What is the value of the expression below? (27^5/3) ^1/5

Answer:

Part 1) [tex]\frac{a^4}{4b^2}[/tex]

Part 2) [tex]-\frac{v^9}{w^6}[/tex]

Step-by-step explanation:

we know that

When divide exponents (or powers) with the same base, subtract the exponents

Part 1) we have

[tex]\frac{3a^{2}b^{-4}}{12a^{-2}b^{-2}}=(\frac{3}{12})(a^{2+2})(b^{-4+2} )=\frac{1}{4}a^{4}b^{-2}=\frac{a^4}{4b^2}[/tex]

Part 2) we have

[tex]\frac{v^3w^{-3}}{-v^{-6} w^3} =-v^{3+6}w^{-3-3}=-v^9w^{-6}=-\frac{v^9}{w^6}[/tex]

Answer:

width =5m

length=18m

Step-by-step explanation:

w=x

l=3x+3

perimeter =2(l+w)

46=2(x+3x+3)

46=2(4x+3)

46=8x+6

46-6=8x

40=8x

x=40/8

x=5

l=3x+3=3*5+3=15+3=18

Final answer:

To find the length and width of a rectangle with a given perimeter, use algebra to solve for the width first, then use that value to find the length. The width is 5 meters and the length is 18 meters based on the given perimeter and the relationship between length and width.

Explanation:

The perimeter of a rectangle is given by the formula P = 2l + 2w, where P is the perimeter, l is the length and w is the width. According to the problem, the perimeter is 46 meters, and the length is 3 meters more than 3 times the width. Therefore, we can express the length as l = 3w + 3. Let's set up the equation using the perimeter formula:

Now that we've found the width to be 5 meters, we can find the length:

The width of the rectangle is 5 meters and the length is 18 meters.

Answer:

The point (9,5) is on the graph of the equation

The graph of the equation is the set of all points that are solutions to the equation

Step-by-step explanation:

we have the linear equation

[tex]y=\frac{1}{3}x+2[/tex]

This is the equation of the line in point slope form

where

the slope is [tex]m=\frac{1}{3}[/tex]

the y-intercept is [tex]b=2[/tex]

Remember that

If a ordered pair is on the graph of the linear equation, then the ordered pair must satisfy the linear equation

The graph of the equation is the set of all points that are solutions to the equation

Verify each statement

case 1) The graph of the equation is a single point representing one solution to the equation

The statement is false

Because the graph of the equation is the set of all points that are solutions to the equation

case 2) The point (9,5) is on the graph of the equation

The statement is true

Because

For x=9, y=5

substitute the value of x and the value of y in the linear equation

[tex]5=\frac{1}{3}(9)+2[/tex]

[tex]5=3+2[/tex]

[tex]5=5[/tex] ----> is true

so

the ordered pair satisfy the linear equation

therefore

The point is on the graph of the equation

case 3) The graph of the equation is the set of all points that are solutions to the equation

The statement is true

case 4) The point (-3,-1) is on the graph of the equation

The statement is false

Because

For x=-3, y=-1

substitute the value of x and the value of y in the linear equation

[tex]-1=\frac{1}{3}(-3)+2[/tex]

[tex]-1=-1+2[/tex]

[tex]-1=1[/tex] ----> is not true

so

the ordered pair not satisfy the linear equation

therefore

The point is not on the graph of the equation

The total deposit made by Simon Wu is $634.22 which includes the amount from two checks, various dollar bills and coins.

Let's break down Simon Wu's total deposit into components and add them up. First, we have two checks: one for $123.45 and another for $432.90. Then, we have cash which can be further broken down into: 3 one-dollar bills, 9 five-dollar bills, 5 ten-dollar bills, 15 quarters, 10 dimes, 18 nickels, and 32 pennies. You need to add all these amounts together to find the total deposit.

Here is a step-by-step calculation:

Final step is to add the value of the checks, the value of the dollar bills and the value of the coins together:

$556.35 + $74 + $3.87 = $634.22

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Answer:

"To the nearest year, it would be about 9 years"

Step-by-step explanation:

11c)

This is compound growth problem. It goes by the formula:

[tex]F=P(1+r)^t[/tex]

Where

F is the future amount

P is the present (initial) amount

r is the rate of growth, in decimal

t is the time in years

Given,

P = 20,000

r = 8% = 8/100 = 0.08

F = double of initial amount = 2 * 20,000 = 40,000

We need to find t:

[tex]F=P(1+r)^t\\40,000=20,000(1+0.08)^t\\2=(1.08)^t[/tex]

To solve exponentials, we can take Natural Log (Ln) of both sides:

[tex]2=(1.08)^t\\Ln(2)=Ln((1.08)^t)[/tex]

Using the rule shown below we can simplify and solve:

[tex]Ln(a^b)=bLn(a)[/tex]

We can write:

[tex]Ln(2)=Ln((1.08)^t)\\Ln(2)=tLn(1.08)\\t=\frac{Ln(2)}{Ln(1.08)}\\t=9.0064[/tex]

To the nearest year, that would be about 9 years

The coordinates of triangle ABC after translation according to given rule are:

A'(0,-2), B'(-1,-10) and C'(6,-4)

Step-by-step explanation:

Given vertices are:

A(-2, 1), B(-3, -7) and C(4, -1)

The translation rule is: (x,y) => (x+2, y-3)

In order to translate the vertices, 2 will be added to x-coordinate and 3 will be subtracted from y-coordinate

So,

A(-2, 1) =>  A' (-2+2, 1-3) => A'(0,-2)

B(-3,-7) = > B'(-3+2, -7-3) => B'(-1, -10)

C(4,-1) => C'(4+2, -1-3) => C' (6, -4)

Hence

The coordinates of triangle ABC after translation according to given rule are:

A'(0,-2), B'(-1,-10) and C'(6,-4)

Keywords: Triangle, Translation

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18 km apart

You subtract 33 and 15

Answer:

810

Step-by-step explanation:

90/100=729/x

100×729= 90x

72900=90x

810 = x

Answer:

£810

Step-by-step explanation:

100% - 10% = 90%

£729 is 90 % after the price was decreased by 10%. Therefore, Divide £729 by 90% to get the original price.

£729/90% = £810

Answer: 9

Step-by-step explanation: The common denominator will be the least common multiple for the two denominators.

To find the least common multiple or lcm of 3 and 9, begin by listing the first few multiples for each number.

Multiples of 6

1 × 9 = 9

2 × 9 = 18

3 × 9 = 27

Notice that we skipped 0 × 9 in our list of multiples. That's because 0 × 6 is 0 according to the zero property of multiplication and our least common multiple can't be 0.

When listing the multiples of 3, it's a good idea to keep an eye on the list of multiples for 9 so that we will notice when we find a least common multiple.

Multiples of 3

1 × 3 = 3

2 × 3 = 6

3 × 3 = 9

Notice that in both lists, we have the least common multiple which is 9.

Therefore, the least common denominator of 9 and 3 is 9.

Answer:

Surface area of the fish tank [tex]332\ square\ feet[/tex]

Step-by-step explanation:

We have to find the surface area of the hospital tank.

As mentioned it does not have a cover.

The tank is in cuboid shape as it has different length [tex](l)[/tex],width [tex](w)[/tex] and height [tex](h)[/tex].

Surface area of a cuboid [tex]=2(lw+wh+hl)[/tex]

But here we have to subtract the surface area of the cover,that is [tex](lw)[/tex].

