Which expression is equivalent to (15²)(15^-7)?

A 15^-21
B -15^4
C 1/15^4
D 1/15^-4

The simplified form of the given expression is [tex]\frac{27}{4x^{12} y^{8} }[/tex].

The given expression is [tex]\frac{4(3x^{2} y^{4} )^{3} }{(2x^{3} y^{5} )^{4} }[/tex].

Exponentiation is a mathematical operation, written as bⁿ, involving two numbers, the base b and the exponent or power n, and pronounced as "b raised to the power of n".

We need to simplify the given expression.

Now, [tex]\frac{4(3^{3}x^{6} y^{12} )}{2^{4} x^{12}y^{20} }[/tex]

⇒[tex]\frac{108x^{6}y^{12} }{16x^{12} y^{20} }[/tex]

⇒[tex]\frac{27}{4x^{12} y^{8} }[/tex]

Therefore, the simplified form of the given expression is [tex]\frac{27}{4x^{12} y^{8} }[/tex].

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Let h represent hamburgers and c represent cheeseburgers

h + c ≤ 100 - The number of burgers sold

3h + 3.5c ≥ 80 - Amount that each burger sells for

The domain of the linear function is (1.5, ∞) and the range of the linear function will be (40, ∞).

The domain means all the possible values of x and the range means all the possible values of y.

A carpet installer charges a flat rate of $40 and $1.50 per square foot for labor.

So the total cost for the labor depends on the amount of carpet installed, the relationship between the total cost for labor and the amount of corporate installed.

Then the domain of the relation is the range of the relation will be

Let y be the total amount and x be the number of square foot.

y = 1.5x + 40

Then the domain of the linear function is (1.5, ∞) and the range of the linear function will be (40, ∞).

The graph is given below.

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[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: final \:\:value = -x + 6 \degree[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \: (7x - 3x) - (5x - 6)[/tex]

[tex]\qquad \tt \rightarrow \: (4x) - 5x - ( - 6)[/tex]

[tex]\qquad \tt \rightarrow \: 4x - 5x + 6[/tex]

[tex]\qquad \tt \rightarrow \: - x + 6[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:6-x

Step-by-step explanation:

The solution is in the image

Answer:

Domain: all real numbers, or (-oo, oo)

Range: (3, oo).

Step-by-step explanation:

The domain is the set of x-values that work when plugged into a function. Here, all values when plugged in produce a real answer, so the answer is all real numbers, or (-oo, oo).

The range is the result of the domain, or the y-values. Since the x^2 will only produce positive numbers, the lowest y-value we can get is 3, and the highest y-value we can get is infinity. So, the answer is (3, oo).

Brainliest, please :)

Answer:

6 hours for daughter alone     Answer A

Step-by-step explanation:

Rate of mom to clean one house =  1 house /3 hrs  = 1/3

rate of daughter   = 1/x

Now find the time to clean one house with their combined rates for one house

1 /   (1/3 + 1/x )    = 2 hrs

1/3 + 1/x = 1/ 2

x + 3 = 3/2 x

3 = 1/2 x

x = 6 hrs   daughter alone

The number of cars that have passed through the intersection after 7 wrecks is 1/5 cars

w = k × c

31 = k × 1,085

31 = 1,085k

k = 1085/31

k = 35

If w = 7

w = k × c

7 = 35 × c

7 = 35c

c = 7/35

c = 1/5 car

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Answer: [tex]\sum^{7}_{n=1} (-2+9n)[/tex]

Step-by-step explanation:

This is an arithmetic series with first term 7 and common difference 9, so the general formula for the nth term of the sequence is [tex]7+9(n-1)=7+9n-9=-2+9n[/tex].

The sequence has 7 terms, so the sigma notation is:

[tex]\sum^{7}_{n=1} (-2+9n)[/tex]

The number of gallons of Jet fuel that is needed to fly for an hour is; 14400 gallons

We are given;

Number of gallons burned = 4 gallons

Time to burn 4 gallons = 3 seconds

Now, for 1 hour there are 3600 seconds and so;

Number of gallons that is burnt in 3600 seconds = 3600 * 4

Number of gallons that is burnt in 3600 seconds = 14400 gallons

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Answer:

- In 45 days = 4,5mm  ;    In 90 days = 9mm

Step-by-step explanation:

in 45 days = 0,1 * 45 = 4,5 mm  ; in 90 days = 0,1 * 90 = 9mm

Answer:

No

Step-by-step explanation:

We know that the 3-4-5 and 9-12-15 right triangles are similar. If you add 6 units to the length of each side of both of these triangles, you obtain 9-10-11 and 15-18-21 triangles, which are not similar since 9/15 is not equal to 10/18.

