What is each expression written as a single natural logarithm?

(a) ln 7+2 ln 5

The number of miles when the cost would be the same is 40 miles.

The equation that represents the total cost for car rentals is a linear function. A linear function is a function with a single variable that is raised to the power of one. A linear function is a straight line when drawn on a graph.

Total cost = constant cost + (cost per mile x number of miles driven)

First rental : $15 + (0.50 x m)

$15 + 0.50m

Second rental : $25 + (0.25 x m)

$25 + 0.25m

When the cost is the same for the car rentals, the two equations would be equal:

$15 + 0.50m = $25 + 0.25m

$25 - $15 = 0.50m - 0.25m

$10 = 0.25m

m = 10 / 0.25

m = 40 miles

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Given the functions f(x) = 4x + 1 and  g(x) = x + 5, the function operation ( f + g )(x) is 5x + 6.

Given the functions in the question;

To evaluate f + g, replace the function designators in f + g with the actual functions and simplify

( f + g )(x) = f(x) + g(x)

( f + g )(x) = (4x + 1) + (x + 5)

Remove the parenthesis and collect like terms

( f + g )(x) = (4x + 1) + (x + 5)

( f + g )(x) = 4x + 1 + x + 5  

( f + g )(x) = 4x + x + 5  + 1

( f + g )(x) = 5x + 6  

Given the functions f(x) = 4x + 1 and  g(x) = x + 5, the function operation ( f + g )(x) is 5x + 6.

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Answer:

9,

Step-by-step explanation:

Answer:

5/7

Step-by-step explanation:

because it is 5/(2+5)

The equation of the line from the given figure is y=-7.

We need to find the equation of the line from the given figure.

The equation of a line is an algebraic form of representing the set of points, which together form a line in a coordinate system. The numerous points which together form a line in the coordinate axis are represented as a set of variables x and y to form an algebraic equation, which is referred to as an equation of a line.

From the given figure, we can see that the line is passing through the point (0, -7).

The slope (m) of the line is 0.

Put m=0 and (0, -7) in y=mx+c and simplify.

That is, -7=c

Now, substitute c=-7 in y=mx+c.

Thus, y=-7

Therefore, the equation of the line from the given figure is y=-7.

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According to the question, the given rational expression can be simplified and as shown below:

Rational expression = [tex]\frac{4x^{2} }{5y}.\frac{7y}{12x^{4} }[/tex]

To simplify the given rational expression, calculate the factors of the numerator as well as denominator. And later divide it from each other. These expressions are also called as polynomial expressions.

Rational expression = [tex]\frac{1}{5}.\frac{7}{3x^{2} }= \frac{7}{15x^{2} }[/tex]

The final expression of the given equation is [tex]\frac{7}{15x^{2} }[/tex].

What is polynomial expression?

Polynomial expression are those equation whose highest degree is two. It is also called as quadratic equation. And it is simplified by performing the factors on the given expressions.

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Answer: 1/3 cup of cat food

Step-by-step explanation:

[tex]\displaystyle\\\frac{2}{3}:2=\\\\ \frac{2}{3}*\frac{1}{2} =\\\\ \frac{(2)(1)}{(3)(2)}=\\\\ \frac{1}{3}\ cup\ of\ cat\ food[/tex]

Answer:

[tex]\frac{\text{dogs}}{\text{total}} = \frac59[/tex]

Step-by-step explanation:

We can say that the amount of cats is [tex]4x[/tex] and the amount of dogs is [tex]5x[/tex], as we know that  [tex]\frac{\text{cats}}{\text{dogs}} = \frac45[/tex]

Therefore, the total amount of animals (cats and dogs) is [tex]9x[/tex].

[tex]\frac{\text{dogs}}{\text{total}} = \frac{5x}{9x} = \frac59[/tex]

The values, when substituted for x in the expression \sqrt{x} , that will result in an irrational number are:

An irrational number can be described as the type of real number  that the representation can not be seen as that of simple fraction and they are been termed as the irrational numbers.

In this case , we can come into conclusion that any number  that posses a non-terminating as well as non-repeating decimal fit in , hence values, when substituted for x in the expression \sqrt{x} , that will result in an irrational number are:

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Answer:

24.5

Step-by-step explanation:

24.5*2 is 49

Answer:

It would take 5 mechanics to repair 22 cars in 5 hours

Step-by-step explanation:

2 garage mechanics take 3 hours to repair 6 cars.

to repair 1 car, 1 garage mechanics take = (2×3)/6 = 1 hour

So In 1 hour, 1 car can be repaired by 1 mechanic

22 cars can be repaired in 1 hour by = 22/1 = 22 mechanics

22 cars can be repaired in 5 hours by = 22/5 = 4.4 = 5 mechanics

(4.4 mechanics are not possible. There should be 5 mechanics)

In the equation b = a -2, which variable is the independent variable and which is the dependent variable ? Explain.

In the given equation b=a-2, a is an independent variable and b is an dependent variable.

Independent variable is variable whose values are unaffected by changes is referred to as an independent variable.

The dependent variable is defined as the variable whose evaluation of the independent variable determines the quality of the dependent variable.

For example, y=x+5

Here, According to changes in the evaluation of the variable "x," the estimation of the variable "y" also varies. The variable "y" is referred to as an dependent variable and the "x" is referred to as an independent variable.

Therefore, In the equation b=a-2, "a" is an independent variable and "b" is an dependent variable.

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The number of possible combinations of ring and bracelet she has is 78

The given parameters are

Rings = 13

Braceletes = 6

The number of possible combinations of ring and bracelet she has is calculated by multiplying the number of rings and the number of bracelets

This is represented as

Possible combination = Rings x Braceletes

Substitute the known values in the above equation

So, we have

Possible combination = 13 * 6

Evaluate the product in the above equation

So, we have

Possible combination = 78

This means that she has 78 possible combinations of ring and bracelet

Hence, the number of possible combinations of ring and bracelet she has is 78

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Based on the given values in the table that shows different speed-distance-time relationships, the value of A is 140 meters and the value of B is 3 hours.

To find the distance, the formula is:
= Speed x time

The distance of A is:

= 35 x 4

= 140 meters

To find the time taken, the formula is:
= Distance / speed

The time in B is:

= 81 / 27

= 3 hours

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Answer:

It is not a function because the number 4 (input) is being used more then once

There is no solution for the equation 2 + √x + 5 = 4 for x ∈ R.

An extraneous solution is one that results from the process of addressing the problem but is not a legitimate solution to the problem, such as the answer to an equation.

A formula known as an equation uses the equals sign (=) to express how two expressions are equal.

Consider the equation,

2 + √x + 5 = 4

√x + 7 = 4

Subtracting 7 from each side of the equation.

√x + 7 - 7 = 4 - 7

√x = - 3

Since √f(x) cannot be negative for x ∈ R.

Hence, there is no solution for x ∈ R of the equation.

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Answer:

B'C' = 16.2 and AB = 2.8

Step-by-step explanation:

the scale factor is 3 , then sides of Δ A'B'C' are 3 times Δ ABC

B'C' = 3 × BC = 3 × 5.4 = 16.2 units

Then

the sides of Δ ABC are [tex]\frac{1}{3}[/tex] times Δ A'B'C'

AB = A'B' ÷ 3 = 8.2 ÷ 3 ≈ 2.7 units ( to the nearest tenth )

[tex]x-4~\geqslant~-1\implies x~\geqslant~-1+4\implies \boxed{x~\geqslant~3} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{multiplying both sides by -5}}{-5(x)\underset{\stackrel{\uparrow }{notice}}{~\leqslant~}-5(3)}\implies -5x~\leqslant~-15\implies -5x= \begin{cases} -15 ~~ \textit{greatest value}\\ -16,-17,-18...-\infty \end{cases}[/tex]

let's recall that for inequalities whenever we divide or multiply or exponentialize by a negative value, we must flip the inequality sign, notice, multiplying by -5, flipped it sideways.

Also let's recall that on the negative side of the number line, the closer to 0, the greater, thus -1 is much much greater than -1,000,000.

Real root of ∛0.064 is 0.02133.

By considering the given expression

∛0.064

=(0.064)^1/3

= (0.021)^1/3

= 0.02133

If a mathematical equation has real roots, then its solutions or roots are real numbers. If an equation has distinct roots, we contend that all of its solutions or roots are not equal. A quadratic equation has real and distinct roots if the discriminant is greater than 0.

If there are no stationary points on the curve, then f has a single real root. If stationary points are found, you could demonstrate using the geometry of the curve that the curve can only intersect the x axis once due to the configuration of the stationary points.

