A printing service charges a set-up fee of $14.50 for each order and 15 cents more for each copy. The total cost, C (in dollars), for an order of x copies is given by the following function.
C (x) = 0.15x + 14.50
What is the total cost for an order of 30 copies?

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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Using trigonometry we know that option (B) "cosθ < 0" is correct.

For a right-angle triangle, the sum of the square of the legs is equal to the hypotenuse side(longest side).

Therefore, for a right triangle

For the triangle that has a² + b² > c², it shows it is not a right triangle.

Cosine law:

Substitute the value then we get:

Subtracting c² on both sides of the inequality:

Adding 2abcosθ on both sides then we get:

cosθ is negative in the second quadrant and third quadrants.

Therefore, using trigonometry we know that option (B) "cosθ < 0" is correct.

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For the given values, the probability that a student watches TV news regularly is 0.833, the probability that a randomly selected college student reads internet news regularly is 0.240.

According to a survey, 83% of college students routinely watch the news on television, while 24% of college students read newspapers on a regular basis.

Additionally, the survey revealed that 20% of college students routinely read newspapers and watch TV news.

(A) Given that a student reads newspapers frequently,

The answer is [P(TV and newspapers)/P] where P(watches TV|reads newspapers) (newspapers)

= 0.20/0.24 = 0.833

(b) Given that a randomly chosen college student watches TV news frequently

The answer is that P(newspapers | watches TV) = [P(newspapers and TV)] / P. (TV)

= 0.20/0.83 = 0.240

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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

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]

In population 1:

Pattern is changing by 13.5 to 11.5 to 8.3

Which is 2 then 3.2.

In population 2:

Population is decreasing by 2.

A recurring arrangement of numbers, forms, colors, and other elements constitutes a pattern in mathematics. The Pattern can be connected to any kind of occasion or thing. When a group of numbers are arranged in a particular way, the arrangement is referred to as a pattern. Patterns can also occasionally be referred to as a series.

Given.

Pattern in which population is changing are:

In population 1:

It is changing by 13.5 to 11.5 to 8.3

Which is 2 then 3.2.

In population 2:

Population is decreasing by 2.

Completing the table:

Population 1            Population 2

      42.8                             29

      38.6                              27

     33.4                              25

      27.2                              23

Graph is mentioned below.

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Using the table, we have the following points:

(x1, y1) ==> (2.5, 3), (3.5, 4.5), (5, 4.8), (5.5, 5.2), (6, 5.5)

Let's find the correlation coefficient.

To find the correlation coefficient, apply the formula:

Where:

n = 5

Σx = 2.5 + 3.5 + 5 + 5.5 + 6 = 22.5

Σy = 3 + 4.5 + 4.8 + 5.2 + 5.5 = 23

Σxy = 2.5⋅3 + 3.5⋅4.5 + 5⋅4.8 + 5.5⋅5.2 + 6⋅5.5 = 108.85

Σx² = 2.5² + 3.5² + 5² + 5.5² + 6² = 109.75

Σy² = 109.6

Plug in values in the formula and solve for r.

We have:

Therefore, the coefficient is 0.94

ANSWER:

0.94

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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There is a 0.6915 = 69.15% probability that a randomly selected adult has a serum albumin level greater than 32.5 g/l.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given by the rule presented below:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation of the albumin levels are given as follows:

[tex]\mu = 35, \sigma = 5[/tex]

The probability that a randomly selected adult has a serum albumin level greater than 32.5 g/l is one subtracted by the p-value of Z when X = 32.5, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (32.5 - 35)/5

Z = -0.5

Z = -0.5 has a p-value of 0.3085.

1 - 0.3085 = 0.6915 = 69.15% probability.

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The inverse of the function y = 2 · x² - 4 is equal to y⁻¹ = √[(x + 4) / 2], such that x ≥ - 4. (Correct choice: B)

In this problem we have a quadratic function, whose inverse has to be found. First, we make the following substitution on the function:

y = x

x = y⁻¹

Now we proceed to clear y⁻¹ by using algebra properties:

x = 2 · (y⁻¹)² - 4

x + 4 = 2 · (y⁻¹)²

(x + 4) / 2 = (y⁻¹)²

√[(x + 4) / 2] = y⁻¹

y⁻¹ = √[(x + 4) / 2], such that x ≥ - 4

The inverse of the function is equal to y⁻¹ = √[(x + 4) / 2], such that x ≥ - 4.

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Coordinates - A pair of integers that show the location of a point on a graph. The first number represents the x-axis, while the second represents the y-axis.

Other names for this type of pair are ordered pair and numbered pair. A proportionate connection is one in which the values are all connected by the same constant value. A proportionate connection is also known as a linear relationship in mathematics.

Assume f(x) and g(x) are two functions that accept a real number as input and return a real number as output.

The intersection points of f(x) and g(x) are then those x values for which f(x)=g(x).

The precise numbers can sometimes be discovered by algebraically solving the equation f(x)=g(x).

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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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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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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

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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The roots of a prabola is where the function intersects the x-axis.

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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A quartic function is a quartic polynomial, which is an integer-coefficients polynomial with a four-degree maximum.

A quartic function is a quartic polynomial, which is an integer-coefficients polynomial with a four-degree maximum.

Quartic in mathematics refers to something that is of the "fourth order," such as a function. One of the following is possible: Quartic function, a fourth-degree polynomial function. Quartic polynomial, a polynomial equation of degree 4, where an is a nonzero polynomial that defines the quartic equation.

A quartic equation, also known as an equation of the fourth degree, is an equation of the form that reduces a quartic polynomial to zero. A quartic function's derivative is a cubic function.

Therefore, the correct answer is option a) quartic.

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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:

5 to the 6th power is:

This, written in expanded form, is:

Based on the given figure, you can conclude:

x-intercepts:

x = 0

x = number in between 100 and 125, approximately 105

x = number greater than 175, approximately 180

y-intercepts:

y = 0

For the second and third x-intercepts there is no possible to specifiy the exact numbers due to the scale units of the graph.

Explanation

Step 1

eliminate the parenthesis applyng distributive property

I hope this helps you

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]

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

When one fails to reject a null hypothesis that is actually wrong, this error is known statistically as a type II error. This term is used in the context of hypothesis testing.

A type II error, often called an error of omission, results in a false negative. When the patient is infected, a disease test, for instance, can return a negative result. This is a type II error because, despite being wrong, we accept the test's negative conclusion.

The difference between a type I and type II error is that a type I error refers to the failure to reject a valid null hypothesis, whereas a type II error refers to the failure to do so. Despite the fact that the error does not happen by accident, it rejects the alternative theory.

The likelihood of mistakenly failing to reject the null hypothesis when it does not apply to the entire population is known as a type II error.

In essence, a type II error is a false negative.

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

Reordering:

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

= -2a + 7 =

= 7 - 2a

Answer:

Is wolfgang Mozart's

Step-by-step explanation:

The central traits of the Classical style are all present in Mozart's music. Clarity, balance, and transparency are the hallmarks of his work, but simplistic notions of its delicacy mask the exceptional power of his finest masterpieces, such as the Piano Concerto No. 24 in C minor, K.

Ratio:

cups of water / pancake mix = (1/2) / 2

For 1 pancake mix, x cups of water:

x / 1 = (1/2) / 2

Solve for x, cross multiply:

2x = ( 1/2) 1

2x = 1/2

Divide both sides by 2

2x/2 = (1/2) / 2

x = 1/4

Answer:

She would need 1/4 cups of water