write 1/10^2 using exponents

Answer:

The height of the building is [tex]1\frac{1}{4}\ feet.[/tex]

Step-by-step explanation:

Given:

Scale drawing is 1/4 inch: 1 foot.

The height of the building in drawing is 5 inches.

Now, to find the actual height of the building.

Let the actual height be [tex]x.[/tex]

The height of the building in drawing = [tex]5\ inches.[/tex]

The ratio of the scale drawing is [tex]\frac{1}{4}\ inch:1\ foot.[/tex]

So, [tex]\frac{1}{4}\ inch[/tex] is equivalent is 1 foot.

Thus, 5 inches is equivalent to [tex]x.[/tex]

Now, to get the actual height of the building by using cross multiplication method:

[tex]\frac{\frac{1}{4}}{1} =\frac{5}{x}[/tex]

[tex]\frac{4}{1} =\frac{5}{x}[/tex]

By cross multiplying we get:

[tex]4x=5[/tex]

Dividing both sides by 4 we get:

[tex]x=\frac{5}{4}[/tex]

[tex]x=1\frac{1}{4}[/tex]

Therefore, the height of the building is [tex]1\frac{1}{4}\ feet.[/tex]

Percent increase without baggage = 46%

Percent increase with baggage = 66%

Step-by-step explanation:

Cost of ticket two weeks ago= Old value = $250

Increased cost = New value = $365

Change = New value - Old value

Change = 365 - 250 = $115

Percent increase = [tex]\frac{Change}{Old\ value}*100[/tex]

Percent increase = [tex]\frac{115}{250}*100[/tex]

Percent increase = [tex]\frac{11500}{250}=46\%[/tex]

There is 46% increase in the price.

Change after additional baggage = 115+50 = $165

Percent increase = [tex]\frac{165}{250}*100[/tex]

Percent increase = [tex]\frac{16500}{250}=66\%[/tex]

Percent increase without baggage = 46%

Percent increase with baggage = 66%

Keywords: percentage, division

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The percent increase in the cost of airline tickets from Orlando to Denver is 46%. If an additional $50 baggage fee is charged, the percent increase is 66%.

To calculate the percent increase, we can use the formula: Percent Increase = ((New Value - Old Value) / Old Value) x 100. In this case, the old value is $250 and the new value is $365. Therefore, the percent increase is ((365 - 250) / 250) x 100 = 46%.

If the airline charges an additional $50 baggage fee, the new ticket price would be $365 + $50 = $415. To calculate the percent increase from the original price, we can use the same formula. The old value is still $250 and the new value is $415. Therefore, the percent increase with the added baggage fee is ((415 - 250) / 250) x 100 = 66%.

Answer:

They are not equivalent

Step-by-step explanation:

We want to determine if 1/2(4 - 2x); 2 - 2x are equivalent.

Let us take the first expression and simplify to see if we can get the second expression.

[tex] \frac{1}{2}(4 - 2x)[/tex]

Let us expand using the distributive property to get:

[tex] \frac{1}{2} (4 - 2x) = \frac{1}{2} \times 4 - \frac{1}{2} \times 2x[/tex]

This simplifies to:

[tex]\frac{1}{2} (4 - 2x) = 2 - x[/tex]

Therefore 1/2(4 - 2x); and 2 - 2x are not equivalent

Answer:

Therefore,

[tex](-2)^{3}=-8[/tex]

Step-by-step explanation:

Simplify

-2^3

[tex](-2)^{3}[/tex]

It is read as negative 2 raised to the power three,

also it is the cube of negative 2

we know that [tex]a^{3}[/tex]given as

[tex]a^{3}=a\times a\times a[/tex]

so for negative a i.e -a

[tex](-a)^{3}=-a\times -a\times -a[/tex]

substituting a = 2 we get

[tex](-2)^{3}=-2\times -2\times -2[/tex]

negative sign multiplied by odd number of times then the sign remains negative.

Therefore,

[tex](-2)^{3}=-8[/tex]

Jason bought 38 stamps and 17 postcards

Solution:

Let "a" be the number of stamps bought

Let "b" be the number of postcards bought

The number of stamps was 4 more than twice the number of post cards

Therefore,

Number of stamps bought = 4 + 2(number of post cards)

a = 4 + 2b ------- eqn 1

Jason bought both 41 cent stamps and 26 cent postcards and spent $20.28

1 dollar is equal to 100 cents

Thus, $ 20.28 is equal to 2028 cents

Therefore, we frame a equation as:

[tex]41 \times a + 26 \times b = 2028[/tex]

41a + 26b = 2028 ----------- eqn 2

Let us solve eqn 1 and eqn 2

Substitute eqn 1 in eqn 1

41(4 + 2b) + 26b = 2028

164 + 82b + 26b = 2028

164 + 108b = 2028

108b = 1864

[tex]b = 17.25 \approx 17[/tex]

Substitute b = 17 in eqn 1

a = 4 + 2(17)

a = 4 + 34

a = 38

Thus Jason bought 38 stamps and 17 postcards

Answer:the answer is 2 between 5

Step-by-step explanation:

Answer:

x=-5, y=-1. (-5, -1).