So the equation for the surface area of the cuboid can be re-framed as [tex]2(wh+hl)+(lw)[/tex]

Plugging the values of [tex]h=8\ ft[/tex] and [tex]l=12\ ft[/tex] and [tex]w=5\ ft[/tex]

Now

Surface area of the tank:

[tex]2(wh+hl)+(lw)[/tex]

[tex]2(5\times 8+8\times 12)+(12\times 5)[/tex]

[tex]2(40+96)+(60)[/tex]

[tex]2(136)+60[/tex]

[tex](272+60)=332\ ft^{2}[/tex]

So the surface area of the fish tank in the hospital is [tex]332\ ( ft)^{2}[/tex]

She bought 54 child tickets and 19 adult tickets.

Step-by-step explanation:

No. of tickets purchased = 73

Cost of tickets = $771

Cost of one child ticket = $9

Cost of one adult ticket = $15

Let,

Child ticket = x

Adult ticket = y

According to given statement;

x+y=73   Eqn 1

9x+15y=771   Eqn 2

Multiplying Eqn 1 by 9;

[tex]9(x+y=73)\\9x+9y=657\ \ \ Eqn\ 3\\[/tex]

Subtracting Eqn 3 from Eqn 2;

[tex](9x+15y)-(9x+9y)=771-657\\9x+15y-9x-9y=114\\6y=114\\[/tex]

Dividing both sides by 6;

[tex]\frac{6y}{6}=\frac{114}{6}\\y=19[/tex]

Putting y=19 in Eqn 1

[tex]x+19=73\\x=73-19\\x=54\\[/tex]

She bought 54 child tickets and 19 adult tickets.

Keywords: linear equations, subtraction

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Final answer:

Anna bought 54 children's tickets at $9 each and 19 adult tickets at $15 each to spend a total of $771 for a field trip to the zoo.

Explanation:

The question is asking us to solve a system of linear equations to find out how many children's and adult's tickets were purchased for a zoo field trip. The total cost of the tickets was $771, with children's tickets costing $9 each and adult's tickets costing $15 each. Anna purchased a total of 73 tickets.

Let's define two variables, C for the number of children's tickets, and A for the number of adult tickets. We have two equations based on the information given:

9C + 15A = 771 (Total cost equation)

C + A = 73 (Total number of tickets equation)

To solve this system, we can use substitution or elimination. Here's how you might solve it using substitution:

From the second equation, we express one variable in terms of the other: A = 73 - C.

Substitute A in the first equation: 9C + 15(73 - C) = 771.

Simplify and solve for C: 9C + 1095 - 15C = 771, which simplifies to -6C = -324, so C = 54.

Use the value of C to find A: A = 73 - 54, so A = 19.

Anna bought 54 children's tickets and 19 adult tickets.

Answer:

Step-by-step explanation:

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the coordinates of the given points:

for A(3, 5) and B(-2, 6):

[tex]m_{AB}=\dfrac{6-5}{-2-3}=\dfrac{1}{-5}=-\dfrac{1}{5}[/tex]

for B(-2, 6) and C(-5, 7):

[tex]m_{BC}=\dfrac{7-6}{-5-(-2)}=\dfrac{1}{-5+2}=\dfrac{1}{-3}=-\dfrac{1}{3}[/tex]

[tex]\large\boxed{m_{AB}\neq m_{BC}}[/tex]

Answer:

i think it is the second answer

Step-by-step explanation:

i think this because the  upside down ? is reflecting the ?

Answer:

One figure is a reflection of the other.

Step-by-step explanation:

Each point of the shape of one figure is equidistant to the equivalent point of the other, observing a symmetry line which perpendicular to the distance between each corresponding pair of points.

Answer:

(3,6)

Step-by-step explanation:

the x input cannot repeat in order for it to be a function

Answer:

[tex]3+3i[/tex]

Step-by-step explanation:

we know that

The formula to calculate the midpoint between two complex numbers (a+bi) and (c+di) points is equal to

[tex](\frac{a+c}{2})+(\frac{b+d}{2})i[/tex]

we have

(1+9i) and (5-3i)

substitute the given values

[tex](\frac{1+5}{2})+(\frac{9-3}{2})i[/tex]

[tex]3+3i[/tex]

Final answer:

The midpoint of the complex numbers 1+9i and 5-3i is calculated using the average of their real and imaginary parts, resulting in the midpoint of 3 + 3i.

Explanation:

To find the midpoint of two complex numbers, 1+9i and 5-3i, we use the midpoint formula for complex numbers which is the average of the real parts and the average of the imaginary parts separately. The formula for the midpoint M is given by:

M = ½(x1 + x2) + ½(y1 + y2)i

For our complex numbers, the real parts are 1 and 5, and the imaginary parts are 9 and -3. Applying the midpoint formula, we get:

M = ½(1 + 5) + ½(9 - 3)i = ½(6) + ½(6)i = 3 + 3i

Therefore, the midpoint of the complex numbers 1+9i and 5-3i is 3 + 3i.

Answer:

Neighborhoods that sheriff patrol in 5/8 of an hour is 3.125.

Step-by-step explanation:

The Time taken to patrol an entire neighborhood   = 3/ 15 hour

Total amount of time, the Sheriff  has to do patrolling = 5/ 8 of an hour.

Now, let us assume the total neighborhoods paroled in the given time  = m

So, [tex]\textrm{ Number of neighborhoods patrolled}  = \frac{\textrm{Total available time}}{\textrm{Time used in 1 paroling 1 neighborhood}}[/tex]

[tex]m = \frac{\frac{5}{8} }{\frac{3}{15} }   = {\frac{5}{8} \times {\frac{15}{3}  =3.125[/tex]

or, the number of neighborhoods covered  = 3.125

Hence, neighborhoods that sheriff patrol in 5/8 of an hour is 3.125.

To find out how many neighborhoods the sheriff can patrol in 5/8 of an hour, divide 5/8 by 3/15, which simplifies to 1/5. The calculation gives us 3.125, meaning the sheriff can complete 3 full neighborhood patrols.

The question involves determining how many neighborhoods a sheriff can patrol in 5/8 of an hour if it takes 3/15 of an hour to patrol one neighborhood. To solve this, we divide the total time available by the time it takes to patrol one neighborhood.

Thus, the sheriff can patrol 3 full neighborhoods in 5/8 of an hour, with some additional time remaining that is not enough to complete a fourth patrol.

The system of equations are p = 150 + 5n and p = 15n

Solution:

Given that, The Parks and recreation department in your town offers a season pass for $150.  

With the season pass you pay $5 per session to use the town's tennis courts.  

Without the season pass you pay $15 per session to use the tennis courts.

We have to write a system of equations to represent the situation

Now, let the number of sessions be "n" and total paying amount be "p"

Then in case of taking season pass  

total amount = season pass cost + $5 per session

p = 150 + 5 x n  

p = 150 + 5n  

And in case of no season pass

total amount = 15 per session

p = 15 x n  

p  = 15n

Hence, the system of equations are p = 150 + 5n and p = 15n

Final answer:

To represent the cost of using the town's tennis courts with and without a season pass, we use two equations: C = 150 + 5x for with a pass, and C = 15x for without a pass, where C is the total cost and x is the number of sessions.

Explanation:

The Parks and Recreation Department offers two options for using the town's tennis courts: with a season pass and without a season pass. We need to write a system of equations to represent the cost for each option depending on the number of sessions a person attends.

Equations

With Season Pass: C = 150 + 5x

Without Season Pass: C = 15x

In these equations, C represents the total cost of using the tennis courts for a given number of x sessions. For the pass option, there is an upfront cost of $150 plus $5 per session. Without the pass, each session costs $15.

These equations can help determine the point at which purchasing a season pass becomes more cost-effective than paying per session.

it's either 2/3 or 66.6 (neverending 6s)

Answer:it changed from $100

Step-by-step explanation:

Michael is left with $181 and it is positive.

Step-by-step explanation:

Balance in Michael's account = $550

Per month withdrawal = $30.75

One year = 12 months

Total amount of withdrawal = Per month withdrawal * months

Total amount of withdrawal =[tex]30.75*12[/tex]

Total amount of withdrawal=[tex]\$369[/tex]

Net change = Balance in account - Amount of withdrawal

[tex]Net\ change= 550-369\\Net\ change=\$181[/tex]

Michael is left with $181 and it is positive.

Keywords: multiplication, subtraction

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The net change in Michael's account balance following the withdrawals is $181.

none of the option.

To find the net change in Michael's account balance following the withdrawals, we need to calculate the total amount withdrawn over one year and then subtract it from the initial balance.

Amount withdrawn per month: $30.75

Number of months: 12 (one year)

Total amount withdrawn over one year: [tex]\(30.75 \times 12 = $369\)[/tex]

Now, to find the net change in Michael's account balance, we subtract the total amount withdrawn from the initial balance:

Initial balance: $550

Total amount withdrawn: $369

Net change = Initial balance - Total amount withdrawn

Net change = $550 - $369

Net change = $181

The net change in Michael's account balance following the withdrawals is $181.

complete question given below:

Michael had $550 in his savings account. He took out $30.75 every month for one year. What is the net change in Michael’s account balance following these withdrawals?

A.-$519.25

B.-$369

C.$369

D.$519.25

Answer:

see the explanation

Step-by-step explanation:

Part 1) Record the coordinates of the given triangle

Looking at the graph

Let

A(-4,2)

B(-2,5)

C(3,2)

Part 2) Translate the given triangle down 2 units and right 5 units. Graph the translation

we know that

A translation of 5 units at right means (x+5)

A translation of 2 units down means (y-2)

so

The rule of the translation is equal to

(x,y) -----> (x+5,y-2)

Apply the rule of the translation at each vertices

A(-4,2) ----->A'(-4+5,2-2)

A(-4,2) ----->A'(1,0)

B(-2,5) -----> B'(-2+5,5-2)

B(-2,5) -----> B'(3,3)

C(3,2) -----> C'(3+5,2-2)

C(3,2) -----> C'(8,0)

using a graphing tool

The graph in the attached figure

Answer:

1. 18.74%

2. 33.34%

3. 45.5%

4. 20%

5. 33.11%

6. 16.38%

Step-by-step explanation:

1. For Shoes, the actual price is $79.99 and the selling price is $65.00.

The discount is [tex]\frac{79.99 - 65}{79.99} \times 100 = 18.74[/tex]%.

2. For 12 pack og golf balls, the actual price is $29.99 and the selling price is $19.99.

The discount is [tex]\frac{29.99 - 19.99}{29.99} \times 100 = 33.34[/tex]%.

3. For Exercise bike, the actual price is $1099 and the selling price is $599.

The discount is [tex]\frac{1099 - 599}{1099} \times 100 = 45.5[/tex]%.

4. For Basketball, the actual price is $49.99 and the selling price is $39.99.

The discount is [tex]\frac{49.99 - 39.99}{49.99} \times 100 = 20[/tex]%.

5. For Sports socks, the actual price is $14.95 and the selling price is $10.00.

The discount is [tex]\frac{14.95 - 10}{14.95} \times 100 = 33.11[/tex]%.

6. For Hockey sticks, the actual price is $299 and the selling price is $250.

The discount is [tex]\frac{299 - 250}{299} \times 100 = 16.38[/tex]%.

