2 1/3 × 3 1/2, giving your answer as a mixed number​

The integral simplifies to ∫[0 to 4] sin(x²) dx.

To evaluate the double integral ∬dxcosyda, where the region D is bounded by y=0, y=x², and x=4, we need to set up the integral in terms of the given bounds and integrate over the region.

The region D is defined as follows:

0 ≤ y ≤ x²

0 ≤ x ≤ 4

To evaluate the integral, we can reverse the order of integration and integrate with respect to y first and then x.

∬dxcosyda = ∫∫D cos(y) dA

Integrating with respect to y first, we get:

∫[0 to 4] ∫[0 to x²] cos(y) dy dx

Integrating cos(y) with respect to y, we have:

∫[0 to 4] [sin(y)] [0 to x²] dx

Now we can evaluate this integral:

∫[0 to 4] [sin(x²) - sin(0)] dx

Since sin(0) = 0, the integral simplifies to:

∫[0 to 4] sin(x²) dx

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Answer:

6

Step-by-step explanation:

Slope is represented by rise/run. Let's use the points (0, -1) and (1, 5). The "rise" from -1 to 5 is 6. The "run" from 0 to 1 is 1. 6/1 is just 6.

The two expressions are not equal, so the function f(x) = 2x² is also not linear.

To determine if a function is linear, we need to verify if it satisfies the linearity property, which states that for any x and y in the domain of the function and any scalars α and β, the function should satisfy f(αx + βy) = αf(x) + βf(y).

Let's examine each function and determine if it is linear:

f(x) = 3x - 2

To check linearity, we need to verify if f(αx + βy) = αf(x) + βf(y). Let's substitute the values:

f(αx + βy) = 3(αx + βy) - 2

= 3αx + 3βy - 2

On the other hand:

αf(x) + βf(y) = α(3x - 2) + β(3y - 2)

= 3αx - 2α + 3βy - 2β

Comparing the two expressions, we can see that they are not equal, so the function f(x) = 3x - 2 is not linear.

f(x) = 2x²

Using the same logic, let's check linearity:

f(αx + βy) = 2(αx + βy)²

= 2(α²x² + 2αβxy + β²y²)

= 2α²x² + 4αβxy + 2β²y²

On the other hand:

αf(x) + βf(y) = α(2x²) + β(2y²)

= 2αx² + 2βy²

The two expressions are not equal, so the function f(x) = 2x² is also not linear.

In conclusion, neither of the given functions is linear since they do not satisfy the linearity property.

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The expression of ⁴√(81x³y⁴z⁸) with rational exponents is: 3x(¾)yz²

The 8 laws of exponents can be listed as follows:

Zero Exponent Law: a^(0) = 1.

Identity Exponent Law: a^(1) = a.

Product Law: a^m × a^n = a^(m+n)

Quotient Law: a^m/a^n = a^(m - n)

Negative Exponents Law: a^(-m) = 1/a^(m)

Power of a Power: (a^m)^n = a^(mn)

Power of a Product: (ab)^m = a^m*b^m

Power of a Quotient: (a/b)^m = a^m/b^m

We are given the algebra expression as:

⁴√81x³y⁴z⁸

This gives us:

81^(1/4) * x^(3/4) * y^(4/4) * z^(8/4)

= 3x^(3/4)yz²

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Answer:

y = 1/3x + 8/3

Step-by-step explanation:

The slope of a line that is perpendicular to the line y = -1/3x + 7 is the negative reciprocal of the slope of the given line, which is -3. So, the slope of the perpendicular line is 1/3.

The point where the perpendicular line intersects the given line is also the point where the two lines intersect, which is (4,2) in this case. So, we can use this point to find the equation of the perpendicular line using the point-slope form of a line:

y - y1 = m(x - x1)

where m is the slope of the line and (x1,y1) is a point on the line.

In our case, the equation of the perpendicular line is:

y - 2 = 1/3(x - 4)

We can simplify this equation to obtain:

y = 1/3x + 8/3

Therefore, the equation of the perpendicular line is y = 1/3x + 8/3.

To determine which set of data most likely has a mean closest to 29.5, we need to analyze the shape and position of the histograms in relation to the value 29.5.

Looking at the histograms described:

The first histogram ranges from 9 to 48, and the upward trend starts from 1 and ends at 33, followed by a downward trend. This histogram suggests that there may be values lower than 29.5, which would bring the mean below 29.5.

The second histogram ranges from 15 to 48, with an upward trend from 1 to 30 and then a downward trend. Similar to the first histogram, it suggests the possibility of values lower than 29.5, indicating a mean below 29.5.

The third histogram ranges from 12 to 56, and the upward trend starts from 1 and ends at 32, followed by a downward trend. This histogram covers a wider range but still suggests the possibility of values below 29.5, indicating a mean below 29.5.

The fourth histogram ranges from 15 to 54 and exhibits multiple trends. While it has fluctuations, it covers a wider range and includes both upward and downward trends. This histogram suggests the possibility of values above and below 29.5, potentially resulting in a mean closer to 29.5.

Based on the descriptions, the fourth histogram, with its more varied trends and wider range, is most likely to have a mean closest to 29.5.

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The optimal values of x and y that minimize the objective-function x + y, subject to the given constraints, are x = 4 and y = 0.

We can find the corner points of the feasible region and evaluate the objective function at those points to determine the optimal solution.

Graph the constraints:

Start by graphing the inequalities:

x + y ≥ 7

5x + 2y ≥ 20

x ≥ 0

y ≥ 0

Plot the lines x + y = 7 and 5x + 2y = 20. To graph x + y = 7, plot two points that satisfy the equation, such as (0, 7) and (7, 0), and draw a line through them. To graph 5x + 2y = 20, plot two points such as (0, 10) and (4, 0), and draw a line through them.

Shade the region that satisfies the inequalities x ≥ 0 and y ≥ 0.

The feasible region will be the shaded region.

Identify the feasible region:

The feasible region is the shaded region where all the constraints are satisfied. In this case, the feasible region will be a polygon bounded by the lines x + y = 7, 5x + 2y = 20, x = 0, and y = 0.

Find the corner points:

Locate the intersection points of the lines and the axes within the feasible region. These are the corner points. In this case, we have the following corner points:

Intersection of x + y = 7 and x = 0: (0, 7)

Intersection of x + y = 7 and y = 0: (7, 0)

Intersection of 5x + 2y = 20 and x = 0: (0, 10)

Intersection of 5x + 2y = 20 and y = 0: (4, 0)

Evaluate the objective function:

Evaluate the objective function, which is x + y, at each corner point:

(0, 7): x + y = 0 + 7 = 7

(7, 0): x + y = 7 + 0 = 7

(0, 10): x + y = 0 + 10 = 10

(4, 0): x + y = 4 + 0 = 4

Determine the optimal solution:

The optimal solution is the corner point that minimizes the objective function (x + y). In this case, the optimal solution is (4, 0) because it has the smallest objective function value of 4.

Therefore, the optimal values of x and y that minimize the objective function x + y, subject to the given constraints, are x = 4 and y = 0.

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Answer:

answer: 1) false  2) true  3) true   4) false

Step-by-step explanation:

A: pass (0,0) (12,6)

slope: 6/12 = 1/2

y = 1/2 x

x=1   y= 1/2

B: pass(0,0) (4,6)

slope: 6/4 = 3/2

y = 3/2 x

y=1  x= 2/3

Answer:

The total change in the number of bushels she has for sale after 5 days is 83.125 bushels

Step-by-step explanation:

The given parameters are;

The initial number pf bushels the farmer has = 120 bushels

The amount of bushels of wheat the farmer sells each day = 16⁵/₈ = 16.625

The number of bushels sold after 5 days = 16.625 × 5 = 83.125 bushels

The total change in the number of bushels she has for sale after 5 days = The number of bushels sold after 5 days

The total change in the number of bushels she has for sale after 5 days = 83.125 bushels.

Answer:

very hard

this is a really hard problem but ignore the graph and pay attention to the numbers

Step-by-step explanation:

Answer:

Option D: x ≥ 1.

Step-by-step explanation:

Here we have the quotient:

\(\frac{\sqrt{15*(x - 1)} }{\sqrt{2*x^2} }\)

Here we have two restrictions for the domain.

first, the denominator can never be zero, so x must be different than zero.

Second, the arguments of the square roots can not be negative.

The one in the denominator is always positive because we have the square of x.

So let's look at the values of x, such that:

15*(x - 1) ≥ 0

(x - 1) ≥ 0

x ≥  1

Note that when x ≥ 1, we are also removing the problem in the denominator, then we can conclude that the fraction is defined when:

x ≥ 1.

The correct option is D

Answer:

77 Fahrenheit

Step-by-step explanation:

Answer:

Step-by-step explanation:

I am in ninth grade and taking Algebra, I can maybe help you, what is it you need help with/are confused about?

Answer:

The key graphical features obtained from a polynomial function are: the zeros, the turning points and the end behaviour. A "zero" of a polynomial function is an input value that produces an output of zero (0).

The peak current for the given circuit is equal to the absolute value of i.

In an alternating current circuit, the peak current is equal to the maximum value of the current over a complete cycle. Since it is given that the current at any given time t (in seconds) in the circuit is; 'i' (in amperes), the peak current can be calculated as the absolute value of i.

For instance, if the current 'i" at any given time t is 5 A, then the peak current in the circuit will also be 5 A.

This is because the peak current represents the maximum magnitude of the current and is independent of the direction of the current.

Therefore, the peak current for the given circuit is equal to the absolute value of i.

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Answer:

Cost price of the cycle = Rs. 1200

Selling price of the cycles = Rs. 1500

SP > CP ⇒ there is a gain.

