What is the relationship between doubling and halving?

Answer:

23.8

Step-by-step explanation:

Solve for the missing side, x, by using the pythagorean theorem:

5² + 3² = x²        **(8-5=3)

x² = 25+9 = 34

x = √34 = 5.831

P = sum of all sides = 5 + 5 + 8 + 5.831 = 23.8

This is an algebraic word problem and it evaluated to be 10 years time before the age of the man will be twice the age of the daughter.

In algebraic word problems, we can represent an unknown number using letters and then carry out basic mathematics operations to get the value of the unknown number.

We shall represent the number of years it will be before the age of the man will be twice the age of the daughter with the letter x so that;

38 + x = 2(14 + x) {open bracket}

38 + x = 28 + 2x

38 - 28 = 2x - x {collect like terms}

10 = x

also x = 10.

Therefore, the agebraic word problem have a solution of 10 years before the age of the man will be twice the age of the daughter.

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A room classified as a group a-2 occupancy has dimensions of 60 feet by 80 feet and is in a sprinklered building. the minimum required separation distance from the nearest exit door is  r is 50 feet

This is determined by the occupancy type of the room, which is classified as a Group A-2 occupancy. According to the International Building Code, Group A-2 occupancies are those that involve assembly uses with an occupant load of 50 or more and with fixed seating. Therefore, the minimum required separation distance from the nearest exit door is 50 feet.  

To calculate this, I referred to the International Building Code (IBC) Chapter 10, which outlines the requirements for means of egress. Section 1020.1 of the IBC states that the required separation distance between an exit door and the nearest obstruction must be at least half the length of the maximum overall diagonal dimension of the room. Since the room has dimensions of 60 feet by 80 feet, the maximum overall diagonal dimension is 100 feet.

Therefore, half of this distance is 50 feet, which is the minimum required separation distance from the nearest exit door.   In addition, the IBC also requires that Group A-2 occupancies be sprinkled, which the room in question is. This means that there may be additional requirements for separation distances for the egress system depending on the specific type of sprinkler system being used.

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a room classified as a group a-2 occupancy has dimensions of 60 feet by 80 feet and is in a sprinklered building. what is the minimum required separation distance from the nearest exit door?

The first equation can be multiplied by -5 to reverse the sign on the x-coefficient: -10x + 30y = 50.

The second equation can be multiplied by -2 to reverse the sign on the y-coefficient: 4x - 4y = -80. To solve these equations, we can add them together, which will eliminate the y-variable and leave us with the x-variable. The equation that results is 6x = -30, which can be solved by dividing both sides by 6 to get x = -5. We can then substitute x = -5 into either of the original equations to find the value of y. For example, when we substitute x = -5 into the first equation, we get -10(-5) + 30y = 50, which simplifies to 50 + 30y = 50, and then 30y = 0, so y = 0. Therefore, the solution to the system is x = -5 and y = 0.

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Answer:

a = 0

(0,3)

Step-by-step explanation:

The total balance in John's account after depositing his paycheck is, 800.47.

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

We have to given that;

The balance in John's account before depositing his paycheck = 249.50

And, He deposit 550.97 in his account.

Here, The balance in John's account before depositing his paycheck = 249.50

Hence, The total balance in John's account after depositing his paycheck is,

⇒ 249.50 + 550.97

⇒ 800.47

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The number of ways in which we can choose four members of the club to serve on the executive committee is 12650 ways.

The act of placing all the components of a set into a certain sequence or order is known as permutation in mathematics. In other terms, the process of permuting is the reordering of the elements of a set if the set is already ordered. Contrary to permutations, the order of selection is irrelevant when choosing elements from a collection using the combination method.

Given that the total number of members in the club is 25.

To choose four executive members for the committee we use the formula of combinations given as follows:

[tex]nCr = \frac{n!}{(n-r)! r!}[/tex]

Substituting the value of n= 25 and r = 4:

[tex]25C 4 = \frac{25!}{(25 -4)! 4!}\\\\\\25C 4 = 12650\\[/tex]

Hence, the number of ways in which we can choose four members of the club to serve on the executive committee is 12650 ways.

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Answer:

8.15

Step-by-step explanation:

halfway means the middle value. Therefore the mean.

