Which expression is equivalent to (10−2 • 45)−2?

1. ten raised to the fourth power divided by four raised to the tenth power)
2. negative ten raised to the fourth power divided by four raised to the tenth power)
3. four raised to the third power divided by ten raised to the fourth power)
4. negative four raised to the third power divided by ten raised to the fourth power)

Answers

Answer 1

The expression that is equivalent to the given expression (10^−2 • 4^5)^−2 is 10^(4) • 4^(−10)

How to determine the expression that is equivalent to the given expression?

The expression is given as

(10−2 • 45)−2

Rewrite the above expression properly as follows:

(10^−2 • 4^5)^−2

Apply the power rule of indices

So, we have

(10^−2 • 4^5)^−2 = 10^(−2 * −2) • 4^(−2 * 5)

Evaluate the product of powers

So, we have

(10^−2 • 4^5)^−2 = 10^(4) • 4^(−10)

Hence, the expression that is equivalent to the given expression (10^−2 • 4^5)^−2 is 10^(4) • 4^(−10)

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Related Questions

Students were asked how they travel to
school. 37% of the students said they
travel by train.
Of these, 24% live more than seven miles
from their school. What percentage of the
students travel over seven miles to school
by train? Give your answer to 2 d.p.

Answers

the percentage of the students travel over seven miles to school by train is 9 %.

Let the total number of students be represented by variable x

now, 37 % of them travel by train.

So, we get that:

By train = 37 % of x

By train = 37 / 100 (x)

By train = 0.37 x

Now, 24 % of them lives 7 miles away from the school.

So, 7 miles away = 24 % of 0.37 x

= 24 / 100 ( 0.37 x )

= 0.24 ( 0.37 x)

= 0.09 x

In percentage:

= 9 %

Therefore, we get that, the percentage of the students travel over seven miles to school by train is 9 %.

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A company makes pencils. they sell each pencil for $10.
Their revenue is represented by R= 10x
The cost to make the pencils is $3 each with a one time start up cost of $5000.
Their cost is represented by C= 3X+5000

1.Find the profit, P, (P=R-C) when the company sells 1000 pens.
2. Find the number of pens they need to sell to break even ( when R=C)

Answers

We have the profit fomula:

P = R - C

= $10.x - ($3.x + 1000)

= $7.x - 1000

1. If the company sells 1000 pens:

P = $7 . 1000 - $1000

= $6000

2. If they want to break even:

P at least = 0

Assume P = 0

=> $7.x - $1000 = 0

=> x = 1000/7 ≈ 142,86

So if they want to break even, they have to sell at least 143 pens

BF is dilated to created WH. The center of dilation is point A where BF=15, WH=20
What is the scale factor that was used to create WH

Answers

Answer:

The scale factor is 4/3

Step-by-step explanation:

Let x = the scale factor

15x = 20  Divide both sides by 15

x =20/15  Which simplifies to 4/3

The scale factor that was used to create WH will be 4/3.

What is the scale factor?

The scale factor is defined as the proportion of the new image's size to that of the previous image decision-making. Dilation is the process of increasing the size of an object while maintaining its shape. Depending on the scale factor, the object's size can be increased or decreased.

Given that BF is dilated to create WH. The center of dilation is point A where BF=15, WH=20

The scale factor will be calculated as below:-

Let x = the scale factor

15x = 20  

Divide both sides by 15

x =20/15  

Which simplifies to 4/3.

x = 4 / 3

Therefore, the scale factor that was used to create WH will be 4/3.

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Evaluate x/2-5y+1.5z when x = 10, y = 8, and z = 4

Answers

Answer:

-29

Step-by-step explanation:

x/2 - 5y + 1.5z
(10)/2 - 5(8) + 1.5(4)

5 - 40 + 6
-35 + 6
-29

Answer:

=10/2-5×8+1.5×4

=5-40+6.0

=-29

leanna cuts some roses in her front garden and another 20 in her back garden. she uses one quarter of her roses to make a bouquet of a dozen flowers. how many roses did leanna cut in her front yard?

Answers

The roses that Leanna cut in her front yard is 28 roses.

How to calculate the value?

From the information, she uses one quarter of her roses to make a bouquet of a dozen flowers. Therefore, the total flowers will be:

= 12 ÷ 1/4

= 12 × 4

= 48 flowers

Since she cuts some roses in her front garden and another 20 in her back garden, the number that she cut in the front garden will be:

= 48 - 20

= 28 flowers.

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What is the answer to this question?

Answers


Not sure if I'm right, but is
it RL- lol

Please help i really need this done :) I added 50 p[oints

Answers

A) Matching the stages of a business life cycle in the correct order is as follows:

ExistenceSurvivalSuccessTake-off Pivot or persistResource MaturityExit Plan.

B) Matching the business life cycle to its description is as follows:

Life Cycle      Description

Exit Plan            The owner decides to sell.

Success            A business owner gets it running and introduces it

                          to the market in its attempt to catch the competition.

What is the business life cycle?

The business life cycle refers to the gradual progress of a business over its lifetime.

A business life cycle can be divided into five broad stages: launch, growth, shake-out, maturity, and decline.  Some management gurus classify the life cycle of a business into the following stages: Existence, Survival, Success, Take-off, and Resource Maturity.

Thus, a successful business declines after its maturity stage.

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What is the difference between Earth's highest mountain and its deepest ocean canyon? What is the difference between Mars' highest mountain and its deepest canyon? Which difference is greater? How much greater is it?​

Answers

earth's difference= 65,233 ft

mars difference= 101,000 ft

greater one is= mars

difference of= 35,767 ft

A train is going on a journey. First it travels east for 50 kilometers. Then it turns north and travels for 22 kilometers. Next it goes west for 50 kilometers. Finally, it travels south for a certain
number of kilometers. At the end of its journey it is back at its original location. How many kilometers did it travel in the southward direction?

Answers

Answer:

It traveled south for 22 kilometers.

Step-by-step explanation:

Think of it as a rectangle. Two sides are 50 kilometers (east and west), and the other two sides are 22 kilometers (north and south).

1/2 ( 2p + 9 ) = p + 5 solve equation

Answers

that is impossible to solve because both sides do not equal eachother

Find f '(a).
f(x) = [tex]\frac{1}{\sqrt{x} +5}[/tex]

Answers

Answer:

[tex]f'(a)=\frac{1}{2a^{3/2}+20a+50\sqrt{a}}[/tex]

Step-by-step explanation:

[tex]f'(x)=\frac{\frac{d}{dx} (\sqrt{x}+5)(1)-(\sqrt{x}+5)\frac{d}{dx}(1)}{(\sqrt{x}+5)^2} \\ \\ =\frac{\frac{1}{2\sqrt{x}}}{(\sqrt{x}+5)^2} \\ \\ =\frac{\frac{1}{2\sqrt{x}}}{x+10\sqrt{x}+25} \\ \\ =\frac{1}{2x^{3/2}+20x+50\sqrt{x}} \\ \\ \therefore f'(a)=\frac{1}{2a^{3/2}+20a+50\sqrt{a}}[/tex]

Determine whether the graph shows a positive correlation, a negative correlation, or no correlation. If there is a positive or negative correlation, describe its meaning in the situation.

Answers

just give an clearly answers

2 1/2 = 1 2/3 divided by y; what does y equal

Answers

Step-by-step explanation:

21/2=12/3

y=10.5*4

Sana nakatulong:)

The area of a square tin plate is 7056 square inches. Find the length of a side of the plate.

Answers

Side of square tin plate = 84 cm

A salesperson sold a pick-up for $18,760. They were paid a 4.5% commission. How much money were they paid?

Answers

the salesperson will be paid $ 844.2 for the one pickup they sell for $ 18,760 as 4.5 % commission is theirs.

We are given that the selling price of a pick up item is given as:

Selling price = $ 18,760

Now, it is also given that, on every sale, the salesperson gain a commission of 4.5 % as their pay.

The money they get paid for one pick up that they sell will be calculated by finding the percentage. So, we get that:

Money = 4.5 % of $ 18,760

Money = 4.5 / 100 × $ 18,760

Money = 0.045 × $ 18,760

Money =  $ 844.2

Therefore, we get that, the salesperson will be paid $ 844.2 for the one pickup they sell for $ 18,760 as 4.5 % commission is theirs.

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A rectangular garden plot measures 12 feet by 25.6 feet.

Answers

Answer:

Do I calculate the area?

