Answer:
To solve this equation, we first need to isolate the ln term on one side of the equation. To do this, we can subtract ln 4 from both sides to get:
ln 4 - ln x - ln 4 = 2 - ln 4
This simplifies to:
-ln x = 2 - ln 4
Next, we can add ln 4 to both sides to get:
-ln x + ln 4 = 2
This simplifies to:
ln 4 - ln x = 2
Now, we can apply the identity ln a - ln b = ln(a/b) to both sides of the equation to get:
ln(4/x) = 2
To solve for x, we can apply the inverse logarithm function (exp) to both sides:
4/x = exp(2)
This simplifies to:
x = 4/exp(2)
Finally, we can evaluate this to get the value of x:
x = 4/exp(2) = 4/7.38905609893065
So the solution is x = 4/7.38905609893065.
Step-by-step explanation:
1. Five-sixths of the students in a math class passed the first test. If there are 36 students in the class, how many did not pass the test? *
Answer:
(1/6) of the students did not pass.
Ans: (1/6)30 = 5 of the students did not pass
To solve this question, we need to first figure out, in fractional form, the number of students who did not pass. The problem tells us that 5/6 of the students passed. Therefore, we know that 1/6 of the students did not pass, because 5/6 + 1/6 = 1. So, all we need to do is multiply 1/6 by the total number of students:
1/6 * 36 = 6
So, 6 students did not pass.
convert logx8=2 to exponential form
Answer:
8 = x²
Step-by-step explanation:
Logarithmic form: logₓ(8) = 2
Exponential form: 8 = x²
Activity: Factor Theorem
Use the Remainder Theorem and Factor Theorem to determine whether the given
binomial is a factor of P(x).
P(x) = 9x³+ 6x - 40 - 2x² + 2x4; binomial: x + 5
the given problem.
The given polynomial is a factor of P(x) because P(-5)=0.
From the remainder theorem, how do you derive the factor theorem?The Remainder Theorem states that if a synthetic division of a polynomial by x = a results in a zero remainder, then x = an is a zero of the polynomial (thanks to the Remainder Theorem), and x an is also a factor of the polynomial (courtesy of the Factor Theorem).
How can you tell if P(x) is a factor of X C?The Factor Theorem states that x - c is only a factor of P(x) when P(c) = 0.
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Please pleaseeeee help me outtt, I need it quickkk will give brainliest
Answer:
-132
Step-by-step explanation:
Split the summation to make the starting value of
k equal to 1.
Answer:S6 = - 132
Step-by-step explanation:
Evaluate the following expression 12xy=2,y=4
Answer:
1/24
Step-by-step explanation:
Solve for y =4
48x=2
Huilan is 7 years older than Thomas. The sum of their ages is 79. What is Thomas’s age?
Answer:
To solve this problem, we can set up the following equation:
Huilan's age + Thomas's age = 79
Let H be Huilan's age and T be Thomas's age. We can then rewrite the equation as:
H + T = 79
We are told that Huilan is 7 years older than Thomas, so we can write the following equation:
H = T + 7
Substituting the second equation into the first equation, we get:
(T + 7) + T = 79
Combining like terms, we get:
2T + 7 = 79
Subtracting 7 from both sides, we get:
2T = 72
Dividing both sides by 2, we get:
T = 36
Therefore, Thomas's age is 36 years.
Step-by-step explanation:
Answer:
let Thomas age be a
there fore, hullans age is a+7
(a+7)+a=79
2a=79-7
2a=72
a=36
Ian is taking a true/false quiz that has four questions on it. The correct sequence of answers
is T, T, F, T. Ian has not studied and yet guesses all answers correctly- He decides he wants
to determine how likely this is to happen using a simulation. He decides to use a fair coin to
do the simulation.
Describe the design of a simulation that would allow Ian to determine how likely it would
be to guess all answers correctly on this quiz.
The design of a simulation that would allow Ian to determine how likely it would
be to guess all answers correctly on this quiz can be Illustrated through a coin.
How to design the simulation?Ian can design a simulation to determine the likelihood of guessing all answers correctly on the quiz by using a fair coin. He can flip the coin four times, with each flip representing a guess on the quiz. If the coin lands heads up, he marks it as a true answer, and if it lands tails up, he marks it as a false answer.
He can repeat this process a large number of times (e.g. 1000) and count the number of times that the sequence T, T, F, T is generated. The proportion of times that this sequence is generated out of the total number of simulations will be an estimate of the probability of guessing all answers correctly on the quiz by chance.
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If 4 people share a 1/2 pound chocolate bar, how much chocolate will each person receive?
Answer:
1/8 pound per person
Step-by-step explanation:
Question 5(Multiple Choice Worth 2 points)
(Sample Spaces LC)
A paper bag has seven colored marbles. The marbles are pink, red, green, blue, purple, yellow, and orange. List the sample space when choosing one marble.
A s= (1, 2, 3, 4, 5, 6
B s=(purple, pink, red, blue, green, orange, yellow}
C s=(g. r, b. y. o, p)
D s= (green, blue, yellow, orange, purple, red)
The sample space when choosing one marble will be B s=(purple, pink, red, blue, green, orange, yellow}
What is sample space?A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space. Events are the subset of possible experiment results. Depending on the experiment, a sample space may contain a variety of outcomes.
A paper bag has seven colored marbles. The marbles are pink, red, green, blue, purple, yellow, and orange. The sample space when choosing one marble will be all the colors. The correct option is B.
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(-3 squared +3) divided by
(10 – 6)
Answer:
research it many my answer will be wrong
3
Step-by-step explanation:
-3 square is 9, adding 3 you will have 12. 10-6 is 4. so dividing 12 by 4 would give you 3.
2) Insert the smallest
digit to make the
number divisible by 8
.
1039_
Answer:
it would be 10392
Step-by-step explanation:
10392÷8=1299
Answer:
10392
Step-by-step explanation:
10391 ÷ 8 = 1298.875
Not divisible by 8
10392 ÷ 8 = 1299
Divisible by 8
800 miles in 5 hours miles per hour
Find the cost of 12 items if the cost function is C(x) = 2x +12
Answer:
$36
Step-by-step explanation:
we need to find the cost of 12 items, and the function of determining the cost is C(x)=2x+12, where x is the number of items (the input value of the function)
we know that there are 12 items, so in this function, x=12
substitute x as 12 in the function; the x in C(x) also gets substituted as 12, as 12 is the input value and the value of C(x) is the output
C(12)=2(12)+12
multiply
C(12)=24+12
add
C(12)=36
that means, for 12 items, the cost will be $36
Johnny earns $15 per hour dog walking. He wants to earn at least $105 to buy a new
bike. At least how many hours does he need to work?
Answer:
it will take Johnny 7 hours
Step-by-step explanation:
It was easy, i divided 105 by 15 and got 7
Have a wonderful day :)
Answer:
7 hours
Step-by-step explanation:
15 * x = 105
--- ---
15 7
x=7
Evaluate the indefinite integral.
integar x4/1 + x^10 dx
Answer:
[tex]\int\ {\frac{x^4}{1 + x^{10}}} \, dx = \frac{1}{5}( \arctan(x^5)) + c[/tex]
Step-by-step explanation:
Given
[tex]\int\ {\frac{x^4}{1 + x^{10}}} \, dx[/tex]
Required
Integrate
We have:
[tex]\int\ {\frac{x^4}{1 + x^{10}}} \, dx[/tex]
Let
[tex]u = x^5[/tex]
Differentiate
[tex]\frac{du}{dx} = 5x^4[/tex]
Make dx the subject
[tex]dx = \frac{du}{5x^4}[/tex]
So, we have:
[tex]\int\ {\frac{x^4}{1 + x^{10}}} \, dx[/tex]
[tex]\int\ {\frac{x^4}{1 + x^{10}}} \, \frac{du}{5x^4}[/tex]
[tex]\frac{1}{5} \int\ {\frac{1}{1 + x^{10}}} \, du[/tex]
Express x^(10) as x^(5*2)
[tex]\frac{1}{5} \int\ {\frac{1}{1 + x^{5*2}}} \, du[/tex]
Rewrite as:
[tex]\frac{1}{5} \int\ {\frac{1}{1 + x^{5)^2}}} \, du[/tex]
Recall that: [tex]u = x^5[/tex]
[tex]\frac{1}{5} \int\ {\frac{1}{1 + u^2}}} \, du[/tex]
Integrate
[tex]\frac{1}{5} * \arctan(u) + c[/tex]
Substitute: [tex]u = x^5[/tex]
[tex]\frac{1}{5} * \arctan(x^5) + c[/tex]
Hence:
[tex]\int\ {\frac{x^4}{1 + x^{10}}} \, dx = \frac{1}{5}( \arctan(x^5)) + c[/tex]
what is the area of 12 1/2 feet long and 11 3/4 feet wide
now, we're assuming this is some rectangular area, and thus is simply the product of both quantities, let's change all mixed fractions to improper fractions firstly.
[tex]\stackrel{mixed}{12\frac{1}{2}}\implies \cfrac{12\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{25}{2}} ~\hfill \stackrel{mixed}{11\frac{3}{4}} \implies \cfrac{11\cdot 4+3}{4} \implies \stackrel{improper}{\cfrac{47}{4}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{25}{2}\cdot \cfrac{47}{4}\implies \cfrac{1175}{8}\implies 146\frac{7}{8}~ft^2[/tex]
Find the distance between the points
(-5/2, 9/4) and(-1/2,-3/4)
Give the exact distance and an approximate distance rounded to at least 2 decimal places.
Make sure to fully simplify any radicals in first answer
Answer:
Step-by-step explanation:
distance = [tex]\sqrt{(-5/2+1/2)^{2} +(9/4+3/4)^{2} }=\sqrt{13}[/tex]=3.61
a geometry class has a total of 25 students. the number of males is 5 more than the number of females. how many males and how many females are in the class
Answer:
10 females, 15 males
Step-by-step explanation:
Let the number of females in the class be x. As the number of males is 5 more than the number of females, which is x, the number of males would be shown as x+5.
The number of females plus the number of males equal 25, so we get this equation:
x + (x+5) = 25
x + x + 5 = 25
2x + 5 = 25
2x = 20
x = 10.
So, there are 10 females, and since there are 5 more males than females, there are 10 + 5 = 15 males.
A company employing 10,000 workers offers deluxe medical coverage (D), standard medical coverage (S) and economy medical coverage (E) to its employees. Of the employees, 30% have D, 60% have 5 and 10% have E. From past experience, the probability that an employee with D, will submit no claims during next year is 0.1. The corresponding probabilities for employees with S and E are 0.4 and 0.7 respectively. If an employee is selected at random;
a) What is the probability that the selected employee has standard coverage and will submit no
claim during next year? b) What is the probability that the selected employee will submit no claim during next year?
c) If the selected employee submits no claims during the next year, what is the probability that the employee has standard medical coverage (S)?
please give full answer
Evaluate 3a for a = 5
Answer:
Hello There!!
Step-by-step explanation:
The answer is 15 as 3a=3×a so 3×5=15.
hope this helps,have a great day!!
~Pinky~
Find the mean absolute deviation (MAD) of the data set of 0.4, 0.2, 0.4, 0.6
Answer:
Assuming data is from population, 0.1
Step-by-step explanation:
The expressions A, B, C, D, and E are left-hand sides of trigonometric identities. The expressions 1, 2, 3, 4, and 5 are right-hand side of identities. Match each of the left-hand sides below with the appropriate right-hand side.
A. tan(x)
B. cos(x)
C. sec(x)csc(x)
D. 1â(cos(x))^2/ cos(x)
E. 2sec(x)
1. sin(x)tan(x)
2. sin(x)sec(x)
3. tan(x)+cot(x)
4. cos(x)/1âsin(x)+1âsin(x)/cos(x)
5. sec(x)âsec(x)(sin(x))2
Answer:
[tex]A.\ \tan(x) \to 2.\ \sin(x) \sec(x)[/tex]
[tex]B.\ \cos(x) \to 5. \sec(x) - \sec(x)\sin^2(x)[/tex]
[tex]C.\ \sec(x)csc(x) \to 3. \tan(x) + \cot(x)[/tex]
[tex]D. \frac{1 - (cos(x))^2}{cos(x)} \to 1. \sin(x) \tan(x)[/tex]
[tex]E.\ 2\sec(x) \to\ 4.\ \frac{\cos(x)}{1 - \sin(x)} +\frac{1-\sin(x)}{\cos(x)}[/tex]
Step-by-step explanation:
Given
[tex]A.\ \tan(x)[/tex]
[tex]B.\ \cos(x)[/tex]
[tex]C.\ \sec(x)csc(x)[/tex]
[tex]D.\ \frac{1 - (cos(x))^2}{cos(x)}[/tex]
[tex]E.\ 2\sec(x)[/tex]
Required
Match the above with the appropriate identity from
[tex]1.\ \sin(x) \tan(x)[/tex]
[tex]2.\ \sin(x) \sec(x)[/tex]
[tex]3.\ \tan(x) + \cot(x)[/tex]
[tex]4.\ \frac{cos(x)}{1 - sin(x)} + \frac{1 - \sin(x)}{cos(x)}[/tex]
[tex]5.\ \sec(x) - \sec(x)(\sin(x))^2[/tex]
Solving (A):
[tex]A.\ \tan(x)[/tex]
In trigonometry,
[tex]\frac{sin(x)}{\cos(x)} = \tan(x)[/tex]
So, we have:
[tex]\tan(x) = \frac{\sin(x)}{\cos(x)}[/tex]
Split
[tex]\tan(x) = \sin(x) * \frac{1}{\cos(x)}[/tex]
In trigonometry
[tex]\frac{1}{\cos(x)} =sec(x)[/tex]
So, we have:
[tex]\tan(x) = \sin(x) * \sec(x)[/tex]
[tex]\tan(x) = \sin(x) \sec(x)[/tex] --- proved
Solving (b):
[tex]B.\ \cos(x)[/tex]
Multiply by [tex]\frac{\cos(x)}{\cos(x)}[/tex] --- an equivalent of 1
So, we have:
[tex]\cos(x) = \cos(x) * \frac{\cos(x)}{\cos(x)}[/tex]
[tex]\cos(x) = \frac{\cos^2(x)}{\cos(x)}[/tex]
In trigonometry:
[tex]\cos^2(x) = 1 - \sin^2(x)[/tex]
So, we have:
[tex]\cos(x) = \frac{1 - \sin^2(x)}{\cos(x)}[/tex]
Split
[tex]\cos(x) = \frac{1}{\cos(x)} - \frac{\sin^2(x)}{\cos(x)}[/tex]
Rewrite as:
[tex]\cos(x) = \frac{1}{\cos(x)} - \frac{1}{\cos(x)}*\sin^2(x)[/tex]
Express [tex]\frac{1}{\cos(x)}\ as\ \sec(x)[/tex]
[tex]\cos(x) = \sec(x) - \sec(x) * \sin^2(x)[/tex]
[tex]\cos(x) = \sec(x) - \sec(x)\sin^2(x)[/tex] --- proved
Solving (C):
[tex]C.\ \sec(x)csc(x)[/tex]
In trigonometry
[tex]\sec(x)= \frac{1}{\cos(x)}[/tex]
and
[tex]\csc(x)= \frac{1}{\sin(x)}[/tex]
So, we have:
[tex]\sec(x)csc(x) = \frac{1}{\cos(x)}*\frac{1}{\sin(x)}[/tex]
Multiply by [tex]\frac{\cos(x)}{\cos(x)}[/tex] --- an equivalent of 1
[tex]\sec(x)csc(x) = \frac{1}{\cos(x)}*\frac{1}{\sin(x)} * \frac{\cos(x)}{\cos(x)}[/tex]
[tex]\sec(x)csc(x) = \frac{1}{\cos^2(x)}*\frac{\cos(x)}{\sin(x)}[/tex]
Express [tex]\frac{1}{\cos^2(x)}\ as\ \sec^2(x)[/tex] and [tex]\frac{\cos(x)}{\sin(x)}\ as\ \frac{1}{\tan(x)}[/tex]
[tex]\sec(x)csc(x) = \sec^2(x)*\frac{1}{\tan(x)}[/tex]
[tex]\sec(x)csc(x) = \frac{\sec^2(x)}{\tan(x)}[/tex]
In trigonometry:
[tex]tan^2(x) + 1 =\sec^2(x)[/tex]
So, we have:
[tex]\sec(x)csc(x) = \frac{\tan^2(x) + 1}{\tan(x)}[/tex]
Split
[tex]\sec(x)csc(x) = \frac{\tan^2(x)}{\tan(x)} + \frac{1}{\tan(x)}[/tex]
Simplify
[tex]\sec(x)csc(x) = \tan(x) + \cot(x)[/tex] proved
Solving (D)
[tex]D.\ \frac{1 - (cos(x))^2}{cos(x)}[/tex]
Open bracket
[tex]\frac{1 - (cos(x))^2}{cos(x)} = \frac{1 - cos^2(x)}{cos(x)}[/tex]
[tex]1 - \cos^2(x) = \sin^2(x)[/tex]
So, we have:
[tex]\frac{1 - (cos(x))^2}{cos(x)} = \frac{sin^2(x)}{cos(x)}[/tex]
Split
[tex]\frac{1 - (cos(x))^2}{cos(x)} = \sin(x) * \frac{sin(x)}{cos(x)}[/tex]
[tex]\frac{sin(x)}{\cos(x)} = \tan(x)[/tex]
So, we have:
[tex]\frac{1 - (cos(x))^2}{cos(x)} = \sin(x) * \tan(x)[/tex]
[tex]\frac{1 - (cos(x))^2}{cos(x)} = \sin(x) \tan(x)[/tex] --- proved
Solving (E):
[tex]E.\ 2\sec(x)[/tex]
In trigonometry
[tex]\sec(x)= \frac{1}{\cos(x)}[/tex]
So, we have:
[tex]2\sec(x) = 2 * \frac{1}{\cos(x)}[/tex]
[tex]2\sec(x) = \frac{2}{\cos(x)}[/tex]
Multiply by [tex]\frac{1 - \sin(x)}{1 - \sin(x)}[/tex] --- an equivalent of 1
[tex]2\sec(x) = \frac{2}{\cos(x)} * \frac{1 - \sin(x)}{1 - \sin(x)}[/tex]
[tex]2\sec(x) = \frac{2(1 - \sin(x))}{(1 - \sin(x))\cos(x)}[/tex]
Open bracket
[tex]2\sec(x) = \frac{2 - 2\sin(x)}{(1 - \sin(x))\cos(x)}[/tex]
Express 2 as 1 + 1
[tex]2\sec(x) = \frac{1+1 - 2\sin(x)}{(1 - \sin(x))\cos(x)}[/tex]
Express 1 as [tex]\sin^2(x) + \cos^2(x)[/tex]
[tex]2\sec(x) = \frac{\sin^2(x) + \cos^2(x)+1 - 2\sin(x)}{(1 - \sin(x))\cos(x)}[/tex]
Rewrite as:
[tex]2\sec(x) = \frac{\cos^2(x)+1 - 2\sin(x)+\sin^2(x)}{(1 - \sin(x))\cos(x)}[/tex]
Expand
[tex]2\sec(x) = \frac{\cos^2(x)+1 - \sin(x)- \sin(x)+\sin^2(x)}{(1 - \sin(x))\cos(x)}[/tex]
Factorize
[tex]2\sec(x) = \frac{\cos^2(x)+1(1 - \sin(x))- \sin(x)(1-\sin(x))}{(1 - \sin(x))\cos(x)}[/tex]
Factor out 1 - sin(x)
[tex]2\sec(x) = \frac{\cos^2(x)+(1- \sin(x))(1-\sin(x))}{(1 - \sin(x))\cos(x)}[/tex]
Express as squares
[tex]2\sec(x) = \frac{\cos^2(x)+(1-\sin(x))^2}{(1 - \sin(x))\cos(x)}[/tex]
Split
[tex]2\sec(x) = \frac{\cos^2(x)}{(1 - \sin(x))\cos(x)} +\frac{(1-\sin(x))^2}{(1 - \sin(x))\cos(x)}[/tex]
Cancel out like factors
[tex]2\sec(x) = \frac{\cos(x)}{1 - \sin(x)} +\frac{1-\sin(x)}{\cos(x)}[/tex] --- proved
What is the name for a polygon with 4 sides
Answer: A. Quadrilateral
Step-by-step explanation:
The name for a polygon with 4 sides is a quadrilateral. Quadrilateral is a two-dimensional shape with four straight sides and four angles. The most common type of quadrilateral is the rectangle, which has four right angles. Other types of quadrilaterals include squares, parallelograms, trapezoids, and rhombuses.
Answer:
quadrilateral!!
Step-by-step explanation:
look at the beginning of the word, quad. Quad means 4 and is referring to a 4 sided figure.
In baseball, each time a player attempts to hit the ball, it is recorded. The ratio of hits compared to total attempts is their batting average. Each player on the team wants to have the highest batting average to help their team the most. For the season so far, Jana has hit the ball 12 times out of 15 attempts. Tasha has hit the ball 9 times out of 10 attempts. Which player has a ratio that means they have a better batting average? Tasha, because she has the lowest ratio since 0.9 > 0.8
B) Tasha, because she has the highest ratio since 27 over 30 is greater than 24 over 30
C) Jana, because she has the lowest ratio since 0.9 > 0.8
D) Jana, because she has the highest ratio since 27 over 30 is greater than 24 over 30
Step-by-step explanation:
as the description says, the higher the ratio the better.
9/10 = 0.9
12/15 = 4/5 = 0.8
so, Tasha has the better batting average, as she has the higher ratio.
9/10 = 27/30
12/15 = 24/30
27/30 is higher than 24/30.
In a school containing 360 children, 198 are girls. What percent of all children are girls? What percent of the children are boys? The number of girls is what percent of the number of boys? The number of boys is what percent of the number of girls?
the number of girls is _____% of the number of boys.
Answer:
1st question :55%
2nd ":122.22%
3rd ":81.82%
a store has a sale where all jackets are sold at a discount of 40%. If the regular price of the jackets is $80, how many jackets could be bought at the sale if a shopper spent $576
Answer:
The shopper can but 12 jackets.
Step-by-step explanation:
80*.6 (100% - 40% = paying 60% or .6) = 48
576 / 48 = 12
Here we have a problem of percentage discounts, such that we need to find how much a given price decreases, and how many jackets we can buy considering the decreased price.
We will find that the number is 12.
Now let's see how we can get that result:
If something has an original price P, and we discount an x% of that price, the new price will be:
[tex]np = P\cdot(1 - x\%/100\%)[/tex]
Here we know that the regular price of a jacket is $80
And we have a discount of 40%
This means that the new price of these jackets will be:
[tex]np = \$80\cdot (1 - 40\%/100\%) = \$80\cdot (1 - 0.4) = \$80\cdot 0.6 = \$48[/tex]
Now we want to know how many of these jackets we can buy with $576
This will be equal to the quotient between the money we have and the new price of each jacket:
[tex]N = \$576/\$48 = 12[/tex]
This means that we can buy exactly 12 jackets at the sale.
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Find, rounded to the nearest hundredth, the diagonal of a rectangle whose sides are 6 and 11.
WHAT IS THE ANSWER. I NEED IT ASAP
Answer:
The length of the diagonal is 12.53
Step-by-step explanation:
Since we have a rectangle, the diagonal is the hypotenuse of a right triangle. So we can use Pythagorean Theorem.
a^2 + b^2 = c^2
We know the two legs are 6 and 11, so we can find the hypotenuse (which is the diagonal) see image.
See image.
X = ?°
please help :)
Answer:
x=17 degrees
Step-by-step explanation:
We know that a right angle is equal to 90 degrees. Therefore, two angles between a right angle have to equal 90. Therefore, 73+x=90. Isolate x and get x=90-73. x=17. Therefore, x=17 degrees.
If this helps please mark as brainliest
Which is the equivalent of 145.12° written in DMS form?
A. 145° 7' 2"
B. 145° 12' 0"
C. 145° 2'36"
D. 145° 7' 12"
Answer:
the answer is
B. 145° 12' 0"
what is the generalised from of 85
Answer:
8 × 10 + 5 × 1. is the correct answer .STAY BRAINLY