if 6 men plough a field in 10 hours how many hours will it taken4 men working at the same rate
Answer: 20/3
Step-by-step explanation:10*4/6=20/3
Out of students appeared in an examination, 30% failed in English, 25% failed in mathematics, 90% passed in at least one subject and 220 students were passed in both subject then, find the number of students appeared in examination
The total number of students appeared in the examination is 488.
Number of students passed in English = 0.7x
Number of students passed in Mathematics = 0.75x
Number of students failed in both subjects = 0.1x
Number of students passed in at least one subject = 0.9x
Number of students passed in both subjects = 220
We know that the total number of students appeared in the examination is x.
So, the number of students who failed in both subjects will be:
0.1x = (number of students failed in English) + (number of students failed in Mathematics) - 220
0.1x = (0.3x) + (0.25x) - 220
0.1x = 0.55x - 220
0.45x = 220
x = 488
To learn more on Percentage click:
https://brainly.com/question/24159063
#SPJ4
The table shows different values for functions f(x) and g(x), which are continuous for all ×20.
The intervals over which there is a value of x for which f(x) = g(x) is given as follows:
[2,3].[5,6].How to solve a system of equations?Considering the graph containing the equations for the system, the solution of the system of equations is given by the point of intersection of all the equations of the system.
The greater functions are given as follows:
f(x) > g(x) for [0,2].g(x) > f(x) for [3,5].f(x) > g(x) for x > 6.When the greater function is exchanged, it means that they intersect, hence the intervals where there is a value of x for which f(x) = g(x) are given as follows:
[2,3].[5,6].More can be learned about a system of equations at brainly.com/question/13729904
#SPJ1
The topology taxi company charges 2. 30 for the first quarter of a mile and 0. 40 for each additional fifth of a mile. Find a linear function which models the taxi fare F as a function of the number of miles driven, m
The linear function that models the taxi fare F as a function of the number of miles driven, m can be written as:
F(m) = 2.30 + 0.40(5m - 0.25)
where 5m - 0.25 represents the total distance traveled in fifth of a mile.
To break this down, we start with the base fare of $2.30 for the first quarter of a mile, which is 1.25 fifth of a mile. Then we add the additional distance traveled beyond the first quarter of a mile, which is given by 5m - 0.25. We multiply this by the per-fifth-of-a-mile charge of $0.40.
For example, if a customer travels 2 miles, then the total distance traveled in fifth of a mile would be 10. So, the fare would be:
F(2) = 2.30 + 0.40(5(2) - 0.25) = 2.30 + 3.95 = $6.25
This means that the taxi fare would be $6.25 for a 2-mile ride with the Topology taxi company.
Learn more about linear function
https://brainly.com/question/15602982
#SPJ4
You are given the following linear programming model in algebraic form, where x, and x2 are the decision variables and Z is the value of the overall measure of performance.
Maximize Z = x1 + 2x^2
Constraint on resource 1: x1 + x2 ≤ 5 (amount available) Constraint on resource 2: x1 + 3x29 (amount available)
a. Identify the objective function, the functional con- straints, and the nonnegativity constraints in this model.
b. Incorporate this model into a spreadsheet. c. Is (x1, x2)= (3, 1) a feasible solution? d. Is (x1, x2)=(1, 3) a feasible solution? e. Use Solver to solve this model.
(a) Objective function: Maximize Z = x1 + 2x2
Functional constraints:
x1 + x2 ≤ 5 (a constraint on resource 1)
x1 + 3x2 ≤ 9 (a constraint on resource 2)
Nonnegativity constraints:
x1 ≥ 0
x2 ≥ 0
(b) Incorporate this model into a spreadsheet, and create a table with columns for x1, x2, and Z.
Enter the objective function in the Z column as "=x1+2*x2".
Enter the constraint on resource 1 as "x1+x2<=5" and the constraint on resource 2 as "x1+3*x2<=9".
Enter the nonnegativity constraints as "x1>=0" and "x2>=0".
(c) Check if (x1, x2) = (3, 1) is a feasible solution, substitute these values into the constraints, and check if they are satisfied:
x1 + x2 ≤ 5: 3 + 1 ≤ 5, so this constraint is satisfied.
x1 + 3x2 ≤ 9: 3 + 3 ≤ 9, so this constraint is also satisfied.
Therefore, (x1, x2) = (3, 1) is a feasible solution.
(d) Check if (x1, x2) = (1, 3) is a feasible solution, substitute these values into the constraints and check if they are satisfied:
x1 + x2 ≤ 5: 1 + 3 ≤ 5, so this constraint is satisfied.
x1 + 3x2 ≤ 9: 1 + 3*3 = 10, which violates this constraint.
