Your family purchases a new car for $20,000. Its value decreases by 15% each year. During what interval does the car's value exceed $10,000? Round your answer to the nearest hundredth.
From the time it was purchased until about years later.

The expressions aaaaaaa, aabbbb, aabbccc, and 3xxyyyz will be a⁷, a²b⁴,  a²b²c³, and 3x²y³z.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

We know that if x is multiplied by n time of x, then we can be written as xⁿ.

1. aaaaaaa = a⁷

2. aabbbb = a²b⁴

3. aabbccc = a²b²c³

4. 3xxyyyz = 3x²y³z

The expressions aaaaaaa, aabbbb, aabbccc, and 3xxyyyz will be a⁷, a²b⁴,  a²b²c³, and 3x²y³z.

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Answer: $171

Step-by-step explanation:

$247 divided by 13 hrs = $19/hr

$19/hr times 9 hrs = $171

The integral ∫₁/₁₀¹⁰[㏒₁₀(10x)/x]dx = 2㏑10

Integration is the process of finding the antiderivative of a fuinction.

Given the integral

[tex]\int\limits^{10}_{\frac{1}{10} } {\frac{log_{10}10x }{x} } \, dx[/tex]

We evaluate the integral as follows

[tex]\int\limits^{10}_{\frac{1}{10} } {\frac{log_{10}10x }{x} } \, dx[/tex]

Now, using the properties of the laws of logarithms, we have ㏒ab = ㏒a + ㏒b

So, [tex]\int\limits^{10}_{\frac{1}{10} } {\frac{log_{10}10x }{x} } \, dx = \int\limits^{10}_{\frac{1}{10} } {\frac{log_{10}10 + log_{10}x }{x} } \, dx \\= \int\limits^{10}_{\frac{1}{10} } {\frac{log_{10}10}{x} } \, dx + \int\limits^{10}_{\frac{1}{10} } {\frac{log_{10}x}{x} } \, dx \\= \int\limits^{10}_{\frac{1}{10} } {\frac{1}{x} } \, dx + \int\limits^{10}_{\frac{1}{10} } {\frac{log_{10}x}{x} } \, dx\\[/tex]

So, using the property of change of base of logarithm, we have that

logx = lnx/ln10

, [tex]\int\limits^{10}_{\frac{1}{10} } {\frac{log_{10}10x }{x} } \, dx = \int\limits^{10}_{\frac{1}{10} } {\frac{1}{x} } \, dx + \int\limits^{10}_{\frac{1}{10} } {\frac{\frac{lnx}{ln10} }{x} } \, dx\\= \int\limits^{10}_{\frac{1}{10} } {\frac{1}{x} } \, dx + \frac{1}{ln10}\int\limits^{10}_{\frac{1}{10} } {\frac{lnx}{x} } \, dx\\= \int\limits^{10}_{\frac{1}{10} } {\frac{1}{x} } \, dx + \frac{1}{ln10}\int\limits^{10}_{\frac{1}{10} } {{lnx} \, dlnx[/tex]

[tex]\int\limits^{10}_{\frac{1}{10} } {\frac{log_{10}10x }{x} } \, dx = {[lnx]_{\frac{1}{10}}^{10} } + {\frac{[lnx]^{2}}{2} }_{\frac{1}{10}}^{10} } \\= ln10 - ln\frac{1}{10} + \frac{1}{2}[[ln10]^{2} - [ln\frac{1}{10}]^{2} ] \\= ln10 + ln10 + \frac{1}{2}[[ln10]^{2} - [-ln10}]^{2} ]\\= ln10 + ln10 + \frac{1}{2}[[ln10]^{2} - [ln10}]^{2} ]\\= 2ln10 + 0\\= 2ln10[/tex]

So, the we see that the integral [tex]\int\limits^{10}_{\frac{1}{10} } {\frac{log_{10}10x }{x} } \, dx = 2ln10[/tex]

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By using Area Model of Multiplication and Division, it can be concluded that the missing number in the area model is 40.

Area Model of Multiplication and Division is a rectangular chart used to multiply and divide two numbers or expressions, where the quotient and divisor determine the length and width of the rectangle.

In this model, we split up a large rectangular area into several smaller rectangular, using number bounds, to make calculations easier.

Now we take a look at our area model 14 x 16 in size.

Area I = 10 x 10 = 100

Area II = 6 x 10 = 60

Area III = 6 x 4 = 24

Using the same way, the missing number, area IV, can be calculated as follows:

Area IV = 10 x 4 = 40

Thus, it can be concluded that the missing number in the area model is 40.

