yesterday, peter the rabbit picked 84 carrots from his garden and ate one-fourth of them. today, he ate 12 carrots. how many carrots are left?

By algebra properties and trigonometric formulas, the trigonometric expression (1 + cos x) / (1 - cos x) - (1 - cos x) / (1 + cos x) is equivalent to trigonometric expression 4 · cos x · csc² x.

In this problem we need to prove the equivalence between two trigonometric expressions, this can be done by using algebra properties and trigonometric formulas. First, write one side of the expression:

(1 + cos x) / (1 - cos x) - (1 - cos x) / (1 + cos x)

Second, use algebra properties to simplify the expression:

[(1 + cos x)² - (1 - cos x)²] / (1 - cos² x)

Third, expand the resulting expression:

(1 + 2 · cos x + cos² x - 1 + 2 · cos x - cos² x) / (1 - cos² x)

4 · cos x / (1 - cos² x)

Fourth, use trigonometric formulas to simplify the expression:

4 · cos x / sin² x

4 · cos x · csc² x

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We can describe the output of the graph for:

This is referred to as a pictorial representation or a diagram that represents data or values in an organized manner.

From the graph given, we can deduce that the variation at 0-1 curve is small while the variation at 3-4 curve is large which is therefore the reason why slow and rapid output were chosen respectiviely.

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The geometric mean of 20 and 30 is 24.49.

What is geometric mean?

The Geometric Mean (GM) in mathematics is the average value or mean that, by calculating the product of the values of the set of numbers, denotes the central tendency of the numbers. In essence, we multiply the numbers together and calculate their nth root, where n is the total number of data values.

We are given two numbers as 20 and 30.

Formula for geometric mean is

G.M = √x₁ × ... × xₐ  

So, using this we get

⇒G.M = √20 × 30

⇒G.M = √600

⇒G.M = 24.49

Hence, the geometric mean of 20 and 30 is 24.49.

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All the inequalities that represent the situation are as follows;

A. 0.5x + 0.25y ≤ 20.

C. 2x + 3y ≤ 120.

A combinations of necklaces and key chains you can make given the situation include the following:

A. 30 necklaces and 20 key chains.

In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of necklaces and number of key chains respectively, and then translate the word problem into algebraic equation as follows:

Based on the table of values (see attachment) and given x ≥ 0 and y ≥ 0, a system of linear inequalities to describe this situation include the following:

0.5x + 0.25y ≤ 20.

2x + 3y ≤ 120.

Next, we would use an online graphing calculator to plot the above system of linear inequalities in order to determine its solution as shown in the graph attached below.

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Right Bisector also known as Perpendicular Bisector is a line that bisects another line segment at a right angle, through the intersection point.

First we will draw a line segment AB = 7 cm with the help ruler, then with vertex A, by using compass take more than half of AB and draw arcs, one each side of AB and mark them X and Y and then with vertex B, by using compass with same length again, cut the previous arcs at X and Y respectively.

Now, with help of ruler join the point X and Y. Thus XY is the perpendicular bisector of line AB.

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Answer: $25.59

Step-by-step explanation: you can multiply 3 times 8.53 which comes too $25.59 but we can add as well.

8.53 + 8.53= 17.06 Now we have to add it 1 more time soo

17.06 + 8.53= $25.59..    

Hope this helps :)

The relations that are functions are 2, 3, 4, 5, 6, and 7.

The ones that aren't functions are 1 and 8.

A relationship maps elements from one set (the domain) into elements from another set (the range), and a relation is a function only if each element of the domain is mapped into only one value of tha range.

For example, if you look at the relation 8, you can see that the input x = 1 is mapped into two different outputs, then this is not a function.

With that in mind, the options that are functions are:

2, 3, 4, 5, 6, and 7.

The ones that aren't functions are 1 and 2.

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Answer:

2/21

simplify 8/84

Answer:

The experimental probability of the next vehicle sold being a minivan is 8/84 = 1/10.

Step-by-step explanation:

The experimental probability of an event can be calculated by dividing the number of successful outcomes by the total number of trials. In this case, we want to find the probability of selling a minivan, so we want to find the number of minivans sold divided by the total number of vehicles sold.

Therefore, the experimental probability can be calculated as follows:

Number of minivans sold / Total number of vehicles sold = 8 / 84

So, the experimental probability that the next vehicle sold will be a minivan is 8/84.

963.9 in³ cubic inches volume  of the treasure chest is taken up by the coins .

What does math's volume mean?

The volume of a 3D object is the amount of actual space it occupies. It is a 2D shape's 3D equivalent of area. Cubic units, such as cm3, are used to measure it. You may calculate this by multiplying its length, height, and width.

