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Solve using the properties of logarithms:
5^㏒(base x) 7 = 7

(See picture for a written version of the equation.)

Answer:

Step-by-step explanation:

This problem is essentially one of finding the matching mean. The given means are ...

1. It should be no trouble to determine that the largest mean belongs to Cathy.

__

2. The mean is the average of the given 2SD limits, so is ...

  (67,785.08 +83,141.16)/2 = 75,463.12 . . . . matches Amanda

Please note that you only need to work with about 3 significant figures:

  (67.8 +83.1)/2 = 75.45 . . . . close enough to let you select Amanda

__

3. The mean is the average of the given 1SD limits, so is ...

  (70.1 +78.2)/2 = 74.15 . . . . matches Benjamin

Answer:

68% of their data lie  between $70,062.37 and $78,187.37

(1 SD from the mean) Benjamin

had the highest average monthly  commission during the past year Cathy

95% of their data lie between $67,785.08 and $83,141.16

(2 SD from the mean) Amanda

Step-by-step explanation:

1. For the system of linear equations to have an infinite number of solutions, the two lines must cross over an infinite number of times, ie. they would be the same line.

Now, if they are the same line and we were to write out both equations in the form y = mx + c, this would mean that the m value (the gradient) and the c value (the y-intercept) would be the same. Thus, the first step is to write out both equations in the form y = mx + c.

a) Equation 1:

3x - 9y = -6

3x = -6 + 9y (Add 9y to both sides)

3x + 6 = 9y (Add 6 to both sides)

(1/3)x + 2/3 = y (Divide both sides by 9)

Thus, the first equation may be written as y = (1/3)x + 2/3

b) Equation 2:

(1/2)x - (3/2)y = c

(1/2)x = c + (3/2)y (Add (3/2)y to both sides)

(1/2)x - c = (3/2)y (Subtract c from both sides)

(1/3)x - (2/3)c = y (Multiply both sides by 2/3)

Thus, the second equation may be written as y = (1/3)x - (2/3)c.

2. Now that we have both equations in the form y = mx + c, we can look at their gradients and y-intercepts:

Equation 1: gradient = 1/3, y-intercept = 2/3

Equation 2: gradient = 1/3, y-intercept = -(2/3)c

As we can see above, the gradients of the two lines are the same, however for them to be the same line their y-intercepts must also be equal. Thus, we must equate the two y-intercepts to find c:

2/3 = -(2/3)c

1 = -c (Multiply both sides by 3/2)

-1 = c (Multiply both sides by -1)

Thus, if the system of linear equations has infinitely many solutions, and c is a constant, the value of c is -1 (answer D).

The value of 'c' for the given system of the linear equations with infinitely many solutions is - 1.

"A linear equation is an equation in which the highest power of the variable is always 1."

Given system of linear equations are

1. [tex]3x - 9y=-6[/tex]

⇒ [tex]x - 3y = - 2[/tex]

Therefore, [tex]a_{1} = 1, b_{1} = -3, c_{1} = -2[/tex]

2. [tex]\frac{x}{2}-\frac{3y}{2} =c[/tex]

⇒ [tex]x - 3y = 2c[/tex]

Therefore,    [tex]a_{2} = 1, b_{2} = -3, c_{2} = 2c[/tex]

For the system of the linear equations with infinitely many solutions,

[tex]2c = -2[/tex]

⇒ [tex]c = -1[/tex]

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Answer:

-6/5

Step-by-step explanation:

Slope = (y2 - y1)/(x2 - x1)

Plug in

Slope = (4 + 2)/(-2 - 3)

Slope = -6/5

Answer:

m = -6 / 5

Step-by-step explanation:

If you are given 2 points (x1, y1) and (x2,y2)

the slope is simply

m = (y2-y1) / (x2-x1)

m = (-2 - 4) / [3 - (-2)]

m = -6 / 5

For this case we must find the zeros of the following function:

[tex]f (x) = (x-7) (x-3) (x-2)[/tex]

If we equate each term to 0 and we clear the variable "x", we will find the values that make the function equal to zero. So:

Thus, the zeros of the function are:

7,3,2

Answer:

Option C

The zeros of the function f(x) = (x - 7)(x - 3)(x - 2) are 7, 3, 2. The correct option is the third option 7, 3, 2

From the question,

We are to determine the zeros of the given function

The given function is

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

To determine the zeros of this function, we will set f(x) = 0

That is ,

f(x) = (x - 7)(x - 3)(x - 2)  becomes

0 = (x - 7)(x - 3)(x - 2)

∴ (x - 7)(x - 3)(x - 2) = 0

Then,

We can write that

x -7 = 0 OR x - 3 = 0 OR x - 2 = 0

∴ x = 7    OR    x = 3    OR   x = 2

Hence, the zeros of the function f(x) = (x - 7)(x - 3)(x - 2) are 7, 3, 2. The correct option is the third option 7, 3, 2

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Answer:

  not really

Step-by-step explanation:

The number of friends (x) is expected to be an integer. 6.5 friends does not really make sense.