Step-by-step explanation:

Answer **please** ill give brainliest!

Answers

Answer:

w = -0.8

sum = 0

Step-by-step explanation:

An additive inverse is when two numbers add up to 0. 0.8+ (-0.8) = 0.

Jean's bedroom is 12 feet by 10 feet. She has chosen a carpet which costs $30.95 per square yard.
This includes installation.

Answers

Answer: i think its 1238 dollars

Step-by-step explanation:

What time does the shipment arrive in Dallas (GMT -6) , if it departs Edmonton (GMT -7) at 14:45 p.m. on Thursday? United Airlines has a 3 hour 45 minutes flight.

Answers

At 17:30 the shipment arrive in Dallas (GMT -6) , if it departs Edmonton (GMT -7) at 14:45 p.m. on Thursday.

                   

The time difference of two zone is -7-(-6) = -1

The shipment departs at 14:45 pm

flight took time = 3:45 min

adding the time = 14:45 + 3:45

                           = 18:30

So it arrived at Dallas at 18:30 according to Edmonton (GMT -7)

It arrived in Dallas according to Dallas (GMT -6) = 18:30 - 1 hour

                                                                                = 17:30

What is time zone?                    

A time zone is a region where everyone adheres to the same standard time for social, business, and legal activities. Because it is simpler for regions that communicate often to maintain the same time, time zones frequently follow national borders and their subdivisions rather than strictly following longitude.

Coordinated Universal Time (UTC), which ranges from UTC12:00 to UTC+14:00, is used to determine all time zones. Most zones have full hour offsets, but some, like those in India, South Australia, and Nepal, have additional offsets of 30 or 45 minutes.

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whatre the values of x and y

Answers

By using the concept of internal angles of a triangle, the solution of the system of linear equations related to the geometrical system is (x, y) = (40, 40).

What are the values of two variables associated with two angles from a right triangle?

In this system we have a geometrical system formed by two right triangles with a common hypotenuse. Right triangles are triangles where one of its internal angles are right angles and the sum of the measures of the internal angles within a triangle equals 180°. Then, this geometrical system can be modelled by using the following linear equations:

(x + 20) + 90 + 30 = 180         (1)

20 + 90 + (y + 30) = 180         (2)

By using the concept of internal angles of a triangle, the solution of the system of linear equations related to the geometrical system is (x, y) = (40, 40).

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COULD YALL PLEASE HELP ME !!!!!!

Answers

Answer:

Adjacent Angles

Step-by-step explanation:

Angles ∠1 and ∠2 are next to each other so adjacent

Show work of how $7.40 for 5 pounds

Answers

Answer:

the answer is $35.40 sir there you go

Step-by-step explanation:

that's the answer which is located above

Answer:

1.48 each

Step-by-step explanation:

you have to divide 7.40/5

Kitchen
Living
Room
Bathroom
Laundry
Bedroom #2
Bedroom #1
Scale: 2 units = 3 feet

Answers

to much long and I want brainliest

Which mixed number is equivalent to the improper fraction?
41
7
O A. 6-1/
OB. 49/
O C. 59/
OD. 6



PLEASE HELP FAST

Answers

Answer:

C -

[tex]5 \frac{6}{7} [/tex]

Riley is starting a running plan to train for a race. In the first week of her running
plan, Riley will run 15 miles. The plan calls for Riley to increase her weekly milage by
3 miles every week. If Riley sticks to the plan, how many miles would she be expected
to run during her 5th week of the training plan?

Answers

Week 1: 15 miles
Week 2: 18 miles
Week 3: 21 miles
Week 4: 24 miles
Week 5: 27 miles

This table displays the height of a balloon as it floats away. A 2-column table with 6 rows. Column 1 is labeled Time (minutes) with entries 10, 11, 12, 13, 14, 15. Column 2 is labeled Height (feet) with entries 64, 73.5, 83, 92.5, 102, 111.5. What is the rate of change for the height as the time increases by 1 minute? Rate of change = Which table shows a constant rate of change of –3? A 2-column table with 4 rows. Column 1 is labeled x with entries 3, 4, 5, 6. Column 2 is labeled y with entries negative 8, negative 5, negative 2, 1. A 2-column table with 4 rows. Column 1 is labeled x with entries 15, 16, 17, 18. Column 2 is labeled y with entries 12, 9, 7, 4. A 2-column table with 4 rows. Column 1 is labeled x with entries negative 2, negative 1, 0, 1. Column 2 is labeled y with entries negative 9, negative 12, negative 16, negative 20. A 2-column table with 4 rows. Column 1 is labeled x with entries negative 22, negative 21, negative 20, negative 19. Column 2 is labeled y with entries 2, negative 1, negative 4, negative 7.

Answers

Using the average rate of change concept, we have that:

The rate of the height is of 9.5 feet per minute.The table with a rate of -3 is given by: A 2-column table with 4 rows. Column 1 is labeled x with entries negative 22, negative 21, negative 20, negative 19. Column 2 is labeled y with entries 2, negative 1, negative 4, negative 7.

What is the average rate of change of a function?

The average rate of change of a function is given by the change in the output divided by the change in the input. Hence, over an interval [a,b], the rate is given as follows:

[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]

For item 1, when the time in minutes changes by 1, the height changes by 9.5 units, hence the rate is given by:

r = 9.5/1 = 9.5 feet per minute.

For item 2, we want a table with a rate of -3, hence, when the first column changes by 1, the second column should always change by -3, hence the table is:

A 2-column table with 4 rows. Column 1 is labeled x with entries negative 22, negative 21, negative 20, negative 19. Column 2 is labeled y with entries 2, negative 1, negative 4, negative 7.

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How can I solve this?

Answers

Step-by-step explanation:

by using formula a²-b²=a+b

a²b=a²-b² like this

Stop light A changes color every 45 seconds and Stop light B changes color every 80 seconds. Both Stop lights just changed. After how many seconds will the stoplights change color at the same time?

Answers

The stoplights will change color after 720 seconds. at the same time again.

Given: Stoplights A and B alternate between changing colors every 45 and 80 seconds, respectively.

One copy of each of the unique components and the common factor make up the Least Common Multiple (LCM).

The least common multiple of 45 and 80 is the amount of seconds before they change color simultaneously once more.

Since 80 = 5 x 2 x 2 x 2 and 45 = 5 x 3 x 3 respectively

A least common multiple of 45 and 80 is equal to 2x2x2x2x3x3x5 = 720.

Hence, the color of the spotlight will change after 720 seconds. at the same time again.

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The proof shows that ABCD is a rhombus. Which of the following is the
missing reason?
Prove: ABCD is a rhombus
Statements
1. ABCD is a parallelogram and
AD= AB.
AB a DC, AD a BC
2.
3.
AB a CD a AD a BC
4. ABCD is a rhombus.
Reasons
1. Given
PREVIOUS
2. ?
3. Transitive property
4. By definition, if all four sides of a
parallelogram are congruent, then
it is a rhombus.
QED
O A. Consecutive sides of a parallelogram are parallel.
B. Opposite sides of a parallelogram are parallel.
C. Opposite sides of a parallelogram are congruent.
O D. Consecutive sides of a parallelogram are congruent.

Answers

From the two column proof below to prove that ABCD is a rhombus, the missing reason is reason 6; C. Opposite sides of a parallelogram are congruent.

How to carry out a two column proof?

Given: ABCD is a parallelogram.

The two column proof that ABCD is a rhombus is;

Statement 1;  ABCD is a parallelogram. AD = AB and AC bisects ∠BCD and ∠BAD

Reason 1; Given

Statement 2; ∠BCA ≅ ∠DCA

Reason 2; Definition of an angle bisector

Statement 3; AC ≅ AC

Reason 3; Reflexive property of congruence

Statement 4; ΔABC ≅ ΔADC

Reason 4; Angle Side Angle Congruence Postulate

Statement 5; AB ≅ AD, BC ≅ DC

Reason 5; Corresponding parts of congruent triangles are equal.

Statement 6; AB ≅ CD, BC ≅ AD

Reason 6; Opposite sides of the parallelogram are congruent

Statement 7; AB ≅ AD, BC ≅ CD

Reason 7; Transitive Property of Congruence

Statement 8;  ABCD is a rhombus

Reason 8: Definition of rhombus

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on july 1 2022 ivanhoe company pays 17,500 to sheridan company for a one year insurance company both companies have fiscal years ending in dec 31

Answers

Answer:

what is the question?

()()()()()()()()()()()()()()

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