In(3x2 - 1) = In(191)

Answers

Answer 1

Given:

The equation is:

[tex]\ln(3x^2-1)=\ln(191)[/tex]

To find:

The solution for the given equation.

Solution:

We have,

[tex]\ln(3x^2-1)=\ln(191)[/tex]

On comparing both sides, we get

[tex]3x^2-1=191[/tex]

[tex]3x^2=191+1[/tex]

[tex]3x^2=192[/tex]

Divide both sides by 3.

[tex]x^2=\dfrac{192}{3}[/tex]

[tex]x^2=64[/tex]

Taking square root on both sides, we get

[tex]x=\pm \sqrt{64}[/tex]

[tex]x=\pm 8[/tex]

Therefore, the solutions of the given equation are -8 and 8.


Related Questions

A certain component is critical to the operation of an electrical system and must be replaced immediately upon failure. If the mean lifetime of this type of component is 100 hours and its standard deviation is 30 hours, how many of these components must be in stock so that the probability that the system is in continual operation for the next 2000 hours is at least 0.95?

Answers

Answer:

Step-by-step explanation:

From the given information:

Assuming we have an integer c to represent the components in the stocks.

Thus, the needed probability can be expressed as:

[tex]P(X_1+X_2+ ........ X_c \ge 2000)[/tex]

To break this down, we have:

[tex]P(\sum X_i \ge 2000) = P \Bigg(\dfrac{\sum X_i - 100n}{\sqrt{n \ Var (X)}} \ge \dfrac{2000-100 n }{\sqrt{n \times 900}} \Bigg )[/tex]

[tex]P \Bigg(\dfrac{\sum X_i - 100n}{\sqrt{n \ Var (X)}} \ge \dfrac{2000-100 n }{\sqrt{n \times 900}} \Bigg )= P (Z \ge 0.95 ) \ \ \ because \ Z_{0.05} = -1.65 \\ \\ \\ \dfrac{2000-100 n }{\sqrt{n \times 900}} = -1.65 \\ \\ \\ \dfrac{100\ n-2000 }{\sqrt{900n}} = 1.65 \\ \\ 100 n -1.65 \sqrt{900 n }-2000 = 0[/tex]

By solving the equation:

n = 23

Thus, relating to the needed condition; n ≥ 23

The needed number of the components that should be in stock should be  at least 23.

GIVING 100 PTS AND BRAINLIEST IF ALL ARE ANSWERED CORRECTLY NOT GUESSED WITH EVIDENCE IF YOU GET THEM ALL CORRECT I WILL THROW IN 200 POINTS

Answers

Answer:

hopefully i got this right lol

Step-by-step explanation:

First Question:

2, 1

Second Question:

I'm assuming the lawn is the shaded region, which to solve you will need to calculate the area of the trapezoid and then subtract that by the area of the building.

EQUATION for area of building: l*w

48 * 64 = 3072^2ft

EQUATION for area of trapezoid: (a+b)/2h

subsitute

(100 + 150)/2 (80) = 10000

10000 - 3072 = 6928^2 ft

Third Question:

Answer: 26 1/4

Explanation: In order to find the volume of any rectangular prism, you need to multiply the length, width, and height. In this case, the equation is: 6 * 1 1/4 * 3 1/2 = 26 1/4

Exponential Functions

Below is a graph of exponential functions label I through VI.

Determine which of the following exponential formula(s) represents II and IV in the graph above.
(a) 10(1.02)t (b) 10(1.05)t
(x) 20(1.02)t (8) 30(0.85)t
(g) 30(0.95)t (∅0 30(1.05)t

a. a and β c. ∈ and 8
b. 8 and a d. β and ∅

Please select the best answer from the choices provided

Answers

Answer:

A. a and β

Step-by-step explanation:

I calculated it logically

(a) [tex]10(1.02)^t[/tex], and b) [tex]10(1.05)^t[/tex] are the formulas that represent II and IV in the graph.

What is an exponential function?

The function which is in format f(x) =aˣ where a is constant and x is variable,  the domain of this exponential function lies   (-∞, ∞).

Here,
We know that the intercept of both II and IV is 10.

If we substitute t = 0 into the exponential formulas, we get the initial value or y-intercept of the graphs. Therefore, the formula that gives an initial value of 10 is a candidate for representing II and IV.

Out of the given options, the formula that gives an initial value of 10 is (a) [tex]10(1.02)^t[/tex] and b) [tex]10(1.05)^t[/tex].

Therefore,  (a) [tex]10(1.02)^t[/tex], and b) [tex]10(1.05)^t[/tex] are the formulas that represent II and IV in the graph above.

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Plz show the work.........

Answers

Answer: 32A

Step-by-step explanation: KYXS

5.4 ⋅ 103 to standard form.

Answers

5.4 * 10^3=5,400 is your answer

How many combinations with repetition are allowed if n = 8 and r = 4?
256
330
1,680
65,536

Answers

Hello, the answer you are looking for should be “330” combinations :)

That should be the answer if I was wrong I’m very sorry

The combinations with repetition are allowed is 330

What is combination?

A combination is a mathematical technique that determines the number of possible arrangements in a collection of items, where the order of the items is not fixed.

Given that, we need to find the number of combinations with repetition are allowed if n = 8 and r = 4

Combinations with repetition = C'(n, r) = (r+n-1)! / (r!(n-1)!)

= (8+4-1)! / 4!(8-1)!

= 11! / 4!7!

= 330

Hence, the combinations with repetition are allowed is 330

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Can you use the values in Pascal’s triangle to find the powers of 11? Explain.

Answers

Answer: Yes!

-Ultimately (it states) all numbers in existence can be extracted from Pascal's Triangle. Using his binomial formation of: (a + b)^0 = 1 , where y is the number you are using. and (a + b)^x is the equation you use to find the answer of that row... the usage of that row, and the formation of its components is how you find the powers of numbers in a given row

-You would be able to find each row of the Triangle, and by using the association of Multiplication, addition, distribution, and If you look at the images below you will notice that to find a power of 11 at it's 6th power, you look at the 6th row of Pascal's Triangle Although not completely relevant, I also added an image of using his Triangle to find the Powers of 2

Step-by-step explanation: Hope this help :D

Answer:

Yes you can

Ultimately (it states) all numbers in existence can be extracted from Pascal's Triangle. Using his binomial formation of: (a + b)^0 = 1 , where y is the number you are using. and (a + b)^x  is the equation you use to find the answer of that row... the usage of that row, and the formation of its components is how you find the powers of numbers in a given row

-You would be able to find each row of the Triangle, and by using the association of Multiplication, addition, distribution, and If you look at the images below you will notice that to find a power of 11 at it's 6th power, you look at the 6th row of Pascal's Triangle Although not completely relevant, I also added an image of using his Triangle to find the Powers of 2

correct on Edge 2021

PLEASE HELP ME FAST I NEED HELP PLEASE

HELP FAST I WILL GIVE BRAINLIEST

Answers

Answer:

1, 2, 7 8

Step-by-step explanation:

1 is the smallest number, 2 is the lower quartile range, 7 is the upper quartile range, and 8 is the largest number

Find the slope (-7,4) and (-7,-8)

Answers

Answer: The slope for this line is not defined.

Step-by-step explanation: We can find the slope of a line using the formula m = y2 -y1/x2 - x1

here, (x1,y1) = (-7,4)

and, (x2,y2) = (-7,-8)

now, m= -8-4/-7+7

        m = -12/0

        So, the slope for this line is not defined as we are getting zero in the denominator.

8. Solve the inequality -4y + 6 < -14.

Answers

Answer:

y > 5

Step-by-step explanation:

Solving an inequality is similar to solving an inequation, one uses inverse operations. The only difference is that when one multiplies or divides by a negative number, then one must remember to flip the inequality sign.

-4y + 6 < -14

Inverse operations,

-4y + 6 < -14

      -6     -6

-4y < -20

/-4    /-4

y > 5

Find the product.
(6t²-8bs) (t² + bs)
Enter the correct answer.

Answers

The product of given equation is      [tex]6t^{4} + 6t^{2} bs-8bst^{2} -8b^{2} s^{2}[/tex] .

Define expression.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)

What is equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

[tex]=(6t^{2} -8bs) (t^{2} + bs)[/tex]

[tex]=6t^{2} (t^{2} + bs) -8bs(t^{2} + bs)[/tex]

[tex]=6t^{4} +6t^{2}bs -8bst^{2} -8b^{2} s^{2}[/tex]

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Enrique weighs five books and rounds the weights to the nearest hundredth.
Which of the weights round to 1.25 pounds?
Add
screer
you sh
Choose all the correct answers.
1.255 pounds
1.252 pounds
1.242 pounds

01.248 pounds
1.245 pounds

Answers

Answer:

1.252

Step-by-step explanation:

5 and up round up 4 and below round down

Write 25 4 as a mixed number.

Answers

Answer:

6 1/4

Step-by-step explanation:

The number 6 with 1/4

so basically see how many times 4 goes in to 25 which is 6 times then take the remainder which is one so 6 1/4

Can i be Brainliest

martha has 17 043 943 957 points. 16 000 points equivilates to 50 $ off. How much money does Martha save?​

Answers

Of course, a businesswoman who is extremely wealthy. Martha has a lot of money thanks to her writing numerous best-selling books, publishing a magazine (shoutout to all the kids from the 1990s whose moms read Martha Stewart Living), appearing on various TV shows, and having her own brand of goods, which includes a CBD line.

How did Martha make her money?Martha Stewart is a lot of things, including a person who built a nativity during her time in jail. Snoop Dogg's close friend. somebody with a large number of peacocks. Martha has a lot of money thanks to her writing numerous best-selling books, publishing a magazine (shoutout to all the kids from the 1990s whose moms read Martha Stewart Living), appearing on various TV shows, and having her own brand of goods, which includes a CBD line She was, in reality,  America's first woman billionaire who had achieved success on her own.Now that Martha is no longer a billionaire (more on why in a bit), it is time to analyze her wealth.Celebrity In 1999, Martha Stewart and her business partner Sharon Patrick combined all of their endeavours into Martha Stewart Living Omnimedia (MSLO), which they then listed on the New York Stock Exchange. By the time trading ended, the stock had increased from $18 per share to $38 per share, making Martha practically instantly worth $1 billion.

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Write the expression for each
phrase.
6 rows of 8

Answers

The answer is 6x8 your welcome

what is 4.8 into cm?

Answers

Answer:

Its 12.192 centimeters :)

Answer:

[tex]\huge \fbox \pink {A}\huge \fbox \green {n}\huge \fbox \blue {s}\huge \fbox \red {w}\huge \fbox \purple {e}\huge \fbox \orange {r}[/tex]

I assume you meant 4.8 m.

1 m = 100 cm

[tex]4.8 \: m \\ = 4.8 \times 100 \\ = 480 \: cm[/tex]

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ

[tex] \huge\blue{ \mid{ \underline{ \overline{ \tt ꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐ }} \mid}}[/tex]

Look at picture please help 32 points!!

Answers

Answer:

SA = 112 cm²

Steps:

to solve this problem we have to calculate the surface area of the whole block and let be SA

first the surface area of the square pyramid:

the area of one triangle = (height × base)/2

given:

height = 6 cm

base = 4 cm

A = (6×4)/2

A = 24/2

A = 12 cm²

since it's a square triangle

then the surface area of the pyramid excluding the base:

Ap = A × 4

Ap = 12 × 4

Ap = 48 cm²

now the inferior part which is a rectangular prisme

Ar = 4(height×lenght)+lenght²

Ar = 4(3×4)+4²

Ar = 4×12+16

Ar = 48+16

Ar = 64 cm²

and now we can calculate the surface area of the whole block

SA = Ap + Ar

SA = 48 + 64

SA = 112 cm²

This tablet shows an example of
was first used by the
>
It

Answers

Answer: the answer is 1.cuneiform & 2.sumerians

Step-by-step explanation: searched it up

Devin purchased a container of sport drink that contains 300 calories. The label says that 80% of the calories are from carbohydrates. How many calories are from carbohydrates?

Answers

Answer: 240 Calories are from Carbohydrates

Step-by-step explanation:

First, we will convert 80% into the decimal 0.8, then we will multiply this by the amount of total calories in the drink to create the following equation:

300 * 0.8 = 240 Calories.

√2 (2-2√10) how do you simplify

Answers

Answer:

2√2- 4√5

Step-by-step explanation:

√2 (2-2√10)

2√2- 2√20

2√2- 2√(4*5)

2√2- 2*2√5

2√2- 4√5

Find the area of the rectangle measurement below 5/4 km x 12/5 km

Answers

Answer:

3km

hope this helps

have a good day :)

Step-by-step explanation:

can someone help will give brainliest

Answers

Answer:

For every hour, Bliqus earns $21.50

Step-by-step explanation:

$430 / 20 = $21.50

$215 / 10 = $21.50

The answer is 21.50

Explanation : it’s just is

You pick a card at random.
1 2 3 4
What is P(1)?

Answers

Answer:  56

Step-by-step d

If YG = 12, then EG is?
How is it not 6? Please help, no links

Answers

Answer:

I THINK ANSWER IS 12 because DIAGONALS BISECT EACHOTHER

4 times a number decreased by 2 is at most 10

Answers

Answer: N is less than or equal to 2

The statement above can be written as
4n - 2 <= 10.

1. Add two on both sides
4n -2+2 <= 10-2

2. Simplify
4n <= 8

3. Divide by 4 on both sides
4n/4 <= 8/4

4. Simplify
N<= 2

Which fraction is represented by the blue portion of the picture?

A. 5/3
B. 1/2
C. 5/8
D. 3/8
E. 2/3
F. 3/5

NO LINKS

Answers

It would be C reason why is because the blue covers 5 out of the 8
Answer: 5/8

Explanation: as for counting all the “blocks” 5 is marked in blue and the total of “blocks” is 8 therefore you can determine that your answer is C.

what's the y intercept of y=-2x+ -20​

Answers

Answer: y=20-2x

Step-by-step explanation:

Find the volume of the cylinder. Round your
answer to the nearest tenth.

Answers

5,024

Formula of volume of a cylinder: V=Bh
V= (3.14 (10)^2) 16
10x10 = 100
(3.14 x 100) 16
(314 x 16)
V = 5,024

please help asap
will give brainliest

Answers

Answer:

m<D should also be 98° due to the congruent angles theorem

Answer:

98

Step-by-step explanation:

Sides AB and DC are parallel.

Sides AD and BC are parallel.

Quadrilateral ABCD is a parallelogram.

Opposite angles of a parallelogram are congruent.

m<D = m<B = 98°

Answer: 98

7 - 13a = 27 solve for A

Answers

Answer:

a = -20/13

Step-by-step explanation:

7 - 13a = 27

-13a = 20

a = -20/13

Let's check

7 - 13(-20/13) = 27

7 + 260/13 = 27

7 + 20 = 27

27 = 27

So, a = -20/13 is the correct answer!

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