Evaluate the integral. (3 + 1/4 u^4 − 2/3 u^9) du

Answer:

Step-by-step explanation:

Given , two air craft carriers are A and B . The carrier A is longer than the carrier B in length.

Total length of two carriers =4178 feet

Difference of two carriers = 14 feet

Let

Length of carrier A =x  feet

And

Legth of carrier B =y feet

According to question  

The I equation is

x+y=4178

The II equation is

x-y= 14

Substitution method:  In this method step I :  we  find value of x or y from the equation I

Step II:  put the value of x or y in II equation then we get the value of another  varaiable x or y  

Step : Again put the obatined value of variable x or y  from  step II   in equation I then we get value of other variable x or y .

By  using substitution method ,

we find value of x from equation I

x= 4178-y

Now, put the value of x in equation II then we get

4178-y-y=14

4178-2y=14

4178-14=2y

4164=2y

[tex]y=\frac{4164}{2}[/tex]

y= 2082

Again , put the value of y in equation I

2082 +x=4178

x= 4178-2082

x=2096

Hence, the length of carrier A = 2096 feet

The length of carrier B= 2082 feet

Final answer:

To solve the problem, we set up two equations based on the given total length and the length difference of the two aircraft carriers. By solving these equations, we find that carrier A is 2096 feet long and carrier B is 2082 feet long.

Explanation:

The student's question involves solving a system of linear equations to find the lengths of two aircraft carriers, A and B. Given that the total length is 4178 feet and the length difference is 14 feet, we can set up the following equations:

Equation 1: A + B = 4178

Equation 2: A - B = 14

To solve for A and B, we can add the two equations together to eliminate B.

This gives us 2A = 4192, hence A = 2096 feet.

Substituting A back into one of the equations, we find B = 2082 feet.

Therefore, carrier A is 2096 feet long and carrier B is 2082 feet long.

Using proportions, it is found that the price of a bottle of dish soap increased $0.43 from 1980 to 1990.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The percent increase, as a proportion, of the CPI is given by:

P = 130.7/82.4 = 1.5862.

Hence, for the price of the bottle:

Pb = $0.74 x 1.5862 = $1.17.

The difference is:

1.17 - 0.74 = $0.43.

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Answer: $0.43

Step-by-step explanation:

The cool dude above me already explained it

Answer: 12

The value of y= 12.

Step-by-step explanation:

We know that the diagonal of rhombus are perpendicular bisector of each other.

i.e. the angle made at the intersection of diagonal is 90 degrees.

Thus , for the given figure m∠1 = 90°

Since it is given that  m∠1 = 8y-6

Thus , 8y-6= 90

⇒8y=96   [Adding 6 both sides]

⇒ y = 12  [Dividing both sides by 8]

Hence, the value of y= 12.

Answer:

The equation of line is [tex]y=\frac{1}{2}(x)+1[/tex].

Step-by-step explanation:

Given information: The line passes through the point (4,3) and (2,2).

If a line passes through the points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], then the equation of line is

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

The line passes through the point (4,3) and (2,2), so the equation of line is

[tex]y-3=\frac{2-3}{2-4}(x-4)[/tex]

[tex]y-3=\frac{-1}{-2}(x-4)[/tex]

[tex]y-3=\frac{1}{2}(x-4)[/tex]

Using distributive property, we get

[tex]y-3=\frac{1}{2}(x)+\frac{1}{2}(-4)[/tex]

[tex]y-3=\frac{1}{2}(x)-2[/tex]

Add 3 on both sides.

[tex]y=\frac{1}{2}(x)-2+3[/tex]

[tex]y=\frac{1}{2}(x)+1[/tex]

Therefore the equation of line is [tex]y=\frac{1}{2}(x)+1[/tex].

volume of the ball = 4/3 * PI *r^3 =

4/3 * 3.14 * 2.86^3 = 97.99 cubic inches

 this is less than the volume of the box, so yes it will fit

Answer:

B.

Step-by-step explanation:

To find 1/4 of 268, you divide 268 by 4. The result of this operation is 67.

Calculating 1/4 of a number involves a simple mathematical operation known as division. In this case, we want to find out what is 1/4 of 268. To do this, you simply divide 268 by 4.

The calculation is as follows:

This means that 1/4 of 268 is 67.

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The percentage of the class that voted for kayaking is 50%.

Given data:

To find the percentage of the class that voted for kayaking, use the fact that the total percentage of votes adds up to 100%.

Hiking got 17% of the vote.

Fishing got 33% of the vote.

Let x be the percentage of the class that voted for kayaking.

Since the total percentage of votes is 100%:

17% + 33% + x = 100%

On solving for x:

x = 100% - (17% + 33%)

x = 100% - 50%

x = 50%

Hence, 50% of the class voted for kayaking.

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Answer:

x + 1 = 4x + 5

Step-by-step explanation:

To solve this set of equation you can just equalize them ot one another, as you can see they are already in Y form, which means that they have already been solved for Y, so that makes things easier for us, we just insert the second equation in the place of Y in the first one, and we can solve for "x".

Answer:

Probability of tails = 0.51

Step-by-step explanation:

Probability is the ratio of number of favorable outcome to the total number of outcomes.

Total number of outcomes = Total number of heads + Total number of tails

                                              = 165 + 172 = 337

Number of favorable outcome = Total number of tails = 172

[tex]\texttt{Probability}=\frac{172}{337}=0.51[/tex]  

To find the probability of the soil being clay given a positive test result, we can use Bayes' rule. Given the probabilities of the different types of soil and the accuracy of the test in each soil type, we can calculate the probability using the law of total probability and Bayes' rule.

To find the probability of the soil being clay given a positive test result, we can use Bayes' rule. Bayes' rule states that P(A|B) = (P(B|A) * P(A)) / P(B), where P(A|B) is the probability of event A happening given that event B has occurred, P(B|A) is the probability of event B happening given that event A has occurred, P(A) is the probability of event A happening, and P(B) is the probability of event B happening. In this case, event A is that the soil is clay and event B is that the test result is positive.

Given that the soil is clay, the test gives a positive result with 48% accuracy. Therefore, P(B|A) = 0.48. The probability of the soil being clay is P(A) = 0.21. To find P(B), we need to consider the probabilities of the test result being positive in each type of soil.

If the soil is rock, the test gives a positive result with 35% accuracy, so the probability of the test result being positive in rock soil is P(B|rock) = 0.35. Similarly, if the soil is sand, the test gives a positive result with 75% accuracy, so the probability of the test result being positive in sand soil is P(B|sand) = 0.75. We can calculate P(B) using the law of total probability: P(B) = P(B|rock) * P(rock) + P(B|clay) * P(clay) + P(B|sand) * P(sand).

Plugging in the given values, we have P(B) = 0.35 * 0.53 + 0.48 * 0.21 + 0.75 * 0.26. Now we can substitute the values into Bayes' rule:

P(clay | positive) = (P(positive | clay) * P(clay)) / P(positive) = (0.48 * 0.21) / P(B).

So the probability that the soil is clay given a positive test result is (0.48 * 0.21) / P(B).