Therefore, (x1, x2) = (1, 3) is not a feasible solution.
(e) Solve this model using Solver in Excel, follow these steps:
Click on the "Data" tab and select "Solver" from the "Analysis" group.
In the Solver Parameters dialog box, set the objective function to "Z" and select "Max" as the optimization goal.
Enter the cell range for the decision variables (x1 and x2).
Enter the cell range for the constraints (resource 1 and resource 2).
Select "Add" to add the nonnegativity constraints for x1 and x2.
Click "OK" to solve the model.
The Solver should output the optimal values of x1 = 2 and x2 = 3/2, with a maximum value of Z = 5.
To know more about Functional constraints refer here:
https://brainly.com/question/30703729#
#SPJ11
a cylindrical tank with radius feet and height feet is lying on its side. the tank is filled with water to a depth of feet. what is the volume of water, in cubic feet?
The volume of water in the cylindrical tank, we need to use the formula for the volume of a cylinder, which is V = πr^2h2h, Therefore the volume of water in the tank is 78.54 cubic feet.
To calculate the volume of water in the cylindrical tank, we need to use the formula for the volume of a cylinder, which is V = πr^2h, where r is the radius of the base and h is the height of the cylinder.
Since the tank is lying on its side, the radius is the same as the height. Therefore, we can use r for both values.
The depth of the water, which we'll call d, is the distance from the bottom of the tank to the surface of the water.
To find the volume of water in the tank, we need to find the height of the water in the tank, which is equal to the radius minus the depth: h = r - d.
Now we can substitute these values into the formula for the volume of a cylinder:
V = πr^2h
V = πr^2(r - d)
V = πr^3 - πr^2d
So the volume of water in the tank is equal to the volume of the cylinder minus the volume of the empty space above the water.
We don't have a specific value for the radius or the depth, so we can't calculate the volume exactly. But we can use the given values in the problem to write the formula in terms of those values:
V = π(radius)^3 - π(radius)^2(depth)
For example, if the radius of the tank is 5 feet and the depth of the water is 2 feet, then the volume of water in the tank is:
V = π(5)^3 - π(5)^2(2)
V = π(125) - π(50)
V = 78.54 cubic feet
Therefore, the volume of water in the tank is 78.54 cubic feet.
Visit here to learn more about volume : https://brainly.com/question/1578538
#SPJ11
the properties of ____________ binary systems are detected by examining a light curve.
The properties of eclipsing binary systems are detected by examining a light curve.
Eclipsing binary systems are a type of binary star system where the stars orbit each other in such a way that they periodically pass in front of each other from the perspective of an observer on Earth. This results in periodic variations in the total amount of light observed from the system, which is known as the light curve.
By studying the shape and timing of the light curve, astronomers can determine a number of properties of the binary system, such as the orbital period, the sizes and masses of the stars, and their distance from Earth.
For example, the duration and depth of the eclipses can be used to estimate the sizes of the stars, while the timing of the eclipses can reveal information about their orbital period and any changes in their orbit over time. By analyzing the light curve in detail, astronomers can gain valuable insights into the structure, behavior, and evolution of binary star systems.
Learn more about binary system at https://brainly.com/question/2824068
#SPJ11
Prorate the following expenses and find the corresponding monthly expense. Melinda spends an average of $32 per week on gasoline and $42 every three months on a daily newspaper.
The prorated monthly cost for gasoline and newspapers is $ _______
Round to the nearest cent as needed as needed.
There are roughly 4.33 weeks in a month. The prorated monthly cost for gasoline and newspapers is $152.56.
So the monthly cost for gasoline is:
$32/week x 4.33 weeks/month = $138.56/month (rounded to the nearest cent)
To prorate the newspaper expenses, we need to first find the monthly cost. $42 every three months is equivalent to $14 per month. Therefore, the prorated monthly cost for newspapers is:
$14/month
To find the total prorated monthly cost for both gasoline and newspapers, we add the two monthly costs together:
$138.56/month + $14/month = $152.56/month (rounded to the nearest cent)
Therefore, the prorated monthly cost for gasoline and newspapers is $152.56.
To prorate Melinda's expenses and find the corresponding monthly expense, follow these steps:
1. Calculate the monthly gasoline expense:
Melinda spends $32 per week on gasoline. Since there are approximately 4 weeks in a month, multiply the weekly cost by 4:
$32 x 4 = $128 per month on gasoline.
2. Calculate the monthly newspaper expense:
Melinda spends $42 every three months on a daily newspaper. Divide the three-month cost by 3 to find the monthly cost:
$42 / 3 = $14 per month on newspapers.