The ratio of the median weekly earnings is 3 : 5

From the graph, we have the median weekly earnings to be:

So, the ratio is:

Ratio = $750 : $1250

Simplify

Ratio = 3 : 5

Hence, the ratio of the median weekly earnings is 3 : 5

In (a), we have:

Ratio = 3 : 5

The scale on the horizontal axis is given as:

1 unit per grid mark

Both rectangles have a width of 1 unit.

So, we have:

Ratio = 3 * 1: 5 * 1

Simplify

Ratio = 3 : 5

Hence, the ratio of the area of the red rectangle to the blue rectangle in graph A is 3 : 5

In (a), we have:

Ratio = 3 : 5

The scale on the horizontal axis is given as:

1 unit per grid mark

The red rectangle has a width of 3 units, while the blue has 5 units as its width

So, we have:

Ratio = 3 * 3 : 5 * 5

Simplify

Ratio = 9 : 25

Hence, the ratio of the area of the red rectangle to the blue rectangle in graph B is 9 : 25

In (a), we have:

Ratio = 3 : 5

The scale on the horizontal axis is given as:

1 unit per grid mark

The red rectangle has a width of 3 units, while the blue has 5 units as its width.

Since the base are squares, we have:

Ratio = 3 * 3  * 3 : 5 * 5 * 5

Simplify

Ratio = 27 : 125

Hence, the ratio of the volume of the red cube to the blue cube in graph C is 27 : 125

The most misleading graph is graph B.

This is so because the blue rectangle and the red rectangle do not have the same width when plotted on the same scale

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The vertex of the absolute value function is (-7,-2)

The function is given as:

f(x) = 3|x + 7| - 2

The above function is an absolute value function.

An absolute value function is represented as:

f(x) = a|x - h| + k

Where:

Vertex = (h,k)

By comparison, we have:

(h,k) = (-7,-2)

Hence, the vertex of the absolute value function is (-7,-2)

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Answer:

Parallel lines have the same slope, so the slope would be 1/3. It would need a different y intercept though or it would be the same line.

Answer:

Transcribed image text: Transform each graph as specified below. (a) The graph of y=f(x) is shown. Graph y=2f(x). (b) the graph of y=g(x) is shown. Graph y=g(2x).

The correct statements are:

Function g has a y-intercept of (0,4)

The range of the function g is (3, ∞).

The function g is positive over the interval (-∞ , ∞ ).

The parent function i.e. exponential function is defined by:

y=f(x)=aˣ

From the graph given below,

1. The graph of the function g is 3 units above the graph of the parent exponential function. as the parent exponential function aˣ cuts the y-axis at (0,1) and the child transformed function cut at (0,4) for which g is 4-1=3 units above the parent function  

2. The domain of the function is set of all the inputs for which function is defined. From the graph of function g, it is clear tha the domain of the function is (-∞ , ∞ ) as the domain of the parent exponential function is also (-∞ , ∞ ).

3. The y-intercept is the point at which function cut the y-axis. Graph of function g cut the y-axis at (0, 4). Therefore, Function g has the y-intercept at (0,4).

4. From the graph it is clear that Function g increases over the interval (-∞, 0) .

5. The range of the function is the output values of the function. From the graph, it is observed that the range of function g is (3, ∞). as its minimum value is 3 then the maximum value is ∞.

6. As, the graph of function g is drawn above the x-axis. Therefore, Function g lies completely on +ve y-axis, so function g is positive over the interval (-∞ , ∞ ).

Therefore The correct statements are:

Function g has a y-intercept of (0,4)

The range of the function g is (3, ∞).

The function g is positive over the interval (-∞ , ∞ ).

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Answer: 20

Step-by-step explanation:

A and B have 57+79-42=94 distinct elements in total.

This means that 114-94=20 elements are in neither A nor B.

Answer:

7x+y

7(7)+1

49+1

50

Step-by-step explanation:

please mark me as brainlest

Answer:

7x + y

x=7 y=1

7(7) + 1

49 + 1

= 50

Answer:

[tex]\boxed{\bf x = 23.5}[/tex]

Step-by-step explanation:

Using the law of sines.

[tex] \bf \cfrac{ \sin(A) }{a} = \cfrac{ \sin(B) }{b} [/tex]

[tex]\bf \cfrac{ \sin(42) }{22} = \cfrac{ \sin(x) }{12} [/tex]

[tex]\bf \cfrac{12}{22} \sin(42) = \sin(x) [/tex]

[tex] \bf \sin(x) = 0.4[/tex]

[tex]\bf x = 23.5[/tex]

The correct classification for √18 is an irrational number, non-repeating decimal.

