The Federal Helium Reserve held about 16 billion
cubic feet of helium in 2010 and is being depleted by
about 2.1 billion cubic feet each year.
a. Give a linear equation for the remaining federal
helium reserves, R, in terms of t, the number of
years since 2010.
b. In 2015, what will the helium reserves be?
c. If the rate of depletion doesn’t change, in what year
will the Federal Helium Reserve be depleted

The quadratic equation numerically (using tables of x- and y- values).

Correct option: (a). The value of x are x = -1 and x = 3.

A quadratic equation is a second-order polynomial equation in a single variable x with the formula; ax² + bx + c = 0, where a 0. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem. The answer could be simple or complicated.

The given quadratic equation is:

x² - 3 = 2x

or, x² - 2x - 3 = 0

or, x² - 3x + x - 3 = 0

or, x (x - 3) +1 (x - 3) = 0

or, (x - 3) ( x +1 ) = 0

or, x = +3 , -1

The value of x are x = -1 and x = 3.

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The company can build 5 child bikes and 15 adult bikes in a week.

The answer is "Yes because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100".

Linear Equations are mathematical statements, which can be used to find an unknown quantity or any value in a given problem. Here we use variables like x, y .. etc. to represent unknown values.

Here we will use Linear Equations to solve the equations.

Here we have

One child bike requires 4 hours to build and 4 hours to test  

Number of hours to build 'c' number of child bikes = 4c

Number of hours to test 'c' number of child bikes = 4c

One adult bike requires 6 hours to build and 4 hours to test.

Number of hours to build 'a' number of adult bikes = 6a

Number of hours to test 'a' number of adult bikes = 4a  

Number of hours taken to build bikes in one week = 120

=> 4c + 6a ≤ 120  --- (1)

Number of hours taken to test the bikes in one week = 100  

=> 4c + 4a ≤ 100 --- (2)  

Assume that

The company can build 5 child bikes and 15 adult bikes in a week

Substitute c = 5 and a = 15 in (1) and (2)

(1) => 4(5) + 6(15) ≤ 120

=> 110 ≤ 120   [ which can be true ]

(2) => 4(5) + 4(15) ≤ 100

=> 80 ≤ 100  [ which can be true ]  

From the above calculations,

Both (1) and (2) are satisfied

Therefore,

The company can build 5 child bikes and 15 adult bikes in a week.

The answer is "Yes because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100".

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Part (A) = Paired, Part (B) = Not Paired, Part (C) = Paired, Part (D) = Paired

Part A:

Compare pre- (beginning of the semester) and post-test (end of the semester) scores of students

Paired, as a subject are the same in both.

Score

A score is a group of 20 (often used in combination with a cardinal number, i.e. fourscore to mean 80), but also often used as an indefinite number.

Part B:

Assess the gender-related salary gap by comparing the salaries of randomly sampled men and women.

Not paired.

Sample

A sample is an outcome of a random experiment. When we sample a random variable, we obtain one specific value out of the set of its possible values. That particular value is called a sample. The possible values and the likelihood of each are determined by the random variable's probability distribution.

Part C:

Compare artery thicknesses at the beginning of a study and after 2 years of taking Vitamin E for the same group of patients.

Paired, as a subject are the same in both.

Vitamin E

Vitamin E is a fat-soluble vitamin with several forms, but alpha-tocopherol is the only one used by the human body.

Part D:

Assess the effectiveness of a diet regimen by comparing the before and after weights of subjects.

Paired, as a subject are the same in both.

Weight

The weight of an object refers to the force of gravity that is acting on the object. Furthermore, its calculation is mass times the acceleration of gravity, w = mg. The SI unit of weight is the newton because weight is a force.

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Compare artery thicknesses at the beginning of a study and after 2 years of taking Vitamin E for the same group of patients.

Paired, as a subject are the same in both.

Vitamin E

Vitamin E is a fat-soluble vitamin with several forms, but alpha-tocopherol is the only one used by the human body.

Answer:

Step-by-step explanation:

Answer:

Jolie will get 45.85 change

Step-by-step explanation:

34.67+19.48=54.48

100.00-54.15=45.85

There are 10.5 1/2 cup servings in a package of cheese that contains 5 1/4 cups altogether.

To find the number of 1/2 cup servings in a package of cheese that contains 5 1/4 cups altogether, we first need to convert the total amount of cheese in cups to a number of 1/2 cup servings.

We can do this by dividing the total amount of cheese by the size of a 1/2 cup serving.

First, we need to convert the amount of cheese in cups to a decimal number. Since there are two 1/2 cups in a cup, the decimal equivalent of 1/2 cup is 0.5. Therefore, the decimal equivalent of 5 1/4 cups is 5.25 cups.

Next, we need to divide the total amount of cheese in cups by the size of a 1/2 cup serving. Since the size of a 1/2 cup serving is 0.5 cups,

we can divide 5.25 cups by 0.5 cups to find the number of 1/2 cup servings as follows:

5.25 cups / 0.5 cups = 10.5

Therefore, there are 10.5 1/2 cup servings in a package of cheese that contains 5 1/4 cups altogether.

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Answer:

To determine how many weeks it will take Clare to save enough money to buy the video game, we need to find the number of weeks it will take for her to save at least $130. Let w be the number of weeks it will take for Clare to save enough money. We can set up the following inequality to represent this situation:

$48 + $5w >= $130

To solve this inequality, we can first add $48 to both sides to get rid of the constant on the left side:

$48 + $48 + $5w >= $130

This simplifies to $96 + $5w >= $130. Subtracting $96 from both sides gives us $5w >= $34. Dividing both sides by $5 gives us w >= 6.8. Since w represents the number of weeks, the solution must be a whole number. Therefore, Clare will need to save for at least 7 weeks in order to have enough money to buy the video game.

The instantaneous rate of change is -6 words per day,

the number of words Alex remembers after 5 days, option (D).

What is the instantaneous rate of change ?

An instantaneous rate is the rate at some instant in time. An instantaneous rate is a differential rate: -d[reactant]/dt or d[product]/dt. We determine an instantaneous rate at time t: by calculating the negative of the slope of the curve of concentration of a reactant versus time at time t.

Have given,

Alex learned 80 new vocabulary words

and after t days he learned,

W(t) = [tex]80 (1-0.1t)^{3}[/tex]

differentiate respect of t

W'(t) = [tex]80 \frac{d}{dt} (1-0.1t)^{3}[/tex]

W'(t) = [tex]80 * 3(1-0.1t)^{2} \frac{d}{dt}(1-0.1t)[/tex]

W'(t) = [tex]240(1-0.1*5)^{2} (0.1)[/tex]

W'(t) = 6

That's mean , the instantaneous rate of change is -6 words per day.

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The length of each individual piece is x/8

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

Number of pieces = 8

Length of timber put together = x

The length of each piece of timber is calculated as

The length of each piece = Length of timber put together/Number of pieces

Substitute the known values in the above equation, so, we have the following representation

The length of each piece = x/8

Hence, the length of each piece is x/8

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Answer:

A.) The sum will be an even integer.

Step-by-step explanation:

The conjecture that can be made about the sum of two even integers and one odd integer is that the sum will be an even integer. This is because even integers are numbers that are divisible by 2, and odd integers are numbers that are not divisible by 2.

For example, consider the sum of the even integer 6 and the odd integer 7. The sum of these two numbers is [tex]6 + 7 = 13[/tex], which is an odd integer. However, if we add another even integer to the sum, such as 4, the resulting sum is [tex]13 + 4 = 17[/tex], which is an even integer. This shows that the sum of two even integers and one odd integer is always an even integer.

This conjecture can be proven using mathematical induction. We can start by showing that the sum of any two even integers and one odd integer is always an even integer. Then, we can assume that the sum of any n even integers and one odd integer is also an even integer. Finally, we can show that the sum of n+1 even integers and one odd integer is also an even integer, using the assumption that the sum of n even integers and one odd integer is even. This will prove that the conjecture is always true.

We determined that normal distribution should be used to construct a confidence interval for these two statistical data.

In statistics, the t-distribution is a system of describing a set of data where most of the data fall close to the mean value and the remaining data adjust the tail on both sides.

The normal distribution is one of the systems of describing a set of data that implies data close to the mean value are more probable to occurrence than the other data.

In the statistics, we use t- distribution when the number of samples is less than 30 and the population standard deviation is unknown to us.

we use normal distribution when the sample size is greater than 30 and the population standard deviation is known.

We are given two set of statistical data and for both case population standard deviation is given, and the size of sample is greater than 30.

hence, we will use normal distribution for both cases.

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......,,........,.....-.......

The median would best describe the centre of the distribution for a highly skewed right histogram of US household income.  The correct option is A.

The median is the value that separates the distribution into two equal parts and is less influenced by extreme values than the mean.

Since a highly skewed right distribution has a long tail on the right side, the mean is likely to be pulled towards that tail, making it an unreliable measure of the centre.

The mode, or most frequently occurring value, may not be useful for describing the centre of a skewed distribution. The variance is a measure of the spread or dispersion of the data, not its centre.

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a) P(X = x₀, Y = 2x₀) = 1/36

P(X = x₀, Y = k) = 1/18 for k between x₀+1 and 2x₀-1 inclusive

Every other event has probability 0. x₀ is any number between 1 and 6 inclusive.

b) P(X = x₀, Y = x₀) = x₀/36

P(X = x₀, Y = k) = 1/36 for k between x₀+1 and 6 inclusive.

x₀ is between 1 and 6 inclusive. Every other event has probability 0.

c) P(X = x₀, Y = x₀) = 1/36

P(X = x₀, Y = k) = 1/18 with k between x₀+1 and 6 inclusive

x₀ between 1 and 6 inclusive. Any other event has probability 0.

Joint probability is the probability of two events happening simultaneously.

Let P(A) = probability that event A takes place and P(B) = probability that event B takes place. Then, probability of event A and B happening together i.e. P(A and B) is called joint probability.

(1) When A and B are independent events: When event A has no impact on event B or vice versa, the two events are said to be independent. For independent events, formula for joint probability is:

P(A and B) = P(A) × P(B)

Example: I am performing two acts at a time (i) tossing a coin and (ii) throwing a dice. What is the probability that the coin shows up “head” and the dice shows up “3”?

There is no doubt that getting “head” on coin and getting “3” on dice are independent events.

Probability of the coin showing up “head” = 1/2

Probability of the dice showing up “3” = 1/6

Therefore, probability of getting “head” on coin and “3” on dice = (1/2)×(1/6) = 1/12

(2) When A and B are dependent events: If event A and event B cannot be considered independent, calculation of joint probability requires knowledge of conditional probability. For dependent events, formula for joint probability is:

P(A and B) = P(A) × P(B, given A) = P(B) × P(A, given B).

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Answer:

7.8125%

Step-by-step explanation:

(4200/3200-1)/4 the difference for every month

so this would result to 7.8125% every month

Answer:

Rate = (Percentage/Base)/Time

Rate =(1 000/3 200)/4

Rate = 0.3125/4

Rate = 0.078125       (convert to percent)

Rate = 7.9%        (nearest tenth)

Step-by-step explanation:

Sphere, right cylinder and cube have more than five planes of symmetry.

Symmetry in mathematics means that when one shape is moved, rotated, or flipped, it looks exactly like the other shape. A symmetrical likeness between two halves of an object, when one half is the mirror image of the other, is defined as being proportionate and balanced. As an illustration, many shapes such as square, rectangle, and circle are symmetric along their respective lines of symmetry.

Given,

Sphere and right cylinder have more than five planes of symmetry.

The number of symmetry planes depends on each solid by definition (a figure of three dimensions). The solid is split into two congruent, mirror-imaged parts by the plane of symmetry.

A cube has nine planes of symmetry, a square pyramid has four, hexagonal prims have thirteen, and spheres and cylinders have an infinite number of planes of symmetry, according to the information presented above.

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Answer nah the correct answer is cylinders cubes and cones

Step-by-step explanation:

seen it irl on edgennuitiy

Answer

Step-by-step explanation:

The trigonometric function -cos(-x) will be not equal to cosx thus option (C) will be correct.

The trigonometric functions found in the four quadrants, as well as their graphs, domains, and differentiation and integration, will all be understood.

The trigonometric function is very good and useful in real-life problems related to the right-angle triangle.

It is known that, by cosine function property,

cos(-x) = cosx

So, -cos(-x) = -(cosx)

-(cosx) ≠ cosx

Hence "Cos(-x) will not equal cosx in the trigonometric function".

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Therease should take her 7th dose on Friday at 9:00AM

What is time ?

Time can be described in mathematics as an ongoing and continuous series of events that take place one after another, from the past through the present, and into the future. The duration of events or the gaps between them can be measured, compared, or even ordered using time.

Time is the ongoing progression of existence and things that happen in what seems to be an irrevocable order from the past, present, and forward into the future.

Time is defined by physicists as the flow of events from the past through the present and into the future. In essence, a system is timeless if it is unchanging. When describing events that take place in three-dimensional space, time can be thought of as the fourth dimension of reality.

The doctor told her to take a dose of 4.8 ml every 12 hours for 7 days.

If Theresa took her first dose at 9:00 AM on Monday,

Simply add 12 hours every time up to the 7th dose,

First dose  ----> 9:00 AM on Monday,

Second dose  ----> 9:00 PM on Monday,

Third dose  ----> 9:00 AM on Tuesday,

Fourth dose  ----> 9:00 PM on Tuesday,

Fifth dose  ----> 9:00 AM on Thursday,

Sixth dose  ----> 9:00 PM on Thursday,

Seventh dose  ----> 9:00 AM on Friday,

Hence, Theresa should take her 7th dose at 9:00 AM on Friday.

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[tex]\frac{1}{(7x)^2}[/tex] is the expression without negative exponents.

What are exponents and indices?

Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself.

An index, or power, is the small floating number that appears after a number or letter. The plural of index is indices.

According to the given question:

(7x)^{-2} is the given indices expression

To expression without negative exponent, the expression

can be written as

[tex](7x)^{-2} = \frac{1}{(7x)^2}[/tex]

Since the exponent -2 is on the whole 7x term. So, the whole term moves to denominator to make the exponent positive.

Therefore [tex]\frac{1}{(7x)^2}[/tex] is the expression without negative exponents

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Step-by-step explanation:

The dance committee expects attendance to number within 25 of last year's 87 students can be expressed using an inequality involving absolute value as:

|x - 87| <= 25

This inequality states that the absolute difference between the number of students attending the dance (x) and 87, which was the number of students attending last year, must be less than or equal to 25. This means that the number of students attending the dance this year must be within 25 of the number of students attending last year.

Answer:

12/27 = 4/9

Step-by-step explanation:

Solve for ?:

?/27 = 4/9

Multiply both sides of ?/27 = 4/9 by 27:

(27 ?)/27 = 27×4/9

27×4/9 = (27×4)/9:

(27 ?)/27 = (27×4)/9

(27 ?)/27 = 27/27×? = ?:

? = (27×4)/9

27/9 = (9×3)/9 = 3:

? = 3×4

3×4 = 12:

Answer: ? = 12

Answer:

12/27 = 4/9

Step-by-step explanation:

To get from one fraction to the other, you must find out what the denominator of the fraction we know (4/9) is being multiplied by to get the denominator of ?/27.

We divide 27 by 9 to get 3 then multiply the numerator (4) by 3 as well to get 12, your answer.

Answer:

Equation 2: y=750-100x

Step-by-step explanation:

In the arrangement of letters and numericals, the total number of different paths can one spell AMC8 are 24 in count.

A basic counting principle is that if there are p ways to do one thing and q ways to do another, then there are p × q ways to do both. Possible results of experiments. The counting principle can be extended to situations where there are two or more alternatives.

We have, the arrangement of letters and numericals in above figure such that

There are three different kinds of paths that are on the above diagram to get the required pattern. The first kind is when you directly count A, M, C in a straight line. The second is when you count A, turn left or right to get M, then go up or down to count 8 and C. The third is the one where you start with A, move up or down to count M, turn left or right to count C, then move straight again to get 8.

There are 8 paths for each kind of path, making for 8×3= 24 paths.

Hence, the required paths are 24 in count.

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Solving a system of equations we will see that they need to use:

Let's define the variables:

x = kilograms of the 10% fat-content chocolate.

y = kilograms of the 30% fat-content chocolate.

We know that they want to create 100kg, then:

x + y  =100

And the fat content must be 18%, then we can write the concentration equation:

0.1*x + 0.3*y = 0.18*100 = 18

The coefficients are the percentages in decimal form.

Now we have a little system of equations:

x + y  =100

0.1*x + 0.3*y = 18

Isolating x on the first one we get:

x = 100 - y

Replacing that in the other equation we get:

0.1*(100 - y) + 0.3*y = 18

10 + 0.2*y = 18

0.2*y = 18 - 10 = 8

y = 8/0.2 = 40

They need to use 40kg of the 30% chocolate and 60kg of the 10% chocolate.

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Answer:

year 1: 90% × 245000 = 220500

year 2: 90% × 220500 = 198450

year 3: 90% × 198450 = 178605

∴ the car price after 3 years is 178605

explanation:

the value of car decreases 10%. that means the car price is 90%

The price of the car after 3 years will be 178605

We can calculate the value in the following way

Rate of decrease in car's price: 10%

Current price of the car: 245000

Value after 1 year, say value1= current value-10% of current value

[tex]value1=245000-\frac{10*245000}{100}[/tex]

=245000-24500

=220500

After 1 year, the next decrement in the price will be based on the value of the car in that year. In other words, we calculate the value after the second year by decreasing by 10% of value1.

Value of car after 2 years, say value2= value1- 10% of value1

[tex]value2=220500- (\frac{10*220500}{100})[/tex]

=220500-22050

=198450

Similarly,

Value of car after 3 years, say value3= value2- 10% of value2

[tex]value3=198450- (\frac{10*198450}{100})[/tex]

=198450-19845

=178605

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The original price is $1049 and the amount saved is $321

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

Cost after discount = $728

Discount = 30% off

The original price is calculated as

Cost after discount = Original price * (1 - Discount)

So, we have

Original price = Cost after discount/(1 - Discount)

This gives

Original price = 728/(1 - 30%)

Evaluate

Original price = 1049

Here, we have

Amount saved = Original price - Cost after discount

So, we have

Amount saved = 1049 - 728

Evaluate

Amount saved = 321

Hence, the amount saved is $321

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Answer: the answer to a is 50% chance the answer to b is also 50% chance

Step-by-step explanation:

a) The type of function for each case is given as follows:

b) The functions for each house are given as follows:

c) The value of each house after 25 years is given as follows:

There is a significant difference in these valuations, as an exponential function increases faster than a linear function.

A function is classified as exponential if when the input variable is changed by one, the output variable is multiplied by a constant.

Hence House 1 is an exponential function, as:

312519.92/303417.40 = 303417.40/294580 = 1.03.

And the definition is given as follows:

294580(1.03)^x.

The value of the house after 25 years is given as follows:

294580(1.03)^25 = $616,785.10.

A function is classified as linear if when the input variable is changed by one, the output variable is increased/decreased by a constant.

Hence House 2 is a linear function, as each year, the value of the house is increased by 9000.

Then the definition is given as follows;

295000 + 9000x.

The value of the house after 25 years is given as follows:

295000 + 9000(25) = $520,000.

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The graph of g is the graph of f translated up 7 units

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

g(x) = f(x) + k

Also, we have the value of k to be

k = 7

From the question, we can interpret g(x) = f(x) + k as f(x) is shifted up by k units

This means that

g(x) = f(x) + k

So, we have

g(x) = f(x) + 7

Hence, the transformation is (a) translated up 7 units

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