How do you convert between exponential and logarithmic form?

The area is covered with 1.4 gallons of water per square foot, approximately 5388.9 gallons of water were used.

We use the formula for the area of a circle: A = πr².

The radius can be determined by dividing the diameter, which is 70 feet, by 2. Therefore, r = 35 feet.

To find the area of the circle, substitute the value of r into the formula for the area of a circle: A = πr².
A = πr²
A = π(35)²
A = 3.14 × 1225
A = 3842.5 square feet
We know that this area is covered with 1.4 gallons of water per square foot, so we can multiply the area of the circle by 1.4 to get the total gallons of water used:

Total gallons of water used = A * 1.4
1.4 × 3842.5 ⇒ 5,379.5 gallons.

Therefore, the total gallons of water used is 5,379.5 gallons.

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The job will take 5 hours time for a crew of 5 people.

Inverse variation means that as one value increases, the other decreases. In this example, as the number of people on the crew increases, the amount of time it takes to complete the job decreases. To solve this problem, we must first find the rate of change. We can do this by dividing 8 hours (the amount of time it took the crew of 3 people) by 3 people, which gives us a rate of 2.67 hours per person. Then, to find the time for the crew of 5 people, we can multiply the rate of change (2.67 hours per person) by the number of people on the crew (5). This gives us a total of 13.35 hours, which can be rounded to 5 hours time.

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Answer:

x=2

Step-by-step explanation:

Answer:

x=2

Step-by-step explanation:

Answer:

z=1.20

Step-by-step explanation:

Just Took Test

the tax estimated to be collected by the government during the financial year 2020/21 is 666.9 billion rands.

why it is and what is a financial year?

The tax estimated to be collected by the government during the financial year 2020/21 is not explicitly given in the table. However, the total revenue collected by the government during the financial year 2020/21 is given, which is:

666.9 billion rands

Therefore, the tax estimated to be collected by the government during the financial year 2020/21 is 666.9 billion rands.

A financial year (also known as fiscal year) is a period of 12 months that a company or government uses for financial reporting and accounting purposes. It does not necessarily correspond to the calendar year, which is a period of 12 months starting on January 1st and ending on December 31st.

The financial year is important because it helps organizations to keep track of their financial performance over a consistent period of time, which facilitates comparison of financial results from year to year. The financial year is often chosen to align with a company's operational cycle, which may be seasonal or have other considerations that affect the timing of revenues and expenses.

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Yes, the triangles ∆AOR and ∆EOD are similar. By Angle-Angle similarity rule, triangle AOR is similar to triangle EOD.

See the above figure, it consists two triangles say ∆AOR and ∆EOD. Now, we check whether both of triangles are similar or not. Similar triangles are are the triangles that have corresponding sides in ratio to each other and corresponding angles equal to each other. It's time to check the similarity property in ∆AOR and ∆EOD.

In ∆AOR, measure of angle R = 105°

In ∆EOD, measure of angle D = 35°

measure of angle DOE = 40°

Sum of interior angles of triangle = 180°

so, measure of angle E = 180° - 35° - 40°

= 105°

Now, in ∆AOR and ∆EOD,

Measure of angle R = measure of angle E = 105° ( since equal angles)

Measure of angle AOR = measure of angle EOD ( corresponding angles)

Thus, two angles of triangle EOD are congruent or equal to the corresponding angles of another triangle, AOR. So, by Angle-Angle ( AA) congruence rule, ∆AOR is similar to the ∆EOD.

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Complete question:

See the above figure, Are the triangles similar? If yes, write a similarity statement and explain how you know they are similar.

Answer:

28√2 units.

Step-by-step explanation:

Let's denote the length of a side of the square as "s". We know that the diagonal of the square is √2 times the length of a side, so we can write:

√2 s = 14

Solving for "s", we can divide both sides by √2:

s = 14 / √2

To simplify this expression, we can rationalize the denominator by multiplying both the numerator and denominator by √2:

s = (14 / √2) x (√2 / √2) = 14√2 / 2 = 7√2

Now we can find the perimeter of the square by adding up the lengths of all four sides:

Perimeter = 4s = 4(7√2) = 28√2

Therefore, the perimeter of the square is 28√2 units.