Answer:

  x = 3  or  x = 6/5

Step-by-step explanation:

The zero product property (or rule) tells you the product will only be zero if one (or more) of the factors is zero. Here, that means the solutions are values of x such that ...

  x -3 = 0   ⇒   x = 3

  5x -6 = 0   ⇒   x = 6/5

Answer:

The number of children's tickets sold was 27

Step-by-step explanation:

Let

x ----> the number of children's tickets sold

y ----> the number of adult's tickets sold

we know that

[tex]6.10x+9.40y=1,179.90[/tex] ----> equation A

[tex]y=4x[/tex] ----> equation B

Solve the system by substitution

Substitute equation B in equation A

[tex]6.10x+9.40(4x)=1,179.90[/tex]

solve for x

[tex]6.10x+37.6x=1,179.90[/tex]

[tex]43.7x=1,179.90[/tex]

[tex]x=27[/tex]

therefore

The number of children's tickets sold was 27

Answer:

C) [tex]\sqrt[3]{2}[/tex]

It is C because [tex]\sqrt[3]{2}=1.2599[/tex] which is the closest to [tex]1\frac{1}{3}[/tex]. Because [tex]\frac{2^{2} }{3}=1\frac{1}{3}[/tex].

Answer:

C) Cube root of 2

Step-by-step explanation:

Answer:

21 centimeters is the answer

a) He will earn $584 for working 36 hours.

b) He will earn $656 for working 39 hours.

c) He will earn $728 for working 42 hours.

Step-by-step explanation:

Amount per hour = $16

Time and a half means 1.5 times more than the original payment.

Therefore, above 35 hours, the earning for one hour,

Extra time per hour = 16*1.5 = $24

A) 36 h

For the first 35 hours, he will get $16 per hour, therefore,

Amount of 35 hours = [tex]35*16= \$560[/tex]

Amount of one hour = $24 (as calculated above)

Total = 560+24 = $584

He will earn $584 for working 36 hours.

B) 39 h

39 h = 35h + 4h

Amount of 35 hours = $560

Amount of extra 4 hours = $24*4 = $96

Total = 560+72 = $656

He will earn $656 for working 39 hours.

C) 42 h

42 h = 35h + 7h

Amount of 35 hours = $560

Amount of extra 7 hours = 24*7 = $168

Total = 560+168 = $728

He will earn $728 for working 42 hours.

Keywords: addition, multiplication

Learn more about addition at:

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The width and length of the rectangle are 7 meters and 10 meters, respectively, as determined by using algebraic expressions to relate the given perimeter with the width and length formulas.

To solve for the length and width of a rectangle given the perimeter, we can use algebra. Since we know the length (L) is 4 meters less than twice the width (W), we can write this relationship as L = 2W - 4. The formula for the perimeter (P) of a rectangular shape is P = 2L + 2W. We are given that the perimeter is 34 meters.

Substituting the expression for L into the perimeter formula gives us:

Since the perimeter is 34 meters, we set 6W - 8 = 34.

Now, we find the length using the expression L = 2W - 4:

Therefore, the width is 7 meters and the length is 10 meters.

The calculated area of the bigger square is 22.5 square cm

How to determie the area of the larger square

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

The square

Where, we have

Area of smaller square = 10 cm²

Using the above as a guide, we have the following:

Area of bigger square  = Area of smaller square * Scale factor²

In this case, we have

Scale factor = 1.5

Substitute the known values into the equation

Area of bigger square = 10 * 1.5²

Evaluate

Area of bigger square = 22.5

Hence, the area of the bigger square is 22.5 square cm

Answer:

212.9 days

Step-by-step explanation:

The bacteria culture initial population is 25 represented by Po and the population after t days is represented by P(t).

Using growth formula:

P(t) = Po ( 1 + r)^t where r is rate in percent and t is time in days

r = 1.28%, P(t) = 375, and Po = 25

substituting this values into the equation above yields

375 = 25 (1 + 1.28/100)^t

375÷25 = ( 1 + 0.0128)^t

15 = (1.0128)^t

take logarithm of both sides

log 15 = log (1.0128)^t remember the law log a^b = b log a

applying the same law gives

log 15 = t log 1.0128

divide both side by log 1.0128

log 15 ÷ log 1.0128 = t log 1.0128 ÷ log 1.0128

t = 212.9 days

Answer:

211 days

Step-by-step explanation:

Answer:7

Step-by-step explanation:

Because it’s the place value of 5