solve 12^x-2=20 round to the nearest ten-thousandth? help, please!
The solution to the equation 12^x - 2 = 20, when solved for x and rounded to the nearest ten-thousandth, is x = 1.4624.
Explanation:To solve the equation 12^x - 2 = 20, we first need to isolate the exponential term. This can be done by adding 2 to both sides of the equation resulting in 12^x = 22. Next, we take the logarithm of both sides to solve for x. We can use any logarithmic base, but common practice is to use base 10 or the natural logarithm (base e). The next steps are:
Take the logarithm of both sides: log(12^x) = log(22).Apply the exponent rule of logarithms: x · log(12) = log(22).Divide both sides by log(12) to solve for x: x = log(22) / log(12).Use a calculator to find the value of x and round to the nearest ten-thousandth.Calculating the value on a calculator gives us x ≈ 1.4624. Therefore, the solution to the equation, rounded to the nearest ten-thousandth, is x = 1.4624.
The correct answer is option (b) "x ≈ 1.2056."
To solve the equation [tex]\(12^{(x-2)} = 20\)[/tex], we can take the logarithm of both sides.
Let's use the natural logarithm (ln) for this:
[tex]\[ \ln(12^{(x-2)}) = \ln(20) \][/tex]
Using the logarithm property [tex]\( \log_a(b^c) = c \cdot \log_a(b) \)[/tex], we can rewrite the left side:
[tex]\[ (x-2) \cdot \ln(12) = \ln(20) \][/tex]
Now, solve for (x):
[tex]\begin{aligned}& x-2=\frac{\ln (20)}{\ln (12)} \\& x=\frac{\ln (20)}{\ln (12)}+2\end{aligned}[/tex]
Now, calculate the value:
[tex]\begin{aligned}& x \approx \frac{\ln (20)}{\ln (12)}+2 \\& x \approx \frac{2.9957}{2.4849}+2 \\& x \approx 1.2056\end{aligned}[/tex]
So, the solution to the equation is approximately [tex]\( x \approx 1.2056 \)[/tex]
Complete Question:
Solve [tex]\(12^{(x-2)} = 20\)[/tex]. Round to the nearest ten-thousandth.
a. x ≈ 1.0792
b. x ≈ 1.2056
c. x ≈ 3.2056
d. x ≈ 1.3010
Natasha has a gross income of $66,429. She can make adjustments of $14,490 for business losses, $3,584 for business expenses, and $4,813 for constitutions to her retirement plan. What's Natasha's adjusted gross income?
A. $109,971
B. $22,887
C. $72,522
D. $43.542
Answer: D. $43,542
Step-by-step explanation:
The adjusted gross income of any person is person's gross income minus the certain deductions.
Given : Natasha has a gross income of $66,429.
She can make adjustments of $14,490 for business losses, $3,584 for business expenses, and $4,813 for constitutions to her retirement plan.
Total deductions : [tex]\$14,490 +\$3,584 +\$4,813=\$22,887[/tex]
Now, Natasha's adjusted gross income will be :-
[tex]\text{Gross income - Total deductions}[/tex]
i.e. [tex]\$66,429-\$22,887=\$43,542[/tex]
Hence, Natasha's adjusted gross income = $43,542
Monica paid sales tax of 1.50$ when she bought a new bike helmet.if the sales tax rate was 5% how much did the store charge for the helmet before tax
Which shows the correct substitution of the values a, b, and c from the equation –2 = –x + x2 – 4 into the quadratic formula?
The correct answer is D. on edg
Shane and his family go to the movie theatre and buys 6 tickets for $12 each. then they spend a total of $31 for popcorn and drinks. how much did shane and his family spend for tickets, popcorn, and drinks at the movie theatre?
Shane and his family spent a total of $103 at the movie theatre, which includes the cost of 6 tickets at $12 each and $31 on popcorn and drinks.
Explanation:Shane and his family bought 6 tickets for $12 each, thus the total cost of the tickets is 6 * $12 which equals $72. Afterwards, they spent an additional $31 on popcorn and drinks. To find out how much they spent altogether at the movie theatre, we have to add the cost of the tickets and the cost of the popcorn and drinks. Therefore, $72 (for the tickets) + $31 (for the snacks) = $103. So, Shane and his family spent a total of $103 at the movie theatre.
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find the value of the polygon. the polygon has 6 interior angles 2 of them are y and 4 of them are (2Y-20)
Which ratio is equal to 5/6 and
Which ratio is not equal to 4/9? ...?
Maya has 5 over 6 cup of ice cream. how many 1 over 4-cup servings are in 5 over 6 cup of ice cream?
there are [tex]\( \frac{10}{3} \) or \( 3 \frac{1}{3} \) servings of \( \frac{1}{4} \)-cup in \( \frac{5}{6} \)[/tex] cup of ice cream.
To find out how many [tex]\( \frac{1}{4} \)-cup servings are in \( \frac{5}{6} \)[/tex] cup of ice cream, we need to divide [tex]\( \frac{5}{6} \) by \( \frac{1}{4} \)[/tex].
We can do this by converting [tex]\( \frac{5}{6} \)[/tex] to have the same denominator as [tex]\( \frac{1}{4} \)[/tex], which is 6, and then dividing:
[tex]\[ \frac{5}{6} \div \frac{1}{4} \][/tex]
To make the denominators the same, we multiply both the numerator and denominator of [tex]\( \frac{5}{6} \) by \( 4 \):[/tex]
[tex]\[ \frac{5 \times 4}{6 \times 4} \div \frac{1}{4} \][/tex]
[tex]\[ = \frac{20}{24} \div \frac{1}{4} \][/tex]
Now, we can divide [tex]\( \frac{20}{24} \) by \( \frac{1}{4} \):[/tex]
[tex]\[ \frac{20}{24} \div \frac{1}{4} \][/tex]
[tex]\[ = \frac{20}{24} \times \frac{4}{1} \][/tex]
[tex]\[ = \frac{20 \times 4}{24 \times 1} \][/tex]
[tex]\[ = \frac{80}{24} \][/tex]
Now, we simplify the fraction:
[tex]\[ \frac{80}{24} = \frac{10 \times 8}{12 \times 2} \][/tex]
[tex]\[ = \frac{10}{3} \][/tex]
Therefore, there are [tex]\( \frac{10}{3} \) or \( 3 \frac{1}{3} \) servings of \( \frac{1}{4} \)-cup in \( \frac{5}{6} \)[/tex] cup of ice cream.
A company makes boxes of cereal. A box usually contains 450 grams of cereal. Here are two options for a special offer. Option A 20% more cereal Option B usual amount of cereal 15% off the price.
Which option is best for the customer
A percentage is a way to describe a part of a whole. The best option for the customer to buy is option A.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
Let the cost price of a cereal box be represented by x.
Given that the box usually contains 450 grams of cereal. Therefore, the unit rate for each option can be written as,
Option A
Weight of cereal = 20% more cereal
= 450 grams + 20% of 450 grams
= 450 grams + 90 grams
= 540 grams
Unit rate for option A = $x / 540 grams
Option B
Cost price of cereal = 15% off the price
= x - 15% of x
= x + 0.15x
= 0.85x
Unit rate for option A = $0.85x / 450 grams
Assume that option A is good. Now, if we subtract unit rate of option B from unit rate of option A then two of the cases are possible, if the value of the result is positive then the unit rate of option A is bigger while if the value is negative unit rate of option B is bigger.
Difference = (x/540) - (0.85x/450)
= (450x - 459x)/243000
= -9x/243,000
= -x/27,000
Further, since the difference is negative, therefore, the unit rate of option B is bigger. But since the value of option B is bigger it is costly and not the correct option to buy.
Hence, the best option for the customer to buy is option A.
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Instructions:Select the correct answer from each drop-down menu.
Angle θ lies in the second quadrant, and sin θ = 35.
cos θ = -4/5 -3/5 3/5 4/5
tan θ = -4/3 -3/4 3/4 4/3
What do I write ?? Someone please help me
Answer:
WrItE wHaT yOu FeElLlLlL
Step-by-step explanation:
The probability that an airplane flight departs on time is 0.89 The probability that a flight arrives on time is 0.87 The probability that a flight departs and arrives on time is 0.81
To answer the questions, we need to use the concepts of probability.
Explanation:To answer the questions, we need to use the concepts of probability.
a. The number of airplanes arrive and depart the airport per hour can be calculated by multiplying the probabilities of a flight departing and arriving on time. Although the exact numbers are not given, the probability of a flight departing and arriving on time is 0.81, which can be used as an estimate.
b. To find the probability that there are exactly 100 arrivals and departures in one hour, we need to use the concept of the binomial distribution. However, we don't have enough information to calculate the probability.
c. To find the probability that there are at most 100 arrivals and departures in one hour, we can use the concept of the cumulative distribution function of the binomial distribution. Again, we don't have enough information to calculate the probability.
The question is about calculating probabilities and involves understanding conditional probability, probability distributions, and statistical methods. It requires more data to answer parts a, b, and c. The remaining parts of the question can be approached with standard statistical methods and concepts.
Explanation:The question pertains to the field of probability within mathematics and involves calculations based on given probabilities for airplane flights departing and arriving on time. The data presented involve conditional probabilities and the characteristics of certain probability distributions. It is essential to understand these concepts to solve the exercises provided. Unfortunately, the given information does not contain sufficient details to answer parts a, b, and c as they require additional specific data about the actual number of flights or arrivals and departures per hour. However, the remaining parts of the question can be approached with standard statistical methods such as using z-scores for normal distributions, applying properties of uniform distributions for waiting times, understanding the concept of rate-determining steps in a process, and conducting hypothesis tests about a population mean given a sample.
Use the given endpoint R and midpoint M of line RS to find the coordinates of the other endpoins.
R(6,0), M(0,2) ...?
James has 6 stamps in his stamp collection. Roy has 12 stamps in his stamp collection. James adds 2 stamps to his stamp collection. After James adds these stamps, what is the ratio of the number of stamps in James's collection to the number of stamps in Roy's collection
gradie dari persamaan garis 3(x-y) =x+5
Find the length of the segment indicated. Round your answer to the nearest tenth if necessary.
The value of x from the given circle is 4.6 units.
From the given figure, the radius is 9.7 units.
What is the circle?A circle is a two-dimensional figure formed by a set of points that are at a constant or at a fixed distance (radius) from a fixed point (center) on the plane. The fixed point is called the origin or center of the circle and the fixed distance of the points from the origin is called the radius.
Here,
9.7 =5.1+x
⇒ x=9.7-5.1
⇒ x=4.6 units
Therefore, the value of x from the given circle is 4.6 units.
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3x^2-18x+24
factor it out???
find the nonpermissible replacement for the variable n in this expression (n-8)/(n-8)
...?
In one week, a family spent $132.19 for groceries. they spent $150.06 the next week. if c represents the increase in their grocery bill from one week to the next, what is c?
a. $17.87
b. $27.87
c. $28.97
d. $282.25
What is the completely factored form of 3x^5 – 7x^4 + 6x^2 – 14x?
A. (x^4+2x)(3x-7)
B. x^4(3x-7)(2x-1)
C. x(x^3+2)(3x-7)
D. x(3x^4-7x^3+6x-14)
answer:
C. x(x^3+2)(3x-7)
hope this helps! :o)
If parallelogram JKLM is rotated 270° clockwise around the origin, what are the coordinates of the endpoints of the side congruent to side KL in the image parallelogram?
A. K’(-4, -6); L’(3, -3)
B. K’(-6, -4); L’(-3, -3)
C. K’(6, 4); L’(3, 3)
D. K’(-4, 6); L’(-3, -3)
Answer:
K′(−6, −4); L′(−3, −3)
Step-by-step explanation:
Got it right on the test
in order for RECT to be a rectangle, what must the value of x be?
Answer:
x = 21
Step-by-step explanation:
If RECT is a rectangle, each of its interior angles are right angles, 90°. Since ∠RTC is split into two angles, the sum of the two angles must be 90°. (Angles that add to 90° are called complementary angles).
∠RTC = ∠RTE + ∠ETC Formula for complementary angles
90 = 2x + 6 + 42 Substitute the angles
90 = 2x + 48 Combined like terms to simplify
Now isolate "x" to solve
90 - 48 = 2x + 48 - 48 Subtract 48 from both sides
42 = 2x
42/2 = 2x/2 Divide both sides by 2
x = 21
Therefore x is 21.
The label on the car's antifreeze container claims to protect the car between −30°C and 130°C. To convert Celsius temperature to Fahrenheit temperature, the formula is C = (F − 32). Write and solve the inequality to determine the Fahrenheit temperature range at which this antifreeze protects the car.
−30 > (F − 32) > 130; −22 > F > 266
−30 < (F − 32) < 130; −22 < F < 266
−30 < (F − 32); −22 < F
(F − 32) < 130; F < 266
The correct answer is B. I took the same test and the answer is B. :) Hope this helps!
Describe the key features of the parabola y2 = 8x.
Answer: The value of p is 2. The parabola opens to the right. The focus is at (2,0). The equation of the directrix is x=-2.
Step-by-step explanation:
Multiply. write in simplest form fraction 6 1 1\2
Breann solved the system of equations below. What mistake did she make in her work? (5 points)
2x + y = 5
x − 2y = 10
y = 5 − 2x
x − 2(5 − 2x) = 10
x − 10 + 4x = 10
5x − 10 = 10
5x = 20
x = 4
2(4) + y = 5
y = −3
She should have substituted 5 + 2x
She combined like terms incorrectly, it should have been 4x instead of 5x
She subtracted 10 from both sides instead of adding 10 to both sides
She made no mistake
Breann correctly solved the system of equations, combining like terms accurately to find x = 4 and y = -3.
Explanation:The mistake Breann made in her calculation was combining like terms incorrectly. When she substituted y with 5 - 2x into the second equation, she arrived at x - 10 + 4x = 10. The correct combination of like terms should be 5x, not 4x, leading to the correct step 5x - 10 = 10. All other steps in her solution are correctly executed. She correctly found the value of x to be 4, and using the first equation, she correctly determined the value of y to be -3.
Write two equivalent fractions for each. 1/2 and 4/5
Divide. Express your answer in lowest terms. You MUST show your work to receive credit for this problem.
-15/16 divided by (-3/4)
Choose the correct description of the graph of the compound inequality 3x + 1 > 10 and 4x 20.
A. A number line with an open circle on 3, a closed circle on 5, and shading in between.
B. A number line with an open circle on 3, shading to the left and a closed circle on 5, shading to the right
C. A number line with an closed circle on 3, shading to the left, and a open circle on 5, and shading to the right
D. A number line with a closed circle on 3, an open circle on 5, with shading in between.
we have in this problem
[tex] 3x+1 > 10 [/tex] ------> inequality [tex] 1 [/tex]
[tex] 4x \leq 20 [/tex] ------> inequality [tex] 2 [/tex]
Solve the inequality [tex] 1 [/tex]
[tex] 3x+1 > 10\\ 3x > 10-1\\ 3x > 9\\ x > 3 [/tex]
the solution is the interval------> (3,∞)
Solve the inequality [tex] 2 [/tex]
[tex] 4x \leq 20\\\\ x \leq \frac{20}{4} \\\\ x \leq 5 [/tex]
the solution is the interval------> (-∞,5]
Find the solution for the system
(3,∞) ∩ (-∞,5]--------> (3,5]
therefore
the answer is the option
A. A number line with an open circle on 3, a closed circle on 5, and shading in between.
Diff Eq dy/dx= (ycos(x))/(1+y^2) initial condition is y(0)=1 work below ...?