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
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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Related Questions
) 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]
[tex]a_{n} = a_{n-2} + a_{n-2} + a_{n-1}[/tex]
where : a1 = 1 way , a2 = 3 ways
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
help me answer this question please
Answers
Answer:
x = 12 ft, y = 24 ft
12 ft x 24 ft
Step-by-step explanation:
12 x 24 = 288 ft²
2(12) + 24 = 48 ft fencing
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
22/7 × 8 × h = 600cm³
25.143h= 600cm³
600÷25.143 = 23.864cm
Height = 23.864cm
Which number does the blue dot represent on the number line?
Answers
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.
What is the length of each support beam?
Answers
Answer:
(b )
Step-by-step explanation:
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can u tell me is this test important or not
Answers
Answer:
Yes, indeed it is one of the most important examinations.
PLEASE HELP FAST
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
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%
What is the answer to this
Answers
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.
Answers
Answer:
500% increase
Step-by-step explanation:
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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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.
Answers
Answer:
1.375 pounds
Step-by-step explanation:
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33x + 55 > 17 solution
Answers
Answer:
Step-by-step explanation:
33x > -38
x > -38/33
Plz help me the question is in the picture
Answers
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 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
Could I get some help with this question? Thanks
Answers
Answer:
I am unable to see the picture if you type it i can possibly help
Step-by-step explanation:
Which of the following statements is NOT true for figures and their dilation when the origin is the center of dilation?
Answers
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.
Which is the equation of a line perpendiculat to the line with the equation 3x + 4y = 7?
Answers
Answer:
What do you need to know?
Step-by-step explanation:
Answer:
Step-by-step explanation:
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:
solve for a. 13/a= 104/152
Answers
0.684a=13
a= 19
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
Easy question look at the photo.
Answers
Answer:
SSS
Step-by-step explanation:
Answer:
Step-by-step explanation:
sss
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
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
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.
There 25 pieces what is the probability of 1st pulling out a circle putting it back then pulling out a square
Answers
Answer:
3.6
Step-by-step explanation: