Translate the following sentence into a mathematical equation. Use A to represent the area, and C to represent the circumference. The area of a circle is the product of the number 1/4(pi) and the square of the circumference 

The largest possible value for the probability of A4 is 0.2000

Since A1, A2, A3, and A4 are events from a common sample space, the sum of their probabilities must be less than or equal to 1.

So, the sum of the probabilities of the events can be expressed as:

P(A1) + P(A2) + P(A3) + P(A4) = 1

From the question, we have

P(A1) = P(A2) = P(A3) = 0.3

Also, we have that

Al and A2 occur simultaneously with a probability of 0.1

This means that the initial equation becomes

P(A1) + P(A2) - P(A1 and A2) + P(A3) + P(A4) = 1

Where

P(A1 and A2) = 0.2

So, we have

0.3 + 0.3 - 0.1 + 0.3 + P(A4) = 1

Evaluate the like terms

P(A4) = 0.2

Hence, the probability is 0.2

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The estimation of the numbers given as 0.87 × 310 will give 270.

You must approximate (eliminate or round off) the decimals to obtain whole numbers before you can use the whole numbers to find the product of two decimals using estimation.

A figure is discovered through estimation.

A value, amount, or size that rounds off to the nearest whole number is said to be approximating.

The estimation of the numbers given as 0.87 × 310 will give:

= 0.9 × 300

= 270.

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Step-by-step explanation:

(b)

logx . logx = 2log x

logx = 2

so x = 100

(c)

2x + 3x= 10

5x = 10

so ×=2

Answer:

The company's largest rug dimensions are either 18 ft by 27 ft Or 12 ft by 18 ft.

Step-by-step explanation:

Given:

Dimension of the smaller rug are 2 ft by 3 ft.

Also One side of the largest rug is 18 ft.

We need to find the possible dimension of largest rug.

Also Given:

Both the smaller rug and larger rugs are similar.

Now By Similar rectangles property which states that;

"When 2 rectangles are similar then their lengths are in proportion."

In this case there are 2 possibilities.

either the largest rug's 18 ft side is similar to the 2 ft side or the 3 ft side

Now let us consider the other side be 'x'.

Now when he largest rug's 18 ft side is similar to the 2 ft side we get;

Now when he largest rug's 18 ft side is similar to the 3 ft side we get;

Hence the company's largest rug dimensions are either 18 ft by 27 ft OR 12 ft by 18 ft.

The sampling distribution is approximately normal.

What is the standard deviation?

Standard Deviation is calculated by first squaring the differences between the observations and the mean and then taking the square root of the sum of the squares of the differences divided by the number of observations - 1.

The Central Limit Theorem tells us that the sampling distribution for the population proportion is approximately normal.

The mean of the sampling distribution is equal to the true population proportion and the standard deviation of the sampling distribution is equal to the true population proportion times (1 - true population proportion) divided by the sample size.

So, the sampling distribution is approximately normal, with the true population proportion as its mean and the true population proportion times (1 - true population proportion) divided by the sample size as its standard deviation.

Hence, the sampling distribution is approximately normal.

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The inequality equation which represents Ten less than twice a number is equal to at least 52 is 10 - 2x ≥ 52 and x ≤ -21

Let

The unknown number = x

Ten less than twice a number is equal to at least 52;

10 - 2x ≥ 52

Subtract 10 from both sides

- 2x ≥ 52 - 10

- 2x ≥ 42

divide both sides by - 2

x ≤ 42/-2

x ≤ -21

Hence, x ≤ -21 is the solution to the inequality 10 - 2x ≥ 52 if x comes first.

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The new revenue can be calculated as R = q*p = 2,000*4 = $8,000.

R(q) is the revenue function for the school lunch program, which is given by the equation q*p, where q is the quantity and p is the price. According to Braley and Nelson's study, the city of Pittsburgh had an increase in price of school lunches. The revenue can be calculated by multiplying the quantity (q) of school lunches with the new price (p) after the increase. Therefore, the new revenue (R) can be calculated by R = q*p. As an example, if the quantity of school lunches is 2,000 and the price is increased to $4, then the new revenue can be calculated as R = q*p = 2,000*4 = $8,000.

R(q) is the revenue function for the school lunch program, which is given by the equation q*p, where q is the quantity and p is the price. According to Braley and Nelson's study, the city of Pittsburgh had an increase in price of school lunches. The revenue can be calculated by multiplying the quantity (q) of school lunches with the new price (p) after the increase. Therefore, the new revenue (R) can be calculated by R = q*p. As an example, if the quantity of school lunches is 2,000 and the price is increased to $4, then the new revenue can be calculated as R = q*p = 2,000*4 = $8,000.

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the annual expenditure of the US federal government is 4 trillion dollars and dollar bill is 0.001m then, the length of four trillion dollars would be 4×[tex]10^{9}[/tex] m

Government spending or expenditure includes all government

consumption, investment, and transfer payments. In national income accounting, the acquisition by governments of goods and services for current use, to directly satisfy the individual or collective needs of the community, is classed as government final consumption expenditure.

Since we have given that annual expenditure = 4 trillion dollars,

1 dollar bill = 0.0001m

so, the thickness would be.

[tex]4*10^{12} *0.001\\\\=4*10^{12}*10^{-3}\\\\=4*10^{9}[/tex]

the length of 4 trillion dollars would be. 4×[tex]10^{9}[/tex]

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Answer:

1 tube of paint is $2.25.

Step-by-step explanation:

We can set this as an equation first. Since we know that the canvas is $6.95 and the total is $24.95, those are the values that we will work with to determine the tube price. We can set the tube price as 8x, x being the tube price, and 8 being the number of tubes Ishi plans to buy. Now, we can set an equation:

6.95 + 8x = 24.95

8x = 18

x = 18/8 (simplified is 9/4, or 2.25)

Answer:

$ 2.25

Step-by-step explanation:

A= $6.95

B= (Cost of each tube) x 8

C= $24.95

A+B = C

The height that the ladder reaches on the building is 10.7 feet

An equation is an expression that uses mathematical operations to show the relationship between numbers and variables. Types of equations are linear, quadratic, cubic and so on.

Trigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.

A 14-foot ladder is leaning against a building. The ladder makes a 50° angle with the ground. Let h represent the height of the building. Using trigonometric ratio:

sin(50) = h/14

h = 14 * sin(50)

h = 10.7 feet

The height is 10.7 feet

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Answer:

$902.36

Step-by-step explanation:

820.33 times 10% = 82.033

add 82.033 to 820.33

820.33 + 82.033 = 902.363

The measure of r is 24°

The opposing angles created by the junction of two lines are known as vertically opposite angles or vertical angles. A pair of angles that are vertically opposed to one another is always equal.

Additionally, the vertical angle and its adjacent angle add up to 180° which is said to be a supplementary angle.

Here we have

3 straight lines are met at a point  

Let's name each name as l, m, and n as the given figure

From the line l  

=> ∠LOM + ∠MON + 122° = 180°  [ Pairs of Linear angles ]

=>  34° + ∠MON + 122° = 180°  

=> ∠MON = 180° - 122°- 34°

=>  ∠MON = 24°  

Here

∠MON and r are two vertically opposite angles

As we know vertically opposite angles are equal

=> r = 24°    

Therefore,

The measure of r is 24°

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Scalar quantities of these do not include direction distance, Force, Acceleration, or Velocity.

scalar, a physical quantity whose sole description is its magnitude. Scalars include, but are not limited to, time, energy, mass, volume, density, and speed.

A scalar quantity is one that doesn't depend on movement in any direction. Vector quantities can have a magnitude and a direction. Scalar quantities have just a magnitude.

All of the option values are scalar, with the exception of impulse. A force can be an impulse. Similar to force, it has both magnitude and direction.

Additional examples of scalar quantities are mass, velocity, distance traveled, time passed, energy, density, volume, temperature, work, etc.

Since speed has a simple magnitude and no discernible direction, it is a scalar number.

A scalar quantity is something like distance. Any quantity that has both a direction and a magnitude is a vector.

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The obtained Z score for the following blood pressures =-2

Enter data in Excel work sheet and use the formulae

=VAR(A1:A6)  and =VAR(B1:B6)  to get the variance

Variance for

Men aged 20-29=42.97

Men aged 60-69=211.77

The variance is substantiaaly larger for the set of blood pressures of men aged 60-69

Enter the data in Excel worksheet and use =AVERAGE(A1:A15) to find mean and calculate is the mean

Mean=15833.33 and is to calculated for finding relative position

Z=38-(27*10)=-232Z=262.7-(200*57)=-11,137.3

Hence 262.7 has higher relative position

=[48-70]/11=-2

Z score=-2

The calculated Z score for the subsequent blood pressures is therefore = -2.

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Answer:37,396

Step-by-step explanation:

The least common denominator or LCD of the given fractions  1/2x-6 and 2x/7x-21 is (2x-6)(7x-21)

A fraction can simply be defined in mathematics as the part of a whole variable or number.

Some types of fractions in mathematics are;

The least common denominator of a fraction is seen as the lowest or smallest number in all the common multiples of the denominator given.

Given the information, the fractions are;

1/2x-6 and 2x/7x-21

It is crucial to identify that the denominator of the two fractions are;

(2x-6)(7x-21)

They are in form of algebraic expressions, thus, the  least common denominator is the product of the expression.

Hence, the lowest common denominator is (2x-6)(7x-21)

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Answer:

Rate : 1 page for every 4 students.  

Unit Rate: 500 pages per ream.40 pages for every blooket.15 pages for evry blooket

Neighter: 25 pages

Step-by-step explanation:

I hope this helps :)

The diffrence between unit rate and rate is the unit rate refers to those rates in which the numerator is 1. Rate would be like there is 1 person per car. Unit rate would mean There are 3 cars for each person.

The measure of ∠ADB is equivalent to 90°.

Geometry is a branch of mathematics that deals with shapes, sizes, angles, and dimensions of objects.

Given is a geometrical image as shown.

We can write -

∠ADC = ∠ADB + ∠BDC

(- 3c + 120°) + (- 10 c + 145°) = 135°

- 3c + 120° - 10c + 145° = 135°

- 13c + 265° = 135°

265° - 135° = 13c

13c = 130

c = 10

Now -

∠ADB = (- 3c + 120) = 90°

∠ADB = 90°

Therefore, the measure of ∠ADB is equivalent to 90°.

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Answer:

6 days

Step-by-step explanation:

12 workers will clean up in 4 days

how many days would it take 8 workers?

let the number of days be x

x=(12×4)/8

x= 6 days

The minimum amount of paint needed to paint the walls of the room would be 2,2 gallon.

To calculate the amount of paint we need to paint the walls of the room we must calculate the area of each of the walls, in this case it would be 4 rectangles with the following dimensions:

According to the above, the area of the walls would be:

Based on the above, it can be inferred that 2.2 gallons of paint are needed to paint all the walls.

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Answer: Yes

Step-by-step explanation:

Answer:

[tex] \sf \textbf{8.608} \: is \: a \: rational \: number[/tex]

Step-by-step explanation:

Rational Numbers: Any number that can be written as a ratio (or fraction) of two integers is a rational number.

Since Zach isolated x^2 in the first equation and then substituted it into the second equation, the resulting equation is equal to: C. 25 - y^2/16 - y^2/9 = 1.

In Mathematics, an equation is sometimes referred to as an expression and it can be defined as a mathematical expression which shows that two (2) or more quantities are equal.

From the information provided above, we have the following system of equations;

x^2 + y^2 = 25 ....... equation 1.

x^2/16 - y^2/9 = 1   ....... equation 2.

By making x^2 the subject of formula in equation 1, we have the following:

x^2 = 25 - y^2     ....... equation 3.

By substituting equation 3 into equation 2, we have the following:

25 - y^2/16 - y^2/9 = 1

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The value of the expression 59 + (1/6)r at r = - 1/2 will be 707/12.

When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expression is given below.

⇒ 59 + (1/6)r

The value of the expression at r = - 1/2 will be given as,

⇒ 59 + (1/6)(-1/2)

⇒ 59 - 1 / 12

⇒ (708 - 1) / 12

⇒ 707 / 12

The value of the expression 59 + (1/6)r at r = - 1/2 will be 707/12.

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The solution for h according to the given equation a = bh as required is; h = a / b.

It follows from the task content that the solution for the given equation for variable, h be determined.

On this note, since the given equation is;

a = bh

To solve for variable, h; divide both sides of the equation by b so that we have;

h = a / b.

Ultimately, the required solution for variable, h is; h = a / b.

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It is in good conditions, the automobile travels at 57 mph.

Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.

A scalar quantity known as distance measures "how much ground an object has traversed" while moving. The term "how far out of place an object is" is referred to by the vector quantity displacement, which is the object's overall change in position.

Simply draw a vector from your initial position to your destination and solve for the length of this line to determine displacement. In the case of a circular 5K path, where your beginning and ending positions are identical, your displacement is 0. Displacement in physics is denoted by s.

"A automobile moves 20 mph more slowly in heavy rain than in bright sunshine."

x - 19 = y

where "x" stands for speed in good weather and "y" stands for speed in bad weather.

"The same distance is covered by the car in two hours in the sun as it is in three hours in the rain."

2x = 3y

where "x" stands for speed in good weather and "y" stands for speed in bad weather.

The speed of the car in good weather, or "x," is what we are looking for. In the second equation, substitute the first equation's value for the variable "y."

x - 19 = y

2x = 3y

2x = 3 (x - 19)

Distribute:

2x = 3x - 57

3x off on both sides equals:

-x = -57

Give both sides a -1:

x = 57

It is in good conditions, the automobile travels at 57 mph.

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Answer:

The derivative of the function f(x) = 3x² + 2√x - 4x at x=1 is

[tex]\boxed{f'(1) = 3}[/tex]

Step-by-step explanation:

We have f(x) = 3x² + 2√x - 4x

[tex]f'(x) = \dfrac{d}{dx}\left(3x^2+2\sqrt{x}-4x\right)\\\\=\dfrac{d}{dx}\left(3x^2\right)+\dfrac{d}{dx}\left(2\sqrt{x}\right)-\dfrac{d}{dx}\left(4x\right)\\\\[/tex]

[tex]\dfrac{d}{dx}\left(3x^2\right) = 6x\\\\[/tex]

[tex]\dfrac{d}{dx}\left(2\sqrt{x}\right) = 2\dfrac{d}{dx}\left(\sqrt{x}\right)\\\\=2\dfrac{d}{dx}\left(x^{\frac{1}{2}}\right)\\\\= =2\cdot \dfrac{1}{2}x^{\frac{1}{2}-1}\\\\\\=\dfrac{1}{\sqrt{x}}\\\\[/tex]

[tex]\dfrac{d}{dx}\left(4x\right)=4[/tex]

Therefore

[tex]f'(x) = 6x+\dfrac{1}{\sqrt{x}}-4\\\\f'(1) = 6(1) + \dfrac{1}{\sqrt{1}} - 4\\\\f'(x) = 6 + 1 - 4\\\\f'(x) = 3\\\\[/tex]

The answer is 9n²-48n+64

The  95% confidence interval for the true average dollar loss in burglaries rounded to the nearest dollar amount is 629 to 727

The variance of  a variate X is the arithmetic mean of the squares of all the deviations of X from the arithmetic mean of the observations and it is denoted by Var(X) or σ². The spread of statistical data is measured by the standard deviation. Distribution measures the deviation of data from its mean or average position. The positive square root of the variance of a variate X is known as the standard deviation.    

Given here: Sample mean x=678, Sample size n=500, Standard deviation σ=560

Standard error=σ.x=σ/√n

                               =560/√500

                               =25.044

Now for a 95% Class interval the value of z=1.960

The margin of error, E=Z×standard error

                             =49.08624

Lower bound=628.9147

upper bound=728.0854

∴ The 95% interval for population mean = 629 to 727

Hence, The  95% confidence interval for the true average dollar loss in burglaries rounded to the nearest dollar amount is 629 to 727

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The ordered pair is not solution to the system of equations.

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. LHS = RHS is a common mathematical formula.

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:

Cameron determined that an ordered pair made a true statement when substituted into one of the equations but not in the other equation.

As, we know we enter the values of the variables into each equation to see if an ordered pair is a solution to the system of two equation. The system has a solution if the ordered pair proves both of the equations.

So, the ordered pair is not solution..

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the height from B to c is 54.95 feet and B to D is 35.01 feet and the height of the steeple is 19.94 feet.

at a point 50 feet from the base of a church, the angle of elevation to the bottom of the steeple and top of steeple are 35 and 47 40' respectively.

We need to find out the height of steeple.

observe the right-angle triangle corresponding to the given problem,

let find the height from the point B to the point D.

the angle of elevation =35

we know about the trigonometric representation of the function tan is.

[tex]tan\theta=\frac{opposite}{adjacent}[/tex]

observing the right-angle triangle ABD as we know

angle =35, adjacent =50 and the opposite leg is x,

[tex]tan35=\frac{35}{50} \\\\x=50tan35\\\\x=35.01 feet[/tex]

now let's find the height from B to C.

angle 2=47°40'

[tex]\theta2=47+\frac{40}{60} \\\\\theta=47.7\\\\now, tan47.7=\frac{y}{50} \\\\y=54.95 feet\\[/tex]

therefore the height of steeple is 54.95-35.01=19.94 feet.

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