The number of ways by using the generating functions and Binomial theorem is

There are various methods to solve the given question. Here's one way to solve it. To distribute 12 identical cookies to 4 distinct children such that all cookies are distributed and each child may receive 0, 1, 2, 3, or 4 cookies, we can use generating functions.

Let's assume that the generating function for the number of ways of distributing the 12 identical cookies to the 4 distinct children is given by:

(1 + x + x₂ + x₃ + x₄)⁴

We need to find the coefficient of x12 in the above equation. Using the Binomial theorem, the above equation can be expanded as:

(1 + x + x₂ + x₃ + x₄)⁴ ⇒ (1 + x + x₂ + x₃ + x₄)(1 + x + x₂  + x₃ + x₄)(1 + x + x₂ + x₃ + x₄)(1 + x + x₂  + x₃ + x₄)

After multiplying the above equation, we need to find the coefficient of x₁₂. The answer to the given question is as follows:

The coefficient of x₁₂ ⇒ 715 ways

Therefore, there are 715 ways to distribute the 12 identical cookies to 4 distinct children such that all cookies are distributed and each child may receive 0, 1, 2, 3, or 4 cookies.

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a. There are 1,000 different possible selections.  b. The probability of winning is 1/1,000, or 0.001.  c. If you win, your net profit is $476.05.  d. The expected value is $0.476.  e. The Pick 4 game is better.

a.  There are 1,000 different possible selections (000 to 999).

b.  The probability of winning is 1/1,000, or 0.001.

c.  If you win, your net profit is $476.05. This can be calculated by,

$477.38 - $1.33 = $476.05

d. The expected value is $0.476. This can be calculated by,

$476.05 * 0.001 = $0.476

e. The Pick 4 game is better.
The expected value of a Pick 3 bet is $0.476, while the expected value of a Pick 4 bet is $0.85. The Pick 4 bet is better because it has a higher expected value. This is because the Pick 4 game has more possible selections, meaning the odds of winning are lower than the Pick 3 game, but the prize is larger. So, the expected value for Pick 4 is larger than Pick 3. The expected value of a bet is the amount of money you can expect to win if you make the same bet over and over again, so a higher expected value means you have a better chance of making a profit in the long run.

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Answer:

x= 100

Step-by-step explanation:

x/5 = 20

multiply both the sides by 5 we get

5× x/5 = 20×5

x = 100

The measure of angle K in the inscribed quadrilateral DUCKDUCKD is equal to the central angle of the circle OOO. This central angle is 360 degrees divided by the number of sides of the quadrilateral, which is 4, so the measure of angle K is 90 degrees.

The measure of angle K in the inscribed quadrilateral DUCKDUCKD is equal to the central angle of the circle OOO. The central angle is the angle formed by two radii inside the circle. When a shape is inscribed in a circle, each of the angles of the shape has the same measure as the central angle of the circle. In this case, the quadrilateral has four sides, so the measure of the central angle is 360 degrees divided by the number of sides of the quadrilateral, which is 4. Therefore, the measure of angle K is 90 degrees. This is true for all inscribed shapes; the measure of each angle is equal to the measure of the central angle of the circle. This is because when a shape is inscribed in a circle, each of its angles touches two radii of the circle. Therefore, the measure of each angle is equal to the measure of the central angle of the circle.

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complete question

Quadrilateral DUCKDUCKD, U, C, K is inscribed in circle OOO. What is the measure of angle K∠Kangle, K? ^circ ∘ degrees

Answer:

We can first write 3 3/4 as an improper fraction:3 3/4 = 15/4Then, using the distributive property, we get:12 • 3 3/4 = 12 • (3 + 3/4) = 12 • 3 + 12 • 3/4 = 36 + 9 = 45Therefore, 12 • 3 3/4 simplifies to 45.

