how long will it take $5000 to grow to $6000 at an annual rate of 9% compounded monthly

The solution of the given logarithm function log(f-3)-log(17-40) is

f < 3.

So no option is correct.

A logarithm function is a mathematical function that describes the relationship between a given number (called the argument or input) and a specified base. The logarithm of a number x with respect to a base b is the power to which b must be raised to give x.

In other words, if we have the equation y = log_b(x), then y represents the power to which the base b must be raised to get x. For example, if b=2, then log_2(8) = 3 because 2 raised to the power of 3 equals 8.

The given expression is:

log(f-3)-log(17-40)

We can simplify this expression using the property of logarithms:

log(a) - log(b) = log(a/b)

So, we get:

log((f-3)/(17-40))

Now, for this expression to have a real solution, the argument of the logarithm must be positive, so we have:

(f-3)/(17-40) > 0

Solving for f, we get:

f - 3 < 0 (since 17-40 is negative)

f < 3

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According to the question there are 35 distinct website graphics that can be created by using at least four of seven different bitmap images.

A website is a collection of related web pages, images, videos, and other digital assets that are hosted on a web server and can be accessed by users over the internet. A website is typically identified by a unique domain name and can be accessed by typing the URL into a web browser.

Using the formula for calculating the number of combinations of size k from a set of size n (n choose k), we can calculate the number of distinct website graphics that can be created by using at least four of seven different bitmap images as follows:

n = 7 (7 different bitmap images)
k = 4 (at least 4 of the 7 bitmap images)
Number of distinct website graphics = (7 choose 4) = 35
Therefore, there are 35 distinct website graphics that can be created by using at least four of seven different bitmap images.

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Answer:

x = 3

y = 23

z = 4

Step-by-step explanation:

To find the values of x, y, and z in the rhombus, we need to use the properties of a rhombus. One of the properties of a rhombus is that its opposite angles are equal. Another property is that its diagonals are perpendicular bisectors of each other.

Let's label the vertices of the rhombus as A, B, C, and D, and the midpoint of diagonal AC as M. We can use the given information to write some equations:

First, we know that diagonal AC is perpendicular to diagonal BD, so we have:

-2x + 6 = 0

Solving for x, we get:

x = 3

Next, we know that diagonal AC bisects angle ACD, so we have:

y = 46/2 = 23

Now, we can use the fact that AM is the perpendicular bisector of CD to find z. Since M is the midpoint of AC, we have:

AM = MC

Using the distance formula, we can find the lengths of AM and MC in terms of z:

AM = sqrt((2z-8)^2 + (5y-4)^2)

MC = sqrt((8-2z)^2 + (5y-4)^2)

Setting these two expressions equal to each other, we get:

sqrt((2z-8)^2 + (5y-4)^2) = sqrt((8-2z)^2 + (5y-4)^2)

Simplifying this equation, we get:

4z - 16 = 16 - 4z

8z = 32

z = 4

Therefore, the values of x, y, and z are:

x = 3

y = 23

z = 4

So, the solution is x=3, y=23, and z=4.

Answer:

Step-by-step explanation:

To find the point at which the two plans cost the same, we can set their total costs equal to each other:

55 + 0.13x = 48 + 0.15x

Simplifying and solving for x, we get:

0.02x = 7

x = 350

Therefore, the plans will cost the same when Lisa drives 350 miles.

To find the cost at this point, we can substitute x=350 into either equation. Let's use the first plan:

Total cost = 55 + 0.13(350) = $97.50

Therefore, if Lisa drives 350 miles, the cost for either plan will be $97.50.

Answer: The value of x will be equal to 5.

Step-by-step explanation:

1. Since all the angles of the given triangle is equal it proves to be an Equilateral Triangle.

2. Now as all the angles are equal the length of side will be equal too.

3. Equating both equations: 3x-3 = 2x+2

3x-2x = 3+2 => x = 5.

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The probability that the number generated is:

1). 94 = 1/4, (2). even = 1/4, (3). odd = 0, (4). less than 32 = 1/25, and (5). greater than 74 = 1/25.

The probability of an event occurring is the fraction of the number of required outcome divided by the total number of possible outcomes.

The total possible outcome = 10

probability of generating 94 = 5/10 × 5/10 = 1/4

probability of generating an even number = 5/10 × 5/10 = 1/4 {all numbers ending with 0,2,4,6, and 8 must be even}

probability of generating an odd number = 0 {since the second digit must be from 0,2,4,6, and 8, hence no odd number can be generated}

probability of generating less than 32 = 2/10 × 2/10 = 1/25 {since the first digit must either be 1 or 3, while the second digit must be either 0 or 2}

probability of generating greater than 72 = 2/10 × 2/10 = 1/25 {since the first digit must either be 7 or 9, while the second digit must be either 6 or 8}.

Therefore, the probability that the number generated is:

1). 94 = 1/4, (2). even = 1/4, (3). odd = 0, (4). less than 32 = 1/25, and (5). greater than 74 = 1/25.

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Answer:

The answer is **C. 2x+y**

* Expand the parentheses: 7x-14y - 5x+15y

* Combine like terms: 2x+y

Here is the step-by-step solution:

1. Expand the parentheses:

```

7(x-2y)-5(x-3y)

= 7x-14y - 5x+15y

```

2. Combine like terms:

```

= (7x-5x) + (-14y+15y)

= 2x + y

```

Step-by-step explanation:

Answer:

Let's simplify the expression step by step:

7(x - 2y) - 5(x - 3y)

= 7x - 14y - 5x + 15y  (distributing the 7 and -5)

= 2x + y              (combining like terms)

Therefore, the simplified expression is 2x + y, which corresponds to option [C].

Step-by-step explanation:

angle 1 = 180 - 74 the angle on a straight line is given as 180

= 106 degrees

Alternate angles are a pair of angles formed by a transversal intersecting two parallel lines. These angles are located on opposite sides of the transversal and on opposite sides of the parallel lines.

The alternate angles are congruent, which means they have the same measure or degree. In other words, if one alternate angle measures x degrees, then its corresponding alternate angle will also measure x degrees.

angle 2 = angle 1

They are vertical angles hence they are equal

angle 3 = 74 degrees

They are  vertical angles as well

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Answer:

area of parallelogram=

base x height

21 in x 18 in

378 in

rounded to nearest ten

380 inches square.

Where is the question?

Answer: 3

Step-by-step explanation:

A = 3 × (1ft)²

A = 3 × 1 ft²

A = 3ft²

Time Series Graph: Plot A

Based on the above plot, earnings first rise till 1997, and then start falling till 2001. After 2001, earnings start rising again. So overall there is an upward trend.

Based on these observations, the answer is Option A, which says:

Option A: There is a general upward trend though there have benn some down years. An upward trend would be helpful to women so that their earnings become equal to those of men.

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Answer:

24/91

Step-by-step explanation:

We can see that the square on the right has a side length of 24 and the square on the left has a side length of 91.

The scale factor = square on right/square on left = 24/91

The equation of this graphed line is equal to y = x/2 - 5.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (-1 + 5)/(8 - 0)

Slope (m) = 4/8

Slope (m) = 1/2.

At data point (0, -5) and a slope of 1/2, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - (-5) = 1/2(x - 0)

y + 5 = x/2

y = x/2 - 5

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The value of your conclusion would be:

⇒ There is sufficient evidence to warrant rejection of the original claim

We have to given that;

For your claim is in the alternative hypothesis and you reject the null hypothesis.

Hence, We know that;

If your claim is in the alternative hypothesis and you reject the null hypothesis, There is sufficient evidence to warrant rejection of the original claim

Thus, The correct option is, B.

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True, option (G) is which is - at least one of the numbers is positive.

A positive integer is a whole number greater than zero, i.e., any number that can be expressed without fractions or decimals, and is greater than zero.

If the difference of two numbers is less than the sum of the numbers, it is always true that at least one of the numbers is positive. As a result, "At least one of the numbers is positive" is the response, which is (G).

Here we assume that x and y are two numbers. The difference between the two numbers is |x - y|, which is always positive.

Now, according to the given condition:

|x - y| < x + y

Simplifying this inequality, we get:

-x + y < x + y

2y > 0

Dividing both sides by 2, we get:

y > 0

Therefore, we can conclude that at least one of the numbers (y) is positive. Note that it is possible for both numbers to be positive or for one number to be positive and the other to be zero.

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The lengths of x of the right angle triangle using pythagoras theorem are:

x = 5

x = 3

x = 10

Pythagoras Theorem is defined as the way in which you can find the missing length of a right angled triangle.

The triangle has three sides, the hypotenuse (which is always the longest), Opposite (which doesn't touch the hypotenuse) and the adjacent (which is between the opposite and the hypotenuse).

Pythagoras is in the form of;

a² + b² = c²

4) Applying Pythagoras theorem, we can find x as:

x = √(13² - 12²)

x = √(169 - 144)

x = √25

x = 5

5) Applying Pythagoras theorem, we can find x as:

x = √(5² - 4²)

x = √9

x = 3

6) Applying Pythagoras theorem, we can find x as:

x = √(8² - 6²)

x = √100

x = 10

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based on the information provided, the probability of selecting a yellow disk is 1/5 or 0.2.

How to solve the problem?

The probability of selecting a yellow disk cannot be 2, as probabilities must always be between 0 and 1.

To calculate the probability of selecting a yellow disk, we can use the formula:

P(yellow) = number of yellow disks / total number of disks

From the information given, we know that there are 5 yellow disks and 25 total disks in the bag. Plugging these values into the formula gives:

P(yellow) = 5/25 = 1/5

Therefore, the probability of selecting a yellow disk is 1/5 or 0.2, which is a decimal value between 0 and 1.

It's possible that there was a typo in the original question or answer, or that some other context is missing which would make sense of the answer being 2. However, based on the information provided, the probability of selecting a yellow disk is 1/5 or 0.2.

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An expression in factored form for the polynomial of least possible degree is y(x) = (x-2)(x+2).

What is polynomial?

Polynomials can be represented in various forms, including standard form, factored form, and expanded form. Standard form is where the polynomial is written with the terms in descending order of degree, with coefficients in front of each term. Factored form is where the polynomial is written as a product of linear factors, and expanded form is where the polynomial is written out in full, with all the terms multiplied together.

A polynomial is a mathematical expression consisting of variables and coefficients, which are combined using addition, subtraction, and multiplication operations. The variables are raised to non-negative integer powers, and the highest power of the variable is called the degree of the polynomial.

For example, the polynomial 2x³ + 3x³ - 4x + 1 has degree 3, as the highest power of x is 3. The coefficients in this polynomial are 2, 3, -4, and 1.

Here, the curve touch two points (-2,0) and (2,0).

So, we can say (-2) and 2 are the root of the polynomial.

We know of a and b are two root of any polynomial then the polynomial will be (x-a)(x-b).

So, the expression is y(x) = (x-2)(x+2).

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Answer:

see explanation

Step-by-step explanation:

Part A:

54$ for 30 pounds = 54/30 = 9/5 dollars per pound
70$ for 40 pounds = 70/40 = 7/4 dollars per pound
42$ for 28 pounds = 42/28 = 3/2 dollars per pound

Part B:
3/2 = 1.5 ($/lb)
7/4 = 1.75 ($/lb)
9/5= 1.8 ($/lb)

The best buy is Woofy Waffles for 1.5 $ per pound

Answer:

5 cm

Step-by-step explanation:

Given two sides of a right triangle, we can find the other side using the Pythagorean theorem, which is

[tex]a^2+b^2=c^2[/tex], where a and b are any of the two legs (e.g., you can set 12 can be a or b) and c is the hypotenuse.

If we allow 12 to b a and 13 to be c, we can solve for b, which is the measure of the other side:

[tex]12^2+b^2=13^2\\144+b^2=169\\b^2=25\\b=5\\b=-5[/tex]

When taking the square root of a number, you always get a negative number and a positive number, since squaring a negative gives a positive answer (e.g. 5^2 = 25 and (-5)^2 = 25).  However, because you can't have a negative answer, the answer is simply b = 5 cm

We can even check our answer by making sure that the sum of the square of the two legs equals the square of the hypotenuse:

[tex]12^2+5^2=13^2\\144+25=169\\169=169[/tex]

Considering both functions, there are no restrictions or exclusions for any real number values in the domain. Therefore, the domain of the composition (f∘g)(x) is all real numbers.

To determine the domain of the composition (f∘g)(x), we need to consider the domains of both functions f(x) and g(x) and determine any restrictions.

The function f(x) =[tex]1x + 2[/tex] does not have any explicit restrictions on its domain. It is defined for all real numbers.

The function g(x) = [tex]x^2 - 2x[/tex] is a quadratic function. Quadratic functions are defined for all real numbers, so there are no restrictions on the domain of g(x).

When we compose functions, we need to ensure that the output of the inner function is within the domain of the outer function. In this case, the composition (f∘g)(x) means we substitute g(x) into f(x), resulting in f(g(x)).

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Dilating a shape will proportionately affect its side lengths.

To find the scale factor between the given triangles, take one side on the larger triangle and divide it by the corresponding side on the smaller triangle. I will divide the triangles' top sides (24 and 8).

[tex]\text{scale factor}=\dfrac{24}{8} =3[/tex]

So, the scale factor used was 3.

Answer: 3

Step-by-step explanation:

I took the quiz so you do not have to!

The height of the kite is 49.2 foot.

We have,

A kite is flying in the air has a 41 ft string attached to it.

The angle of elevation of the kite is 47 degrees.

Using Trigonometry

sin 41 = P/H

sin 41 = P/ 75

0.6560 = P / 75

P = 49.2 foot

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Answer:

x = [tex]\frac{65}{17}[/tex]

Step-by-step explanation:

[tex]\frac{x}{13}[/tex] = [tex]\frac{5}{17}[/tex] ( cross- multiply )

17x = 13 × 5 = 65 ( divide both sides by 17 )

x = [tex]\frac{65}{17}[/tex] ≈ 3.8 ( to the nearest tenth )

a) The direct variation equation is y = 33x.

b) The customer can pay the company to collect 15 bins.

c) The customer can get approximately 16 bins (rounded to the nearest whole number) removed for $500 with a $30 tip included.

A) The direct variation equation to represent the cost would be y = kx, where y represents the cost, x represents the number of bins collected, and k is the constant of proportionality. In this case, since the cost is $33 for each bin collected, the value of k is 33. Therefore, the direct variation equation is y = 33x.

B) To find the number of bins a customer can pay the company to collect for $500, we can set the cost (y) equal to $500 and solve for x (the number of bins). Thus, we have:

y = 33x

500 = 33x

x = 500/33

x ≈ 15.15

Therefore, the customer can pay the company to collect 15 bins (rounded to the nearest whole number) for $500.

C) If the customer plans to tip the recycling company $30, the total cost would be $500 + $30 = $530. We can set the cost (y) equal to $530 and solve for x:

y = 33x + 30

530 = 33x + 30

500 = 33x

x ≈ 15.91

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The answer of the given question based on the trigonometric identities is , A. sin(-Θ) = -B , b. tan(-Θ) = -A , C. cos(Θ + 2π) = B/√(A² + B²) , D. tan(Θ + π) = -A.

Trigonometric identities are equations in mathematics that use trigonometric functions and hold true regardless of the value of the variables. These identities can be applied to simplify or alter trigonometric expressions, as well as to trigonometric function-based equations.

To determine the required values, we can utilise sine and tangent definitions along with trigonometric identities:

a. sin(-Θ) = -sin(Θ) = -B (using the property that sine is an odd function)

b. tan(-Θ) = -tan(Θ) = -A (using the property that tangent is an odd function)

c. cos(Θ + 2π) = cos(Θ) = B/√(A² + B²) (using the Pythagorean identity, since cos²(Θ) + sin²(Θ) = 1)

d. tan(Θ + π) = (tan(Θ) + tan(π))/(1 - tan(Θ)tan(π) = (-A + 0)/(1 + A0) = -A

Therefore, the values are:

a. sin(-Θ) = -B

b. tan(-Θ) = -A

c. cos(Θ + 2π) = B/√(A² + B²)

d. tan(Θ + π) = -A

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The complete question is:

If tan (θ) = A, sin(θ)= B,

Then find the following:

a. sin(-θ)=

b. tan(-θ)=

c. cos(θ+ 2π) =

d. tan(θ+ π)=

The answer of the given question based on the trigonometric identities is , A. sin(-Θ) = -B , b. tan(-Θ) = -A , C. cos(Θ + 2π) = B/√(A² + B²) , D. tan(Θ + π) = -A.

Trigonometric identities are equations in mathematics that use trigonometric functions and hold true regardless of the value of the variables. These identities can be applied to simplify or alter trigonometric expressions, as well as to trigonometric function-based equations.

To determine the required values, we can utilise sine and tangent definitions along with trigonometric identities:

a. sin(-Θ) = -sin(Θ) = -B (using the property that sine is an odd function)

b. tan(-Θ) = -tan(Θ) = -A (using the property that tangent is an odd function)

c. cos(Θ + 2π) = cos(Θ) = B/√(A² + B²) (using the Pythagorean identity, since cos²(Θ) + sin²(Θ) = 1)

d. tan(Θ + π) = (tan(Θ) + tan(π))/(1 - tan(Θ)tan(π) = (-A + 0)/(1 + A0) = -A

Therefore, the values are:

a. sin(-Θ) = -B

b. tan(-Θ) = -A

c. cos(Θ + 2π) = B/√(A² + B²)

d. tan(Θ + π) = -A

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The complete question is:

If tan (θ) = A, sin(θ)= B,

Then find the following:

a. sin(-θ)=

b. tan(-θ)=

c. cos(θ+ 2π) =

d. tan(θ+ π)=

We can actually see here that the equation for the population P in terms of time t in minutes will be: P = 404 × 2^(t/36).

We can see here that looking at the change in population, we can use the following:

P = P₀ × 2^(t/Δt).

Where:

P₀ = initial population = 404 bacterias

t = time elapsed (in minutes).

Δt = time it takes for the population to double (36 minutes).

Thus, we see that substituting this, we have:

P = 404 × 2^(t/36).

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Answer:  1/125 in it's simplest form

Step-by-step explanation: