solve the following exponential equation. express irrational solutions in exact form and as a decimal rounded to three decimal places. 3^1-4x = 4x

Answers

Answer 1

The irrational solution of an exponential function, 3⁽¹⁻⁴ˣ⁾ = 4ˣ in exact form, is equals to the 0.190 in a decimal rounded to three decimal places.

Exponential function:

The exponential function is a mathematical function of the form f(x) = aˣ , where "x" is a variable and "a" is a constant called the base of the function, which must be greater than 0. The most commonly used exponential base is the transcendental number e, which is approximately equal to 2.71828.

We have given an exponential equation is

3⁽¹⁻⁴ˣ⁾ = 4ˣ

Require to solve this Exponential equation.

Now, 3⁽¹⁻⁴ˣ⁾= 4ˣ

taking logarithm both sides we get,

ln ( 3⁽¹⁻⁴ˣ⁾ ) = ln(4ˣ)

=> (1-4x) ln(3) = xln(4) [using ln( aˣ)= x ln(a) ]

=> ln (3) - 4x ln (3) = x ln (4)

=> ln (3) = x ln(4) + 4x ln(3)

=> ln (3) = x[ ln (4) + 4 ln (3) ]

=> x = ln (3) / [ ln (4) + 4 ln (3) ]

=> x ~ 0.190

Therefore, solution set is ln (3) / [ ln (4) + 4 ln (3) ].

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Solve The Following Exponential Equation. Express Irrational Solutions In Exact Form And As A Decimal

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If -3y - 6 + 7y = 14, then y =?

Answers

Answer:

you solve for y and you'll get the final answe

Answer:

5

Step-by-step explanation:

- 3y - 6 + 7y = 14

7y - 3y = 14 + 6

4y = 20

y = 20 / 4

y = 5

Which number does the blue dot represent on the number line?

Answers

it represents C -12
The blue dot represents -12, the line is going forward 3 points and back 3. So each point is worth 3 points. Moving back 4 points equals -12.

can u tell me is this test important or not

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Answer:

Yes, indeed it is one of the most important examinations.

33x + 55 > 17 solution

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Answer:

Step-by-step explanation:

33x > -38

x > -38/33

What is the total surface area of a rectangular prism whose net is shown 19 in. 17in. 6.in.

Answers

Answer:

1078in

Step-by-step explanation:

Surface area =2(wl+hl+hw)

2·(17·19+6·19+6·17)=1078in

A machine used to fill beverage cans is supposed to put exactly 12 ounces of beverage in each can, but the actual amount varies. The standard deviation of fill volumes is 0.05 ounce. How large a sample of cans must be selected to estimate the population mean fill volume with a 95% confidence interval that has a margin of error of 0.008 ounce? Round your answer UP to the nearest integer.

Answers

Answer:

A sample of 151 cans must be selected.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

The standard deviation of fill volumes is 0.05 ounce.

This means that [tex]\sigma = 0.05[/tex]

How large a sample of cans must be selected to estimate the population mean fill volume with a 95% confidence interval that has a margin of error of 0.008 ounce?

We need a sample of n.

n is found when M = 0.008. So

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]0.008 = 1.96\frac{0.05}{\sqrt{n}}[/tex]

[tex]0.008\sqrt{n} = 1.96*0.05[/tex]

[tex]\sqrt{n} = \frac{1.96*0.05}{0.008}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.96*0.05}{0.008})^2[/tex]

[tex]n = 150.1[/tex]

Rounding up:

A sample of 151 cans must be selected.

5
Given volume of rectangular prism is 432 m.
h
12 m
4 m
Find height?

Answers

Answer:

9m

Step-by-step explanation:

volume = length x width x height so

432 / 12 / 4 = 9


1. It takes 45 minutes for two people to clean six identical rooms. How
long would it take five people to clean 20 of the same rooms at the same
rate?​

Answers

Answer:

To clean 20 identical rooms 5 people will take 1 hour .

Hope It Helps You.

Help please I’ll give the brainliest

Answers

Answer:

Step-by-step explanation:

a)

5.75x + 3.25y ≤ 625

b)

55 youth shirts

5.75x + 3.25 (55) ≤ 625

5.75x + 178.75 ≤ 625

5.75x  ≤ 446.25

x ≤ 77.6086....

so 77 adult t-shirts

A rectangle measures 2 1/2 meters by 1 3/4 meters. What is its area?

Answers

Answer:

4 3/8

Step-by-step explanation:

1. We can use the formula

Area = L (length) x W (width)

2. The area is unknown so we can substitute it for a

  The length and width are both known, so we can plug them in.

a= 2 1/2 x 1 3/4

3. Solve by multiplying

a=4 3/8

Area of the rectangle is [tex]4\frac{3}{8}[/tex] meter square

What is Area?

Area is the quantity that expresses the extent of a region on the plane or on a curved surface

What is rectangle?

Rectangle is a quadrilateral with four right angles

Area of the rectangle = Length × Width

Length of the rectangle = [tex]2\frac{1}{2} =\frac{5}{2}[/tex]

Width of the rectangle = [tex]1\frac{3}{4}=\frac{7}{4}[/tex]

Area of the rectangle = [tex](\frac{5}{2}).(\frac{7}{4})=\frac{35}{8}=4\frac{3}{8}[/tex] meter square

Hence, the area of the rectangle is [tex]4\frac{3}{8}[/tex] meter square

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Can someone help me pls?

Answers

Answer:

x = 17.2

Step-by-step explanation:

cos 35 = x/21

0.8192(21) = x

x = 17.2

Which is the equation of a line perpendiculat to the line with the equation 3x + 4y = 7?

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Answer:

What do you need to know?

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Answer:

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There 25 pieces what is the probability of 1st pulling out a circle putting it back then pulling out a square

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help me answer this question please​

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Answer:

x = 12 ft, y = 24 ft

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Step-by-step explanation:

12 x 24 = 288 ft²

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At Yogurtland, the scale says that Brooke has 9 ounces of chocolate yogurt in her cup. Brielle's yogurt weighs 13 ounces. How many pounds of frozen yogurt did they buy altogether? Express your answer as a mixed number.

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Answer:

1.375 pounds

Step-by-step explanation:

have a nice night mate

:)

mark brainliest please :)

solve for a. 13/a= 104/152

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13/a = 0.684
0.684a=13
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What is the length of each support beam?

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Answer:

(b )

Step-by-step explanation:

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Answer:

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Step-by-step explanation:

Easy question look at the photo.

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SSS

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Answer:

Step-by-step explanation:

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Answer:

The answer is x = 8

Step-by-step explanation:

In 1995, there were 20 wolves in Yellowstone. In 2005 there were 120. Find the percent of change.

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Answer:

500% increase

Step-by-step explanation:

volume of a cylindrical can of juice is 500cm3 and the diameter of its base is 8 cm find the height of the can of pineapple juice

Answers

Answer:

23.864cm

Step-by-step explanation:

volume of a cylinder is found by using the above formula pie × radius² × height = AREA

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600÷25.143 = 23.864cm

Height = 23.864cm

) Cars are parked in line as they come off the assembly lines. There are three models: red cars which take up 2 spaces, blue cars which also take up 2 spaces, and green cars which take up only 1 space. Let an be the number of ways of filling the first n parking spaces with red, blue and green cars.

Answers

Answer:

Hello your question has some missing information below is the complete question

answer :

[tex]a_{n} = a_{n-2} + a_{n-2} + a_{n-1}[/tex]

Step-by-step explanation:

Red car and Blue car take up 2 spaces each

Green cars take up 1 space

lets determine the number of ways of filling up the parking spaces

i) First lets assume the last space is filled by Green car then there will be [tex]n^{th}[/tex] space occupied hence there will be ( n - 1 ) spaces left to be filled in [tex]a_{n-1}[/tex] ways

ii) lets assume the last space is filled by either a Red car or a Blue car then there will be [tex]n^{th} + ( n -1 )^{st}[/tex]  parking space occupied hence there will be

( n - 2 ) spaces left to be filled in [tex]a_{n-2}[/tex] ways

Hence A closed formula for [tex]a_{n}[/tex]

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HURRY IM TIMED ON EDGE Which is the best estimate for the percent equivalent to 3/8?
26%
279%
37%
38%

Answers

Answer:

C.) 37%

Step-by-step explanation:

[tex]\frac{3}{8}[/tex] as a percentage is 37.5%

[tex] \purple{ \huge{\mathtt{✨Answer✨}}}[/tex]

C. 37%

Which of the following statements is NOT true for figures and their dilation when the origin is the center of dilation?

Answers

Do u have certain question?

Answer:

Here are two ways to help with dilation as cm counting can help and so can division.

Step-by-step explanation:

1. Image of a Button enlarged 5 times and shows it is 6cm image is divided by 5 and shows a decimal 1.2   etc. so you write 1.2cm

2. Coordinates shown of A : B : C can be found from their cm measurement we measure the AB and BC measure being; Adjacent (m1) and Hypotenuse (m2) in cm and include any decimals. alternately if they are difficult to count then we take coordinates of AB BC or any adjacent and hypotenuse coordinates to suit y2-y1 / x2-x1 and enter those as our measure and just ensure they are turned positive to enter into calculator.

Note m = measure here found after the above is done.

Then Calculate Adjacent / Hypotenuse = m1/m2 = multiplier

Then input the multiplier to cos-1 found on your shift button.

For Tom's savings account, the interest earned varies jointly with the principal and amount of time (in years) since opening the account. If Tom opened the account 3 years ago with $1,200 and earned $144 in interest, how much interest will he have earned 8 years after opening the account?​

Answers

Answer: 384 or 528 depending if you have to add the interest he already earned

Step-by-step explanation:

which statement about this triangle is true?
tan 0= 4/5
sin 0 = 3/5
cos 0 = 3/5
sin 0 = 3/4

Answers

Answer:

I'm not sure but I believe it is than 0=4/5

Consider the probability that no less than 95 out of 152 registered voters will vote in the presidential election. Assume the probability that a given registered voter will vote in the presidential election is 61%. Approximate the probability using the normal distribution. Round your answer to four decimal places.

Answers

Answer:

0.3821 = 38.21% probability that no less than 95 out of 152 registered voters will vote in the presidential election.

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Normal probability distribution

Problems of normally distributed distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].

Assume the probability that a given registered voter will vote in the presidential election is 61%.

This means that [tex]p = 0.61[/tex]

152 registed voters:

This means that [tex]n = 152[/tex]

Mean and Standard deviation:

[tex]\mu = E(X) = 152*0.61 = 92.72[/tex]

[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{152*0.61*0.39} = 6.01[/tex]

Probability that no less than 95 out of 152 registered voters will vote in the presidential election.

This is, using continuity correction, [tex]P(X \geq 95 - 0.5) = P(X \geq 94.5)[/tex], which is 1 subtracted by the pvalue of Z when X = 94.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{94.5 - 92.72}{6.01}[/tex]

[tex]Z = 0.3[/tex]

[tex]Z = 0.3[/tex] has a pvalue of 0.6179

1 - 0.6179 = 0.3821

0.3821 = 38.21% probability that no less than 95 out of 152 registered voters will vote in the presidential election.

a number n increased by 18​

Answers

Answer:

n+18

Step-by-step explanation:

Answer: n+18

Step-by-step explanation:

CONCEPT:

- a increased by b=a+b

- a decreased by b= a-b

- a multiply by b=ab

- a divided by b=a/b

SOLVE:

A number n increased by 18

(n) increased by (18)

n+18

Hope this helps!! :)

Please let me know if you have any questions

Plz help me the question is in the picture

Answers

10.5 or 10 1/2 basically ten and a half
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