Answers
Answer:
b. e^9.45 = x
see last example and this explains whole numbers and decimals.
Step-by-step explanation:
Another example we can Solve 100=20e^2t .
Solution
100 = 20e^2t
5 = 20e ^2t
in 5 = 2t
Therefore t = in5/ 2
Step 1 was ; Divide by the coefficient of the power
Step 2 was ; Take ln of both sides. Use the fact that ln(x) and ex are inverse functions
Step 3 was; Divide by the coefficient of t
Another example;
Solve e^2x−e^x = 56 .
Solution
Analysis
When we plan to use factoring to solve a problem, we always get zero on one side of the equation, because zero has the unique property that when a product is zero, one or both of the factors must be zero. We reject the equation e^x=−7 because a positive number never equals a negative number. The solution ln(−7) is not a real number, and in the real number system this solution is rejected as an extraneous solution.
Another example is;
Solve e^2x=e^x+2 .
Answer
Q&A: Does every logarithmic equation have a solution?
No. Keep in mind that we can only apply the logarithm to a positive number. Always check for extraneous solutions.
Last example determines decimals ;
Solve lnx =3 .
Solution
lnx^x=3=e^3
Use the definition of the natural logarithm
Graph below represents the graph of the equation. On the graph, the x-coordinate of the point at which the two graphs intersect is close to 20 . In other words e^3≈20 . A calculator gives a better approximation: e^3≈20.0855 .
The graph below represents the graph of the equation. On the graph, the x-coordinate of the point at which the two graphs intersect is close to 20 . In other words e^3≈20 . A calculator gives a better approximation: e^3≈20.0855 .
It shows values of graphs of y=lnx and y=3 cross at the point (e^3,3) , which is approximately (20.0855,3) .
See graph below.
Related Questions
For the rhombus below, find the measures of ∠1, ∠2, ∠3, and ∠4.
Answers
Answer:
∠1 = 116 ° , ∠2 = 32° , ∠3 = 116 ° and ∠4 = 32°
Step-by-step explanation:
∠2 = 32° (The diagonals of a rhombus bisect pairs of opposite angles)
Opposite sides of a rhombus are parallel ,so
∠2 = ∠4 (Alternate interior angles )
∠4 = 32°
32° + ∠4 + ∠3 = 180° (angle sum property of a triangle)
64° + ∠3 = 180°
∠3 = 180 - 64
∠3 = 116°
∠3 =∠1 (in a rhombus opposite angles are equal )
∠1 = 116°
Consider the probability that at most 85 out of 136 DVDs will work correctly. Assume the probability that a given DVD will work correctly is 52%. Specify whether the normal curve can be used as an approximation to the binomial probability by verifying the necessary conditions.
Answers
Answer:
Since both [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex], the necessary conditions are satisfied.
0.9945 = 99.45% probability that at most 85 out of 136 DVDs will work correctly.
Step-by-step explanation:
Test if the normal curve can be used as an approximation to the binomial probability by verifying the necessary conditions.
It is needed that:
[tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex]
Binomial probability distribution
Probability of exactly x successes 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 z-score 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 p-value, 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 DVD will work correctly is 52%.
This means that [tex]p = 0.52[/tex]
136 DVDs
This means that [tex]n = 136[/tex]
Test the conditions:
[tex]np = 136*0.52 = 70.72 \geq 10[/tex]
[tex]n(1-p) = 136*0.48 = 65.28 \geq 10[/tex]
Since both [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex], the necessary conditions are satisfied.
Mean and standard deviation:
[tex]\mu = E(X) = np = 136*0.52 = 70.72[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{136*0.52*0.48} = 5.83[/tex]
Consider the probability that at most 85 out of 136 DVDs will work correctly.
Using continuity correction, this is [tex]P(X \leq 85 + 0.5) = P(X \leq 85.5)[/tex], which is the p-value of Z when X = 85.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{85.5 - 70.72}{5.83}[/tex]
[tex]Z = 2.54[/tex]
[tex]Z = 2.54[/tex] has a p-value of 0.9945.
0.9945 = 99.45% probability that at most 85 out of 136 DVDs will work correctly.
I will give brainly.
How do you determine if a slope is positive or negative?
Answers
You have to find the slope .
How?
Take 2points
(x1,y1)(x2,y2)Slope formula[tex]\\ \rm\Rrightarrow \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Step-by-step explanation:
What the Slope Means A positive slope means that two variables are positively related—that is, when x increases, so does y, and when x decreases, y also decreases. Graphically, a positive slope means that as a line on the line graph moves from left to right, the line rises.
Lavania is studying the growth of a population of fruit flies in her laboratory. After 6 days she had nine more than five times as many fruit flies as when she began the study. If she observes 20 fruit flies on the first day of the study, write and evaluate an expression to find the population of fruit flies Lavania observed after 6 days
a. write an expression for the population of fruit flies Lavania observed after 6 days
b. find the population of fruit flies Lavania observed after 6 days
Answers
Answer:
A. 20•5+9
B.109 flies
g (1) = ?
Evaluate piecewise functions
Answers
Answer:
g(1) = 1
Step-by-step explanation:
g(1) with x = 1 corresponds to x ≠ - 2, - 1 with g(x) = x³ - x² + 1 , then
g(1) = 1³ - 1² + 1 = 1 - 1 + 1 = 1
Answer:
g ( 1 ) = 1
Step-by-step explanation:
→ Substitute x = 1 into x³ - x² + 1
( 1 ) ³ - ( 1 )² + 1
→ Simplify
1 - 1 + 1 = 1
A plumber charges $65 for a diagnostic check. After the check, it is $85 per hour for the work. With $320 in your wallet, how many hours of Work can you afford?
Answers
Answer:
3 hours
Step-by-step explanation:
first, you subtract 65 from 320 to cover the diagnostic check.
Then, you subtract 85 from the remaining cash three times and you'll get 0
Ursula has a new team member, Tom, who came from another worksite. Tom is constantly trying to make new suggestions and explain how things used to work his old job. How should Ursula respond? a) Avoid him as much as possible b) Nod her head but ignore the details c) Politely suggest that he stop making new suggestions d) Listen to his suggestions to see what might work
Answers
9514 1404 393
Answer:
d) Listen to his suggestions to see what might work
Step-by-step explanation:
A supervisor or team leader cannot be expected to know everything, or be completely up-to-date with the latest innovations. A lot of what comprises "best practice" is developed on the job, or propagated by personnel transfers or word of mouth. A different point of view can often be beneficial, planting the seed for a beneficial change, even if the specific suggestion is not workable.
Ursula should pay attention to all of her team members, Tom included.
Which graph is a function?
Answers
Answer:
B
Step-by-step explanation:
A function is a relation in which each input, x, has only one output, y.
There are two ways to determine if a relation is a function:
1. If each x-input has only one, unique y-output, then it's a function. If some x-inputs share the same y-outputs, it's not a function.
2. Vertical Line Test on Graphs:
To determine whether y is a function of x, when given a graph of relation, use the following criterion: if every vertical line you can draw goes though only 1 point, the relation can be a function. If you can draw a vertical line that goes though more than 1 point, the relation cannot be a function.
Since we're given a graph relation, let's test both of the answers out.
If I were to draw a vertical line in a specific place on the first graph, I'd be hitting more than one point in the coordinate plane.
If I were to draw a vertical line in a specific place on the second graph, I'd only be hitting one point in the coordinate plane.
Therefore, choice B is a function.
Find the gradient of the straight line joining the two points. (1,7) and (-1,-7)
Answers
Points: (-1,-7), (1,7)
Formula (y=mx+b):
y = 7x
Slope m: 7
Y-intercept b: 0
Parallel lines: 7x + any number
Must click thanks and mark brainliest
Find the length of side
x to the nearest tenth.
Answers
The degree of the polynomial function f(x) is 4. The roots of the equation f(x) =0 are -2,-1,1 and 3. Which graph could be the graph of f(x)?
Answers
Answer:
top right
Step-by-step explanation:
roots of an equation = x-intercepts
Answer:
top right is the answer from my calculatins
Help me please I don’t know what to do
Answers
A solution to a system
Is the point two lines cross each other.
3. The lines cross at y = 0 and x = 2, so the solution is x = 2
4. The lines do not cross so there are no solutions.
5. It looks like there is one line which means the two lines are identical so there are infinite solutions
Answer:
Step-by-step explanation:
3) y = x - 2
y = -x +2
Both lines are intersecting at (2 , 0).So, (2, 0) is the solution of the equations.
(2,0)
4) Both lines are parallel to each other and they will never intersect. So, it has no solution.
5) Both lines are coincide. So all points in the line are solutions of the equations.
Infinity solutions
find the square root of 121/225
Answers
Answer:
11/15 or .73333333...
Step-by-step explanation:
heres how i went about it:
think of it as a fraction,
121
------
225
to find the sqyare root of a fraction you would find the square root of each number individually
√121=11
√225=15
then you divide them and get .73333333333333333...
bad at explaining but hope this helped <3
Which equation represents a line that passes through (4,1/3) and has a slope of 3/4?
Oy- 3/4= 1/3(x-4)
Oy-1/3= 3/4(x-4)
Oy- 1/3= 4(x-3/4)
Oy-4 = 3/4(x-1/3)
Answers
Step-by-step explanation:
With this kind of problem, we're looking at an equation in the form
y - y1 = m(x - x1)
(m = slope)
so we can substitute m, y1, and x1 with the values we're given.
y - y1 = m(x - x1)
y - 1/3 = 3/4(x - 4)
Answer:
y - 1/3 = 3/4(x - 4)
Let f(x) = e ^3x/5x − 2. Find f'(0).
Answers
Answer:
Step-by-step explanation:
Our friend asking what the actual function is has a point. I completed this under the assumption that what we have is:
[tex]f(x)=\frac{e^{3x}}{5x-2}[/tex] and used the quotient rule to find the derivative, as follows:
[tex]f'(x)=\frac{e^{3x}(5)-[(5x-2)(3e^{3x})]}{(5x-2)^2}[/tex] and simplifying a bit:
[tex]f'(x)=\frac{5e^{3x}-[15xe^{3x}-6e^{3x}]}{(5x-2)^2}[/tex]and a bit more to:
[tex]f'(x)=\frac{5e^{3x}-15xe^{3x}+6e^{3x}}{(5x-2)^2}[/tex] and combining like terms:
[tex]f'(x)=\frac{11e^{3x}-15xe^{3x}}{(5x-2)^2}[/tex] and factor out the GFC in the numerator to get:
[tex]f'(x)=\frac{e^{3x}(11-15x)}{(5x-2)^2}[/tex] That's the derivative simplified. If we want f'(0), we sub in 0's for the x's in there and get the value of the derivative at x = 0:
[tex]f'(0)=\frac{e^0(11-15(0))}{(5(0)-2)^2}[/tex] which simplifies to
[tex]f'(0)=\frac{11}{4}[/tex] which translates to
The slope of the function is 11/4 at the point (0, -1/2)
If a, b, c are in A.P. show that
a (b + c)/bc,b(c + a) /ca, c(a-b )/bc
are in A.P.
Answers
Answer:
Step-by-step explanation:
[tex]\frac{a(b+c)}{bc} ,\frac{b(c+a)}{ca} ,\frac{c(a+b)}{ab} ~are~in~A.P.\\if~\frac{ab+ca}{bc} ,\frac{bc+ab}{ca} ,\frac{ca+bc}{ab} ~are~in~A.P.\\add~1~to~each~term\\if~\frac{ab+ca}{bc} +1,\frac{bc+ab}{ca} +1,\frac{ca+bc}{ab} +1~are~in~A.P.\\if~\frac{ab+ca+bc}{bc} ,\frac{bc+ab+ca}{ca} ,\frac{ca+bc+ab\\}{ab} ~are~in~A.P.\\\\divide~each~by~ab+bc+ca\\if~\frac{1}{bc} ,\frac{1}{ca} ,\frac{1}{ab} ~are ~in~A.P.\\if~\frac{a}{abc} ,\frac{b}{abc} ,\frac{c}{abc} ~are~in~A.P.\\if~a,b,c~are~in~A.P.\\which~is~true.[/tex]
A sailor on a trans-Pacific solo voyage notices one day that if he puts 625.mL of fresh water into a plastic cup weighing 25.0g, the cup floats in the seawater around his boat with the fresh water inside the cup at exactly the same level as the seawater outside the cup (see sketch at right).
Calculate the amount of salt dissolved in each liter of seawater. Be sure your answer has a unit symbol, if needed, and round it to 2 significant digits.
You'll need to know that the density of fresh water at the temperature of the sea around the sailor is 0.999/gcm3. You'll also want to remember Archimedes' Principle, that objects float when they displace a mass of water equal to their own mass.
Answers
Answer:
can you say again please
plot the points (0, -2) (4, 1)
Answers
Have a nice day/night!
Will mark brainliest
Plz solve on a paper or draw on the picture thx in advance
Answers
9514 1404 393
Answer:
the red angle has no specific value
Step-by-step explanation:
There is sufficient information here to specify all of the angles except the two unknown angles in the 70° (dark blue) triangle. Those two angles must total 110°, but that measure cannot be allocated between them based on the information in the diagram.
The attachments show that all of the given angle constraints can be met while the red angle may vary considerably. It can range through the interval (0°, 110°), but cannot be either of those end values.
If a over 2 equals b over 3 then b over a equals what?
Answers
b/a
a=2/3b
b=3/2a
4b/9a
I need help please ive been stuck on it
Answers
Answer:
$3,300
Step-by-step explanation:
The salary given falls in the third range, meaning it should get a 5.5% income tax on the $60,000.
5.5% = 0.055
0.055 * $60,000 = $3,300
Therefore, the state income tax owed on the provided salary is $3,300.
Convert degrees to radians
Answers
Answer:
it's answer is
[tex] \frac{25}{18} [/tex]
find the side of a cube whose surface area is 150² m
Answers
Answer:
6 m
Step-by-step explanation:
[tex]surface \: \: area = 4 {s}^{2} [/tex]
s is side
[tex]150 = 4 {s}^{2} \\ {s}^{2} = 37.5 \\ s = 6.1 \: m[/tex]
There are 6 identical square faces
Area of each face = 150 / 6 = 25 m^2
Edge length = sr(25) = 5 m
Solve one and two tenths plus eight and one eighteenth
Answers
47
Is this it?
1 plus 2(10) plus 8 plus 1(18)
Convert 653 in base 7 to base 10
Answers
6*102=600
5*101=50
3*100=3
Adding all to get Ans=65310
Step2 converting 65310 to 7
The equation calculation formula for 65310 number to 7 is like this below.
7|653
7|93|2
7|13|2
7|1|6
7|1|1
Ans:16227
consider the differential equation x3y ''' + 8x2y '' + 9xy ' − 9y = 0; x, x−3, x−3 ln(x), (0, [infinity]). Verify that the given functions form a fundamental set of solutions of the differential equation on the indicated interval. The functions satisfy the differential equation and are linearly independent since W(x, x−3, x−3 ln(x)) = ≠ 0 for 0 < x < [infinity].
Answers
Verifying that a given expression is a solution to the equation is just a matter of plugging in the expression and its derivatives, and making sure that the given expressions are indeed linearly independent.
For example, if y = x, then y' = 1 and the other derivatives vanish. So the DE after substitution reduces to
9x - 9x = 0
which is true for all 0 < x < ∞.
To check for linear independence, you compute the Wronskian, which, judging by what you wrote, you've already done...
34 Proportions
Mathematics, Pre-Algebra
Question 2
A boat can travel 21 miles on 7 gallons of gasoline. How far can it travel on 17 gallons?
Answers
Answer:
51 miles
Step-by-step explanation:
hope it's clear and understandable
:)
Look at the image to receive the answers
Answers
Answer:
345.4 using the 3.14 for pi
345.6 using the pi button
Step-by-step explanation:
The surface area of a cylinder is given by
SA=2 pi rh+2 pir^2
The radius is 5 and the height is 6
SA = 2·pi·5·6+2·pi·5^2
SA = 60pi + 50pi
110pi
Letting pi = 3.14
SA =345.4
Letting pi = pi button
= 345.57519 = 345.6
Enter the degree of the polynomial below.
6x + 9x + 3x – 4410 - 9x5 – 5x6
A. 9
B. 10
c. 6.
OD. 4
Answers
Answer:
the answer is d
Step-by-step explanation:
Answer please answer!!
I need the answer asap
Answers
Answer:
35 cm
Step-by-step explanation:
is the correct answer
