(b)Use integration by parts (state the formula and identify u and du clearly) to evaluate the In 2³ integral ∫4-1 Inx³ / √x dx. Give an exact answer. Decimals are not acceptable.

Answer:

The like terms in this expression are 24a and -8a, and -12b and 12b.

Step-by-step explanation:

The like terms 24a and -8a can be combined by adding the coefficients and the variables, which gives us 24a - 8a = 16a.

The like terms -12b and 12b can be combined by adding the coefficients and the variables, which gives us -12b + 12b = 0.

So the like terms in this expression are 24a, -8a, and -12b, 12b.

Answer:

0.66666667

Step-by-step explanation:

Answer:

3 will divide 2 but since 3cannot get into 2, there will be 0. and 0 would be added to the 2 to make it 20

then 3 gets into 20 six times remainder 2 but still continues.

however, since 6 is greater than 5, it can be round down to get 0.67/0.667

The required probability for the given event is given as 0.5.

Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.

The probability of any event always lie in the close interval of 0 and 1 [0,1].

Given that,

The probability of a door being locked is 70% = 0.7

Total number of keys is 10.

The number of keys being carried is 2.

Thus, there can be two cases for getting through the door.

Case 1: The door is locked.

The probability to open the door by 1 key is 1/10.

Then, the probability to open the door by 2 keys is 2/10 = 1/5.

Case 2: The door is open.

In this case no keys are needed which means the chance of getting through is the probability of door not being locked which is given as,

1 - 0.7 = 0.3.

Now, the overall probability should consider both the cases as,

P(getting through the door) = P(Door is closed and keys open it)

+ P(The door is open)

= 0.3 + 1/5

= 0.3 + 0.2

= 0.5.

Hence, the probability to get through the door without returning for more keys is 0.5.

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Answer:

B isa the answer for me it might be wrong for you or switch them

Step-by-step explanation:

Answer:

Rational: 3.0, 2/5, -9

Irrational: pie, 8, 2.42..

Answer:

-9 (rational)

Sq. root of 8 (irrational)

3.0 (rational)

2/5 (rational)

2.42... (rational)

Pi (irrational)

Step-by-step explanation:

Answer: 1 3/8

Step-by-step explanation:

Answer:

B??

Step-by-step explanation:

Answer

The sequence is geometric.

a = 1.5

r = -3

Explanation

Given:

The sequence given is: 1.5, -4.5, 13.5, -40.5

What to find:

If the sequence is geometric, also to find a, r.

Solution:

To check if it's geometric, we shall solve the following:

This shows that the sequence is geometric.

The first term, a, of the sequence is 1.5.

And the common ratio, r = (second term/first term) = (-4.5/1.5) = -3.

Hence, the sequence is geometric, a = 1.5 and r = -3.

Answer:

Step-by-step explanation:c

Show the figure, please.

Answer:

Step-by-step explanation:

What figure

The total price of the shoes, including tax is $39.944.

Given is that a pair of shoes usually sells for $56. The shoes are 40% off, and sales tax is 6%.

We can write the total cost of shoes as -

{x} = 56 - {40% of 56} + 6% of {40% of 56}

{x} = 56 - {40/100 x 56} + 6/100 x {40/100 x 56}

{x} = 56 - 22.4 + 1.344

{x} = 56 - 21.056

{x} = 34.944

Therefore, the total price of the shoes, including tax is $39.944.

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The logical assumption used is: An arithmetic sequence is a set of discrete values, whereas a line is a continuous set of values.

An arithmetic sequence is a set of numbers where, with the exception of the first term, each term is obtained by adding a fixed constant to the term before it. Every pair of following terms in the sequence has the same fixed constant, which is known as the common difference. A1 stands for the first term in an arithmetic sequence, while an is used to represent the nth term.

A solid line symbolises continuous numbers, whereas the classmate's logical presumption is that an arithmetic series comprises of discrete values. This presumption is untrue, though, as a line can effectively represent an arithmetic series.

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The answer is Positive Linear Correlation.

A scatter plot is a graphical representation of data points where each point represents two variables, typically plotted on the horizontal and vertical axes.

To construct a scatter plot, we need two sets of data:

one for the x-axis and one for the y-axis.

The data points are then plotted on the graph with the x-value along the horizontal axis and the y-value along the vertical axis.
To answer your question, I need to know what data you have to construct the scatter plot.

Once you provide me with the data, I can help you create the scatter plot and answer any questions you may have about it.
In general, scatter plots are used to identify any patterns or trends in the data.

By visually examining the scatter plot, we can determine whether the data points are positively or negatively correlated, or if there is no correlation between the two variables.

