In the figure below, circle 1 is a unit circle. Circle 2 has a diameter that is one and half times longer than that of circle 1, and circle 3 has a diameter that is twice as long as that of circle 1. If angle Z is equal to 2 radians, what is the length of the arc between points I and J?

Answer:

48 gallons of paint are needed.

Step-by-step explanation:

Set up a proportion.

Like this: x is for the unknown number of gallons.

[tex]\frac{3}{75} = \frac{x}{1200}\\ 75(x)= 3(1200)\\ 75x=3600\\x= 3600/75\\x= 48 Answer[/tex]

The conditional statement for "The vertices of a triangle are not collinear" is "if the points are not collinear then they are vertices of triangle."

Conditionals are commands used in programming languages to handle choices. Particularly, conditionals carry out various calculations or actions based on whether a boolean condition defined by the programmer evaluates to true or false.

The hypothesis is a prediction of what will transpire in your experiment. The words "IF" and "THEN" are frequently used when writing the hypothesis. For instance, "I will fail the test if I don't study." Your independent and dependent variables are reflected in the "if" and "then" statements.

"The vertices of a triangle are not collinear" has a conditional statement that reads, "If the points are not collinear, then they are vertices of the triangle."

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-7a - 2y + 7 + 2y + 5a

Reordering:

(-7a + 5a) + (-2y + 2y) + 7 =

= -2a + 7 =

= 7 - 2a

Given the rectangle ABCD, you can identify that it is divided into two Right Triangles:

• You can find the length of the rectangle by applying the following Trigonometric Function:

In this case, you can set up that:

Then, substituting values and solving for "l", you get:

• In order to find the width of the rectangle, you can use this Trigonometric Function:

In this case, you can say that:

Therefore, substituting values and solving for "w", you get:

• Now you need to use the following formula for calculating the area of a rectangle:

Where "l" is the length and "w" is the width.

Substituting the length and the width of the given rectangle into the formula and evaluating, you get:

Hence, the answer is: Option C.

The composite function's value, (gof)(5), is equivalent to 6.

A mathematical procedure called composite combines two functions, f and g, to produce a third function, h(x), where g(x) is the sum of f(x) and h(x).

Given the aforementioned functions,

f(x) = x^2-6x+2 and;

g(x) = -2x

The composite function is known as the gof (5)

(gof) = g(f(x)) where;

f(x) = g(x2-6x+2) and;

f(x) = -2(x2-6x+2).

Substitute the given functions into the composite;

g(f(5)) = -2(5^2-6(5)+2)

g(f(5)) = -2(-3) = 6

The comparable composite value is provided by this.

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Answer:

Yes, it is a linear function.  For every input there is only 1 output.

Step-by-step explanation:

The after tax cost of debt for the bond is 2.73%

Given,

The face value of the bond, FV = $1000

Present value of the bond, PV = $995.28

Maturity period = 19 years

Coupon rate = 3.5%

Total tax rate = 22%

We have to find the after tax cost of debt for the bond.

The bond pays interest semiannually ;

so coupon rate = 3.5/2 = 1.75

Coupon payment , pmt= 0.0175 x 1000 = $17.5

Maturity, nper = 19 years x 2 = 38

Compute yield rate using spreadsheet = Rate(nper,pmt,-PV, FV)

Then,

= RATE(38, 17.5, -995.28, 1000)

Rate or yield is computed as 3.5%

The present value is negative as it is a cash outflow.

The cost of debt is 3.5%

The tax rate is 22%

After tax cost of debt = 3.5 (1 - 0.22)  = 2.73%

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After all the transaction, money left in the bank account is $15.8872.

Given that, you open your bank account on April 16 with a tax refund check of $145.00. You pay Sell Phone $65.34 on April 18.

A tax refund is a reimbursement to a taxpayer for any excess amount paid to the federal government or a state government.

On  April 16th balance in the account = $145.00 cost of phone = $65.34 on April 18.

Balance on April 18 = 145.00-65.34

= $79.66

Deposited check $9.76 on 23rd April for 35 hours

Balance on 23rd April = 79.66+9.76

=$89.42

Since, the check deposited only for 35 hours, again balance on 24th April will be $79.66

On 24th April you brought clothes from BargainsRUs for

61.32+4% of 61.32

= 61.32+2.4528

= $63.7728

So, the remaining balance in the account = 79.66-63.7728

=$15.8872

Therefore, after all the transaction, money left in the bank account is $15.8872.

