Subtract the sum of -4/7 and -5/7 from the sum of 1/2 and -21/22

The equation log(8x+2) = 3 can be rewritten in exponential form as 10^3 = 8x+2. Simplifying, we get:

1000 = 8x + 2

998 = 8x

x = 124.75

Therefore, the solution to the equation is x = 124.75, which is an approximation to 3-decimal places.

To verify the solution, we can substitute x = 124.75 back into the original equation and check if both sides are equal:

log(8(124.75) + 2) = log(1000)

log(1000) = 3

Since both sides are equal, we can conclude that x = 124.75 is indeed the solution to the equation.

Note that it is important to check the solution obtained from solving the equation as sometimes the solution may not be valid due to the domain of the function involved in the equation.

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To define a method computeval() that takes one integer parameter and returns the parameter plus 7, you can use the following code:

For example, if the input is 3, the output is 10:

Answer:

see below

Step-by-step explanation:

Answer:

5%

Step-by-step explanation:

Solving our equation

r = 4537.5 / ( 9075 × 10 ) = 0.05

r = 0.05

converting r decimal to a percentage

R = 0.05 * 100 = 5%/year

The interest rate required to

accumulate simple interest of $ 4,537.50

from a principal of $ 9,075.00

over 10 years is 5% per year.

Answer:

C.15.5r

Step-by-step explanation:

Answer:

13.5r

Step-by-step explanation:

Just took it

The absolute value of the expression is given by:

\(\[\left| \frac{2z_1 7z_2}{2z_1 - 7z_2} \right| = \frac{|k|\cdot |14i - 49k|\cdot |z_1^3|}{|z_1|\cdot |4 - 28ki + 49k^2|}.\]\)

Let's start by simplifying the expression inside the absolute value:

\(\[\frac{2z_1 \cdot 7z_2}{2z_1 - 7z_2}.\]\)

To make progress, we'll multiply both the numerator and denominator by the conjugate of the denominator:

\(\[\frac{2z_1 \cdot 7z_2}{2z_1 - 7z_2} \cdot \frac{2z_1 + 7z_2}{2z_1 + 7z_2}.\]\)

Expanding the numerator, we have:

\(\[2z_1 \cdot 7z_2 \cdot (2z_1 + 7z_2) = 14z_1^2z_2 + 49z_1z_2^2.\]\)

Expanding the denominator, we have:

\([(2z_1)(2z_1) + (2z_1)(7z_2)] + [(7z_2)(2z_1) + (7z_2)(7z_2)] = 4z_1^2 + 14z_1z_2 + 14z_1z_2 + 49z_2^2 = 4z_1^2 + 28z_1z_2 + 49z_2^2.\)

Putting it all together, the expression becomes:

\(\[\frac{14z_1^2z_2 + 49z_1z_2^2}{4z_1^2 + 28z_1z_2 + 49z_2^2}.\]\)

Now, we can take the absolute value:

\(\[\left| \frac{14z_1^2z_2 + 49z_1z_2^2}{4z_1^2 + 28z_1z_2 + 49z_2^2} \right| = \frac{|14z_1^2z_2 + 49z_1z_2^2|}{|4z_1^2 + 28z_1z_2 + 49z_2^2|}.\]\)

Since\($\frac{z_2}{z_1}$\) is pure imaginary, we have \($z_2 = ki z_1$\) for some real number \($k.$\) Substituting this into the expression, we get:

\(\[\frac{|14z_1^2(ki z_1) + 49z_1(ki z_1)^2|}{|4z_1^2 + 28z_1(ki z_1) + 49(ki z_1)^2|}.\]\)

Simplifying, we have:

\(\[\frac{|14kz_1^3i + 49k^2z_1^3i^2|}{|4z_1^2 + 28kz_1^2i - 49k^2z_1^2|} = \frac{|14kz_1^3i - 49k^2z_1^3|}{|z_1^2(4 - 28ki + 49k^2)|}.\]\)

Since\($2z_1 \neq 7z_2,$\) we have \($2 \neq 7ki,$\) which implies \($k \neq \frac{2}{7i}.$\)Therefore, \($4 - 28ki + 49k^2 \neq 0,$ so $z_1^2(4 - 28ki +49k^2) \neq 0,$\) which means we can cancel it from the expression:

\(\[\frac{|14kz_1^3i - 49k^2z_1^3|}{|z_1^2(4 - 28ki + 49k^2)|} = \frac{|14kz_1^3i - 49k^2z_1^3|}{|z_1^2|\cdot |4 - 28ki + 49k^2|}.\]\)

Since \($|ab| = |a|\cdot |b|,$\) we have:

\(\[\frac{|14kz_1^3i - 49k^2z_1^3|}{|z_1^2|\cdot |4 - 28ki + 49k^2|} = \frac{|14ki - 49k^2|\cdot |z_1^3|}{|z_1^2|\cdot |4 - 28ki + 49k^2|}.\]\)

Finally, we can simplify the expression further:

\(\[\frac{|14ki - 49k^2|\cdot |z_1^3|}{|z_1^2|\cdot |4 - 28ki + 49k^2|} = \frac{|k|\cdot |14i - 49k|\cdot |z_1^3|}{|z_1|\cdot |4 - 28ki + 49k^2|}.\]\)

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As a result, we have demonstrated: 1 / (cos(x) - cot(x)) = cos (x) + cot(x) as the right side of the equation .

Trig ratios are ratios between the sides and angles of a right triangle. The sine, cosine, and tangent are the three main trigonometric ratios (tan). These are their definitions: The ratio of a right triangle's hypotenuse's length to the height of the opposite end is known as the sine (sin) of an angle. The ratio of a right triangle's neighbouring side to hypotenuse length is known as the cosine (cos) of an angle. The ratio of a right triangle's adjacent side's length to its opposite side's length is the angle's tangent (tan).

given

cot + csc(x) (x)

= cos(x)/sin(x) 1/sin(x) (x) [using the csc(x) and cot(x) definitions]

= (cos(x) + 1) / sin (x) [combining the phrases by reducing them to a single value]

The right side of the equation will then be made simpler:

(csc(x) - cot(x)) = 1

= 1 / (1/cos(x)/sin(x) - sin(x)) [using the csc(x) and cot(x) definitions]

= Sin(x) / Cos(x) [using the reciprocal and a denominator that is simpler]

We shall now demonstrate that the left and right sides are equal:

Sine (1 + cos(x)) (x)

= [(1 + cos(x))] / [(1 + sin(x)] *[1 - cos(x)] / (1 - cos(x)] [by adding 1 - cos(x) to the numerator and denominator]

= sin(x) * (1 - cos(x) / (1 - cos2(x)) [reduce the numerator]

= sin2(x)/sin(x)*(1 - cos(x)) [by applying the formula sin2(x) = 1 - cos2(x)]

= Sin(x) / Cos(x) [removing the common sin(x) factor]

As a result, we have demonstrated: 1 / (csc(x) - cot(x)) = csc(x) + cot(x) as the right side of the equation .

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Answer:

4 class sessions

Step-by-step explanation:

Let x represent the number of the class session. We have the equation

15x + 65 = 125

15x = 60

x = 4 class sessions

So, there were 4 class sessions in the course.

Answer:

multiply

Step-by-step explanation:

2345567 in the subtract 578431111

Answer:

n = 8

Step-by-step explanation:

(n/2) - 10 = -6

       + 10   +10

\(\frac{n}{2}\) = 4

\(2*\frac{n}{2} = 4*2\)

n = 8

Answer:

x + 2

--------

49

Step-by-step explanation:

that's the answer

Answer:

In this particular case, Circle M has circumference 11π, or approximately 34.6 units.

Step-by-step explanation:

The circumference of a circle of diameter d is C = πd.

In this particular case, Circle M has circumference 11π, or approximately 34.6 units.