To determine the type of correlation, we can visually inspect the scatter plot. We see that as x increases, y tends to increase as well, indicating a positive linear correlation.

This can help us make predictions or draw conclusions about the relationship between the variables.
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The given situation shows an arithmetic sequence and the number of sales in the week 50 can be determined by using the nth term formula of arithmetic sequence. The sales in all 50 weeks can be determined by using the formula for sum of finite arithmetic sequence.

An arithmetic sequence is an ordered set of numbers that have a constant difference called a common difference between consecutive terms. Each term is obtained by adding the common difference to the previous term.

In the given situation, the first term (a) is the number of sales to be made in the first week. Hence, a = 10

The common difference (d) is the number added to get the number of sales in the next week. Hence,

d = 1

Hence, in the 2nd week the number of sales should be 11 and in 3rd week it should be 12.

Using the formula for nth term and n = 50,

an=a+(n-1)d

a50=10+(50-1)1

a50=10+(49)1

a50=10+49=59

The formula of finding the sum of the finite arithmetic sequence:

Sn=(n/2)(a1+an)

S50=(50/2)(10+59)

S50=25(69)=1725

Hence, the number of sales in the 50th week is 59 and the total number of sales made in the 50 weeks is 1725.

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Answer:

Step-by-step explanation:

A spring has a force formula of F = k*x

f = 125 N

x = 0.15 m

125 = k*0.15

k =833.33

F = ?

k = 833.33

x = 0.25 m

F = 833.33 * 0.25

F = 208.33 N

You could do this without solving for k

F1/F2 = x1/x2

F1 = 125 N

F2 = ?

x1 = 0.15

x2 =0.25

125 / F2 = 0.15 / 0.25               Cross multiply

125 * 0.25 = 0.15 * F2              Divide by 0.15

125*0.25 /0.15 = F2

F2 = 208.33 just as you got above

The equation of the parabola with focus (2,5) and directrix x=18 is (x - 18)² + (y - 5)² = (y - (5 + (18 - 2) / 2))².

A parabola is a conic section, the intersection of a right circular conical surface and a plane parallel to a generating

straight line of that surface.

The focus of a parabola is a fixed point on the interior of a parabola used in the formal definition of the curve.

The directrix is a straight line perpendicular to the axis of symmetry and placed symmetrically with respect to the focus.

The axis of symmetry is the line through the focus and perpendicular to the directrix.

The vertex of a parabola is the point where its axis of symmetry intersects the curve. It is the point where the parabola changes direction or "opens

up" or "opens down.

The directrix is a fixed straight line used in the definition of a

parabola. It is placed such that it is perpendicular to the axis of symmetry and at a distance from the vertex equal to the

distance between the vertex and focus. It is the line that is equidistant to the focus and every point on the curve.Here's

the solution to the given problem:

The distance between the directrix and the focus is equal to p = 16 (since the directrix is x = 18, the parabola opens to the left, so the distance is measured horizontally)

The vertex is (h,k) = ((18+2)/2,5) = (10,5)

Then we can use the following formula: (x - h)² = 4p(y - k)

Substitute the vertex and the value of p. (x - 10)² = 64(y - 5)

Expand and simplify. (x - 10)² + (y - 5)² = 64(y - 5)

The equation of the parabola is (x - 10)² + (y - 5)² = 64(y - 5).

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The height of the prism is approximately 13.69 feet.

We have,

The volume of a rectangular prism is given by the formula V = lwh,

where l, w, and h are the length, width, and height of the prism, respectively.

We are given that the base of the prism has dimensions 9 feet by 5.2 feet, so we can substitute l = 9 and w = 5.2 into the formula to get:

655.2 = (9)(5.2)(h)

Simplifying this equation gives:

655.2 = 47.88h

Dividing both sides by 47.88 gives:

h = 655.2/47.88 ≈ 13.69

Therefore,

The height of the prism is approximately 13.69 feet.

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Answer:

The coordinates of a point are a pair of numbers that define its exact location on a two-dimensional plane. Recall that the coordinate plane has two axes at right angles to each other, called the x and y axis.

Based on the equation in the question , the R2 would be 0.934.

To compute R2, we need to use the formula:

R2 = SSR / SST

Given that SSR = 14,141.7 and

SST = 15,128.4,

We can substitute these values into the formula:

R2 = 14,141.7 / 15,128.4

R2 ≈ 0.934

b. To compute Ra2, we need to subtract R2 from 1:

Ra2 = 1 - R2

Substituting the value of R2 we calculated in part a:

Ra2 ≈ 1 - 0.934

Ra2 ≈ 0.066

c. A large R2 value indicates that the estimated regression equation explains a large amount of the variability in the data.

