variety Pack: $0.61 x (24/18) = $0.81
So, the better buy would be Gatorade Thirst Quencher Sports Drink Variety Pack as it has a lower cost per bottle.
I hope that helps! Let me know if you have any other questions.
Assume the distribution of IQ scores for adults can be modeled with a normal distribution with a mean score of 100 points and a standard deviation of 10 points. What percentage of adults have an IQ score higher than 128 points?
The percentage of adults who have an IQ score higher than 128 points using the z score is 0.26%.
Given that,
The distribution of IQ scores for adults can be modeled with a normal distribution.
Mean, μ = 100
Standard deviation, σ = 10
We have to find the percentage of adults who have an IQ score higher than 128 points.
z score = (x - μ) / σ
= (128 - 100) / 10
= 2.8
Percent of adults who are below 2.8 = 0.9974
Percent of adults who are above 2.8 = 1 - 0.0026 = 0.26%
Hence the required percentage is 0.26%.
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find the length of the diagonal for a rectangle whose measurements are 5cm by 12cm
The length of the diagonal for this rectangle is 13 cm.
To find the length of the diagonal for a rectangle with measurements of 5 cm by 12 cm, you can use the Pythagorean theorem. The theorem states that in a right-angled triangle, the square of the length of the hypotenuse (diagonal in this case) is equal to the sum of the squares of the other two sides (length and width).
In this case, the length is 5 cm and the width is 12 cm. Using the Pythagorean theorem:
Diagonal² = Length² + Width²
Diagonal² = 5² + 12²
Diagonal² = 25 + 144
Diagonal² = 169
Now, take the square root of 169 to find the length of the diagonal:
Diagonal = √169
Diagonal = 13 cm
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