PART B ONLY
Given: Evaluate the integral
∫x^12ln(x) dx
Solved: 1/13ln(x)x^13 - 1/169x^13 + C
(b) The application of integration by parts corresponds to applying the product rule to what product: [ ??? ]

Answer:

Unfortunately, the provided statement does not contain sufficient information to determine the loan term of the truck.

Step-by-step explanation:

The loan term refers to the length of time over which the loan for the truck is scheduled to be repaid. It is typically determined at the time of purchase and specified in the loan agreement.

To determine the loan term of the truck, we would need to know additional information such as the date of purchase, the loan agreement terms, the payment schedule, and any other relevant details about the loan.

Answer:

The first one

Step-by-step explanation:

In mathematics, the term linear function refers to two distinct but related notions: In calculus and related areas, a linear function is a function whose graph is a straight line, that is, a polynomial function of degree zero or one. So going in that order gives you a linear function.

A linear function increases at a constant rate of change, which means that for every 1 unit that x changes, y always changes at a same rate.

For example, if x moves 1, y moves 5 constantly. Every time x moves 1, y moves 5.

In this case every time x in the first table increases by 1, y increases by 6, so that is a linear function.

The second table is not linear because when x increases by 1,  y decreases by 1. But the second time, when x increases by 1, y decreases by 2! -2 is not equal to -1.

The third and fourth tables are not linear for the same reasons.

Therefore,

The answer is D.

⊰_________________________________________________________⊱

Answer:

Step-by-step explanation:

\(\large\displaystyle\text{$\begin{gathered} \sf{Substitute \ the \ values \ into \ the \ formula \ y-y_1=m(x-x_1)} \\ \sf {parallel \ lines \ have \ same \ slopes, \ thus} \\ \sf{slope \ of \ the \ 2nd \ line = 3}\\ \sf{now \ substitute \ the \ values} \\ \sf {y-(-5)=3(x-4)}\\ \sf{y+5=3(x-4) (It's \ Point-Slope\;Form, \ see \ below \ for \ slope-intercept)}\\ \sf {y+5=3x-12} \\ \sf{y=3x-12-5} \\ \sf{y-3x-17} \end{gathered}$}}\)

\(\pmb{\tt{done \ !!}}\)

⊱_________________________________________________________⊰

Answer:

228 cm²

Step-by-step explanation:

The base of the pyramid is a regular quadrilateral (a square), so there are 4 congruent lateral faces.

The total surface area is therefore:

A = 36 cm² + 4 (48 cm²)

A = 228 cm²

You need to multiply by 5 instead of 6 because each pair of opposite faces on a cuboid has the same area, so by considering one face from each pair, you ensure that you don't count any face twice.

When calculating the total surface area of a cuboid, you need to understand the concept of face pairs.

A cuboid has six faces, but each face has a pair that is identical in size and shape.

Let's break down the reasoning behind multiplying by 5 instead of 6 in the given scenario.

To find the surface area of a cuboid, you can add up the areas of all its faces.

However, each pair of opposite faces has the same area, so you avoid double-counting by only considering one face from each pair. In this case, you have five pairs of faces:

(1) top and bottom, (2) front and back, (3) left and right, (4) left and back, and (5) right and front.

By multiplying the average area of a pair of faces by 5, you account for all the distinct face pairs.

Essentially, you are considering one face from each pair and then summing their areas.

Since all the pairs have the same area, multiplying the average area by 5 gives you the total surface area.

When dividing 150 by 4 (to find the average area of a pair of faces), you are essentially finding the area of a single face.

Then, by multiplying this average area by 5, you ensure that you account for all five pairs of faces, providing the total surface area of the cuboid.

Thus, multiplying by 5 is necessary to correctly calculate the total surface area of the cuboid by accounting for the face pairs while avoiding double-counting.

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F(x) = 2x³ - x² + 5x − 3 is the polynomial that is in standard form. Thus, option D is correct.

Algebraic expressions called polynomials can include exponents that are multiplied, divided, or added. Different types of polynomials exist. specifically, monomial, binomial, and trinomial. A polynomial with only one term is referred to as a monomial. A polynomial with two unlike terms is referred to as a binomial. An algebraic expression with three terms is known as a trinomial.

