Help me solve this inequality!

The effective annual interest rate of the investment is approximately 5.4%.

To find the effective annual interest rate, we need to consider the compounding frequency and the total accumulated amount after the specified time period. In this case, the investment is compounded monthly, and it accumulates to $773.45 after 2 years.

Convert the nominal interest rate to the monthly rate:

Since the interest is compounded monthly, we need to convert the nominal yearly interest rate to the monthly rate. Assuming a nominal interest rate of \(\(r\)\), the monthly rate can be calculated as \(\(i = \frac{r}{12}\)\).

Calculate the effective annual interest rate:

To find the effective annual interest rate, we can use the formula:

\(\((1 + i)^{12} = (1 + \text{effective annual interest rate})\)\).

Rearranging the formula and solving for the effective annual interest rate, we have:

\(\(\text{effective annual interest rate} = (1 + i)^{12} - 1\)\).

Substitute the values and calculate:

In this case, the accumulated amount is $773.45 after 2 years. By substituting the values into the formula, we have:

\(\(773.45 = 700(1 + \frac{r}{12})^{24}\)\).

Solving for \(\(r\)\), we find:

\(\(\frac{r}{12} \approx 0.0045\)\).

Converting the monthly rate to the effective annual interest rate, we get:

\(\((1 + \frac{r}{12})^{12} - 1 \approx 0.054\),\) which is equivalent to 5.4%.

Therefore, the effective annual interest rate of the investment is approximately 5.4%.

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Answer:

7918

Step-by-step explanation:

If you round Earth's diameter, I believe that it is 7,918 miles.

Answer:

v-2>1

v-2+2>1+2

v>3

Therefore, C

A checking account is used for daily basis transaction and a debt and is usually associated with it.Saving accounts is just used for saving money.It has a time limit then you can withdraw your money.It is not on daily basis.

A bank account that allow the user to withdraw the money ,pay bill,transfer money to other person or make a purchase anything by writing checks.Check accounts typically don't earn interest.By checking accounts we can easily deposit and withdraw money for daily transaction.

Saving accounts are intended for storing your money which you don't plan to use daily.saving accounts earns interest at your money.saving account is designed for the accumulation of money in a safe place for future use.saving accounts offer easy access to your money in any emergency.so keeping your money in a saving account means that your money is safe for your future use.

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Answer:

14 bags

Hope this helps :)

Step-by-step explanation:

1. 1800 ÷ 3 = 600

2. 8400 ÷ 600 = 14 bags

Answer:

4

Step-by-step explanation:

1800/3 = 600

We know that every pound covers 600 square feet:

8400/600 = 14

14/4 = 3.5 (round up) so it would become 4.

I know I am late but here :)

The rate of constant for the above-given first-order reaction is b.) 8.77 × 10–3 h–1.

The half-life of a first-order reaction can be calculated using the equation t1/2 = ln(2)/k, where t1/2 is the half-life and k is the rate constant.

In this case, we know that the reaction goes to half completion in 79 hours. Therefore, the half-life is also 79 hours.

Plugging this into the equation, we get:

79 = ln(2)/k

Solving for k, we get:

k = ln(2)/79

Using a calculator, we can evaluate this expression to get:

k = 8.77 × 10–3 h–1

Therefore, the correct answer is b) 8.77 × 10–3 h–1.

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Answer: The paint mixer should mix 2.75 gallons of 30% gloss paint and 1 gallon of 15% gloss paint to make 3.75 gallons of paint that is 20% gloss.

To calculate the number of gallons of each paint that the mixer should mix, we need to use the formula: C1V1 + C2V2 = C3V3, where C1 and V1 are the concentration and volume of the first paint, C2 and V2 are the concentration and volume of the second paint, and C3 and V3 are the concentration and volume of the mixture. Using this formula and the given information, we can set up the equation:0.30V1 + 0.15V2 = 0.20(3.75)Simplifying the equation, we get:V1 + V2 = 3.75And, rearranging it, we get:V2 = 3.75 - V1.Substituting this in the first equation, we get:0.30V1 + 0.15(3.75 - V1) = 0.20(3.75).Simplifying and solving for V1, we get:V1 = 2.75.

Therefore, the mixer should mix 2.75 gallons of 30% gloss paint and 1 gallon of 15% gloss paint to make 3.75 gallons of paint that is 20% gloss.

