(Solving Equations Using Square and Cube Roots LC)

Solve y3 = −27.

Answer:

Step-by-step explanation:

You want the area of a 16-unit circle using different values for pi.

The formula for the area of a circle is ...

  A = πr² . . . . . . where r is half the diameter

For the different values of pi, this will be (in square units) ...

  π(8²) = 64π . . . . exact

  3.14(8²) = 200.96 . . . . using 3.14 for π, slightly low

  22/7(8²) = 201 1/7 . . . . using 22/7 for π, slightly high

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Answer:

8x-(-4x-6)=42

8x+4x+6=42

12x=42-6

12x=36

x=36/12

x=3

substitute in an equation of your choice

8(3)-y=42

24-y=42

24-42=y

-18=y

Step-by-step explanation:

Answer:

x= 4 y= -10

Step-by-step explanation:

8x - y = 42

-4x - 6 = y

rearrange -4x - 6 =y to -4x -y = 6

8x - y = 42

-4x - y = 6

4x = 48

48/4 = 12

x=4

subsitute x with 4 adn solve for y = -22

y= -10

First, multiply the signs to get rid of the parenthesis.

Second, solve the products.

Third, solve the addition between the negative numbers.

At last, solve the difference.

i gotchu what do u want

The price per night for a Suite room for check-in on Friday and Saturday would be amount $278.50 .

The price per night for a Suite room for check-in on Friday and Saturday would be amount $278.50.

1. Calculate the price of a Deluxe room for check-in on Sunday until Thursday:

$223 / 1.70 = $131.18

2. Calculate the price of a Deluxe room for check-in on Friday and Saturday:

$131.18 x 1.25 = $163.98

3. Calculate the price of a Suite room for check-in on Friday and Saturday:

$163.98 x 1.70 = $278.50

The price per night for a Suite room for check-in on Friday and Saturday would be $278.50.

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Answer:

he keep 36$

Step-by-step explanation:

2/5 is 40% plus the 50% thats 90% so he only keep 10% which is 36$

Answer: He kept 36$

Step-by-step explanation:

It depends on the rotational speed of the wheel. To calculate this speed, we need to know the angular velocity of the wheel.

The maximum speed of a point on the outside of the wheel, 15 cm from the axle, if we assume that the wheel is rotating at a constant rate, we can use the formula v = rω, where v is the speed of the point on the outside of the wheel, r is the radius of the wheel (15 cm in this case), and ω is the angular velocity of the wheel. Therefore, the maximum speed of a point on the outside of the wheel would be directly proportional to the angular velocity of the wheel.
The formula to calculate the maximum linear speed (v) is:
v = ω × r
where v is the linear speed, ω is the angular velocity in radians per second, and r is the distance from the axle (15 cm, or 0.15 meters in this case).
Once you have the angular velocity (ω) of the wheel, you can plug it into the formula and find the maximum speed of a point on the outside of the wheel.

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The domains of the arithmetic sequence An = -6n - 107 are

1, 2, 3, 4, 5, 6, and so on.

It is a sequence where the difference between each consecutive term is the same.

We have,

An = -6n - 107

For n = 1,

A1 = - 6 - 107 = -113

For n = 2,

A2 = -12 - 107 = -119

For n = 3,

A3 = -18 - 107 = -125

For n =4,

A4 = -24 - 107 = -131

For n = 5,

A5 = -30 - 107 = -137

For n = 6,

A6 = -36 - 107 = -143

Thus,

The domains are 1, 2, 3, 4, 5, 6, and so on.

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Answer:

5.1 yd

Step-by-step explanation:

tan(25°) = x/11

x = 11tan(25°)=5.1 yd

Answer:

Some People Have Curly Brown Hair Turns Permanently Black

Step-by-step explanation:

Sin=p/h

Cos=b/h

Tan=p/b

Answer:

"SOHCAHTOA" is a helpful mnemonic for remembering the definitions of the trigonometric functions sine, cosine, and tangent i.e., sine equals opposite over hypotenuse, cosine equals adjacent over hypotenuse, and tangent equals opposite over adjacent, (1) (2) (3) Other mnemonics include.

Step-by-step explanation:

Answer:

The other length is 9 feet.

Step-by-step explanation:

Answer:

Assuming that the  purpose of the rest of the paint into to cover the rest ofe the board he would have 2 and 2/3 left

Step-by-step explanation:

Answer:

\( {8x}^{3} + 27 \\ = {8x}^{3} + {3}^{3} \\ let : 8x \: be \: a \\ : 3 \: be \: b \\ = > {a}^{3} + {b}^{3} : \\ {(a + b)}^{3} = (a + b)( {a}^{2} + 2ab + {b}^{2} ) \\ {(a + b)}^{3} = ( {a}^{3} + 3{a}^{2} b + 3a {b}^{2} + {b}^{3} ) \\ ( {a}^{3} + {b}^{3} ) = {(a + b)}^{3} - 3ab(a + b) \\ \therefore( {8x}^{3} + 27) = {(8x + 3)}^{3} - 72(8x + 3)\)

Misrepresentation means that one party (in this case Joe) is knowing selling or marketing things as something they are not. Yes this would be misrepresentation, because if Joe knows this is a lie, he is spreading false information KNOWINGLY

The equation is y = 6.25x.

Linear equations are equations whose highest power of the variables is 1. The graph of a linear equation is a straight line.

A nonlinear equation is an equation whose highest power of the variables is not 1 and the graph is not a straight line.

We have that;

x = the number of hours Steven babysits

y = the amount he charges

For x = 6 hours

y = $37.50

y/x = 37.5/6

=6.25

Also for x = 8 hours

y = $50

y/x = 50/8

=6.25

Therefore

y = 6.25x

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(a)The probability that the selected individual owns shares in the balanced fund is 8%, that is 0.08.

(b)The probability that the selected individual owns shares in a bond fund is 26%.

(c)The probability that the selected individual does not own shares in a stock fund is 57%.

(a) A probability is a number that indicates how likely an event is to occur. In this case, the event is the selected individual owning shares in the balanced fund. The percentage of customers who own shares in the balanced fund is given as 8%. This means that if 100 customers own shares in just one fund, 8 of them would own shares in the balanced fund.

(b) To find the probability that the individual owns shares in a bond fund, we need to add up the percentages of customers who own shares in each of the bond funds:

Short bond: 14%

Intermediate bond: 7%

Long bond: 5%

Total bond funds: 14% + 7% + 5% = 26%

So, the probability that the selected individual owns shares in a bond fund is 26%.

(c) To find the probability that the selected individual does not own shares in a stock fund, we need to find the complement of the probability that the individual owns shares in a stock fund. The probability that the individual owns shares in a stock fund is the sum of the percentages of customers who own shares in each of the stock funds:

Moderate-risk stock: 25%

High-risk stock: 18%

Total stock funds: 25% + 18% = 43%

So, the probability that the selected individual does not own shares in a stock fund is 1 - 43% = 57%.

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--The question is incomplete, answering to the question below--

"A mutual fund company offers its customers a variety of funds: a money-market fund, three different bond funds (short, intermediate, and long-term), two stock funds (moderate and high-risk), and a balanced fund. Among customers who own shares in just one fund, the percentages of customers in the different funds are as follows.

Money-market 23%

High-risk stock 18%

Short bond 14%

Moderate-risk stock 25%

Intermediate bond    7%

Balanced 8%

Long bond 5%  

A customer who owns shares in just one fund is randomly selected.

(a)What is the probability that the selected individual owns shares in the balanced fund?

(b) What is the probability that the individual owns shares in a bond fund?

(c) What is the probability that the selected individual does not own shares in a stock fund?"

1. The accumulated amount for the investment at CAPITEC is R36,750.

2. The accumulated amount for the investment at FNB is R33,480.

3. Lebo will earn more interest if she invests her money at Capitec than at FNB.

The accumulated amount for the investment at Capitec with a principal amount of R30,000 invested at a simple interest rate of 7.5% for 3 years can be calculated as follows:

\(= Principal + (Principal * Rate * Time)\\= R30,000 + (R30,000 * 0.075 * 3)\\= R30,000 + R6,750\\= R36,750\)

The accumulated amount for the investment at FNB with a principal amount of R30,000 invested at a compound interest rate of 3.5% per annum for 3 years can be calculated using the compound interest formula:

\(= Principal * (1 + Rate)^Time\\= R30,000 * (1 + 0.035)^3\\= R30,000 * 1.116\\= R33,480\)

Now, based on the calculations, the investment at Capitec will yield R36,750 after 3 years while the investment at FNB will yield R33,480 after 3 years. Therefore, Lebo will earn more interest if she invests her money at Capitec than at FNB.

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Answer:

Step-by-step explanation:

When James is twice as old as John, the difference in their ages will be John's age: 10. That is 5 years from now, so John's age now is 10 -5 = 5.

John is 5 years old.

__

3 years ago, John was 2 and James was 12. Their total age at that time was 14.

Answer:

monomial

Step-by-step explanation:

monomial eg 14 , x , 15x , -50 , -70x

The written form of the expression 4(3x + 2) - 9 is "Four times the quantity of three times x plus two, minus nine."

To simplify the expression, we can distribute the 4 to the terms inside the parentheses:

4(3x + 2) - 9

= 12x + 8 - 9

= 12x - 1

The simplified expression is 12x - 1. We have multiplied 4 by both terms inside the parentheses, resulting in 12x and 8, and then subtracted 9 from that. Finally, we combined like terms by keeping the 12x as it is and subtracting 1 from it, giving us the simplified form 12x - 1.

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Answer:

acute angle

Step-by-step explanation:

The acute angle is the angle that has an amplitude of less than 90°. The obtuse angle, on the other hand, has a width greater than 90°. The right angle measures 90° and its sides are orthogonal.

Answer:

an angle less than 90° is an acute angle

Step-by-step explanation:

an angle less than 90° is an acute angle

an angle equal to 90° is a right angle

an angle greater than 90° but less than 180° is an obtuse angle

an angle greater than 180° is a reflex angle

Machlab Equipment should use the Net Present Value (NPV) as the computational method to make its decision.

The Net Present Value (NPV) is a widely used computational method for investment decisions. It takes into account the initial investment cost, annual operating costs, and expected cash flows over the life span of the machines. By discounting these cash flows to their present value, the NPV determines the profitability and economic viability of each machine.

To compare the three machines, Machlab Equipment can calculate the NPV for each interest by subtracting the initial investment cost from the present value of the expected cash inflows. The Equivalent Annual Cost (EAC) and Bottom-up Operating Cash Flow methods may provide useful information but may not capture the overall profitability and financial impact of the investment.

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The exact value of the area under the graph of f(x) over the interval [a,b] is False.

If f(x) is a constant function, meaning it has the same value for all x, then the graph of f(x) over the interval [a, b] will be a horizontal line.

The area under a constant function over any interval is simply the product of the constant value and the width of the interval.

However, the formula for the area of a rectangle is not applicable in this case because the graph of a constant function does not form a rectangle.

The area under a constant function is a rectangle only when the function is a constant height (y-value) over the entire interval, which is not the case for arbitrary constant functions.

To compute the exact value of the area under the graph of f(x) over the interval [a, b] when f(x) is a constant, you simply need to multiply the constant value by the width of the interval, which is (b - a).

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Answer:

y = 1/2x+2

Step-by-step explanation:

first find x intercepts : to find x intercept put 0 in y

1/2x+2 = 0

1/2x= -2

x = -4 the graph shows x intercept at 4

next find y intercept : to find y intercept put 0 into x

=1/2*0+2

=2

the graph shows y crosses at 2.

Answer:

y = 1/2x+2

well, she's 13 now, and when she'll be 21 that's 8 years later, so

\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$6439\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &8 \end{cases}\)

\(A = 6439\left(1+\frac{0.04}{1}\right)^{1\cdot 8}\implies A=6439(1.04)^8 \implies \stackrel{ \textit{yeap, she will \checkmark} }{A \approx 8812.22}\)

Answer: If the air-plane travels 1020 km in one hour, then it will cover 4250 km in 25/6 hours.