Answer:

\(13- 0.75 * (12) + 8 * (\frac{1}{2} ) = 13-9+4\\\\13-5=8\)

Step-by-step explanation:

Evaluate 13-0.75w+8x13−0.75w+8x13, minus, 0, point, 75, w, plus, 8, x when w=12w=12w, equals, 12 and x=\dfrac12x= 2 1 ​ x, equals, start fraction, 1, divided by, 2, end fraction.

For this case we have the following expression:

 \(13-0.75w + 8x\)

Evaluate for the following values:

 w = 12

 x = 1/2

 We Substituting the values we have:

\(13- 0.75 * (12) + 8 * (\frac{1}{2} ) = 13-9+4\\\\13-5=8\)

Answer:

63%

Step-by-step explanation:

First you want to take 3.50-2.87

Then you get .63

Then you are going to want to convert that to a percentage which is 63%

（This should be right but if its not please let me know）

Answer:

Step-by-step explanation

Step #1

3.50-2.87  will equal 0.63

Step #2

put 0.63 over 3.50 times that by 100 and you 63 and 350 so you divide that and get 0.18 which equals 18% your welcome loves

Answer:

Step-by-step explanation:

(a) To find the probability that it is raining when you arrive in Oneirabad on a random day, we need to use the law of total probability.

Let A be the event that it is raining, and B be the event that it is the Wet season.

P(A) = P(A|B)P(B) + P(A|B')P(B')

Given that the Wet season lasts for 1/3 of the year, we have P(B) = 1/3. The probability that it is raining during the Wet season is 3/4, so P(A|B) = 3/4.

The Dry season lasts for 2/3 of the year, so P(B') = 2/3. The probability that it is raining during the Dry season is 1/6, so P(A|B') = 1/6.

Now we can calculate the probability that it is raining when you arrive:

P(A) = (3/4)(1/3) + (1/6)(2/3)

= 1/4 + 1/9

= 9/36 + 4/36

= 13/36

Therefore, the probability that it is raining when you arrive in Oneirabad on a random day is 13/36.

(b) Given that it is raining when you arrive, we can use Bayes' theorem to calculate the probability that your visit is during the Wet season.

Let C be the event that your visit is during the Wet season.

P(C|A) = (P(A|C)P(C)) / P(A)

We already know that P(A) = 13/36. The probability that it is raining during the Wet season is 3/4, so P(A|C) = 3/4. The Wet season lasts for 1/3 of the year, so P(C) = 1/3.

Now we can calculate the probability that your visit is during the Wet season:

P(C|A) = (3/4)(1/3) / (13/36)

= 1/4 / (13/36)

= 9/52

Therefore, given that it is raining when you arrive, the probability that your visit is during the Wet season is 9/52.

(c) Given that it is raining when you arrive, the probability that it will be raining when you return to Oneirabad in a year's time depends on the season. If you arrived during the Wet season, the probability of rain will be different from if you arrived during the Dry season.

Let D be the event that it is raining when you return.

If you arrived during the Wet season, the probability of rain when you return is the same as the probability of rain during the Wet season, which is 3/4.

If you arrived during the Dry season, the probability of rain when you return is the same as the probability of rain during the Dry season, which is 1/6.

Since the season you arrived in is independent of the weather when you return, we need to consider the probabilities based on the season you arrived.

Let C' be the event that your visit is during the Dry season.

P(D) = P(D|C)P(C) + P(D|C')P(C')

Since P(C) = 1/3 and P(C') = 2/3, we can calculate:

P(D) = (3/4)(1/3) + (1/6)(2/3)

= 1/4 + 1/9

= 9/36 + 4/36

= 13/36

Therefore, the probability that it will be raining when you return to Oneirabad in a year's time, given that it is raining when you arrive, is 13/36.

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The volume of the smaller container is 22 cubic inches, which corresponds to option A, 11 in³, when rounded to the nearest whole number.

The volume of a cylinder is given by the formula V = πr^2h, where r is the radius of the base and h is the height.

If the smaller container is similar in shape to the original cylinder with a scale factor of 1/2, then its height and radius must be half of that of the original cylinder.