Monomials - The term "monomial" refers to algebraic expressions with a single term. In other words, it is an expression that includes any number of similar terms. Hence the name "Bi"nomial," binomials are algebraic expressions with two unlike terms. Trinomials - Trinomials are algebraic expressions with three dissimilar terms, hence the name "Tri"nomial.

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(a) The mean of the data item from the group data is 161.

(b) The deviation from the mean for each data is -6,-5,1,3 and 7. respectively.

(c) The sum of the deviation is 0

Grouped data are data formed by aggregating individual observations of a variable into groups, so that a frequency distribution of these groups serves as a convenient means of summarizing or analyzing the data.

(a) To find the mean of the data, we use the formula below.

Formula:

Where:

Substitute these values into equation 1

(b) To calculate the deviation from the mean (M') for each of the data item we use the formula below.

M' = x-M

For data 115,

For data 156,

For data 162,

For data 164,

For data 168,

(c) The sum of the deviation is

Hence, the mean, the diaviation from the mean is -6,-5,1,3 and 7  and the sum of the deviation of the data is 161 and 0 respectively,

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The integers in the set s: {-2,-3,-4,-5} will make the inequality 4p-7 \(\geq\) 9p+8 true are : -3, -4, -5

Let's solve the inequality first

4p -7 \(\geq\)  9p  +8

Taking p's on the same side we will get :

-7 - 8 \(\geq\) 9p - 4p

-15 \(\geq\) 5p

Divide by 5 into both sides

-3 \(\geq\) p

i.e. p \(\leq\) -3

Therefore p must be less than or equal to -3

From the set, we have the numbers -3,-4,-5 which are less than or equal to -3

Hence the integers -3,-4,-5 will make the  inequality 4p-7 \(\geq\) 9p+8 true

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Answer:

the appointment was 1 mile away from Alex's house for every minute of driving time at 50 mph.

Step-by-step explanation:

Let's call the distance from Alex's house to the appointment "d".

If Alex drives 50 mph, he will cover this distance in d/50 hours.

If he leaves 15 minutes (or 0.25 hours) early and drives 40 mph, he will cover the same distance in (d/40) + 0.25 hours.

Since both of these times are the same (since Alex arrives on time), we can set them equal to each other and solve for d:

d/50 = (d/40) + 0.25

Multiplying both sides by 200 (the least common multiple of 50 and 40) to get rid of the denominators, we get:

4d = 5d + 50

Subtracting 4d from both sides, we get:

d = 50

Therefore, the appointment is 50 miles away from Alex's house.

As you mentioned, the equation X/50 = the appointment was __ miles away from Alex house can be used to solve the problem. Plugging in X = 50 gives:

50/50 = 1

So the appointment was 1 mile away from Alex's house for every minute of driving time at 50 mph.

We have proven that △ABD ≅ △CBD based on the given information and the SAS congruence criterion.

To prove that △ABD ≅ △CBD, we can use the SAS (Side-Angle-Side) congruence criterion.

Given:

∠BDA ≅ ∠BDC (Both are right angles)

D is the midpoint of AC¯¯¯¯¯

AB¯¯¯¯¯ ≅ BC¯¯¯¯¯

BD¯¯¯¯¯ bisects ∠B

Proof:

Since D is the midpoint of AC¯¯¯¯¯, we have AD ≅ CD by the definition of a midpoint.

AB¯¯¯¯¯ ≅ BC¯¯¯¯¯ (Given)

BD¯¯¯¯¯ is a common side for both triangles.

∠BDA ≅ ∠BDC (Given)

To apply the SAS congruence criterion, we need to show that one pair of corresponding sides and the included angle are congruent in both triangles.

AD ≅ CD (Side) - This is true as D is the midpoint of AC¯¯¯¯¯.

∠BDA ≅ ∠BDC (Included Angle) - Both are right angles.

By the SAS congruence criterion, we can conclude that △ABD ≅ △CBD.

Therefore, we have proven that △ABD ≅ △CBD based on the given information and the SAS congruence criterion.

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Six (6) confidence intervals or hypothesis tests would need to be done to make significant statements for each pair-wise comparison.

In an ANOVA F test, the null hypothesis is that the means of all the treatments are equal, and the alternative hypothesis is that at least two of the means are different. If the null hypothesis is rejected at the 5% significance level, this means that the differences between the means are statistically significant and the treatments can be considered different.

Since there are four treatments, there are 6 possible pairs of treatments. These tests would determine whether the means of each pair of treatments are significantly different from each other.

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Answer:

45

Step-by-step explanation:

Answer:

Hope this helps ;)

Step-by-step explanation:

To find the time it takes the T-shirt to reach its maximum height, we need to find the value of t when the velocity of the T-shirt is zero, because at this point the T-shirt has reached its maximum height and starts falling back down. We can find the velocity of the T-shirt by taking the derivative of the height equation with respect to time:

v(t) = h'(t) = 72

The velocity of the T-shirt is a constant 72 feet per second, so it will never reach a velocity of zero and will never reach its maximum height. The T-shirt will keep going up indefinitely.

If the problem had specified that the T-shirt was launched with an initial upward velocity of -72 feet per second (meaning it was launched downward), then we could have found the time it takes the T-shirt to reach its maximum height by setting v(t) = 0 and solving for t. In this case, we would find that t = 1, so it would take the T-shirt 1 second to reach its maximum height. The maximum height would be h(1) = -16 + 72(1) + 6 = 62 feet.

Answer:

Step-by-step explanation:

Shannon is designing a rectangular flag.

Therefore, all the interior angles of this flag measure 90°.

m∠1 + m∠2 = 90°

Since, ∠2 is 3 times as great as the measure of ∠1.

m∠2 = 3(m∠1)

Therefore, m∠1 + 3(m∠1) = 90°

4(m∠1) = 90°

m∠1 = 22.5°

m∠2 = 3(m∠1)

        = 3(22.5)°

        = 67.5°

m∠3 + m∠4 = 90° [Interior angle of a rectangle]

She thinks ∠3 and ∠4 are equal,

m∠3 = m∠4

m∠3 + m∠3 = 90°

2m∠3 = 90°

m∠3 = 45°

m∠4 = m∠3 = 45°

m∠2 = m∠6 [Opposite angles of a parallelogram are equal]

Therefore, m∠2 = m∠6 = 67.5°  

Finally she wants the measure of ∠6 is half of the measure of ∠5.

m∠6 = \(\frac{1}{2}\)(m∠5)

67.5° = \(\frac{1}{2}\)(m∠5)

m∠5 = 2(67.5)°

        = 135°

Answer: Shannon is designing a rectangular flag.

Therefore, all the interior angles of this flag measure 90°.

m∠1 + m∠2 = 90°

Since, ∠2 is 3 times as great as the measure of ∠1.

m∠2 = 3(m∠1)

Therefore, m∠1 + 3(m∠1) = 90°

4(m∠1) = 90°

m∠1 = 22.5°

m∠2 = 3(m∠1)

       = 3(22.5)°

       = 67.5°

m∠3 + m∠4 = 90° [Interior angle of a rectangle]

She thinks ∠3 and ∠4 are equal,

m∠3 = m∠4

m∠3 + m∠3 = 90°

2m∠3 = 90°

m∠3 = 45°

m∠4 = m∠3 = 45°

m∠2 = m∠6 [Opposite angles of a parallelogram are equal]

Therefore, m∠2 = m∠6 = 67.5°  

Finally she wants the measure of ∠6 is half of the measure of ∠5.

m∠6 = (m∠5)

67.5° = (m∠5)

m∠5 = 2(67.5)°

       = 135°

Step-by-step explanation:

Both a ray and a line segment have two endpoints . A ray is bounded on one side , but a line segment is not bounded on either side.

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A two-sample z-test for a difference in population proportions is the appropriate method for analyzing the results.

Z-test is a statistical test often utilizes to find the difference in mean. It is coupled with variances and sample size to find the appropriate results. It is a hypothetical test where normal distribution is seen.

z-test holds numerous advantages such as it indicates difference in small size groups making it more usable. Moreover, it is also reliable in non-normal distribution of data and is efficient while taking multiple groups in a single analysis. The question has two different popular proportion and hence the two sample z-test will suitable to compare the means.

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The value of the variable 'x' at y = 2 in the equation x + y = 2 will be 2.

In other words, the collection of all feasible values for the parameters that satisfy the specified mathematical equation is the convenient storage of the bunch of equations.

The equation is given below.

x + y = 4

The degree of the equation is one. Then the equation is a linear equation.

The value of the variable 'x' at y = 2 is given as,

x + 2 = 4

x = 4 - 2

x = 2

The value of the variable 'x' at y = 2 in the equation x + y = 2 will be 2.

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The complete question is given below.

In the equation x + y = 4, what is the value of x if y = 2?

The measure of the central angle is 0.75 radians

An equation is an expression that can be used to show the relationship between two or more numbers and variables using mathematical operators.

The area of a figure is the amount of space it occupies in its two dimensional state.

The length of an arc with an angle of Ф is given by:

Length of arc = (Ф/360) * (π * diameter)

The diameter is 16 cm and intercepted arc length is 6 cm, hence:

Length of arc = (Ф/360) * (π * diameter)

6 = (Ф/360) * (π * 16)

Ф = 42.97°

Ф = 42.97° * π/180 = 0.75 radian

The measure of the central angle is 0.75 radians

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Answer: y=1.25

Step-by-step explanation:

First things first you have to find what is in the bracket things (i don’t know what it’s called) So 3 - 7 is -4y but since it’s absolute it’s going to be 4y.

So now you’ve got 4y - 10 = -5. Your going to want to eliminate 10 so, subtract 10 to both sides giving you 4y = -5

Lastly to get y by itself you need to divide it by its self so, 4y divided by 4. Do it to both sides. This gives you…

Y = 1.25

Answer:

(m÷3)+2in

Step-by-step explanation:

(m÷3) represents the division of Myron's height and 3

+2 is the extra 2 inches

Hope this helps! :)

Answer:

4

Step-by-step explanation:

Inside a function, a certain unique input cannot ever have more than one output. All of the other tables have more than one output for only one input.

Answer:

The last one, D it is not a function because the domain (x) does not repeat.

Step-by-step explanation:

To find whether it is a function or not ALL YOU NEED TO DO is check if the domain (x) repeats, it also includes negative numbers like if the domain is

-2, 3, 5, 2  it will be a function because none of these numbers repeat. Yes the number "-2, and 2" repeat BUT one is negative and one is positive, therefore it is a function because they are different numbers when they are negative and positives.

Also just wanted to mention if the (y) repeats it does not matter. It can repeat even a million times, but if the domain numbers (x) do not repeat, therefore it is a function.

Answer:

I do not have access to Annexure A and Annexure B, so I cannot collect the data, draw the frequency table or pie chart, or answer the last question. However, I can provide a general explanation of how to calculate the mean, mode, median, and range from a set of data.

To find the mean (average) of a set of data, add up all the values in the set and divide by the number of values. For example, if the maximum temperatures of the 30 days are:

25, 28, 29, 27, 26, 30, 31, 32, 29, 27, 26, 24, 23, 25, 28, 30, 32, 33, 34, 31, 29, 28, 27, 26, 25, 24, 23, 21, 20, 22

The sum of the values is:

25 + 28 + 29 + 27 + 26 + 30 + 31 + 32 + 29 + 27 + 26 + 24 + 23 + 25 + 28 + 30 + 32 + 33 + 34 + 31 + 29 + 28 + 27 + 26 + 25 + 24 + 23 + 21 + 20 + 22 = 813

Dividing by the number of values (30), we get:

Mean = 813/30 = 27.1

To find the mode of a set of data, identify the value that occurs most frequently. In this example, there are two values that occur most frequently, 27 and 29, so the data has two modes.

To find the median of a set of data, arrange the values in order from smallest to largest and find the middle value. If there are an even number of values, take the mean of the two middle values. In this example, the values in ascending order are:

20, 21, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 27, 27, 28, 28, 29, 29, 29, 30, 30, 31, 31, 32, 32, 33, 34

There are 30 values, so the median is the 15th value, which is 28.

To find the range of a set of data, subtract the smallest value from the largest value. In this example, the smallest value is 20 and the largest value is 34, so the range is:

Range = 34 - 20 = 14

To create a frequency table for the maximum temperature data, we need to group the data into intervals and count the number of values that fall into each interval. For example, we could use the following intervals:

20-24, 25-29, 30-34

The frequency table would look like this:

Interval | Frequency

20-24 | 4

25-29 | 18

30-34 | 8

To calculate the size of the angles for the pie chart, we need to find the total frequency (30) and divide 360° by the total frequency to get the proportion of each interval in degrees. For example, for the interval 25-29:

Proportion = Frequency/Total frequency = 18/30 = 0.6

Angle = Proportion * 360° = 0.6 * 360° = 216°

We can repeat this calculation for each interval to obtain the angles for the pie chart.

