a. A tank holds 1000 liters of pure water. Brine which contains 0.05 kg of salt per liter enters the tank at the rate of 5 liters per minute. The solution is kept thoroughly mixed and is drained from the tank at the rate of 5 liters per minute. If m is the mass of salt in the tank at time t, which of the following options describes the rate of change of the mass of salt in the tank? dm/dt=(50−m)/200
dm/dt=0.05−(m/200)
dm/dt=0.25−(m/200)
dm/dt=−m/200
​

Answer: yes that is a function

Step-by-step explanation:

It is a function because every y value has a unique x value

Answer:

A. 76%

Step-by-step explanation:

70+6=76 squares are shaded

The degree of the monomial expression -3xy²z(-2x²yz) is derived to be equal to 8.

A monomial is a type of algebraic expression that consists of only one term. It is an expression in which the variables and their exponents are multiplied together, with no addition or subtraction involved. The degree of a monomial is the sum of the exponents of its variables.

Given the monomial:

-3xy²z(-2x²yz)

We can simplify it by multiplying the coefficients and adding the exponents of the variables:

-3(-2)x^(2+1) y^(2+1) z^(1+1)

= 6x³y³ z²

Therefore, the degree of the given monomial expression is: 3 + 3 + 2 = 8.

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This will give us the quotient, which will be the formula for the rational function.f(x) = \((x^2 + 2x - 3) / (x^2 + x - 2)f(x) = (x + 3)(x - 1) / (x + 2)(x - 1)f(x) = (x + 3) / (x + 2)\)Thus, the formula for the rational function graphed above is\(:f(x) = (x + 3) / (x + 2)\)

Use the following terms in your answer, "find a formula for the rational function graphed below. the function has a horizontal asymptote of y?"Rational function graphed belowThe horizontal asymptote of the function is y = 1, as shown by the dotted line. A rational function is a function that can be written as the ratio of two polynomial functions, where the denominator is not zero. A rational function can have horizontal, vertical, or oblique asymptotes, depending on the behavior of the function as x approaches infinity or negative infinity.In this case, the horizontal asymptote is at y = 1, which means that as x gets very large or very small, the function approaches this value. To find a formula for the rational function, we need to use the given information about the horizontal asymptote.The general form of a rational function is: f(x) = (ax^2 + bx + c) / (dx^2 + ex + f)To find a formula for the given function, we need to determine the coefficients of this general form. Since we know that the horizontal asymptote is y = 1, we can use long division or synthetic division to divide the denominator by the numerator.

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Answer:

1/38

Step-by-step explanation:

1/4 ÷ 19/2

1/4 × 2/19

1 × 2 over 4 × 19 = 2/76

2 ÷ 2 over 76 ÷ 2 = 1/38

Therefore:

1/4 ÷ 19/2 =

1/38

Hope this helps!

Answer:

hey will you be my friend

I yes then text me

The equation of the function that is graphed as line b is,

⇒ y = - 2x - 1

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line b are (- 1, 1) and (- 2, 3).

Now,

Since, The equation of line passes through the points ( (- 1, 1) and (- 2, 3).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (3 - 1)) / (- 2 + 1)

m = 2 / - 1

m = - 2

Thus, The equation of line with slope - 2 is,

⇒ y - 1 = - 2 (x + 1)

⇒ y - 1 = - 2x - 2

⇒ y = - 2x - 1

Therefore, The equation of the function that is graphed as line b is,

⇒ y = - 2x - 1

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Final Answer: All Real Numbers

Steps/Reasons/Explanation:

Question: Solve for a. \(4(a + 3)=12 + 4a\).

Step 1: Expand.

\(4a + 12 = 12 + 4a\)

Step 2: Cancel \(4a\) on both sides.

\(12 = 12\)

Step 3: Since both sides equal, we would have infinitely many solutions.

~I hope I helped you :)~

Answer:1

Step-by-step explanation:1

Answer:

Step-by-step explanation:

(7^2)^-7

7^-14

1/7^14

Answer:

I don’t understand

Step-by-step explanation:

i don’t understand

Answer:

Option B.

Step-by-step explanation:

If you begin with one dollar a day there will get you more by the end of the month because on day 2 your on 201 already which is more than you get in that month with one cent.