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Answer:

14.04 miles/hours

Step-by-step explanation:

yw

The mean absolute deviation for the group of household incomes is approximately 14.8 (rounded to the nearest tenth).

To calculate the mean absolute deviation (MAD) for a group of data, we follow these steps:

Find the mean (average) of the data set.

Subtract the mean from each data point, obtaining the deviations.

Take the absolute value of each deviation.

Find the mean of the absolute deviations.

Given the household incomes for 10 different households:

38, 45, 76, 93, 50, 54, 29, 44, 62, 31

Let's calculate the MAD step by step:

Find the mean (average):

Mean = (38 + 45 + 76 + 93 + 50 + 54 + 29 + 44 + 62 + 31) / 10

Mean = 482 / 10

Mean = 48.2

Calculate the deviations:

Deviation for each data point = Data point - Mean

Deviation for 38 = 38 - 48.2 = -10.2

Deviation for 45 = 45 - 48.2 = -3.2

Deviation for 76 = 76 - 48.2 = 27.8

Deviation for 93 = 93 - 48.2 = 44.8

Deviation for 50 = 50 - 48.2 = 1.8

Deviation for 54 = 54 - 48.2 = 5.8

Deviation for 29 = 29 - 48.2 = -19.2

Deviation for 44 = 44 - 48.2 = -4.2

Deviation for 62 = 62 - 48.2 = 13.8

Deviation for 31 = 31 - 48.2 = -17.2

Take the absolute value of each deviation:

Absolute deviation for each data point = |Deviation|

Absolute deviation for -10.2 = 10.2

Absolute deviation for -3.2 = 3.2

Absolute deviation for 27.8 = 27.8

Absolute deviation for 44.8 = 44.8

Absolute deviation for 1.8 = 1.8

Absolute deviation for 5.8 = 5.8

Absolute deviation for -19.2 = 19.2

Absolute deviation for -4.2 = 4.2

Absolute deviation for 13.8 = 13.8

Absolute deviation for -17.2 = 17.2

Find the mean of the absolute deviations:

Mean Absolute Deviation (MAD) = (10.2 + 3.2 + 27.8 + 44.8 + 1.8 + 5.8 + 19.2 + 4.2 + 13.8 + 17.2) / 10

MAD = 148 / 10

MAD = 14.8

To the nearest tenth, this means that the mean absolute deviation for the group of household incomes is around 14.8.

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Answer:

fitting a simple linear regression first select the cell in data set second on the analyse it ribbon tap in statistical analysis group click fit model and then click the simple degradation model 3rd the wild drop down list select the response variable 4th in the X drop down let's select the predicated

Answer:

see explanation

Step-by-step explanation:

8(16) + 8(6) ← factor out 8 from each term

= 8(16 + 6)

= 8(22)

= 8 × 22

= 176

Answer:

-2.5

Step-by-step explanation:

-2.5 is a rational number and no an integer while 10/5 can be an integer because when it is simplified it equals 2 so your answer would be -2.4

The vertex is at (-2, -9).

From the equation:

y = x² + 4x - 5

Transpose the c-value to the left side of the equation:

y + 5 = x² + 4x

Complete the square of the expression on the right side of the equation to get a perfect square trinomial:

y + 5 = x² + 4x + 4 - 4

by adding and subtracting 4 to the right side of the equation to maintain its balance.

Add the numbers on the left and factor the trinomial on the right:

y + 9 = (x + 2)²

Transpose the number across to the right side to get the equation into the vertex form, y = a(z-h)² + k:

y = (x + 2)² - 9

Make sure the addition and subtraction signs are correct to give the proper vertex form.

Here, the vertex is at (-2, -9).

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Given:-

To find:-

Answer:-

1) Firstly we are told to transpose the c value to LHS .

With respect to standard form of a quadratic equation, \( ax^2+bx + c \) ,the value of c here will be -5 . So on transposing c to LHS , we have;

\(\implies y + 5 = x^2 + 4x\\\)

w) Next we are told to complete the square on the RHS of the equation. For that add and subtract 4 .

\(\implies y + 5 = x^2 + 4x + 4 - 4 \\\)

\(\implies y + 5 =\{ (x)^2 + 2.2.x + 2^2 \}- 4\\\)

The terms inside the curly brackets are in the form of \( a^2+2ab + b^2\) , which is the whole square of \( (a + b )\) . That is \( ( a + b)^2\) . So , we can rewrite it as ,

\(\implies y + 5 = (x +2)^2 - 4 \\\)

\(\implies y + 5 + 4 = (x+2)^2 \\\)

3) Next we have to add the number on the left and factor the trinomial on right as ,

\(\implies y + 9 = (x+2)^2 \\\)

4) Now we are told to transpose the number on the LHS to RHS and get the equation into vertex form which is \( y = a(z-h)^2+ k \) .