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Answer:

The solution to the equation 5i + 4 = 14 + 4i is i = 10.

Step-by-step explanation:

To solve for i in this equation, isolate the variable (i) on one side of the equation. To do this, we'll subtract 4 from both sides:

5i + 4 - 4 = 14 + 4i - 4

This leaves us with:

5i = 10 + 4i

Next, we'll subtract 4i from both sides:

5i - 4i = 10 + 4i - 4i

This leaves us with:

i = 10.

So the solution to the equation 5i + 4 = 14 + 4i is i = 10.

Answer:

60x

30x

after mixing (60+30)x=90x

sold for=70x

gain=(90x-70x)/90x×100

20x/90x×100%

=22.22%

Answer:

548km^2

Explanation:

if the surface area is 137 km, and then it has a dialation of 4, then all you need to do is multiply by 137 by 4, which equals 548. That means the surface area of cylinder B is 548 km^2. Hope that helps.

The value of balance after 6 years compounded quarterly is , $44,450

A quick and easy method of calculating the interest charge on a loan is called a Simple interest.

Given that;

You deposit 35000 in an account that pays 2.3% annual interest.

We know that;

Amount = P (1 + r/4)⁴ⁿ

Where, P is the starting amount, r is interest rate and n is time.

Substitute all the value we get;

Amount = P (1 + r/4)⁴ⁿ

Amount = 35000 (1 + 0.023/4)²⁴

Amount = 35000 (4.023/4)²⁴

Amount = 35000 × 1.01²⁴

Amount = 35000 × 1.27

Amount = $44,450

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The actual balance is $36,400.68 which lower than the goal of $150,000. The Option D is correct.

The Formula to use to derive the actual balance is: P[((1 + r/n)^(n*t)) - 1) / (r/n)] where: FV = future value, P = monthly deposits, r = interest rate, t = time in years, n = number of compound in a year

From the given:

P = 200

r = 2.85% 0.0285

t = 30 years

n = 12 (compounded monthly)

Future value = 200((1 + 0.0285/12)^(12(30)) - 1) / (0.0285 / 12)

Future value = $113,599.32

The difference between the actual balance and the employee's goal is:

= $150,000 - $113,599.32

= $36,400.86

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The direction of point P is (2.5, 3.3). In this way, the point P that separates the line fragment from K to L with a 1 to 5 proportion has the coordinate (2.5, 3.3).

Given a line segment from K to L, and the proportion of the division as 1 to 5, we can find the direction of point P that separates the line section into the predetermined proportion.

The direction of point P can be tracked down utilizing the accompanying recipe:

P = (1 - t) K + t L

where t is the relative separation from direct K toward point P. To fulfill the 1 to 5 proportion, we can set t = 1/6.

Subbing the qualities into the equation, we get:

P = (1 - 1/6) K + 1/6 L

= 5/6 K + 1/6 L

To find the genuine direction of point P, we want to substitute the directions of K and L into the equation. For instance, if K = (3, 4) and L = (7, 8), the direction of point P can be determined as:

P = (5/6)(3, 4) + (1/6)(7, 8)

= (15/6, 20/6)

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60 kilometres per x litres can be expressed algebraically as 60/x km/L.

Algebra is a branch of mathematics that is used to manipulate symbols and equation in order to solve the problems algebra help to solve problems involving unknown quantities into the block relationship between different variable it is a powerful tool that can be used to solve the and analyze a variety of mathematical problem and equation.

This can be used to represent the relationship between the number of kilometres travelled and the number of litres of fuel that was used. For example, if a car travelled 240 kilometres using 4 litres of fuel, the expression would be 60/4 km/L, which would equal 15 km/L.

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Answer:

y = 1500 * 0.9575^t

Step-by-step explanation:

Where 0.9575 is equal to 1 - 0.0425, which represents a decrease of 4.25% each year.

To solve this, you can use the geometric mean theorem. The leg of a right triangle is the geometric mean between the hypotenuse and the portion of the hypotenuse adjacent to the leg.

So that means that 28/y = y/12. You can then use means and extremes of proportions to simplify, and you get y^2 = 336, a.k.a  y = 4 root 21.

Then you do the same thing but with x.

28/x = x/16

x^2 = 448

x = 8 root 7

Answer:

B. x = 8√7, y = 4√21

Step-by-step explanation:

Look at the largest right triangle so the hypotenuse equals 12 + 16 = 28

According to the Pythagorean Theorem: y^2 + x^2 = 28^2

Then for the 2 smaller right triangles, they all the the same side, just called it z

so y^2 = 12^2 + z^2 => z^2 = y^2 - 12^2

and x^2 = 16^2 + z^2 => z^2 = x^2 - 16^2

then y^2 - 12^2 = x^2 - 16^2

y^2 - 144 = x^2 - 256

y^2 = x^2 - 112

Using the first equation

y^2 + x^2 = 28^2 => x^2 = 784 - y^2

So we have y^2 = x^2 - 112

and x^2 = 784 - y^2

then y^2 = (784 - y^2) - 112

y^2 + y^2 = 784 - 112

2y^2 = 672

y^2 = 336

y = 4√21

x^2 = 784 - y^2 = 784 - 336 = 448

x = 8√7

Answer:

-193

Step-by-step explanation:

x+52+67+75=1

x+119+75=1

x+194=1

-194.    -194

x=-193

The difference in elevation between the height of mountain and height of valley measuring from sea level is equal to 6594 feet.

Since it is given that the height of mountain from the sea level is 6874 feet and the height of valley is 280 feet. Therefore to calculate the difference in elevation, the heights will be subtracted from one another to get a value which will show the elevation. Since both the heights are measured from the sea level which is taken as constant, so no extra calculations will be needed.

Elevation difference = Height of mountain - height of valley

Elevation difference = 6874 - 280 = 6594 feet

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Answer:

Step-by-step explanation:

First you would take .75n = .75 * 12 shirts

.75 * 12 = 9

You then would take 9 + 9.99 which obviously is 18.99$

Answer = 18.99$ per 12 T-shirts

Answer:

12

Step-by-step explanation:

√7 =2.65

√200 = 14.14

so 3,4,5,6,7,8,9,10,11,12,13,14

The circumstances in which the median rather than the mean is the preferred measure of central tendency is when there is a skewed distribution (a few extreme scores), an open-ended distribution or undetermined scores.

Central tendency is defined as the summative measure that tries to describe the entire set of data with a single value representing the mean or center of the distribution.

A skewed distribution occurs when one tail is longer than the other.

Therefore, in this type of distribution, the median should be chosen as the preferred measure of central tendency.

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The difference between city a and city b is 33,107 feet, with city a being 33,107 feet higher than city b.

Step 1: Identify the problem.

How much higher is city a than city b?

Step 2: Gather information.

City a has an elevation of 13,764 feet above sea level while city b has an elevation of 19,343 feet below sea level.

Step 3: Analyze the information.

City a is 13,764 feet above sea level, and city b is 19,343 feet below sea level. To find the difference, we need to subtract 19,343 from 13,764.

Step 4: Formulate a solution.

The difference between the two cities is 33,107 feet. City a is 33,107 feet higher than city b.

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The perimeter of the triangle is 16+8√2.

The sum of the lengths of the sides is the perimeter of any polygon.

Perimeter = Sum of the three sides

There is a general formula for the perimeter of a triangle:

P=a+b+c

There are three steps to calculate the perimeter of a triangle:

Step 1: write the measurements of all the sides, and check that all the sides should have the same unit.

Step 2: Now, calculate the sum of all the sides.

Step 3: Then, give the answer along with the unit.

The given information is the two sides of a triangle are a=b=8 and c=8√2.

Now substitute all the given values in the above formula we get:

P=8+8+8√2

P=16+8√2.

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The system of linear and exponential functions passing through (1,12) is given as follows:

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

For the function to pass through point (1,12), we have that when x = 1, y = 12, hence one example of a linear function is given as follows:

y = 2x + 10.

An exponential function is defined as follows:

y = a(b)^x.

When x = 1, y = 12, hence one example is given as follows:

y = 6(2)^x.

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Answer:

D. Has a slope of 3/4 and passes through the point (0,1)

Step-by-step explanation:

The y-intercept is (0, 1), so this line passes through (0, 1).

slope = m = rise/run

Start at (0, 1). Go up 3. That is a rise of 3. Now go right 4. That is a run of 4.

slope = rise/run = 3/4

Answer: D. Has a slope of 3/4 and passes through the point (0,1)

In triangle XYZ The image will be in the second quadrant hence Joseph is correct

In the rectangle, the image of A' will be in the quadrant III hence Chad is correct

Rotation in transformation refers to the process of rotating an object around a fixed point by a certain angle, changing its orientation.

The fixed point is known as the center of rotation, and the angle of rotation determines the extent to which the object is rotated.

In 2D graphics, rotation can be represented by a matrix multiplication,

Inn the triangle rotation, the transformation rule is for 90° clockwise rotation

In the rectangle rotation, this is equivalent to reflection over the line y = x

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The midpoint between the endpoints (9, -1) and (1, 15) is equal to (5, 7).

In order to determine the midpoint of a line segment with two (2) endpoints, we would add each point together and divide by two (2).

Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]

Substituting the given parameters into the midpoint of a line segment formula, we have the following;

Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]

Midpoint = [(9 + 1)/2, ((-1) + 15)/2]

Midpoint = [(10)/2, (14)/2]

Midpoint = (5, 7).

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Using simple mathematical operations, we know that the positive difference between the mass of the fish and fisherman is 26.25.

An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value.

The operation's arity is determined by the number of operands.

The addition, subtraction, multiplication, division, exponentiation, and modulus operations are carried out via the arithmetic operators.

So, we know that:

Fish: 75kg + 75/4

75 + 18.75

93.75

Fisherman: 100kg + 100/5

100 + 20

120

Positive difference: 120 - 93.75 = 26.25

Therefore, using simple mathematical operations, we know that the positive difference between the mass of the fish and fisherman is 26.25.

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The point of C is, (- 7, - 5).

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

Triangle ABC with points A (9,1) B (2,7) C(-2,-5) was translated 3 units left, 2 units down and then was reflected across the line y = x.

Now, Triangle ABC with points A (9,1) B (2,7) C(-2,-5) was translated 3 units left, 2 units down.

Hence, The point of C is,

⇒ C = (- 2, -5) + (- 3, - 2)

⇒ C = (- 5, - 7)

Since, It was reflected across the line y = x.

Hence, The point of C is,

⇒ C = (- 7, - 5)

Thus, The point of C is, (- 7, - 5).

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

You want to find the slopes of the lines shown in the attached graphs.

The slope of a line is its "rise" divided by its "run":

  m = rise/run

To determine slope from a graph, start at an identified point on the left, and count the grid squares up (+) or down (-) to the same horizontal line as the identified point on the right. This is the "rise". Then count the grid squares horizontally to the identified point. This is the "run". The slope is the ratio of these numbers.

1. rise 4, run 6, slope 4/6 = 2/3

2. rise -3, run 4, slope -3/4

3. rise -6, run 3, slope -6/3 = -2

4. run = 0; division by 0 is "undefined", so the slope is "undefined"

5. rise 4, run 1, slope 4/1 = 4

6. rise 0, run (anything), slope 0/1 = 0

__

Additional comment

It is helpful to remember that a horizontal line has a slope of 0, and a vertical line has a slope that is "undefined." Slope is positive if the line goes up to the right. It is negative if the slope goes down to the right.

Because the slope of a vertical line is "undefined," its equation cannot be written in "slope-intercept" form.

Here, points are marked on the lines. When that is not the case, it usually works well to identify points where the line crosses an intersection of grid lines.

You can also use grid crossings to check your answer for the slope. For example, the line on graph 3 crosses grid intersections that are 2 down and 1 over from the marked points (and other grid intersections), confirming a slope of -2.

If there are 50 marbles in a bag and 35 of them are brown, and Otti takes one marble and put it back afterwards and does it 300 times, then the estimated number of brown marbles Otti takes is around 105.

The expected number of brown marbles Otti takes can be estimated by multiplying the probability of drawing a brown marble (35/50) by the number of times he draws (300).

(35/50) × 300 = 105

This gives an estimated result of 105 brown marbles. It's important to note that this is just an estimate and the actual number could be different. The variation in the actual number of brown marbles Otti takes can be attributed to the randomness of the process.

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Yes, 12 refrigerators and 11 pianos overload the truck, because 12 refrigerators and 11 pianos weighs more than 7100 lb.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

Given that, a truck that can carry no more than 7100 lb is being used to transport refrigerators and upright pianos

Let the number of refrigerators be x and the number of pianos be y.

Each refrigerator weighs 250 lb and each piano weighs 425 lb.

Here, 250x+425y≤7100

Will 12 refrigerators and 11 pianos overload the truck

Now, put x=12 and y=11 in the inequality 250x+425y≤7100, we get

250×12+425×11≤7100

7675≤7100 not true

Therefore, the inequality represent the given scenario is 250x+425y≤7100.

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