Remember that the volume of a cylinder is given by:

volume = (height)*pi*(radius)^2

Where pi = 3.14

Then here the volume of each coin is:

V = (0.0625 in)*3.14*(1.7 in)^2 = 5.67 in³

And there are 230 coins, so the total volume is

V = 170 * 5.67 in³

    = 963.9 in³

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Answer:

Step-by-step explanation:

the answer is 85.41 in^3

I got it right and I got to flvs .

Answer: The best graph to illustrate June's situation is a cost-volume-profit (CVP) graph, which shows the relationship between the revenue, cost, and volume of goods sold.

In June's case, her fixed costs (the cost of the sewing machine) are constant and do not change regardless of the number of quilts she makes and sells. Her variable costs (the raw materials) are directly proportional to the number of quilts she makes and sell. Her revenue is directly proportional to the number of quilts she sells.

The CVP graph will show a line representing fixed costs, a line representing variable costs, and a line representing revenue. The point at which the total costs (fixed costs + variable costs) equal the revenue represents the break-even point, at which June neither makes a profit nor incurs a loss. Beyond this point, June will make a profit, and before this point, she will incur a loss.

The CVP graph can be used to determine the break-even point and to make predictions about the future financial performance of a business, based on changes in volume, costs, or price.

Step-by-step explanation:

The correct order of the ratios from the least to the greatest is given below:

4/2, 11 to 2, 22:3, 30/4, 36:5

Least to greatest: 4/2 = 2, 11:2 = 5.5, 22:3 = 7.33, 30:4 = 7.5, 36:5 = 7.2

15/4, 19 to 5, 53/15, 4:1, 18 to 6

Least to greatest: 15/4 = 3.75, 19:5 = 3.8, 53:15 = 3.53, 4:1 = 4, 18:6 = 3

7:11, 8:12, 6:10, 1/2, 7:4

Least to greatest: 7:11 = 0.6364, 6:10 = 0.6, 8:12 = 0.6667, 1/2 = 0.5, 7:4 = 1.75

A ratio in mathematics demonstrates how many times one number is present in another.

For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six.

The ratio of oranges to the overall amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.

Therefore,

The ratios listed in the question are ordered from least to greatest by converting each ratio into a decimal and comparing the values.

In each case, the fraction is divided, the ratio of two numbers is expressed as a decimal, and then the decimals are ordered from least to greatest.

For example, in the first list, the ratio "11 to 2" is expressed as the decimal 11/2, which is equal to 5.5. The other ratios are similarly expressed as decimals and then ordered to get the final answer.

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These terms describe various aspects of quantitative analysis and measurement in different scientific fields such as analytical chemistry, biology, and statistics.

A. Sensitivity - the ability of a measurement method or instrument to detect small changes in the quantity being measured.

B. Detection limit - the minimum amount of a substance that can be reliably detected by a measurement method or instrument.

C. LOQ (Limit of Quantitation) - the minimum concentration of a substance that can be accurately quantified by a measurement method or instrument.

D. Limit of Linearity - the range of concentrations of a substance over which the measurement method or instrument produces proportional results.

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Distinguish between the following terms:

A. sensitivity and detection limit

B. Log and limit of linearity

C. quantitation by calibration curve and the method of standard addition.

D. confidence interval and confidence limits

The speed of the Atlas V Rocket was approximately 8,727.27 miles per hour, based on the given information that it could go one mile in 0.11 seconds.

To find the speed of the Atlas V Rocket, we need to use the formula:

speed = distance / time

In this case, the distance is 1 mile, which is equal to 1609.34 meters. The time is 110th of a second, which is equal to 0.1 seconds (since there are 10 tenths in a second).

So, plugging these values into the formula, we get:

speed = 1609.34 meters / 0.1 seconds

speed = 16093.4 meters per second

Therefore, the Atlas V Rocket traveled at a speed of 16093.4 meters per second.

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4214.7 is the balance in the account after 2 months .

What does compound and simple interest mean?

A fixed proportion of the principal amount borrowed or lent is what is known as simple interest and is paid or received over a given period of time.

                               Borrowers are required to pay interest on interest in addition to principal because compound interest accrues and is added to the total amount of interest from earlier periods.

P = $4200

R = 2.1% = 2.1/100 = 0.021  =

    T = 2 month = 2/12 = 1/6

   I = PRT

    = 4200 * 0.021 * 1/6 = 14.7

Amount = P + I = 4200 + 14.7  = 4214.7

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The formula (D) f(n) = 65 − 9(n − 1) represents the arithmetic sequence for 65, 56, 47, 38, 29 ….

