Find the exact value of the logarithmic expression without a calculator. Show all work
log3 4√27

We have 72-tenths left.

Any number of equal parts is represented by a fraction, which also represents a portion of a whole. When used in conversational English, a fraction indicates the number of components of a particular size, as in one-half, eight-fifths, and three-quarters.

To divide 80 tenths by 9 ones, we first convert the 9 ones to tenths. 9 ones is equivalent to 90 tenths.

Next, we divide 80 by 90:

80 / 90 = 0.8888... (rounded to four decimal places)

To multiply, we multiply 0.8888... by 9:

0.8888... * 9 = 8

Finally, to subtract, we subtract 8 from 80:

80 - 8 = 72

So, we have 72-tenths left.

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Answer:

Step-by-step explanation:

Sandra, Deacon, and Breanna read a total of 5 + 6 + 7 = 18 books. Since one book was read by all three children, we need to subtract it once from the total. Therefore, they read 18 - 1 = 17 different books.

Sara needed 8 test tubes for 3 different experiments. The first experiment required 2 test tubes, leaving 8 - 2 = 6 test tubes for the other two experiments. Since the two experiments required the same number of test tubes, each one required 6/2 = 3 test tubes.

It is unclear what the question is asking. Please provide more information or a specific question.

Branson and his sister Beatrice combined their allowance of $7 each to buy a movie for $12. They spent a total of 7 x 2 = $14 on the movie. Therefore, they had 14 - 12 = $2 left to buy fruit salad. They bought 2 containers of fruit salad for $1 each, leaving them with $0. They split the containers evenly between them, so each of them got 2/2 = 1 container of fruit salad.

Before Cam broke his right arm, he could type 9 words per minute on his phone. After he broke his arm, he could only type 6 words per minute. The difference between the number of words he could type in 5 minutes before and after he broke his arm is 5 x (9 - 6) = 5 x 3 = 15 words.

Gisselle saved $6 every week for 8 weeks, so she saved a total of 6 x 8 = $48. She found a used bicycle for $50, so she did not have exactly enough for the bicycle. She was $50 - $48 = $2 short.

a. Each marble has a volume of 0.013 liters.

b. 23.4 liters of water would be necessary if William uses 200 marbles.

a. To determine the volume of each marble, we can use the information that 85 marbles fill a tank with a volume of 20.9 liters of water:

Volume of each marble = (26 liters - 20.9 liters) / 85 marbles = 0.26 liters - 0.247 liters/marble = 0.013 liters/marble

So, each marble has a volume of 0.013 liters.

b. To determine the amount of water necessary if William uses 200 marbles, we can use the formula:

Volume of water = Total volume of tank - Volume of marbles

Volume of water = 26 liters - (200 marbles * 0.013 liters/marble) = 26 liters - 2.6 liters = 23.4 liters

So, 23.4 liters of water would be necessary if William uses 200 marbles.

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Complete question:

William has a 26-liter glass tank. First, he wants to put some marbles in it, all of the same volume. Then, he wants to fill the tank with water until it is completely full. If he uses 85 marbles, he will have to add 20.9 liters of water.

a. What is the volume of each marble?

b. How much water is necessary if William uses 200 marbles?

The probability that the student is female and studying abroad is equal to 0.057. It means 5.7% of student is female studying abroad.

Given,

Undergraduate students who study abroad = 9.5% = 0.095 undergraduate

female students who travel for study. = 0.60

male undergraduates who travel for study. = 0.40

undergraduate female students who do not study abroad. = 0.49

Those male undergraduates who do not study abroad. = 0.51

Probability refers to potential. It is a field of mathematics that generally examines how the random events happen. The value is expressed as a number between 0 and 1. To determine how likely an event is to occur, probability has been introduced in mathematics.

We know that ,

the probability that the student is female and studying abroad =

0.60 * 0.095 = 0.057

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The required 2 properties to describe the relationship between DE and AC are  1. DE || AC and 2. DC = AC / 2.

Similar triangles are those triangles that have similar properties,i.e. angles and proportionality of sides.

Here,
From the figure,
AD = BD and BE = EC

It implies that D and E are the midpoints of the side AB and BC,
So, 1. for the given triangle line joining the midpoints of the triangle always parallel to the third side of the triangle.
DE || AC

And when DE || AC then the measure of DE is equal to half of the measure of AC.
DC = AC / 2

Thus, the required 2 properties are 1. DE || AC and 2. DC = AC / 2.

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a) The mode of the list is 7

b) The median of the list is 7.

c) The mean is 5.4

d) The range is 7

What is the Mean, Mode and Median?

Mean: The mean is the average of a set of numbers, calculated by adding up all the numbers and dividing by the total number of numbers in the set.

Mode: The mode is the most frequently occurring number in a set of numbers.

Median: The median is the middle value in a set of numbers when the set is sorted in ascending or descending order.

a) Mode: The mode of the list is 7, as it is the number that occurs most frequently (3 times).

b) Median: To find the median, the list must first be sorted in ascending order:

1, 2, 3, 4, 5, 7, 7, 7, 8, 8

The median of the list is 7.

c) Mean: The mean is found by adding up all the numbers in the list and dividing by the total number of items:

(3 + 7 + 2 + 4 + 7 + 5 + 7 + 1 + 8 + 8)/10 = 54/10 = 5.4

d) Range: The range is the difference between the largest and smallest numbers in the list:

8 - 1 = 7

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Expanding the expression a(b + c) = ab + ac, the value of ac is positive if both a and c are positive or if both a and c are negative.

By Multiplying the term outside the brackets by each term inside the brackets

Using this method you can distribute the outer terms into the inner terms. You can multiply the term outside the brackets by the first term inside the brackets. Then multiply the outside term by the second term. If there are more than two tribes, then continue to distribute the tribes until the tribe has no remainder. Keep the signs (positive or negative) in parentheses.

For example:

2(x-3) = 10

2(x) – (2)(3) = 10

2x – 6 = 10

We also know that the distribution characteristic state is a(b + c) = ab + ac.

Because plus times plus is plus and minus times minus is plus. When expanding the phrase a(b + c) = ab + ac, the value of ac is positive if both a and c are positive, and the value of ac is negative if both a and c are negative.

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To correct the error, Lonnie should write 3 3/4 instead of three and three over four.

A fraction is a mathematical concept that can be used to express a portion of a whole or a number that can be written as the ratio of two integers. In a fraction, the top number is referred to as the numerator, while the bottom number is referred to as the denominator.

Here,

Lonnie has made a mistake in writing the number of packages of pasta. The correct way to write the amount of pasta is 3 3/4 packages. The fraction 1/3 of a fourth package of pasta means that Lonnie has 1/3 of the fourth package and the three whole packages, making it a mixed number, which is a whole number and a fraction combined. To correct the error, Lonnie should write 3 3/4 instead of three and three over four.

Thus, to correct the error, Lonnie should write 3 3/4 instead of three and three over four.

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The distance of the probe is given by the equation A = 2.546 light years

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

The distance traveled by the space probe = 1.7 light years

Now , the value of 1 light year = 9.461 x 10¹³

So , the distance traveled by the space probe = 1.7 x value of 1 light year

On simplifying the equation , we get

The distance traveled by the space probe D = 1.7 x 9.461 x 10¹³

The distance traveled by the space probe D = 16.0837 x 10¹³ km

The distance traveled by the space probe D = 1.60837 x 10¹⁴ km

The distance to Proxima Centauri = 4.246 light years

So , the remaining distance is A = distance to Proxima Centauri - distance traveled by the space probe

On simplifying the equation , we get

The remaining distance is A = 2.546 light years

Hence , the equation is A = 2.546 light years

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If you believe that bit plane slicing is lossy, then 1st-order extrapolation or 2D bilinear interpolation cannot fully recover the original image.

What is extrapolation and interpolation?

Extrapolation is an estimation based on extending a known sequence of data beyond what is absolutely known.

Interpolation is the estimation of a value in a sequence of values between two known values.

