The length of a rectangle is twice the width. Given that the perimeter of the rectangle is 24 feet, how many square feet are in the area of the rectangle?

Since the cost of the renovation or overhauling of the existing line would be recovered in Year 4 and the NPV of the new production line is $-360,000, Crane Manufacturing should renovate.

Renovation restores an old asset to a better state.  Replacement rids the old in preference for a new asset.

When the two investment options are weighed, a better choice can be arrived at.

Year 1 = $93,324 ($280,000 x 33.33%)

Year 2 = $124,460 ($280,000 x 44.45%)

Year 3 = $41,468 ($280,000 x 14.81%)

Year 4 = $20,748  ($280,000 x 7.41%)

Total cost = $280,000

NPV of new production line = $-360,000

Thus, based on the cost recovery of the old production line and the negative NPV of the new production line, Crane Manufacturing should renovate.

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Should Crane replace or renovate the existing line?

The values of h and r to maximize the volume are r = 4 and h = 2

From the question, we have the following equation

2r + 2h = 12

Divide through by 2

r + h = 6

Subtract r from both sides of the equation

h = 6 - r

Hence, the formula for h in terms of r is h = 6 - r

The volume of a cylinder is

V = πr²h

Substitute h = 6 - r in the above equation

V = πr²(6 - r)

Hence, the function V(r) is V = πr²(6 - r)

V = πr²(6 - r)

Expand

V = 6πr² - πr³

Integrate

V' = 12πr - 3πr²

Set to 0

12πr - 3πr² = 0

Divide through by 3π

4r - r² = 0

Factor out r

r(4 - r) = 0

Divide through by 4

4 - r = 0

Solve for r

r = 4

Hence, the single critical point on the interval [0. 6] is r = 4

We have:

V = πr²(6 - r)

and

V' = 12πr - 3πr²

Determine the second derivative

V'' = 12π - 6πr

Set r = 4

V'' = 12π - 6π* 4

Evaluate the product

V'' = 12π - 24π

Evaluate the difference

V'' = -12π

Because V'' is negative, then the single critical point is a global maximum

We have

r = 4  and h = 6 - r

Substitute r = 4  in h = 6 - r

h = 6 - 4

Evaluate

h = 2

Hence, the values of h and r to maximize the volume are r = 4 and h = 2

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Using the normal distribution, there is a 0.1587 = 15.87% probability that’s a car picked at random is traveling at more than 100 km/hr.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

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

The mean and the standard deviation are given, respectively, by:

[tex]\mu = 90, \sigma = 10[/tex]

The probability that’s a car picked at random is traveling at more than 100 km/hr is one subtracted by the p-value of Z when X = 100, hence:

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

[tex]Z = \frac{100 - 90}{10}[/tex]

Z = 1

Z = 1 has a p-value of 0.8413.

1 - 0.8413 = 0.1587.

0.1587 = 15.87% probability that’s a car picked at random is traveling at more than 100 km/hr.

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She needs to lay 11 slabs on each row to make a square

The total number of slabs is given as:

Total = 121 slabs

Let this represent the area of the slab.

The area of a square is calculated as:

Area = Length^2

Substitute the known values in the above equation

Length^2 = 121

Take the square root of both sides

Length = 11

Hence, she needs to lay 11 slabs on each row to make a square

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Answer:

C ≈ 14.18

Step-by-step explanation:

Question Given:

A circle has an area of 16mm². Find it's circumference.

Formula:

C = 2√πA

Solve:

C = 2√πA

C = 2√(3.14 × 16)

C = 2√50.24

C = 14.1760361173

C ≈ 14.18

Hence, Circumference is approximately 14.18.

~Kavinsky

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

Area of Circle :

[tex]\qquad \sf  \dashrightarrow \: \pi {r}^{2} [/tex]

Now, it's given that area of circle is : 16 mm²

Let's calculate Radius ~

[tex]\qquad \sf  \dashrightarrow \: \pi {r}^{2} = 16[/tex]

[tex] \qquad \sf  \dashrightarrow \: {r}^{2} = \cfrac{16}{ \pi} [/tex]

[tex]\qquad \sf  \dashrightarrow \: r = \sqrt{ \cfrac{16}{ \pi} } [/tex]

[tex]\qquad \sf  \dashrightarrow \: r = { \cfrac{4}{ \sqrt{ \pi} } }[/tex]

Now,

[tex]\qquad \sf  \dashrightarrow \: circumference = 2\pi r[/tex]

[tex]\qquad \sf  \dashrightarrow \: c = 2 \pi \cfrac{4}{ \sqrt{ \pi} } [/tex]

[tex]\qquad \sf  \dashrightarrow \: c = 8 \sqrt{ \pi} [/tex]

[ for approximate value take pi = 3.14 ]

[tex]\qquad \sf  \dashrightarrow \: c = 8 \sqrt{3.14} [/tex]

[tex]\qquad \sf  \dashrightarrow \: c \approx 8 \times 1.77[/tex]

[tex]\qquad \sf  \dashrightarrow \: c \approx 14.18 \: \: mm[/tex]

Answer:

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a. The decimal number 0.00000896 can be written as 8.96 × [tex]10^{-6}[/tex] in scientific notation.

b. 1.1105 pounds is written in standard notation as 1.1105 pounds.

We have,

(a) To write the number 0.00000896 moles per liter in scientific notation, we move the decimal point to the right until there is one

non-zero digit to the left of the decimal point.

The number of decimal places we moved to the decimal point will be the exponent of 10 in the scientific notation.

So,

= 0.00000896

= 896/100000000

= 896 x 100/100 x [tex]10^{-8}[/tex]

= 896/100 x [tex]10^{-8 + 2}[/tex]

= 8.96 × [tex]10^{-6}[/tex]

(b)

To write the number 1.1105 pounds in standard notation, we simply write the number as it is, without any scientific notation or exponent.

1.1105 pounds is written in standard notation as 1.1105 pounds.

Thus,

a. The decimal number 0.00000896 can be written as 8.96 × [tex]10^{-6}[/tex] in scientific notation.

b. 1.1105 pounds is written in standard notation as 1.1105 pounds.

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Using proportions, it is found that you would expected the white counter to be chosen 128 times.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

From the table, the proportion of the white counter is given as follows:

p = 32/(32 + 18) = 32/50 = 0.64.

Hence, out of 200 trials, the number of trials in which the white counter is expected to be chosen is given by:

0.64 x 200 = 128 times.

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Answer:

x=-4, x=9

Step-by-step explanation:

We write this into words:

difference = subtraction

square = ^2

a number = x

is equal to = =

5 times that number = 5x

x^2-36 = 5x

write in standard form

x^2-5x-36

what adds to -5 and multiplies to -36?

-9 and 4!

(x-9)(x+4)

x-9 = 0

x= 9

x+4 = 0

x=-4

Answer:

9

Step-by-step explanation:

Let the number = x.

x² - 36 = 5x

x² - 5x - 36 = 0

(x - 9)(x + 4) =0

x = 9 or x = -4

Answer: 9

By De Moivre's formula, the cubic roots of the complex number are 3 + i 4, - 4.96 + i 0.60 and 1.96 - i 4.60.

Herein we have a complex number in rectangular form, from which we need its magnitude (r) and direction (θ) and the De Moivre's formula as well. The root formula is introduced below:

[tex]z^{\frac{1}{n} } = r^{\frac{1}{n} }\cdot \left[\cos \left(\frac{\theta + 2\pi\cdot k}{n}\right) +i\,\sin \left(\frac{\theta + 2\pi\cdot k}{n}\right)\right][/tex], for k ∈ {0, 1, ..., n - 1}      (1)

Where n is the grade of the complex root.

The magnitude and direction of the complex number are 125 and 0.886π radians, respectively. Thus, by the De Moivre's formula we obtain the following three solutions:

k = 0

z₁ = 2.997 + i 4.002

k = 1

z₂ = - 4.964 + i 0.595

k = 2

z₃ = 1.967 - i 4.597

By De Moivre's formula, the cubic roots of the complex number are 3 + i 4, - 4.96 + i 0.60 and 1.96 - i 4.60.

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The value of x in the equation is 26.7

0.75x + 1.5y = 40

−1.5x − 1.5y = −60

add both equation to eliminate y .

Therefore,

−1.5x + 0.75x = -0.75x

1.5y + (- 1.5y) = 0

40 + (-60) = -20

Hence,

-0.75x  = - 20

divide both sides by -0.75

-0.75x / -0/75 = - 20 / -0.75

x = - 20 / -0.75

x = 26.6666666667

x = 26.7

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The level of significance on 0.05 exists at 83%.

The sample size (n) specified by the local cable company exists 300 which exists quite large.

According to the Central limit theorem, the sampling distribution of sample proportion observes a normal distribution with mean p and standard deviation

[tex]$\sqrt{\frac{p(1-p)}{n}}$[/tex]

Since the sampling distribution of sample proportions observes a normal distribution utilize the z-test for one proportion to execute the test.

The hypothesis is:

[tex]$H_{0}$[/tex]: The proportion of U.S. households that owned two or more televisions exists at 83 %, i.e. p = 0.83

[tex]$H_{1}$[/tex]: The proportion of U.S. households that owned two or more televisions exists less than 83 %, i.e. p < 0.83

Decision Rule:

At the level of significance [tex]$\alpha=0.05$[/tex] the critical region for a one-tailed z-test is:

[tex]$Z \leq-1.645[/tex]

By using the z table for the critical values.

So, if [tex]$Z \leq-1.645$[/tex]  the null hypothesis will be rejected.

Test statistic value:

[tex]$z=\frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

Here [tex]$\hat{p}$[/tex] exists the sample proportion.

Compute the value of [tex]$\hat{p}$[/tex] as follows:

[tex]$&\hat{p}=\frac{X}{n} \\[/tex] [tex]$&=\frac{240}{300} \\[/tex]

= 0.80

To compute the value of the test statistic as follows:

[tex]$z=\frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}}$[/tex]

[tex]$=\frac{0.80-0.83}{\sqrt{\frac{0.83 \cdot(1-0.83)}{3000}}}$[/tex]

The test statistic exists at -1.383 which exists more than -1.645.

Therefore, the test statistic lies in the acceptance region.

Thus we fail to reject the null hypothesis.

At a 0.05 level of significance, we fail to reject the null hypothesis noting that the proportion of U.S. households that owned two or more televisions exists at 83%.

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The particle will stop at D.

If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

In pentagon ABCDE shown above, each side is 1 cm. If a particle starts at point A and travels clockwise 723 cm along ABCDE, then

Number of sides = 5

Let x be the one complete revolution.

5 x = 725

x = 145

Now, 145 - 2 = 143

Hence, it will stop at D which is 2 less than A.

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The answer is |-4 - 1|.

If you solve this absolute value, the answer would be 5 and if you look at the number line, the distance between the two dots is 5 units.

|-4 - 1| --> |-5| --> 5

in an absolute value, there are no negative numbers so the -5 becomes 5.

Answer:

4x³ + 4x² + 5

Step-by-step explanation:

3x³ - 2x + 8 + 2x² + 5x + x³ + 2x² - 3x - 3.

4x³ - 2x + 8 + 2x² + 5x + 2x² - 3x - 3

4x³ + 4x² - 2x + 8 + 5x - 3x - 3

4x³ + 4x² + 8 - 3

4x³ + 4x² + 5

Applying precedence of operations, the result of the expression is of 161.

Power operations are done before multiplication/division, which are also done before addition/subtraction.

Operations inside brackets or parenthesis also take precedence.

In this problem, the operation is:

[3 x 2^5 + 13 x (-2)] + 7[8 - (4 - 9)]

First the power:

[3 x 32 + 13 x (-2)] + 7[8 - (4 - 9)]

Now the multiplications on the first bracket, and the subtraction on the second:

[96 - 26] + 7[8 - (-5)]

Then, applying the parenthesis to the negative number, we have that:

[96 - 26] + 7[8 - (-5)] = 70 + 7 x 13 = 161.

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[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{3 \times 2^5 + 13(-2)] + 7[8 - (4 - 9)]}[/tex]

[tex]\mathsf{= 3\times32 + 13\times -2 + 7[8 - (4 - 9)] }[/tex]

[tex]\mathsf{= 96 + 13\times -2 + 7(8 - (4 - 9))}[/tex]

[tex]\mathsf{= 96 - 26 + 7(8 - (4 - 9))}[/tex]

[tex]\mathsf{= 70 + 7(8 - (4 - 9))}[/tex]

[tex]\mathsf{= 70 + 7(8 - (-5))}[/tex]

[tex]\mathsf{= 70 + 7\times13}[/tex]

[tex]\mathsf{= 70 + 91}[/tex]

[tex]\mathsf{= 161}[/tex]

[tex]\huge\text{Therefore, your answer should be: }[/tex]

[tex]\huge\boxed{\frak{161}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

[tex]x^{\frac{1}{2} } + 48[/tex]

Step-by-step explanation:

This is hard to explain, but basically you use exponent rules to switch it to an exponent

[tex](\sqrt[4]{x^{2} +4} )^{3}[/tex]

It's easiest if you calculate [tex]4^{3}[/tex] first

4³ = 4 x 4 x 4 = 48

Then convert the root to a fraction exponent

[tex]\sqrt[4]{x^{2}} = x^{\frac{2}{4}} = x^{\frac{1}{2} }[/tex]

Combine them using addition, since addition was in the problem

[tex]x^{\frac{1}{2} } + 48[/tex]

I hope this helps!