Let's denote the height and radius of the original cylinder as h1 and r1 respectively, and the height and radius of the smaller container as h2 and r2 respectively. Then we have:

h2 = (1/2)h1

r2 = (1/2)r1

We also know that the volume of the original cylinder is 88 cubic inches, so we can write:

V1 = πr1^2h1 = 88

Substituting the expressions for h2 and r2 in terms of h1 and r1 into the formula for the volume of the smaller container, we get:

V2 = πr2^2h2 = π[(1/2)r1]^2[(1/2)h1] = (1/4)πr1^2h1

Since the original cylinder has a volume of 88 cubic inches, we can substitute this value for V1 to get:

88 = πr1^2h1

Solving this equation for h1, we get:

h1 = 88/(πr1^2)

Substituting this expression for h1 into the formula for V2, we get:

V2 = (1/4)πr1^2(88/(πr1^2)) = 22

Therefore, the volume of the smaller container is 22 cubic inches, which corresponds to option A, 11 in³, when rounded to the nearest whole number.

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If we convert every rational number into on from i.e. decimal we can write the order from greatest to least which is 3/4 > 5/7 > 0.70> 68%.

The format of rational numbers is p/q, where p and q can both be integers and q must be greater than zero. Therefore, natural numbers, whole numbers, integers, fractions of integers, and decimals are all examples of rational numbers (terminating decimals and recurring decimals).

From the word "ratio," the word "rational" was derived. Rational numbers are thus closely related to the idea of fractions, which stand for ratios. In other words, a number is a rational number if it can be expressed as a fraction in which both the numerator and the denominator are integers.

Convert into decimal

0.70 = 0.7

3/4 = 0.75

68% = 0.68

5/7 = 0.71

0.75 >  0.71>  0.7> 0.68

3/4 > 5/7 > 0.70> 68%

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Based on the given information, the z-score for the actor is denoted as z, and the z-score for the actress is denoted as 2.

To compare the relative B of the ages, we need the z-scores for both the actor and the actress, which are obtained by subtracting the population mean from their respective ages and dividing by the population standard deviation. The z-score indicates the number of standard deviations a particular value is away from the mean. The higher the absolute value of the z-score, the more extreme the value is compared to the population.

Without the specific values of z and 2, it is not possible to determine which individual has the more extreme age when winning the award.

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Answer:

Step-by-step explanation:

The volume formula can be used to find the height and width of a box with volume 4368 in³ and height 1 in greater than width.

The volume formula is ...

  V = LWH

Substituting given information, using w for the width, we have ...

  4368 = (24)(w)(w+1)

We want to find the value of w.

  182 = w² +w . . . . . . . . divide by 24

  182.25 = w² +w +0.25 = (w +0.5)² . . . . . . add 0.25 to complete the square

  13.5 = w +0.5 . . . . . . . . take the positive square root

  w = 13 . . . . . . . . . . . . subtract 0.5

  h = w+1 = 14

The height of the box is 14 inches; the width is 13 inches.

__

Additional comment

By "completing the square", we can arrive at the exact dimensions of the box, as we did above. Note that we only added 0.25 to the equation to do this.

For numbers close together, the geometric mean (root of their product) is about the same as the arithmetic mean (half the sum):

  \(\sqrt{w(w+1)}\approx\dfrac{w+(w+1)}{2}=w+\dfrac{1}{2}\\\\w\approx\sqrt{182}-\dfrac{1}{2}\approx12.99\)

Using this approximation to arrive at the conclusion w=13 saves the steps of figuring the value necessary to complete the square, then adding that before taking the root.

When you divide or multiply by a negative number, you must change the direction of the inequality sign. This is because of this rule of inequalities: As you can see, x is originally less than y. But, when it’s multiplied by a negative number, x becomes greater than y. That’s because smaller negative numbers are closer to 0, making them worth more.

Answer:

m = 0

Step-by-step explanation:

The answer is 0, I used the slope formula to figure this out...May I have brainliest? Thanksss!

