what is 10 1/2 % of 62

a.) The number of pounds of empty cans needed by the class is 200 pounds.

b.) The number of empty cans needed by the class to collect are 5486 cans.

The books will cost a total amount of $ 50.

If $ 0.25 per pound is the current price for aluminium at the recycling centre, the number of pounds the class will have to collect is found by dividing the total amount needed by cost per pound is,

⇒ 50/0.25 = 200

b.) Six empty cans weigh 3.5 ounces.

1 pound = 16 ounces

200 pounds = 200 × 16 = 3200 number of ounces

3200/3.5 = 914.29

914.29 × 6 = 5485.7 cans ≈ 5486 cans

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The probability that the sample mean will be within 5 points of the population mean is 0.95 or 95%

The Central Limit Theorem (CLT), a foundational idea in statistics, holds that, regardless of the underlying population distribution, the distribution of the sample means will be about normal given a big enough sample size. The CLT is crucial because it enables us to draw conclusions about a population based on a sample, even when the population is not normal.

According to the CLT, as the sample size grows, sample means will approach population means and their standard deviations will fall. The standard error, also known as the standard deviation of the sample means, is calculated by dividing the standard deviation of the population by the square root of the sample size.

According to the Question

The sample mean for a random sample of 100 individuals is most likely to be within 5 points of the population mean. The distribution and standard deviation of the population, however, would determine the precise likelihood. The standard error may be used to determine a confidence interval for the population mean if the population standard deviation is known. A 95% confidence interval is frequently used, which is equivalent to 1.96 standard deviations from the mean. In this instance, especially with a large sample size, there is a good likelihood that the sample mean will be within 5 points of the population mean.

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Answer: 640

Step-by-step explanation:

6.4 * 100 = 640

The value of the sides, NM and OL are 16 and 8 respectively

To determine the value of x, we have the note the properties of a parallelogram.

The properties of a parallelogram includes;

Then, we have;

NM = OL

substitute the values

x + 12 = 2x + 8

Now, collect like terms

x = 4

NM = 4 + 12 = 16

OL = 16

Hence, the value are 4 and 16

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Answer:

H (Height) = 3

Step-by-step explanation:

We have the formula A = 1/2(a+b)h

Let's identify all variables

A = 24

a = 9

b = 7

h = ?

Lets plug all that in:

24 = 1/2(9+7)h

9+7 = 16

24 = 1/2(16)h

Half of 16 is 8 so to simplify the rest...

24 = 8h

To get h alone we will divide both sides of the equation by 8

24/8 = h

24/8 = 3

Making H = 3

Answer:

I think 3/20 of a chance of putting 3 frosted cookies in bags to sell.

Step-by-step explanation:

Hope it helps! =D

ALGOL 68 is a language that prioritized orthogonality as a key design requirement. ALGOL 68's primary objectives and design tenets are as follows:

1. a thorough and clear design;

2. an orthogonal design

3. Safety

4. Efficiency: Mode-independent parsing, independent compilation, loop optimization, representations in small and big character sets, static mode verification, etc.

As a programming language, Algol 68 offers certain unique and practical concepts that were ground-breaking at the time and have appeared, in varying degrees, in various languages afterwards.

Orthogonal design, which means that core concepts stated in the language can be used anyplace that usage can be said to "make sense." Completeness and clarity of explanation (as facilitated by the adoption of two-level grammar, which sparked many critical reactions).

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The dimensions of the new practice court is 45.5 feet by 29.5 feet.

The equations should be completed as 160 = 2W + 2L; W = L - 16

Mathematically, the perimeter of a rectangle can be calculated by using this mathematical expression;

P = 2(L + W) or P = 2L + 2W

Where:

Since the width of the rectangular lot is 16 feet less than the length, we have:

W = L - 16

Substituting the given parameters into the perimeter formula, we have;

160 = 2L + 2W

160 = 2(L - 16) + 2L

160 = 2L - 32 + 2L

160 = 4L - 32

4L = 182

L = 45.5 feet.

For the width, we have:

W = L - 16

W = 45.5 - 16

W = 29.5 feet.

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The slope-intercept form of the linear function is given as follows:

y = 0.8x + 8.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The graph crosses the y-axis at y = 8, hence the intercept b is given as follows:

b = 8.

When x increases by 10, y increases by 8, hence the slope m is given as follows:

m = 8/10

m = 0.8.

Then the function is defined as follows:

y = 0.8x + 8.

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To find the fraction of the states that Jorge's family has visited, we can use the formula:

visited states / total states

In this case, Jorge's family has visited 38 states out of a total of 50 states, so the fraction of states they have visited is:

38 / 50

You can simplify this fraction by dividing both the numerator and denominator by the greatest common divisor of 38 and 50 which is 2, so the fraction is

19/25

So, Jorge's family has visited 19/25 of the states in America.

