Use the procedures developed in this chapter to find the general solution of the differential equation. 2ex y" - y = ex + e-x -X y = Get + c₂e + e*tan¯¹(e*) + e*tan¯¹(ex) – 1

Answer:

the x-coordinate and y-coordinate change places.

Step-by-step explanation: so you reflect a point across the line y = x, the x-coordinate and y-coordinate change places. If you reflect over the line y = -x, the x-coordinate and y-coordinate change places and are negated (the signs are changed). the line y = x is the point (y, x). the line y = -x is the point (-y, -x).

Answer: 60cm

Step-by-step explanation:

6 times 2 is 12

12 times 5 is 60

The p-value for the hypothesis test H₀:μ = 10 against H₁:μ<10 with variance unknown and n = 10 is approximately 0.047.

To determine the p-value, the test statistic is calculated as follows:

t = (sample mean - hypothesized mean) / (standard error of the mean)

The sample mean is calculated as follows:

x = Σx / n

where Σx is the sum of the sample values and n is the sample size.

The hypothesized mean is 10.

The standard error of the mean is calculated as follows:

SE = σ / √n

where σ is the population standard deviation and n is the sample size.

Plugging in the values for the sample mean, hypothesized mean, sample standard deviation, and sample size, we get the following test statistic:

t = (2.5 - 10) / (1.5 / √10) = -4.66

The critical value is found using the t-distribution with n-1 degrees of freedom. The t-distribution is a probability distribution that is used to calculate the p-value for a hypothesis test when the population standard deviation is unknown. The degrees of freedom is the number of data points minus the number of parameters estimated. In this case, the degrees of freedom is 10-1=9.

The critical value for a two-tailed hypothesis test with a significance level of 0.05 and 9 degrees of freedom is 2.306.

The test statistic (-4.66) is less than the critical value (2.306). Therefore, we reject the null hypothesis and conclude that there is sufficient evidence to support the alternative hypothesis.

The p-value is the probability of obtaining a test statistic that is at least as extreme as the one observed, assuming that the null hypothesis is true. The p-value for the test statistic -4.66 is approximately 0.047. This means that there is a 4.7% chance of obtaining a test statistic that is at least as extreme as -4.66 if the population mean is actually 10.

Therefore, the best approximation for the p-value for the test statistic is 0.047.

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Answer:

6c-8-2c+(-16)=0

6c-2c-8-16=0

6c-2c=16+8

4c=24

c=24/4

c=6

Answer:

4c - 24

Step-by-step explanation:

6c−8−2c−16

(6c−2c)+(−8−16)

4c - 24

The image contains the answer to the questions.

The required solutions to the given quadratic function are below as:

\(y=\dfrac{-1+\sqrt{11}}{2},\:y=-\dfrac{1+\sqrt{11}}{2}\quad\)

The quadratic function is defined as a function containing the highest power of a variable is two.

The quadratic function is given in the question:

2y² + 2y - 5 = 0

Compare the given function to the standard quadratic function f(x) = ax² + b x + c.

We get a = 2, b = 2 and c = -5

Using the quadratic formula to solve the above quadratic function

\(y = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\)

Substitute the values of a = 2, b = 2 and c = -5 in the above formula

\(y=\dfrac{-2\pm \sqrt{2^2-4\cdot \:2\left(-5\right)}}{2\cdot \:2}\)

\(y=\dfrac{-2\pm \:2\sqrt{11}}{2\cdot \:2}\)

Separate the solutions as:

\(y=\dfrac{-2+2\sqrt{11}}{2\cdot \:2},\:y=\dfrac{-2-2\sqrt{11}}{2\cdot \:2}\)

\(y=\dfrac{-1+\sqrt{11}}{2},\:y=-\dfrac{1+\sqrt{11}}{2}\quad\)

Therefore, the required solutions to the given quadratic function are below as:

\(y=\dfrac{-1+\sqrt{11}}{2},\:y=-\dfrac{1+\sqrt{11}}{2}\quad\)

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Answer:

Step-by-step explanation:

hello,

\(15x^2-10x=15(x^2-\dfrac{10}{15}x)=15(x^2-\dfrac{2}{3}x)\)

and we can write that

\((x-\dfrac{2}{2*3})^2=(x-\dfrac{1}{3})^2=x^2-\dfrac{2}{3}x+\dfrac{1}{9}\)

so

\(x^2-\dfrac{2}{3}x= (x-\dfrac{1}{3})^2-\dfrac{1}{9} \ so\\15x^2-10x=15(x^2-\dfrac{2}{3}x)=15[(x-\dfrac{1}{3})^2-\dfrac{1}{9} ]=15(x-\dfrac{1}{3})^2-\dfrac{15}{9}\\=15(x-\dfrac{1}{3})^2-\dfrac{5}{3}\)

Then

\(15x^2-10x+\dfrac{5}{3}=15(x-\dfrac{1}{3})^2\)

then, I would say that you need to add 5/3 to make a perfect square

hope this helps

The width and the length of the piece of metal are 6.279 inches and 26.279 inches, respectively.

In this question, we must find the dimensions of the metal sheet, with which a box is done. The volume of the box is represented by the volume formula of a right-angled parallelepiped:

V = [(w + 20) - 8] · (w + 8) · 4

V = 4 · (w + 12) · (w + 8)

V = 4 · (w² + 20 · w + 96)

V = 4 · w² + 80 · w + 384

Where w is the width of the metal sheet, in inches.

If we know that V = 1044 in³, then the dimensions of the piece of metal is:

1044 = 4 · w² + 80 · w + 384

4 · w² + 80 · w - 660 = 0

(w - 6.279) · (w + 26.279) = 0

The width and the length of the piece of metal are 6.279 inches and 26.279 inches, respectively.

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The confidence interval for the proportion of left-handed golfers is of:

(0.12, 0.18).

A confidence interval is calculated as the sample mean plus/minus the margin of error, hence the bounds of the confidence interval are given as follows:

In the context of this problem, these parameters are given as follows:

Hence the lower bound of the confidence interval for the proportion of left-handed golfers is:

0.15 - 0.03 = 0.12.

The upper bound of the confidence interval for the proportion of left-handed golfers is:

0.15 + 0.03 = 0.18.

Then the interval is:

(0.12, 0.18).

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Answer:

See Explanation

Step-by-step explanation:

Given

\(1\ can = 2.2m^2\)

Required

Determine the number of cans for the wall

The dimension of the wall is not given. So, I will use the following assumed values:

\(Length=20m\)

\(Width = 44m\)

First, calculate the area of the wall

\(Area = Length * Width\)

\(Area = 20m * 44m\)

\(Area = 880m^2\)

If \(1\ can = 2.2m^2\)

Then \(x = 880m^2\)

Cross Multiply:

\(x * 2.2m^2 = 1 * 880m^2\)

\(x * 2.2m^2 = 880m^2\)

\(x * 2.2 = 880\)

Make x the subject

\(x = \frac{880}{2.2}\)

\(x = 400\)

400 cans using the assume dimensions.

So, all you need to to is, get the original values and follow the same steps

Answer:

I think its 110mi squared

Answer:

11o mi Squared

Step-by-step explanation:

The best estimate for the sum of 2, 9, 10, and 11 is 6. To find the estimate, we add up the given numbers.

Adding 2, 9, 10, and 11 gives us a sum of 32. However, none of the options provided match this sum. Option B, \(1 + 2 + 1 + 2 = 6\), is the closest estimate to the actual sum.

While it is not the exact sum, it is the best estimate among the given options. It is important to carefully read the options and select the closest approximation when an exact match is not available.

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The regular expression excludes strings like "1000" or "100000" because they have an even number of 0s following the 1.

The set of all bit strings made up of a 1 followed by an odd number of 0s can be represented by the regular expression:

1(00)*

Breaking down the regular expression:

1: The string must start with a 1.

(00)*: Represents zero or more occurrences of the pattern "00". This ensures that the 1 is followed by an odd number of 0s.

Examples of valid bit strings in this set include:

10

100

10000

1000000

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Answer:

Add by 4

Step-by-step explanation:

-3+4=1

1+4=5

5+4=9

9+4=13

The area left for children for playing 114464 sq. m

As per the given data inside a park:

The length of the park is 400 m

The breadth of the park is 300 m

The formula for the area of the park = Length × Breadth

= (400 × 300) sq. m

= 120000 sq. m

The width of the walking track inside the park is 4 m

The length of the park without the walking track

= 400 − (4 + 4) m

= 400 − 8 m

= 392 m

The breadth of the park without the walking track

= 300 − (4 + 2) m

= 300 − 8 m

=292 m

Area of the park without the walking track:

= 392 × 292

= 114464 sq. m

Therefore the area left for children for playing other than the walking track is 114464 sq. m.

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First, let's calculate the Profit functions which is P(x)=R(x)-C(x)

Let's continue simplifying the function

The profit function is a polynomial function, so the domain is all the real numbers which means x can be any real number

Domain=(-∞,∞)

Calculating x=-10 doesn't make sense because x in all the functions is the number of items, and doesn't make sense to have -10 items, so x shouldn't be negative numbers.

And Calculating x=1000 doesn't make sense either because the problem says "The maximum capacity of the company is 110 items" so if we have x=1000 we are exceeding the limit of items that the company can handle.

Now let's calculate the profit when producing 40 and 50 items (we just need to evaluate those values in the function):

The profit when the company produces 50 items is 500 and the profit when the company produces 40 items is 550.

The company should choose to produce 40 items because is a higher profit in contrast to making 50 items.

According to the function, when we replace the values in X we can see that the term (X^2) grows more than the term X and as you can see the term X^2 is negative which decreases the final result of the profit. Another way to see this is by drawing the function

As you can see the function is a parable and when the number of items "X" is very high the function tends to decrease. The function starts to grow in profit until 40 items (when you find the maximum value of profit) and then the profit function decreases.

The simplified expression of (5.1)(5.1^2)^4 is (5.1)^9

The expression is given as:

(5.1)(5.12)4

Rewrite the expression properly as follows:

(5.1)(5.1^2)^4

Rewrite the expression properly as follows:

(5.1)(5.1^2)^4 = (5.1) * (5.1^2)^4

Apply the power law of indices

(5.1)(5.1^2)^4 = (5.1) * (5.1^8)

Apply the power law of indices

(5.1)(5.1^2)^4 = (5.1)^(1 + 8)

Evaluate the sum

(5.1)(5.1^2)^4 = (5.1)^9

Hence, the simplified expression of (5.1)(5.1^2)^4 is (5.1)^9

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Given:

Diameter of ball = 8 cm

To find:

The volume of the ball.

Solution:

We know that the radius of sphere is half of is diameter.

It is given that the the diameter of ball is 8 cm. So, the radius of the ball is:

\(r=\dfrac{8}{2}\)

\(r=4\)

The radius of the ball is 4 cm.

The volume of a sphere is:

\(V=\dfrac{4}{3}\pi r^3\)

Where r is the radius of the sphere.

Putting \(\pi = 3.14, r=4\) in the above formula, we get

\(V=\dfrac{4}{3}(3.14)(4)^3\)

\(V=\dfrac{4}{3}(3.14)(64)\)

\(V=267.946667\)

\(V\approx 267.95\)

Therefore, the volume of the ball is about 267.95.

It would take 5040 cubic inches of water to completely fill the aquarium.

We know that the formula for the volume of cuboid :

V = length × width × height

Let us assume that l represents the length of the aquarium, w represent the width and h represents the height.

Here, l = 20 inches

w = 14 inches

and h = 18 inches

Using the formula for the volume of cuboid, the volume of aquarium would be,

V = l × w × h

V = 20 × 14 × 18

V = 5040 cu.in.

Therefore, it would take 5040 cu.in. of water.

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Answer:

(x - 4)(x - 12)

Step-by-step explanation:

Given

x² - 16x + 48

Consider the factors of the constant term (+ 48) which sum to give the coefficient of the x- term (- 16)

The factors are - 4 and - 12, since

- 4 × - 12 = + 48 and - 4 - 12 = - 16 , thus

x² - 16x + 48 = (x - 4)(x - 12)

Answer:

the correct option is (x-4)(x-12)

Step by Step explanation:-

x^2-16x+48

x^2-12x-4x+48

by taking the common factor out,

x(x-12)-4(x-12)

(x-4)(x-12)

Hope it helps you!

Answer:4 x 1,424 = 5,696

Step-by-step explanation:

To multiply 4 by 1,424, we first multiply the ones digit of 1,424 by 4, which gives us 4 x 4 = 16. We write down the 6 and carry the 1.

Next, we multiply the tens digit of 1,424 by 4, which gives us 4 x 2 = 8. We add the carried 1 to get 9, and write down the 9 in the tens place. We carry the remaining 1.

Then, we multiply the hundreds digit of 1,424 by 4, which gives us 4 x 4 = 16. We add the carried 1 to get 17, and write down the 7 in the hundreds place. We carry the remaining 1.

Finally, we multiply the thousands digit of 1,424 by 4, which gives us 4 x 1 = 4. We add the carried 1 to get 5, and write down the 5 in the thousands place.

Putting it all together, we get 5,696 as the product of 4 and 1,424.

Answer: 5696

Step-by-step explanation:

1424 is 1000+400+ 20+4

multiply each by 4

4000+1600+80+16

This equals 5696

With enough practice, you'll be able to do it in your head!

Answẻ:  34

25 ½ :3/4 = 34

Answer:

Below.

Step-by-step explanation:

25 1/2 = 51/2

We divide this by 3/4 :

51/2 / 3/4

= 51/2 * 4/3

= 17*2

= 34

So we can cut 34 pieces of length 3/4.

Answer:

A. yes

B. yes

Step-by-step explanation:

In both nets, the rectangles can be folded to touch every edge of both triangular bases.

Answer: Disagree.

Step-by-step explanation:

I Disagree because the Triangles in Exhibit B have only 2 equal sides while the triangles in A have all equal sides.

Only (d) 1 equation can you write to represent a single line using a point-slope equations

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

Equation = Linear equation

A linear equation can only be represented with one equation

When it is represented with multiple equations, the equations are equivalent equations

This means that the equations can be converted to one another

Hence, the solution is (d) 1 equation

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Answer: 20

Step-by-step explanation:

You divide -915 by -50 and get 18.3 days but you round up to 20 hope it helps

Ratio analysis can be made more meaningful in all the following ways except by focusing more on long-term solvency than on short-term solvency.

Ratio analysis is a mathematical technique for analyzing a company's financial documents, such as the balance sheet and income statement, to gather knowledge about its liquidity, operational effectiveness, and profitability. Fundamental equity research is built on ratio analysis.

In order to get insights into profitability, liquidity, operational effectiveness, and solvency, ratio analysis examines line-item data from a company's financial statements.

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The full question:

ratio analysis can be made more meaningful in all the following ways except by?

Answer:

Step-by-step explanation:

add a better picture

Answer:

60 dogs

Step-by-step explanation:

40/8 = 5 dogs per hour

12 x 5 = 60 dogs in 12 hours

George's unpaid balance of $756 from the end of the month of January is multiplied by the 27.6% annual percentage rate to get the credit card balance as of the first day of February, which is $802.00.

$756 x 0.276

= $208.256

$756 + $208.256

= $802.256

$802.00 (rounded to the nearest cent)

George's credit card balance as of the first day of February is determined by his average daily balance from the month of January. His average daily balance was $756, and his unpaid balance at the end of the month was $802.

To calculate the credit card balance, the unpaid balance of $756 is multiplied by the 27.6% annual percentage rate, which gives us $208.256.

When $208.256 is added to the unpaid balance,

we get $802.256.

This is then rounded to the nearest cent, which gives us $802.00 as the credit card balance as of the first day of February.

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