Screen printing a batch of shirts requires 1 minute per shirt in addition to 6.07 minutes of initial setup time. If it takes 13.07 minutes to screen-print a batch of shirts, how many shirts are in the, batch?

The answer is [tex]\boxed {\frac{dy}{dx} = \frac{y^{x}logy-yx^{y-1}}{x^{y}logx-xy^{x-1}}}[/tex].

Apply logarithmic differentiation on each side.

LHS

RHS

Equating both sides

1. The average daily balance for this credit card account is $187.74.

2. The finance charge for the month of April is $249.22.

The average daily balance for April is the total of the balance for every day in the billing cycle divided by the number of days in the billing cycle.

A billing cycle for a credit card account is usually one month.

Interest rate = 16.15% compounded monthly

Date       Activity            Amount     Balance  

April 1    Beginning Balance          $1,000.00

April 5   Purchase           29.10         1,029.10

April 12  Payment      −225.00           804.10

April 15  Purchase         97.25            901.35

April 23 Purchase         19.00           920.35

April 26 Purchase        28.40           948.75

April 30 Ending Balance                  948.75

Total                                            $5,632.05

Average daily balance = $187.735 ($5,632.05/30 days)

Daily interest rate = 0.04425 (16.15%/365)

Finance charge = $249.22 ($187.74 x 0.04425 30 days)

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Answer:

x = 30 degrees

Step-by-step explanation:

angles MNO, LNM, and KNL make a straight line: 105+45+y = 180 --> y = 30 degrees

KNL = 30 degrees

angle KLN is 90 degrees, a triangle is equal to 180 degrees

2x+30+90 = 180

2x = 60

x = 30 degrees

The value of the car after 5 years is 8527.02 dollars

Depreciation is the reduction in the value of an asset over time due to elements such as wear and tear. For example a car is said to "depreciate" in value after a discovery of a faulty transmission.

The value after 5 years can be found as follows:

Rate = 18% = 18 / 100 = 0.18

Initial Value  = $23,000

time = 5 years

Therefore,

y = 23000(1 + 18%)⁵

y = 23000(1 - 0.18)⁵

y = 23000(0.82)⁵

y = 23000 × 0.3707398432

y = 8527.0163936

y = 8527.02 dollars

Therefore, the value of the car after 5 years is 8527.02 dollars

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Using an exponential function, it is found that the value of the car after 5 years will be of $8,527.

A decaying exponential function is modeled by:

[tex]A(t) = A(0)(1 - r)^t[/tex]

In which:

For this problem, the initial cost and the decay rate are given as follows:

A(0) = 23000, r = 0.18.

Hence the value of the boat after t years is given as follows:

[tex]A(t) = A(0)(1 - r)^t[/tex]

[tex]A(t) = 23000(1 - 0.18)^t[/tex]

[tex]A(t) = 23000(0.82)^t[/tex]

The value after 5 years will be of:

[tex]A(5) = 23000(0.82)^5 = 8527[/tex]

The value of the car after 5 years will be of $8,527.

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The probability that at least 8 patients show improvement is; 0.94

The formula for Binomial Probability Distribution is;

P(X = r) = nCr * p^(r) * (1 - p)^(n - r)

where;

n = number of trials

r = number of specific events you wish to obtain

p is  probability of success

From the question, we have;

n = 12

r = 8

p = 81% = 0.81

The probability that at least 8 patients show improvement is expressed as;

P(X ≥ 8) = P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12)

Using online binomial probability calculator gives us;

P(X ≥ 8) = 0.11954 + 0.22649 + 0.28967 + 0.22453 + 0.07977

P(X ≥ 8) = 0.94

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Answer: answer is B

Step-by-step explanation:

use Pythagorean theorem to find other side. And sine is opposite side over hypotenuse.

the value of sin ∅ is 12/ 13

From the given question,

We have,  cos ∅= 5/13

From the trigonometric identities, we have that

[tex]sin^2\alpha + cos^2\alpha = 1[/tex]

Then , let's substitute the value of cos ∅

[tex]sin^2\alpha +(\frac{-5}{13} )^2 = 1[/tex]

Let make sin the subject of formula and find the squares of the fraction

sin²∅ = [tex]1 - \frac{25}{169}[/tex]

Find the LCM

sin²∅ = [tex]\frac{169 - 25}{169}[/tex]

Find the difference

sin²∅ = [tex]\frac{144}{169}[/tex]

Find the square root

sin∅ = [tex]\sqrt{\frac{144}{159} }[/tex]

sin∅ = [tex]\frac{12}{13}[/tex]

In quadrant II , sin is positive, so we have

sin ∅ = 12/ 13

Thus, the value of sin ∅ is 12/ 13

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hi

f°g  mean apply  g(x) and  then use result of  g(x) as  "x" in f(x)

so as  g(x) = x² +1   and  f(x) = 3x+2

so if we call  g(x)   X  we have  

f( X) =  3 X +2

now we replace  " X"  for it's value

f(X) =  3 ( x² +1) +2

f(X) =  3x² +3 +2

f(X) = 3x² +5

so  f°g = 3x² +5

After the tax and the tip are counted, we conclude that each friend must pay $30.

We know that the meal cost is $72.50.

Now, there is a 6.75% sales tax and a 15% tip on the waiter (we assume that the tip is based on the total meal cost, after the tax is applied).

Then the total meal cost is:

C = $72.50*( 1 + 6.75%/100%) = $72.50*(1 + 0.0675) = $77.39

Now we also need to add the tip, which is a 15% of that, so the total cost with the tip included is:

C' = $77.39*(1 + 15%/100%) = $88.998 = $90

(Where we rounded up).

Then, if there are 3 friends, each one must pay:

$90/3 = $30

Each friend must pay $30.

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The value of angle 20 is as follows:

m∠20 = 50.9 degrees.

When parallel lines are cut by a transversal, angle relationships are formed. This include corresponding angles, alternate angles , vertical angles etc.

Therefore, line l and m are parallel lines cut by the two transversal.

Hence,

m∠6 ≅ m∠20 (alternate angles)

Therefore, alternate angles are congruent

m∠20 = 2x - 4

m∠19 + m∠20 = 180 (angles on a straight line)

5x - 8 + 2x - 4 = 180

7x - 12 = 180

7x = 180 + 12

7x = 192

x = 192 / 7

x = 27.4285714286

x = 27.43

Therefore,

m∠20 = 2(27.43) - 4

m∠20 = 50.8571428571

m∠20 = 50.9 degrees.

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Answer:

D.  I, II, and III

Step-by-step explanation:

A discontinuous function is a function which is not continuous.  

If f(x) is not continuous at x = a, then f(x) is said to be discontinuous at this point.

To prove whether a function is discontinuous, find where it is undefined.

A rational function is undefined when the denominator is equal to zero.

Therefore, to find the values that make a rational function undefined, set the denominator to zero and solve.

Function I

Denominator:  x - 2

Set to zero:  x - 2 = 0

Solve:  x = 2

Therefore, this function is undefined when x = 2 and so the function is discontinuous.

Function II

Denominator:  4x²

Set to zero:  4x² = 0

Solve:  x = 0

Therefore, this function is undefined when x = 0 and so the function is discontinuous.

Function III

Denominator:  x² + 3x + 2

Set to zero:  x² + 3x + 2 = 0

Solve:  

⇒ x² + 3x + 2 = 0

⇒ x² + x + 2x + 2 = 0

⇒ x(x + 1) + 2(x + 1) = 0

⇒ (x + 2)(x + 1) = 0

⇒ x = -2, x = -1

Therefore, this function is undefined when x = -2 and x = -1, and so the function is discontinuous.

Therefore, all three given functions are discontinuous.

The largest possible total area of the four pens is 285610 ft²

An equation is an expression that shows the relationship between two or more numbers and variables.

Let y represent the length of the pen and x represent the width of the pen.

Hence:

Perimeter = x + y + x + y + x + x + x = 2y + 5x

2y + 5x = 3380    

y = (3380 - 5x)/2      (2)

Area (A) = xy

A = x * (3380 - 5x)/2      

A = (3380x - 5x²)/2      

The maximum area is at A' = 0, hence:

A' = (1/2)(3380 - 10x)

0 = (1/2)(3380 - 10x)

10x = 3380

x = 338 ft.

2y + 5(338) = 3380    

y = 845 ft.

Largest possible total area = 338 * 845 = 285610 ft²

The largest possible total area of the four pens is 285610 ft²

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The equivalent expression of 1/2 * 1/2 *1/2 is 2^-3

The expression is given as:

1/2 * 1/2 *1/2

Apply the product law of indices

1/2 * 1/2 *1/2 = (1/2)^3

Apply the power law of indices

1/2 * 1/2 *1/2 = (2^-1)^3

This gives

1/2 * 1/2 *1/2 = 2^-3

Hence, the equivalent expression of 1/2 * 1/2 *1/2 is 2^-3

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Answer:

18.4 units

Step-by-step explanation:

We can use the distance formula, d = [tex]\sqrt{(x_{1}-x_{2}) ^{2} +(y_{1}-y_{2}) ^{2}}[/tex] to find the length of the line segment.

d = [tex]\sqrt{(x_{1}-x_{2}) ^{2} +(y_{1}-y_{2}) ^{2}}[/tex] = [tex]\sqrt{(5+12) ^{2} +(-10+3) ^{2}}[/tex] = [tex]\sqrt{(17) ^{2} +(7) ^{2}}[/tex]=[tex]\sqrt{338}[/tex]=18.38

The real engine is 65.25 feet long

The scale is given as:

Scale = 87 feet to 1 foot

The scale length is given as

Scale length = 9 inches

Convert inches to feet

Scale length = 9/12 feet

The actual length is then calculated as:

Actual = 87 * 9/12 feet

Evaluate

Actual = 65.25 feet

Hence, the real engine is 65.25 feet long

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The converse, inverse and contrapositive of each conditional statement include:

A conditional statement can be defined as a type of statement that can be written to have both a hypothesis and conclusion. Thus, it typically has the form "if P then Q."

Where:

P and Q represent sentences.

In this scenario, we would write the converse, inverse and contrapositive of each conditional statement as follows:

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The quotient of the given expression is 1/3

Fractions are written as a ratio of two integers

Given the expression below'

-1/9 / (-1/3)

Change the division to multiplication

-1/9 * -3/1

1/9 * 3/1

1/3

Hence the quotient of the given expression is 1/3

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Answer:

1.  x = -1  y= -2
2. infinitely many solutions

3. x = 6 y= -7

4.no solution

5. x = -3 y = -17

6. x= 3 y = 7

Step-by-step explanation:

1) y=x-1

7x+6y= -19

6y= -19 -7x

y= (-7x-19)/6

since x-1 and (-7x-19)/6 are both equal to y they are equal to each other

this is how to get x

x-1 = (-7x-19)/6

6x-6 = -7x-19

13x = -13

x = -1

now put back -1 in the equation to get y

y=x-1

y = -1 -1

y= -2

2)-10x+2y=-12

y=5x-6

2y= -12 + 10x

y= -6 + 5x

y = 5x - 6

5x-6 = 5x - 6

0 = 0

when something is

equal to itself its

infinitely many solutions

(when something is not equal to something its no solution)

((when something is equal to just one answer its one solution)

3) y= -4x+17

y=x-13

-4x+17 = x-13

30 = 5x

x = 6

y=x-13

y=6-13

y= -7

4) -3x-15y=8

x+5y=5

-3x-15y=8 -> y = -1/15(3x-8)

5y=5-x -> y= 1/5 (5-x)

-1/15(3x-8) = 1/5 (5-x)

-x-8/3 = 5-x

0 = 23/3

(when something is not equal to something its no solution)

5) -3x+6y=-3

3x-y=8

-3x+6y= -3 -> y = 1/6(3x-3)

3x-y=8 -> y = 3x-8

1/6(3x-3) = 3x-8

3x-3 = 18x-48

x-1 = 6x - 16

5x = -15

x = -3

3x-y=8

3(-3)-y=8

-9-8 = y

y = -17

6) -6x+6y=24

-3x-8y=1

-6x+6y=24 -> y = 1/6(6x+24) -> y = x+4

-3x-8y=1 -> -3x-1 = 8y -> y = 1/8 (-3x-1)

1/8 (-3x-1) = x+4

-3x-1 = 8x+32

11x = 33

x= 3

-6x+6y=24

-6(3)+6y=24

-18 + 6y = 24

6y = 24 + 18

6y = 42

y = 7

Step-by-step explanation:

++++5

+++++++_2

1=false

true

false

false

The solution of the inequality by method of interval is x = [5,∝) and x = [-2,0]∪[8,-∝).

The first inequality is (x² - 25)/(x + 10) ≥ 0

⇒ x² - 25 ≥ 0

⇒ x² ≥ 25

∴ x ≥ 5

Thus the domain of the given inequality from method of interval is x = [5,∝).

The second inequality is (x + 2)(x² - 64)/(x² + 45) ≤ 0

⇒ (x + 2)(x² - 64)≤ 0

Either (x + 2)≤ 0 or (x² - 64)≤ 0

Either x ≤ -2 or x ≤ 8

Thus , the combined domain of the given inequality from method of interval is x = [-2,0]∪[8,-∝) .

Therefore, the solution of the inequality by method of interval is x = [5,∝) and x = [-2,0]∪[8,-∝).

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The number of dogs in the animal shelter which comprise of cats, dogs, and rabbits is 84 dogs.

Total animals = 5 × 47

= 235

235 = d + (d + 20) + 1/2(d + 20) - 5

235 = d + d + 20 + 1/2d + 10 - 5

235 = 2 1/2d + 25

235 - 25 = 2 1/2d

210 = 2 1/2d

d = 210 ÷ 2 1/2

d = 210 ÷ 5/2

= 210 × 2/5

= 420/5

d = 84 dogs

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Parallelogram is the quadilateral  ABCD with vertices A(-1,0), B(4, 0),

C(5, 4), and D(0, 4)

A parallelogram is a quadrilateral whose opposite sides are parallel and equal.

first, find the length of the sides of the quadilateral.

AB = [tex]\sqrt{(4-(-1))^2+0-0^2} \\[/tex]= [tex]\sqrt{5^2+0}[/tex] = [tex]\sqrt{25}[/tex] = 5

BC = [tex]\sqrt{(5-4)^2+(4-0)^2}[/tex] = [tex]\sqrt{1^2+4^2}[/tex] = [tex]\sqrt{1+16} = \sqrt{17}[/tex]

CD = [tex]\sqrt{(0-5)^2+(4-4)^2} = \sqrt{(-5)^2+0} = \sqrt{25-0} = 5[/tex]

DA = [tex]\sqrt{(-1-0)^2+(0-4)^2} = \sqrt{(-1)^2+(-4)^2} = \sqrt{1+16} = \sqrt{17}[/tex]

opposite side length is equal.

so quadilateral is parallelogram.

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The most precise name for quadrilateral ABCD with vertices

A(-1,0), B(4, 0), C(5, 4), and D(0, 4) is parallelogram.

Hence, the most precise name for quadrilateral ABCD with vertices A(-1,0), B(4, 0), C(5, 4), and D(0, 4) is a parallelogram.

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Answer:

Step-by-step explanation:

hello here is an solution

The equation of the inverse function of the function f(x) = 3(x + 5)^2 - 4 is f-1(x) = -5 + √[1/3(x + 4)]

Inverse functions are the opposite of an original equation. This means that for a function f(x), the inverse of the function f(x) is f-(x); it also represents the opposite function

The function f(x) is given as

f(x) = 3(x + 5)^2 - 4

Express f(x) as y

So, we have

y = 3(x + 5)^2 - 4

Swap the positions of x and y

So, we have

x = 3(y + 5)^2 - 4

Add 4 to both sides of the equation

So, we have

x + 4 = 3(y + 5)^2

Divide through by 3

So, we have

1/3(x + 4) = (y + 5)^2

Take the square root of both sides

So, we have

√[1/3(x + 4)] = y + 5

Subtract 5 from both sides of the equation

So, we have

y = -5 + √[1/3(x + 4)]

Rewrite as

f-1(x) = -5 + √[1/3(x + 4)]

Hence, the equation of the inverse function of the function f(x) = 3(x + 5)^2 - 4 is f-1(x) = -5 + √[1/3(x + 4)]

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The inverse function of the given function is [tex]\mathbf{= \dfrac{28+7x}{x-1}}[/tex]

A function g is the inverse of a function f, if and only if the values of y= f(x), x = g(y).

From the formula given:

[tex]\mathbf{y=f(x) = \dfrac{x+28}{x-7}}[/tex]

Let's substitute x with y;

[tex]\mathbf{y= \dfrac{x+28}{x-7}}[/tex]

[tex]\mathbf{x=\dfrac{y+28}{y-7}}[/tex]

Solve for y;

[tex]\mathbf{= \dfrac{28+7x}{x-1}}[/tex]

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The weighing of the man on the earth given the ratio is 174 pounds

Equate the ratio

6 : 1 = x : 29

6/1 = x/29

6 × 29 = 1 × x

174 = x

x = 174 pounds

Complete question:

The ratio of the weight of an object on the earth to the moon is 6:1. If a man weighs 29 pounds on the moon, calculate his weighing on the earth.

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Answer:

7

Step-by-step explanation:

haha

for

for

haha

but

birthday

can

7 answer

Answer:

the answer is -2/729

Step-by-step explanation:

When you're given the first term and the common ratio, you just need to multiply the first term by the common ratio and then raise to the power of the nth term minus 1.

In this case, 6(-1/3)^7