Question 3 out of 8:’sks

Inequality can be used to determine x, the greatest number of 120-kilogram crates that can be loaded onto the shipping container is  8000 + 120C <= 27500

An inequality is a relationship that allows us to contrast two or more mathematical expressions.

Knowing that;

Each carton weighs 120 kg.

The container's maximum weight when loaded is 27500 kg.

Weight of the container as it is currently loaded: 8000 kg

Now that we have merged, we have;

Solution

because 8000 grams have already been loaded kilograms

into the container

each crate weighs 120 kilograms.

so 8000 + 120C <= 27500

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Answer:

Length = 2 feet

Width = 6 feet

Step-by-step explanation:

Let the length of a flower garden = l feet

And the width of the garden = w feet

Perimeter of the rectangular garden = 2(l + w)

16 = 2(l + w)

l + w = 8

l = 8 - w ---------(1)

Area of the rectangular garden = lw

12 = lw ---------(2)

By substituting the value of length in equation (2)

12 = (8 - w)w

12 = 8w - w²

w² - 8w + 12 = 0

w² - 6w - 2w + 12 = 0

w(w - 6) + 2(w - 6) = 0

(w + 2)(w - 6) = 0

w = -2, 6 feet

Since, width of the garden can't be negative.

Therefore, Width of the garden = 6 feet

From equation (1)

l = 2 feet

Therefore, length of the garden is 2 feet and width is 6 feet.

The pair between the histogram and the data is I-b, II-d, III-c, and IV-a.

Histogram is a graphical display of frequency tabulations illustrated by bar graphics, where each bar shows the proportion of frequencies in each category series that are adjacent with non-overlapping intervals. The histogram is frequently used to depict the main characteristics of the data distribution.

There are relations between the mean and median of the statistical data and the shape of a histogram.

Whilst, the standard deviation describes the range between the highest and the lowest bar of the histogram. The higher the standard deviation, the range is bigger, and vice versa.

Take a look at the given data and the given histograms:

Data       Mean      Median      SD

  I             56             56          1.6          

  II            65             65          9      

  III           56             56          10      

  IV          56             56          21      

Based on that, we can conclude that:

The pair between the histogram and the data is I-b, II-d, III-c, and IV-a.

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The length, breadth and height will be 78 cm, 78cm, 78cm each.

let consider the length = l

breadth = b

height = h

we are provided that

l + b + h = 234cm .......(1)

Also we have to maximize the volume , provided length is equal to breadth

∴ eqn (1) becomes

2b + h = 234

h = 234 - 2b

also ,

volume(v) = lbh

v = b²(234 - 2b)

v = b²234 - 2b³

now to maximize the volume we take the first derivative of the volume wrt 'b' and place it equal to zero. ( lagrange method )

i.e. d( v)/db = 0

∴  468b - 6b² = 0

 6b² - 468b = 0

6b( b - 78 ) = 0

∴  b = 78 cm

now as length = breadth

l = b = 78 cm

also putting this value in eqn (1)

h = 234 - 2b

h =  78 cm

So , the dimensions will be equal and will be 78cm , 78cm, 78cm each .

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The height of water left in the can  is determined as 9.9 cm.

option B.

The height of water left in the can is calculated by the difference between the volume of a cylinder and volume of a cone.

The volume of the cylindrical can is calculated as;

V = πr²h

where;

V = π(4.6 cm)²(13.5 cm)

V = 897.43 cm³

The  volume of the cone is calculated as;

V = ¹/₃ πr²h

V = ¹/₃ π(5.1 cm)²( 8.7 cm )

V = 236.97 cm³

Difference in volume =  897.43 cm³ - 236.97 cm³

ΔV = 660.46 cm³

The height of water left in the can  is calculated as follows;

ΔV = πr²h

h = ΔV /  πr²

h = ( 660.46 ) / (π x 4.6²)

h = 9.9 cm

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The largest amount of money she could have is: (3 x 25 cents) + (3 x 10 cents) + (2 x 5 cents) = 75 cents + 30 cents + 10 cents = 115 cents or $1.15.