The rate of the slower cyclist is 16 mph while the rate of the faster cyclist is 21 mph.

let us assume the following;

x = rate of slower cyclist

x + 5 = rate of faster cyclist

We know that formula for distance is;

distance = travel time*rate

Thus;

2x + 2(x + 5) = 74

Since the two cyclists are a distance of 74 miles apart after a time 2 hours. Thus;

2x + 2x + 10 = 74

4x + 10 = 74

4x = 74 - 10

4x = 64

x = 64/4

x = 16

Rate of faster cyclist = 16 + 5 = 21 mph

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Answer:

0.28

Step-by-step explanation:

Depreciation Expense per mile:

= (Cost of delivery truck - Salvage value) ÷ Expected miles driver

=(33000-2760)÷108000=0.28 per mile

Answer:

Volume=96.7

Step-by-step explanation:

V=πr^2h=

V=π·1.8^2·9.5=

96.69822

Answer:

See below.

If the correct sum is 1155, then Ken had 495 stamps, and Henry had 660 stamps.

Step-by-step explanation:

Henry had h stamps.

Ken had k stamps.

After giving away 2/3 of his stamps, Henry ended up with 1/3 of his stamps, or h/3.

After giving away 3/4 of his stamps, ken ended up with 1/4 of his stamps, or k/4.

h/3 = k/4

h + k = 1156

4h = 3k

h = 1156 - k

4(1156 - k) = 3k

4624 - 4k = 3k

4624 = 7k

k = 4624/7

Stamps left: 0.25 × 4624/7 = 1156/7

h = 1156 - k

h = 1156 - 4624/7

h = 8092/7 - 4624/7

h = 3468/7 =495.43

Stamps left: 1/3 × 3468/7 = 1156/7

Total number of stamps left: 1156/7 + 1156/7 = 2312/7 = 330.29

The problem is solved correctly, but the numbers given must be incorrect since you cannot have a fraction of a stamp.

See attachment for the graph of the piecewise function h(x)

The function is given as:

h(x) = | -4,    x < 3

         | x + 5,    x >= 3

The above function is a piecewise function.

It has 2 separate functions at two domains

This means that we plot the sub-functions in the piecewise function at their respective domain

See attachment for the graph of the piecewise function h(x)

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The number of months taken for the toenail to completely regenerate itself is 13 months

It is the quantity of an amount of something at a rate of one of another quantity.

We have,

Toenail grows:

0.05 mm per day

0.05 mm = 1 day

[ 1 inch = 25.4 mm ]

So,

1 mm = 1/25.4 inch

0.05 x 1/25.4 inch = 1 day

0.0019 inch = 1 day

Divide both sides by 0.0019

1 inch = 1/0.0019 day

1 inch = 526.32 days

Multiply 3/4 on both sides.

3/4 inch = 3/4 x 526.32 days

3/4 inch = 395 days _____(1)

We can assume,

1 month = 30 days

Multiply 395/30 on both sides.

395/30 months = 395 days

13 months = 395 days _____(2)

From (1) and (2) we get,

3/4 inch = 13 months

Thus,

The number of months taken for the toenail to completely regenerate itself is 13 months.

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If a 1L IV contains 60meq of kcal and the IV was discontinued after 400ml has infused, then the amount of IV received by the patient is 24meq of kcal.

Calculation for the Amount of IV

It is given that,

1L IV contains 60meq of kcal

⇒ 1000 mL of IV contains 60meq of kcal

⇒ 1 mL of IV will contain 60 / 1000 meq of kcal

As per the question,

The amount of IV infused in the patient = 400 mL

⇒ The amount of IV received by the patient in meq of kcal = 400 × (60 / 1000)

= 4 × 6

= 24 meq of kcal

Hence, the patient receives 24meq of kcal amount of IV.

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Answer:

Step-by-step explanation:

If it is not Monday, then there are students in the gym.

Negation: It is not Monday and there are not students in the gym.

Statement: It is Monday or there are students in the gym.

Equivalent: If there are not students in the gym, then it is Monday.

Neither: There are not students in the gym or it is not Monday.

Answer:

x = 106 degrees

Step-by-step explanation:

x + 104 + 40 + 110 = 360

x + 254 (No more 254)

- 254 (Again no more 254)

x = 106

Answer:

t = 4b

Step-by-step explanation:

Each bag costs 4 dollars.

hope this helps! <3

Answer:

-5/9

Step-by-step explanation:

-4x - 1 = 5x +4   Add 4x to both sides

-1 = 9x + 4    Subtract 4 from both sides

-5 = 9x  Divide both sides by 9

-5/9 = x