WhAt is 3.242424 as a mixed number

The solutions are: x = ln(2) for 2eˣ = 4,  x = ln(25)/4 for e⁴ˣ = 25, x = ln(72) for eˣ = 72 and x = ln(124)/3 for e³ˣ = 124.

To solve these equations using natural logarithm, we can use the following rules:

Using these rules, we can solve the given equations as follows:

2eˣ = 4

Divide both sides by 2 to get

eˣ = 2.

Take the natural logarithm of both sides to get

ln(eˣ) = ln(2).

Using rule 1 above, we can simplify ln(eˣ) to x, and we get

x = ln(2).

e⁴ˣ = 25

4x = ln(25).

Divide both sides by 4 to get

x = ln(25)/4.

eˣ = 72

Take the natural logarithm of both sides to get

x = ln(72).

e³ˣ = 124

Take the natural logarithm of both sides to get

3x = ln(124).

Divide both sides by 3 to get

x = ln(124)/3.

For the second set of equations, we use the same rule as above

So, we have

ln(x - 3) = 2

x - 3 = e²

x = e² + 3.

x ≈ 10.389.

Therefore, the solution is x ≈ 10.389.

ln(2t) = 4

2t = e⁴

t = 0.5 * e⁴

t ≈ 27.299.

Therefore, the solution is t ≈ 27.299.

Read more about logarithm at

https://brainly.com/question/24160402

#SPJ1

Answer:y - x=1

Step-by-step explanation:

Answer: 1.5 : 6 = 1 : 4

Step-by-step explanation: Change values to whole numbers.

Convert any decimal numbers to integers by multiplying both sides by 101 = 10 to eliminate all, 1, decimal places.

We then have:

1.5 : 6 = 15 : 60

Try to reduce the ratio further with the greatest common factor (GCF).

The GCF of 15 and 60 is 15

Divide both terms by the GCF, 15:

15 ÷ 15 = 1

60 ÷ 15 = 4

The ratio 15 : 60 can be reduced to lowest terms by dividing both terms by the GCF = 15 :

15 : 60 = 1 : 4

Therefore:

1.5 : 6 = 1 : 4

Answer:

length= 125

width= 100

Step-by-step explanation:

let width have a length of x m

therefore length= (x+25)m

perimeter=2(length +width)

p=2((x+25)+x)

p=4x+50

but we have perimeter to be 450,, we equate it to 4x+50 above,

450=4x+50

4x=400

x=100 m

length= 125

width= 100

Answer:

You ready chose the answer

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

The equation to use for CONTINUOUS compounding is :

FV = PV e^(it)

18532.08 = 8327 * e^( i*10)        where i is the interest in decimal form

18532.08/8327  = e^(10i)

2.225541 = e^(10i)             now take natural log  (ln) of both sides to get

.8000 = 10i

i = .08     or 8% interest

A function showing the value of the account after t years, where the annual growth rate can be found from a constant in the function is f(t) = 2900 × (1.0624)^t and APY is 6.24%.

Compound interest in simple words is the interest earning for your savings with the interest which those savings earn.

The formula for calculating the amount in Compound Interest is,

A = P( 1 + \(\frac{r}{n}\) )ⁿᵇ

where A is the amount, P is the principal, r is the rate of interest, n is the number of times interest compounded in a year and b is the number of years.

Here, P = $2900, r = 6.1% = 0.061, n = 4 (quarterly) and b = t years

A = 2900 (1 + \(\frac{0.061}{4}\))^4t

A = 2900 (1.0153)^4t

A = 2900 × (1.0624)^t

So A can be said as a function of t.

f(t) = 2900 × (1.0624)^t

Percentage of growth per year (APY) = ( 1 + \(\frac{r}{n}\) )ⁿ - 1

                                                              = (1 + \(\frac{0.061}{4}\))⁴ - 1

                                                              = 1.0624 - 1

                                                              = 0.0624 = 6.24%

Hence the function of the value of the account after t years is f(t) = 2900 × (1.0624)^t, where the value 1.0624 is a constant.

Percentage of growth per year is 6.24%.

To learn more about Compound Interest, click:

https://brainly.com/question/29335425

#SPJ1

In the provided text is a questionnaire or form related to a research tool for assessing a campaign in the community.

The first question asks whether the campaign pursues its aims, with the options of answering "YES" or "NO." The respondent is then instructed to elaborate on their answer.

A questionnaire is a research tool   used to collect data by presenting a series of questions to respondents,typically in a written format.

Questionnaires are an important research tool as they allow researchers to gather   large amounts of data from a large number of participants in   a standardized and efficient manner.

They provide a structured approach to collecting information,allowing for easy analysis and comparison   of responses.

Questionnaires can be used in various   research settings and are particularly useful for collecting quantitative data,measuring attitudes, opinions, behaviors, and gathering demographic information.

Learn more about Research Tool at:

https://brainly.com/question/28982692

#SPJ1

got u

Step-by-step explanation:

the answer is 10x+20

Answer:

The graph of the line \(y=\frac{2}{3}x+3\) that contains the point (-3,1) with a slope of 2/3 is attached below.

Step-by-step explanation:

We know that the slop-intercept form of the equation is

\(y=mx+b\)

where m is the slope, and b is the y-intercept.

Given the slope = m = 2/3, and point (-3, 1)

\(1=\frac{2}{3}\left(-3\right)+b\)

\(-\frac{2}{3}\cdot \:3+b=1\)

\(-2+b=1\)

\(b=3\)

so the equation of line will be:

\(y=mx+b\)

\(y=\frac{2}{3}x+3\)

Also, the graph of the line \(y=\frac{2}{3}x+3\) that contains the point (-3,1) with a slope of 2/3 is attached below.

Answer:

1. wire is approx. 143.96 ft

2. pole is approx. 106.55 ft

Step-by-step explanation:

Mapping the information on the SOHCAHTOA picture below:

Φ = 46

wire = hypotenuse

adjacent side = 100

CAH is most suitable:

cos 46° = 100/wire => wire = 100/cos 46 ≈ 143.96

pole = opposite side + 3

TOA is most suitable:

tan 46° = (pole-3)/100 => pole = 3 + 100 * tan 46 ≈ 106.55

Answer:

One convergence criteria that is useful here is that, if aₙ is the n-th term of this sequence, then we must have:

Iaₙ₊₁I < IaₙI

This means that the absolute value of the terms must decrease as n increases.

Then we must have:

\(\frac{(x -2)^n}{n*3^n} > \frac{(x -2 )^{n+1}}{(n + 1)*3^{n+1}}\)

We can write this as:

\(\frac{(x -2)^n}{n*3^n} > \frac{(x -2 )^{n+1}}{(n + 1)*3^{n+1}} = \frac{(x -2)^n}{(n + 1)*3^n} * \frac{(x - 2)}{3}\)

If we assume that n is a really big number, then:

n + 1 ≈ 1

And we can write:

\(\frac{(x -2)^n}{n*3^n} > \frac{(x -2)^n}{(n)*3^n} * \frac{(x - 2)}{3}\)

Then we have the inequality

\(1 > (x - 2)/3\)

And remember that this must be in absolute value, then we will have that:

-1 < (x - 2)/3 < 1

-3 < x - 2 < 3

-3 + 2 < x < 3 + 2

-1 < x < 5

The first option looks like this, but it uses the symbols ≤≥, so it is not the same as this, then the correct option will be the second.

Answer:

True

Step-by-step explanation:

Slope:

The slope of an equation represents how the y value changes as the x values changes, defined as: \(\frac{\text{change in y}}{\text{change in x}}\), so the slope of 60 can be represented as: \(\frac{60}{1}\), which tells us the amount of water (y-axis) increases by 60 units each hour (x-axis), or in other words, the rate at which the amount of water changes each hour.

Step-by-step explanation:

Option F is correct. it equals to root 2

Check the picture below.

Given number is 2.703.

Its a decimal number

Hence three is not the hundredth place holder.

See below

\(\\ \sf\longmapsto 3\times \dfrac{1}{1000}\)

Answer: Half of them are even and half of them are odd.

Step-by-step explanation:

The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.

The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.

Therefore, out of the given numbers, half of them are even and half of them are odd.

________________________________________________________

Answer:

150

Step-by-step explanation:

To solve this problem, first start setting up the equation.

Start with bob first - this is the easiest. Let x = bob

To get the part for susie - he has $24 more than twice the amount of bob, so his part of the equation would be set up as: 2x + 24

Combine these parts:

x + (2x + 24)

Combined they have $150, so you would set the equation above equal to 150

x + (2x + 24) = 150

Combine like terms:

3x + 24 = 150

Solve the equation for x

3x   +   24   =   150

      -   24         -24

3x               =   126      isolate x by itself on one side of the equation

divide both sides by 3 to get x by itself

3x    =    126

3              3

x    =   42

Now that you have solved for x, you know the amount that bob has... $42

With this information you can substitute 42 for x in the equation that was created for susie

2x + 24   would now by (2*42) + 24  which is $108

So, the amount that bob has is $42 and susie has $108

You can double check your work by adding $42 and $108 together to see if you get $150 (which you do)

Hope this helps!!!

Answer: 252 i think i tried and i think its right

Answer: B

Step-by-step explanation:

Substitution method

solve the equation for Y by putting the variable on the left. -3 = y - 2x would become y = 2x - 3

Plug Y into the top equation. 2(2x - 3) + 6 =4x

4x - 6 + 6 = 4x

Combine like terms

4x - 0 = 4x

4x = 4x

Infinite Solutions

The value of x is -15

Functions are simply defined as expressions or rules showing the relationship between two variables.

These variables are listed as;

From the information given, we have that;

g(x) =x  -1, if g(x) = -16

Now, we have to equate the two functions, we get;

x - 1 = -16

collect the like terms, we get;

x =-16 + 1

add the values, we have;

x = -15

Learn more about functions at: https://brainly.com/question/11624077

#SPJ1

The complete question:

Given g(x) =x  -1, if g(x) = -16, find x.

Answer:

1 solution

Step-by-step explanation:

-5 - 11r = 6 ( -2r - 3 )

Distribute:

-5 - 11r = -12r - 18

Add 18 to both sides:

13 - 11r = -12r

Add -11r to both sides:

13 = -r

Divide each side by -1:

-13 = r

1 is your answer

Hope this helps!

Add the amount it was reduced to the new price:

3.49 + 31.38 = 34.87

Original price = $34.87

Answer:

When finding the unknown original price, add the sale reduction to the new sale price to get the old sale price.

\(3.49 + 31.38 = 34.87\)

Therefore, the original sales price was 34.87

Answer:

Rs 1000.97

Step-by-step explanation:

x = original price

new price =   x (1.0909)(1.0833)(1.077) = 1274

                         x = Rs 1000.97

Linear Scale Factor:

1) Enlargement. Scale Factor = 18/6 = 3

2) Reduction. Scale factor = 6/12 = 1/2

The expression with the correct coefficients in each block is given as follows:

20x³ + 0x² - 7x.

The functions in the context of this problem are defined as follows:

The operation is given as follows:

f(x)g(x) + h(x).

Hence, to obtain the resultant function, we apply the definitions into the operation and the simplify, applying the distributive property and combining the like terms, as follows:

4x(5x² - 4) + 9x = 20x³ - 16x + 9x = 20x³ - 7x.

As there is no x² term, the coefficient of zero multiplies the term x².

More can be learned about functions at https://brainly.com/question/31895757

#SPJ1

Answer:

Step-by-step explanation:

1. The measurement is actual and should be considered as such. Estimate is approximate most of the time.

2. The error is:

3. Percent error:

Answer:

3.75 inches is the correct answer..

Answer:

A. 3.75 inches

Step-by-step explanation:

The question is asking for the amount of inches not kilometers, so options B and D are automatically incorrect. I took the three inches and divided it by the four kilometers to kind inches per kilometer. The times the inches by five to get the correct answer;

3 inches = 4 kilometers

3 / 4 = 0.75

0.75 = 1 kilometer

0.75 x 5 = 3.75

3.75 inches = 5 kilometers

I hope this helps!