Determine the interval on which the solution exists. Do not solve (t2−9)y′−lnty=3t,y(4)=−3.

Answer:it b

Step-by-step explanation:

The volume of oil exiting the pipe is approximately 100 cu in/hr, 2,400 cu in/day, and 1.39 cu ft/day when converting cu in/day to cubic feet per day.



To calculate the volume of oil exiting the pipe every hour, you would need to know the flow rate of the oil in cubic inches per hour. Let's assume the flow rate is 100 cubic inches per hour.To find the volume of oil exiting the pipe every day, you would multiply the flow rate by the number of hours in a day. There are 24 hours in a day, so the volume of oil exiting the pipe every day would be 100 cubic inches per hour multiplied by 24 hours, which equals 2,400 cubic inches per day.

To convert the volume from cubic inches per day to cubic feet per day, you would need to divide the volume in cubic inches by the number of cubic inches in a cubic foot. There are 1,728 cubic inches in a cubic foot. So, dividing 2,400 cubic inches per day by 1,728 cubic inches per cubic foot, we get approximately 1.39 cubic feet per day.

Therefore, the volume of oil exiting the pipe is approximately 100 cubic inches per hour, 2,400 cubic inches per day, and 1.39 cubic feet per day.

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Answer:

\(y=\frac{1}{2}x-3\)

Step-by-step explanation:

Start by writing the equation out as it is given in the question (in this case, in standard form).

\(3x-6y=18\)

Next, subtract \(3x\) from both sides.

\(3x-3x-6y=18-3x\\-6y=18-3x\)

Switch around the \(18\) and the \(-3x\).

\(-6y=-3x+18\)

Finally, divide the equation by \(-6\) to get rid of the \(y-variable\) coefficient, which is \(-6\).

\(\frac{-6y}{6}=\frac{-3x+18}{-6}\\y=\frac{1}{2}x-3\)

As shown in that last step, the equation is slope intercept form is: \(y=\frac{1}{2}x-3\)

Answer:

y = 1/2x - 3.

Step-by-step explanation:

3x - 6y = 18

-6y = -3x + 18

Divide through by -6:

y = 1/2x - 3.

Khalid can make a maximum of 7 batches of muffins using the available cornmeal because he only has 2 bags of cornmeal, and each bag provides 25 cups. Hence, the correct answer is (a) 7.

To calculate the maximum number of batches, we need to consider the total amount of cornmeal available and the amount required per batch. Khalid has 2 bags of cornmeal, with each bag containing 25 servings. Since one serving is equivalent to one cup, each bag has 25 cups of cornmeal.For each batch of muffins, 2.5 cups of cornmeal are required. Therefore, to determine the maximum number of batches, we divide the total amount of cornmeal by the amount required per batch: 25 cups / 2.5 cups per batch = 10 batches.

However, Khalid can only make a maximum of 7 batches because he only has 2 bags of cornmeal, and each bag provides 25 cups. Hence, the correct answer is (a) 7

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The angle x in the circle is 74 degrees.

The central angle is formed at the centre of a circle due to the intersection of any two radii within the circle.

The central angle of an arc is the central angle subtended by the arc.

The measure of an arc is the measure of its central angle.

Therefore,

x = 74 degrees

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Therefore, if a person were to guess on every question, the probability of receiving a grade of 70 or above is approximately 0.007538, or about 0.75%.

Probability is a branch of mathematics that deals with the study of random events and their likelihood of occurrence. It is used to quantify the chance or likelihood of an event happening, expressed as a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to occur. The basic idea behind probability is to study the possible outcomes of an event and assign probabilities to each outcome based on some assumptions or prior knowledge. Probability can be used to solve a variety of problems, from predicting the weather to analyzing the stock market, and it has applications in many fields, including science, engineering, finance, and statistics.

Here,

The probability of guessing the correct answer to any one multiple-choice question with three options is 1/3. Since there are 10 questions on the test, the probability of guessing all 10 correctly is \(\frac{1}{3} ^{10}\), which is approximately 0.000005904.

To calculate the probability of receiving a grade of 70 or above, we need to determine the minimum number of correct answers required for this grade. Assuming that a score of 70 or above requires at least 7 out of 10 questions to be answered correctly, we can use the binomial distribution to calculate the probability of getting at least 7 correct answers:

P(X ≥ 7) = Σ\(^{10} Ck*\frac{1}{3} ^{k}*\frac{2}{3} ^{10-k} \lim_{k=7\to \ 10}\)

Using a calculator or software, we can find that this probability is approximately 0.007538.

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Answer:

= 15x + 1.

Step-by-step explanation:

Sum and the length of all three sides

8x - 4 + x + 5 + 6x

8x + x + 6x - 4 + 5

15x + 1.

Answer:

could you put the picture?

Add the picture please.

the answer of course is bobbies

Answer

the answer if b in the above

The amount of blue paint required = 3/2 cups

Ratio:

Comparing two or more quantities that have units is known as the Ratio. It shows the numerical relation between two quantities like how small or big a quantity is when compared to each other.

The general form of a ratio is a: b

Here we have,

2/3 cups of white paint and 2 and 2/3 cups of blue paint

Then ratio of white to blue paint = 2/3 : 2 (2/3)

= 1:2   [ divided by 2/3 ]

In the second condition, we have 3/4 cups of white paint, here we want to give the same shade then the ratio of paint must be the same as above

Let x be the amount of blue paint that we need  

Then the ratio of white paint to blue = 3/4: x

From the given condition,

=>  3/4 : x  = 1 : 2

=> 3/4 / x = 1/2

=> 3/4x = 1/2  

=> 3(2) = 4x(1)

=> x = 6/4 =

=> 3/2

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the partial fraction decomposition of the integrand 16/(\(x^2\) - 16) is:

16\(/(x^2\)- 16) = 2/(x - 4) - 2/(x + 4)

To find the partial fraction decomposition of the integrand, we first factor the denominator.

The denominator, \(x^2\) - 16, can be factored as (x - 4)(x + 4).

The partial fraction decomposition of the integrand is:

16/(\(x^2\) - 16) = A/(x - 4) + B/(x + 4)

To find the values of A and B, we can use a common denominator and equate the numerators:

16 = A(x + 4) + B(x - 4)

Expanding the right side:

16 = Ax + 4A + Bx - 4B

Now, we group the x and constant terms:

16 = (A + B)x + (4A - 4B)

By comparing coefficients, we get the following equations:

A + B = 0      (coefficient of x)

4A - 4B = 16   (constant term)

From the first equation, we get A = -B. Substituting this into the second equation:

4(-B) - 4B = 16

Simplifying:

-8B = 16

Dividing both sides by -8:

B = -2

Substituting B = -2 into A = -B:

A = -(-2) = 2

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Answer:

i say the 3rd row

Step-by-step explanation:

Answer:

i need a picture or something

Step-by-step explanation:

as a sigma level of less than 99% indicates a high rate of defects.

What is the percentage?

A percentage that represents a tenth of a quantity. One percent, denoted by the symbol 1%, is equal to one-hundredth of something; hence, 100 percent denotes the full thing, and 200 percent designates twice the amount specified. A portion per hundred is what the percentage denotes. The percentage refers to one in a hundred. The % sign is used to denote it.

We can calculate the sigma level of the scheduling process using the formula:

Sigma level = (1 - (Number of defects / Number of opportunities)) * 100%

In this case, the number of opportunities is the total number of students enrolled in the major, which is 90. The number of defects is the number of students who were not able to schedule the elective into their course of study, which is 14. So we have:

Sigma level = (1 - (14 / 90)) * 100% ≈ 84.44%

So the sigma level of the scheduling process is approximately 84.44%. This suggests that there is room for improvement in the scheduling process, as a sigma level of less than 99% indicates a high rate of defects.

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Answer:

No

Step-by-step explanation:

if im wrong forgive me if im right please mark brainleast

Answer:22

Step-by-step explanation: since f(8) so x=8

substitiuting x in 2x+6

                                      f(8)= 2x8+6=22

so f(8)=22

Hope this helps! :)

Answer:

there is no picture but the y intercept can be either positive or negative. it is the point where the x is 0 and the y is a number. it lies on the y axis.

Step-by-step explanation:

Answer:

Y intercept is is where the line crosses the y-axis (touches the y-axis).

Step-by-step explanation:

The direction in which the maximum rate of change of f occurs at the point (5, 6, -1) is approximately (-0.17, -0.11, -0.98).

To find the maximum rate of change of the function f at the given point (5, 6, -1) and the direction in which it occurs, we can calculate the gradient of f at that point.

The gradient vector represents the direction of maximum increase of the function, and its magnitude represents the rate of change in that direction.

The gradient vector (∇f) of f(x, y, z) = (8x + 5y)/z can be found by taking the partial derivatives with respect to each variable:

∂f/∂x = 8/z

∂f/∂y = 5/z

∂f/∂z = -(8x + 5y)/z^2

Evaluated at the point (5, 6, -1), we have:

∂f/∂x = 8/(-1) = -8

∂f/∂y = 5/(-1) = -5

∂f/∂z = -((8(5) + 5(6))/(-1)^2) = -46

So, the gradient vector (∇f) at the point (5, 6, -1) is (-8, -5, -46).

The maximum rate of change of f at this point is given by the magnitude of the gradient vector:

|∇f| = √((-8)^2 + (-5)^2 + (-46)^2) = √(64 + 25 + 2116) = √2205 = 47.

Therefore, the maximum rate of change of f at the point (5, 6, -1) is 47.

To determine the direction in which this maximum rate of change occurs, we normalize the gradient vector by dividing it by its magnitude:

Direction vector = (∇f) / |∇f| = (-8/47, -5/47, -46/47).

Hence, the direction in which the maximum rate of change of f occurs at the point (5, 6, -1) is approximately (-0.17, -0.11, -0.98).

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Answer:

First you make 3/10=0.3 the 1/3=0.33 then 0.3+0.33=0.63

The probability of an event happening is calculated by possible events divided by total events.

From a standard deck of 52 cards, there are 13 spades.

So the possible events are 13 and the total events are 52

This will be:

prob = 13/52 = 1/4

The answer is 1/4

Answer:

ok

Step-by-step explanation:

1-55

In order for f(x) to be a linear function, determine the value of k in the data set.

x = {-7, -2, 2, 5}

f(x) = {-15, k, 3, 9}

The value of k is {-5}.

Given that to find the value of k in the data set such that the data set represents a linear function.

Linear Function is a straight line on the coordinate plane is represented by a linear function. The formula for a linear function is f(x) = mx + b, where m and b are real values.

Here, f(x) or y is the dependent variable, m is a slope of the line, x is the independent variable and b is the y-intercept.

Here,(x,f(x)) are {(-7,-15),(-2,k),(2,3),(5,9)}

The slope of the function,

(x, f(x)) = (2,3) and (5,9)

Slope formula is m=\(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\).

Slope m= \(\frac{9-3 }{5-2}\)

Slope m=\(\frac{6}{3}\)

Slope m=2.

Using the point slope form, determine the linear function's equation.

\(y-y_{1} =m(x-x_{1})\)

Here, \((x_{1},y_{1})=(-7,-15)\) and m=2

We get

y + 15 = 2 (x + 7)

y = 2x - 1

Now at x = -2 and f(x) = k

k = 2(-2) - 1

k = -4-1

k=-5

Therefore, the value of k is -5.

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Step-by-step explanation:

cos (3x-7)

0,9335804265

sin (2x+5)

0,1736481777

The solution for the inequality | x | + 9 ≤ 7 is (option d) x ≤ -2 and x > -16

You can solve an inequality by: adding the same amount to each side; taking the same amount away from each side; multiplying or dividing each side by the same positive amount. The inequality symbol needs to be turned around if either side is multiplied or divided by a negative number. Therefore, the answer is x > 1.

Given,

The expression:   | x | + 9 ≤ 7

If | x | ≤ a ⇒ -a ≤ x ≤ a

Then,

-7 ≤ | x | + 9 ≤ 7

⇒ -7 - 9 ≤ x ≤ 7 - 9

⇒ -16 ≤ x ≤ -2

That is x ≤ -2 and x > -16.

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The correct statement among the options (a)-(e) is d. neither the subjects nor the people administering the treatments know who received a treatment and who received an inactive substance.

In a double-blind, placebo-controlled experiment, both the subjects and the people administering the treatments are unaware of which participants received the active treatment and which received the placebo (inactive substance).

This is done to minimize bias and ensure the validity of the results. By keeping both the subjects and the administrators blinded to the treatment assignments, the study can effectively evaluate the true effects of the treatment without any potential influence from expectations or biases.

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The basic function equivalent to the piecewise-defined function f(x) = x if x ≥ 0 and -x if x < 0 is f(x) = |x|, which represents the absolute value of x.

The given piecewise-defined function f(x) has different expressions for different intervals. For x greater than or equal to zero, f(x) takes the value of x. For x less than zero, f(x) is equal to -x. We need to find a basic function that captures this behavior.

Among the options provided, f(x) = |x| is equivalent to the given piecewise function. The absolute value function, denoted by |x|, returns the positive value of x regardless of its sign. When x is non-negative, |x| equals x, and when x is negative, |x| is equal to -x, mirroring the conditions of the piecewise-defined function.

The function f(x) = |x| represents the absolute value of x and matches the behavior of the given piecewise-defined function, making it the equivalent basic function.

In summary, the basic function equivalent to the piecewise-defined function f(x) = x if x ≥ 0 and -x if x < 0 is f(x) = |x|, which represents the absolute value of x.

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The solution to the equation \((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2\) is 10.3891

From the question, we have the following parameters that can be used in our computation:

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2\)

Using the following trigonometry ratio

sin²(x) + cos²(x) = 1

We have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = (\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + 1 + e^2\)

The sum to infinity of a geometric series is

S = a/(1 - r)

So, we have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = \frac{1/2}{1 - 1/2} + \frac{9/10}{1 - 1/10} + 1 + e^2\)

So, we have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 1 + 1 + 1 + e^2\)

Evaluate the sum

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 3 + e^2\)

This gives

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 10.3891\)

Hence, the solution to the equation is 10.3891

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