3. Add the monthly gasoline and newspaper expenses together to find the total prorated monthly cost:
$128 (gasoline) + $14 (newspapers) = $142 per month.
The prorated monthly cost for gasoline and newspapers is $142.00.
Learn more about expenses at: brainly.com/question/29850561
#SPJ11
What is the sum of the series? 38 Σ j=1 ( j3 − 25j )
475,684
512,735
530,556
548,131
Answer:
530, 556 C.
Step-by-step explanation:
Just did it
Answer:
c
Step-by-step explanation:
The standard deviation of a numerical data set measures the __________ of the data. Select the most appropriate term that makes the statement true.
A 50th percentile
B average
C most frequent value
D variability
E size
The standard deviation of a numerical data set measures the variability of the data. It is a widely used measure in statistics that helps to determine how spread out the values are within a given data set.
By calculating the standard deviation, we can better understand the range and distribution of values in the data set, as well as identify potential outliers. This measure is particularly important in fields such as finance, science, and engineering, where understanding the variability in data can be crucial for making informed decisions and predictions. So, the most appropriate term that makes the statement true is D: variability.
To learn more about standard deviation click here
brainly.com/question/23907081
#SPJ11
Expand and state your answer as a polynomial in standard form. (4x^ 5+y^5 )^2
The standard form of the given expression is [tex](16x^{10} + y^{10} + 8x^{5}y^{5})[/tex].
A function that applies only integer dominions or only positive integer powers of a value in an equation such as the monomial, binomial, trinomial, etc. is a polynomial function. Example: ax+b is a polynomial.
To expand a polynomial in standard form no variable should appear within parentheses and all like terms should be combined.
Here, we have
[tex](4x^{5} + y^{5})^{2}[/tex]
Following the formula,
[tex](a + b)^2 = a^{2} + b^{2} + 2ab[/tex]
[tex](4x^{5} + y^{5})^{2} = (4x^{5})^{2} + (y^5)^{2} + 2 (4x^{5}) ( y^{5})[/tex]
[tex](4x^{5} + y^{5})^{2} = 16x^{10} + y^{10}+ 8x^{5} y^{5}[/tex]
Therefore, the standard polynomial form of this given expression is [tex](16x^{10} + y^{10} + 8x^{5}y^{5})[/tex]. This is a standard form of polynomial because the terms here are written in degrees which are in descending order, and each term has a variable raised to a power and a coefficient. If we add, subtract, or multiply two polynomials, we know that the result is always a polynomial too.
To learn more about polynomials in standard form:
https://brainly.com/question/23069138
#SPJ4
what function would you use to identify a value’s rank as a percent, excluding 0 and 1?
The function can be found using command PERCENTRANK(array, x, [significance])
How to identify a value's rank as a percent?To identify a value's rank as a percent, excluding 0 and 1, we can use the PERCENTRANK function. This function calculates the rank of a value as a percentage of the total number of values in the range, excluding 0 and 1.
The syntax of the PERCENTRANK function is as follows:
PERCENTRANK(array, x, [significance])
where array is the range of cells that contains the data, x is the value for which we want to calculate the rank, and significance is an optional argument that specifies the number of digits to use in the calculation.
For example, the formula =PERCENTRANK(A1:A10, 8) would calculate the rank of the value 8 in the range A1:A10 as a percentage, excluding 0 and 1.
Learn more about value's rank as a percent
brainly.com/question/20714718
#SPJ11
is there any time at which the plots using the exponential and logistic equations appear to coincide?
Yes, there is a specific time at which the plots using the exponential and logistic equations appear to coincide. This occurs when the population size is equal to half of the carrying capacity, which is also known as the inflection point.
At this point, the rate of population growth using the logistic equation is equal to the rate of population growth using the exponential equation. Before the inflection point, the logistic equation will show a slower growth rate than the exponential equation due to limiting factors such as food or space.
After the inflection point, the logistic equation will show a decrease in growth rate as the population approaches its carrying capacity. Therefore, the inflection point is an important concept to understand when comparing the exponential and logistic models in population ecology.
Learn more about population growth here:
brainly.com/question/18415071
#SPJ11
why do we imply by using 98.6 degrees, a level of precision that may be misleading? why not simplify it by just using 98 degrees or rounding up to 99 degrees?
Using a level of precision such as 98.6 degrees can be misleading, and rounding up to 99 degrees or simplifying it to 98 degrees might seem like a more logical approach.
However, it is important to remember that this value was based on a relatively small sample size, and the precision of the measurements may not have been as high as we would expect today.
Additionally, advances in technology have allowed for more accurate and precise measurements of body temperature, and studies have shown that the average body temperature in modern populations is actually slightly lower than 98.6 degrees Fahrenheit.
While using a value such as 98.6 degrees Fahrenheit as a benchmark for normal body temperature may be convenient and familiar, it is important to recognize that this value is not necessarily accurate or meaningful in all situations.
By understanding the concept of precision and the history behind this benchmark, we can make more informed decisions about how we use and interpret this value in medical contexts.
To know more about precision here
https://brainly.com/question/28234389
#SPJ1
If a and b are integers and c is an irrational number, what type of number will c produce?
a Irrational number
b Not enough information
c Neither
dRational number
I need help with these can u at least show me how to solve this
The volume of each sphere rounded to two decimal places are as follows;
Volume = 267.95 in³.Volume = 7,234.56 ft³. Volume = 267.95 yd³.Volume = 44,579.63 in³.Volume = 33.49 yd³.Volume = 14,130 ft³.Volume = 24,416.64 in³.Volume = 50,939.17 ft³.How to calculate the volume of a sphere?In Mathematics and Geometry, the volume of a sphere can be calculated by using the following mathematical equation (formula):
Volume of a sphere, V = 4/3 × πr³
Where:
r represents the radius.
By substituting the given parameters into the formula for the volume of a sphere, we have the following;
Volume of sphere, V = 4/3 × 3.14 × 4³
Volume of sphere, V = 803.84/3 = 267.95 in³.
Volume of sphere, V = 4/3 × 3.14 × 12³
Volume of sphere, V = 21,703.68/3 = 7,234.56 ft³.
Volume of sphere, V = 4/3 × 3.14 × 22³
Volume of sphere, V = 803.84/3 = 267.95 yd³.
Volume of sphere, V = 4/3 × 3.14 × 7³
Volume of sphere, V = 133,738.88/3 = 44,579.63 in³.
Volume of sphere, V = 4/3 × 3.14 × 2³
Volume of sphere, V = 100.48/3 = 33.49 yd³.
Volume of sphere, V = 4/3 × 3.14 × 15³
Volume of sphere, V = 42,390/3 = 14,130 ft³.
Volume of sphere, V = 4/3 × 3.14 × 18³
Volume of sphere, V = 73,249.92/3 = 24,416.64 in³.
Volume of sphere, V = 4/3 × 3.14 × 23³
Volume of sphere, V = 152,817.52/3 = 50,939.17 ft³.
Read more on volume of a sphere here: brainly.com/question/20394302
#SPJ1
The x-axis of each graph has the diameter of a circle in meters. Label the Y axis on each graph with the appropriate measurement of a circle radius, M, circumference, M, or area M2.
The labels of the y-axis of the graphs, and areas, and circumferences obtained based on the formula for the area and circumference of a circle are;
1. First part
First graph;
The y-axis label is; area (m²)
Second graph;
The y-axis label is; radius (m)
Third graph;
The y-axis label is; Circumference (m)
Second part; The area of circle B is 4,500 in²Third part; The circumference is 1 9/11 mFourth part; The circumference of Clare's circle is 75 cmWhat is the equation for the area and the circumference of a circle based on the diameter, D, of the circle?The area of a circle is; A = π × (D²)/4
The circumference of a circle is; C = π·D
The equation for the radius of a circle is r = D/2
The equation for the circumference of a circle is; C = π·D
The equation for the area of a circle is; A = π·D²/4
Therefore, equation for the radius and the circumference are straight line equation, with the slope of the equation for the circumference (π), being larger than the slope of the equation for the radius (1/2)
The variation of the area and the diameter is; A ∝ D², therefore, the shape of the graph for the area is a cup shaped parabola.
The label on the y-axis of the graphs are therefore;
First graph y-axis label is; Area (m²)
Second graph y-axis label is; Radius (m)
Third graph y-axis label is; Circumference (m)
Second part;
Area of circle A = 500 in²
Diameter of circle B = 3 × The diameter of circle A
Let D represent the diameter of circle A, we get;
Area of circle A = 500 in² = π·D²/4
D² = 4 × 500/π = 2000/π
The diameter of circle B = 3·D
Area of circle B = π·(3·D)²/4 = π·9·D²/4
π·9·D²/4 = π × 9 × (2000/π)/4 = 4,500
The area of circle B is 4,500 in²Third part;
The distance Lin's bike travels = 100 meters
Number of times the wheels rotate = 55 times
The circumference of her wheel is therefore; 100 m ÷ 55 = 1 9/11 mFourth part;
The circumference of the circle Priya drew = 25 cm
Diameter of the circle Clare drew = 3 × The diameter of the circle Priya drew
The diameter of Priya's circle = 25/π
Diameter of Clare's circle = 3 × 25/π = 75/π
Circumference of Clare's circle = π × 75/π = 75
The circumference of Clare's circle = 75 cmLearn more on the diameter of a circle here: https://brainly.com/question/14192891
#SPJ1
Which recursive formula represents the sequence that represents the pattern?
Answer:
A
Step-by-step explanation:
a recursive formula allows a term in the sequence to be found from the preceding term.
here the pattern of squares is
1, 4, 16
each term is 4 times the preceding term
then recursive formula is
[tex]a_{n}[/tex] = 4[tex]a_{n-1}[/tex] : a₁ = 1
Suppose that yi (t) and y2 (t) are solutions to the following differential equation such that the Wronskian (yl. y2) (to=1) = 20. Find the Wronskian (y1, y2) (t) for any t. [Hint: see proof at top of page 143] dy(t) +e-3ty(t) = 0 dt d'y(t) (t + 4) dt2
Find the derivative of the function. Everything in parenthesis
is under the square root. y = (√2 − x) · ln
We can use the product rule of differentiation to find the derivative of the given function. The final answer is -1 + (√2 - x) / E.
To find the derivative of the given function, we can use the product rule of differentiation.
y = (√2 − x) · lnE
Let's call the first factor (sqrt(2) - x) as u and the second factor ln(E) as v.
Now,
u' = -1 (as the derivative of x is 1)
v' = 1 (as the derivative of ln(E) is 1)
Using the product rule, we get:
y' = u'v + uv'
= (-1) * ln(E) + (√2 - x) * (1/E) * (1)
= -ln(E) + (√2 - x) / E
Simplifying further,
y' = -1 + (√2 - x) / E
Therefore, the derivative of the given function y = (√2 − x) · lnE is -1 + (√2 - x) / E.
For more about differentiation:
https://brainly.com/question/31539041
#SPJ11
The accompanying table (attached) shows fictitious data for three samples.
(a) Compute SS(between) and SS(within).
(b) Compute SS(total), and verify the relationship between SS(between), SS(within), and SS(total).
(c) Compute MS(between), MS(within), and spooled
SS(between) = 11.59, SS(within) = 22.33. SS(total) = 33.92, verifying the relationship SS(total) = SS(between) + SS(within). MS(between) = 5.795, MS(within) = 1.489, s^2(pooled) = 2.261.
(a) To compute SS(between) and SS(within), we first need to calculate the grand mean and the group means. The grand mean is the average of all the data points, while the group means are the averages of each sample.
Grand mean = (9 + 6 + 7 + 5 + 8 + 6)/18 = 6.33
Sample 1 mean = (9 + 6 + 7)/3 = 7.33
Sample 2 mean = (5 + 8)/2 = 6.5
Sample 3 mean = (6 + 6)/2 = 6
SS(between) measures the variation between the sample means and the grand mean:
[tex]$SS_{between} = 3[(7.33 - 6.33)^2 + (6.5 - 6.33)^2 + (6 - 6.33)^2] = 11.59$[/tex]
SS(within) measures the variation within each sample:
[tex]$SS_{within} = \sum\limits_{i=1}^n (x_i - \bar{x})^2 = (9-7.33)^2 + (6-7.33)^2 + (7-7.33)^2 + (5-6.5)^2 + (8-6.5)^2 + (6-6)^2$[/tex]
SS(within) = 22.33
(b) To compute SS(total), we simply sum the squared deviations of all the data points from the grand mean:
[tex]SS_{total} = \sum\limits_{i=1}^n (x_i - \bar{x}_{grand})^2 = (9-6.33)^2 + (6-6.33)^2 + (7-6.33)^2 + (5-6.33)^2 + (8-6.33)^2 + (6-6.33)^2$[/tex]
SS(total) = 42.33
We can verify the relationship between SS(between), SS(within), and SS(total) by checking that:
SS(total) = SS(between) + SS(within)
In this case, we have:
SS(total) = 11.59 + 22.33 = 33.92
(c) To compute MS(between) and MS(within), we need to divide SS(between) and SS(within) by their respective degrees of freedom (df):
df(between) = k - 1 = 3 - 1 = 2
df(within) = N - k = 18 - 3 = 15
MS(between) = SS(between)/df(between) = 11.59/2 = 5.795
MS(within) = SS(within)/df(within) = 22.33/15 = 1.489
To compute the pooled variance, we first calculate the pooled sum of squares:
SS(pooled) = SS(between) + SS(within) = 11.59 + 22.33 = 33.92
Then, we can compute the pooled variance as:
[tex]$s_{pooled}^2 = \frac{SS_{pooled}}{N-k} = \frac{33.92}{15} = 2.261$[/tex]
To learn more about grand mean
https://brainly.com/question/29037885
#SPJ4
Complete question:
The accompanying table shows fictitious data for three samples. (a) Compute SS(between) and SS(within). (b) Compute SS(total), and verify the relationship between SS(between), SS(within), and SS(total). (c) Compute MS(between), MS(within), and Spooled Sample 2 1 3 23 18 20 29 12 16 17 15 25 23 23 19 Mean 25.00 15.00 19.00 2.74 SD 2.83 3.00 The following ANOVA table is only partially completed. (a) Complete the table. (b) How many groups were there in the study? (c) How many total observations were there in the study? df SS MS 4 Source Between groups Within groups Total 964 53 1123
Confirm that the integral test is applicable and use it to determine whether the series converges. (5 pts) 5k + 2 Κ=1 4. Determine whether the series converges. -k Σ(1-1) k=1"
We cannot use the integral test to determine whether the series [tex]∑(5k+2)/(4^k)[/tex] converges. The series [tex]∑(-1)^k / k[/tex]converges.
The integral test can be applied to a series ∑a_n if:
All the terms a_n are positive.
The terms a_n are decreasing.
The series is infinite.
Let's check these conditions for the series [tex]∑(5k+2)/(4^k)[/tex]:
All the terms are positive since 5k+2 and [tex]4^k[/tex] are positive for all k.
To check if the terms are decreasing, we can calculate the ratio of consecutive terms:
[tex](5(k+1)+2)/(4^(k+1)) * 4^k/(5k+2)[/tex]
= (5k+7)/(5k+2)
Since the numerator is greater than the denominator, the terms are increasing. Therefore, the series does not satisfy the second condition of the integral test.
Hence, we cannot use the integral test to determine whether the series [tex]∑(5k+2)/(4^k)[/tex] converges.
For the second series, let's rewrite it as:
[tex]∑(-1)^k / k[/tex]
This is an alternating series where the absolute values of the terms are decreasing (since 1/k is decreasing). Therefore, we can apply the alternating series test, which states that if the terms of an alternating series are decreasing in absolute value and converge to zero, then the series converges.
In this case, the terms do converge to zero since[tex]lim(k→∞) |1/k| = 0[/tex]. Moreover, since the terms are decreasing in absolute value, we can conclude that the series converges.
Hence, the series [tex]∑(-1)^k / k[/tex]converges.
To know more about integral test refer to-
https://brainly.com/question/28157842
#SPJ11
samantha owns 7 different mathematics books and 5 different computer science books and wish to fill 5 positions on a shelf. if the first 3 positions are to be occupied by math books and the last 2 by computer science books, in how many ways can this be done?
To determine the number of ways Samantha can arrange her mathematics books and computer science books on the shelf, we can use the concept of permutations.
1. First, we'll arrange the 3 mathematics books in the first 3 positions. Since Samantha has 7 mathematics books to choose from, she can arrange them in 7P3 ways:
7P3 = 7! / (7-3)! = 7! / 4! = 7 x 6 x 5 = 210 ways
2. Next, we'll arrange the 2 computer science books in the last 2 positions. Since Samantha has 5 computer science books to choose from, she can arrange them in 5P2 ways:
5P2 = 5! / (5-2)! = 5! / 3! = 5 x 4 = 20 ways
3. Now, we need to multiply the number of ways to arrange the mathematics books by the number of ways to arrange the computer science books since these are independent events:
Total ways = 210 (mathematics books) x 20 (computer science books) = 4200 ways
So, Samantha can arrange her 7 mathematics books and 5 computer science books in 4200 different ways, with the first 3 positions occupied by math books and the last 2 by computer science books.
Learn more about permutations here: brainly.com/question/30649574
#SPJ11
An initial amount of $2700 is invested in an account at an interest rate of 6.5% per year, compounded continuously. Assuming that no withdrawals are made, find the amount in the account after seven years.
Do not round any intermediate computations, and round your answer to the nearest cent.
The amount in the account after seven years is approximately $4,582.72.
Compounding refers to the process of earning interest not only on the principal amount of an investment but also on the interest that the investment has previously earned.
The continuous compounding formula is given by:
[tex]A = Pe^{(rt)}[/tex]
where A is the amount in the account, P is the initial principal, e is the base of the natural logarithm (approximately 2.71828), r is the annual interest rate (as a decimal), and t is the time in years.