The first option (A) will give you more money than option (B).

A geometric progression is a sequence in which any element after the first is obtained by multiplying the previous element by a constant which is called a common ratio denoted by r.

The difference between every two successive terms in a sequence is the same this is known as an arithmetic progression (AP).

Given that

Case A). Doubling each day

1 + 2+ 4 + 8 + 16 .... it is form a GP series with common ratio (r) 4/2 = 2

Number of terms (n)

Sum =  30( \(2^{30}\) - 1)/(2 - 1) = $2147483464.

Case B). Adding $100 each day

1 + (101 + 201 + 301 ....) it is form a ap series with common difference d = 201 - 101 = 100.

Number of terms = 29

Sum = 1 + 29/2 + [ 2 (101) + 28(100)] = $43530

Hence it is clear that case (A) will give you more money.

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The calculation would have three significant figures, since both original numbers have three significant figure.

The number of significant figures in a calculation is determined by the number of significant figures in the original numbers used in the calculation. For example, if we have the calculation 3.14 + 2.7 = 5.84, the answer will have three significant figures because the original numbers, 3.14 and 2.7, each have three significant figures.

In general, significant figures are determined by counting all non-zero digits, plus any zeros that come between non-zero digits, such as in the numbers 10.0 and 0.07. If a number is a decimal, the zeros after the decimal point are also significant, such as in the number 0.07. Zeros that come before the first non-zero digit are not significant, such as in the number 0.0007.

In the above example, the calculation would have three significant figures, since both original numbers have three significant figures.

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Complete quetion:

What is the number of significant figures in the calculation 3.14 + 2.7 = 5.84?

Your net worth change by zero dollars.

Net worth is the difference between asset and liability.  

In other words net worth is the sum of all assets owned by a person or a company, minus any obligations or liabilities.

Therefore, since he took $5,000 out of the bank to purchase a car worth $5,000 his net worth will change by zero dollars.

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Answer:

The coordinates are (15,-55).

The probability that the sample mean will be within plus minus 2 of the population mean if the sample size is n = 100 between z-scores of 0 and 2.5 using a z-table.

The standard deviation of the sample distribution, commonly known as the standard error, can be computed using the formula given that the population mean is 100 and the standard deviation is 16:

Standard Error = Standard Deviation / sqrt(sample size)

Let's determine the likelihoods for sample sizes of n = 100 and n = 400:

For n = 100:

Standard Error = 16 / sqrt(100) = 16 / 10 = 1.6

We can determine the z-scores for the upper and lower boundaries to establish the likelihood that the sample mean will be within plus or minus 2 of the population mean:

Lower Bound z-score = (Sample Mean - Population Mean) / Standard Error

Lower Bound z-score = (100 - 100) / 1.6

Lower Bound z-score = 0

Upper Bound z-score = (Sample Mean - Population Mean) / Standard Error

Upper Bound z-score = (104 - 100) / 1.6

Upper Bound z-score = 4 / 1.6

Upper Bound z-score = 2.5

We can calculate the region under the normal distribution curve between z-scores of 0 and 2.5 using a z-table or statistical software. This shows the likelihood that the sample mean will be within +/- 2 standard deviations of the population mean.

For n = 400:

Standard Error = 16/√400

Standard Error = 16/20

Standard Error = 0.8

We determine the z-scores by following the same procedure as above:

Lower Bound z-score = (Sample Mean - Population Mean) / Standard Error

Lower Bound z-score = (100 - 100) / 0.8

Lower Bound z-score = 0

Upper Bound z-score = (Sample Mean - Population Mean) / Standard Error

Upper Bound z-score = (104 - 100) / 0.8

Upper Bound z-score = 4 / 0.8

Upper Bound z-score = 5

Once more, we may determine the region under the normal distribution curve between z-scores of 0 and 5 using a z-table or statistical software.

A larger sample size, like n = 400, has the benefit of a lower standard error. The sampling distribution of the sample mean will be more constrained and more closely resemble the population mean if the standard error is less.

As a result, there is a larger likelihood that the sample mean will be within +/- 2 of the population mean. In other words, the estimate of the population mean gets more accurate and dependable as the sample size grows.

