evaluate
[tex] {3}^{x} - {3}^{x - 2} = 24[/tex]
Evalutae this formula and solve for x​

Units of volume are cm³ and cubic meter.

Volume is the measure of the capacity that an object holds.

A unit of volume is a unit of measurement for measuring volume or capacity, the extent of an object or space in three dimensions.

For example, if a cup can hold 100 ml of water up to the brim, its volume is said to be 100 ml.

Given units of measurement,

G² - It is not unit of volume

cm³- It is unit of volume

m² - It is not unit of volume

kg³ - It is not unit of volume

cubic meter = meter³ - It is unit of volume

Hence, cm³ and cubic-meter are units of volume.

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Answer:

We can start by using logarithmic properties. If a, b, and c are positive numbers, then:

loga^b = b * loga

Using this property, we can rewrite the expression as:

x^(logy - logz) * y^(logz - logx) * z^(logx - logy) = x^(logy/logx - logz/logx) * y^(logz/logy - logx/logy) * z^(logx/logz - logy/logz)

Using the change-of-base formula, we can simplify the exponents:

x^(logy/logx - logz/logx) = (logy/logx) / (logz/logx) = logy/logz

Similarly,

y^(logz/logy - logx/logy) = logz/logx

and

z^(logx/logz - logy/logz) = logx/logy

Now, we can substitute these results back into the original expression:

x^(logy - logz) * y^(logz - logx) * z^(logx - logy) = logy/logz * logz/logx * logx/logy

By the transitive property of logarithms, we have:

logy/logz * logz/logx * logx/logy = logy/logx

Finally, using the change-of-base formula again, we can simplify this result:

logy/logx = y^(1/logx) / x^(1/logx)

Since y and x are positive numbers, their exponents must also be positive. Therefore, we have:

y^(1/logx) / x^(1/logx) = 1

So,

x^(logy - logz) * y^(logz - logx) * z^(logx - logy) = 1

And we have proven that the expression is equal to 1.

Step-by-step explanation:

Answer:

x≥−1

Step-by-step explanation:

The domain of the inverse of a function is the range of the original function. The range of the cubic root function is y≥−1, so the domain of its inverse would be x≥−1.

Answer:

x≥−1, x is greater than or equal to negative 1

Step-by-step explanation:

The inverse of a function switches the roles of x and y, making the original range the new domain and the original domain the new range. In this case, the original domain is x≥7 and the range is y≥−1, so the inverse has a domain of y≥−1 and a range of x≥7 :)

1930.54 can be written in standard form as 1.93054 × 10³. Option D is correct.

A number can be written in standard form to make it simpler to read. It is frequently used for extremely high or extremely low figures. Mathematics and other science fields employ the use of standard form, which is similar to scientific notation.

When a decimal number is multiplied by a power of 10, it is said to be expressed in standard form.

Similar to scientific notation, standard form represents a number as a decimal number times a power of 10. (i.e a*10^b)

From the given information:

1930.54 can be written in standard form as 1.93054 × 10³

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The range of values in which at least 88.89% of the fake prices will lie if the standard deviation is $53,500 will be  $84,600 and $391,600.

What does standard deviation mean in plain English?

The term "standard deviation" (or "") refers to the degree of dispersion of the data from the mean.

                         Data are said to be more closely grouped around the mean when the standard deviation is low and more dispersed when the standard deviation is high.

The lower boundary of the range is calculated by subtracting two standard deviations from the average sale price

$238,100 - $53,500 = $84,600

The upper boundary of the range is calculated by adding two standard deviations to the average sale price

$238,100 + $53,500 = $391,600

Therefore, the range of values in which at least 88.89% of the fake prices will lie is between $84,600 and $391,600.

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The pair of equivalent radical expression is option D. √180 and 3√20.

Radicals are defined as the nth root of a number using the symbol  [tex]\sqrt[n]{x}[/tex].

This is the opposite form of the exponential functions.

[tex]\sqrt[n]{x}[/tex] can be written in the exponential form as [tex]x^{1/n[/tex].

A.√45 can be written as the square root of (15 × 3).

√45 = √(15 × 3) ≠ 3√15

B. √75 cannot be written as 3√5, since, if we have to take 3 outside, inside he root there must be 3² = 9. But 75 is not a multiple of 9.

C. √54 = √(9 × 6) = 3√6 ≠ 9√6

D. √180 = √(9 × 20) = √9 × √20 = 3√20

Hence the correct option is D.

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The clear question is given below.

Which of the following is a pair of equivalent radical expressions?

A. √45 and 3√15

B. √ 75 and 3√5

C. √54 and 9√6

D. √180 and 3√20

Answer:

x = 6

Step-by-step explanation:

the opposite sides in a rectangle are congruent.

since the rectangles are similar then the ratios of corresponding sides are in proportion, that is

[tex]\frac{5x}{18}[/tex] = [tex]\frac{10}{x}[/tex] ( cross- multiply )

5x² = 18 × 10 = 180 ( divide both sides by 5 )

x² = 36 ( take square root of both sides )

x = [tex]\sqrt{36}[/tex] = 6

Correct answer to the given question about Courtney's affordable car loan within her budget is option D. $27,425. 75.

To determine the maximum car loan that Courtney can afford, you need to calculate the total amount she will pay over 6 years and make sure it's less than the total amount she can afford to pay each month ($400) multiplied by the number of months (6 years x 12 months per year = 72 months).

First, calculate the total amount of interest she will pay over 6 years at 7.5% annual interest: $400 x 7.5% = $30

Next, calculate the monthly payment by dividing the annual interest amount by 12 months:$30 / 12 = $2.50

So, the monthly payment (not including the car loan amount) is $400 + $2.50 = $402.50.

Finally, you can calculate the maximum car loan amount by subtracting the monthly payment from the total amount she can afford to pay each month, and then dividing by the number of months:

$400 x 72 months = $28,800

$28,800 / $402.50 = 71.37

So, Courtney can afford a maximum car loan of $71,370.

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Answer:

141°

Step-by-step explanation:

In order to find the missing angle, we must first find the total sum of all the interior angles. To find this we use the following equation:

(n – 2) × 180°

Where n is equal to the number of sides

There are 7 sides therefore:

(7 – 2) × 180°

5 × 180°

900°

The sum of the total angles in the heptagon is 900°

We then must subtract all of the known angles

900 - 148 = 752

752 - 90 = 662

662 - 142 = 520

520 - 130 = 390

390 - 129 = 261

261 - 120 = 141

The missing angle is 141°

The value of sin(x) in terms of cos(x) is √1 - cos²(x). The value of sin(x) is 3/5.

Since x is an angle in the second quadrant, sin(x) is positive and cos(x) is negative.

To write sin(x) in terms of cos(x), we can use the identity sin²(x) + cos²(x) = 1 and solve for sin(x):

                                sin²(x) + cos²(x) = 1

                                sin²(x) = 1 - cos²(x)

                                sin(x) = ± √(1 - cos²(x))

Since sin(x) is positive in the second quadrant, we have:

                               sin(x) = √(1 - cos²(x))

To show that cos(x) = -4/5, we can use the given equation:

                               3sin(x) - 4cos(x) = 5

We can rearrange this equation to get cos(x) on one side:

                              4cos(x) = 3sin(x) - 5

                              cos(x) = (3sin(x) - 5) / 4

Now we can substitute the expression for sin(x) that we found earlier:

                              cos(x) = (3√(1 - cos²(x)) - 5) / 4

Multiplying both sides by 4 and simplifying, we get:

                              4cos²(x) + 3cos(x) - 4 = 0

This is a quadratic equation in cos(x). We can solve it using the quadratic formula:

                             cos(x) = [-3 ± √(3² - 4(4)(-4))] / (2(4))

                             cos(x) = (-3 ± 7) / 8

                             cos(x) = 1/2 or cos(x) = -4/5

Since x is in the second quadrant, we have cos(x) < 0, so cos(x) = -4/5.

Finally, we can use the expression for sin(x) that we found earlier to get:

                            sin(x) = √(1 - cos²(x))

                            sin(x) = √(1 - (-4/5)²)

                            sin(x) = √(1 - 16/25)

                            sin(x) = √9/25

                            sin(x) = 3/5

Therefore, the exact value of sin(x) is 3/5.

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(1) The amount of interest he paid in the first year altogether is 302,000.

(2) The monthly installment is 25,166.67 per month

(1) The amount of interest he paid in the first year is 1.8 million x 9% = 162,000.

So, in the first year, he paid a total of 162,000 + 140,000 = 302,000.

(2) To calculate the monthly installment, we first need to find out the total amount he paid in a year and then divide it by 12:

302,000 ÷ 12 = 25,166.67

So, he paid 25,166.67 per month.

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Answer:

Step-by-step explanation:

You want to know the total paid during the first year of a $1.8M loan at 9% if the balance is reduced by $140,000 after 12 monthly payments. You also want to know the amount of the monthly payment.

The remaining balance of an amortized loan is given by the formula ...

  FV = PV(1 +r)^n - <future value of payments>

where r is the monthly interest rate, and n is the number of months.

Using the given loan values, we have ...

  1,800,000 -140,000 = 1,800,000(1 +0.09/12)^12 -<payment value>

Solving for the future value of the payments, we find ...

  <payment value> = 1,800,000(1.093806898) -1,660,000 = 308,852.42

This is the future value of the payments made, so some further calculation is required to find the amount of the payment.

  <payment future value> = P((1+r)^n -1)/r = P(1.0075^12 -1)/0.0075

  P = <payment future value>/12.5075864

  P = 308,852.42/12.5075864 = 24693.21

The amount of the monthly payment was $24,693.21.

12 monthly payments were made in the first year, so the total paid was ...

  12 × $24,693.21 = $296,318.52 . . . . total paid in the first year

__

Additional comment

The attachment confirms these numbers. It is the output of an online remaining balance calculator. The difference of $0.04 between the bottom two numbers is a consequence of rounding. The given payment actually reduces the balance by $140,000.04.

The probability that a student who has skipped many classes has a GPA less than 2.0 is 0.5.

To calculate this probability, we can use the data from the table given. If a student has skipped many classes, they are in the "Many Skips" category. From the table, we can see that there are 200 students in the "Many Skips" category and 100 of them have a GPA of less than 2.0. Therefore, the probability of a student with many skips having a GPA less than 2.0 is given by:

P(GPA < 2.0 | Many Skips) = 100/200 = 0.5

This means that if we randomly select a student who has skipped many classes, there is a 50% chance that their GPA will be less than 2.0. This calculation provides insight into the relationship between attendance and GPA, and it suggests that skipping many classes is associated with a lower GPA.

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The initial payment for the first 3 years of an interest-only loan for a $141,000 5/130-year ARM at 5% would be $7050.

An ARM, or Adjustable Rate Mortgage, is a type of mortgage loan where the interest rate can change over time. The 5/1 in the loan term "5/130-year ARM" means that the initial rate is fixed for the first 5 years and can change once every year thereafter for the remaining life of the loan (in this case, 130 years).

For an interest-only loan, the borrower pays only the interest due on the loan for a set period of time, in this case, the first 3 years. The interest payment can be calculated as:

Interest payment = Loan amount * Interest rate

The loan amount in this case is $141,000 and the interest rate is 5%, so the interest payment is:

Interest payment = $141,000 * 0.05 = $7050

So, the initial payment for the first 3 years of an interest-only loan for a $141,000 5/130-year ARM at 5% would be $7050.

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The number of ways can a person toss a coin 12 times so that the number of heads is between 7 and 11 inclusive is 1585.

Combinations are methods for choosing elements from collections of objects. Unlike permutations, selection order is unimportant. The number of combinations can be counted in simpler situations.  

The formula for combinations is given by

Here we have

Number of tosses = 12 times

The number of heads is between 7 and 11 inclusive    

Number of ways of getting 7 heads and 5 tails

= 12! / (7!5!) = 792  

Number of ways of getting 8 heads and 4 tails

= 12!/(8!4!) = 495    

Number of ways of getting 9 heads and 3 tails

= 12!/(9!3!) = 220  

Number of ways of getting 10 heads and 2 tails

= 12!/ (10!2!) = 66

Number of ways of getting 11 heads and 1 tail

= 12! / (11!1!) = 12  

Total number of ways = 792 + 495 + 220 + 66 + 12

= 1585

Therefore,    

The number of ways can a person toss a coin 12 times so that the number of heads is between 7 and 11 inclusive is 1585.

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The classifications are done as follows

6. < 2 : acute angle

7. < ABC : angle on a straight line

8. < 2 = 41 degrees

9. x = 45

In the figure, BE bisects < DBC hence < 2 = < 3 = y

98 + < 2 + < 3 = 180

y + y = 180 - 98

2y = 82

y = 41

In the figure, < WXY = 88 where the adjacent angles are

< WXZ = 4x - 3 and < ZXY = 2x + 1

4x - 3 + 2x + 1 = 88

4x + 2x = 88 + 3 - 1

2x = 90

x = 45

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Answer: Lincoln drove 15 miles in 12 minutes, so he drove a total of 60 minutes because 60/12 = 5.

Thus, Lincoln drove a total of 15 * 5 = 75 miles.

Step-by-step explanation:

Answer:

Slope is -5/3

Step-by-step explanation:

Let [tex](x_1,y_1)\rightarrow(-8,7)[/tex] and [tex](x_2,y_2)\rightarrow(-2,-3)[/tex]:

[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{-3-7}{-2-(-8)}\\ \\m=\frac{-10}{-2+8}\\\\m=-\frac{10}{6}\\ \\m=-\frac{5}{3}[/tex]

The value of P in this triangle is equal to 14.

In Mathematics, the basic proportionality theorem states that when any of the two (2) sides of a triangle is intersected by a straight line which is parallel to the third (3rd) side of the triangle, then, the two (2) sides that are intersected would be divided proportionally and in the same ratio.

By applying the basic proportionality theorem to the given triangle, we have the following:

24/p = 12/(21 - p)

By cross-multiplying, we have the following:

12p = 24(21 - p)

12p = 504 - 24p

36p = 504

p = 504/36

p = 14.

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Answer:

Sarah purchased 2 first class tickets and 5 coach tickets.

Step-by-step explanation:

Let's call the number of first class tickets purchased "x".

The number of coach tickets purchased would be 7-x.

We know that the total spent on first class tickets was $1170 * x and the total spent on coach tickets was $320 * (7-x).

The total budget was $3940, so we can set up the following equation:

$1170 * x + $320 * (7-x) = $3940

Expanding the right side:

$1170 * x + $320 * 7 - $320 * x = $3940

Combining like terms:

$800 * x = $3940 - $320 * 7

Subtracting $320 * 7 from both sides:

$800 * x = $3940 - $2240

$800 * x = $1700

Dividing both sides by 800:

x = 2.125

Since x must be a whole number, Sarah purchased 2 first class tickets and 5 coach tickets.

Answer:

f(x) = -1 - 7/2 x*3

f(2) = -1 -7/2 (2)*3

f(2) = -1 -7/2 (8)

f(2) = -1 -56/2

f(2) = -1 -28

Answer:

y'(9) = -7/3.

Step-by-step explanation:

We start by differentiating the given equation with respect to x:

d/dx(√x + √y) = d/dx(10)

1/(2√x) + (1/2)y'(x)/√y = 0

Simplifying, we get:

y'(x) = -√y/√x

To find y'(9), we plug in x = 9 and y = y(9) = 49:

y'(9) = -√49/√9 = -7/3

Therefore, y'(9) = -7/3.

Answer:

1/ At 10km, they will cost the same.

2/ It costs $199.50

Step-by-step explanation:

We know

Rental Company A, a rental car costs $55.50, and every kilometer costs $14.40.

Let Y represent the total cost, and x is the number of kilometers. We have the equation

y = 14.40x + 55.50

Rental Company B, a rental car costs $91.50, and every kilometer costs $10.80.

y = 10.80x + 91.50

How many kilometers will they cost the same?

14.40x + 55.50 = 10.80x + 91.50

3.6x = 36

x = 10 km

How much will it cost?

y = 14.40(10) + 55.50

y = 144 + 55.50

y = $199.50

The correct statement regarding the solution of the expression is given as follows:

Miguel made no mistakes.

The expression for this problem is defined as follows:

32/[2(2³ - 4)].

The parenthesis has precedence, and inside the parenthesis, the cube has precedence, hence:

32/[2(8 - 4)] = 32/[2(4)]

Multiplying in the denominator and then dividing the numerator by the denominator, the result is given as follows:

32/[2(4)] = 32/8 = 4.

Meaning that no mistake was made.

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The percentage of No purchase is 26%, the computer is 59.9% and the printer is 22%.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that he collected the following data during a recent week: 327 customers visited the store, 196 purchased computers, 72 purchased printers, and 87 made no purchase.

The percentage of No purchase is:-

P = 87 / 327

P = 26%

The percentage of computer purchases:-

P = 196 / 327

P = 59.9%

The percentage of printer purchases is:-

P = 72 / 327

P = 22%

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Answer:

x=5

Step-by-step explanation:

5x+2=8x-13

add the 13

5x+15=8x

subtract the 5x

15=3x

divide by 3

x=5

Answer: the answer is C

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

It's like connecting the dots

For example, BD. When you draw a line from B to D, you have to touch O at some point.

That happens for all of them except one, which is a.) AB.

When you connect points A and B, you never touch point O

Edit; What the other person said is right actually. I'm wrong. He gets my 5 stars.

The left Riemann sum approximation is 14.892

From the question, we have the following parameters that can be used in our computation:

f(x) = 3^x

The left Riemann sum can be expressed as:

[tex]R_n = h \sum_{i=1}^{n} \frac{4}{a + ih}[/tex]

Such that:

h = (b - a)/n

In this case, a = 2, b = 3.5, n = 3, and f(x) = 3^x

So, the left Riemann sum approximation is:

Approximation = (3.5-2)/3 * (f(2 + 1/3 * (3.5-2)) + f(2 + 2/3 * (3.5-2)) + f(2 + 3/3 * (3.5-2)))

Approximation = 0.5/3 * (3^(2 + 1/3 * (3.5-2)) + 3^(2 + 2/3 * (3.5-2)) + 3^(2 + 3/3 * (3.5-2)))

Approximation = 14.892

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The answers to questions 2, 3, and 4 can be used to assess the effectiveness of a technique after a procedure is finished.

Were the steps completed in order?

This is a crucial question to ask since it reveals the steps in the process and their chronological order, allowing the processes to be adjusted as necessary in the future.

What could be done differently in the future?

It is crucial since it can identify existing problems as well as those that can develop in the future, and it will aid in resolving them.

Was the expected outcome reached?

The most crucial question to ask is what result you want the process to produce; if not, you'll need to adjust the phases and the process.

Evaluation: Evaluation is the methodical conclusion of any topic, problem, or subject using predetermined standards or criteria. To judge their worth or value, the step and the methods are analyzed and assessed.

Therefore, the answers to questions 2, 3, and 4 can be used to assess the effectiveness of a technique after a procedure is finished.

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