In terms of the last question, it is not clear what is meant by "which data collection best describe the maximum and why?". If you could provide more context or clarification, I would be happy to try to help.

The dimensions of the another rectangle is 2 cm and 4 cm.

According to the statement

We have to find that the perimeter of another rectangle.

So, For this purpose, we know that the

The perimeter of a shape is defined as the total length of its boundary.

From the given information:

The perimeter of a pool is 150 m. the rectangle at the right is a scale drawing of the pool. The length of each square on the grid represents 1 cm. draw another scale drawing of the pool using the scale 25 m to 2 cm.

Then

From the given rectangle,

Length of the rectangle = 5 cm

Width of the rectangle = 10 cm

Ratio of length : width = 1 : 2

Perimeter of the rectangle = 2(l + b)= 150 cm

l + b = 75 -----(1)

Since, l : b = 1 : 2

l/b = 1/2

b = 2l ------(2)

From equations (1) and (2),

l + 2l = 75

3l = 75

l = 25 m

Width 'b' = 2(25) = 50 m

Now we've to draw a rectangle with a scale = 25 : 2

Therefore, multiplier factor = 25/l = 25/2

l = 2 cm

Similarly,

50/w = 25/2

w = 4 cm

Now we are able to draw a rectangle with length = 2 cm and width = 4 cm.

So, The dimensions of the another rectangle is 2 cm and 4 cm.

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Answer:

21.2 square meters

Step-by-step explanation:

The area of a parallelogram is base • height.

So:

1. Calculate the area of what you can get for $50. 5 • 212 = 1060 square meters.

2. Now you divide the first price ($50) by the desired price ($1). This one is easy because 50 / 1 = 50, but I'm putting this here for future reference in case you need to solve a problem that has a desired price that's greater than $1.

3. Divide the answer to step one by the answer to step two to get the area you can have painted for $1. 1060 / 50 = 21.2 square meters.

Answer:

a) the required probability is 0.0013

b) the required probability is 0.0288

c) the required probability is 0.9759

Step-by-step explanation:

Given the data in the question;

let x be the thickness measurements

Given that X follows a Normal distribution with mean μ = 5.4

standard deviation σ = 0.8

then z = x-μ / σ = x-5.4 / 0.8   follows standard Normal

a) probability that the thickness is less than 3.0 mm

P( x<3 ) = P( x-5.4 / 0.8  <  3-5.4 / 0.8 ) = P( Z < -3.00 ) = 0.0013

Therefore, the required probability is 0.0013

b) the thickness is more than 7.0 mm

P( x>7 ) = P( x-5.4 / 0.8  >  7-5.4 / 0.8 ) = P( Z > 2.00)

= 1 - P( Z ≤ 2)

= 1 - 0.9772

= 0.0288

Therefore, the required probability is 0.0288

c) the thickness is between 3.0 mm and 7.0 mm

P(3< x<7 ) = P( x<7) - P(x<3)

= P( x-5.4 / 0.8  >  7-5.4 / 0.8 )  - P( x-5.4 / 0.8  <  3-5.4 / 0.8 )

= P( Z< 2 ) - P( Z < -3)

= 0.9772 - 0.0013

= 0.9759

Therefore, the required probability is 0.9759

If Liam has 9/16 gallon, he has enough white paint to make 8 gallons of light green paint

A word problem in mathematics is a maths question written as one sentence or more that requires the application of mathematics knowledge to a 'real-life' scenario.

Given that 6 gallons of light green paint use 3/8 gallon of white paint, this can be expressed as:

3/8 gallons of white paint = 6 gallons of light green

We are to determine if 9/16 gallons will be enough to make 8 gallons of light green paint. This can be expressed as

9/16 gallons of white paint = x

Divide both expressions

3/8 x 16/9 = 6/x

2/3 = 6/x

By cross multiplying

2x = 3 x 6

2x = 18

x = 18/2

x = 9

This shows that if Liam has 9/16 gallon, he has enough white paint to make 8 gallons of light green paint

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Answer:

in all they will take 330 hours to make 11 tables

Step-by-step explanation:

multiple 5 x 6 x 11=330

Answer:

it will take 69 hours to make 11 tables

Step-by-step explanation:

34.5+34.5=69 (hence proved)

Answer:

[2x-4]<x-1 so we take off the brackets so

2x-4<x-1

group like terms so

2x-x<-1+4

x < 3