(8 + 8.3)/2

= 8.15

Answer:

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

Step-by-step explanation:

the equation of a line in slope- intercept form is

f(x) = mx + c ( m is the slope and c the y- intercept )

given f(- 5) = 2, that is when x = - 5 , y = 2

f(7) = - 4, that is x = 7, y = - 4

the 2points (- 5, 2 ) and (7, - 4 ) lie on the line

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 5, 2 ) and (x₂, y₂ ) = (7, - 4 )

m = [tex]\frac{-4-2}{7-(-5)}[/tex] = [tex]\frac{-6}{7+5}[/tex] = [tex]\frac{-6}{12}[/tex] = - [tex]\frac{1}{2}[/tex] , then

f(x) = - [tex]\frac{1}{2}[/tex] x + c ← is the partial equation of the line

to find c substitute either of the 2 points into the partial equation

using (- 5, 2 ) , then

2 = - [tex]\frac{1}{2}[/tex] (- 5) + c = [tex]\frac{5}{2}[/tex] + c ( subtract [tex]\frac{5}{2}[/tex] from both sides )

- [tex]\frac{1}{2}[/tex] = c

f(x) = - [tex]\frac{1}{2}[/tex] x - [tex]\frac{1}{2}[/tex] ← equation of line

Answer:

0.850

Step-by-step explanation:

The first step is to write the number in standard form. Then, you place the decimal point in the quotient above the decimal point of the dividend. Then, divide and bring down the other digits such as hundredths, thousandth, and ect.

Runge Kutta method is used for finding approximate solution of differential equation

The term differential equation in math is defined as method of finding the derivative of a function.

This process is used to find the instantaneous rate of change in function based on one of its variables and the common example is the rate change of displacement with respect to time, called velocity.

Here we have to identify the method that is  is used for finding approximate solution of differential equation

As per the definition of differential equation, here we have know that the best suitable method for the given situation is Runge Kutta method.

Because in this method we have done  provides the approximate value of y for a given point x and it only the first order ODEs can be solved using the Runge Kutta RK4 method.

Therefore, the correct option is (c).

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The scale factor from the cliff in the drawing to the actual cliff is equal to 1/3.

In Geometry, a scale factor is the ratio of two corresponding side lengths or diameter in two similar geometric figures, which can be used to either horizontally or vertically enlarge (increase) or reduce (decrease or compress) a function that represents their size.

Mathematically, the scale factor of a geometric figure can be calculated by dividing the dimension of the image by the dimension of the pre-image (actual figure):

Scale factor = Dimension of image (new figure)/Dimension of pre-image(original figure)

Scale factor = 12/36

Scale factor = 1/3.

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Answer:

Step-by-step explanation:

36ft/12in

36 divided by 12 =3 feet per inch

Answer:

Step-by-step explanation:

Add 25% of 120 to 120

and you get 150 so boom there it is

Answer : 25% difference

y-intercept: (0,19)

The y-intercept of an equation is the point where the graph of the equation crosses the y-axis. In this case, when x = 0, the equation simplifies to y = 19, so the y-intercept of the graph is (0, 19).

The coefficient of the x² term is 0.9, which is positive, so the parabola opens upwards.

So the answer is

Parabola opens upward.

The third side of the right angle triangle is 5 units.

A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

Therefore, the side of the right triangle can be found using Pythagoras's theorem as follows:

c² = a² + b²

where

Therefore, using Pythagoras's theorem,

6² - (√11)² = b²

36 - 11 = b²

b² = 25

square root both sides of the equation

b = √25

b = 5 units

Therefore.

third side = 5 units.

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A ratio table is a way to compare two or more related quantities. To write a ratio table in 7th grade, you need to:

1. Identify the two or more related quantities you are comparing.

2. Create a table with two columns. Label the first column with the first quantity and the second column with the second quantity.

3. Put the combined ratio in the first row of the table.

4. Put the ratio for the first quantity in the second row of the table.

5. Put the ratio for the second quantity in the third row of the table.

6. In the fourth row, put the combined ratio of the ratios from the previous rows.

7. Repeat steps 4-6 until you have the desired number of rows.

8. Check to make sure that all of the ratios in the table are equivalent.

Once you have completed these steps, you should have a completed ratio table

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A function that represents the balance y (in dollars) of the investment account after t year is y = $120 × (1 + 0.064/4)^(4t).

The balance of an investment account is the sum of all deposits and withdrawals to/from an investment account, considering the manager's compensation calculation.

After the trading interval ends and compensation is paid out, the account balance will equal the equity.

Let y be the investment account balance (in dollars) after t years. Then,

y = $120 × (1 + 0.064/4)^(4t)

Where the interest rate is 6.4% and is compounded quarterly.

So the interest rate per quarter is 0.064/4.

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The equation of a curve which intersects at right angles every curve of the family y = 1 / x + k is: y = x^3 / 3. The correct option is D.

The given equation:

y = 1/x + k.

And since y’ = –1 / x^2

So, the desired curve satisfies:

y’ = x^2

From the given equation we get:

dy / dx = –1 / x^2

any suitable function would have the negative reciprocal slope, so:

df / dx = x^2 / 1 = x^2

So, f(x) = x^3 / 3

Hence, the equation that intersects at right angles of  y = 1 / x + k is y = x^3 / 3.

Generally, an intersection curve consists of the common points of two transversally intersecting surfaces, which means that at any common point the surface normal are not parallel. This restriction excludes cases in which the surfaces are touching or have surface parts in common.

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It is possible for this statement to be true for a vending machine that occasionally dispenses more or less than 6 oz of coffee per cup.

The term "on average" or "on the average" refers to the mean or expected value of a distribution. The vending machine may have some variations in the amount of coffee it dispenses, but on average it dispenses 6 oz of coffee per cup.

It is possible that the vending machine may dispense more or less than 6 oz of coffee per cup due to machine variations, incorrect calibration, or maintenance issues. However, as long as the mean or average amount of coffee dispensed over a certain period of time is 6 oz per cup, the statement is considered true.

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Answer:

f(y - 3) = y - 2

Step-by-step explanation:

to find f(y - 3) , substitute x = y - 3 into f(x) , that is

f(y - 3) = y - 3 + 1 = y - 2

The radius of convergence of series (cn dn)xn is 14.

The radius of convergence of a power series (cn xn) is the distance from the origin to the point beyond which the series no longer converges. It is denoted by R and it's calculated by using the formula:

R = 1/lim sup|cn|^(1/n)

The radius of convergence of a product of two series (cn xn) and (dn xn) is the minimum of the radius of convergence of the individual series.

So, in this case, since the radius of convergence of the series cn xn is 14 and the radius of convergence of the series dn xn is 15, the radius of convergence of the product series (cn dn)xn is

min(14, 15) = 14

Therefore, the radius of convergence of the product series (cn dn)xn is 14.

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The final velocity and displacement after 5 seconds are 19.3m/s and 59m and the acceleration is 0.7m/s²

The equations of motion are a set of mathematical equations that describe the motion of an object in terms of its position, velocity, and acceleration. These equations are used in physics, engineering, and other fields to predict and analyze the motion of objects.

The equations are;

v = u + at ...eq(i)

v² = u² + 2as ...eq(ii)

s = ut + 1/2 at² ...eq(iii)

2.

From the first equation of motion;

v = u + at

v = 4.3 + 3(5)

v = 19.3m/s

The displacement after 5 minutes will be

From third equation of motion;

s = ut + 1/2 at²

s = 4.3 * (5) + 1/2(3)(5)²

s = 59m

1)

distance = 1.0 * 10²m

time = 12.11s

acceleration = ?

Acceleration = velocity / time

velocity = distance / time

velocity = 1.0×10² / 12.11

velocity = 8.23m/s

acceleration = velocity / time

acceleration = 8.23 / 12.11

acceleration = 0.7 m/s²

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Kathy can make 10 headbands from 3/4 of a yard of fabrics.

An equation is an expression composed of variables and numbers linked together by mathematical operations.

The unit rate is the ratio of two different units. The unit rate must always have a denominator equal to 1.

Kathy has 3/4 of a yard of fabric. She needs 3/10 of a yard to make a 4 headband.

Hence:

3/10 yards = 4 head band

For 3/4 yard:

number of headbands = 3/4 yard * 4 headband per 3/10 yard = 3/4 * 4 / (3/10) = 3/4 * 4 * 10/3 = 10

Kathy can make 10 headbands

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Answer:

2x^2 + 8x + 3 in 2( x + 2 )^2 + q form is 2( x + 2 )^2 - 5

Answer:

it would be the 3rd one I did this in middle school

Step-by-step explanation:

pls give brainly if It's right

A single ticket's estimated earnings are around -$0.9442, which indicates that a consumer may expect to lose approximately $0.9442 for each ticket purchased.

To find the expected winnings of a single ticket, we need to calculate the weighted average of the winnings based on the probabilities of winning each prize.

The probabilities of winning each prize are as follows:

1st prize: 1 winner out of 10,000 tickets sold (probability = 1/10,000 = 0.0001)

2nd prize: 3 winners out of 10,000 tickets sold (probability = 3/10,000 = 0.0003)

3rd prize: 5 winners out of 10,000 tickets sold (probability = 5/10,000 = 0.0005)

Consolation prize: 20 winners out of 10,000 tickets sold (probability = 20/10,000 = 0.0020)

No prize: (1 - (probability of winning any prize)) = 1 - (0.0001 + 0.0003 + 0.0005 + 0.0020) = 0.9971

Now, let's calculate the expected winnings:

Expected winnings = (Probability of 1st prize × $3000) + (Probability of 2nd prize × $1000) + (Probability of 3rd prize × $500) + (Probability of consolation prize × $100) + (Probability of no prize × -$2)

Expected winnings = (0.0001 × $3000) + (0.0003 × $1000) + (0.0005 × $500) + (0.0020 × $100) + (0.9971 × -$2)

Expected winnings ≈ -$-0.9442

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The complete question:

A club is holding a raffle. Ten thousand tickets have been sold for $2 each. There will be a 1st prize of $3000, 3 second prizes of $1000 each, 5 third prizes of $500 each and 20 consolation prizes of $100 each. Find the expected winnings of a single ticket.

x  -2        98        498      998     2998

p  .9971  .0020  .0005  .0003   .0001

2.21 × 10^20 is expressed in scientific notation.

What does scientific notation consist of?

Writing extremely large or extremely small numbers is done using scientific notation. When a number in the range of 1 to 10 is multiplied by a power of 10, the result is represented in scientific notation.

                         For instance, 650,000,000 can be expressed using scientific notation as 6.5 108. In scientific notation, a number is expressed in the form n10ab, where an is an integer such that 1|a|10 and b is also an integer.

The decimal point has to go 20 places to the left to give the number 2.21; that means the exponent on the 10 is 20.

= 2.21E20

= 2.21 × 10^20

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Answer:

Probably  c:  f(x) = y + 3

Step-by-step explanation:

See attached worksheet

Answer: For the first geometric sequence, the missing value is:

1 = -3/2, -2 = 7

To find the missing value, we can use the formula:

an = ar^(n-1)

Where a1 is the first term, r is the common ratio, and n is the term number.

So we know that:

a1 = 1, r = -3/2, n = 3

Plugging these values into the formula:

an = ar^(n-1)

an = 1 * (-3/2)^(3-1) = 1 * (-3/2)^2 = 1 * 9/4 = 9/4

So the missing value is 9/4.

For the second geometric sequence, the missing value is:

2 = 6, 7 = 192

To find the missing value, we can use the formula:

an = ar^(n-1)

Where a1 is the first term, r is the common ratio, and n is the term number.

So we know that:

a1 = 2, r = 7/6, n = 11

Plugging these values into the formula:

an = ar^(n-1)

an = 2 * (7/6)^(11-1) = 2 * (7/6)^10 = 2 * (7/6)^10 = 2 * 7^10 / 6^10 = 9261

So the missing value is 9261.

Step-by-step explanation:

The equation y = 3x describes the relationship between x and y in the table.

What is the slope intercept?

The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line. An example of a linear equation is y=mx + b.

A relationship that when graphed produces a straight line. Equation. A mathematical sentence that sets 2 expressions equal to each other.

This equation shows that for every increase of 1 in the value of x, y increases by 3.

This is consistent with the values in the table, where for each increment of 1 in x, y also increases by 3.

Hence, The equation y = 3x describes the relationship between x and y in the table.

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