The correct classification of √18 is an irrational number.An irrational number is a number that cannot be expressed as a fraction (ratio) of two integers and cannot be written as a terminating or repeating decimal.

√18 cannot be simplified to a fraction, and when expressed as a decimal, it is a non-repeating decimal that continues indefinitely without a pattern.

Therefore, the correct classification for √18 is an irrational number, non-repeating decimal.The number √18 is the square root of 18. An irrational number is a number that cannot be expressed as a fraction of two integers (a/b) where a and b are integers and b is not equal to zero.

When we calculate the square root of 18, we find that it is approximately 4.24264. However, this decimal representation continues indefinitely without repeating or terminating. It does not settle into a pattern of digits that repeats infinitely like a rational number or terminate after a finite number of decimal places.

Since √18 cannot be expressed as a fraction and its decimal representation is non-repeating and non-terminating, it falls under the category of an irrational number.

Therefore, the correct classification of √18 is an irrational number, specifically a non-repeating decimal.

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27

Solution:

21 + ( -3 ) ( -2 )

21 + 6

27

Therefore, The answer is 27.

Answer:

  (b)  0.5431

Step-by-step explanation:

The proportion of adult tickets sold is the ratio of the total number of adult tickets sold to the total number of tickets sold. Those totals are found on the bottom line of the table.

__

  proportion = (adult tickets)/(total tickets) = 126/232 ≈ 0.5431

Approximately 0.5431 of the tickets sold were adult tickets.

Answer:

B) 0.5431

Step-by-step explanation:

edge 2023

The table with greater proportionality is table 3.

The constant of proportionality is the ratio between two directly proportional quantities.

As, the constant proportionality is

k= y/x

For table 1,

k = 1/1 = 2/2 =1

For table 2,

k = 6/1= 12/2 = 2

For table 3,

k = 5/1 = 10/2 = 5

For table 4,

k = 4/1 = 8/2 = 4

Hence, table 3 is with greater proportionality.

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The distribution of X is X ~ N (20 , 6) and the probability that this American will receive no more than 24 Christmas cards this year is 0.7486.

a. Distribution

X ~ N (20 , 6)

b. P(x ≤24)

= P[(x - μ ) / σ  (24 - 20) / 6]

= P(z  ≤0.67)

=  0.74857

=0.7486

Hence:

Probability = 0.7486

c. P(21 < x < 26)

= P[(21 - 26)/ 6) < (x - μ  ) / σ   < (24 - 20) / 6) ]

= P(-0.83 < z < 0.67)

= P(z < 0.67) - P(z < -0.)

=  0.74857- 0.2033

= 0.54527

Hence:

Probability =0.54527

d. Using standard normal table ,

P(Z < z) = 66%

P(Z < 0.50) = 0.66

z = 0.50

Using z-score formula,

x = z×  σ +  μ

x = 0.50 × 6 + 20 = 23

23 Christmas cards

Therefore the distribution of X is X ~ N (20 , 6) and the probability that this American will receive no more than 24 Christmas cards this year is 0.7486.

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Answer:

42.86%

Step-by-step explanation:

Our percent fraction is 42.857142857143/100, which means that 37 as a percentage is 42.86%

Here we are going to show you step by step how to convert the fraction 3/7 to a percentage.

In the fraction 3/7, 3 is the numerator and 7 is the denominator.

First, we are going to divide the numerator by the denominator. Therefore, we are going to divide 3 by 7.

A percentage shows a number as a proportion of one hundred.

Now we are going to multiply 0.72 by 100 to get the percentage.

Therefore, the answer to 3/7 percent is

Note: If necessary, we round to the nearest hundred.

[tex]\red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}[/tex]

Hey there!

10/4

≈ 10 ÷ 2 / 4 ÷ 2

≈ 5/2

≈ 2 1/2

Therefore, your answer should be:

2 1/2

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

The expression of base area of box will be 4x + x²

The area of a a rectangle occupies is the space it takes up inside the limitations of its four sides. The dimensions of a rectangle determine its area. Basically, the area formula is the product of the rectangle's length and width.

Given,

Length = 4+x

width = x

height = x²+1

We have to find the expression of base area of box

Given the length, width, and height

The formula for area of rectangle is as follow:

Area of rectangle = length x width

Area of rectangle = (4+x) x (x)

Area of rectangle = 4x + x²

Hence the expression of base area of box will be 4x + x²

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Answer:

I believe its A. 37

Step-by-step explanation:

That seems to be the measure of B