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The quotient property of radicals requires the indices of the radicals to be the same. Thus, it is not possible to write the expression (5√3 + 2√2) as a single radical.What is the quotient property of radicals?

The quotient property of radicals states that for any non-negative numbers x and y with y ≠ 0, if n is an integer greater than 1, then the following property holds:√(x/y) = √x/√yNow let's take a look at the question at hand. We can see that the two radicals have different indices. Therefore, the quotient property of radicals does not apply. As a result, it is not possible to simplify the expression as a single radical. Therefore, the expression (5√3 + 2√2) cannot be written as a single radical.

The quotient property of radicals states that when dividing radicals, the indices (or roots) of the radicals involved must be the same. In other words, for the quotient property to be applicable, the radicals being divided must have the same root.

If the radicals have different indices, it is generally not possible to simplify the expression into a single radical. This is because the rules of radical arithmetic require the indices to be the same in order to combine or simplify radicals.

For example, let's consider the expression √2 / √3. Here, the radicals have different indices (square root and cube root), so we cannot combine them into a single radical using the quotient property. The expression √2 / √3 cannot be simplified further because the indices do not match.

However, it's important to note that even though the quotient property does not apply in such cases, it does not mean that the expression is mathematically invalid or cannot be manipulated further. It simply means that the expression cannot be simplified into a single radical using the quotient property. Other algebraic techniques or operations may be necessary to further simplify or manipulate the expression if desired.

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The given information is the quotient property of radicals requires the indices of the radicals to be same.

Yes, it is not possible to write [tex]$8\sqrt{2}+5\sqrt{3}$[/tex] as a single radical because the quotient property of radicals requires the indices of the radicals to be the same.

The quotient property of radicals is a mathematical concept that explains how to divide two radicals with the same index. If r is a non-negative number and s is a non-negative number, then:

[tex](\frac{r}{s})^{n}=\frac{r^{n}}{s^{n}}[/tex]

The property of quotient states that the quotient of the same degree radicals is equal to the same degree root of the quotient of the radicands. If a and b are non-negative numbers and n is an integer greater than 1:

[tex](\frac{a}{b})^{n}=\frac{a^{n}}{b^{n}}\sqrt[n]{\frac{a}{b}}[/tex]

[tex]=\frac{\sqrt[n]{a}}{\sqrt[n]{b}}[/tex]

If you look at the terms [tex]$8\sqrt{2}$ and $5\sqrt{3}$[/tex], you can tell that their indices are not the same. The term [tex]$8\sqrt{2}$[/tex] has an index of 2 while the term [tex]$5\sqrt{3}$[/tex] has an index of 3. The quotient property of radicals requires the indices of the radicals to be the same. Therefore, you cannot add or subtract two radicals that do not have the same index.

Example: [tex]$8\sqrt{2}+5\sqrt{3}$[/tex] can be rearranged as [tex]$8\sqrt{2}+0\sqrt{3}+5\sqrt{3}$[/tex]. Then using distributive property, it can be written as [tex]$(8+0)\sqrt{2}+5\sqrt{3}$[/tex]. In conclusion, it is not possible to write [tex]$8\sqrt{2}+5\sqrt{3}$[/tex] as a single radical.

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Answer:

a subtraction

Step-by-step explanation:

C.

Subtraction Property of Equality

The correct answer is D.

The variable of time that could cause a student’s GPA to increase is studying.

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Answer:

$220.5

Step-by-step explanation:

To answer this simply multiply the number of hours (25.2) times the hourly wage 8.75 and you'll get the answer

25.2 times 8.75 equals 220.5

The formula for the kth payment Pₖ is Pₖ = (1/10 * PV) + (PV * r).

To find a formula for the kth payment Pₖ, we can start by calculating the monthly interest rate and the total number of payments.

Given that the loan is payable in 10 years, we have a total of 10 payments. The loan amount PV is 500,000 pesos, and the effective annual interest rate r is 18%.

First, let's calculate the monthly interest rate:

Monthly interest rate = (1 + r)^(1/12) - 1

Substituting the values, we have:

Monthly interest rate = (1 + 0.18)^(1/12) - 1 ≈ 1.4337% or 0.014337

Now, let's find the kth payment Pₖ. Since the borrower pays 50,000 pesos in principal at the end of each year, which is 1/10 of the loan amount, we can modify the formula to:

Pₖ = (1/10 * PV) + (PV * r)

Substituting the given values, we have:

Pₖ = (1/10 * 500,000) + (500,000 * 0.014337)

Simplifying, we get:

Pₖ ≈ 50,000 + 7,168.5 ≈ 57,168.5 pesos

This formula gives the kth payment Pₖ for any specific year during the loan term.

Now, let's construct an amortization schedule for this loan:

Year | Payment | Principal | Interest | Balance

--------------------------------------------------

1    | 57,168.5 | 50,000   | 7,168.5  | 450,000

2    | 57,168.5 | 50,000   | 7,168.5  | 400,000

3    | 57,168.5 | 50,000   | 7,168.5  | 350,000

...

10   | 57,168.5 | 50,000   | 7,168.5  | 0

In each year, the principal payment remains constant at 50,000 pesos, and the interest payment gradually decreases as the outstanding balance decreases. The balance reaches zero after 10 years, indicating that the loan has been fully paid off.

Please note that the actual schedule may vary slightly due to rounding errors and the specific date of the first payment.

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Answer:

Hi! You're uspposed to check the equality, and it is false. 8/10 is not equal to 6/5.

However, If you add the two together by making the common denominator 10, you will get 20/10 or 2.

Answer:

4/5=6/5 :3

Step-by-step explanation:

Answer:

x=15

supplementary angle equals 180

Answer:

Step-by-step explanation:

Common difference = 5

a₁ = 24

a₆ = a₁ + (6-1)5 = 49

Answer:

14

Step-by-step explanation:

First you figure out what the value of x is, and then you must add the numbers in the Participates in Sports column to get 14

Answer:

308.5 lol

Step-by-step explanation:

Answer:

∠x = 59°

Step-by-step explanation:

∠ECD = 52°   because they are alternate angles and will be equal

∠x = 180° - 52° - 69° = 59°  because the sum of the interior angles of a triangle = 180°

Answer: y=-2

Step-by-step explanation:

Based on the location of the line and the focus of the parabola, the equation of the line will be y = -2.

The line is a horizontal line which means that the primary focus will be on the y axis.

The focus of the parabola is at F(6, 4) and the line is to be 6 units below this focus which means that the line on the y axis will be at:

= 4 - 6

= -2

This leaves the formula of the line as y = -2.

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Answer:

141.3

Step-by-step explanation:

27.78% of the total area is covered with red.

       (Ф/360) x πr²

We have the given semicircle as shown in image.

Total green coloured area -

A[G] = 2 x {(Ф/360) x πr²}

A[G] = 2 x (40/360 x πr²}

A[G] = (2/9)πr²

Now -

A[R] = πr²/2 - (2/9)πr²

A[R] = πr²{1/2 - 2/9}

A[R]% = (πr²{1/2 - 2/9}/πr²) x 100

A[R]% = (1/2 - 2/9) x 100

A[R]% = (9 - 4)/18 x 100

A[R]% = 5/18 x 100

A[R]% = 500/18

A[R]% = 27.78%

Therefore, 27.78% of the total area is covered with red.

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Answer: $7,915.98

Step-by-step explanation: This is an exponentially decaying problem, so that means we use the formula ab^x.

The a value is the original price or the starting point, which is 15,000. The b value is the ratio in which it decreases or increases. It is decreasing, so we subtract 12 from 100, which is 88. The ratio should be in decimal form, so it is 0.88. Finally, the x should be the exponent, the amount of times it is getting multiplied by the ratio. So the equation would be 15,000(0.88)^5.

Then, we solve.

0.88 * 0.88 * 0.88 * 0.88 * 0.88 = 0.5277319168

Then 0.5277319168 * 15,000 = 7,915.978752.

Of course, we round to the nearest hundredth, which is 7,915.98. Hope this helped.

Answer:

scale factor 3 is the answer.

Step-by-step explanation:

Length = 18 in

Breadth = 3 in

height = 10 in

Volume of cuboid = l × b × h

V = 18 × 3 × 10

V = 540 in³

540 in³ is the original volume. The volume needs to be tripled, so multiply the original volume with 3

V = 540 × 3 = 1620 in³

∴ 1620 in³ will be the new volume if it's tripled and the scale factor is 3.

Answer:

1413 sq ft.

Step-by-step explanation:

Area of a semicircle=(1/2)*πr²

Radius=30ft

A=(1/2)*3.14*30²=1413 sq ft.

Answer:

3rd one im pretty sure

Step-by-step explanation:

Answer:

triangle bby

Step-by-step explanation:

Step-by-step explanation:

Right because there's an angle of 90

Answer:-x • (w2 - 12)

 ——————————————

       3w      

Answer:

$30

Step-by-step explanation:

1 person = $ 2

18 person = 2 × 18 = $36

winner = $6

profit = 36 - 6 = $30

Answer:

[tex]\dfrac{x+y}{2}[/tex]

Step-by-step explanation:

Let first number be x and another number is y.

A rational number is a fraction that can be expressed in the form of x/y.

A rational number between x and y is given by :

[tex]R=\dfrac{x+y}{2}[/tex]

So,

If x and y are two rational numbers such that x < y , then [tex]\dfrac{x+y}{2}[/tex] is a rational number in between x and y.

Answer:

4 revolutions per second

Step-by-step explanation:

60 revs / 15 secs = 4 revs/sec

Answer:

4 revolutions per second

Step-by-step explanation:

60/15 = 4

If your car gets 29 miles per gallon, the cost to drive 300 miles when gasoline costs $3.20 per gallon is approximately $33.10.

One way to determine the cost of driving 300 miles is to divide the number of miles by the miles per gallon (MPG) and then multiply by the cost of gasoline per gallon.

Divide 300 miles by 29 MPG to get the total number of gallons of gasoline needed:

300 ÷ 29 ≈ 10.34 gallons

Round up to the nearest whole number to get 11 gallons

Multiply the number of gallons by the cost per gallon of gasoline:

$3.20/gallon x 11 gallons = $35.20

Therefore, it will cost $35.20 to drive 300 miles when gasoline costs $3.20 per gallon with a car that gets 29 miles per gallon.

We know that 1 US gallon equals 3.785411784 liters. Therefore, the car travels 29 x 3.785411784 = 109.724897 liters in 1 US gallon.

So, the cost of traveling 300 miles will be 300/29 = 10.34482759 gallons.

So, the cost of traveling 300 miles will be $3.2 x 10.34482759 = $33.10344828. Therefore, the cost of traveling 300 miles will be $33.10 approximately.

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(1) The statement that, "The $2 million is appropriate cash-inflow for the new edition of the book" is False because the cash-inflow is $1.8 million.

(2) The statement that, "Companies should use accounting profits, not cash flows, to make capital budgeting decisions" is False because, companies should focus on cash flows.

Part (1) The $2 million is not appropriate "cash-inflow" for "new-edition" of book. The $2 million represents "expected-sales" revenue from the new edition of "Foundation of Finance," but it does not take into account any costs or expenses associated with producing or marketing the book.

It is mentioned that $200,000 would have been spent on existing past edition of textbook. This expense needs to be deducted from expected sales revenue to determine the appropriate cash inflow.

So, appropriate cash-inflow for the new edition would be $2 million minus $200,000, which equals $1.8 million.

So, the statement is False.

Part (2) : Companies should use cash flows, not accounting-profits, to make capital budgeting decisions. Accounting-profits, also known as net income or earnings, are calculated based on accrual accounting principles and include non-cash items such as depreciation and amortization.

When making capital budgeting decisions, it is essential to consider the actual "cash-flows" generated by an investment project. Cash flows represent the cash inflows and outflows that occur over a specific period, and they are crucial for evaluating the feasibility and profitability of an investment.

Therefore, the statement is False.

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This indicates that the baby's weight is 0.64 standard deviations below the mean weight of newborn babies.

To calculate the z-score, we use the formula:

In this case, the observed weight is 6.70 pounds, the mean weight is 7.5 pounds, and the standard deviation is 1.25 pounds.

Plugging these values into the formula, we get:

Calculating this, we find that the z-score is approximately -0.64.

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P-value is less than the level of significance α = 0.05, we reject the null hypothesis and conclude that the mean time to assemble at the end of a 3-week training period is less for the new training procedure.

a. Performing the test using the classical approach α=0.05

Hypothesis test:

Null hypothesis H₀: The mean time for the new procedure = the mean time for the standard procedure

Alternative hypothesis H₁: The mean time for the new procedure < the mean time for the standard procedure (one-tailed test)

Level of significance α = 0.05

Since population standard deviations are unknown, we will use the t-test to conduct the hypothesis test.

Below is the calculation of the t-test.(For detailed calculation of t-test, please refer to the image attached)

Using a t-distribution table with df = 14 (n1 + n2 - 2), the critical value for a one-tailed test at α = 0.05 is -1.761.

The test statistic (-2.029) is less than the critical value (-1.761), so we reject the null hypothesis and conclude that the mean time to assemble at the end of a 3-week training period is less for the new training procedure.

b.Performing the above test assuming population variances are equal

Hypothesis test

Null hypothesis H₀: The mean time for the new procedure = the mean time for the standard procedure

Alternative hypothesis H₁: The mean time for the new procedure < the mean time for the standard procedure (one-tailed test)Level of significance α = 0.05

Since population variances are assumed to be equal, we will use the pooled t-test to conduct the hypothesis test.

Below is the calculation of the pooled t-test.(For detailed calculation of pooled t-test, please refer to the image attached)

Using a t-distribution table with df = 16 (n₁ + n₂ - 2), the critical value for a one-tailed test at α = 0.05 is -1.746.

The test statistic (-2.029) is less than the critical value (-1.746), so we reject the null hypothesis and conclude that the mean time to assemble at the end of a 3-week training period is less for the new training procedure.

c. Performing the above test (#2) using the p-value approach.

Hypothesis test:

Null hypothesis H₀: The mean time for the new procedure = the mean time for the standard procedure

Alternative hypothesis H₁: The mean time for the new procedure < the mean time for the standard procedure (one-tailed test)

Level of significance α = 0.05

Since population variances are assumed to be equal, we will use the pooled t-test to conduct the hypothesis test.

The test statistic is -2.029, which corresponds to a p-value of 0.0328.

Since the p-value is less than the level of significance α = 0.05, we reject the null hypothesis and conclude that the mean time to assemble at the end of a 3-week training period is less for the new training procedure.

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