An arithmetic sequence is one in which each phrase grows by adding or removing a certain constant, k.

In a geometric sequence, each term rises by dividing by or multiplying by a certain constant k.

For instance, a1 = 25 and a(n) = a(n-1) + 5.

Each word in an arithmetic sequence increases by adding or subtracting a certain constant, k.

As opposed to a geometric sequence, where each term is increased by dividing or multiplying a certain constant k, this one does not.

For instance, a(n) = a(n-1) + 5 and a1 = 25.

So, we have the sequence:

65, 56, 47, 38, 29 …

Now, the difference is 65 - 56 = -9

Now, the first term is 65.

Then, the equation which represents its formula is f(n) = 65 − 9(n − 1).

Therefore, the formula (D) f(n) = 65 − 9(n − 1) represents the arithmetic sequence for 65, 56, 47, 38, 29 ….

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Complete question:

An arithmetic sequence begins with 65, 56, 47, 38, 29 … Which option below represents the formula for the sequence?

(A) f(n) = 56 − 9(n)

(B) f(n) = 56 + 9(n −1 )

(C)  f(n) = 65 + 9(n −1 )

(D) f(n) = 65 − 9(n − 1)

There would be 30 trapezoids to create 5 hexagons.

An hexagon is a six-sided polygon. It is made up of six equilateral triangles and six trapezoids. To create an hexagon using pattern blocks, you need 10 equilateral triangles and 20 trapezoids. Therefore, to create 5 hexagons

The exact number of trapezoids needed to create three hexagons depends on the size and shape of the hexagons. However, in general, you would need at least 18 trapezoids.

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To create 5 hexagons using pattern block trapezoids, you would need 15 trapezoids. This is because 3 trapezoids form one hexagon.

In geometry, a hexagon can be divided into 6 equilateral triangles. In the context of pattern blocks, these triangles are often used to construct other shapes. Now, considering that a trapezoid in pattern blocks is usually made up of 2 of these triangles, it takes 3 trapezoids to create one hexagon. Hence, to create 5 hexagons, you would need 5 x 3 trapezoids, which equals 15 trapezoids.

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Answer: y= -1

Step-by-step explanation:

1) Distribute the 4 to the y and the -6 to get 4y-24, so our new equation is -36= 8y+4y-24.

2) Add like terms 8y and 4y to get 12y. Our new equation is -36=12y-24.

3) Remove the constant -24 by adding 24 to both sides to get -12=12y.

4) Remove the coefficient 12 by dividing 12 on both sides to get y= -1  

The fraction of the students live more than 4 miles from school is 3/10.

A fraction represents a part of a number or any number of equal parts.

A fraction consisting of a quotient and remainder is a mixed fraction. we can convert the mixed fraction to improper fraction by first dividing the numerator by denominator and then taking the quotient as whole number and remainder as the numerator of proper fraction keeping the denominator same.

Given;

The percentage of students live more than 5 miles away=30%

Now,

The fraction;

=30/100

To convert it into the simplest from;

=30/100

=3/10

Therefore, the fraction in simplest form will be 3/10.

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The complete question is;

At Charles Walters Middle School, 30% of the students live more than 4 miles from school.What fraction of the students live more than 4 miles from school? Write your answer as a fraction in simplest form. ?​

The transformation that maps △UVW to △EFG is (d) (x, y) = (-2x, -2y)

From the question, we have the following parameters that can be used in our computation:

The figure

From the figure, we can see that

Triangle EFG is twice the triangle UVW in side lengths

This means that

(x, y) = (2x, 2y)

The orientations are 180 degrees apart

So, we have

(x, y) = (-2x, -2y)

Hence, the transformation is (d) (x, y) = (-2x, -2y)

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If reid takes a 2 quart pitcher of lemonade to the table and pours it all equally into 9 glasses, each glass contains approximately 0.888 cups (or 7/8 cups) of lemonade.

The problem states that Reid has a 2 quart pitcher of lemonade, which is equivalent to 8 cups. This is because there are 4 cups in one quart, so 2 quarts would be 2 x 4 = 8 cups.

Reid pours this entire amount of lemonade equally into 9 glasses. This means that the amount of lemonade in each glass will be the same. To find out how much lemonade goes in each glass, we need to divide the total amount of lemonade by the number of glasses.

We can use the following formula:

amount per glass = total amount / number of glasses

Plugging in the values we know, we get:

amount per glass = 8 cups / 9

Dividing 8 cups by 9 gives us a decimal value of 0.888..., which means that each glass contains approximately 0.888 cups of lemonade. This value is an approximation, since we rounded to the nearest thousandth place.

We can also express this value as a fraction by simplifying 0.888... as follows:

0.888... = 888.../1000...

= 8/9

Therefore, we can say that each glass contains 7/8 cups or approximately 0.888 cups of lemonade.

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Answer:yes

Step-by-step explanation:correct becuase

Answer:

Answer is ADB

Step-by-step explanation:

I believe that's the answer

If Paul uses the function y = 8x + 38 to model the situation, then the model predicts a score of:

86 for 6 hours of homework.

In the given problem, we are given a linear equation of the form y = 8x + 38, where y represents the score obtained by Paul and x represents the number of hours of homework done by Paul.

To predict the score for 6 hours of homework, we need to substitute 6 for x in the equation and solve for y. By substituting x = 6 in the equation, we get:

Therefore, the model predicts a score of 86 for 6 hours of homework.

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The measure of each angle in complementary angles with measures 3x and 6x - 18 degrees is 36° and 54°.

We are given two angles 3x and 6x - 18 and these angles are complementary angles.

Complementary angles are those whose combined angle is 90 degrees or less. In other terms, two angles are said to be complimentary if they combine to make a right angle.

So, sum of 3x and 6x - 18 is 90°

     3x + 6x - 18 = 90°

                    9x = 108°

                      x = 12°

So, 3x = 3 × 12 = 36°

     6x - 18 = 6 × 12- 18 = 54°

Hence, the measure of each angle is 36° and 54°.

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The probability that a person responded Yes or was under the Age of 55 was C. 57 %

The probability that a person who responded either said yes or was under the Age of 55 is:

= Probability that a person answers yes + probability that a person is under 55 - Probability that a person was under 55 and answered yes

The probability a person who responded either said yes or was under the Age of 55 is therefore:

= ( 25 / 103 ) + ( 59 / 103 ) - 17 / 103

= 57 %

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The two statements  a iff b and (not a) iff (not b) has been explained

The two statements are known as biconditionals, which state that two statements are true if and only if each other.

"a iff b" means that "a" is true if "b" is true, and "a" is false if "b" is false. In other words, "a" and "b" have the same truth value.

"(not a) iff (not b)" means that "not a" is true if and only if "not b" is true, and "not a" is false if and only if "not b" is false.

Therefore, these two statements are equivalent because they express the same idea: "a" and "b" have the same truth value. If "a" is true, then "b" is true, and if "a" is false, then "b" is false. Similarly, if "b" is true, then "a" is true, and if "b" is false, then "a" is false.

These statements are true in cases where both "a" and "b" have the same truth value. If both are true or both are false, then the statements are true. If "a" is true and "b" is false, or vice versa, then the statements are false.

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Answer:

So, for the values 5.6, 6, and 7, the inequality 15 < 3x is true. For the values 5, 3, 3/4, and 4.5, the inequality 15 < 3x is false.

Step-by-step explanation:

For the inequality 15 < 3x to be true, 3x must be greater than 15. To determine whether each value will make the inequality true, we can substitute each value for x and see if the inequality holds.

For x = 5.6, 3x = 16.8, which is greater than 15, so the inequality is true and the value 5.6 makes the inequality true.

For x = 5, 3x = 15, which is equal to 15, so the inequality is false and the value 5 does not make the inequality true.

For x = 3, 3x = 9, which is less than 15, so the inequality is false and the value 3 does not make the inequality true.

For x = 6, 3x = 18, which is greater than 15, so the inequality is true and the value 6 makes the inequality true.

For x = 7, 3x = 21, which is greater than 15, so the inequality is true and the value 7 makes the inequality true.

For x = 3/4, 3x = 2.25, which is less than 15, so the inequality is false and the value 3/4 does not make the inequality true.

For x = 4.5, 3x = 13.5, which is less than 15, so the inequality is false and the value 4.5 does not make the inequality true.

So, for the values 5.6, 6, and 7, the inequality 15 < 3x is true. For the values 5, 3, 3/4, and 4.5, the inequality 15 < 3x is false.

Answer:

  6 years

Step-by-step explanation:

You want the length of time it takes for a $50 investment to total $3200 if it doubles in value each year.

The value of the investment can be described by ...

  v = 50·2^t

where t is the number of years.

You want t when v=3200:

  3200 = 50·2^t

  64 = 2^t

  log(64) = t·log(2) . . . . . take logarithms

  t = log(64)/log(2) = 6

It will take 6 years for her investment to reach $3200.

__

Additional comment

If you're familiar with powers of 2, you recognize that 64 = 2⁶. Comparing exponents in ...

  64 = 2^t

  2^6 = 2^t . . . . . use 2^6 for 64

we can see that t=6. The logarithms are used to formalize this comparison.