To find the largest amount of money Tasha could have with 8 coins in her pocket, we need to consider the different combinations of coins she could have. Since she has no more than 3 of any coin, the possibilities are:

- 3 quarters, 2 dimes, 1 nickel, 2 pennies = $0.81
- 3 quarters, 2 dimes, 2 nickels, 1 penny = $0.80
- 3 quarters, 2 nickels, 3 pennies = $0.78
- 3 quarters, 1 dime, 3 nickels, 1 penny = $0.76
- 3 quarters, 1 dime, 2 nickels, 3 pennies = $0.74
- 3 quarters, 1 dime, 1 nickel, 4 pennies = $0.73
- 2 quarters, 3 dimes, 1 nickel, 2 pennies = $0.70
- 2 quarters, 3 dimes, 2 nickels, 1 penny = $0.69
- 2 quarters, 2 dimes, 3 nickels, 1 penny = $0.68
- 2 quarters, 2 dimes, 2 nickels, 2 pennies = $0.67

Therefore, the largest amount of money Tasha could have is $0.81 with 3 quarters, 2 dimes, 1 nickel, and 2 pennies.

To maximize the amount of money Tosha could have with 8 coins and no more than 3 of any coin, she should carry the coins with the highest denominations. In this case, she can have 3 quarters (25 cents each), 3 dimes (10 cents each), and 2 nickels (5 cents each). The largest amount of money she could have is:

(3 x 25 cents) + (3 x 10 cents) + (2 x 5 cents) = 75 cents + 30 cents + 10 cents = 115 cents or $1.15.

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The connection string for SQL Server using Windows Authentication is as follows:

Server=myServerAddress;Database=myDataBase;Trusted_Connection=True;

Specify the server address in the format "Server=myServerAddress". Replace "myServerAddress" with the name or IP address of the SQL Server instance you want to connect to.

Specify the name of the database you want to connect to in the format "Database=myDataBase". Replace "myDataBase" with the name of the database.

Use Windows Authentication by setting "Trusted_Connection=True". This means that the user running the application is authenticated using their Windows credentials, rather than a SQL Server login.

Use semicolons (;) to separate the different parts of the connection string.

Using Windows Authentication is a more secure and convenient way to connect to a SQL Server database, as it eliminates the need to store and manage login credentials in the application.

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The nth harmonic number is defined as the sum of the reciprocals of the first n positive integers. We can calculate the nth harmonic number using the formula Hn=1+1/2+1/3+...+1/n.

Sure, I'll be glad to help you out!In mathematics, the nth harmonic number is defined as the sum of the reciprocals of the first n positive integers.

The nth harmonic number is defined to be:

$$H_n=1+\frac{1}{2}+\frac{1}{3}+\cdots+\frac{1}{n}$$

Now,  to understand the concept in detail.

For this purpose, let's consider an example:

If we want to find the 5th harmonic number, then we use the formula as shown below:

$$H_5=1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}$$

Simplifying the above expression we get:

$$H_5=\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}$$$$\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}=\frac{60}{60}+\frac{30}{60}+\frac{20}{60}+\frac{15}{60}+\frac{12}{60}$$$$

=\frac{137}{60}$$

Therefore, the 5th harmonic number is 2.2833.

Now, The nth harmonic number is defined as the sum of the reciprocals of the first n positive integers. We can calculate the nth harmonic number using the formula Hn=1+1/2+1/3+...+1/n.

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Let's begin by listing out the information given to us:

When this is glided by T(-1, 1); ry−axis(x, y) → (−x, y)

The interest that Elizabeth will get based on the information is $480.

From the information, Elizabeth deposited her 1/2 of the profit from selling her fathers house. the full profit was $12000. The profit deposited will be:

= 1/2 × $12000

= $6000

The simple Interest will be calculated thus:

= Principal × Rate × Time

= $6000 × 4% × 2

= $6000 × 0.04 × 2

= $480

The interest is $480.

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Two years ago, elizabeth deposited her 1/2 of the profit from selling her fathers house. the full profit was $12000. she was promised 4% simple interest. How much was the interest?

The simplified radical expression by rationalizing the denominator is, \(\frac{-6}{\sqrt{5y}}\times\frac{\sqrt{5y}}{\sqrt{5y}}\) = \(\frac{-6\sqrt{5y}}{5y}$$\) = $\frac{-6\sqrt{5y}}{5y}$.

To simplify the radical expression by rationalizing the denominator, multiply both numerator and denominator by the conjugate of the denominator.

The given radical expression is \($\frac{-6}{\sqrt{5y}}$\).

Rationalizing the denominator

To rationalize the denominator, we multiply both the numerator and denominator by the conjugate of the denominator, \($\sqrt{5y}$\)

Note that multiplying the conjugate of the denominator is like squaring a binomial:

This simplifies to:

(-6√(5y))/(√(5y) * √(5y))

The denominator simplifies to:

√(5y) * √(5y) = √(5y)^2 = 5y

So, the expression becomes:

(-6√(5y))/(5y)

Therefore, the simplified expression, after rationalizing the denominator, is (-6√(5y))/(5y).

\($(a-b)(a+b)=a^2-b^2$\)

This is what we will do to rationalize the denominator in this problem.

We will multiply the numerator and denominator by the conjugate of the denominator, which is \($\sqrt{5y}$\).

Multiplying both the numerator and denominator by \($\sqrt{5y}$\), we get \(\frac{-6}{\sqrt{5y}}\times\frac{\sqrt{5y}}{\sqrt{5y}}\) = \(\frac{-6\sqrt{5y}}{5y}$$\)

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Answer:

what grade are you in? Maybe i can help :)

Answer:

a=750

Step-by-step explanation:

Answer:

I THINK IT WORKS

TRY IT

Answer: 2.5, 5.4

Step-by-step explanation:

\(-16t^2 +126t=213\\\\16t^2 -126t+213=0\\\\t =\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(213)}}{2(16)}\\\\t \approx 2.5, 5.4\)

Answer:

PC=9

Step-by-step explanation:

A²+B²=C²

4²+8.1²=C²

16+65.61=C²

81.61=C²

≈81=C²

PC=9

Answer:

it's the third one trust me

Answer:

i think that the answer is 1.000

Step-by-step explanation:

Answer:

C)

AKA

a= 22/150; b= 14.7%

AKA

a = StartFraction 22 over 150 EndFraction; b = 14.7 percent

__________________________________________________

I am very sorry if this was wrong for you, but it was correct for me.

Brainliest would be apreaciated, but if not thats completley ok.

Sorry I dont have an explaination im not very good at those.

Sorry abt my spelling i know i suck.

And sorry I could not help earlier.

hope it helped :)

Answer: C)

AKA

a= 22/150; b= 14.7%

AKA

a = StartFraction 22 over 150 EndFraction; b = 14.7 percent

Answer:20

Step-by-step explanation:

Answer:

the real answer is 28588

Step-by-step explanation:

The exponential equation is solved and the population in 2020 is given by the relation P ( A ) = 27,369

The exponential growth or decay formula is given by

x ( t ) = x₀ × ( 1 + r )ⁿ

x ( t ) is the value at time t

x₀ is the initial value at time t = 0.

r is the growth rate when r>0 or decay rate when r<0, in percent

t is the time in discrete intervals and selected time units

Given data ,

Let the initial population be P ( 0 ) = 4,200

Let the population in 10 years be P ( 1 ) = 5,000

Now , the population in 100 years is P ( 100 ) =

The exponential growth formula is given by

x ( t ) = x₀ × ( 1 + r )ⁿ

r = ln(5,000/4,200) / 10 = 0.017

Now we can use this value of r to predict the population in 2020, which is 100 years after 1920:

P(100) = 5,000 × e^(0.017 × 100) = 27,369

Hence , the predicted population of Centerville in 2020, assuming exponential growth, is 27,369

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Expression which represents the amount of money spend by each woman is equal to [ 9 + 1.35 + (one- half)(3.50 + 1.74)].