The formula which relates distance, speed, and time is given by d = rt, where d is the distance traveled, r is the rate of travel or the speed, and t is the time traveled. To find out the distance an aircraft will travel in t = 25/6 hours, we must first find out the speed r of the aircraft in kilometers per hour (km/hr) as shown:

d = rt

1,020 km = r(1 hr)

(1,020 km)/(1 hr) = [r(1 hr.)]/(1 hr)

1,020 km/hr = r(1 hr./1 hr)

1,020 km/hr = r(1)

r = 1,020 km/hr

Now, calculating the distance the aircraft will travel in t = 25/6 hours, we have:

d = rt

= (1,020 km/hr)(25/6 hr)  

= (1,020)(25/6) km

= (1,020/6)(25) km

= (170)(25) km

= 4,250 km

Answer:

4250 km

Step-by-step explanation:

\(\Large\bf{GiveN,} \\ \)

⠀⠀⠀\( \textbf{Distance\:covered\: in \:1\:hour} \)

⠀⠀⠀⠀⠀\( \implies \)\(\bf\dfrac{25}{6}\) × 1020

⠀⠀⠀⠀⠀\( \implies \)\(\bf\dfrac{25×1020}{6×1}\)

⠀⠀⠀⠀⠀\( \implies \)\(\bf\dfrac{25500}{6}\)

⠀⠀⠀⠀⠀⠀ \(\small{\underline{\mathcal{\green{ =\:4250\:km}}}}\)

\( \therefore\)\( {\:\:\:Distance\: covered\: in \:25/6\:hrs\:by\:plane}\)\( {⠀⠀⠀⠀⠀= 4250\:km}\)

Answer:

40.3333333333 repeating

Step-by-step explanation:

The effect on the trial balance if the purchase of marketable securities of $1,000 had been recorded to the equipment account in error is that the trial balance would not be in balance anymore.

A trial balance is a financial statement that summarizes all the accounts of a company's general ledger with its debit balances and credit balances to check if they are equal. When the purchase of marketable securities of $1,000 is recorded to the equipment account in error, this means that the entry was recorded in the wrong account. The equipment account would be overstated by $1,000 and there would be no change in the marketable securities account, thus leading to a mismatch between the total debit and credit amounts recorded. As a result, the trial balance would not be in balance anymore.

Explanation:A trial balance is a summary of all the accounts of a company's general ledger. It's a statement that lists all the debit balances in one column and all the credit balances in another column, which is used to confirm the accuracy of the accounts before preparing the financial statements of a company. The totals of both columns should match if the trial balance is correct. If not, it indicates an error that needs to be corrected.

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Answer:

610 tickets for $8, and 240 tickets for $12.

Step-by-step explanation:

x + y = 850

8x + 12y = 7760

x = 850 - y

8(850-y) + 12y = 7760

6800 - 8y + 12y = 7760

4y = 960

y= 240

x + 240 = 850

x= 610

Answer:

240 = no. of $12 tickets

610 = no. of $8 tickets

Step-by-step explanation:

Let x = no. of $12 tickets

y = no. of $8 tickets

12x = income from selling x $12 tickets

8y = income from selling y $8 tickets

If they are to make a profit of 4000, then they need to have a total income from sales of $7760

So,  x + y = 850         and              12x + 8y = 7760

            y = 850 - x                         12x + 8(850 - x) = 7760

                                                       12x + 6800 - 8x = 7760

                                                          4x + 6800 = 7760

                                                                      4x = 960

                                                                        x = 240 = no. of $12 tickets

            y = 850 - 240

              = 610 = no. of $8 tickets

Discount is 0.354838, Discount percentage is 35.4838 %.

According to the question

A shop item is marked down from r 6.20 to r 4.

A discount is an amount that is subtracted from the regular price of an item.

Based on the given conditions

= \(\frac{6.2-4}{6.2}\)

Solving 6.2 - 4, we get 2.2

= 2.2/6.2

Discount = 11/31 = 0.354838

Percentage discount is a discount that is given to a product or service that is given as an amount per hundred. For example, a percentage discount of 20% would mean that an item that originally cost $100 would now cost $80.

Discount percentage = \(\frac{11}{31}\) × 100

= 35.4838 %

Hence,

Discount is 0.354838, Discount percentage is 35.4838 %.

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