Jorge's family has visited 19/25 of the states in America.

Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.

In this case, Jorge's family has visited 38 states out of a total of 50 states, so the fraction of states they have visited is:

38 / 50

You can simplify this fraction by dividing both the numerator and denominator by the greatest common divisor of 38 and 50 which is 2, so the fraction is

19/25

19 out of the 25 American states have been visited by the Jorge family.

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Answer:

5

Step-by-step explanation:

log(5)5=1

5^2-1 = 5^1 = 5

The speed of the jet in still air is 525miles per hour and the speed of the jet stream is 75miles per hour

speed is defined as the rate of change of distance with time. It is measured in meter per second and it is a scalar quantity. It has other units like miles per hour, kilometers per hour e.t.c

The speed of the jet with jet stream = displacement /time = 1800/3 = 600 miles/hour

The speed of the jet against = distance /time = 1800 / 4 = 450 miles per hour

The speed of the jet in still air will be the average speed of the jet to and fro. = (600+450)/2

= 1050/2

= 525 miles per hour

Therefore the speed of the jet in still air = 525 miles per hour

Also, the the jet stream speed = 525- 450 = 75 miles per hour.

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Answer:

The dimensions of the rectangular tract of land with a perimeter of 44 kilometers and an area of 120 square kilometers are:

Length = 10 kilometers

Width = 12 kilometers

Explanation: To find the dimensions of a rectangular tract of land when its perimeter and area are known, you can use the formulas:

Perimeter = 2(length + width)

Area = length * width

We know that:

Perimeter = 44 kilometers

Area = 120 square kilometers

So, we can use these values to set up the following equation:

44 = 2(length + width)

And we can solve for length and width.

44 = 2(length + width)

22 = length + width

And now we know that the sum of the length and width of the rectangular tract is 22 kilometers.

Now we have to use the area formula:

Area = length * width

120 = length * width

We can use the value we have for the sum of the length and width to find either the length or the width of the rectangular tract.

For example, we can use the equation:

length = 22 - width

And substitute it into the area equation:

120 = (22 - width) * width

And then we can solve for width:

120 = 22 * width - width^2

width^2 - 22 * width + 120 = 0

We can use the quadratic formula to solve for width.

width = (22 +/- sqrt(22^2 - 4 * 1 * 120))/ 2

So,

width = (22 +/- sqrt(484 - 480))/ 2

width = (22 +/- sqrt(4))/ 2

width = (22 +/- 2)/ 2

width = (24)/ 2

width = 12

So, the width of the rectangular tract is 12 kilometers.

And we can use the equation:

length = 22 - width

to find the length

length = 22 - 12 = 10

So, the dimensions of the rectangular tract of land with a perimeter of 44 kilometers and an area of 120 square kilometers are:

Length = 10 kilometers

Width = 12 kilometers

[tex]27\cdot 9^{3x}\implies 3^3\cdot (3^2)^{3x}\implies 3^3\cdot 3^{6x}\implies {\Large \begin{array}{llll} 3^{3+6x} \end{array}}[/tex]

Answer:

y=4x+2

Step-by-step explanation:

slope (12-0)/(5-2)=4

y=4x+b

plug in (2,0)

b=2

y=4x+2

Elle can buy maximum 0.6 liters of goat milk and 1.2 liters of cow's milk.

What System of linear inequalities?

A system of linear inequalities is similar to a system of linear equations, except that it is made up of inequalities rather than equations. To represent scenarios with various restrictions, systems of linear inequalities are utilized.

Let x be the number of liters of goat milk and y be the number of liters of cow's milk that Elle wants to buy. We know that:

x + y ≤ 80 (because Elle wants to spend at most Php80)

130x + 65y ≤ 80 (because each liter of goat milk costs Php130 and each liter of cow's milk costs Php65)

This is a system of linear inequalities, and the solution set is the set of all possible combinations of x and y that satisfy both inequalities.

The inequality 130x + 65y ≤ 80 represents a line in the plane, and the inequality x + y ≤ 80 represents a region that is "bounded" by this line.

The solution set for the inequalities are x <= 0.6 and y <= 1.2.

So, Elle can buy maximum 0.6 liters of goat milk and 1.2 liters of cow's milk.

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Answer:

5 bags

Step-by-step explanation:

if there are 5 pounds of trail mix and each bag needs to contain 1 pound, that can be equally divided into 5 bags where each bag contains 1 pound each

The ratio of servings to cones is 47:4.

In mathematics, a ratio is a way of comparing two or more values. It is usually represented as a fraction, with the values being separated by a colon (:). For example, if you have 7 apples and 4 oranges, the ratio of apples to oranges would be 7:4. This can also be written as 7/4 or 1.75. Ratios can also be written as a decimal or a percentage. Ratios can be used to compare quantities, sizes, or measurements in different units.

If the ratio of servings to cups is 7:47:47:4, that means for every 7 servings, there are 47 cups.

Since the servings came in either a cup or a cone, but not both, the ratio of servings to cones is the remaining portion of servings that are not accounted for in the ratio of servings to cups.

So, it's 7 servings + 47 cups = 47 servings + 4 cups.

Therefore, the ratio of servings to cones is 47:4.

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The balance of Jamie's checking account in the month of May is given as follows:

$20.

The balance in the month of May is obtained applying the proportions in the context of this problem.

He swiped his card for $69 in the restaurant which caused this account to be overdrawn by nine, hence the June balance is of:

-9 + 69 = $60.

The balance in Jamie's checking account in the month of June was thrice the amount of what it was in the month of May, hence the May's balance is given as follows:

3x = 60

x = $20.

The problem asks for the balance of the checking account in the month of May.

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The bottom of the ladder is 9 feet from the wall.

Using the Pythagorean Theorem, we can calculate the distance from the wall. The Pythagorean Theorem states that for a right triangle, the sum of the squares of the sides is equal to the square of the hypotenuse. In this case, the hypotenuse is 15 feet and the side adjacent to the wall is 12 feet.

The formula for the Pythagorean Theorem is a^2 + b^2 = c^2.

We can solve for the distance from the wall (a). a^2 = c^2 - b^2, so a^2 = 15^2 - 12^2, which equals a^2 = 225 - 144, so a^2 = 81. Taking the square root of both sides, a = 9 feet.

Therefore, the bottom of the ladder is 9 feet from the wall.

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The odds of choosing a red and a blue are 6/20 (4/20), or 3/5.

The balls in the bag are unaware of what was drawn the first time because the two choices are separate.

Six of the 20 pebbles in the bag are red. The odds of selecting a red are 6/20.

Four of the 20 pebbles in the bag are blue. Picking a blue one has a 4/20 chance.

Multiplying the odds of each event will yield the likelihood of two independent events.

The likelihood of selecting a red followed by a blue is 6/20 (4/20), or 3/5.

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Answer:

4

Step-by-step explanation:

It says 5g is 20. To figure out the value of g, you need to divide 5g by 5, and 20 by 5, which gives the answer of g=4

Answer:

A) ΔDFG

and

C) ΔFEG

Answer: FEG

Step-by-step explanation:

It can't be the others, so process of elimination.

The difference in lengths between the hypotenuse and the longest leg of the triangle is 4.

Pythagoras theorem states that for a right angled triangle, the square of the hypotenuse is the sum of the squares of base and altitude.

By Pythagoras Theorem,

Hypotenuse² = (Leg 1)² + (Leg 2)²

(AB)² = (BC)² + (AC)²

c² = 16² + 12²

c² = 256 + 144

c² = 400

c = √400

c = 20

Length of longest leg = 16

Difference = 20 - 16 = 4

Hence 4 is the difference between the length of the hypotenuse and the longest leg.

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Answer:

In Explanation

Step-by-step explanation:

The constant of proportionality is a value that relates two variables that have a proportionate relationship. It is often represented by the letter "k".

For example, if two variables x and y are directly proportional, their relationship can be represented by an equation of the form y = kx, where k is the constant of proportionality. In this equation, the value of k represents the ratio of y to x and it is constant, meaning that it does not change as the values of x or y change.

In physics, the constant of proportionality also appears in many mathematical models of natural phenomena, such as Hooke's law (F = km) which relates the force applied on an object (F) to its displacement (x) with a spring constant (k), and Ohm's law (V = IR) which relates the voltage (V) across a resistor to the current (I) flowing through it with a resistance constant (R).

The constant of proportionality can have different units of measure depending on the context and is used to make quantitative predictions about the relationship between the variables. In some cases, it can be used to determine the behaviour of a system or physical process.

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The number representing the property of tripled a number two times and getting result 819 is equal to 91.

Let us consider a required number be 'x'.

Triple a given number is represented by 3x.

Tripled a tripled number again is expressed as  3 × ( 3x  )

Result of a tripled a tripled number is equal to 819

⇒ 3 × ( 3x  ) = 819

⇒ 9x = 819

Divide both the side by 9 we get,

⇒9x /9 = 819 /9

⇒ x = 91

Therefore, the required number having property of tripled and tripled a number again with result 819 is equal to 91.

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The value of your declining channel in 2016, given the depreciation rate, would be $ 40. 99

The value of the channel can be found by the formula :

= Original value of the channel x ( 1 - rate of depreciation ) ^ number of years

Rate of depreciation = 13 %

Number of years :

= 2016 - 2002

= 14 years

The value of the channel is therefore:

= 288 x ( 1 - 13 %) ¹⁴

= $ 40. 99

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