In this case, we have P = 2700, r = 0.065, and t = 7. Plugging these values into the formula, we get:
[tex]A = 2700e^{(0.0657)} \\A= $4,582.72[/tex]
Therefore, the amount in the account after seven years is approximately $4,582.72.
To know more about compounding follow
https://brainly.com/question/28020457
#SPJ1
Determine the quadrant in which u/2 lies, and (b) find the exact values of sin(u/2), cos(u/2), and tan(u/2) using the half-angle formulas.
Using half-angle formulas When u = 120 degrees, sin(u/2) = √3 / 2, cos(u/2) = 1/2, and tan(u/2) = √3.
To determine the quadrant in which u/2 lies, we need to know the sign of u/2. If u is positive, then u/2 is also positive, and if u is negative, then u/2 is also negative. If u is equal to 0, then u/2 is also equal to 0.
To find the exact values of sin(u/2), cos(u/2), and tan(u/2) using the half-angle formulas, we need to know the values of sin(u) and cos(u) as well as the quadrant in which u/2 lies.
The half-angle formulas are as follows:
sin(u/2) = ±√((1 - cos(u)) / 2)
cos(u/2) = ±√((1 + cos(u)) / 2)
tan(u/2) = sin(u/2) / cos(u/2)
The signs of sin(u/2) and cos(u/2) depend on the quadrant in which u/2 lies. If u/2 is in the first or fourth quadrant, then sin(u/2) is positive, and if u/2 is in the second or third quadrant, then sin(u/2) is negative. If u/2 is in the first or second quadrant, then cos(u/2) is positive, and if u/2 is in the third or fourth quadrant, then cos(u/2) is negative.
To determine the values of sin(u/2) and cos(u/2), we first need to find the value of cos(u) using the half-angle formula:
cos(u) = 1 - 2 sin^2(u/2)
Once we have found the value of cos(u), we can use the half-angle formulas to find the values of sin(u/2) and cos(u/2).
For example, if u = 120 degrees, then u/2 = 60 degrees, which is in the first quadrant. We know that cos(u) = -1/2, so we can use the half-angle formulas to find the values of sin(u/2) and cos(u/2):
sin(u/2) = √((1 - cos(u)) / 2) = √((1 + 1/2) / 2) = √(3/4) = √3 / 2
cos(u/2) = √((1 + cos(u)) / 2) = √((1 - 1/2) / 2) = √(1/4) = 1/2
tan(u/2) = sin(u/2) / cos(u/2) = (√3 / 2) / (1/2) = √3
Therefore, when u = 120 degrees, sin(u/2) = √3 / 2, cos(u/2) = 1/2, and tan(u/2) = √3.
To know more about half-angle formulas refer here:
https://brainly.com/question/30400810
#SPJ11
Juan weighs 185 pounds. Water makes up 68% of his body weight. How much does the water in his body weight
The requried water present in Juan's body weight is 57.13 kilograms or 117.13 pounds.
To find out how much water is in Juan's body weight, we need to multiply his body weight by the percentage of his weight that is water:
Water weight = Body weight × Percentage of body weight that is water
First, we need to convert Juan's weight from pounds to a more suitable unit for the calculation, such as kilograms:
185 pounds = 84.09 kilograms
Calculate the water weight:
Water weight = 84.09 kg x 68/100 = 57.13 kg
Therefore, the water in Juan's body weight is 57.13 kilograms or 117.13 pounds.
Learn more about the percentage here:
https://brainly.com/question/14615119
#SPJ1
Calculate the taylor polynomials T2(x) and T3(x) centered at x= a for (x)=22sin(x), a=r/2. (express numbers in exact form. Use symbolic notation and fractions where needed. )T2(x)=__________T3(x)=____________
The Taylor polynomials T2(x) and T3(x) for f(x) = 2sin(x) centered at a = r/2 are T2(x) = r - (x-r/2)² and T3(x) = r - (x-r/2)² + (x-r/2)³/3.
To find the Taylor polynomials T2(x) and T3(x) for f(x) = 22sin(x) centered at a = r/2, we need to find the values of the function and its derivatives at x = a and substitute them into the Taylor polynomial formulas.
First, we find the values of f(x) and its derivatives at x = a = r/2:
f(a) = 22sin(a) = 22sin(r/2)
f'(x) = 22cos(x)
f'(a) = 22cos(a) = 22cos(r/2)
f''(x) = -22sin(x)
f''(a) = -22sin(a) = -22sin(r/2)
f'''(x) = -22cos(x)
f'''(a) = -22cos(a) = -22cos(r/2)
Using these values, we can now write the Taylor polynomials:
T2(x) = f(a) + f'(a)(x-a) + f''(a)(x-a)²/2
T2(x) = 22sin(r/2) + 22cos(r/2)(x-r/2) - 22sin(r/2)(x-r/2)²/2
T2(x) = 22sin(r/2) + 11cos(r/2)(x-r/2) - 11sin(r/2)(x-r/2)²
T3(x) = T2(x) + f'''(a)(x-a)³/6
T3(x) = 22sin(r/2) + 11cos(r/2)(x-r/2) - 11sin(r/2)(x-r/2)² - 11cos(r/2)(x-r/2)³/3
Therefore, the Taylor polynomials T2(x) and T3(x) for f(x) = 22sin(x) centered at a = r/2 are:
T2(x) = 22sin(r/2) + 11cos(r/2)(x-r/2) - 11sin(r/2)(x-r/2)²
T3(x) = 22sin(r/2) + 11cos(r/2)(x-r/2) - 11sin(r/2)(x-r/2)² - 11cos(r/2)(x-r/2)³/3
Learn more about the Taylor polynomials at
https://brainly.com/question/31419648
#SPJ4
"Is the polynomial function: f(x, y, z) =
x^22−xz^11−y^24 z homogeneous or not.
Justify it."
The polynomial function f(x, y, z) = x^22 − xz^11 − y^24 z is not homogeneous because its terms have different degrees and it does not satisfy the condition of homogeneity.
A polynomial function is said to be homogeneous if all its terms have the same degree. In the given function f(x, y, z) = x^22 − xz^11 − y^24 z, the degree of the first term is 22, the degree of the second term is 11+1 = 12, and the degree of the third term is 24+1 = 25. Since the degrees of the terms are not the same, the function is not homogeneous.
Another way to justify this is by checking if the function satisfies the condition of homogeneity, which is f(tx, ty, tz) = t^n f(x, y, z) for some integer n and any scalar t. Let's consider t = 2, x = 1, y = 2, and z = 3. Then,
f(2(1), 2(2), 2(3)) = f(2, 4, 6) = 2^22 − 2(6)^11 − 2^24(6)
= 4194304 − 362797056 − 25165824
= -384642576
and
2^n f(1, 2, 3) = 2^n(1)^22 − 2^n(1)(3)^11 − 2^n(2)^24(3)
= 2^(n+22) − 2^(n+1)3^11 − 2^(n+25)3^2
For these two expressions to be equal, we would need n = -11, which is not an integer. Therefore, the function is not homogeneous.
Learn more about polynomial here :-
https://brainly.com/question/31738743
#SPJ11
If n=10, x ¯ (x-bar)=35, and s=16, construct a confidence interval at a 99% confidence level. Assume the data came from a normally distributed population.
The confidence interval is (18.52, 51.48) and the normal distribution is solved
What is Confidence Interval?The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval. Within a specific level of confidence, this is the range of values you anticipate your estimate to fall within if you repeat the test. In statistics, confidence is another word for probability.
With a 95 percent confidence interval, you have a 5 percent chance of being wrong. With a 90 percent confidence interval, you have a 10 percent chance of being wrong. A 99 percent confidence interval would be wider than a 95 percent confidence interval
Confidence Interval CI = x + z ( s/√n )
where x = mean
z = confidence level value
s = standard deviation
n = sample size
Given data ,
To construct a confidence interval for a normally distributed population when the sample size is less than 30, we use the t-distribution instead of the standard normal distribution.
The formula for a confidence interval for the population mean, μ, is:
A = x + z ( s/√n )
And , Where n is the sample mean, s is the sample standard deviation, n is the sample size, and z is the z-score for the desired level of confidence and degrees of freedom (df = n - 1)
In this case, n = 10, μ = 35, and s = 16
The degrees of freedom are df = n - 1 = 9
To find the t-score for a 99% confidence level and 9 degrees of freedom, we can use a t-distribution table or a calculator. Using a calculator, we get:
z = 3.250
Substituting the values into the formula, we get
35 ± 3.250 * (16/√10)
Simplifying the expression, we get:
35 ± 16.48
The lower limit of the confidence interval is:
35 - 16.48 = 18.52
The upper limit of the confidence interval is:
35 + 16.48 = 51.48
Hence , the 99% confidence interval for the population mean μ is (18.52, 51.48)
To learn more about confidence interval click :
https://brainly.com/question/16807970
#SPJ2
¡cuantas unidades se deben producir para que el costo sea el más bajo posible?
[tex]c(x)=800-10x+0.25x^{2}[/tex]