Step-by-step explanation:

6x-6y=-24

y=3x+14

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

6x-6(3x+14)=-24

6x-18x-84=-24

-12x-84=-24

-12x=-24+84

-12x=60

x=60/-12

x=-5

y=3(-5)+14=-15+14=-1

Answer:

12 months

Step-by-step explanation:

A company employs 72 workers. It plans to increase the number of employees by 6 per month.

Let x = number of months when the company increases the number of workers. Then in x months, the number of workers increases by 6x and the total number of workers will be (72+6x).

They plan to increase the number of workers until it has twice its current workforce. So

[tex]72+6x=2\cdot 72[/tex]

Solve this equation:

[tex]72+6x=144\\ \\6x=144-72\\ \\6x=72\\ \\x=12[/tex]

Answer:

ITS RUTH

Step-by-step explanation:

To know who earned the most commission, one must multiply the number of items sold by each salesperson by their respective commission rates. The one with the highest total is the salesperson who earned the most commission.

To determine who earned the most commission, you first need to have concrete data. This should include the number of items each salesperson sold and the commission rate or amount associated with each item.

Multiply the number of items each person sold by the respective commission to get the total commission earned by each salesperson.

The salesperson with the highest total commission is the one who earned the most. For instance, if salesperson A sold 50 items with a commission of $2 per item, their total commission would be 50*2 = $100.

If salesperson B sold 30 items at $5 per item, their total would be 150.

Hence, in this situation salesperson B earned more commission even though they sold fewer items.

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Carlos made the mistake that he did not combine like terms (3 x and 2 x) properly and did not use addition property of equality.

Step-by-step explanation:

Carlos did the work as 3 x + 2 x - 6 = 24

We need to find his mistake that he made in above given.

Here, he did not add the like terms (3 x and 2 x)

             3 x + 2 x = 5 x

Therefore, his work should be

             5 x  - 6 = 24

Also, he did not use addition property of equality. It means the equation remains same even though the same number gets added on both sides. It would be

                          5 x  - 6 = 24

                                 + 6 = + 6

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

                           5 x = 30

Dividing 30 by 5, we get answer as '6'. Hence,

                            [tex]x=\frac{30}{5}[/tex] = 6

So, stated the above two are the mistakes found in carlos work.

Answer:

Basically, because when you want to find the difference between 2.4 and 1.7 using models, you take away the same amount of squares as if you were finding the difference between 240 and 170 using models.

Answer:

Option C. (0,-5)

Step-by-step explanation:

See the attached figure.

As shown the shaded area represents the solution of the given inequality:

y < 6x - 4

The given options are the points:

A. (0,3) B.(0,11) C. (0,-5) D.(0,4)

Comparing the given points to the graph.

So, the point that will lie at the shaded area represent  solution to the linear inequality.

So, point (0,-5) is a solution to the linear inequality.

The answer is option C. (0,-5)

Note: the line y = 6x-4 is graphed using the table on the graph.

Answer:

see explanation

Step-by-step explanation:

Given

2x³ - x² + 18x - 9 = 0 ( factor the first/second and third/fourth terms )

x²(2x - 1) + 9(2x - 1) = 0 ← factor out (2x - 1) from each term

(2x - 1)(x² + 9) = 0

Equate each factor to zero and solve for x

2x - 1 = 0 ⇒ 2x = 1 ⇒ x = [tex]\frac{1}{2}[/tex]

x² + 9 = 0 ⇒ x² = - 9 ⇒ x = ± 3i

The equation has 1 real solution and 2 complex solutions

x = [tex]\frac{1}{2}[/tex] ← real solution

x = ± 3i ← complex solutions

Hey there!

3^3 + 7 ( 2(4)

3^3 = 3 × 3 × 3 = 9 × 3 = 27

27 + 7 (2(4) - 6)

2 × 4 = 8

27 + 7 × 8 - 6

8 - 6 = 2

27 + 7 × 2

7 × 2 = 14

27 + 14 = 41

Answer: 41

Good luck on your assignment and enjoy your day!

~LoveYourselfFirst:)

Answer: 2x= 8, so this would mean it would be:

3^3+7x2

3+7x2

10x2

20

Step-by-step explanation: answer is 20, i think.

The correct answer is E. Both functions are linear, only crossing the x-axis once and the y-axis once.

We can see from the graph that both Function A and Function B are straight lines. This means they are linear functions.

Linear functions also have only one x-intercept and one y-intercept. The x-intercept is the point where the line crosses the x-axis, and the y-intercept is the point where the line crosses the y-axis.

The y-intercept for both Function A and Function B is at (0,0). The x-intercept for Function A is at (-2,0) and the x-intercept for Function B is at (1,0).

Therefore, both statements in choice E are true.

The other statements in the question are not true.

Choice A, Both functions have negative rates of change, is not true. Function A has a negative rate of change, but Function B has a positive rate of change.

Choice B, Both functions have the same rate of change, is not true, as discussed above.

Choice C, When graphed, Function A and Function B are parallel, is not true. Parallel lines would never intersect, but the two functions intersect at the origin.

Choice D, Function A has a greater rate of change than Function B, is not true. The slope of Function B is steeper than the slope of Function A, so Function B has a greater rate of change.

Answer:

-13/2

Step-by-step explanation:

slope is calculated as (y2-y1)/(x2-x1)

(x1, x2) is (1,6) and (y1,y2) is (3,-7)

doing (y2-y1)/(x2-x1) gives us ((-7)-6)/(3-1)

= -13/2

The slope between the points (1,6) and (3,-7) is calculated as -6.5 using the slope formula.

The slope between two points (1,6) and (3,-7) can be calculated using the slope formula: m = (y2 - y1) / (x2 - x1),

where (x1, y1) and (x2, y2) are the coordinates of the points.

In this case, substituting the values in, we get:

m = (-7 - 6) / (3 - 1) = -13 / 2 = -6.5.

Thus, the slope between the points (1,6) and (3,-7) is -6.5.

Answer:

The probabiliy of selecting a person who prefeers rap if the person is female an be calculated as the proportion of women who prefeer rap music: 23.6%.

Step-by-step explanation:

Answer:

2y-5

Step-by-step explanation:

friend: y

Brother: y-5

y+y-5

aka

2y-5

Answer:

1

Step-by-step explanation:

This is because 13 is a primary number

Final answer:

The number 1 is a factor of 13, which is a prime number with only two factors: 1 and 13 itself.

Explanation:

One number that is a factor of 13 is 1. This is because the factors of a number are integers that can be multiplied together to produce the original number. Since 13 is a prime number, its only factors are 1 and itself, 13. Factors are integers that multiply together to result in the original number. In the case of 13, the only combinations that yield 13 are 1 × 13 and 13 × 1. Since prime numbers have no other divisors besides 1 and the number itself, there are no additional factors for 13. This characteristic distinguishes prime numbers from composite numbers, emphasizing their unique role in number theory and their indivisibility by integers other than 1 and the number itself.

Answer:

the answer is the second one

Answer:

B&C are the answers.

50.27 in²

Step-by-step explanation:

The area is given as;

A= 16π in²

The symbol π is the pie

The value of π=3.14159265359

Finding the area in terms of pi could mean replacing π with the actual value as;

A=16×3.14159265359 = 50.27 in² (answer in 2 decimal places)

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Answer:

4.64

Step-by-step explanation:

To simplify mixed numbers you can write them either as a fraction or as a decimal number.

Fraction:

first we need to express both parts of mixed number through the same denominator - 1 has 25/25, so that means 4 has 100/25.

Now we can write that as 100/25 and 16/25, which is (100+16)/25 = 116/25

Decimal number:

This time, we convert this fraction part of a number to decimal. Simply dividing, we get that 16/25 equals 0.64. So 4 and 0.64 is 4.64.

Step-by-step explanation:

[tex]f(x)=\dfrac{x^2-4x+2}{x+7}\\\\f(-1)=\text{put}\ x=-1\ \text{to}\ f(x):\\\\f(-1)=\dfrac{(-1)^2-4(-1)+2}{-1+7}=\dfrac{1+4+2}{6}=\dfrac{7}{6}[/tex]

Answer:

C, 48

Step-by-step explanation:

all you have to do is divide 60 by 5 to get 12.

Then you have to times 12 with the 4 to get 48 which is C.

Answer:

need options?

Step-by-step explanation:

Answer:

Step-by-step explanation:

$7 - 4x = $15

-4x = $15 - $7

-4x = $8

x = $8/-4

x = $-2

So,

$8x + $2

= $8(-2) + $2

= $-16 + $2

= $ -14