In this case, R2 is approximately 0.934, which means that the estimated regression equation explains about 93.4% of the variability in the data.

So, the answer is "Yes".

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The given equation, 16x² - y² + 16z² = 4, represents a quadric surface known as an elliptic paraboloid.

To determine the classification, we can examine the coefficients of the squared terms. In this case, the coefficients of x², y², and z² are positive, indicating that the surface is bowl-shaped. Additionally, the signs of the coefficients are the same for x² and z², indicating that the bowl opens upward along the x and z directions.

The negative coefficient of y², on the other hand, means that the surface opens downward along the y direction. This creates a cross-section in the shape of an elliptical parabola.

Considering these characteristics, the given equation represents an elliptic paraboloid.

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The number that was coded is 45.

First, note that if you raise any integer between 1 and 76 to the power 17, the result will be an integer with many digits.

However, since we are reducing the result modulo 77, we only need to consider remainders when dividing this large number by 77.

To compute the remainder when raising a number to a power modulo 77, you can use the repeated squaring algorithm. Here's how it works:

Start with the base number, which is the secret digit you want to code (let's call it x).

Compute \(x^2\) modulo 77.

Compute\((x^2)^2\) modulo 77.

Repeat step 3 a total of 15 times. At this point, you have computed x^16 modulo 77.

Multiply \(x^{16}\) by x modulo 77 to get \(x^{17}\) modulo 77.

Alternatively, you can use a built-in function in most programming languages to compute modular exponentiation.

For example, in Python, you can use the pow() function with three arguments: the base, the exponent, and the modulus. Here's how you can use it:

x = 25  

for i in range(1, 77):

   if pow(i, 17, 77) == x:

       print(i)

       break

This code will print the secret digit that corresponds to the remainder of 25 when raised to the power of 17 and reduced modulo 77, which is 45.

Therefore, the number you coded is 45.

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If the tank begins with 103 gallons, then 93 gallon will remain after 2 seconds

The quantity of fuel releases from the container = 5 gallon per second

Consider the fuel remaining in the container = y

Consider the number of seconds that have passed since the fuel started dispensing = x

Then x and y satisfy a linear relationship

The quantity of fuel in the tank at the beginning = 103 gallon

Time taken = 2 seconds

Then the equation will be

y = 103 - 5x

Time taken is x = 2

y = 103 - 5× 2

y = 103 - 10

y = 93 gallon

Hence, if the tank begins with 103 gallons, then 93 gallon will remain after 2 seconds

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          (1,1)

Hope that helps :)

Answer:

9 < √97 < 10

Step-by-step explanation:

√97 is a little less than √100

Which is 10

9 < √97 < 10

=====================================================

Explanation:

Consider that 81 < 97 < 100 is a true statement. Note the 81 and 100 are perfect squares such that 81 = 9^2 and 100 = 10^2

We can apply the square root to all three sides to get the following

\(81 < 97 < 100\\\\\sqrt{81} < \sqrt{97} < \sqrt{100}\\\\\sqrt{9^2} < \sqrt{97} < \sqrt{10^2}\\\\9 < \sqrt{97} < 10\\\\\text{The number }\sqrt{97} \text{ is between 9 and 10}\\\\\)

Using a calculator, we can help verify this

\(\sqrt{97} \approx 9.85\)

Answer:

I dont understand the problem because of the way its written out but I believe that the value of x itself is 1.

x=1

Step-by-step explanation:

1 x 4 = 4

(hope it helps a bit)

The radian measure of (5π/6) expressed in degrees is 150°.

To convert degrees to radians, we can use the formula: radians = degrees * (π/180).

To find the degree measure of 150° expressed in radians, we can substitute the value into the formula:

radians = 150 * (π/180).

Simplifying this equation, we get: radians = (5π/6).

Therefore, the degree measure of 150° expressed in radians is (5π/6).

To convert radians to degrees, we use the formula: degrees = radians * (180/π).

To find the radian measure of (5π/6) expressed in degrees, we substitute the value into the formula: degrees = (5π/6) * (180/π).

Simplifying this equation, we get: degrees = 150.

Therefore, the radian measure of (5π/6) expressed in degrees is 150°.

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Answer:

The surface area of a prism is the sum of the area of all its external faces. We can also use the formula: Surface area of prism = 2 × area of base + perimeter of base × height.

Step-by-step explanation:

this should help YOU solve it

Answer:

101

Step-by-step explanation:

I time 41x2 than add 19