Find the integrals:
∫1÷(x(㏑x-π)^4)dx

Using it's concept, the range of function g is given by:

B. [tex]\{y|y \in \mathbb{R}, y \neq -4, -3\}[/tex]

The range of a function is the set that contains all possible output values for the function. In a graph, it is the values of y.

In this graph, y assumes all values except y = -3 and y = -4, hence the range is given by:

B. [tex]\{y|y \in \mathbb{R}, y \neq -4, -3\}[/tex]

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Answer:

d.

Step-by-step explanation:

k gets 3^3

a gets 4^2

subtract 3^3-4^2=d.

The time taken by the boat to travel 32 miles downstream is 2.1 hours and for upstream 3.56 hours.

Speed is defined as the ratio of the time distance traveled by the body to the time taken by the body to cover the distance.

Given that:-

The time taken by the boat upstream will be calculated as:-

( B + W ) Td = D

( 12 + 3 ) Td = 32

( 15 ) Td = 32

Td = 32 / 15 = 2.1 hours

The time taken by the boat downstream will be calculated as:-

( B - W ) Tu = D

( 12 - 3 ) Tu = 32

9 Tu = 32

Tu = 32 / 9 = 3.56 hours.

Therefore the time taken by the boat to travel 32 miles downstream is 2.1 hours and for upstream 3.56 hours.

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Based on the function given, the year when the cost of mailing a first class letter would reach 60 cents is 2007.

If the cost of mailing a first-class letter is 41 cents, then the inflation rate has not stayed constant.

0.60 = 0.29 (1.046)^t

0.60 / 0.29 = (1.046)^t

log (2.07) = t x log (1.046)

t = 16 years

Added to 1991:

= 1991 + 16

= 2007

The cost of mailing a first-class ticket was 41 cents however which means that inflation was not constant.

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A bond purchased at a premium, it will have a yield to maturity and current yield that is lower than its coupon rate.

This is usually above its face value which may be as a result of the interest rate being higher than the current market interest rates.

When a bond is traded at a premium, the yield to maturity and current yield will be lower than its coupon rate.

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The domain of the function g(x) is x >= 5

The complete question is added as an attachment

From the graph, we have the smallest value of x to be 5.

And the value of x increases to the right

This means that:

x >= 5

Hence, the domain of the function g(x) is x >= 5

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The distance between the start and end points is 28.3 miles.

Remember that the distance between two points (x₁, y₁) and (x₂, y₂) is:

[tex]d = \sqrt{(x_1 - x_2)^2 + (y_2 -y_1)^2}[/tex]

Here the initial point is (0mi, 0mi).

If we define the north as positive y-axis and east as the positive x-axis, after that Thomas travels 24 miles north and 15 miles west his new position is:

(-15mi, 24mi).

The distance is then:

[tex]d = \sqrt{(-15mi - 0mi)^2 + (24mi - 0mi)^2} = 28.3mi[/tex]

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Answer: The truck is carrying 55 large boxes and 60 small boxes

Step-by-step explanation:

Let x represent the number of large boxes

Therefore,

The number of small boxes = 115 - x

[tex]\therefore[/tex] According to the question

60x + 25(105 -x) = 4550

60x + 2625 - 25x = 4550

35x = 4550 - 2625

35x = 1925

x = 55

Number of large boxes = x = 55

Number of small boxes = 115 - 55 = 60

Answer:

Step-by-step explanation:

1y + 12 = 6 (1y + 1)

1y + 12= 6y + 6

12 - 6 = 6y - 1y

6 = 5y

y = 6/5

y = 1.2

I don't what you meant by rounding to 2 decimal points so my answer is

Answer:

  (c)  714.96 = 21.6(w +4.7)

Step-by-step explanation:

The area of the rectangular park will be the product of its length and width. This relation is used to write an equation to find the original width of the park.

Let w represent the original width of the park in meters. The new width is 4.7 meters more, so is represented by (w +4.7).

The length of the park is given as 21.6 meters. The area is given as 714.96 square meters.

The various dimensions of the park are related by the area formula:

  A = LW

  714.96 = 21.6(w +4.7)

Answer: The answer is C i took the k12 5.21 unit test

Step-by-step explanation:

The true statement is (a) it is a function

For a relation to be a function, the following must be true:

Each x value must be paired with exactly one y value

From the table of values, all x values have exactly one y value

This means that the relation is a function

Hence, the true statement is (a) it is a function

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The correct option regarding whether the relation is a function is:

It is a function.

A relation represents a function if each input X is mapped to only one output Y.

In this problem, this statement is true(input 3 is mapped to output 10 twice, same output so ok), hence it is a function.

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Answer:

Step-by-step explanation:

1) [tex]FB \parallel CG[/tex], [tex]\angle BFE[/tex] and [tex]\angle C[/tex] are supplementary (given)

2) [tex]\angle ABF \cong \angle C[/tex] (corresponding angles theorem)

3) [tex]\angle BFE[/tex] and [tex]\angle ABF[/tex] are supplementary (supplements of congruent angles are congruent)

4) [tex]CA \parallel FE[/tex] (converse of the same-side interior angles theorem)

With the use of formula, the interest rate is 18.2%

The Interest is the product of the principal, time and the rate in percentage. That is, I = PTR / 100

Where

Substitute all the parameters into the formula

80 = (880 x 0.5R)/100

cross multiply

8000 = 440R

R = 8000/440

R = 18.2%

Therefore,  the (simple) interest rate is 18.2%

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Tony will have 486 cookies if he bakes 10 batches more.

Take two points from table: (8, 234), (9, 252)

Find slope:

[tex]slope: \dfrac{y_2 - y_1}{x_2- x_1} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]

[tex]\rightarrow slope \ (m) : \dfrac{252-234}{9-8} = 18[/tex]

This determines that one batch of cookies has 18 cookies.

So, if he bakes 10 more batches:

(10 × 18) = 180 cookies

Total cookies he then will have:

306 cookies + 180 cookies = 486 cookies.

The regression equation is (d) log(y) = 0.064x + 1.706

The table of values is given as:

x   2   3   4   5   6

y   73  77  85  101  133

Calculate the logarithm of the y values.

So, we have:

x          2   3   4   5   6

log(y)   1.86  1.89  1.93  2  2.12

Next, we enter the above values in a regression calculator.

From the calculator, we have the following summary:

The regression equation is then represented as:

log(y) = bx + a

Where:

b = SP/SSX = 0.64/10 = 0.064

a = MY - bMX = 1.96 - (0.064*4) = 1.706

So, we have:

log(y) = 0.064x + 1.706

Hence, the regression equation is (d) log(y) = 0.064x + 1.706

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The probability that the red balls can be drawn before the green ball is drawn is 3/8.

The probability is the measure of the likelihood of an event to happen.

Given:

red balls= 3

white balls = 4

green balls = 1

So, Probability of red balls

=3/8

Probability of green balls

=1/7

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None solutions to the system exist.

Given statement: A system of three linear equations in three variables is inconsistent.

Concept: If a, b, c and r are real numbers (and if a, b, and c are not all equal to 0) then ax + by + cz = r is called a linear equation in three variables. (The “three variables” are the x, the y, and the z.) The numbers a, b, and c are called the coefficients of the equation.

We know that if a system has no solution, then it is known as inconsistent.

[If there are one, two, or an infinite number of solutions to the system, then it is called consistent.]

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The bisector of angle APQ passes through O and this is illustrated below.

From the information given, the center is O. and the circle passes through O and cuts at K.

In this case, it should be noted that the circles are equal according to the SAS test.

Here, AOB + APQ = 180° (Linear pair)

2AOB = 180

AOB = 90.

Therefore, the bisector of angle APQ passes through O.

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Answer:

1.

p=M/V. by rearranging this formula you get

V=M/p

V=560kg/7kg/m³

=80m³ b/c kg canceled kg

2.

p=M/V

=352kg/220m³

=1.6kg/m³

Answer:

all are the properties of square

Step-by-step explanation:

all are correct

Answer:

  1/216

Step-by-step explanation:

The ratio of volumes of similar shapes is the cube of the scale factor. The filled portion of the cone is similar to the entire cone.

If the filled height is 1/6 of the total height, the scale factor for linear dimensions is 1/6.

The scale factor for the volume is the cube of the scale factor for linear dimensions. it is ...

  (1/6)³ = 1/216

The volume of the filled portion of the cup is 1/216 of the volume of the cup.

Based on the type of transaction that Fantastic Catering completed, the types of accounting basis they are in will be:

                                        Cash Basis                               Accrual Basis

May 1                                    (2,700)                                          0

May 5                                    (240)                                            (240)

May 9                                   2,700                                          2,700

May 14                                  (2,400)                                             0

May 23                                     0                                                2,900

May 31                                     0                                                 (1,800)

May 31                                     0                                                 ( 900 )

May 31                                      0                                                ( 730)

The cash basis is used for when cash transactions have happened. There has to be cash changing hands for this to be recorded like the prepaid rent and the payment for kitchen equipment.