As given in the question,

Condition for the expression:

Sally and Anne both went for a movie.

Each one purchased a drink.

Shared one popcorn and one veggie bought by them.

Consider movie ticket price = 9

drink price = 1.35

Popcorn price = 3.50

Veggie price = 1.74

Explanation for different expressions are:

1. one-half (9 + 1. 35 + 3. 50 + 1. 74)

Here sum of all the amount is divided equally, which is not correct as movie ticket and drink they have purchased individually.

2.  9 + 1. 35 + one-half (3. 50 + 1. 74)

This is correct option as it represents :

Movie ticket price = 9

Drink = 1.35

one-half (3. 50 + 1. 74) = one popcorn and one veggie divided equally.

3. 18 + 2. 70 + one-half (3. 50 + 1. 74)

As per consideration of price this is not correct option.

Movie ticket price =18

Drink = 2.70

one-half (3. 50 + 1. 74) = one popcorn and one veggie divided equally.

4. 9+1. 35+2(3. 50+1. 7)

This is not correct option as popcorn and veggie price is doubled.

Therefore, expression which represents the amount of money spend by each woman is equal to [ 9 + 1.35 + (one- half)(3.50 + 1.74)].

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The four integers are 3, 6, 6, and 13.

Since the median of the four integers is 6, the two middle integers are 6. Let the other two integers be x and y.

Since the mean of the four integers is 7,

the sum of the four integers is 4*7=28.

The sum of the two middle integers, 6 and 6, is 12,

so the sum of x and y is 28-12=16.

Since the range of the four integers is 10, the difference between the maximum and minimum integers is 10. Since the maximum integer is either x or y and the minimum integer is either x or y, the difference between x and y is 10.

If x>y, then x=y+10. If y>x, then y=x+10. Since the sum of x and y is 16, we can set up the following system of equations:

x+(x+10)=16

2x+10=16

2x=6

x=3

y=x+10

3+10=13

y=12

Therefore, the four integers are 3, 6, 6, and 13. The mode of the four integers is 6.

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Answer:

27

55

62

Step-by-step explanation:

the slope is m= -1/5.

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.

y_2 - y₁ = m(x₂ - x₁).

here, we have,

the slope of the line that passes through the points (-1, 6) and (14, 3)

Slope: m=  y_2 - y₁/(x₂ - x₁).

              = 3-6/14+1

              = -1/5.

hence, the slope is m= -1/5.

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Given the series 2, 4, 7, 11, 16, the next number in the series is 22.

Note that series usually have an underlying pattern. In this case, the pattern is that the number added to the previous number to get the new one is increasing arithmetically.

that is

1 +1  = 2
2 + 2 = 4
3 + 4 = 7
4 + 7 = 11
5 + 11 = 16


As you can see , aded 1, then 2, then 3 and so on. Hence it means that we must add 6 to the previous number to get the next number:

That is


6 + 16 = 22

Hence, 22 is the next number in the series.

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The payback period is longer than Project B. Hence, even if the total cash inflows are the same for both projects, the timing of the cash flows is different. This difference in cash flow timing leads to different project evaluations.

For Project A: Initial Investment: $875,000, Sale of old equipment: $30,000, Incremental Revenues: $380,000, Incremental Cash Costs: $175,000, Major overhaul at the end of 3 years: $80,000, Initial working capital: $60,000

Equipment life: 6 years, Salvage value at the end of 6 years: $0

For Project B: Initial Investment: $875,000

Equipment life: 6 years: Salvage value at the end of 6 years: $90,000, Revenues: Year 1: $150,000

Year 2: $250,000

Year 3 to 6: $450,000, Cash costs: Year 1: $125,000, Year 2: $175,000, Year 3 to 6: $210,000, Hurdle rate: 8%

The requested analysis has to be done using Net Present Value (NPV), Profitability Index (PI), Payback Period (PBP), and Internal Rate of Return (IRR) calculations.

Formula view for each of the measures is given below: Net Present Value (NPV) calculation: Negative cash flows have to be entered with a negative sign and positive cash flows with a positive sign.

We have to use the NPV formula as given below: NPV = PV of cash inflows - PV of cash outflows

where, PV = Present Value of Cash Flow, i = The time period, n = The total number of time periods, r = Discount rate (hurdle rate)

Profitability Index (PI) calculation: Profitability Index is the ratio of present value of cash inflows to the present value of cash outflows.

The formula for PI is as follows: Profitability Index = PV of Cash Inflows / PV of Cash Outflows

Payback Period (PBP) calculation: Payback Period is the time period required to recover the initial investment. The formula for Payback Period is as follows: Payback Period = Initial Investment / Annual Cash Inflows

Internal Rate of Return (IRR) calculation: IRR is the discount rate at which the present value of cash inflows equals the present value of cash outflows. The IRR formula is as follows: NPV = 0 = PV of cash inflows - PV of cash outflows

Summing up the above-mentioned formulas, the calculations for Project A and Project B are shown below:

Calculations for Project A: Calculations for Project B:

Evaluation and brief explanation of relative benefits:

For Project A: Net Present Value (NPV)

= $34,328.70 > 0

Profitability Index (PI) = 1.039 > 1,

Payback Period (PBP) = 3.87 years < 6 years

Internal Rate of Return (IRR) = 13.03% > 8%

For Project B: Net Present Value (NPV)

= $191,738.43 > 0

Profitability Index (PI) = 1.22 > 1

Payback Period (PBP) = 2.84 years

< 6 years

Internal Rate of Return (IRR) = 18.28%

> 8%

The NPV and PI are positive for both projects, which means that they are expected to be profitable.

However, the payback period is less than the life of the project only for Project B. Also, the IRR is higher than the hurdle rate for both projects, but it is higher for Project B.

Hence, Project B is more preferable than Project A.

Project A and Project B are not identical because of their different cash flow patterns.

Project A has higher cash outflows in the initial years, which reduces the NPV and PI.

Also, the payback period is longer than Project B. Hence, even if the total cash inflows are the same for both projects, the timing of the cash flows is different. This difference in cash flow timing leads to different project evaluations.

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Answer: $54.45

Step-by-step explanation:

      First, we will find the price of one towel.

-> We will divide the cost by the towels bought.

$39.60 / 8 = $4.95

     Now, we can find the price of 11 towels.

-> We will multiply the cost of one towel by 11 to find the total cost.

$4.95 * 11 = $54.45

Answer:

$54.45

Step-by-step explanation:

Given:

Number of towels = 8

Money spent on towels = $39.60

To Find:

What is the price, in dollars, of 11 towel?

Solve:

Since, each towels cost the same amount then we can divide the cost by number of towels.

39.60/8 = 4.95

Thus, Each towel costs $4.95

Then we are trying to find the price in dollars of 11 towels.

Knowing that 1 towels cost $4.95 then 11 towels:

4.95 × 11 = $54.45

Kavinsky

1.

The value of y in the diagram where ACD and BCD are straight lines is 109°

∠CED = 95°

2. ∠CBD is 134°

The value of b in the figure where ABC, ADF and BDE are straight line is 54°

1.

ACD and BCD are straight lines.

∠ACB = 180 - 34 - 75 = 71° (sum of angle in a triangle)

Therefore,

y = 180 - ∠ACB (angle on a straight line)

y = 180 - 71 = 109°

∠DCE = 71° (vertically opposite angles)

∠CED = 180 - 71 - 14 = 95° (sum of angles in a triangle)

2.

ABC, ADF and BDE are straight line.

The sum of the opposite interior angle is equals to the exterior angle.

Therefore,

∠CBD = 93 + 41

∠CBD = 134°

∠EDF = 93°(vertically opposite angles)

b = 180 - 33 - 93 = 54° (sum of angles in a triangle)

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