Bit plane slicing is a lossy compression technique, which means that some information from the original image is lost during the compression process. The purpose of bit plane slicing is to reduce the size of an image by removing less significant bits from each pixel. As a result, the quality of the image is reduced.

1st-order extrapolation and 2D bilinear interpolation are techniques used to estimate or predict missing or unknown values from a given set of data. These techniques can be used to enhance the quality of an image, but they cannot recover the original image in cases where information has been lost through compression or degradation. In other words, they can only improve the quality of the image to a certain extent, but they cannot restore it to its original state.

So, if you believe that bit plane slicing is lossy, then 1st-order extrapolation or 2D bilinear interpolation cannot fully recover the original image, although they may help to improve its quality to some extent.

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Answer:

[tex]4g^5[/tex]

Step-by-step explanation:

[tex]\sqrt{16g^{10}}=\sqrt{16}*\sqrt{g^{10}}=4g^5[/tex]

The length of the base, AB, can be found to be 12. 49 cm

The base length can be found using the Pythagoras Rule which is:

c ² = a ² + b ²

a = CD which is the height

c = AC

So we can find half od base length when we divide the shape into a right angled triangle :

8 ² = 5 ² + b²

b ² = 64 - 25

b = √ 39

b = 6. 24 cm

Double of this would be:

= 12. 49 cm

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well, we know angle θ is in the III Quadrant, that means the sine or opposite side and cosine or adjacent side are both negative, whilst of course the hypotenuse is just a radius amount thus is always positive.

[tex]\sin(\theta )=\cfrac{\stackrel{opposite}{-3}}{\underset{hypotenuse}{4}}\hspace{5em}\textit{let's find the \underline{adjacent side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2 - b^2}=a ~~ \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \pm\sqrt{4^2 - (-3)^2}=a \\\\\\ \pm\sqrt{7}=a\implies \stackrel{III~Quadrant}{-\sqrt{7}=a}\hspace{5em} \boxed{\cos(\theta )=\cfrac{\stackrel{adjacent}{-\sqrt{7}}}{\underset{hypotenuse}{4}}}[/tex]

So the total cost of tying the lace around the tablecloth is $18.36.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical phrase with two equal sides separated by an equal sign is called an equation. An example of an equation is 4 + 6 = 10.

Here,

The length of the boundary of the square table cloth is 4 times its side length, so the length of the boundary is 4 * 54 cm = 216 cm.

To convert the length from centimeters to meters, we divide by 100:

216 cm / 100 = 2.16 meters

Finally, to find the cost of sticking the lace around the table cloth, we multiply the length of the lace by the cost per meter:

2.16 meters * ₹8.5 per meter = ₹18.36

So the cost of sticking the lace around the table cloth is ₹18.36.

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The answer is 38.7% which is option b., is Jordan's DTI (debt-to-income) ratio to the nearest tenth.

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

To calculate Jim's DTI (debt-to-income) ratio, we need to divide his total monthly debt payments by his gross monthly income.

His total monthly debt payments are:

$2,600 (mortgage payment)

$250 (lease payment)

$500 (credit card payments)

$400 (speed boat payment)

then,

Total Monthly Debt Payments =  $3750

now,

His gross monthly income is his annual salary of $102,000 divided by 12 months which is $8,500

we get,

DTI = Total Monthly Debt Payments / Gross Monthly Income

= $3,750 / $8,500 + 1200

=0.387

=38.7%

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To subtract two fractions, we must find a common denominator and subtract the numerators.

The entire circle represents one whole.

To find the fraction for the shaded region, we must subtract [tex]\dfrac{1}{2}[/tex] and [tex]\dfrac{3}{7}[/tex] from one whole:

[tex]1-\dfrac{1}{2}-\dfrac{3}{7}[/tex]

One whole minus half the whole would leave us with just half:

[tex]\dfrac{1}{2}-\dfrac{3}{7}[/tex]

Now, to find a common denominator, multiply the numerator and denominator of each fraction by the denominator of the other fraction:

[tex]\dfrac{1*7}{2*7}-\dfrac{3*2}{7*2}\\\\= \dfrac{7}{14}-\dfrac{6}{14}[/tex]

Now, subtract normally:

[tex]\dfrac{7}{14}-\dfrac{6}{14}\\\\= \dfrac{1}{14}[/tex]

[tex]\dfrac{1}{14}[/tex]

well, first off, let's see how much was it in tax for the $200 purchase, since we know it was a whooping $14.50.

now, if 200(origin amount) is the 100%, what's 14.50 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 200 & 100\\ 14.50& x \end{array} \implies \cfrac{200}{14.50}~~=~~\cfrac{100}{x}\implies 200x=1450 \\\\\\ x=\cfrac{1450}{200}\implies x=\stackrel{\%}{7.25}[/tex]

now, let's check how much will that be for $76

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{7.50\% of 76}}{\left( \cfrac{7.50}{100} \right)76}\implies 5.7[/tex]

Metric System is a decimal system of measurement that is based on the meter, kilogram, and second and is used in most countries around the world. It is also known as the International System of Units (SI).

The Metric System is the most common measuring system used in the world today. It is a decimal system based on the meter, kilogram, and second and is officially known as the International System of Units (SI). This system was initially developed in France in the late 18th century and is now used in most countries around the world. The Metric System is based on powers of 10 and each unit is related to the next unit by a factor of 10. For example, a kilometer is equal to 1000 meters, a milliliter is equal to 0.001 liters, and a centimeter is equal to 0.01 meters. The Metric System is used to measure length, area, mass, weight, temperature, and volume. It is used in many different industries and applications including science, engineering, medicine, and agriculture. The Metric System has become the international standard for scientific measurements and is accepted by most countries as the preferred system of measurement. The Metric System is also easier for students to learn and use than other systems of measurement.

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The unit rate for 2/3 pound for every 1/4 table spoon will be 2.667 pounds per table spoon.

The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.

In 1/4 table spoon, there is 2/3 pound. Then the units rate is given by the division of the numbers 2/3 and 1/4. Then the rate is given as,

Rate = (2/3) ÷ (1/4)

Rate = (2/3) x (4/1)

Rate = 8 / 3

Rate = 2.667 pounds per table spoon

The unit rate for 2/3 pound for every 1/4 table spoon will be 2.667 pounds per table spoon.

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The minimum number of rotations required for a 3500 km race is 52,800 rotations.

This is calculated by dividing the total distance of the race, 3500 km, by the circumference of the wheel, which is 2πr, where r is the radius of the wheel. The radius of the wheel must be between 27.5 cm (half of 55 cm) and 37.5 cm (half of 75 cm). So, the minimum number of rotations is given by 3500/(23.14r), where r is the minimum radius of the wheel. Substituting in r = 27.5 cm, we get the minimum number of rotations required for a 3500 km race as 52,800.

To arrive at this result, we must first calculate the circumference of the wheel, which is given by 2πr, where r is the radius of the wheel. Since the diameter of the wheel must be between 55 cm and 75 cm, the radius of the wheel must be between 27.5 cm (half of 55 cm) and 37.5 cm (half of 75 cm).

We then divide the total distance of the race, 3500 km, by the circumference of the wheel, which is given by 2πr. Substituting in the minimum radius of the wheel, 27.5 cm, we get the minimum number of rotations required for a 3500 km race as 52,800.

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It is not possible to determine the probability of survival on the second try if the cylinder is not spun, as the outcome of the first try has no bearing on the outcome of the second try if the cylinder is not spun.

The cylinder serves to randomly distribute the bullet among the chambers, so if the cylinder is not spun, the bullet will remain in the same chamber, and the outcome of the second try will be determined by the initial placement of the bullet in the cylinder.

In a typical scenario where a revolver with a single bullet is used, the probability of survival on the first try is 1/6, and the probability of survival on the second try (assuming the cylinder is spun) is also 1/6. However, without spinning the cylinder, the outcome of the second try is fixed and cannot be determined probabilistically.

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The standard error of the sample proportion p is approximately 0.281

The standard error of the sample proportion p can be calculated by taking the square root of the sample proportion's variance, which is given by-

p(1-p)/n, where p is the sample size,

The random sample(n) is equal to 500

The adults who indicate the unemployment is 304

Now the sample proportion

p=304/n

p=304/500

p= 0.608

Now the standard error is

SE= √p(1-p)/n

Now put the value here

SE=√0.608(1-0.608)/500

SE=0.021833

Therefore, the standard error of the sample proportion is 0.0218

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For quadrilateral ABCD,

m∠AED = 145°

m∠DAE = 145°

m∠BCE = 145°

Consider the following diagram.

ABCD is a rhombus.

Here, the measure of angle EDA=35º

From the figure we can observe that,

∠AED + ∠EDA =180° ................(Linear pair of angles)

⇒ ∠AED = 180° - 35°

⇒ ∠AED = 145°

Also,

∠DAE + ∠EDA = 180° (Linear pair)

⇒ ∠DAE = 180° - 35°

⇒ ∠DAE = 145°

Now we find m∠BCE

We can observe that ∠BCE and ∠DAE are opposite angles .

So, ∠BCE = ∠DAE

⇒ m∠BCE = 145°

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The complete question is:

Quadrilateral ABCD is a rhombus. Given that m∠EDA=35º, what are the measures of m∠AED, m∠DAE, and m∠BCE

Answer:

see below

Step-by-step explanation:

perimeter = 2*(6.25x - 3.5 + 3.5 x +6) =2(9.75x+2.5) = 19.5x+5

The slope is -2/5

You have a point at (0,3) and (5,1).  If you create a slope triangle, it'll go down 2 and right 5.

The letter on the number line that stands in for the numerals after it On the number line, B stands for -38.

The number line that displays negative numbers is presented to us. On the number line, we are aware that the number rises as we travel to the right.

As per the data given in the above question are as bellow,

The details provided are as bellow,

We can observe that the number line has a grading scale of 1, meaning that each subsequent mark is separated by one unit.

B is four points away from a 42.

This suggests that to get B, we just need to add 4 to -42.

So:

B = -42 + 4

B = -38

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Note : The complete question would be as bellow,

What integer does the letter B represent on the number line above?

What integer does the letter B represent on the number - 1

Liters of water (w) it would take to water 40 flower pots, if it took 9 liters of water to water 24 flower pots when assuming same amount of water is used on each pot is 15.

Therefore the answer is 15.

To find the amount of water Vito would need to water 40 flower pots, we can use the following formula:

w = (9 liters) * (40 pots) / (24 pots)

Simplifying:

w = 15 liters

So, Vito would need 15 liters of water to water 40 flower pots, assuming he uses the same amount of water on each pot.

--The question has some errors, answering to the question below--

"Vito uses 9 liters of water to water 24 flower pots. He is wondering how many liters of water (w) it would take to water 40 flower pots. He assumes he'll use the same amount of water on each pot."

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The information provided doesn't mention Nobu's tomato, so it's not possible to determine how much heavier Anya's tomatoes are than Nobu's tomato without more information.

Answer:

81/100

Step-by-step explanation:

First we need to find a common multiple of 10 and 100.  It's going to be 100, so we chance 7/10 to 70/100.

Now that the denominator matches for both of them, now we add.

70/100 + 11/100 = 81/100

Based on the Tuesday rate, $100 United States dollars is equal to 843.64 French francs.

1. From the tables, the Tuesday rate is 0.119 US dollars to 1 French franc.

2. To find the exchange rate, multiply the number of US dollars by the exchange rate: 100 x 0.119 = 11.90.

3. To find the amount in French francs, divide the US dollars by the exchange rate: 11.90 / 0.119 = 843.64 French francs.

Therefore, $100 United States dollars is equal to 843.64 French francs based on the Tuesday rate.

At the Tuesday exchange rate, one hundred United States dollars is equal to eight hundred and forty-three point sixty-four French francs. This means that for every one hundred US dollars, you can get eight hundred and forty-three point sixty-four French francs in exchange.

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