⇒ Gain = SP - CP = 1500 - 1200 = Rs. 300

∴ Gain Percentage =

CP

Gain

(100)%

=

1200

300

(100)%=25%

∴ The shopkeeper makes a profit of 25%

The correct answer is option  c. bell-shaped. The normal distribution is a type of continuous probability distribution that is symmetrical and bell-shaped, often referred to as the "bell curve".

In honour of German mathematician Carl Friedrich Gauss, it is often referred to as the Gaussian distribution. A single peak at the centre and a progressive drop in density as one proceeds away from the centre define this distribution.

The normal distribution is a significant probability distribution because it may be used to describe a wide range of natural occurrences, including measurements of people's heights and weights, test scores, and other phenomena.

The likelihood of specific outcomes is also described using it in statistics. In hypothesis testing, the normal distribution is frequently utilised since it is thought that the data will follow a normal distribution.

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Answer:

673.82 cm³

Explanation:

cylinder volume : \(\sf \pi r^2h\)

\(\rightarrow \sf \pi (4.3)^2(11.6)\)

\(\rightarrow \sf 673.82 \ cm^3\)

Therefore , the solution of the given problem of number line comes out to be option D is correct .

The number line, a representation of real numbers integers in visual form, is a tool for teaching mathematics. An intensity line is depicted by it. Every actual number is used to represent a point just on real number, or every precise number is used to represent a position. The separations between increments on a number line are equation. The numbers on a line can only be replied in the manner indicated by those numbers. The number's intended usage will be determined by the question it answers.

Here,

Given :

Because multiplying two negative integers together

results in a positive number,

the meaning of -16 is not -4.

as a result: -4 will turn into 16

So, option D is correct .

Therefore , the solution of the given problem of number line comes out to be option D is correct .

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Answer:

x/7 + 9 = 6

Step-by-step explanation:

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Answer:

the answer is 2

Step-by-step explanation:

Answer:

She can make 2 bags of 4, and she will have 3 bananas left.

Step-by-step explanation:

4 + 4 + 4 = 12; that is 1 banana too many since she only has 11 bananas.

She has 11 bananas, so she has 4 + 4 + 3 = 11.

She can make 2 bags of 4, and she will have 3 bananas left.

Residual Plot A indicates that the linear model is not appropriate because the fanned pattern shows that the model's predicting power decreases as the values of the explanatory variable increases. Residual Plot B indicates that the linear model is appropriate because the scattered residuals suggest a linear relationship.

Residual Plot A shows a fanned pattern which indicates that the linear model is not appropriate. This means that the model's predicting power decreases as the values of the explanatory variable increases. This suggests that the relationship between the dependent and independent variables is not linear and a different model may be necessary. Residual Plot B, on the other hand, shows a scattered pattern which suggests that the linear model is appropriate. The scattered pattern indicates that the data points are randomly distributed, which is a sign of a linear relationship. This indicates that the linear model is an appropriate fit for the data.

the complete question is :

Tell what each of the residual plots to the right indicates about the appropriateness of the linear model that was fit to the data. (a). Choose the best answer for residuals plot A. The fanned pattern indicates that the linear model is not appropriate. The model's predicting power decreases as the values of the explanatory variable increases. B. The fanned pattern indicates that the linear model is not appropriate. C. The model's predicting power increases as the values of the explanatory variable increases. The scattered residuals plot indicates an appropriate linear model. (b). Choose the best answer for residuals plot A. The scattered residuals plot indicates an appropriate linear model. B. The curved pattern in the residuals plot indicates that the linear model is not appropriate. The relationship is not linear. C. The fanned pattern indicates that the linear model is not appropriate. The model's predicting power decreases as the values of the explanatory variable increases.

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Answer:

27 Grams

Step-by-step explanation:

The mean score of 90, and percentile of Bob's score of 80, gives Bob's exam score as approximately 92.5%

The Z-Score of the 80th percentile is 0.8416

The formula for Z-Score is presented as follows;

\(z = \frac{x - \mu}{ \sigma} \)

Where;

\( \sigma = The \: standard \: deviation\)

\( \mu = The \: mean = 90\%\)

x = The given score

Taking the mean as a proportion, we have;

\( \sigma = \sqrt{\frac{\mu \cdot (1-\mu)}{n}}\)

Which gives;

\( \sigma = \sqrt{\frac{0.9 \times (1-0.9)}{100}}= 0.03\)

Therefore, when z = 0.8416, gives;

\(0.8416 = \frac{x - 0.9}{ 0.03} \)

x = 0.8416 × 0.03 + 0.9 ≈ 0.925

Therefore;

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Answer: 144m

Step-by-step explanation:

6x6=36

(9 x 3) x 1/2 = 13.5

13.5 x 8(bc there are 8 triangles) = 108

108 + 36 = 144

Hope this helps! Please let me know if you need more help or think my answer is incorrect. Brainliest would be MUCH appreciated. Have a wonderful day!

Answer:

The area would be 13.

Step-by-step explanation: