please help this is a final

Answer:

x = 1

Step-by-step explanation:

since y = e^x is a function that has unique y-values for any x-value (there are no 2 x-values that have the same y-value), we know that

e^x1 = e^x2 means that

x1 = x2

so, in our case

e^(3x - 2) = e^x

means

3x - 2 = x

we can also apply the logarithm on both sides to prove that

ln(e^(3x - 2)) = ln(e^x)

3x - 2 = x

so, now, we subtract x from both sides

2x - 2 = 0

add 2 to both sides

2x = 2

and divide both sides by 2

x = 1

Hello !

Answer:

\(\Large \boxed{\sf x=1}\)

Step-by-step explanation:

We want to find the value of x that satisfies the following equation :

\(\sf e^{3x-2}=e^{x}\)

Let's remember :

Let's apply \(\sf ln\) to both sides of the equality :

\(\sf ln(e^{3x-2})=ln(e^{x})\)

With the previous property :

\(\sf 3x-2=x\)

Now let's substract x from both sides :

\(\sf 3x-2-x=x-x\\2x-2=0\)

Add 2 to both sides :

\(\sf 2x-2+2=2\\2x=2\)

Finally, let's divide both sides by 2 :

\(\sf \frac{2x}{2} =\frac{2}{2}\\ \boxed{\sf x=1}\)

Have a nice day ;)

Answer:

A. picture A.........................

Answer:

The coreect answer o

is 14

Answer:

11 times

Step-by-step explanation:

So if you look at the point where the line is on two real numbers at the top of the grid, it shows that it cost $10 for every 5 rides. So if you find the unit rate, divide 10 by 5 to see how much each ride cost, you get that each ride cost $2. Then just divide $22 by $2 and you get 11. Hope this helps, comment if you need more help

For Rob Herndon to achieve his goal of paying off $430,000 in 10 years, he needs to make $34,186.97 at 5% compounded annually.

A future value refers to a value on a future date based on an assumed growth rate of interest over some period.

The future value can be determined using the FV formula or table.

We can also compute the future value using an online finance calculator as follows:

N (# of periods) = 10 years

I/Y (Interest per year) = 5%

PV (Present Value) = $0

FV (Future Value) = $430,000

Results:

PMT = $34,186.97

Sum of all periodic payments = $341,869.70

Total Interest= $88,130.30

Thus, for Rob Herndon to achieve his goal of paying off $430,000 in 10 years, he needs to make $34,186.97 at 5% compounded annually.

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The little lines theu each section are telling you all those sections are identical, which mean they are the same length.

You are told one section is 10, which means x is also 10

X = 10

Answer:

20

Step-by-step explanation:

62 = 3x+2

60 = 3x

20 = x

lol yw now make me brainiest pls

Answer:

66-18b or maybe 11/3

Step-by-step explanation:

-6+9(8-2b)

-6+72-18b

72-6=66

66-18b

The Multiplicative inverse of 1/16 ÷ 1/81 +-1/8​ is 16/79

1/16 ÷ 1/81   +    -1/8

1/16 ÷ 1/81   = 81/16

+    -1/8  = - 1/8

81/16  - 1/8

Then,

= 81/16  - 2/16

= (81 - 2)/16

= 79/16

Multiplicative inverse = 16/79

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The way in which this data-collection method produce bias in obtaining an estimate of all drivers who are satisfied with the company’s truck drivers is that: D. This sample may lead to voluntary response bias because drivers can choose to call the phone number and register an opinion.

A sampling bias can be defined as a type of bias in which members of an intended population are selected in such a way that some members have a higher or lower sampling probability (chances) than the other members.

This ultimately implies that, a sampling bias would occur when members of an intended population are selected incorrectly and as such resulting in a sample that is not representative of the entire population.

Generally speaking, a voluntary response sample is a data-collection technique (method) that is always biased because it only include individuals who choose to volunteer, unlike a simple random sample.

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1/2 miles

Explanation

to find the total distance, we need to add the distance, so

remember how to add fraction numbers:

then

Step 1

add the distances

so, the answer is

I hope this helps you

Answer:

okay i'll keep this in mind

Step-by-step explanation:

Answer:

The image of P on the curve is (0,-3).

Step-by-step explanation:

On the curve with equation y=f(x)-1

On this curve, the output is subtracted by 1 from the original function.

The point P(0,-2) lies on the curve with equation y=f(x).

Input: 0, output: -2

-2 -1 = -3

So

The image of P on the curve is (0,-3).

The best interpretation for the expression 85h + 75 is;

The charge for each hour worked is $85

The initial charge before commencement of work per hour is $75

The general formula of the equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

Now, the slope may also be called the rate of change of the output with the input while the y-intercept represents the initial value or the value of the output when the input is zero.

Now, we are given the equation for total bill as;

T = 85h + 75

where h is number of hours worked

Thus;

The charge for each hour worked is $85

The initial charge will be $75 before commencement of work per hour.

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Answer:

- Banking Operations salary in India with less than 1 year of experience to 10 years ranges from ₹ 1.4 Lakhs to ₹ 7 Lakhs with an average annual salary of ₹ 3.1 Lakhs based on 261 latest salaries

Answer:

A

Step-by-step explanation:

The probability that the individual must stop at at least one light that is 0.45.

Probability is the mathematical tool or procedure of predicting how likely a given event is going to happen.

Given is that there are two traffic lights on the route used by a certain individual to go from home to work. Let {E} denote the event that the individual must stop at the first light, and define the event {F} in a similar manner for the second light. Suppose that -

We can write -

P{E ∪ F} = P{E} + P{F} - P{E ∩ F}

P{E ∪ F} = 0.4 + 0.2 - 0.15

P{E ∪ F} = 0.6 - 0.15

P{E ∪ F} = 0.45

Therefore, the probability that the individual must stop at at least one light that is 0.45.

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There is 9,000 Joule energy present in the bulb

Gravitational Potential Energy

The energy that an object store due to its height in a gravitational field is known as gravitational potential energy.

It can be calculated by using  the equation below

U=m.g.h

Where:

m = mass of the object

h  = height

g  = acceleration due to gravity, or

Since the weight of an object of mass m can be calculated as:

W = m.g

The gravitational potential energy is:

U = W.h

The bell of weight W=180 N at the top of a tower is h=50 m high. Thus its energy is:

U = 180 N * 50 m

U = 9000 Joule

Hence, The bell has 9,000 Joule energy.

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Answer:

ypu are going to have to give us a problem to solve or a question.

Step-by-step explanation:

this is a statement

The simplification of the expressions in the question using the rules of indices are as follows;

1.) 6·e⁰ + (11·f)⁰ - 5/g⁰ = 2

2. (3⁻⁴ + 5⁻³)⁻¹ = \(49\frac{31}{206}\)

3. (3⁻⁴ + 5⁻³)⁻² = \(2415\frac{32685}{42436}\)

4.) \(\dfrac{-5\cdot \left(m^{-4}\cdot n^{-5} \right)^{-3}}{10\cdot c^{-5} \cdot d^6 \cdot e^{-8}}\) = \(\dfrac{c^5\cdot e^8}{2\cdot d^5}\)

5.)  \(\dfrac{-5\cdot \left(m^{-4}\cdot n^{-5}\right)^{-3 }}{7\cdot \left(p^{-6} \cdot q^8\right)^{-4}} =\dfrac{-5\cdot m^{12}\cdot n^{15}\cdot q^{32}}{7\cdot p^{24}}\)

An index or indices is the power by which a number or variable or expression raised.

1.) 6·e⁰ + (11·f)⁰ - 5/g⁰

6·e⁰ + (11·f)⁰ - 5/g⁰ = 6 × 1 + 1 - 5/1

6 × 1 + 1 - 5/1 = 6 + 1 - 5 = 2

Therefore;

6·e⁰ + (11·f)⁰ - 5/g⁰ = 2

2.) (3⁻⁴ + 5⁻³)⁻¹

(3⁻⁴ + 5⁻³)⁻¹ = (1/(3⁴) + 1/(5³))⁻¹ = 1/(1/(3⁴) + 1/(5³))

1/(1/(3⁴) + 1/(5³)) = 1/(1/81 + 1/125) = 1/((125 + 81)/(81×125))

1/((125 + 81)/(81×125)) = (81 × 125)/(125+81) = 10125/209

10125/206 = 49 + 31/206

(3⁻⁴ + 5⁻³)⁻¹ = \(49 \frac{31}{206}\)

3.) (3⁻⁴ + 5⁻³)⁻²

(3⁻⁴ + 5⁻³)⁻² = 1/((1/3⁴ + 1/5³)²)