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The ratio of fruit juice to lemonade in the second batch is 21:16

Ratios are denoted by the sign ":", and they are used to making comparison between units of different quantities

The ratio is given as:

\(F : L = 21 : 14\)

Where:

When 2 litres are added to the original amount of lemonade, the ratio becomes

\(F : L = 21 : 16\)

Hence, the ratio of fruit juice to lemonade in the second batch is 21:16

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Answer:

D.1440

Step-by-step explanation:

V=lxwxh

10x12x12

1440

The essay will need to be in your own words of course, but the basic idea is to replace x with 0 and solve for y to get the y intercept. To get the x intercept, replace y with 0 and solve for x.

Here's an example

2x+5y = 10

Let's find the x intercept

2x+5y = 10

2x+5(0) = 10

2x = 10

x = 5 is the x intercept

Now we'll do the y intercept

2x+5y = 10

2(0)+5y = 10

5y = 10

y = 10/5

y = 2 is the y intercept

The x intercept is the location where the graph crosses the x axis. The y intercept is where the graph crosses the y axis.

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

3 and 1/3 pounds = flour

5 = containers

Step 02:

We must apply the algebraic rules to find the solution.

The answer is:

2/3 pounds of flour

a. The replacement free cash flows is $255,000

b.  The Payback Period time required to recover the initial investment is 2.7778 years.

d. By calculating the NPV at various discount rates, we can determine the rate at which NPV is closest to zero.

a. To calculate the replacement free cash flows, we need to consider the cash flows associated with the new fleet of trucks. Here's the calculation:

Initial cash outflow: Purchase cost of new trucks + Shipping cost

= $350,000 + $50,000

= $400,000

Annual cash flows:

Operating cost savings:

Diesel fuel savings: $250,000 - $150,000 = $100,000

Maintenance cost savings: $35,000 - $10,000 = $25,000

Net operating working capital reduction: $20,000

Total operating cost savings per year: $100,000 + $25,000 + $20,000 = $145,000

Revenue increase:

Revenue growth rate: 10%

Year 1 revenue increase: $800,000 * 10% = $80,000

Year 2 revenue increase: $800,000 * 10% = $80,000

Year 3 revenue increase: $800,000 * 10% = $80,000

Year 4 revenue increase: $800,000 * 10% = $80,000

Year 5 revenue increase: $800,000 * 10% = $80,000

Salvage value: Market value of the new trucks at the end of 5 years = $30,000

Free cash flows:

Year 0: Initial cash outflow = -$400,000

Year 1: Cash flow = Operating cost savings + Revenue increase = $145,000 + $80,000 = $225,000

Year 2: Cash flow = Operating cost savings + Revenue increase = $145,000 + $80,000 = $225,000

Year 3: Cash flow = Operating cost savings + Revenue increase = $145,000 + $80,000 = $225,000

Year 4: Cash flow = Operating cost savings + Revenue increase = $145,000 + $80,000 = $225,000

Year 5: Cash flow = Operating cost savings + Revenue increase + Salvage value = $145,000 + $80,000 + $30,000 = $255,000

b. The Payback Period is the time required to recover the initial investment. To calculate it, we sum the cash flows until they equal or exceed the initial investment. Here's the calculation:

Payback Period = Number of years to recover initial investment

= 2 years (Year 1 cash flow + Year 2 cash flow)

+ (Remaining investment / Year 3 cash flow)

= 2 years + ($400,000 - $225,000) / $225,000

= 2 years + 0.7778 years

= 2.7778 years

c. To calculate the Net Present Value (NPV) and Profitability Index (PI), we need to discount the cash flows using the given discount rate of 15%. Here's the calculation:

Discount rate: 15%

Present value factor for each year:

Year 0: 1 / (1 + Discount rate)^0 = 1

Year 1: 1 / (1 + Discount rate)^1 = 0.8696

Year 2: 1 / (1 + Discount rate)^2 = 0.7561

Year 3: 1 / (1 + Discount rate)^3 = 0.6575

Year 4: 1 / (1 + Discount rate)^4 = 0.5718

Year 5: 1 / (1 + Discount rate)^5 = 0.4972

NPV calculation:

NPV = (Year 0 cash flow) + (Year 1 cash flow * Present value factor) + (Year 2 cash flow * Present value factor) + ...

= -$400,000 + ($225,000 * 0.8696) + ($225,000 * 0.7561) + ($225,000 * 0.6575) + ($225,000 * 0.5718) + ($255,000 * 0.4972)

Profitability Index calculation:

PI = NPV / Initial investment

= NPV / $400,000

d. To calculate the Internal Rate of Return (IRR), we find the discount rate that makes the NPV equal to zero. Here's the calculation:

IRR = Discount rate that makes NPV equal to zero

By calculating the NPV at various discount rates, we can determine the rate at which NPV is closest to zero.

e. Based on the information provided, we can determine if the fleet should be replaced by considering the Payback Period, NPV, Profitability Index, and IRR.

If the Payback Period is within the company's acceptable timeframe and the NPV is positive, or the Profitability Index is greater than 1, and the IRR exceeds the company's required rate of return, then replacing the fleet would be financially favorable. If any of these criteria are not met, it would indicate that the replacement may not be the best option.

Please note that the calculation of IRR requires further information, and the final decision should consider additional factors such as qualitative aspects, operational requirements, and strategic considerations.

Without the specific values for cash flows in each year, it is not possible to provide a definitive answer to whether the fleet should be replaced based on the given information.

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Answer:

x = 127 ft

Step-by-step explanation:

Answer:45 ft

Step-by-step explanation:X^2= (90ft)^2 + (90ft)^2

first possibility

radius 4

height 5.97

second possibility

radius 6

height 2.66

Answer:3x+6=2x+21 base angle of isosceles triangle

3x-2x=21-6

X=15

<J=3×15+6=51

<k=2×15+21=51

,<I=180-51-51=78

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

7s-3s-2t+7t-4st

4s+5-4st

Answer: y = -3/5x - 6

Step-by-step explanation:

There are a few equations that can be used for this, but the simplest one would be y = mx + b

We are given:

y = -3

m = -3/5 (slope)

x = -5

b = ?

Our equation is this, we are solving for b

==> -3 = -3/5 ( -5) + b

==> -3 = -3/5 ( -5) + b ( multiply the brackets)

==> -3 = 3 + b ( subtract 3 to both sides)

==> -6 = b

Now we can make the desired equation in slope intercept form;

y = -3/5x - 6

Hope this helped! Have a great day :D

Answer:

Its D

Step-by-step explanation:

Took the test.

Based on the information given regarding the triangle, the triangle pairs can be mapped to each other will be D. Triangles X Y Z and A B C are shown. Both triangles are congruent. Triangle X Y Z is rotated down and to the left to form triangle A B C. It is also slightly higher than triangle A B C.

It should be noted that a translation is a slide, and this implies that the function has the same shape graphically, but on the other hand, the graph of the function slides to a different position on the coordinate plane.

In this case, the triangle pairs can be mapped to each other using both a translation and a rotation about C. Therefore, the correct option is D.

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Data that provide labels or names for groupings of like items are known as categorical data. Categorical data is used to group data into specific categories or classes based on a shared characteristic or attribute.

Categorical data can be divided into two main types: nominal and ordinal. Nominal data are labels that represent categories with no inherent order or ranking. For example, gender, eye color, or country of origin are nominal categories. Ordinal data, on the other hand, represent categories that have a natural order or ranking. Examples of ordinal categories include education level (high school, college, graduate school) or income level (low, medium, high).

Categorical data is often represented using graphs and charts, such as bar charts or pie charts, to visually display the frequency and distribution of each category. Categorical data is an important tool for data analysis as it allows researchers and analysts to identify patterns and relationships between different categories, and to make informed decisions based on the data.

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Answer:

Either the abscissa is positive and the ordinate is negative or the abscissa is positive and the ordinate is negative. So, a point could be either (+,-), which lie in quadrant IV, or it could be of the type (-,+), which lie in quadrant II.

Answer:

Answer choice A. Slope -1

Step-by-step explanation:

If we plot the two points on a graph we can see that the points go from left to right, starting from a higher point to a lower point. This means the slope is negative. B and D are the same choice, but just in different words, and 0 cannot be positive or negative. and C is positive, not negative. So it is A. I hope this helps, and I hope it's not wrong, but I don't think it is.