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Answer:

70

Step-by-step explanation:

as the discount is 20 thus the original price would be 70

Answer:

1.55 is the correct answer

Answer:

If you like to round 1.553 to the nearest hundredth, leaving only two numbers after the decimal point, then ask your teacher for help instead of letting yourself down. The result you'll get is 1.55

Step-by-step explanation:

Number Rounded to Nearest 100th

1.553 1.55

1.554 1.55

1.555 1.56

1.556 1.56

1.557 1.56

1.558 1.56

1.559 1.56

1.56          1.56

1.561 1.56

1.562 1.56

It should be noted that when Albert uses a grid to multiply 27 by 13, the product that will be gotten will be 351.

What isn't a product?

It should be noted that in mathematics, a product or an expression that specifies factors to be multiplied is the outcome of multiplication.

The multiplicand, multiplier, and product are the components of a multiplication sentence. The first number is the multiplicand, the second number is the multiplier, and the result is the product.

It should be noted that based on the information, we want to multiply 27 and 13. This will be illustrated thus:

= 27 × 13

= 351

Therefore, when when Albert uses a grid to multiply 27 by 13, the product that will be gotten will be 351.

Note that the information is incomplete and was solved based on the available information given.

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The median of the set of data is 14 1/ 2

It is important to note that the median is the middle number of a given set of data.

Given the set of data;

12, 14, 15 , 16

Let's find the median;

There are two numbers in the middle, so we take their sum, and divide by 2, we have;

Median = 14 + 15/2

Find the sum of the numerators

Median = 29/ 2

Median = 14 1/2

Thus, the median of the set of data is 14 1/ 2

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Based on the given numbers, the number that is divisible by 4 are: 152, 76, and 4,788.

The numbers that are divisible by four need to meet certain requirements and the first one is that they should end in an even number.

The numbers divisible by 4 are:

= 152/4 = 38

= 76 / 4 = 19

= 4,788 / 4

= 1,197

This shows that these numbers are divisible by 4.

In conclusion, the numbers that are divisible by 4 are 152, 76, and 4,788.

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The given function is exponential growth and the y-intercept is y=3.

Given that the given function is y=3(4ˣ).

Exponential growth or decay describes the process of reducing or growing an amount by a consistent percentage rate over a period of time and it is represented by the function y=a(1-b)ˣ where, y is the final amount, a is the original amount and b is the growth or decay factor and x is the amount of time passed.

If a is positive and b is greater than 1 then it is exponential growth.

If a is positive and b is less than 1 but greater than 0 then it exponential decay.

The graph of the given function y=3(4)ˣ is shown in the attached image.

From the graph, it is visible that the given function is an exponential growth because a is 3 and it is positive and it is greater than 1.

Now, we will find the y-intercept by substituting x=0, we get

y=3(4⁰)

y=3(1)

y=3

Hence, the given function or situation y=3(4ˣ) as an example of exponential growth and the y-intercept is 3.

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The probability that a person selected randomly from the survey group is not in statistics given they are in AQR is 0.75

The Venn diagram represents the given parameter

From the Venn diagram, we have the following values

n(not statistics and AQR) = 21

n(AQR) = 21 + 7

Evaluate the sum

n(AQR) = 28

The probability that a person selected randomly from the survey group is not in statistics given they are in AQR is then calculated as

P(not statistics | AQR) = n(not statistics and AQR)/n(AQR)

So, we have

P(not statistics | AQR) = 21/28

Evaluate the quotient

So, we have

P(not statistics | AQR) = 0.75

Hence, the probability that a person selected randomly from the survey group is not in statistics given they are in AQR is 0.75

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Answer:

Infinite many solutions.

Explanation:

Equation's:

make y the subject:

eq 1

eq 2

Solve:

       y = y

5 - 2x =  5 - 2x

As both sides are equal, the system of equations have infinite solutions.

The distance between points A and B is 14 units.

A horizontal line with evenly spaced numerical increments is referred to as a number line. How the number on the line can be answered depends on the numbers present.

According to the number line,

Point A lie at - 2 on the number line and point B lie at 12 on the number line.

Now from 0 to point B,

The distance between point 0 and B is 12 units.

And from point A to 0 the distance is 2 units.

Therefore,

The total distance between points A and B will be:

AB = AO + OB

AB = 2 units + 12 units

AB = 14 units

Hence, the correct option is (D) 14 units.

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