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathtt{12\times 3\dfrac{3}{4}}[/tex]

[tex]\mathtt{= 12 \times \dfrac{3\times4+3}{4}}[/tex]

[tex]\mathtt{= 12\times\dfrac{12 + 3}{4}}[/tex]

[tex]\mathtt{= 12\times\dfrac{15}{4}}[/tex]

[tex]\mathtt{= \dfrac{12}{1}\times\dfrac{15}{4}}[/tex]

[tex]\mathtt{= \dfrac{12\times15}{4\times1}}[/tex]

[tex]\mathtt{= \dfrac{180}{4}\rightarrow 180\div4 \rightarrow \bold{12(3 + \dfrac{3}{4}})\rightarrow 12(3) + 12(\dfrac{3}{4})\rightarrow 36 + 9}[/tex]

[tex]\mathtt{= 45}[/tex]

[tex]\huge\text{Therefore your answer should be:}[/tex]

[tex]\huge\boxed{\mathtt{12(3 + \dfrac{3}{4})\ which\ gives\ you\ \bf 45}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

1 and -1

Step-by-step explanation:

[tex]5 - \sqrt[3]{( {x}^{2} - 9 } = 7[/tex]

[tex] - \sqrt[3]{( {x}^{2} - 9} = 7 - 5[/tex]

[tex]- \sqrt[3]{( {x}^{2} - 9} = 2[/tex]

[tex] \sqrt[3]{( {x}^{2} - 9} = - 2[/tex]

Cube both sides of the equation:

[tex] {x}^{2} - 9 = { - 2}^{3} [/tex]

[tex] {x}^{2} - 9 = - 8[/tex]

[tex] {x}^{2} = - 8 + 9[/tex]

[tex] {x}^{2} = 1[/tex]

[tex] {x}^{2} - 1 = 0[/tex]

[tex](x - 1)(x + 1) = 0[/tex]

[tex]x = 1 \: \: or \: \: x = - 1[/tex]

[tex]5-\sqrt[3]{x^2-9}=7\implies 5=\sqrt[3]{x^2-9}+7\implies -2=\sqrt[3]{x^2-9} \\\\\\ (-2)^3=(\sqrt[3]{x^2-9})^3\implies -8=x^2-9\implies 1=x^2 \\\\\\ \pm\sqrt{1}=x\implies \pm 1 = x[/tex]

The 99% confidence interval for the average length (in inches) of all six-month-old boys is 27.74 in. to 27.98 in. The correct answer is E

This is calculated using the average length (27.6 in.) and standard deviation (0.28 in.) recorded by the pediatrician. To calculate the confidence interval, you need to calculate the margin of error. The margin of error is found using the following formula:

ME = (Critical Value) x (Standard Deviation/√Sample Size)

For a 99% confidence interval, the critical value is 2.58. Therefore, the margin of error for this sample is (2.58) x (0.28/√50) = 0.24 in. This means that the 99% confidence interval for the average length of all six-month-old boys is 27.6 in. ± 0.24 in., or 27.74 in. to 27.98 in. The correct answer is E

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Answer: The diameter of the drawing of the planet= 14 mm

Step-by-step explanation:

Given: In a drawing of the solar system the scale is 1 mm = 500 km

which means [tex]1 \ km=\frac{1}{500}mm[/tex] on the drawing.

The diameter of planet =7000 kilometers.

Then the diameter of the drawing of the planet [tex]=\frac{7000}{500}=14[/tex]

Therefore, the diameter of the drawing of the planet= 14 mm.

Robert is currently 10 years old. Given that five years ago Sharon was twice as old as Robert was then, we can set up the following equation: y + 5 = 2(y)

We are given the information that Sharon is five years older than Robert, and five years ago Sharon was twice as old as Robert was then. This means we can create a system of equations to solve for Robert's age.

Let x = Robert's current age

Let y = Robert's age five years ago

Given that Sharon is five years older than Robert, we can set up the following equation:

x + 5 = Sharon's current age

Given that five years ago Sharon was twice as old as Robert was then, we can set up the following equation:

y + 5 = 2(y)

Solving the first equation for x, we get x = Sharon's current age - 5. Substituting this into the second equation, we get:

y + 5 = 2(Sharon's current age - 5)

Solving this equation for y, we get y = (Sharon's current age - 5)/2.

Since Sharon is five years older than Robert, Sharon's current age is x + 5. Substituting this into our equation for y, we get:

y = (x + 5 - 5)/2

Simplifying this equation, we get y = x/2. This means that Robert's age five years ago was half of his current age.

Since we know that Robert is currently 10 years old, Robert's age five years ago was 5. Therefore, Robert is currently 10 years old.

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Answer:

-27V + 4

Step-by-step explanation:

i think

To estimate the proportion of Hispanic customers in a particular state to within 0.04 accuracy and with 99% confidence, you need a sample size of 397 customers.

