Determine whether each statement is always, sometimes, or never true.
ln t=log e t

Answer:

Step-by-step explanation:

rgvm

Answer:the answer is A haha

Step-by-step explanation:

i just did this kahn academy lesson-

Answer:

X = 4

Step-by-step explanation:

The function y=0.0015(10)ˣ showcases exponential growth.

So,

Given function: y=0.0015(10)ˣ

If we put x = 1 as follows:

Then, if we put x = 2 as follows:

Hence, we see that 0.15 > 0.15.

Therefore, the function y=0.0015(10)ˣ showcases exponential growth.

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The probability that a girl is chosen is 1/10 and the probability that a left-handed girl is chosen is 11/20.

Probability may be defined as the possibility of occurrence of an event. Probability of an event can be 0 or 1 but it can never be negative. If probability is 0 then the event will not occur and if probability is 1 then the event will definitely occur. Probability is given by the formula.

Probability = Favorable outcomes/Total number of outcomes.

Here, total number of outcomes = 20.

Now in the first case we need to find probability of picking a girl so favorable outcome is 2.

Probability of picking a girl = 2/20

Probability of picking a girl = 1/10

In the second case we need to find probability of picking a left-handed girl, so the favorable outcomes are 2 + 9 = 11 as total number of girls are 2 and total number of left-handed people are 9.

Probability of picking left-handed girl = 9 + 2/20

Probability of picking left-handed girl = 11/20

Thus, probability that a girl is chosen is 1/10 and the probability that a left-handed girl is chosen is 11/20.

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The large square covers more

(See attachment below)

Explanation- The large square has the highest dimension and by extension, it has the highest area.

This means that, less large squares will be needed to cover more areas compared to other sizes of the squares

Area of the square =(side)².

square, in geometry, a plane figure with four equal sides and four right (90°) angles. A square is a special kind of rectangle and a special kind of parallelogram.

By observation,

9 small squares are equivalent to one large square, implying that the 5 large squares are giving us 45 small squares.

4 small squares can fit into one medium square, implying that the 10 medium squares are giving us 40 small squares.

There are only 10 small squares.

Hence, the large square covers more of the plane

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Using the properties of logarithm the value of the expression is   [tex]log_{2}4 - log_{2}16 = -2[/tex]

We have been given two logarithm terms that is the first term is  [tex]log_{2}4[/tex] and second term is [tex]log_{2}16[/tex].

The propertied of logarithm that we are going to use are

          [tex]log a^{m} = m * log a[/tex]     and   [tex]log_{a} a = 1[/tex]

First we will find the value of the two terms and operate the above mentioned properties of logarithm to obtained the values of the logarithm.

Thus,

                [tex]log_{2}4 = log_{2}2^{2} \\ = 2* log_{2}2\\ = 2*1\\ = 2[/tex]         

Similarly,            

                 [tex]log_{2}16 = log_{2}2^{4} \\ = 4* log_{2}2\\ = 4*1\\ = 4[/tex]                          

Now subtracting both the terms by substituting its respective values which we have calculated above, we get

[tex]log_{2}4 - log_{2}16 = 2 - 4 = -2[/tex]

Thus the value of the expression is [tex]log_{2}4 - log_{2}16 = -2[/tex]

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Answer:

Step-by-step explanation:

Answer:

what is the correct solution

Step-by-step explanation:

After solving the given inequality the answer is x∈(-∞, 1].

To solve the inequality:

Given: 2(4)x⁺³≤8

Then,

[tex]\begin{aligned}&2 \cdot 4 x^3 \leq 8\\&8 x^3 \leq 8\\&8 x^3+(-8) \leq 8+(-8)\\&8 x^3-8 \leq 8-8\\&8 x^3-8 \leq 0\\&2^3 \cdot x^3-2^3 \leq 0\\&2^3\left(\frac{2^3 \cdot x^3}{2^3}-\frac{2^3}{2^3}\right) \leq 0\\&8\left(x^3-1\right) \leq 0\\&x^3-1 \leq 0\\&x^3-1^3 \leq 0\end{aligned}[/tex]