1/((1/3⁴ + 1/5³)²) = 1/((1/81 + 1/125)²)

1/((1/81 + 1/125)²) = 1/(((125 + 81)/(81 × 125))²)

1/(((125 + 81)/(81 × 125))²) = 1/((206/10125)²)

1/((206/10125)²) = (10125)²/(206)² = 102515625/42436

102515625/42436 = 2415 32685/42436

(3⁻⁴ + 5⁻³)⁻² = \(2415\frac{32685}{42436}\)

4.)  \(\dfrac{5\cdot (2\cdot a^{-1}\cdot b^3)^0}{10\cdot c^{-5}\cdot d^6\cdot e^{-8}}\)

\(\dfrac{5\cdot (2\cdot a^{-1}\cdot b^3)^0}{10\cdot c^{-5}\cdot d^6\cdot e^{-8}} = \dfrac{5\times 1}{10\times \left(\frac{1}{c^5}\times d^6 \times \frac{1}{e^8} \right) }\)

\(\dfrac{5\times 1}{10\times \left(\frac{1}{c^5}\times d^6 \times \frac{1}{e^8} \right) } = \dfrac{5}{10\times \left(\frac{d^6}{c^5\times e^8} \right) }\)

\(\dfrac{5}{10\times \left(\frac{d^6}{c^5\times e^8} \right) } = \dfrac{1}{2\times \left(\frac{d^6}{c^5\times e^8} \right) }\)

\(\dfrac{1}{2\times \left(\frac{d^6}{c^5\times e^8} \right) } = \dfrac{c^5\times e^8}{2\cdot d^6}\)

\(\dfrac{5\cdot (2\cdot a^{-1}\cdot b^3)^0}{10\cdot c^{-5}\cdot d^6\cdot e^{-8}}= \dfrac{c^5\times e^8}{2\cdot d^6}\)

5.) \(\dfrac{-5\cdot \left(m^{-4}\cdot n^{-5} \right)^{-3}}{7\cdot \left(p^{-6}\cdot q^8\rright)^{-4}}\)

\(\dfrac{-5\cdot \left(m^{-4}\cdot n^{-5} \right)^{-3}}{7\cdot \left(p^{-6}\cdot q^8\right)^{-4}} =\dfrac{-5\cdot \dfrac{1}{\left(\frac{1}{m^{4}}\times \frac{1}{n^{5}} \right)^{3}} }{7\cdot \dfrac{1}{\left(\frac{1}{p^{6}}\times q^8\right)^{4}} }\)

\(\dfrac{-5\cdot \dfrac{1}{\left(\frac{1}{m^{4}}\times \frac{1}{n^{5}} \right)^{3}} }{7\cdot \dfrac{1}{\left(\frac{1}{p^{6}}\times q^8\right)^{4}} } = \dfrac{-5\cdot {\left(m^4\times n^5\right)^3} }{7\cdot \left( \dfrac{p^6}{q^8\right)^{4}} }\)

\(\dfrac{-5\cdot {\left(m^4\times n^5\right)^3} }{7\cdot \left( \dfrac{p^6}{q^8\right)^{4}} } = \dfrac{-5\cdot {\left(m^{12}\times n^{15}\right)} }{7} \times \left(\dfrac{q^8}{p^6}\right)^4 }\)

\(\dfrac{-5\cdot {\left(m^{12}\times n^{15}\right)} }{7} \times \left(\dfrac{q^8}{p^6}\right)^4 } = \dfrac{-5\cdot {\left(m^{12}\times n^{15}\right)} }{7} \times \left(\dfrac{q^{32}}{p^{24}}\right) }\)

\(\dfrac{-5\cdot {\left(m^{12}\times n^{15}\right)} }{7} \times \left(\dfrac{q^{32}}{p^{24}}\right) } = \dfrac{-5\times {m^{12}\times n^{15}\times q^{32}} }{7\times p^{24}}\)

\(\dfrac{-5\cdot \left(m^{-4}\cdot n^{-5} \right)^{-3}}{7\cdot \left(p^{-6}\cdot q^8\right)^{-4}} = \dfrac{-5\times {m^{12}\times n^{15}\times q^{32}} }{7\times p^{24}}\)

6.) (3·x⁻⁴·y⁻⁵·z⁻²)⁻²

(3·x⁻⁴·y⁻⁵·z⁻²)⁻² = \(3\cdot \left(\dfrac{1}{\left(\dfrac{1}{x^4} \cdot \dfrac{1}{y^5} \cdot \dfrac{1}{z^2} } \right)^2\right)\)

\(3\cdot \left(\dfrac{1}{\left(\dfrac{1}{x^4} \cdot \dfrac{1}{y^5} \cdot \dfrac{1}{z^2} } \right)^2\right) = 3\cdot \left(x^4\cdot y^5\cdot x^2\right)^2\)

3·(x⁴·y⁵·x²)² = 3·x⁸·y¹⁰·x⁴

Therefore;

(3·x⁻⁴·y⁻⁵·z⁻²)⁻² = 3·x⁸·y¹⁰·x⁴

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Real numbers are:

\(i^6\), 2 - 7i², -12, and √(-5)².

Complex numbers are:

7 - 5i, √-6, 0 + 9i, and -i² + i³.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

A complex expression is in the form a + ib

Where i is the imaginary number.

a)

\(i^6\)

i² = -1

i³ = -i

So,

\(i^6\) = \(i^{2\times3\) = \((i^2)^{3\) = (-1)³ = -1

This is a real number.

b)

2 - 7i²

= 2 - 7 x (-1)

= 2 + 7

= 9

This is a real number.

c)

7 - 5i

This is a complex number.

d)

√-6

= √-1 x √6

= i√6

This is a complex number.

e)

0 + 9i

= 9i

This is a complex number.

f)

-12

This is a real number.

g)

√(-5)²

= √25

= 5

This is a real number.

h)

-i² + i³

= -(-1) + (-i)

= 1 - i

This is a complex number.

Thus,

Real numbers are \(i^6\),2 - 7i², -12, and √(-5)².

Complex numbers are 7 - 5i, √-6, 0 + 9i, and -i² + i³.

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Therefore, sin(0) = -√305/41 when 0 is an angle in quadrant IV.

Trigonometry is a branch of mathematics that deals with the study of relationships between the angles and sides of triangles. It is used to solve problems in many fields, including engineering, physics, astronomy, and architecture. Trigonometry involves the use of functions such as sine, cosine, and tangent to relate the angles and sides of a right triangle. It also includes the study of trigonometric identities, equations, and graphs, as well as applications of trigonometry in real-world situations.

Here,

If 0 is an angle in quadrant IV, then cosine is positive and sine is negative. We can use the Pythagorean identity to find the value of sin(0):

sin²(0) + cos²(0) = 1

sin²(0) = 1 - cos²(0)

sin(0) = -√(1 - cos²(0))

substituting the given value of cos(0):

sin(0) = -√(1 - (4√47/41)²)

sin(0) = -√(1 - (16*47/41))

sin(0) = -√(1 - 736/41)

sin(0) = -√(305/41)

sin(0) = -(√305)/√(41)

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Answer:

Step-by-step explanation:

follow the Pemdas order of operations

add and subtract (left to right)

apply the rule +(-a)=-a

+(-78)=-78

=54-78-(-39)

54-78=-24

=-24-(-39)

apply the rule -(-a)=+a

-(-39) =+39

=-24 +39

-24+39=15

=15

Answer:

452.4 cm^2

Step-by-step explanation:

\(a = 4\pi {r}^{2} \\ a = 4 \pi \times (6)^{2} \\ a = 452.4 \: cm^{2} \)

I hope that is useful for you :)

Answer:

$1200

Step-by-step explanation:

Answer:

Here’s all the answers

Answer:

9,420 colors making exactly 1 car of each color exist

Step-by-step explanation:

Since there is no additional information, such as the number of colors we have to assume the maximum. Since there are over 10 million colors that exist and there is at least one car of each color, then there would be a maximum of 9,420 colors making exactly 1 car of each color exist. On the other end of the spectrum would be 2 colors making 4,710 cars of each color.

The number of different possible colors of vehicle can be found using the relation

\( \frac{9240}{c} \)

The number of different colors possible :

The number of different possible colors can be obtained using the expression :

\( \frac{9240}{c} \)

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Answer:

Since we know the dot product of unit vectors, we can simplify the dot product formula to a⋅b=a1b1+a2b2+a3b3. we can use the same formula, but with a3=b3=0, a⋅b=a1b1+a2b2.

Step-by-step explanation: