cos theta = -5/6
180° <0<270°

Answer:

acute = 30,right angle = 90,obtuse = 135,line = 180

1

Explanation:

7/7 - 2/5

Using compatible numbers:

7/7 = 1 as it is closer and equal to 1

so we have: 1 - 2/5

2/5 is approximately 0 as it is closer to 0 than 1

= 1 - 0 = 1

7/7 - 2/5 using compatible number = 1

The complete question is

"Find the general solution of the given differential equation

y''-y=0, y1(t)=e^t , y2(t)=cosht

The function \(y(t)=e^t\)  is the solution of the given differential equation.

The function y(t)=cosht is the solution of given differential equation.

The function is a type of relation, or rule, that maps one input to specific single output.

Given;

\(y_1(t) = e^t\)

Given differential equations are,

y''-y = 0

 So that,  

\(y' (t) = e^t, y'' (t) = e^t\)

Substitute values in the given differential equation.

\(e^t -e^t=0\)

Therefore, the function \(y(t)=e^t\)  is the solution of the given differential equation.

Another function;

\(y(t)=cosht\)  

So that,  

\(y"(t)=sinht\\\\y"(t)=cosht\)

Hence, function y(t)=cosht is solution of given differential equation.

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Answer:c

Step-by-step explanation:

Answer: C

Step-by-step explanation:

The algebraic expression x³y⁴ - x⁴y⁴ is factorized to be x³y⁴(1 - x) using their highest common factor HCF

The H.C.F. defines the highest common factor present in between given two or more numbers or mathematical expression.

The two terms x³y⁴ and x⁴y⁴ of the algebraic expression x³y⁴ - x⁴y⁴ have their highest common factor to be x³y⁴ such that:

x³y⁴ × 1 = x³y⁴

x³y⁴ × x = x⁴y⁴

and

x³y⁴ - x⁴y⁴ = x³y⁴ × 1 - x³y⁴ × x

x³y⁴ - x⁴y⁴ = x³y⁴(1 - x)

Therefore, the algebraic expression x³y⁴ - x⁴y⁴ is factorized to be x³y⁴(1 - x) using their highest common factor HCF

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Answer:

5.7

Step-by-step explanation:

Equilateral triangle means all the sides are the same length. So each side is basically \(\sqrt{11}\) times 2

After we know that, we then look to the Pythagorean theorum:

a^2 + b^2 = c^2

Before that, we have to find what the length of the hypotenuse is. 90 degrees equals \(\sqrt{11}\) times 2. So plug this info into the equation:

\(\sqrt{11}\)^2 + b^2 = \(2\sqrt{11}\)^2

11 + b^2 = 4(11)

11 + b^2 = 44

b^2 = 33

b = \(\sqrt{33}\)

b = 5.744 = 5.7

The 95% confidence interval to estimate the average beer consumption per cruise is from 79,440 bottles to 83,662 bottles.

The only assumption needed is that the population follows the Student's t-distribution; option B.

a. Construct a 95% confidence interval:

The formula for a confidence interval, CI, for the population mean (μ) is:

CI = sample mean ± (critical value * standard error)

Given:

Sample mean (x) = 81,551 bottles

Sample standard deviation (s) = 4,572 bottles

Sample size (n) = 15

Confidence level = 95%

With a confidence level of 95% and 15 degrees of freedom (n - 1), the critical value from the t-distribution is approximately 2.131.

Standard error (SE) = s / √n

SE = 4572 / √15

Lower limit of the confidence interval = x - (critical value * SE)

Upper limit of the confidence interval = x + (critical value * SE)

The confidence interval:

Lower limit = 81551 - (2.131 * (4572 / √15))

Upper limit = 81551 + (2.131 * (4572 / √15))

Lower limit ≈ 79440 bottles

Upper limit ≈ 83662 bottles

b. Assumptions about the population:

The only assumption needed is that the population follows the Student's t-distribution. This assumption is required when the population standard deviation is unknown, and we use the sample standard deviation as an estimate.

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The points that lie in the feasible region of this maximization problem are (-1,1) and (1,1).

The given constraints are: 14X + 4Y ≤ 28 and X − Y ≤ 2

In order to determine which of the points belong to the feasible region of this maximization problem, we need to check each point one by one. Let's evaluate each point and check which of the points lie in the feasible region. The points are given as below:x = −1, y = 2.5

The two constraints are:14X + 4Y ≤ 28 and X − Y ≤ 2

For the point (x,y) = (-1,2.5), we have:

14(-1) + 4(2.5) = 7 > 0;

Therefore, the point (-1,2.5) satisfies the first constraint.

Next, we need to check whether the point (-1,2.5) satisfies the second constraint:X − Y = -1 - 2.5 = -3.5 < 2

Since the second constraint is not satisfied, (-1,2.5) is not in the feasible region.

x = −1, y = 1

For the point (x,y) = (-1,1), we have:14(-1) + 4(1) = 10 > 0;

Therefore, the point (-1,1) satisfies the first constraint

.Next, we need to check whether the point (-1,1) satisfies the second constraint:X − Y = -1 - 1 = -2 < 2

Since the second constraint is satisfied, (-1,1) is in the feasible region.

x = 4, y = 2For the point (x,y) = (4,2), we have:14(4) + 4(2) = 64 > 0;

Therefore, the point (4,2) satisfies the first constraint.Next, we need to check whether the point (4,2) satisfies the second constraint:X − Y = 4 - 2 = 2 < 2

Since the second constraint is not satisfied, (4,2) is not in the feasible region.

x = 2, y = 1

For the point (x,y) = (2,1), we have:

14(2) + 4(1) = 32 > 0;

Therefore, the point (2,1) satisfies the first constraint.Next, we need to check whether the point (2,1) satisfies the second constraint:X − Y = 2 - 1 = 1 < 2

Since the second constraint is satisfied, (2,1) is in the feasible region.

x = 1, y = 1

For the point (x,y) = (1,1), we have:

14(1) + 4(1) = 18 > 0;

Therefore, the point (1,1) satisfies the first constraint.

Next, we need to check whether the point (1,1) satisfies the second constraint:X − Y = 1 - 1 = 0 < 2

Since the second constraint is satisfied, (1,1) is in the feasible region.

Hence, the two points that belong to the feasible region are (-1,1) and (1,1).

Therefore, the correct answer is: The points that lie in the feasible region of this maximization problem are (-1,1) and (1,1).

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Answer:

x --> -19 = 38

Answer:

44

Step-by-step explanation:

The question is entering from the positive direction, thus 44 and not 38.

Answer:

Ans C

m=4/5

X1= -7

Y1 = 9

Y-Y1=m(X-X1)

Y-9=4/5(X-(-7))

Y-9=4/5(X+7)

Events that have no outcomes in common  are said to be disjoint or mutually exclusive.

Two sets are known to be mutually exclusive when they have no common elements. Mutually exclusive events are those that cannot take place at the same moment.

If two events are considered disjoint events, then the probability of both events occurring at the same time will be zero.

Set A = {2, 4, 6, 8, 10, 12, 14, 16}

Set B = {1, 3, 5, 7, 9, 11, 13, 15}

A and B do not have any numbers in common, so P (A ∩ B) = 0. Therefore, A and B are mutually exclusive.

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The product of x * 5 * 5 is 25x.

The product of 1 * 3 * 3 * 5 is 45.

The product of 1/3 * 2 * 5 is 10/3 or 3.33 (rounded to two decimal places).

To find the product of expressions, you multiply the numbers or variables together according to the given expression.

1. Product of x * 5 * 5:

To find the product of x, 5, and 5, you multiply them together:

x * 5 * 5 = 25x

2. Product of 1 * 3 * 3 * 5:

To find the product of 1, 3, 3, and 5, you multiply them together:

1 * 3 * 3 * 5 = 45

3. Product of 1/3 * 2 * 5:

To find the product of 1/3, 2, and 5, you multiply them together:

1/3 * 2 * 5 = (1 * 2 * 5) / 3 = 10/3 or 3.33 (rounded to two decimal places)

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The total cost of repayment over 5 years is $23,300.

A loan repayment refers to the act of paying back money previously borrowed from a lender.

To get total cost of repayment, we must principal amount, the interest rate and the duration of the loan.

The formula to get total cost of repayment is given by \(Total Cost of Repayment = Principal + Interest\)

Interest = Principal * Interest Rate * Time

Given:

Principal amount is $20,000

Interest rate is 3.3%

Duration is 5 years.

Interest = $20,000 * 0.033 * 5

Interest = $3,300

Total Cost of Repayment = Principal + Interest

= $20,000 + $3,300

= $23,300.

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Answer:

\(\frac{x}{2}\)

Step-by-step explanation:

the y-value is when the x-value is divided by 2

The distance between City X and City Y = 440 miles Radius of the Earth, R = 3690 miles Let’s consider two cities X and Y, as shown below. As shown in the figure above, the difference in latitude of the two cities will be the arc length between point P and Q.

So, we need to find the arc PQ, which is the difference in latitude. We have given the distance XY, which is nothing but the chord length. Let’s find the angle subtended by the chord XY at the center of the Earth O. We can find this angle using the formula;angle = (chord length/2*radius of the earth)angle = (440/2*3690) angle

= 0.06 radians Now, we can find the arc PQ by using the formula;arc length PQ = radius of the earth * angle subtended by the chord PQ arc length PQ = 3690 * 0.06 arc length

PQ = 221.4 miles

Therefore, the difference in latitude between City X and City Y is 221.4 miles.

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Answer:

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Given a parabola in standard form, y = ax² + bx + c ( a ≠ 0 ), then

minimum/ maximum value is the y- coordinate of the vertex.

The x- coordinate of the vertex is

\(x_{vertex}\) = - \(\frac{b}{2a}\)

y = x² - \(\frac{5}{3}\) x + \(\frac{31}{36}\) ← is in standard form

with a = 1 and b = - \(\frac{5}{3}\) , thus

\(\frac{x}{vertex}\) = - \(\frac{-\frac{5}{3} }{2}\) = \(\frac{5}{6}\)

Substitute this value into y

y = (\(\frac{5}{6}\) )² - \(\frac{5}{3}\) (\(\frac{5}{6}\) ) + \(\frac{31}{36}\)

   = \(\frac{25}{36}\) - \(\frac{25}{18}\) + \(\frac{31}{36}\) = \(\frac{1}{6}\)

Since a > 1 then the vertex is a minimum, thus

minimum value = \(\frac{1}{6}\) → A

Subtract the tips from total earned:

400-253 = 147

Now Divide by hours worked:

147/28 = 5.25

Hourly rate is $5.25

The classifications L and M are independent.

As the sample size decreases, the accuracy of the results of an experiment can decrease or become less reliable.

When the sample size decreases, the accuracy of the experiment's results can decrease or become less reliable. The smaller the sample size, the less representative it is of the population being studied. As a result, it will be less probable that the sample provides an accurate depiction of the entire population.

Use α = .05 and Independent; Performing the hypothesis test for independence of two classifications L and M, using the data from the given cross-classification table with α = .05 and independent: Null hypothesis: There is no relationship between the two classifications Alternative hypothesis: There is a relationship between the two classifications The formula for calculating the chi-square test statistic is: χ² = ∑(O - E)²/E, where O = observed frequency in each category, E = expected frequency in each category.

We must first calculate the expected frequency for each cell. We use the formula E = (row total * column total) / grand total expected frequencies for the given table is: Thus, the chi-square test statistic, calculated as per the formula above, is χ² = 0.942With α = .05 and degrees of freedom = (2 - 1) * (2 - 1) = 1, the critical value of χ² is 3.84.As the calculated value of χ² = 0.942 < 3.84, it falls in the acceptance region. Therefore, we cannot reject the null hypothesis. Therefore, we may conclude that the classifications L and M are independent.

Repeat the exercise using the given table. We repeat the same procedure to calculate the expected frequencies for each cell and then calculate the chi-square test statistic as follows: Expected frequencies for the given table is: Thus, the chi-square test statistic, calculated as per the formula above, is χ² = 0.933With α = .05 and degrees of freedom = (2 - 1) * (2 - 1) = 1, the critical value of χ² is 3.84.As the calculated value of χ² = 0.933 < 3.84, it falls in the acceptance region. Therefore, we cannot reject the null hypothesis. Therefore, we may conclude that the classifications L and M are independent.

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Infer means to guess or reach a conclusion, especially based on an indirect hint.

The passage suggests that the main reason the narrator considers Great Expectations to be the best gift he ever received is that reading the book convinced him that he wanted to be a writer.

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The mean, variance, and standard deviation of the distribution is 20.74, 1.3210, and 1.1493, respectively.

First, the mean can be found using the following formula:

Mean = ∑x(p(x))

Mean = (19)(0.22) + (20)(0.20) + (21)(0.32) + (22)(0.14) + (23)(0.12)

Mean = 4.18 + 4 + 6.72 + 3.08 + 2.76

Mean = 20.74


Next, the variance can be found using the following formula:

Variance = ∑(x-mean)²(p(x))

Variance = (19-20.74)²(0.22) + (20-20.74)²(0.20) + (21-20.74)²(0.32) + (22-20.74)²(0.14) + (23-20.74)²(0.12)

Variance = 0.5362 + 0.0552 + 0.0173 + 0.1754 + 0.5369

Variance = 1.3210


Finally, the standard deviation can be found using the following formulas:

Standard deviation = √variance

Standard deviation = √1.3210

Standard deviation = 1.1493


So, the mean is 20.74, the variance is 1.3210, and the standard deviation is 1.1493, all rounded to 4 decimal places.

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Answer:

12/2.54 ≈ 4.72 inches

Answer:

8x+140=180

8x=40

x=5°

Step-by-step explanation:

Sum of angles in a straight line=180°

Answer:

37deg

Step-by-step explanation:

The variance of X, where X takes the values 28, 46, 73, and 73 with equal probability, is 364.5.


To find the variance of a random variable X, you need to follow these steps:
1. Calculate the mean (average) of X.
2. Calculate the squared difference between each value of X and the mean.
3. Calculate the expected value of the squared differences.
4. The result obtained in step 3 is the variance of X.
Let’s apply these steps to the given values of X: 28, 46, 73, and 73.
Step 1: Calculate the mean (average) of X.
Mean(X) = (28 + 46 + 73 + 73) / 4 = 220 / 4 = 55
Step 2: Calculate the squared difference between each value of X and the mean.
(28 – 55)^2 = 27^2 = 729
(46 – 55)^2 = 9^2 = 81
(73 – 55)^2 = 18^2 = 324
(73 – 55)^2 = 18^2 = 324
Step 3: Calculate the expected value of the squared differences.
Expected value = (729 + 81 + 324 + 324) / 4 = 1458 / 4 = 364.5
Step 4: The result obtained in step 3 is the variance of X.
Variance(X) = 364.5
Therefore, the variance of X, where X takes the values 28, 46, 73, and 73 with equal probability, is 364.5.

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The Value of the double integral is 9/2.

To Evaluate the double integral ∫∫D x dA, we need to express the region D as a type I or type II region, and then integrate over that region.

For D enclosed by the lines y = x, y = 0, x = 3, we can see that the region is a right triangle with vertices at (0,0), (3,0), and (3,3), so it can be expressed as a type I region with:

a. D = {(x, y) | y ≤ x ≤ 3, 0 ≤ y ≤ x}

or as a type II region with:

b. D = {(x, y) | 0 ≤ y ≤ 3, y ≤ x ≤ 3}

To evaluate the double integral using either of these regions, we can use iterated integrals.

Using a type I region:

∫∫D x dA = ∫0³ ∫y³ x dy dx

= ∫0³ ∫0x x dy dx

= ∫0³ ½x² dx

= 9/2

Using a type II region:

∫∫D x dA = ∫0³ ∫0y y dx dy

= ∫0³ ½y² dy

= 9/2

.

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Answer:

<1 and <2 are remote interior angles of <6

<2 and <3 are remote interior angles of <4