_____

There are all kinds of ways this might make sense, but none of them are supported by the information given in the problem statement.

No, the solution (6.5,$ 95.25) do not make a sense.

Since, the number of people going for a movie can't be in decimals.

The function h(x) represents the amount of money spent where x is the number of friends at the movies.

The domain of such a function has to be whole numbers.

Because the number of people that go for a movie must exist as a whole they can't exist in decimals.

( i.e. either no one will go.

1 will go.

2 friends will go and so  on)

i.e. the domain is the set of all non-negative integers.

Answer:

-77 assuming you meant to write -2x^2+5x-8 instead of -2x^2+5-8

Step-by-step explanation:

You could multiply it out and see...

(-2x^2+5x-8)(4x-9)

(-2x^2)(4x-9)+(5x)(4x-9)+(-8)(4x-9)

-8x^3+18x^2+20x^2-45x-32x+72

-8x^3+38x^2-77x+72

Coefficient of x^3 is -8

Coefficient of x^2 is 38

Coefficient of x is -77

Constant term is 72

Answer:

D. The function is odd because it is symmetric with respect to the origin.

Step-by-step explanation:

We have been given a graph of a function. We are asked to determine whether our given function is odd or even.

We know that a function is even, when it is symmetric with respect to the y-axis.

We also know that a function is odd, when it is symmetric with respect to the origin.

Upon looking at our given graph, we can see that it is symmetric about the origin, therefore, option D is the correct choice.

The function is odd because it is symmetric with respect to the origin.

(Option D)

We will determine whether the function is shown in the graph is even or odd.

Let us recall how to distinguish whether the function graph is included in an even or odd function.

Even Functions

Odd Functions

Generally, the functions that we face are neither even nor odd.

ANSWER

[tex]S.A = 125 {in}^{2} [/tex]

EXPLANATION

The total surface area of a square pyramid is the area of the 4 triangular faces plus the area of the square base.

This is given by the formula!

[tex]S.A = 4 \times \frac{1}{2} bh + {l}^{2} [/tex]

From the diagram, the base is 5 inches and the height is 10 inches.

We substitute the values to get:

[tex]S.A = 4 \times \frac{1}{2} \times 5 \times 10 + {5}^{2} [/tex]

This simplifies to;

[tex]S.A = 100 + 25[/tex]

[tex]S.A = 125 {in}^{2} [/tex]

Answer:

303.66 in²

Step-by-step explanation:

The area (A) of a trapezoid is

A = [tex]\frac{1}{2}[/tex] h (a + b)

where h is the perpendicular height and a, b the parallel bases

here h = 12.6, a = 19 and b = 29.2, so

A = 0.5 × 12.6 × (19 + 29.2)

  = 0.5 × 12.6 × 48.2 = 303.66 in²

Answer: THIRD OPTION.

Step-by-step explanation:

The area of a trapezoid can be calculated with this formula:

[tex]A=\frac{h}{2}(B+b)[/tex]

Where "h" is the height, "B" is the long base and "b" is the short base.

You can identify that:

[tex]h=12.6in\\B=29.2in\\b=19in[/tex]

Therefore, you need to substitute these values into the formula  [tex]A=\frac{h}{2}(B+b)[/tex] to calculate the area of that trapezoid. This is:

 [tex]A=\frac{12.6in}{2}(29.2in+19in)\\\\A=303.66in^2[/tex]

This matches with the third option.

Answer:

Hi

Step-by-step explanation:

Please make sure you have posted all the information. i will be glad to help however it doesnt seem that all the instructions aare there

Answer:

She has $10 left.

Step-by-step explanation:

There are 13 tags. Every tag is 5$.

13 tags times 5 dollars equals 65 dollars spent.

75 dollars minus 65 dollars spent = 10 dollars left.

Ruby has 10 dollars left.

Ruby is left with 10 dollars. .

Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter. Each object in a graph is called a node.

Ruby had a budget of up to $75 dollar to spend.

Total tags=13

Each tag is $5.

So,

Ruby spent on 13 tags

= 13*5

= $65

Thus, Ruby left with

=75 - 65 dollars

= 10 dollars.

Hence, Ruby has 10 dollars left.

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Answer:

13.75

Step-by-step explanation:

3b + d = 8.75

2b + 2d = 7.50

(3b + d = 8.75) times 2

(2b + 2d = 7.50) times -3

6b + 2d = 17.5

-6b + (-6d) = -22.5

the b's cancel out, 2d - 6d = -4d and 17.5 - 22.5 = -5

-4d = -5 Divide it and d = 1.25

then plug in 1.25 for d.