\(\implies\underline{\underline{ y = (x+2)^2 - 9}} \\\)

This is our required answer in vertex form. Also on comparing to the standard equation of vertex form, we have;

\(\implies vertex = ( -2,-9) \\\)

and we are done!

If points d and f are on side ab and points e ang g are on side ac then line segment de and fg are parallel.

Given There is a triangle abc.

Parallel lines are those lines that do not meet at any point. If we draw a triangle abc and plot points d and f are marked on side ab and points e and g are marked on side ac then the line segment fg is parallel to de because both the line segments are drawn from the points which are on the sides opposite to each other. We have assumed a simple triangle because no description is given for the triangle.

Hence the line segment fg is parallel to de if drawn points d and f marked on ab and points e and g are marked on ac.

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Answer:D-E is parallel to FG which is parallel to B-C meaning all three are parallel

Step-by-step explanation:

The domain of the square root function is x≥0.

What is a function?

Any relation in which each input has exactly one output is referred to as a function. To put it another way, the function outputs one value exactly for each input value. Because one is mapped to two different values, the graph above depicts a relation rather than a function. But if one were instead mapped to a single value, the relation above would become a function. Furthermore, output values could be identical to input values.

The x-values are input into the function machine. The function machine then performs its operations and outputs the y-values. The function within can be any function.

The square root function's purpose must now be considered. The positive number that results in the input after being squared is returned as the principal root or output. Since y will be bigger than or equal to 0, we may be certain of that.

To find out a perfect square we need to find out square root is an integer.

Hence, The domain of the square root function is x≥0.

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The expressions that will give you a difference of 5 are: -3 - (-8) and 1 - (-4).

The difference of two expressions is determined by subtracting one from the other.

Find the difference of each of the expressions given to determine which will give us 5.

-3 - (-8)

= -3 + 8

= 5

-2 - 3 = -5 [this is not the same as 5]

1 - (-4)

= 1 + 4

= 5

7 - (-2)

= 7 + 2

= 9

-3 - (-8) and 1 - (-4) will give us a difference of 5.

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The domain of the function f(x) = x² - 2x + 1 is all real numbers, which is denoted as (-∞, +∞).

To find the domain of the function f(x) = x² - 2x + 1, we determine the set of all possible values for x that make the function well-defined.

The given function is a polynomial-function, and polynomial functions are defined for all real numbers. So, the domain of f(x) = x² - 2x + 1 is the set of all real numbers, which can be represented as (-∞, +∞).

It means that any real-number can be substituted into the function, and it will give a valid output. There are no limitations on the possible values of x in this case.

Therefore, the domain is all real numbers.

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The given question is incomplete, the complete question is

Find the domain of the function f(x) = x² - 2x + 1.

Farmer has 5 types of animals in his farm, including cows, goats, horses, sheep, and dogs. He has a database that indicates the number of animals in each category. This can be done using a Python dictionary.

Let us consider the Python code to determine the number of animals in each category.```
animal_dict = {"Cow": 10, "Goat": 20, "Horse": 8, "Sheep": 25, "Dog": 15}
print("Number of Cows in the Farm:", animal_dict["Cow"])
print("Number of Goats in the Farm:", animal_dict["Goat"])
print("Number of Horses in the Farm:", animal_dict["Horse"])
print("Number of Sheeps in the Farm:", animal_dict["Sheep"])
print("Number of Dogs in the Farm:", animal_dict["Dog"])```

In the code, `animal_dict` is the dictionary that contains the number of animals in each category. The `print` statement is used to display the number of animals in each category. The output for the above code will be:```
Number of Cows in the Farm: 10
Number of Goats in the Farm: 20
Number of Horses in the Farm: 8
Number of Sheeps in the Farm: 25
Number of Dogs in the Farm: 15```

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The steady-state response is given by the expression below;x = X1sin(ωt − α)We know that; For a damped system with sinusoidal forcing, the steady-state amplitude is given by;X1 = (F0/m) / [(ωn2 − ω2)2 + (2ζωnω)2]0.5To find the phase angle α, we use;tan α = 2ζωnω / (ωn2 − ω2)

Hence, α = tan-1 [2ζωnω / (ωn2 − ω2)]Given ζ = 0.5, ωn = 13 rad/s and ω = 3.1 rad/s, Substituting in the expressions above;X1 = (150/1) / [(13² − 3.1²)² + (2 × 0.5 × 13 × 3.1)²]0.5 = 0.1062 rad

Substituting again;α = tan-1 [2 × 0.5 × 13 × 3.1 / (13² − 3.1²)] = 71.688° = 71.688°Therefore, α = 71.688° to 3 decimal places.

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The cross sectional area of the cargo trailer floor, which is a composite figure consisting of a square and an isosceles triangle, indicates that the volume of the inside of the trailer is about 3,952 ft³.

A composite figure is a figure comprising of two or more regular figures.

The possible cross section of the trailer, obtained from a similar question on the internet, includes a composite figure, which includes a rectangle and an isosceles triangle.

Please find attached the cross section of the Cargo Trailer Floor created with MS Word.

The dimensions of the rectangle are; Width = 6 ft, length = 10 ft

The dimensions of the triangle are; Base length 6 ft, leg length = 4 ft

Height of the triangular cross section = √(4² - (6/2)²) = √(7)

The cross sectional area of the trailer, A = 6 × 10 + (1/2) × 6 × √(7)

A = 60 + 3·√7

Volume of the trailer, V = Cross sectional area × Height

V = (60 + 3·√7) × 6.5 = 3900 + 19.5·√7

Volume of the trailer = (3,900 + 19.5·√(7)) ft³ ≈ 3952 ft³

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Answer:

Step-by-step explanation:

4x/7 - x/21

You have to change the first term 4x/7 to a common denominator of 21.

4x/7 = 12x/21

(21 divided by 7 is 3 and then 3 times four is 12.)

then subtract:  12x/21 - x/21 = 11x/21

The statement "if the dot product of two nonzero vectors is zero, the vectors must be perpendicular to each other" is true. The dot product of two vectors is zero if and only if the vectors are perpendicular.

The dot product of two vectors is defined as the product of their magnitudes and the cosine of the angle between them. When the dot product is zero, it means that the cosine of the angle between the vectors is zero, which occurs when the vectors are perpendicular.

In other words, the dot product being zero indicates that the vectors are at a 90-degree angle to each other, supporting the statement that they are perpendicular.

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On solving the logarithmic function, 2 ln x+3 ln 4=4, we get value of x as is x = √e⁴ - 63.

In mathematics, the opposite of exponentiation is the logarithm. This means that the logarithm of a given number, base b, represents the exponent to which that number must be increased in order to get a certain number, x.

Given equation is -

2 ln x + 3 ln 4=4

⇒ ln x² + ln 4³ = 4

⇒ ln (x² + 4³) = 4

⇒ taking e

⇒ log e(x² + 4³) = 4

⇒ e⁴ = x² + 4³

⇒ e⁴ = x² + 63

⇒ x = √e⁴ - 63

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The measures 3.1, 4.8, and 10.2 cannot be the side lengths of a triangle.

"It states that the sum of any two sides must be greater than the third side."

For given question,

we have been given the measures 3.1, 4.8, and 10.2  

We need to check whether given measures can be the side lengths of a triangle.

First we check whether the given measures obey triangle inequality or not.

3.1 + 4.8 = 7.9

7.9 < 10.2

This means, the measures 3.1, 4.8, and 10.2 do not obey triangle inequality

Therefore,  the measures 3.1, 4.8, and 10.2 cannot be the side lengths of a triangle.

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By applying the z-score concept, it can be concluded that the manufacturer should announce a guaranteed mileage of 44528 miles.

z-score is the standard value or the amount of deviation of a value from the mean.

z = (x - μ) / σ   where:

x = the observed value

μ = the mean

σ = the standard deviation

From the problem we get:

μ = 47,900 miles

σ = 2,050 miles

No more than 5% of the tires will have to be replaced, P(X) = 0.05.

So it is X when Z = -1.645.

Now we want to find the x:

             z = (x - μ) / σ

    -1.645 = (x - 47900) / 2050

-3372.25 = x - 47900

            x = 47900 - 3372.25

               = 44527.75

               ≈ 44528 miles

Thus the manufacturer should announce a guaranteed mileage of 44528 miles.

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