Then,

[tex]\begin{aligned}&(x-1)\left(x^2+x+1\right) \leq 0\\&\left\{\begin{array}{l}x-1=0 \\x^2+x+1=0\end{array}\right.\\&\left\{\begin{array}{l}(x-1)+1=1 \\x_1=\frac{-1+\sqrt{1-4}}{2} \\x_2=\frac{-1-\sqrt{1-4}}{2}\end{array}\right.\\&\left\{\begin{array}{l}x-1+1=1 \\x_1=\frac{-1+\sqrt{-3}}{2} \\x_2=\frac{-1-\sqrt{-3}}{2}\end{array}\right.\\&\left\{\begin{array}{l}x=1 \\x_1=\frac{-1+\sqrt{3} \cdot \sqrt{-1}}{2} \\x_2=\frac{-1-\sqrt{3} \cdot \sqrt{-1}}{2}\end{array}\right.\end{aligned}[/tex]

So,

[tex]\begin{aligned}&\left\{\begin{array}{l}x=1 \\x_1=\frac{-1+\sqrt{3} \cdot i}{2} \\x_2=\frac{-1-\sqrt{3} \cdot i}{2}\end{array}\right.\\&\left\{\begin{array}{l}x=1 \\x_1=-\frac{1}{2}+\frac{\sqrt{3}}{2} i \\x_2=-\frac{1+\sqrt{3} \cdot i}{2}\end{array}\right.\\&\left\{\begin{array}{l}x=1 \\x_1=-\frac{1}{2}+\frac{\sqrt{3}}{2} i \\x_2=-\frac{1}{2}-\frac{\sqrt{3}}{2} i\end{array}\right.\\&\left\{\begin{array}{l}x \leq 1 \\x \geq 1\end{array}\right.\end{aligned}[/tex]

So, finally, it gives:

[tex]2 \cdot 4 x^3 \leq 8\\2 \cdot 4 \cdot 0^3 \leq 8\\\begin{aligned}&x \leq 1 \\&x \in(-\infty, 1]\end{aligned}[/tex]

Therefore, after solving the given inequality the answer is x∈(-∞, 1].

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SportCo manufactured 6400 basketballs

SportCo manufacturers fixed expenses for producing basketballs = $46,270

Variable expense incurred per basketball produced = $6.50

Total expenses incurred by SportCo for producing basketballs= $87,870

Fixed costs are costs that remain constant regardless of whether more or fewer goods or services are produced or sold.

An expense for the company that varies according to how much is produced or sold is called a variable cost. Depending on a company's production or sales volume, variable costs grow or fall. They climb as production rises and reduce as production declines.

Let x be the number of basketballs produced by the manufacturer SportCo.

Formulating the equation we get:

Fixed cost + Variable cost*Number of basketballs produced = Total expenses incurred by the manufacturer

46270 + 6.5(x) = 87870

6.5(x) = 41600

x = 6400

Therefore, the number of basketballs produced is 6400 by the manufacturer.  

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Answer:

61

Step-by-step explanation:

Answer:The probability would be 5 out of 12.

Answer:

6:22, 9:33

Step-by-step explanation:

When writing equivalent ratios, you use two of the numbers from the original ratio and multiply them evenly to get an equivalent ratio.

[tex]\mathrm{p:q~or~\frac{p}{q} = \frac{x(p)}{x(q)}}\\\mathrm{\frac{6 \times 2}{11 \times 2} = 6:22}\\\mathrm{\frac{6 \times 3}{11 \times 3} = 9:33}[/tex]

Answer:

6:22 and 9:33

Step-by-step explanation:

Answer: 6:22 and 9:33

Think of the ratio like a fraction, one way to find an equivalent ratio is to simplify the current ratio. But in this case, we are unable because we can divide 3 by 3 to get one, but not 11 by 3.

3 divided by 3 = 1

11 divided by 3 = does not evenly divide

Another way is to multiply both numbers by the same number.

3 times 2 = 6

11 times 2 = 22

And we can just keep doing the same with different numbers.

3 times 3 = 9

11 times 3 = 33

value of x in given exponential equation is  =  1

In, mathematics a exponential function or equation is inverse of logarithmic function. That means, we can easily convert the logarithmic function into exponential function and vice versa. The basic form of the logarithm function can be written as  [tex]a^x[/tex] .

where, a is the base of function

           x is the expression

Mathematically, if  [tex]log_aN = x[/tex] is an logarithmic function then, this can be converted to exponential function as  [tex]a^x = N[/tex].

There are many formulas that are given to us for solving several simple and complex problems based on exponential functions and exponential equations.

Some important formulas of exponents :

According to given statement,

4^3x = 64

=> 4^3x = 4³

=> 3x = 3

=> x = 1

Thus solution for this equation is x =1.

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Inverse of the given function F(x) = 3 x³- 4 is F⁻¹(x) = ∛[ ( y + 4 ) / 3 ]

Given is a function of x, F(x) = 3 x³- 4

These question can be solved by following 4 easy steps

Step 1 : Switch the F(x) with the variable y

This implies, F(x) = 3 x³- 4 becomes y =  3 x³- 4

Step 2 : Interchange the variable x and y in the above obtained equation

This implies, from the equation y = 3 x³- 4, we get

x =  3 y³- 4

Step 3 : Solve the new obtained equation for y

This implies, we have to simplify the equation by rearranging the terms to get the equation in terms of the variable x.

x =  3 y³- 4

=> x + 4 = 3 y³

=> 3 y³ = x + 4

=> y³ = ( x + 4 ) / 3

=> y = ∛( x + 4 ) / 3

Hence we obtain the required equation.

Step 4 : Switch the variable y with F⁻¹(x)

This implies, y = ∛( x + 4 ) / 3 becomes F⁻¹(x) = ∛( x + 4 ) / 3

Therefore, we get the inverse of the given function F(x) = 3 x³- 4 as F⁻¹(x) = ∛( x + 4 ) / 3

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The bacterial cell length is 62.5 times smaller than the amoeba cell.

An equation is an expression that shows the relationship between two or more numbers and variables.

The length of a bacterial cell is about 4 x 10⁻⁶ m, and the length of an amoeba cell is about 2.5 x 10⁻⁴ m

Hence:

Ratio of Amoeba length to bacteria length = (2.5 x 10⁻⁴ m) / (4 x 10⁻⁶ m) =   62.5

The bacterial cell length is 62.5 times smaller than the amoeba cell.

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Answer:

the answer in scientific notation with the significant amount of digits is 6.25 x 10^2.

Step-by-step explanation:

you have to solve the equation and divide 0.00025 by 0.00004

you will get 6.25

and if you divide 2.5 by 4 you get 0.625 you have to move the decimal over to the right by 2 so you get the exponent of 2

The answer in scientific notation with the significant amount of digits is 6.25 x 10^2

The value of x is 14 and the measure of angle J s 103

The given angles are external angles of parallel lines and a transversal

So, we have:

6x - 7 + 7x + 5 = 180

Evaluate the like terms

13x = 182

Divide both sides by 13

x = 14

Substitute x = 14 in J = 7x + 5

J = 7 x 14 + 5

Evaluate

J = 103

Hence, the value of x is 14 and the measure of angle J s 103

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The values of x and angle J are 14 and 103 degrees respectively.

It is important to note that angles on a transversal line are supplementary, that is, they sum up to 180 degrees

Given the angles as;

Equate the angles

6x - 7 + 7x + 5 = 180

collect like terms

6x + 7x = 180 +2

13x = 182

Make 'x' the subject

13x/ 13 = 182/ 13

x = 14

But angle J = 7x + 5 = 7(14) + 5 = 98 + 5 = 103

Thus, the values of x and angle J are 14 and 103 degrees respectively.

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The statement about the function y = −14x − 2 that is true is that A. As the value of x increases, the value of y increases. B.

It should be noted that the information is to get the dtatement about the function y = −14x − 2 that is true.

y = −14x − 2

Let's use x = 1

y = −14x − 2

y = -14(1) - 2 = -16

When x = 2, y = −14x − 2.

y = -14(2) - 2 = -40

It shows that as x increases, y will also increase.

Therefore, the correct option is A.

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The value in Mexican pesos of an item that costs 15 Chinese yuan is 0.474 x.

x yuan to y dollars = f(x)

f(x) = 0.15 x

y dollars to x yuan =

y= 0.15 x

x =  [tex]\frac{y}{0.15}[/tex]

y dollars to x pesos =g(y)

g(y) =14.07 y

x pesos to y dollars

x = 14.07 y

y = [tex]\frac{x}{14.07}[/tex]

Substituting the result of second into first,

pesos → dollars → yuan

Lets call this function, h(x) = converts x pesos into y yuan.

h(x) = ( [tex]\frac{x}{14.07}[/tex] )/ 0.15

= 0.474 x

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Rick paddles in still water at a rate of 6.5 mph. The rate of the current is 1.5 mph.

The rate at which an object moves from one point to another is also called speed. It can be measured by dividing the distance over time.

rate = distance/time

Let x = rate at which Rick paddles

c = rate of the current

If Rick paddles a kayak 20 miles upstream in 4 hours, and going upstream means the current is against your direction, then the equation for the travel is:

x - c = 20 miles/4 hours

x - c = 5     (equation 1)

If the return trip downstream takes him 2.5 hours, and downstream means that the current is going the same direction as you are, then the equation for the downstream travel is:

x + c = 20 miles/2.5 hours

x + c = 8     (equation 2)

Using elimination method, solve the two equations.

x + c = 8

x - c = 5

2x     = 13

x = 6.5

rate at which Rick paddles = 6.5 mph

Substitute x in equation 1 and solve for c.

x - c = 5     (equation 1)

6.5 - c = 5

c = 6.5 - 5

c = 1.5

rate of the current = 1.5 mph

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The answer to the question is 1350.68

so we are given $500 is deposited at the start of the first year and the interest rate is 2 percent

so the interest =2/100×500 =$10

total amount =$510

we are given that $200 is deposited at the start of the next year, now total amount =$710

interest rate is 2 percent

so the interest =2/100×710 =$14.2

total amount =$724.2

we are given that  $600 is deposited at the start of the following year now total amount =1324.2

interest rate is 2 percent

so the interest =2/100×1324.2 =$14.2

total amount =$1350.68

Hence the answer is $1350.68

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Answer:

The answer to your question is going to be c

The product of 3.82 x 0.63 is 2.4066.

One of the four fundamental mathematical operations, along with addition, subtraction, and division .In mathematics refers to the continual addition of sets of identical size Multiplication in elementary algebra is the process of figuring out what happens when a number is multiplied by itself. Each of the numbers and is referred to as a factor of the product, which is the outcome of a multiplication is called as multiplication.

Given that,

The product of      

 3.82

x 0.63

 1146

2292 x

000 x  x

 2.4066

Therefore, the product of 3.82 x 0.63 is 2.4066.

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The value of  f(0) = 2 and f(-2) = -2 given the equation that we have in this image.

The function that we have here is given as

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

We have to find the value of f(-2)

= 2(-2) - 2 / (-2 + 1) (-2 - 1)

= - 4 - 2 / -1(-3)

= -6 / 3

= -2

Hence  f(-2) = -2

Next we have to find f(0)

2(0) - 2 / (0 + 1) (0 - 1)

= -2 / 1 * -1

= -2 / -1

= 2

Hence we can say that the value of  f(0) = 2 and f(-2) = -2 given the equation that we have in this image.

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Answer:

d=-2/3f+7

Step-by-step explanation:

4(x+2)

hope this helps

Answer:

Step-by-step explanation:

Answer:

y = 8.40x

y = the total amount that he earned and x = the number of hours that he worked.

Step-by-step explanation:

The result of simplifying the expression -(-27)⁻⁴/₃ using the exponent rules is 1/81

To solve this exercise we have to resolve algebraic operations following the exponent rules.

-(-27)⁻⁴/₃ =

(27)⁻⁴/₃

As we have a negative exponent, you have to pass the exponent to the denominator:

1/(27)⁴/₃

As we have a fractional exponent, you must convert the exponent to root:

1/[tex]\sqrt[3]{}[/tex](27)⁴

1/[tex]\sqrt[3]{}[/tex](531441)

1/81

In mathematics an exponent is the number of time that a number, called (base) is multiplied by itself. It is also called, power or index.

Example: 3² = 3*3 = 9

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According to the linear equation , the number of visits Valeria must make to earn a free movie ticket is 14.

According to the statement

We have to find that the linear equation.

So, For this purpose, we know that the

The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line.

From the given information:

She receives 80 rewards points just for signing up.She earns 7.5 points for each visit to the movie theater.She needs 185 points for a free movie ticket.

then

The linear equation becomes:

The equation that can be used to represent the explanation given in the question is : 185 = 80 + 7.5x

Then

Combine similar terms

185 = 80 + 7.5x

185 -80 = 7.5x

105 = 7.5x

x = 105 /7.5

x = 14.

So, According to the linear equation , the number of visits Valeria must make to earn a free movie ticket is 14.

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