2b + 2(1.25) = 7.50

2b + 2.5 = 7.50

2b = 5

b= 2.5

3(2.5) + 1.25 = 8.75 ? Yes.

2(2.5) + 2(1.25) = 7.50 ? Yes.

4(2.5) + 3(1.25) = 13.75.

Answer:

The correct option is:

a) seasons; "This is the

A semicolon is most commonly used to link (in a single sentence) two independent clauses that are closely related in thought.When a semicolon is used to join two or more ideas (parts) in a sentence, those ideas are then given equal position or rank.

Step-by-step explanation:

Answer:

A.  seasons: "This is the

Step-by-step explanation:

Answer:

64 people/m^2

Step-by-step explanation:

The population density can be found by diving the number of people by the amount of area

I assume that the answer should be in metre squares or the area should be 1.95 million km^2

124000000/(1.95*1000000)

=63.5897...

=64 people/m^2

Answer:

64M people/km^2

Step-by-step explanation:

To calculate the density of population you just have to divide the population by the area of the country or region that you are calculation, in this case it wouldbe like this:

Density of population= [tex]\frac{124 M}{1.95 km^{2}  }[/tex]

D= [tex]\frac{124 M}{1.95 km^{2}  }[/tex]= 63,58 M[tex]\frac{M}{km^{2} }[/tex]

So rounded to the neares whoel number would be 64 M people per squared kilometer.

Answer:$2,000

Step-by-step explanation:

Answer:

(x-y)(y-x)

Step-by-step explanation:

because x-y=y-x

Answer:

  A.  y + 1 = -2(x – 5)

Step-by-step explanation:

For a line with slope m through point (h, k), the equation is ...

  y -k = m(x -h)

Fill in your values of m=-2, h=5, k=-1 and you have ...

  y -(-1) = -2(x -5)

  y +1 = -2(x -5) . . . . . . simplify. Matches selection A.

Answer:

1.25(w)-12.50=C

Answer:

  x + y = -2

Step-by-step explanation:

When you are given the equation of a line in standard form (or close to it, as here), you can make the equation for a perpendicular line through a given point by ...

Here, if we make the left side of the equation be ...

  x + y =

we have done the first part of the above recipe. For the second part, we put the point values in for the variables:

  x + y = (-1) + (-1) = -2

The equation of the perpendicular line is ...

  x + y = -2

The answer is:

The range of the function is:

Range: y>2

or

Range: (2,∞+)

To calculate the range of the following function (exponential function) we need to perform the following steps:

First: Find the value of "x"

So, finding "x" we have:

[tex]y=2(5^{x}-1)\\\frac{y}{2}=5^{x}-1\\\\\frac{y}{2}-1=5^{x}\\\\Log_{5}(\frac{y}{2}-1)=Log_5(5^{x})\\\\x=Log_{5}(\frac{y}{2}-1)[/tex]

Second: Interpret the restriction of the function:

Since we are working with logarithms, we know that the only restriction that we found is that the logarithmic functions exist only from 0 to the possitive infinite without considering the number 1.

So, we can see that if the variable "x" is a real number, "y" must be greater than 2 because if it's equal to 2 the expression inside the logarithm will tend to 0, and since the logarithm of 0 does not exist in the real numbers, the variable "x" would not be equal to a real number.

Hence, the range of the function is:

Range: y>2

or

Range: (2,∞+)

Note: I have attached a picture (the graph of the function) for better understanding.

Have a nice day!

Answer: x=243

Step-by-step explanation:

The answer is B.

I tried putting 9 for a and 7 for B. cos(9-7)+cos(9+7) = 2cos(9)cos(7)

[tex]\bf \textit{Product to Sum Identities} \\\\ cos(\alpha)cos(\beta)=\cfrac{1}{2}\left[\cfrac{}{}cos(\alpha-\beta)\quad +\quad cos(\alpha+\beta)\right] \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ cos(a)cos(B)=\cfrac{1}{2}\left[\cfrac{}{}cos(a-B)+cos(a-B) \right] \\\\\\ 2cos(a)cos(B)=cos(a-B)+cos(a-B)[/tex]

Answer:

Step-by-step explanation:

The distributive property lets you multiply each term inside parentheses by a factor outside parentheses. Here, we've gone from 4(x -1) to 4x -4.

The commutative property lets you change the order of elements of a sum or product. Here, we've gone from 3 + ( ) to ( ) + 3.

The associative property lets you move the parentheses from one group of elements of a sum or product to a different group of elements of the same sum or product. Here, we moved the parentheses from the first two terms to the last two terms of the sum.

_____

Comment on these properties in relation to the Order of Operations

The order of operations for evaluating an expression virtually ignores all of these properties, with the possible exception of the distributive property.

For evaluation of numerical expressions, any sum inside parentheses is evaluated to a single number before the multiplication implied by the parentheses is done. Hence the distributive property is not needed. (The distributive property must be used to remove parentheses when literal or mixed expressions are being evaluated.)

Likewise, the associative and commutative properties are ignored, because operations of addition or multiplication are always carried out left-to-right according to the order of operations. In actual practice, the associative and commutative properties can be used to simplify the evaluation of expressions, provided they are used properly and the meaning of the expression is not altered.

Answer: B. 548

Step-by-step explanation:

You know that the exponential regression equation [tex]y = 14.08* 2.08^x[/tex] models the number of fish in a lake.

You know that the variable "x" represents the year. Therefore, ir order to predict the number of fish in year 5, you need to substitute [tex]x=5[/tex] into the given exponential regression equation.

Then, you get:

[tex]y = 14.08* 2.08^x\\\\y = 14.08* 2.08^5\\\\y=548.17[/tex]

Rounded to the nearest whole number:

[tex]y=548[/tex]

Answer:

The correct answer option is C. 548.

Step-by-step explanation:

We are given that the number of fish in a lake can be modeled by the following exponential regression equation:

[tex] y = 1 4 . 0 8 \times 2 . 0 8 ^ x [/tex]

where [tex]x[/tex] represents the number of year.

We are to determine whether which of the given answer options best predict the number of fish in year 5.

[tex] y = 1 4 . 0 8 \times 2.08^5[/tex]

[tex]y = 548.17[/tex] ≈ 548

Answer:

The correct answer is option B.  65

Step-by-step explanation:

To find the measure of <VYX

Central angle of arc VW = 44°

Therefore m<VXY = 44/2 = 22°

And central angle of arc XZ = 86° therefore <XVY = 86/2 = 43

To find the mesure of <XYZ

m<XYZ = m<VXY + m<XVY

  = 22 + 43

 = 65°

Therefore the correct answer is option B. 65°

Answer:

  B.  that one thing is equal to another.

Step-by-step explanation:

An equation has a "left side", an "equal sign", and a "right side." It shows the left side is equal to the right side (one thing is equal to another).

___

An equation may or may not involve variables and unknown quantities.

Answer:

HL

Step-by-step explanation:

HL (Hypotension-Leg) postulate of congruence : In two right triangles if the hypotenuses are equal and any two corresponding legs are equal in both triangles then the triangles are congruent.

In the given right triangles MAE and TON,

AM = OT,

EM = NT,

Thus, by the HL postulate,

Δ MAE ≅ Δ TON

First option is correct.

Answer:

Total = 14,000 * 1 + (.06 / 365) ^365*5

Total = 14,000 * 1.0.000164383561643836^1,825

Total = 14,000 * 1.3498255274

Total = 18,897.56

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Write each parabola in standard form.

f(x) = x²

f(x) = (x − 0)² + 0

For p(x), complete the square.

p(x) = -50 + 14x − x²

p(x) = -(x² − 14x + 50)

p(x) = -(x² − 14x + 49 + 1)

p(x) = -(x² − 14x + 49) − 1

p(x) = -(x − 7)² − 1

The transformation from f(x) to p(x) includes a reflection about the x-axis, a shift right 7 units, and a shift down 1 unit.

The answer is A.

Answer:

No, he did not score 3,

Because, 2 times of 5 is 10 and the sum of 10 and 5 is 15.

Step-by-step explanation:

Let x be the score of Skylar,

Since, Wyatt scored 2 times as many goals as Skylar.

So, Wyatt's score = 2x

Thus, total scores = x + 2x = 3x

According to the question,

3x = 15

x = 5

Hence, Skyler have scored 5 goals.

Because, 2 times of 5 is 10 and the sum of 10 and 5 is 15.

Final answer:

Skylar could have scored 3 goals because, based on the information provided, they scored 5 goals after solving the equation that evaluates the total goals scored by both Skylar and Wyatt.

Explanation:

To determine if Skylar could have scored 3 goals, given that Wyatt scored 2 times as many goals as Skylar and together they scored 15 goals, we can set up a simple algebraic equation. Let's denote the number of goals Skylar scored as S, which means that Wyatt scored 2S goals.

The total number of goals is the sum of the goals scored by both Skylar and Wyatt, which is S + 2S = 15. This simplifies to 3S = 15. By dividing both sides of the equation by 3, we get S = 5.

Therefore, Skylar could have scored 3 goals because the calculations show that Skylar scored 5 goals.