Answer:

III

Step-by-step explanation:

Number 3 did. The contains the (-1,1) and (5,-2)

Answer:

lll

Step-by-step explanation:

its the number 3 so A

Answer:

four nine dollar books

Step-by-step explanation:

36 divivded by 9

Answer: The value of x is 29°,  the measure of angle 1 is 123°, and the measure of angle 2 is 57°.

Step-by-step explanation:

A linear pair is the same as a straight line meaning that the sum of the two angles has to equal 180 degrees.

In this case, add both angles and set them to equal to 180 in order to solve for x.

(4x + 7) + (2x-1) = 180   Combine like terms on the left side.

(4x + 2x) + ( 7 - 1) = 180

   6x + 6 = 180   Now subtract 6 from both sides

         -6      -6

    6x = 174    Divide both sides by 6

x = 29  

Since x is  29  degrees we will input it into the expression for the angles and solve for the real value.

m ∠1 = 4(29) + 7

m ∠1  = 116 + 7

m ∠1   = 123  

If the measure of angle 1 is 123 degrees then you can subtract that from  180 to find the measure of angle two or you can use the expression.

m ∠2 = 2(29) -1

m ∠2 = 58 - 1

m ∠2  = 57  

Answer:

so devaki is 6 years old and her father would be 30 years old  

Step-by-step explanation:

The net income for Griffin's Goat Farm, Inc., was \(\$184,340\).

The operating cash flow (OCF) for Kerber's Tennis Shop, we can use the following formula:

\(OCF = EBIT + Depreciation - Taxes + \triangle Working Capital\)

where EBIT is earnings before interest and taxes.

Calculate EBIT by subtracting interest expense from operating income:

EBIT = Operating Income - Interest Expense

We do not have the information for operating income, but we can use the fact that interest expense was. \(\$165,000\) to calculate EBIT.

EBIT = Interest Expense / (1 - Tax Rate)

= \(\$165,000 / (1 - 0)\)

= \(\$165,000\)

Calculate the change in working capital (Δ Working Capital). We are told that the company reduced its net working capital investment by \(\$69,000\), which means that working capital increased by  \(\$69,000\).

Therefore:

\(\triangle Working Capital = \$69,000\)

Now, we can calculate OCF:

OCF = EBIT + Depreciation - Taxes + Δ Working Capital

=\(\$165,000 + 0 - 0 +\ $69,000\)

=\(\$234,000\)

Therefore, the firm’s 2018 operating cash flow (OCF) was \(\$234,000\) .

To calculate the net income for Griffin's Goat Farm, we can use the following formula:

Net Income = EBIT - Interest Expense - Taxes

where EBIT is earnings before interest and taxes. We can calculate EBIT as:

EBIT = Sales - Costs - Depreciation

= \(\$686,000 - \$332,000 - \$65,000\)

=\(\$289,000\)

Next, we need to calculate taxes. We are given a tax rate of 24%, so:

Taxes = Tax Rate x (EBIT - Depreciation)

= \(0.24 \times (\$289,000 - \$65,000)= \$56,160\)

Now, we can calculate net income:

Net Income = EBIT - Interest Expense - Taxes

= \(\$289,000 - \$48,500 - \$56,160= \$184,340\)

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Answer:

59

Step-by-step explanation:

The diagonals of an isosceles trapezoid are equal.

MO and NP are diagonals.  Therefore MO = NP

12y - 37 = 5y + 19

7y = 56

y = 8

MO = 12(8) - 37 = 96 - 37 = 59

NP = 5(8) + 19 = 40 + 19 = 59

7 units are the measurement of the segment NP.

In Mathematics, a polygon can be defined as a two-dimensional geometric figure that consists of straight line segments and a finite number of sides. Additionally, some examples of a polygon include the following:

• Triangle

• Quadrilateral

• Pentagon

• Hexagon

• Heptagon

• Octagon

• Nonagon

Generally speaking, the measure of the angle at the center of a regular polygon is equal to 360 degrees. Therefore, the smallest angle of rotation that maps (carries) a regular polygon onto itself can be calculated by using this formula:

α = 360/n

Since MNOP is an isosceles trapezoid, the non-parallel sides MN and OP have the same length. Therefore, we can set up an equation using the given lengths of the sides:

MP = NO

Substituting the given expressions for these lengths, we get:

16x - 13 = 9x + 8 + 5y + 19

Simplifying and rearranging terms, we get:

7x - 5y = 36 ........(1)

Similarly, we can set up another equation using the given lengths of the diagonals MO and PN:

MO + PN = MP + NO

Substituting the given expressions for these lengths, we get:

12y - 37 + 5y + 19 = 16x - 13 + 9x + 8

Simplifying and rearranging terms, we get:

17y - 16x = 42 ........(2)

Now, we have two equations (1) and (2) with two variables (x and y). Solving this system of equations, we get:

x = 7, y = 9

Substituting these values back into the given expressions for PN and NO, we get:

PN = 5y + 19 = 5(9) + 19 = 64

NO = 9x + 8 = 9(7) + 8 = 71

Therefore, the measure of segment NP is:

NP = NO - PN = 71 - 64 = 7

So, the measure of segment NP is 7 units.

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The probability that Bob hits his first home run before his 25th plate appearance of the season is 0.3511, which is approximately 35.11%.

The probability that Bob hits his first home run before his 25th plate appearance of the season, denoted as P, can be expressed mathematically as:

P = 1 - P(X ≥ 25)

where P(X ≥ 25) is the probability that Bob hits his first home run on or after his 25th plate appearance.

Given that  

\(\[ P(X \geq 25) = \left(1 - p\right)^{25-1} \]\)

, where p = 1/18.38 = 0.0544, we can substitute the values:

\(\[ P = 1 - \left(1 - 0.0544\right)^{25-1} \]\)

Simplifying further:

P = 1 - 0.6489

Hence, the mathematical expression for the probability that Bob hits his first home run before his 25th plate appearance is:

P = 0.3511

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The probability that Bob hits his first home run before his 25th plate appearance of the season is \(1 - (1 - (1/18.38))^{24}\).

To find the probability that Bob hits his first home run before his 25th plate appearance of the season, we can use the concept of geometric probability. Geometric probability is used to calculate the probability of a specific event occurring within a sequence of independent trials.

In this case, Bob hitting a home run is the event we are interested in, and each plate appearance represents an independent trial. We are given that Bob hits a home run once every 18.38 plate appearances.
To calculate the probability, we need to find the complement of the event (the probability of not hitting a home run in the first 24 plate appearances) and subtract it from 1.
The probability of not hitting a home run in one plate appearance is 1 minus the probability of hitting a home run, which is 1 - (1/18.38).
To find the probability of not hitting a home run in the first 24 plate appearances, we raise this probability to the power of 24, since each plate appearance is an independent trial.
So, the probability of not hitting a home run in the first 24 plate appearances is ( \(1 - (1 - (1/18.38))^{24}\).
To find the probability of hitting the first home run before the 25th plate appearance, we subtract the probability of not hitting a home run in the first 24 plate appearances from 1.

Calculating this probability, we find that Bob has approximately a 49.2% chance of hitting his first home run before his 25th plate appearance of the season.

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To identify the surface with the given vector equation, we need to examine the coefficients of the variables in each component of the equation. In this case, we have:

r(u,v) = (u+v)i + (3-v)j + (1+4u+5v)k

This represents a vector-valued function in three-dimensional space. To see what surface it describes, we can look at the coefficients of u, v, and constants in the equation.

The coefficient of u is 4 in the k-component, so the surface will have a slope in the u-direction. The coefficient of v is 5 in the k-component, so the surface will also have a slope in the v-direction. The constant term is 1 in the k-component, so the surface will be offset by 1 unit in the positive k-direction.

Based on this information, we can conclude that the surface described by the given vector equation is a plane with a slope in the u and v directions, and is offset from the origin by 1 unit in the positive k-direction.

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