The accrual basis is used for all payments and revenue including both cash transactions and those that are recorded on account such as the banquet on May 23 and accrued salaries.

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1. The amount of money in the account after 10 years is 42,317.96 dollars.

2. it will take Pamela and Kevin 7.5 hours to complete the task together

Question(1)

Using compound interest formula,

[tex]A = p(1 + \frac{r}{n} )^{nt}[/tex]

where

Therefore,

p = 30,000

r = 3.5% = 0.035

t = 10

n = 1

Therefore,

[tex]A = 30000(1+\frac{0.035}{1} )^{1X10}[/tex]

A = $42,317.96

Question 2:

Pamela takes 12 hours to complete a task.

Kelvin takes 20 hours to complete same task.

The time it will take both of them can be computed as follows:

using rate principle,

let

x = time it will take both of them to do the work together.

[tex]\frac{1}{x}=\frac{1}{12} + \frac{1}{20}[/tex]

[tex]\frac{1}{x}=\frac{20+12}{240}[/tex]

[tex]\frac{1}{x}=\frac{32}{240}[/tex]

cross multiply

240 = 32x

x = 240 / 32

x = 7.5 hours

Therefore,  it will take Pamela and Kevin 7.5 hours to complete the task together

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Answer: A

Step-by-step explanation:

By the exterior angle theorem,

[tex]x+y=138\\\\\implies y=138-x[/tex]

The value of x will be -7. The expression is solved using the identity.

Exponents can also be written as logarithms. The other number is equal to a logarithm with a number base. It's the exact inverse of the exponent function.

Given expression;

[tex]\rm log_2(\frac{1}{128}) = x[/tex]

The expression is solved using the identity as;

[tex]\rm log_e1 = x\\\ e^x=1[/tex]

Apply the identity;

[tex]\rm log_2(\frac{1}{128}) = x \\\\ 2^x = \frac{1}{128}\\\\ 2^x = \frac{1}{2^7} \\\\ 2^x = 2^{-7} \\\\ x = -7[/tex]

Hence the value of x will bed -7.

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Answer:

55 Wide and 75 Long works.

Step-by-step explanation:

Since the Perimeter of the original is likely 80 + 80 +50 + 50 = 260 since it it a rectangular lot, 55 + 75 + 55 + 75 = 260 as well, meaning no change in perimeter. Now when we look at the area 80 x 50 = 4000, but

55 x 75 = 4125, leading to a larger plot

The graph of the system of inequalities can be seen below.

Here we have the inequalities:

y < -(1/3)*x + 1

y ≤2x-3

To graph the first inequality, we need to graph the line -(1/3)*x + 1 with a dashed line (because the symbol < was used) and shade the region below that line.

For the second inequality we need to graph the line 2x-3 with a solid line this time, and again, shade the region below the line.

The graph of the system is shown in the image below.

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Answer:

15

Step-by-step explanation:

Supplementary angles add to 180 degrees

Let the supplement be x

x+165 = 180

x +165-165= 180-165

x = 15

The supplement is 15

Answer:

Hello! The answer is 15°.

Step-by-step explanation:

Supplementary angles add up to 180°.

To find the measure of each angle, we can now set up an equation because we have the total that supplementary angles add up to:

x + 165 = 180

Now, we can subtract 165 from both sides to get x by itself:

x + 165 = 180

    -165  -165

This leaves us with:

x = 15

Answer:

  tan(α+β) ≈ -5.8688

Step-by-step explanation:

You can use the formula for the tangent of the sum of angles, or you can use a calculator to find the angles. The latter is much simpler.

  tan(α+β) = tan(arccos(0.871) +arccos(0.338))

  tan(α+β) ≈ -5.8688

Note that the two angles total slightly more than 90°, so the tangent of their sum is a large negative number.

The use of trig identities also requires a calculator, and many more steps.

The tangent of the angle can be found from the cosine using ...

  tan(x) = √((1/cos(x))² -1)

  tan(α) = √((1/0.871)² -1) ≈ √(1.1481056² -1) ≈ 0.56404479

  tan(β) = √((1/0.338)² -1) = √(2.9585799² -1) ≈ 2.7844559

And the tangent of the sum of angles is ...

  tan(α +β) = (tan(α) +tan(β))/(1 -tan(α)tan(β))

  tan(α+β) = ((0.56404479 +2.7844559)/(1 -(0.56404479)(2.7844559))

  tan(α+β) = 3.3485007/(1 -1.5705579)

  tan(α+β) ≈ -5.8688

__

Additional comment

The approximate angles are ...

  α ≈ 29.4249°

  β ≈ 70.2448°

Then α+β ≈ 99.6699°