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To find the answer, we just have to look for the complement fraction of 9/10, which is found by subtracting from 1

Observe that the complement of 9/10 is the answer because that's the amount of energy that stays in the plant.

The derivative of y =  [ 1/x(x+4) - 1/(5x + 1) - 1/(3x + 7) ] is

y' =  [tex]\sqrt{\frac{x(x-4)}{(5x+1)(3x+7)} }[/tex] x 1/2  [1/x(x+4) - 1/(5x + 1) - 1/(3x + 7)]

The derivative of a function f(x) represents its rate of change.

We have,

y = [tex]\sqrt{\frac{x(x-4)}{(5x+1)(3x+7)} }[/tex]

Putting log on both sides.
[ log a² = 2 log a ]

log y = 1/2 log [tex]\frac{x(x+4)}{(5x+1)(3x+7)}[/tex]

log y = 1/2 [ log x(x+4) - log (5x +1)(3x + 7) ]

log y = 1/2 [ log x(x+4) - log(5x + 1) - log (3x + 7) ]

Derivation on both sides.

[ d(logx)/dx = 1/x ]

d (log y) / dx = d [ {1/2 log x(x+4) - log(5x + 1) - log (3x + 7)} ] / dx

1/y y' = 1/2[ 1/x(x+4) - 1/(5x + 1) - 1/(3x + 7) ]

y' = y/2 [ 1/x(x+4) - 1/(5x + 1) - 1/(3x + 7) ]

y' =  [tex]\sqrt{\frac{x(x-4)}{(5x+1)(3x+7)} }[/tex] x 1/2  [1/x(x+4) - 1/(5x + 1) - 1/(3x + 7)]

Thus,

The derivative of y =  [ 1/x(x+4) - 1/(5x + 1) - 1/(3x + 7) ] is

y' =  [tex]\sqrt{\frac{x(x-4)}{(5x+1)(3x+7)} }[/tex] x 1/2  [1/x(x+4) - 1/(5x + 1) - 1/(3x + 7)]

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Check the picture below.

Combining the three different transformations—rotations, reflections, and translations—will result in congruent shapes. Actually, any pair of congruent shapes can be matched to one another using a combination of one or more of these three transformations.

There are four possible transformations of a point, line, or geometric figure, each of which changes the object's shape and/or location. Pre-Image denotes the shape of the object before transformation, while Image denotes the final position and shape of the object.

We now know that during rigid transformations, the size and shape of the figures are maintained (reflections, translations, and rotations). The pre-image and the image are always in agreement.

Matt has the following transformational abilities:

Reflection (Flip)

A reflection keeps its original shape because the comparable points from the pre-image to the image stay at the same distance from the line of reflection.

Rotations as a Congruence Transformation

Rotations as a Congruence Transformation

A figure twists when it rotates. The figurine looks to have fallen over, although being the same size and shape. A great illustration of a rotation in the actual world is a clock. The connecting arms of a clock rotate around its axis every hour or every day. A rotation is defined by its degree; common rotations include 90 degrees, 180 degrees, and 270 degrees. The figure completes a full 360-degree rotation before returning to its starting point. A rotation must include indicate the clockwise or counterclockwise direction. This information can be used to calculate the degree, quantity, and direction of a revolution.

Translational congruence transformation

We refer to a movement as a translation when an object or shape is moved from one place to another without changing its size, shape, or orientation. Every point on an item or shape is moved by the same amount and in the same direction during a translation, sometimes referred to as a slide.

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If a standard deviation for binomial distribution n = 48 p = 3/5 . The standard deviation is 3.39.

Using this formula to determine or find the  standard deviation for the binomial distribution

σ =√np(1−p)

Where:

n = 48

p = 3 / 5 or 0.6

σ  = ?

Let plug in the formula so as to determine the standard deviation

σ =√ (48) (0.6) ( 1 - 0.6)

σ =√ (48) (0.6)  (0.4)

σ =√ 11.52

σ = 3.39

Therefore we can conclude that  3.39 is the standard deviation.

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The equation of the line with slope -2 and passing through the point (3,-2) is y+2x-4=0.

The point-slope formula is used to find the equation of the line passing through a point (a,b) and having a slope of m.

A straight line equation of the form (y-b) = m(x-a), where m is the slope of the line and (a,b) are the coordinates of a given point on the line, is the standard form given for the point-slope form of the line.

A point (3,-2) and a slope -2 are given.

Use the standard Point-slope form of the line to find the equation of the line.

(y-b) = m(x-a)

Put the given values in the Point-slope equation.

y-(-2)=-2(x-3)

Simplify the equation to get the equation of the line.

y+2=-2x+6

y+2x-4=0

So, the equation of the line is y+2x-4=0.

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Answer:

C

Step-by-step explanation:

[tex]x^2 - 2x - 1 = 0\\x^2 = 2x + 1\\x^4 = 4x^2 + 4x + 1\\x^4 = 4(2x + 1) + 4x + 1\\x^4 = 8x + 4 + 4x + 1\\x^4 = 12x + 5[/tex]

5 to the 6th power is:

This, written in expanded form, is:

length:15 cm

width: 14 cm

Explanation

Step 1

Let

w represents the width of the rectangle

l represents the length of the rectangle

a)The width of a rectangle is 4 less than the length,hence

write this in math terms, replace

b)the area of the rectangle is 165 square cm

the area of a rectangle is given by

Step 2

now, solve the equations

a) replace the w from equation (1) into equation(2)

b) now, we have a quadratic equation in the form

hence, we can use the quadratic formula to solve

let

a=1

b=-4

c=-165

replace

therefore

as we are searchinf for a distance, the only valid answer is 15

so, the answer is length= 15 cm

c) finally, replace the l value into equation (1) to find the width

therefore, the width is 11 centimeters

I hope this helps you

Explanation

Step 1

eliminate the parenthesis applyng distributive property

I hope this helps you

We will have the following:

So, the simplification is equal to 1.1.

***Explanation***

First, we multiply all the values that are asked to be multiplied, and we also operate all the exponents. [We recall that a value at the power of a number is the number of times the value is multiplied by itself], then we get that:

Finally we operate the simpler and lower in the hierarchy of operations expressions:

Answer:

1 == B No Solutions

2 == A One Solution

3 == C Infinitely Many Solutions

Explanation:

We first find go through each system and see which has one solution, no solutions, and infinitely many solutions.

1.

x

Explanation:

If we have a function g(x) = -f(x), then g(x) will be f(x) reflected across the x-axis.

If g(x) = f(x) - c, g(x) will be f(x) shifted c units down

If g(x) = f(x + c), g(x) will be f(x) shifted c units to the left.

In this case, the initial function is f(x) = |x| and g(x) = -|x + 3| - 2, then

g(x) = -f(x + 3) - 2

Therefore, g(x) will be the initial function reflected across the x-axis, shifted 3 units to the left and 2 units down.

Answer:

So, the graph for y = -|x + 3| - 2 will be:

The graph of function d is a reflection across the y-axis of the graph of function t.

In Geometry, there are different types of transformation and these include the following:

A reflection can be defined as a type of transformation which moves every point of the object by producing a flipped but mirror image of the geometric figure.

In Geometry, a reflection across the y-axis (y = x) of a graph is given by this transformation rule (x, y) → (-x, y). This ultimately implies that, function t(x) = -4x + 72 would be transformed to function d:

d(x) = -(-4x) + 72.

d(x) = 4x + 72.

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Complete Question:

The temperature (in degrees Fahrenheit) x hours after 5 p.m. is represented by t(x) = -4x + 72. The temperature x hours after 10 a.m. is represented by d(x) = 4x + 72. Describe the transformation from the graph of t to the graph of d.

Chicago Cubs score between -2.86 and 10.58 runs every game, or at least 75% of their total.

The Chebyshev's Theorem calculates the minimal percentage of observations that are within a certain range of standard deviations from the mean. A wide variety of probability distributions can be used with this theorem. Another name for Chebyshev's Theorem is Chebyshev's Inequality.

Given Mean (X) = 3.86, Standard deviation (SD) = 3.36

According to Chebyshev’s Theorem,

1-1/k^2  proportion of values lies between Mean ± (k × SD )

Given k = 2.

k = x - mean /SD

1-1/k^2 =1-1/2^2

⇒1-1/4=1-0.25

⇒0.75

Therefore Proportion Value = 75%

If k= 2

75% Chebyshev’s intervals are

Lower Limit = Mean - (k × SD )

⇒3.86 - (3.36×2)

⇒3.86 - 6.72 = - 2.86

Upper Limit = Mean + (k × SD )

⇒3.86 + (3.36 × 2)

⇒3.86+6.72 = 10.58

Hence the Chicago Cubs score between -2.86 and 10.58 runs every game, or at least 75% of their total.

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The total cost of transporting 12 tons is $8000 and number of tons the company transporting is 23.

The total cost of transporting 12 tons can be calculated by keeping the value of number of tons in the formula.

Total cost = 6500 + 125×12

Performing multiplication on the Right Hand Side of the equation

Total cost = 6500 + 1500

Performing addition on the Right Hand Side of the equation

Total cost = 8000

The number of tons can be calculated by keeping the total cost in the formula.

9375 = 6500 + 125n

125n = 9375 - 6500

Performing subtraction on Right Hand Side of the equation

125n = 2875

n = 2875 ÷ 125

Performing division

n = 23

So, the total cost is $8000 and number of tons is 23.

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9 + 3x ≥ -6​

9 is adding on the left, then it will subtract on the right

3x ≥ -6​ - 9

3x ≥ -15

3 is multiplying on the left, then it will divide on the right

x ≥ -15/3

x ≥ -5

Answer:

0.053

Step-by-step explanation:

the probability of taking a Boston creme first is 6/19 (19 is the total doughnuts in the box), then the probability of taking a chocolate glazed second would be 3/18 (bc there would be 18 left after taking one first). then multiply these fractions together. as a decimal you get 0.053 to 3 decimal places

The proof that Q R S T is a parallelogram is given and enumerated in the following paragraph.

A mathematical proof is a deductive argument for a mathematical declaration that demonstrates that the provided assumptions logically ensure the conclusion.

The proof that the above-named geometrical shape is a parallelogram goes thus:

Statements                                            Reasons

1. [tex]\overline{QR}[/tex] ≅ [tex]\overline{ST}[/tex]                                 Given

2. [tex]\overline{RS}[/tex] ≅ [tex]\overline{QT}[/tex]                                 Given

3. [tex]\overline{RT}[/tex] ≅ [tex]\overline{TR}[/tex]                                 Reflexive Property

4. [tex]\Delta QRS[/tex]  ≅ [tex]\Delta STQ[/tex]                  SSS Congruence Theorem

5. A 1  ≅  A 4                   CPCTC Property

6. A 2  ≅  A3            CPCTC Property

7. QR | ST                    Alternate Interior Angles Converse

8. QT | RS                    Alternate Interior Angles Converse

9. Q R S T is a parallelogram         Definition of parallelogram      

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Suppose that the relationship between the tax rate t on imported shoes and the total sales S (in millions of dollars) is given by the function below. The tax rate t that maximizes revenue for the government is 66.992%.

Revenue can be defined as the amount or the income a person or an organization generated from the sales of goods and services.

Given function :

Total sale  = S(t) = 7−6∛t

Hence,

Expression for Revenue rate = r(t) = tS(t)

Now let substitute and solve  expression

r(t) = t (7−6∛t)

= 7t−6(t)^4/3

Differentiate the expression

d[r(t)] dt = r′(t)

r′(t) = 7− (4/ 3) 6(t)^1/3

=7−8(t) ^1/3 ........ expression (1)

Maximum revenue

r′(t) = 0

Substitute and solve expression (1)

0 =7−8(t)^1/3

(t) = (7/8)^3

= 0.66992 × 100

= 66.992%

Therefore we can conclude that the tax rate t that maximizes revenue is 66.992%.

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The complete question is :

Suppose that the relationship between the tax rate t on imported shoes and the total sales S (in millions of dollars) is given by the function below. Find the tax rate t that maximizes revenue for the government. (Round your answer to three decimal places.)

S(t)=7−6∛t