Solve the following differential equation dy/dx = e^{2x} - 3y and y = 1 when x = 0
y =
Hint: Recognize this as a first-order linear differential equation and follow the general method for solving these and use the initial conditions to find the integration constant.

Step-by-step explanation:

the answer is in the picture ☝️

Answer:

Choosing five CDs where not all of them are pop.

Step-by-step explanation:

Answer:

B)  choosing five CDs where not all of them are pop

Step-by-step explanation:

E2020

The statement "The mean decreases as the degrees of freedom increase" is not true about chi-square distributions.

In fact, the mean of a chi-square distribution is equal to its degrees of freedom. It does not decrease as the degrees of freedom increase.

The mean remains constant regardless of the degrees of freedom. This is an important characteristic of chi-square distributions.

Regarding the other statements:

In summary, the statement that is not true about chi-square distributions is that the mean decreases as the degrees of freedom increase.

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Answer:6

Step-by-step explanation:

since it is A half circle it is the hhalf Value of the area of the full circle

Answer:

y = 6x + 10

Step-by-step explanation:

This is because the slope is 6 and the y intercept is 10, therefore the answer is y = 6x + 10

A. The point estimate from this sample is 124 bushels per acre as the point estimate. B.  Therefore, the margin of error would be 12 / 2 = 6 bushels per acre. C. The 99% confidence interval of 118 to 130 bushels per acre means that we can be 99% confident that the true mean yield of the new variety of corn falls within this range.

A. The point estimate is the best estimate of the true mean yield based on the sample data. In this case, the point estimate would be the midpoint of the confidence interval. Calculating the average of the upper and lower limits, we have (118 + 130) / 2 = 124 bushels per acre as the point estimate.

B. The margin of error is the range around the point estimate within which the true population mean is likely to fall. To calculate the margin of error, we take half the width of the confidence interval. In this case, the width of the interval is 130 - 118 = 12 bushels per acre. Therefore, the margin of error would be 12 / 2 = 6 bushels per acre.

C. The 99% confidence interval of 118 to 130 bushels per acre means that we can be 99% confident that the true mean yield of the new variety of corn falls within this range. It provides a range of values where the population mean is likely to be, based on the sample data. The 99% confidence level indicates that if we were to repeat the sampling process multiple times, 99% of the resulting confidence intervals would contain the true population mean yield.

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Yes. Since the correlation coefficient is positive (r = 0.75), it indicates a positive linear relationship between the scores given by the French and Romanian judges.

A) Can't tell. The correlation coefficient alone does not provide information about the magnitude or direction of the scores. It only indicates the strength and direction of the linear relationship between the scores given by the French judge and the Romanian judge. Therefore, we cannot determine if the Romanian judge tends to give higher scores than the French judge based solely on the correlation coefficient.

B) Can't tell. Similarly, the correlation coefficient does not provide direct information about which judge tends to give higher scores. It only reflects the strength and direction of the linear relationship between their scores. Without additional data or analysis, we cannot conclude if the French judge tends to give higher scores than the Romanian judge.

C) Yes. Since the correlation coefficient is positive (r = 0.75), it indicates a positive linear relationship between the scores given by the French and Romanian judges. When the Romanian judge gives high marks, there is a tendency for the French judge to give high marks as well. However, it does not imply a perfect correlation or absolute certainty, as other factors and considerations may influence their scoring decisions.

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Is this selection (A) the best one? a high positive number. The result of multiplying a negative number by a positive number is always negative.

The result of multiplying two numbers, whether they are positive or negative, is always positive. 3 plus 4 equals 12. The result is minus 12 since there is only one optimistic and one negative number.

Why does adding two negative numbers together results in a positive number?

Repeated subtraction equals multiplication by a negative. Negative numbers were reduced in negative value after they have been multiplied together. Students may easily relate both ideas thanks towards this comparison among both multiplication and addition.

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Answer: D:22,

14,040-12,500=1540.  

1540/70 = 22

For this question, since we need to show that Eric and Nancy contributes the same amount to their monthly income, we just need to equate both expressions with each other, and then solve for the value of x.

In order to check if we got the right answer, we just need to substitute the value of x to both equations.

Therefore, we can conclude that Eric and Nancy has to sell 6 fish tanks each.

Answer:

a = 9

Step-by-step explanation:

Let's make the demoninators of the 2 fractions the same :
(2a+8)/10 - (5a +15)/10 = 5

(2a + 8 - 5a + 15)/10 = 5

=> -3a + 23 = 50
=> -3a = 27
=> a = 9

under the restrictions that c is negative to ensure strict concavity, the utility function u(w) = -(b - w)c displays increasing absolute risk aversion.

To ensure that u(w) is strictly increasing, we need the derivative of u(w) with respect to w to be positive for all values of w. Taking the derivative, we have du(w)/dw = -c. For u(w) to be strictly increasing, -c must be positive, which implies c must be negative.

To ensure that u(w) is strictly concave, we need the second derivative of u(w) with respect to w to be negative for all values of w. Taking the second derivative, we have d²u(w)/dw² = 0. Since the second derivative is constant and negative, u(w) is strictly concave.

Now, let's examine the concept of increasing absolute risk aversion. If a utility function u(w) exhibits increasing absolute risk aversion, it means that as wealth (w) increases, the individual becomes more risk-averse.

In the given utility function u(w) = -(b - w)c, when c is negative (as required for strict concavity), the absolute risk aversion increases as wealth (w) increases. This is because the negative sign implies that the utility function is concave, indicating that the individual becomes more risk-averse as wealth increases.

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The area of the shaded region is given as follows:

85.245 cm².

The area of a rectangle is given by the multiplication of it's dimensions, hence it is given as follows:

Ar = 13.8 x 7.6

Ar = 104.88 cm².

The area of a circle of radius r is given by the equation presented as follows:

A = πr²

The radius for this problem is of r = 2.5 cm, hence the area is given as follows:

A = π x 2.5²

A = 19.635 cm²

Hence the area of the shaded region is given as follows:

104.88 - 19.635 = 85.245 cm².

The diagram is given by the image presented at the end of the answer.

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Answer:

multiple choice answers?

Step-by-step explanation:

The Answer is 95 miles using distance rule of maths.

What is distance in math?

As its name implies, any distance formula outputs the distance (the length of the line segment). In coordinate geometry, there is a number of formulas for finding distances, such as the separation between two points, the separation between two parallel lines, the separation between two parallel planes, etc.

So if we mark their position in x-y plane. one is not x line and another one is in y line.

So the coordinates of the points are (57,0) and (0,76)

The distance between them is √(y²+x²)

= √(57²+76²)

=√ (3249 + 5776)

= 95 miles

Hence the distance between them is 95 miles.

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Answer:

A x >= 0

Step-by-step explanation:

a function is a defined mathematical operation (or a sequence of operations) that uses input values (typically called "x") and calculates the corresponding results (typically called "y").

so, y = f(x)

and (x,y) are then usually the coordinates on the grid.

the domain is the range or interval of numbers the function is using (x) to create results (y).

so, look at the graph !

for what values of x do you see the functional line drawn ?

that means, the functional line goes along only what part of the x-axis ?

I see it starts at x=0 and then continues all the way to the right and clearly further.

for me that means f(x) calculates values for every positive x we can think of. and including 0.

it does not do anything for any negative x-values.

so, clearly answer A (x>=0) is right.

The total interest you will earn in 30 years is approximately $241.61.

To calculate the total interest earned in 30 years, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt) - P
Where:
A = the future value of the investment
P = the principal amount (initial deposit)
r = the annual interest rate (in decimal form)
n = the number of times the interest is compounded per year
t = the number of years
In this case, the principal amount is $200, the annual interest rate is 3% (or 0.03 as a decimal), the interest is compounded monthly (so n = 12), and the time period is 30 years (so t = 30).
Plugging in these values into the formula:
A = 200(1 + 0.03/12)^(12*30) - 200
Now we can simplify and calculate:
A = 200(1.0025)^(360) - 200
A = 200(2.208040033) - 200
A ≈ 441.6080066 - 200
A ≈ 241.6080066

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Answer:

B

Step-by-step explanation:

O Citizens who are healthy contribute more to their communities.

( I don't think this is math related).

Step-by-step explanation:

\((4 \times 6) + 9\)

Follow PEMDAS

\(24 + 9 \\ = 33\)

Answer:

33

Step-by-step explanation:

\((4x6)+9?\)

Ill take it as

\((4*6)+9\)

\(4*6=24\\24+9=33\)

True. In compound time signatures, the top number represents the number of beats per measure. Compound time signatures are typically used for music that has a more complex rhythmic structure, and they are characterized by the subdivision of each beat into three equal parts (known as triplets).

The most common compound time signatures are 6/8, 9/8, and 12/8, with each representing six, nine, and twelve beats per measure respectively.
In 6/8 time, for example, there are two beats per measure, each of which is subdivided into three equal parts. This results in a feeling of two larger beats, each consisting of three smaller beats. In 9/8 time, there are three beats per measure, each of which is subdivided into three equal parts. This results in a feeling of three larger beats, each consisting of three smaller beats. Similarly, in 12/8 time, there are four beats per measure, each of which is subdivided into three equal parts, resulting in a feeling of four larger beats, each consisting of three smaller beats.
Overall, the top number in a compound time signature represents the number of larger beats per measure, while the bottom number represents the duration of each beat (usually an eighth note).

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Given data vending machine is designed to dispense a mean of 7.2 oz of coffee into an 8-oz cup. Standard deviation, σ = 0.3 Oz Amount is normally distributed Want to find out the percentage of times the machine will dispense less than 7.47 oz Calculation value is calculated as;

\($$Z = \frac{x-\mu}{\sigma}$$\)

Where x is the value of interest, µ is the mean and σ is the standard deviation

\(= $${\frac{7.47-7.2}{0.3}} = 0.9$$\)

Using the Z table, the area to the left of 0.9 is 0. 8186.Thus, the percentage of times the machine will dispense less than 7.47oz is 81.86% approximately. In statistics, the term “standard deviation” refers to the measurement of the amount of data spread.

To calculate the probability of a specific value being less than a given value in a normal distribution, we can use the Z table. Once we find the Z score, we can look up its corresponding area on the Z table to determine the probability.

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Step-by-step explanation:

here's your answer hope it helps you

Using the central angle theorem, we can find the arm length of BD to be 118units.

Option C is correct.

The angle that an arc occupies at the centre of a circle is twice as large as the angle it occupies anywhere else around the circle's circumference, according to the central angle measure theorem.

Here in the question,

Length of the arc AC = 59.

As we can see that there is a quadrilateral inscribed inside the circle.

Arc AC = 1/2 arc BD

⇒ arc BD = 2 × arc length AC

⇒ arc BD = 2 × 59

⇒ arc BD = 118.

Therefore, the length of the arc BD = 118 units.

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Using the central angle theorem, we can find the arm length of BD to be 118units.

Option C is correct.

The angle that an arc occupies at the centre of a circle is twice as large as the angle it occupies anywhere else around the circle's circumference, according to the central angle measure theorem.

Here in the question,

Length of the arc AC = 59.

As we can see that there is a quadrilateral inscribed inside the circle.

Arc AC = 1/2 arc BD

⇒ arc BD = 2 × arc length AC

⇒ arc BD = 2 × 59

⇒ arc BD = 118.

Therefore, the length of the arc BD = 118 units.

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Answer:

h≅ 8 yards

Step-by-step explanation:

Given data

Volume of cone= 301.44 cubic yards

Radius of cone= 6 yards

Required

The Height of the cone

The expression for the volume of a cone is given as

V= 1/3πr^2h

Substitute

301.44= 1/3* 3.142*6^2*h

301.44= 37.704*h

Divide both sides by 37.704

h= 301.44/37.704

h= 7.99

h≅ 8 yards

Answer:

The answer would be 23.5 gallons of gas.

Step-by-step explanation:

You take away 14.4 gallons from the max capacity (19.1). Which gets you 4.7, the you take that away from 12.8 gallons. Which gets you 8.1 gallons. Then you take away 3.7 from 19.1 (15.4). Then add 8.1 and 15.4(23.5) So 23.5 is how many gallons of gas was used.

Hope this helps!

We want to see how much gas did Simpsons use on the trip.

The total amount of gas used in this trip is 23.5 gallons of gas.

We know that:

The maximum capacity of the tank is 19.1 gal.

The trip starts with 12.8 gal on the tank.

After two hours, he fills the tank to capacity with 14.4 gal.

Then at this moment, he had:

19.1 gal - 14.4gal = 4.7 gal.

Knowing that he started with 12.8 gal, this means that at this point the total amount of gas used is:

12.8 gal - 4.7 gal = 8.1 gal.

Ok, now the car has 19.1 gal of gas. We know that at the end of the trip, the car has 3.7 gallons of gas, then the amount consumed this time is:

19.1 gal - 3.7gal = 15.4 gal

The total amount consumed is:

8.1gal + 15.4 gal = 23.5 gal

So we can conclude that the total amount of gas used in this trip is 23.5 gallons of gas.

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Answer:

Answer:

the ratio of boys to the total students is 15:27

Step-by-step explanation:

Since we know there are 15 boys and 12 girls, we can add those to know there are 27 total students. Therefore, the ratio it 15:27

Answer:

15:27

=5:9 (if answer is needed in simplest form)

Step-by-step explanation:

B  :  G   : Total

15 :   12 : 15+12=27

hence boys to total is 15:27

                                    =5:9 (if answer is needed in simplest form)

a. The control limits for the 3-sigma x-bar chart are: UCL x-bar = 61.744 lb. and LCL x-bar = 59.756 lb.

b. The control limit for the 3-sigma R-chart is UCL R = 4.051 lb., rounded to three decimal places.

(a) To determine the control limits for the 3-sigma x-bar chart, we need to use the given information of the sample size, overall mean, and average range.

For the x-bar chart, the control limits are calculated using the formula:

Upper Control Limit (UCL x-bar) = overall mean + (A2 * average range)

Lower Control Limit (LCL x-bar) = overall mean - (A2 * average range)

Where A2 is a constant depending on the sample size. For a sample size of 7, the value of A2 is 0.577.

Substituting the values into the formula, we get:

Upper Control Limit (UCL x-bar) = 60.75 + (0.577 * 1.78) = 61.744

Lower Control Limit (LCL x-bar) = 60.75 - (0.577 * 1.78) = 59.756

Therefore, the control limits for the 3-sigma x-bar chart are: UCL x-bar = 61.744 lb. and LCL x-bar = 59.756 lb.

(b) To calculate the control limits for the 3-sigma R-chart, we only need the value of the average range.

The control limits for the R-chart are calculated as follows:

Upper Control Limit (UCL R) = D4 * average range

Lower Control Limit (LCL R) = D3 * average range

For a sample size of 7, the values of D3 and D4 are 0 and 2.282, respectively.

Substituting the values into the formula, we get:

Upper Control Limit (UCL R) = 2.282 * 1.78 = 4.051 lb.

Therefore, the control limit for the 3-sigma R-chart is UCL R = 4.051 lb., rounded to three decimal places.

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Number of Excavation                                  Height of Soils(inches)

0                                                                       3 ins

1                                                                        5 ins

5                                                                       13 ins

10                                                                      23 ins

A word problem is a type of mathematics exercise where the majority of the issue's context is supplied in spoken language as opposed to mathematical notation.

A math word problem is a question that is phrased as one or more sentences and asks students to use their mathematical understanding to solve an issue from "real world."

In order for kids to understand the word problem, they must be familiar with the terminology that goes along with the mathematical symbols that they are used to.

It is already noted that when Levi starts digging the hole is already 3 inches dip with soil

In each excavation he digs 2 inches of soil each

So, when number of Excavation is :

Zero :  the inches of soil is 3 inches

One : the inches of soil is 3+2 = 5 inches

Five : the inches of soil is 3+2*5 = 13 inches

Ten :the inches of soil is 3 + 2*10 = 23 inches

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