Differentiating y = x^3 ln 2x/e^x Sin x is: y' = x^2 [(3 ln 2x/e^x Sin x + 3/x) - 2 ln 2x/e^x Sin x cos x + cos x].
What is Differentiation?Differentiate y can be find using the product and chain rule.
Using the chain rule
v'(x) = [1/(2x/e^x)] * (2e^x - e^x*2x) / (2x/e^x)^2
v'(x) = [e^x(2-e^x)] / (2x)^2
Using the product rule
y' = 3x^2 ln(2x/e^x) sin(x) + x^3 [e^x(2-e^x)] / (2x)^2 sin(x) + x^3 ln(2x/e^x) cos(x)
Simplifying
y' = 3x^2 ln(2x/e^x) sin(x) + (x/2) [2-e^x] sin(x) + x^3 ln(2x/e^x) cos(x)
So,
derivative of y is:
y' = 3x^2 ln(2x/e^x) sin(x) + (x/2) [2-e^x] sin(x) + x^3 ln(2x/e^x) cos(x)
Therefore the differentiate of y is 3x^2 ln(2x/e^x) sin(x) + (x/2) [2-e^x] sin(x) + x^3 ln(2x/e^x) cos(x).
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Ms. Monti bought * adult tickets and y
children's tickets to an ice-skating show. She spent a total of $145. The equation below describes the relationship
between x and y.
25x + 15y = 145 The ordered pair (4, 3) is a solution of the equation. What does the solution
(4, 3) represent?
A Ms. Monti bought 4 adult tickets and
3 children's tickets. B Adult tickets cost $4 each and
children's tickets cost $3 each. C Ms. Monti spent $4 on adult tickets
and $3 on children's tickets. D The cost of 4 adult tickets equals the
cost of 3 children's tickets.
PLEASE HELP (WILL GIVE BRAINLIEST)
Answer:
V = 3 × 2 × 6 = 36 cubic centimeters
apllo traveld 48 leauges in 3 day then he tripled his rate how long would it take him to travel 336 leagues at this new speed
Suppose f(x) =8^3x and g(x) =8^4x which of these function operations are correct select all that apply
Suppose [tex]f(x) =8^{3x[/tex] and [tex]g(x) =8^{4x[/tex], function operations that are correct include the following:
A. (f + g)(x) = [tex]8^{3x} + 8^{4x}[/tex]
B. (f × g)(x) = [tex]8^{7x}[/tex]
C. (f - g)(x) = [tex]8^{3x} - 8^{4x}[/tex]
What is an exponent?In Mathematics, an exponent is a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.
This ultimately implies that, an exponent is represented by the following mathematical expression;
bⁿ
Where:
the variables b and n are numerical values (numbers) or an algebraic expression.n is referred to as a superscript or power.By applying the division and multiplication law of exponents for powers of the same base to the functions, we have the following:
(f × g)(x) = [tex]8^{3x+ 4x}=8^{7x}[/tex]
(f ÷ g)(x) = [tex]8^{3x- 4x}=8^{-x}[/tex]
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Solve the following system of equations using matrices (row operations). If the system has no solution, say that it is
inconsistent.
2x-4y= -4
3x+3y= 2
Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.
OA. The solution is.
(Simplify your answers.)
OB. There are infinitely many solutions. The solution can be written as {(x,y) |x=y is any real number).
(Simplify your answer. Type an expression using y as the variable.)
OC. The system is inconsistent.
Inc
Claim: fewer than 7.4% of homes have only a landline telephone and no wireless phone. Sample data: A survey by the National Center for Health Statistics showed that among 13,323 homes 5.77% had landline phones without wireless phones. Complete parts (a) and (b).
There is sufficient evidence to suggest that the proportion of homes with only a landline phone is less than 7.4%.
Null hypothesis: p ≥ 0.074
proportion of homes with only a landline phone is greater than or equal to 7.4%
Alternative hypothesis: p < 0.074 (proportion of homes with only a landline phone is less than 7.4%)
where p is the true proportion of homes in the population that have only a landline phone.
(b) Compute the test statistic and p-value assuming the null hypothesis is true, using a significance level of α = 0.05.
To compute the test statistic, we first need to calculate the sample proportion:
p cap= 0.0577
The test statistic is given by:
z = (p cap - p) / √p(1-p)/n
where n is the sample size. Substituting the values, we get:
z = (0.0577 - 0.074) / √0.074(1-0.074)/13323)
= -12.28
the p-value is less than 0.0001, which is much smaller than the significance level of 0.05.
Therefore, we reject the null hypothesis and conclude that there is sufficient evidence to suggest that the proportion of homes with only a landline phone is less than 7.4%.
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Y= 4(x+ 3)^2 -100 I need the answerrrrr
Answer:A frequency table is a type of statistic used to organize and display data.
What is data set?
A data set is a collection of related data records or observations, usually containing information about a particular subject or area of study. Data sets can be used to analyze trends, make predictions, and provide insights into various phenomena. Data sets can be collected from a variety of sources, such as surveys, experiments, simulations, or other research methods. They are typically organized into tables and can include both quantitative and qualitative data.
It is a chart that shows how often something occurs within a given set of data. The categories in a frequency table are the different values or categories of data, and the frequencies are the number of times each category occurs.
Relative frequency is the ratio of the number of times a category occurs in the data set to the total number of values in the data set. It is usually expressed as a percentage or decimal. For example, if the data set contains 20 values and the category "A" occurs 5 times, the relative frequency of "A" is 25%.
Cumulative frequency is the sum of the frequencies up to a given point in the data set. It is used to show how many values are below or above a certain category. For example, if the data set contains 20 values and the category "A" occurs 5 times, the cumulative frequency of "A" is 5. This means that there are 5 values that are below or equal to "A" in the data set.
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The applet has eight pairs of triangles. Each group member should choose 1–2 pairs of triangles. Use them to help you answer the following questions.
Which pair(s) of triangles do you have?
Can each pair be composed into a rectangle? A parallelogram?
I don't have access to the applet you are referring to. Can you please provide more information or context about the applet so I can better assist you?
Selena took a pizza out of the oven, and it started to cool to room temperature (68°F). She will serve the pizza when it reaches 130°F. She took the pizza out at 5:00 P.M. Use regression to find when she can serve it.
Selena can serve the pizza at around 6:40 P.M.
How to explain the regressionThe regression line should have the equation y = -1.7x + 300, where y is the temperature, x is the time in minutes since the pizza was taken out of the oven, -1.7 is the slope of the line, and 300 is the y-intercept.
Set y (the temperature) to 130°F, and solve for x (the time).
130 = -1.7x + 300
-170 = -1.7x
x ≈ 100
According to the regression model, the pizza will reach 130°F after about 100 minutes after it was taken out of the oven. Therefore, Selena can serve the pizza at around:
= 5 + 1:40
= 6:40 P.M.
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Do the following using Matlab: Generate 10 numbers between 1 and 6, calculate the mean. Generate 100 numbers between 1 and 6. calculate the mean. Generate 1000 numbers between 1 and 6, calculate the mean. There is a command in Matlab to generate numbers. Do not include the numbers when you submit the project. The project should show the commands used and the results only The idea is to roll a die using Matlab commands, instead of doing it manually. Roll a die 10 times and record the outcome and then find the average of the outcomes. Then compare the means for the cases of 10, 100 & 1000. On page 2 of lecture 10, we found that the mean of rolling a die to be 3.5. Therefore, your answer will be close to 3.5 every time you repeat the experiment for larger numbers.
We can see that the means we got from Matlab are close to 3.5 for larger numbers of rolls.
We have,
To generate numbers between 1 and 6 in Matlab, we can use the "randi" command.
To generate 10 numbers, we can use:
```matlab
numbers10 = randi([1, 6], [1, 10]);
mean10 = mean(numbers10);
disp(mean10);
```
To generate 100 numbers, we can use:
```matlab
numbers100 = randi([1, 6], [1, 100]);
mean100 = mean(numbers100);
disp(mean100);
```
To generate 1000 numbers, we can use:
```matlab
numbers1000 = randi([1, 6], [1, 1000]);
mean1000 = mean(numbers1000);
disp(mean1000);
```
After running these commands, we will get the means for generating 10, 100, and 1000 numbers between 1 and 6.
As mentioned in the question, the mean of rolling a die is 3.5.
Therefore,
We can see that the means we got from Matlab are close to 3.5 for larger numbers of rolls.
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(a) The equation of a straight line, 4, is given as y=-²x = ³
(i) State the gradient of the line, l₁.
(ii)The point A (b, 4) lies on the line l₁. Determine the value of b.
(iii) A line, 12, passing through the point (0,-5), is perpendicular to l₁. Find the equation of the straight line l2.
please help me!!!!!!
The line of reflection of the given image is:
A reflection across y = -3
What is the Line of Reflection?A line of reflection is a line that lies between two identical mirror images, so the distance of any point of one figure from the line will equal the distance of the same point of the mirror image (flipped figure).
The definition above tells us that if we are given two images, such as mirror images of each other, the line of reflection can be determined by calculating the midpoint from any two points of the figures.
Looking at the given image, the center point of the mirror images is seen as y = -3
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Use technology to help you test the claim about the population mean, , at the given level of significance, , using the given sample statistics. Assume the population is normally distributed.
The null hypothesis and the alterative hypothesis are [tex]H_0[/tex] : [tex]\mu[/tex] > 1220
[tex]H_\alpha[/tex]: [tex]\mu[/tex] ≤ 1220.
The standardized test statistic is 1.725.
We have,
[tex]\mu[/tex] > 1220,
α = 0.03
[tex]\sigma[/tex] = 202.17
X = 1249.88
n= 300
a) According to the claim and the sample statistics, the null hypothesis and the alterative hypothesis are given by:
[tex]H_0[/tex] : [tex]\mu[/tex] > 1220
[tex]H_\alpha[/tex]: [tex]\mu[/tex] ≤ 1220
b) The standardized test statistic is
=| [tex](\mu[/tex] - X) / ([tex]\sigma[/tex] / √n)|
= |( 1220 - 1249.88) / (202.17/√300)|
= |(-29.88)/ 17.320|
= |-1.725|
= 1.725
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Solve the following for θ, in radians, where 0≤θ<2π.
4sin2(θ)−7sin(θ)−4=0
Select all that apply:
0.4
3.61
1.66
5.81
1.4
3.07
Answer:
3.615.81Step-by-step explanation:
You want solutions to the equation 4sin(θ)² -7sin(θ) -4 = 0 on the interval [0, 2π].
GraphA graph of the left-side expression shows it has a value of 0 at ...
θ ≈ 3.61 or 5.81.
CheckUsing a calculator to check the offered answer choices, we find the values of θ that best satisfy the equation are θ = 3.61 or 5.81. (For this purpose, ±0.02 ≈ 0.)
Algebraic solutionWe can let x = sin(θ). Then the equation is ...
4x² -7x -4 = 0
x² -7/4x = 1
(x -7/8)² = 1 +(7/8)² = 113/64
x = (7 ±√113)/8
The value (7+√113)/8 is greater than 1, so the only value of x that is useful here is x = (7-√113)/8. The angles in the desired range are ...
{π - arcsin((7 -√113)/8), 2π +arcsin((7 -√113)/8)} ≈ {3.61, 5.81} . . . radians
Answer this please for LARGE REWARD
Answer:
19.5625
Step-by-step explanation:
[tex]\frac{2(12) + 4(15) + 16 +18 + 2(20) + 22 +3(25) +2(29)}{16}[/tex] = [tex]\frac{313}{16}[/tex] = 19.5625
We add up all the numbers that are represented on the graph and then divide that by 16 because there are 16 numbers.
Helping in the name of Jesus.
A
Find the approximate volume of a cylinder with a radius of 5 ft. and height of 40 ft.
Use the approximation 3.1416 or the calculator in your calculations. Round your answer to the nearest hundredth.
B
Find the approximate volume of a cylinder with a diameter of 2 ft. and height of 6 ft.
Use the approximation 3.1416 or the calculator in your calculations. Round your answer to the nearest hundredth.
Answer: Part A) 3,141.59 Part B) 75.40
Step-by-step explanation:
Sorry if this is wrong.
PLEASE HELP (WILL GIVE BRAINLIEST
The exact volume of the soup can is 18.375 π cubic inches. So, correct option is C.
The volume of a cylinder can be found by multiplying the area of the base (circle) by the height of the cylinder. In this case, the diameter of the base is 3.5 inches, which means the radius is 1.75 inches (since radius = diameter/2).
So the area of the base can be calculated as:
π × (1.75 in)² = π × 3.0625 in²
The height of the cylinder is given as 6 inches.
Therefore, the exact volume of the soup can would be:
π × (1.75 in)² × 6 in = π × 3.0625 in² × 6 in = 18.375 π cubic inches (rounded to two decimal places)
So, correct option is C.
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Cindy has a new job offer but will need a new car for the job. After planning a budget, they determine that they can afford to pay at most $215 per month for a 6-year car loan. If an annual percentage rate of 2.1% is available to finance the car loan, calculate the value of the most expensive car loan that Cindy can afford. Round to the nearest whole
number
The value of the most expensive car loan that Cindy can afford is $13,712
We are given that;
Amount= $215
Percentage= 2.1%
PMT = 215 i = 0.021 / 12 = 0.00175 (the annual interest rate divided by 12 months) n = 6 × 12 = 72 (the number of months in 6 years)
Now,
The formula for the present value of an annuity is:
PV = PMT × (1 - 1/(1 + i)^n) / i
where:
PV = present value PMT = payment amount i = interest rate per period n = number of periods
Plugging these values into the formula, we get:
PV = 215 × (1 - 1/(1 + 0.00175)^72) / 0.00175 PV = 215 × (1 - 0.888) / 0.00175 PV = 215 × 0.112 / 0.00175 PV = 13,712
Therefore, by the percentage the answer will be $13,712.
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In circle R, find arc length of arc GH
The length of the arc GH is 13.3 cm
What is length of an arc?The length of an arc is the distance that runs through the curved line of the circle making up the arc.
The length of an arc is expressed as;
l = tetha/360 × 2πr
tetha = R
R = 360-( 170+80)
R = 360-250
R = 110°
l = 110/360 × 2 × 3.14 × 6.4
l = 4787.2/369
l = 13.3 cm (1.dp)
therefore the length of the arc GH is 13.3 cm
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Add and simplify 12ft. 8in. + 16ft. 11in.
Answer:
Step-by-step explanation:
29 ft
7 in
What is the sum of 3.0 x 4.1 x 5.5
Answer: 67.65
Step-by-step explanation:
Multiply 3.0*4.1 and you get 12.3
Then take that sum and multiply it by the 5.5
So 12.3*5.5=67.65
I'm needing help with setting up these equations
The sides show that we have an equilateral triangle
What is the measure of each of the sides?An equilateral triangle is a triangle in which all three sides are of equal length. Since all three sides are equal, all three angles are also equal and measure 60 degrees each.
We know that;
12x - 22 = 10x - 6
Collect like terms;
12x - 10x = -6 + 22
2x = 16
x = 8
Thus the sides of the triangle are;
12(8) - 22 = 74
10(8) - 6 = 74
7(8) + 18 = 74
In the second triangle;
4x - 25 = x + 14
4x - x= 14 + 25
3x = 39
x = 13
Thus the sides are;
4(13) - 25 = 27
13 + 14 = 27
6(13) - 51 = 27
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Just Need the blanks filled in PLEASE HELP
The Equation based on the function will be: t = (1/0.07) * ln(P/1,500,000)
How to explain the functionInitially, the exponential expression is extracted and formulated as follows:
It should be noted that to obtain e^(0.07t) = P/1,500,000
Secondly, in order to determine the value of t, take the natural logarithm of both sides of the equation such that:
Take ln(e^(0.07t)) = ln(P/1500000)
It can now be represented by 0.07t = ln(P/1500000)
Finally, on dividing both components of the term through 0.07, it results in the isolation of t where:
Equation: t = (1/0.07) * ln(P/1,500,000)
In conclusion, this function's inverse describes the number of years, since the year 1990, for a determined population figure, P - its formation being previously outlined above.
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Question 4
A is at -6 and B is at 9. Find the point, T, so that T is three-fifths of the distance from A to B.
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
1
2 3 4 5 6 7 8 9 10
The location of point T on the number line is 3
Calculating the location of point TFrom the question, we have the following parameters that can be used in our computation:
A = -6
B = 9
T = three-fifths of the distance from A to B.
Using the above as a guide, we have the following:
T = A + 3/5 *(B - A)
Substitute the known values in the above equation, so, we have the following representation
T = -6 + 3/5 *(9 + 6)
Evaluate
T = 3
Hence, the location is 3
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2. Tell if the number shown is written in scientific notation. If it is, write correct, if incorrect
explain why and correct the mistake.
A. 0.5045 x 10
B. 2.804 x 10"
C. 12.04 x 10
The number shown is not written in scientific notation because the 10 do not raise to power of any number, and exponential on the second value do not represent a particular power.
What is Scientific notation?Scientific notation can be described as the way of writing very large as well as very small numbers.
It should be noted that the number is written in scientific notation which is been done as a result of the number falling between 1 and 10 and then this number is been multiplied by a power of 10 instance of this is 6.5 ✕ 10^8, then we can see that none of the given values have the sa,me expresion with this example.
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14. A clothing store has a cost of producing t-shirts at $4.50 per unit. The store also has a
monthly rent charge of $500. The store sells each t-shirt for $12.00 each.
Write an equation to model the store's profits each month:
Answer:
there gonna have to buy 120 to pay the rent
A group of student athletes were asked which organized sport they participate in. Each athlete participates in exactly 1 sport. The results are shown in this frequency table. How many baseball and basketball players are there? Enter your answer in the box. players
14
6
9
8
12
10
12 baseball and 9 basketball players are there. The frequency of a value in the data is its occurrence.
One approach to display data is in a frequency table. To summarise bigger collections of data, the data are organised and counted. You can examine the distribution of the data across various values using a frequency table. The frequency of a value in the data is its occurrence. We can immediately see how frequently each value appears in a table. 12 baseball and 9 basketball players are there.
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(a + 2)/(1 + a + a ^ 2) - (a - 2)/(1 - a + a ^ 2) - (2a ^ 2)/(1 + a ^ 2 + a ^ 4)
In which quadrant does the point (-25, 15) lie ?
The point (-25, 15) lies in the third quadrant above the x-axis and left to the y-axis.
The four quadrants are formed by the intersection of the x-axis and the y-axis on a Cartesian plane. The point (-25, 15) is represented by the coordinates (-25) and (15) on the x and y-axis, respectively. Since the x-coordinate is negative, the point lies to the left of the y-axis.
Similarly, since the y-coordinate is positive, the point lies above the x-axis. Therefore, the point (-25, 15) is located in the third quadrant, which is below the x-axis and to the left of the y-axis. In this quadrant, both the x and y-coordinates are negative.
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math hw for tonight
help solve this problem! Thank you!
ap cal bc
Answer:
3t^2i + 2tj is the correct answer.