To accurately estimate the proportion of Hispanic customers in a particular state to within 0.04 accuracy and with 99% confidence, you will need a sample size of 397 customers. To calculate this, you will need to use the formula:
n = ( 2z × p* × q*) / e2
Where:
- n is the sample size
- z is the Z-score associated with the confidence level (in this case, it is 2.58 for 99%)
- p* is the planning value for the population proportion (in this case, it is not known, so it should be set to 0.5)
- q* is the compliment of p* (in this case, q* = 1 - 0.5 = 0.5)
- e is the desired accuracy (in this case, e = 0.04).
Substituting the values into the formula:
n = (2.582 × 0.5 × 0.5) / 0.042 = 397.

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We have ,

Cost of jacket , (F) = $48.10 

Saving per day, (A)  = $1.85 

We have to find the no. of days(n) of saving to have the sufficient amount for jacket. 
We know , 

A × n = F 

=> n = F/A 

=> n = $48.10/$1.85 

=> n = 26  

It will take 26 days for Caden to have enough money for the jacket. 

The answer of the given question based on the following equations are  the order of the variables from least to greatest is c, a, b, since c = 18 is the smallest, followed by a = 36, and b = 72 is the largest.

A variable is  symbol or letter used to represent  value that can change or vary. Variables are commonly used in the algebra and other branches of mathematics to represent the unknown quantities, as well as in a scientific and engineering applications to represent the physical parameters and measurements.

In algebra, variables are typically represented by the letters such as x, y, z, a, b, c, etc.

To solve this problem, we first need to solve each equation for its respective variable, a, b, and c.

a - 5 = 31

Adding 5 to both sides, we get:

a = 36

1/2b - 5 = 31

Adding 5 to both sides and multiplying by 2, we get:

b = 2(31 + 5) = 72

2c - 5 = 31

Adding 5 to both sides and dividing by 2, we get:

c = (31 + 5)/2 = 18

Therefore, the order of the variables from least to greatest is c, a, b, since c = 18 is the smallest, followed by a = 36, and b = 72 is the largest.

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Answer: $100,000

Step-by-step explanation:

$100,000. This is because the balance in the account varies jointly with principal, the annual interest rate, and time measured in years with a constant of proportionality of 1. Therefore, the balance in the account at the end of 50 years is 10,000 × 1 × (1 + 0.05)50, which is equal to $100,000.

Answer:

$35000

Step-by-step explanation:

account worth = deposit + simple interest

/ 100

 intrest = deposit x year x simple interest

10000×50×5/100=25000

account worth = deposit + simple interest

 = 10000 + 25000

 = $ 35000

The area of the parallelogram will equal to Area of the rectangle

The area of a parallelogram is given by the formula:

Where A is the area of the parallelogram,

b is the length of the base of the parallelogram,

h is the height of the parallelogram.

The area of a rectangle is given by the formula:

Where A is the area of the rectangle  

l is the length of the rectangle  

w is the width of the rectangle.

Here we have a Parallelogram    

Where the height of the parallelogram is 4.5 cm and the length is 7 cm  

Using the formula,

Area of parallelogram = 4.5 cm × 7 cm = 31.5 cm²

From the data,

The length of a rectangle is 7 cm and width is 4.5 cm

Using the formula,

Area of the rectangle = 7 cm × 4.5 cm = 31.5 cm²  

Therefore,

The area of the parallelogram will equal to Area of the rectangle

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The complete question is given in the picture

False. A data set of the heights of 12-year-old boys would not necessarily follow a normal distribution pattern as it may be skewed or not evenly distributed around the mean.

False. A normal distribution is a type of probability distribution that takes the shape of a bell curve. It is characterized by having an equal number of values on either side of the mean, with the values in the middle being more numerous than those on the outside. A data set of the heights of all 12-year-old boys who live on a given street in the city of Grand Rapids would not necessarily fit this pattern. It is possible that the data set may be skewed in one direction or the other, depending on the height of the tallest and shortest boys in the group. It is also likely that the data will not be evenly distributed around the mean, as some boys may be taller or shorter than others.

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The size of angle x is equal to 100°.

Based on the identical isosceles triangles ΔABD and ΔACD, we can logically deduce the following:

m∠DAB = 25°

AD = BD = CD

In triangle ΔABD, we have:

AD = BD (Given)

m∠DBA = ∠DAB (Angle opposite to equal sides are congruent)

m∠DBA = 25°.

Next, we would determine the measure of m∠ADB;

m∠DBA + m∠DAB + m∠ADB = 180° (Sum of angle in a triangle)

25° + 25° + m∠ADB = 180°

m∠ADB = 180° - 50°

m∠ADB = 130°.

Since ΔABD and ΔACD are two identical isosceles triangles, we have:

m∠DCA = m∠DBA

m∠DCA = 25°

Similarly, we have:

m∠DAC = m∠DAB = 25°

m∠ADC = m∠ADB = 130°

Generally speaking, we know that a complete revolution (circle) is equal to 360°:

m∠ADC + m∠ADB + m∠CDB = 360°

130° + 130° + x = 360°

x = 360° - 260°

x = 100°.

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The equation of the line that is perpendicular to line m and passes through the point (3, 2) is y = (2/5)x + 4/5.

To find the equation of a line that is perpendicular to line m, we need to know the slope of line m.

The slope of line m can be found using the two given points on the line, (0, -3) and (-2, 2):

slope of line m = (change in y) / (change in x) = (2 - (-3)) / (-2 - 0) = 5 / (-2) = -5/2

A line perpendicular to m will have a slope that is the negative reciprocal of -5/2. The negative reciprocal is obtained by flipping the fraction and changing its sign.

slope of line perpendicular to m = -1 / (-5/2) = 2/5

Now we have the slope of the line perpendicular to m and a point that it passes through, (3, 2). We can use the point-slope form of the equation of a line to find its equation:

y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.

Substituting in the values we have:

y - 2 = (2/5)(x - 3)

Simplifying:

y - 2 = (2/5)x - (6/5)

y = (2/5)x - (6/5) + 2

y = (2/5)x + 4/5

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Devon's height when he was in second grade was 312 feet 3 and 1 half feet.

The proper explanation of this answer is given below. Devon's height .

To arrive at this answer, we must subtract 116 feet from 423 feet, which is the height that Devon is currently measuring as a fifth grader. 423 feet - 116 feet = 307 feet. However, we know that his height was 312 feet 3 and 1 half feet, which is 5 feet more than 307 feet. Therefore, we can add 5 feet to 307 feet to get the answer, 312 feet 3 and 1 half feet.

The height that Devon is now measuring as a fifth grader is 423 feet, so we must subtract 116 feet from that measurement to get this answer. 307 feet Equals 423 feet minus 116 feet. Yet, we are aware of his height, which was 312 feet 3 and a half feet, or 5 feet taller than 307 feet. In order to obtain the solution, 312 feet 3 and a half feet, we can add 5 feet to 307 feet.

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1. An equation for Lin is y = 1/3x + 8.

2. An equation for Diego is y = 2/3x + 6.

3. The intersection point of the solution is (6, 10).

Let there have total number of balloons are y.

Lin fills her balloons at a rate of 1/3 ounce per second.

So she filled 1/3 x balloons.

She has already filled balloons with 8 ounces of water.

So the required equation is;

y = 1/3x + 8.................(1)

Diego fills her balloons at a rate of 2/3 ounce per second.

So he filled 2/3 x balloons.

He has already filled balloons with 6 ounces of water.

So the required equation is;

y = 2/3x + 6.................(2)

To determine the intersecting point we solve the both equation.

Subtract equation 1 and 2, we get

1/3x + 8 - 2/3x - 6 = 0

-1/3x + 2 = 0

Subtract 2 on both side, we get

-1/3x = -2

Multiply by -3 on both side, we get

x = 6

Now put the value of x in equation 1

y = 1/3 × 6 + 8

y = 10

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The store will make a net profit of $1,111.25 from selling the plants.

The first step is to calculate the total revenue from selling the plants:

Next, we need to calculate the cost of buying the plants from the wholesaler:

Cost of plants = 500 x $2.49

Cost of plants = $1,245.00

The net profit is then the difference between the total revenue and the cost of buying the plants:

Net profit = Total revenue - Cost of plants

Net profit = $2,356.25 - $1,245.00

Net profit = $1,111.25

Therefore, the store will make a net profit of $1,111.25 from selling the plants.

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