The unit rate is the same as the ? Of a equation

The value of A when we rewrite 6^x as A^x/4 is 3/2

An algebraic expression can simply be defined as a mathematical expression that consists of terms, factors, constants, coefficients and variables.

They are also known as expressions made up of arithmetic operations, such as;

From the information given, we have that;

The function is given as;

6^x

Here, the coefficient or rather the base is 6

To determine the value of A when ^^x is given as A^x/4

The value of A would be;

6/4 = 3/2

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The range of the exponential function y based on its equation and the context of the problem is; 0 < y ≤ 45529

The range of a function is the set that contains all possible output values for the function.

In this question, the function is given as: y = 45,529(0.78)^x.

It is an exponential function with initial value 45,529 and rate of change  of 0.78.

Now, it should be noted that exponential functions that are not shifted down, such as this one, are never negative nor zero. Thus, the range also has the restriction y > 0, and is given by:

D. 0 < y ≤ 45529

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Answer:

40 in^3

Step-by-step explanation:

Volume of a box is given by

V = l*w*h

V = 4*2*5

   = 40 in^3

No, the rank of the product of two n by n square matrices A and B, denoted as AB, cannot be less than n-1 if both A and B have ranks of n-1.

According to the Rank-Nullity theorem, for any matrix M, the sum of its rank and nullity is equal to the number of columns in M. In this case, the number of columns in AB is n, so the sum of the rank and nullity of AB must be n.

If rank(A) = rank(B) = n-1, it means that both A and B have nullity 1. The nullity of a matrix is the dimension of its null space, which consists of all vectors that get mapped to the zero vector when multiplied by the matrix. Since both A and B have rank n-1, their null spaces consist only of the zero vector.

Now, considering AB, if the rank of AB were less than n-1, it would mean that the nullity of AB is greater than 1.

However, this would violate the Rank-Nullity theorem since the sum of the rank and nullity of AB must be n, which is the number of columns.

Therefore,  if rank(A) = rank(B) = n-1, the rank of AB cannot be less than n-1.

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Answer:

1.61.6 248248

Step-by-step explanation:

The function is continuous in the domain x ≥ 3/4

Here we have a root function:

f(x) = ⁴√(4x - 3)

This is an even degree root function, so we have problems when the argument is negative.

Then the allowed values (where the function is defined, and thus, continuous) are:

4x - 3 ≥ 0

4x ≥ 3

x ≥ 3/4

There the function is continuous.

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1. Number of athletes did not own any of the three items = 259 - 228

= 31.

2. Number of athletes own a convertible and a TV but not a store = 44 - 9

= 35.

3. Number of athletes own a convertible or a TV = 110 + 91 - 44

= 157.

4. Number of athletes owned exactly one type of item = 60 + 13 + 71 = 144.

5. Number of athletes owned at least one type of item = 259 - 31

= 228

6. Number of athletes own a TV or a store, but not a convertible = 13 + 34 +71

= 118.

The number of athletes did not own any of the three items need to subtract the number of athletes who own at least one item from the total number of athletes surveyed.

Total number of athletes surveyed = 259

Number of athletes own at least one item = 110 + 91 + 120 - 15 - 43 - 44 + 9 = 228

Number of athletes who did not own any of the three items = 259 - 228 = 31.

The number of athletes who owned a convertible and a TV but not a store need to subtract the number of athletes who own all three items from the number of athletes who own a convertible and a TV.

Number of athletes who own a convertible and a TV = 44

Number of athletes who own all three items = 9

Number of athletes who own a convertible and a TV but not a store = 44 - 9 = 35

The number of athletes who owned a convertible, or a TV need to add the number of athletes who own a convertible to the number of athletes who own a TV and then subtract the number of athletes own both a convertible and a TV.

Number of athletes who own a convertible or a TV = 110 + 91 - 44

= 157.

The number of athletes owned exactly one type of item need to add up the number of athletes who own a convertible only the number of athletes own a TV only and the number of athletes who own a store only.

Number of athletes own a convertible only = 110 - 15 - 9 = 86

Number of athletes own a TV only = 91 - 44 - 9 = 38

Number of athletes own a store only = 120 - 15 - 43 - 9 = 53

Number of athletes owned exactly one type of item = 60 + 13 + 71 = 144.

The number of athletes who owned at least one type of item can use the result from part (1).

Number of athletes who owned at least one type of item = 259 - 31

= 228

The number of athletes who owned a TV or a store but not a convertible need to subtract the number of athletes who own all three items, and the number of athletes own a convertible and a TV from the number of athletes own a TV or a store.

Number of athletes own a TV or a store = 91 + 120 - 43 - 9 = 159

Number of athletes own a TV or a store not a convertible = 13 + 34 +71

= 118.

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The slope of a horizontal line is always zero.

What is slope?

The slope of a line is a measure of how steep the line is. It represents the rate at which the y-coordinate of the line changes with respect to the x-coordinate. Symbolically, it is represented by the letter m, and can be calculated using the following formula:

m = (y₂ - y₁) / (x₂ - x₁)

where (x₁, y₁) and (x₂, y₂) are any two points on the line.

The slope of a horizontal line is always zero. This is because a horizontal line has the same y-coordinate at every point, and therefore, there is no change in the y-coordinate for any change in the x-coordinate.

By definition, the slope of a line is the change in y divided by the change in x. In the case of a horizontal line, the change in y is always zero, since the y-coordinate does not change. So, no matter what value of x you choose, the slope of a horizontal line will always be:

slope = change in y / change in x = 0 / (any non-zero value of x) = 0

So, the slope of a horizontal line is always zero.

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How to solve your problem

x^{2}-21=100

Quadratic formula

Factor

1

Move terms to the left side

x^{2}-21=100

x^{2}-21-100=0

2

Subtract the numbers

x^{2}\textcolor{#C58AF9}{-21}\textcolor{#C58AF9}{-100}=0

x^{2}\textcolor{#C58AF9}{-121}=0

3

Use the quadratic formula

x=\frac{-\textcolor{#F28B82}{b}\pm \sqrt{\textcolor{#F28B82}{b}^{2}-4\textcolor{#C58AF9}{a}\textcolor{#8AB4F8}{c}}}{2\textcolor{#C58AF9}{a}}

Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.

x^{2}-121=0

a=\textcolor{#C58AF9}{1}

b=\textcolor{#F28B82}{0}

c=\textcolor{#8AB4F8}{-121}

x=\frac{-\textcolor{#F28B82}{0}\pm \sqrt{\textcolor{#F28B82}{0}^{2}-4\cdot \textcolor{#C58AF9}{1}(\textcolor{#8AB4F8}{-121})}}{2\cdot \textcolor{#C58AF9}{1}}

4

Simplify

Evaluate the exponent

Multiply the numbers

Add the numbers

Evaluate the square root

Add zero

Multiply the numbers

x=\frac{\pm 22}{2}

5

Separate the equations

To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.

x=\frac{22}{2}

x=\frac{-22}{2}

6

Solve

Rearrange and isolate the variable to find each solution

x=11

x=-11

SOLUTION

By Pythagoras theorem,

Evaluate for x

Hence,

Answer: 2/5

Step-by-step explanation:

\(\frac{6-2}{6-(-4)}=\frac{4}{10}=\boxed{\frac{2}{5}}\)

Answer:

1) 7/8     8/7

2) 4.4

3) 3.7

4) 2.8

Step-by-step explanation:

Length of bottom side of Figure A: 8 cm

Length of bottom side of Figure B: 7 cm

From Figure A to Figure B, the scale factor is 7/8.

7/8

8/7

5 × 7/8 = 35/8 = 4.375

4.4

3.2 × 8/7 = 3.657...

3.7

3.2 × 7/8 = 2.8

2.8

Answer:

0.76 = 76% probability that a tourist visited at least one of these places

Step-by-step explanation:

I am going to solve this question using the probabilities as Venn sets.

We have that:

Event A: Tourist visited Beinjing.

Event B: Tourist visited Xi'an.

61 percent of the tourists to China visited the Forbidden City, the Temple of Heaven, the Great Wall, and other historical sites in or near Beijing.

This means that \(P(A) = 0.61\)

33 percent visited Xi'an with its magnificent terracotta soldiers, horses, and chariots, which lay buried for over 2000 years.

This means that \(P(B) = 0.33\)

18 percent of the tourists went to both Beijing and Xi'an.

This means that \(P(A \cap B) = 0.18\)

What is the probability that a tourist visited at least one of these places?

This is

\(P(A \cup B) = P(A) + P(B) - P(A \cap B)\)

We already found these values. So

\(P(A \cup B) = 0.61 + 0.33 - 0.18 = 0.76\)

0.76 = 76% probability that a tourist visited at least one of these places

Answer:

 in a right triangle, the square of the length of the hypotenuse (the side across from the right angle) is equal to the sum of the squares of the other two sides. So if the length of the hypotenuse is c and the lengths of the other two sides are a and b, then c^2 = a^2 + b^2.Apr 24, 2017

It is difficult to make a general statement about whether tennis coaches generally get paid more than football coaches in Jacksonville or elsewhere, as the salaries of coaches are influenced by a Wide range of factors

As an AI language model, I do not have access to up-to-date information about salaries of coaches in Jacksonville. However, in general, the salaries of coaches vary widely depending on a number of factors, such as the type of sport, the level of competition, the location, the success of the team, and the budget of the institution.

In terms of tennis and football, football is generally considered to be a more popular and high-profile sport than tennis in the United States, which could result in higher salaries for football coaches at the collegiate level. Football also typically generates more revenue and has larger budgets for athletic programs, which could also influence the salaries of coaches.

However, there are also factors that could affect the salaries of tennis coaches. For example, if a tennis program has a particularly successful season or has produced successful players, the coach may negotiate a higher salary. Additionally, some colleges may place a greater emphasis on tennis or have larger budgets for tennis programs, which could also impact the salaries of coaches.

Overall, it is difficult to make a general statement about whether tennis coaches generally get paid more than football coaches in Jacksonville or elsewhere, as the salaries of coaches are influenced by a wide range of factors. It is also important to note that salaries can vary widely between individual institutions, even within the same sport, and that negotiations between coaches and their institutions can play a significant role in determining salaries.

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Answer:

x^2 -12x+35

Step-by-step explanation:

(x−5)(x−7)

FOIL

first  x*x = x^2

outer -7x

inner -5x

last -7*-5 = 35

Add them together

x^2 -7x-5x +35

x^2 -12x+35

Answer:

Step-by-step explanation:

x*x=2x

x*-7=-7x

-5*x=-5x

-5*-7=+35

2x-12x+35

A

Option 2 is the correct graph for the function f(x) = \(4[(1/2)^{x}]\) .

Given ,

f(x) = \(4[(1/2)^{x}]\)

Mathematically the graph will of exponential in nature.

So,

Let us assume few values to understand the nature of graph.

Firstly,

Let x= 1

f(x) = \(4[(1/2)^{1}]\)

f(x) = 2

Let x = 2

f(x) = \(4[(1/2)^{2}]\)

f(x) = 1

Let x = 3

f(x) = \(4[(1/2)^{3}]\)

f(x) = 0.5

Thus from these values of f(x) corresponding to the values of x second graph will be correct .

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We are given the following line equation:

We are asked to determine the x and y-intercepts of the line. To do that, we will convert the given equation into the following form:

Written in that form the value of "a" is the x-intercept and the value of "b" is the y-intercept. Therefore, we need to divide the given equation by 20 in order to get a 1 on the right side:

Simplifying we get:

Therefore, the y-intercept is 4 and the x-intercept is 5.

The coordinates of the midpoint of a segment with two endpoints ( 22, 4 ) and ( 15, 7 ) is ( 37/2, 11/2 ).

The center of a line segment is known as the midpoint. It is the centroid of the segment and of the ends, and it is equally distant from both of them. It cuts the section in half.

Consider the two endpoints of the segments as:

A( 22, 4 ) and B( 15, 7 )

Let M( x, y ) be the midpoint of the line segment.

Then AM = MB = ( 1/2 )AB

Therefore, the points will also the halfway from the midpoint.

Therefore,

M( x, y ) = ( 1/2 )A + ( 1/2 )B

M( x, y ) = 1/2( 22, 4 ) + ( 1/2 )( 15, 7 )

M( x, y ) = ( 11, 2 ) + ( 15/2, 7/2 )

M( x, y ) = ( 11 + 15/2, 2 + 7/2 )

M( x, y ) = ( 37/2, 11/2 )

Therefore, the coordinate of the midpoint of the line segment is ( 37/2, 11/2 ).

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Airplane 1 had the fastest rate of descent during its landing.

To compare the rates of descent of the two airplanes, we need to convert both rates to a common unit of measurement. Let's convert both rates to feet per minute (ft/min) to make the comparison easier.

Airplane 1 had a rate of descent of -130 ft/s, which is equivalent to:

-130 ft/s × 60 s/min = -7800 ft/min

Airplane 2 had a rate of descent of -97/8 ft/s, which is equivalent to:

(-97/8) ft/s × 60 s/min = -729.375 ft/min

Comparing these two rates, we can see that Airplane 1 had the faster rate of descent during its landing:

-7800 ft/min (Airplane 1) > -729.375 ft/min (Airplane 2)

Therefore, Airplane 1 had the fastest rate of descent during its landing.

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The function is, A(x)=(-x^2+240x) m^2

Let the length (L) = x m

From the question, we have

perimeter (P)=480 m

The perimeter of the rectangular playground is

P=2(L+W)

480=2(x+W)

240=x+W

W=(240-x)m

The area, A=L*W

=x(240-x)

=-x^2+240x

A(x)=(-x^2+240x) m^2

The function is, A(x)=(-x^2+240x) m^2

Multiplication:

Mathematicians multiply two or more numbers to determine the sum of the parts. It is a fundamental mathematical operation that is frequently used in real-world situations. Multiplication is used when groups of like sizes need to be combined. Multiplication is a mathematical operation that illustrates the fundamental idea of adding the same number repeatedly. The product of two or more numbers is what results from multiplying them, and the factors are the quantities that are multiplied. Multiplying the numbers makes it simpler to repeatedly add the same number.

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Answer:

Hope this will help.

Answer:

I am not sure if you're accustomed to using a z-score and table of probabilities or technology, so I will answer using both!

a) Since you're choosing one person from the population, you will use the mean and standard deviation from the population.  z= (210.9-197.5)/8.6 = 1.56 Using a table of normal probabilities,

P(x>210.9)= 1-P(z<1.56)= 1- 0.9406=0.0594

Using technology: normalcdf(210.9, 1E99, 197.5, 8.6)=0.0596

b) Since you're calculating the population for a sample to occur, you need to get a mean of the sampling distribution and standard deviation of the sampling distribution.

Meanpop=Meansampling dist.=197.5

St. Devsampling dist.= Stdpopulation/√n = 8.6/√15 = 2.22

Using technology, P(X>196.20)= normalcdf( 196.20, 1E99, 197.5, 2.22) = 0.7209

c) You only have to worry about the sample size in a sampling distribution if you either do not know the shape of the distribution of the population or if the distribution of the population is not normally distributed. Since this population is normally distributed (as stated in the given information), then your sample size does not have to be greater than 30.

Step-by-step explanation:

Answer:

Step-by-step explanation:

=mean=sum of data /no of data

=2+3+4/3

=9/3

=3