Answers
1) Let's rewrite it as a logarithmic expression of the following exponential one. Let's do it step by step.
[tex]\begin{gathered} e^6=x \\ \ln e^6=\ln x \\ \ln(x)=6 \end{gathered}[/tex]Note that when we apply the natural log on both sides, we use one of those properties that tell us that we can eliminate the log since the base of a natural log is "e", as well as, "e" is the base of that power.
2) To rewrite in the exponential form we can do the following:
[tex]\ln(3)=y\Leftrightarrow e^y=3[/tex]Note that in this case, we have used the definition of logarithms.
Related Questions
What is the sign of mlio Choose 1 answer: Positive Negative Neither positive nor negative the sum is zero.
Answers
The sign will be positive.
On a particular day, the amount of untreated water coming into the plant can be modeled by f(t) = 100 + 30cos(t/6) where t is in hours since midnight and f(t) represents thousands of gallons of water. The amount of treated water at any given time, t, can be modeled by g(t) = 30e^cos(t/2)a) Define a new function, a′(t), that would represent the amount of untreated water inside the plant, at any given time, t.b) Find a′ (t).c) Determine the critical values of this function over the interval [0, 24).
Answers
a)The amount of untreated water inside the plant will be the difference between the difference f(t) - g(t), then, a(t) can be defined as follows:
[tex]a(t)=100+30cos(\frac{t}{6})-30e^{cos(\frac{t}{2})}[/tex]b) the derivative of a(t) is the following:
[tex]a^{\prime}(t)=-5sin(\frac{t}{6})+15sin(\frac{t}{2})e^{cos(\frac{t}{2})}[/tex]c) the critical values of a(t) over the interval [0, 24) are:
[tex]\begin{gathered} t=0 \\ t=6\pi \end{gathered}[/tex]can you please solve this for me I'll make sure to give the best review
Answers
-9 is an integer
the location of -9 is with 41
6.3 is a repeating decimal
the location is with 5.86666...
-4/5 is a fraction
the location is with 11/12
can u pls help me with this question and this is homework
Answers
the probability is:
[tex]\frac{15+5}{50}=\frac{20}{50}=\frac{2}{5}[/tex]so the answer is 2/5
Tank B, which initially contained 80 liters of water, is being drained at a rate of 2.5 liters per minute. How many liters of water remain in the tank after 7 minutes?
Answers
Tank B originally had 80 liters of water.
Water is being drained off the tank at a rate of 2.5 liters per minute.
After 7 minutes have passed, the tank has lost 7*2.5 = 17.5 liters of water.
This means the tank still has 80 - 17.5 = 62.5 liters of water.
After 7 minutes 62.5 liters of water remain in the tank
Find the probability of at least 2 girls in 6 births. Assume that male and female births are equally likely and that the births are independent events.0.6560.1090.2340.891
Answers
We need to use Binomial Probability.
Of 6 births, we want to find the probability of at least 2 of them being girls.
To solve this, we need to find:
Probability of exactly 2 girls
Probability of exactly 3 girls
Probability of exactly 4 girls
Probability of exactly 5 girls
Probability of exactly 6 girls
If we add all these probabilities, we get the probability of at least 2 girls.
To find the probabilities, we can use the formula:
[tex]_nC_r\cdot p^r(1-p)^{n-r}[/tex]Where:
n is the number of trials (in this case, the number of total births)
r is the number of girls we want to find the probability
p is the probability of the event occurring
[tex]_nC_r\text{ }is\text{ }the\text{ }combinatoric\text{ }"n\text{ }choose\text{ }r"[/tex]The formula for "n choose r" is:
[tex]_nC_r=\frac{n!}{r!(n-r)!}[/tex]Then, let's find the probability of exactly 2 girls:
The probability of the event occurring is:
[tex]P(girl)=\frac{1}{2}[/tex]Because there is a 50% probability of being a girl or a boy.
let's find "6 choose 2":
[tex]_6C_2=\frac{6!}{2!(6-2)!}=\frac{720}{2\cdot24}=15[/tex]Now we can find the probability of exactly 2 girls:
[tex]Exactly\text{ }2\text{ }girls=15\cdot(\frac{1}{2})^2(1-\frac{1}{2})^{6-2}=15\cdot\frac{1}{4}\cdot(\frac{1}{2})^4=\frac{15}{4}\cdot\frac{1}{16}=\frac{15}{64}[/tex]We need to repeat these calculations for exactly 3, 4, 5, and 6 girls:
Exactly 3 girls:
let's find "6 choose 3":
[tex]_6C_3=\frac{6!}{3!(6-3)!}=\frac{720}{6\cdot6}=20[/tex]Thus:
[tex]Exactly\text{ }3\text{ }girls=20\cdot(\frac{1}{2})^3(1-\frac{1}{2})^{6-3}=20\cdot\frac{1}{8}\cdot\frac{1}{8}=\frac{5}{16}[/tex]Exactly 4 girls:
"6 choose 4":
[tex]_6C_4=\frac{6!}{4!(6-4)!}=\frac{720}{24\cdot2}=15[/tex]Thus:
[tex]Exactly\text{ }4\text{ }girls=15\cdot(\frac{1}{2})^4(1-\frac{1}{2})^{6-4}=15\cdot\frac{1}{16}\cdot\frac{1}{4}=\frac{15}{64}[/tex]Exactly 5 girls:
"6 choose 5"
[tex]_6C_5=\frac{6!}{5!(6-5)!}=\frac{720}{120}=6[/tex]Thus:
[tex]Exactly\text{ }5\text{ }girls=6\cdot(\frac{1}{2})^5(1-\frac{1}{2})^{6-5}=6\cdot\frac{1}{32}\cdot\frac{1}{2}=\frac{3}{32}[/tex]Exactly 6 girls:
"6 choose 6"
[tex]_6C_6=\frac{6!}{6!(6-6)!}=\frac{720}{720\cdot0!}=\frac{720}{720}=1[/tex]Thus:
[tex]Exactly\text{ }6\text{ }girls=1\cdot(\frac{1}{2})^6(1-\frac{1}{2})^{6-6}=\frac{1}{64}\cdot(\frac{1}{2})^0=\frac{1}{64}[/tex]now, to find the answer we need to add these 5 values:
[tex]\frac{15}{64}+\frac{5}{16}+\frac{15}{64}+\frac{3}{32}+\frac{1}{64}=\frac{57}{64}=0.890625[/tex]To the nearest tenth, the probability of at least 3 girls is 0.891, thus, the last option is the correct one.
Decompose the fraction 11 /12 towingtwo ways
Answers
Given:-
[tex]\frac{11}{12}[/tex]To find:-
Decompose the fraction in two ways.
Way one,
[tex]\frac{11}{12}=\frac{5}{12}+\frac{6}{12}[/tex]Way two,
[tex]\frac{11}{12}=\frac{10}{24}+\frac{12}{24}[/tex]WILL GIVE BRIANLYEST 100 POINTS ACULLY 200 BC IM GIVING EXTRA POINTS
Answers
Answer:
the mean would increase to a value to about 24.6
Q2: median is 7.
Step-by-step explanation:
Answer:
Q1) the mean would increase in value to about 24.6
Q2) 7
David’s watch broke. He decides to get it fixed instead of replacing it. Since David is a loyal customer, he received a coupon in the mail for a discount. The total cost to repair the watch can be represented by 0.07r + (r – 20), where r represents the original cost of the repair. Explain what each part of the expression represents in the context of the problem.
Answers
→ r represents the original cost of the repair.
→ 0.07r represents the tax.
→ (r – 20) represents the discount
Given,
The total cost to repair the watch can be represented by 0.07r + (r – 20), where r represents the original cost of the repair.
Explain what each part of the expression represents in the context of the problem.
Now, According to the question:
Given the following algebraic expression:
0.07r + (r – 20)
In the context of fixing David’s broken watch, the variable r represents the original cost of the repair while 0.07r most likely represents the amount of money charged as tax. Lastly the expression (r – 20) represents the discount on fixing David’s broken watch.
What each part of the expression represents in the context of the problem include the following:
→ r represents the original cost of the repair.
→ 0.07r represents the tax.
→ (r – 20) represents the discount
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HELP ASAPwrite an expression to represent:"the sum of a number b and 24"
Answers
The sum of a number 'b' and 24 can be written like this:
[tex]b+24[/tex]Graph the solution to the following system of inequalities.y>3x+7y≤−3x-8
Answers
Step 1. Graphing the first inequality.
The first inequality is:
[tex]y>3x+7[/tex]to graph this, we need to graph the line 3x+7, which compared with the slope-intercept equation
[tex]y=mx+b[/tex]where m is the slope and b is the y-intercept, the line
[tex]y=3x+7[/tex]is a line with a slope of 3 and a y-intercept at 7:
SInce the inequality is:
[tex]y>3x+7[/tex]The solution just for this inequality are the values greater than the red line, but not including the red line so we represent is a dotted line and a shaded part above:
Step 2. Graph the second inequality.
The second inequality is:
[tex]y\le-3x-8[/tex]As we did with the first inequality, we graph the line -3x-8 first.
comparing -3x-8 with the slope-intercept equation:
[tex]y=mx+b[/tex][tex]y=-3x-8[/tex]we can see that the slope m is -3 and the y-intercept b is -8. This line is shown in blue in the following diagram along with our results for the previous inequality:
Since the inequality form is:
[tex]y\le-3x-8[/tex]We shade the values below this blue line:
The final solution will be the intersection between the red part and the blue part:
5. The domain of f(x) = -2x + 1 is {-4, -1, 0, 2}. Find the range.
Answers
Explanation:
The function is f(x) = -2x + 1
Domain = {-4, -1, 0, 2}
Note that the domain is a set of of all the values of x ( i.e. the independent variable)
The range is a set of the corresponding value of f(x) for each value of x in the domain.
For x = -4
f(-4) = -2(-4) + 1 = 8 + 1
f(-4) = 9
f(-1) = -2(-1) + 1 = 2 + 1
f(-1) = 3
f(0) = -2(0) + 1 = 0 + 1
f(0) = 1
f(2) = -2(2) + 1 = -4 + 1
f(2) = -3
Therefore the set of all the values above which is the range will be given as:
Range = { 9, 3, 1, -3}
tristan asked his coworkers about how much time they spent commuting each morning Find the median
Answers
SOLUTION
In a box and whisker plot, the firt dot on the box is Q1
The second dot on the box is Q2
The third dot on the box is Q3
Q2 is the median
From what we see,
[tex]Q2=25[/tex]Hence the answer is 25, option D
In Square ABCD, AE = 3x + 5 and BD = 10x + 2.What is the length of AC?
Answers
Let's begin by identifying key information given to us:
We have square ABCD
[tex]\begin{gathered} AE=3x+5 \\ BD=10x+2 \\ BD=2\cdot AE \\ 10x+2=2(3x+5) \\ 10x+2=6x+10 \\ \text{Put like terms together, we have:} \\ 10x-6x=10-2 \\ 4x=8 \\ \text{Divide both sides by ''4'', we have:} \\ \frac{4x}{4}=\frac{8}{4} \\ x=2 \\ \\ \end{gathered}[/tex]For a square, the diagonals are equal, AC = BD
[tex]\begin{gathered} AC=BD \\ AC=10x+2 \\ x=2 \\ AC=10(2)+2=20+2 \\ AC=22 \end{gathered}[/tex]What is the distance between A(5,-2) and B(-2,4)?
Answers
Answer:
[tex]\sqrt{85}[/tex]
Step-by-step explanation:
Let's use the distance formula to solve for the distance between the two given points!
d = [tex]\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2 }[/tex]
Now, we input the points:
(5-(-2) + (-2-4)
(which will equal...)
(7) + (-6)
Now we input the solutions we got here to the distance formula:
[tex]d =\sqrt{(7)^2 + (-6)^2[/tex]
(we simplify....)
[tex]7^2 = 49\\(-6)^2 = 36[/tex]
input these solutions into the distance formula again...
[tex]\sqrt{49 + 36} = \sqrt{85}[/tex]
85 is not a number that can be square rooted properly, nor does it have any perfect squares available to divide equally.
Therefore, we conclude that the distance between A(5, -2) and B(-2,4) is [tex]\sqrt{85}[/tex].
A tee box is 48 feet above its fairway. When a golf ball is hit from the tee box with an initial vertical velocity of 32 ft/s, the quadratic equation 0 = -16t^2+ 32t +48 givesthe time t in seconds when a golf ball is at height 0 feet on the fairway.What is the height of the ball at 1 second and is the ball at its maximum height at 1 second (explain)?
Answers
Answer:
Step by step explanation:
Ana has $75 and saves an additional $13 per week. Which equation can be used to findhow many weeks it will take until she has $452?75 + w = 4520 75 + 13w = 45213w = 75 = 452452 + 13w = 75
Answers
Here, we want to get an equation
Firstly, since we do not have the number of weeks, we can represent it with a variable (a letter)
In this case, we shall be representing it with w
Since she saves $13 in a week, in w weeks, the amount saved will be;
13 * w = $13w
Now, recall that she has $75 before she started saving. What this mean is that at the end of the w weeks, the amount she will have will be ;
[tex]13w\text{ + 75}[/tex]We now proceed to equate this to the total she wants to save and we finally have the complete equation below;
[tex]13w\text{ + 75 = 452}[/tex]Takashi is driving to his grandmother's house. he is driving at a constant speed and will not make any stops along the way. Takashi’s distance in miles from his grandmother’s house h hours after leaving can be described by equationA. Identify and interpret the independent variable? B. Identify and interpret the coefficient? C. Identify and interpret the constant term ?D. Identify and interpret the dependent variable?
Answers
Let's begin by listing out the information given to us:
To calculate Takashi's distance from his grandmother's house is given by the formula:
[tex]\begin{gathered} distance=speed\cdot time \\ h=v\cdot t \end{gathered}[/tex]Independent variable refers to the variable that stands by itself and whose value is not affected by the other
Dependent variable refers to the variable whose value is affected by the value of another variable
A. The distance (h) does not change irrespective of Takashi's speed, hence it is the independent variable
B. The coefficient is the speed (v)
C. The constant is time (t)
D. The speed (v) changes with variation in time, hence it is the dependent variable
find the reference angle for -0.8pi
Answers
Answer:
What is Meant by the Reference Angle? In mathematics, the reference angle is defined as the acute angle and it is measuring less than 90 degrees. It is always the smallest angle, and it makes the terminal side of an angle with the x-axis.
Find the slope of line segment AB where the coordinates of A are
(3,-3) and B are (1,2).
A: -2/5
B: -5/2
C: 2/5
D: 5/2
Answers
The slope formula is y2-y1 over x2-x1 from there you should get your answer. Hope this helps.
I need to find the equation of a circle I will include picture
Answers
Given,
The center of the circle is (6, -3).
The coordinates of the point, circle is passing through (6,6).
The general equation of the circle is,
[tex](x-h)^2+(y-k)^2=r^2[/tex]Here, x, y are the coordinates of the point.
h and k are the center of the circle.
r is the radius of the circle.
Substituting the value of h, k , x and y in the equation of circle then,
[tex]\begin{gathered} (6-6)^2+(6-(-3))^2=r^2 \\ 0+9^2=r^2 \\ r=9 \end{gathered}[/tex]So, the radius of the circle is 9.
Substituting the value of h, k and r in the general equation of circle.
[tex]\begin{gathered} (x-6)^2+(y-(-3))^2=9^2 \\ x^2+36-12x+y^2+9+6y=81 \\ x^2+y^2-12x+6y-36=0 \end{gathered}[/tex]Hence, the equation of circle is x^2+y^2-12x+6y-36=0
Classifying systems of linear equations from graphsFor each system of linear equations shown below, classify the system as "consistent dependent," "consistent independent," or "inconsistent." Then, choose thebest description of its solution. If the system has exactly one solution, give its solution.System ASystem B System C
Answers
Consistent dependant system- System B: It has infinite number of solutions, in this case, the graphs of the lines are the same.
Consistent independent system- System C: It has exactly one solution. In this case, both lines cross each other at exactly one point.
Solution : (-2,-2)
Inconsistent: System A.
When a system has no solution, lines never cross each other.
write an algebraic model for the statement then solve the model the sum of a number and -9 is -21
Answers
Answer:
[tex]x + ( - 9) = - 21[/tex]
[tex]x - 9 = - 21[/tex]
[tex]x = - 12[/tex]
What value n makes the eauqation n x 3/4 = 3/16
Answers
Answer:
N = 1/4
Step-by-step explanation:
Okay, so 1/4 is equal to N.
3/4 x1/4=3/16
There are 39 chocolates In a box call identically sheet dear 16 off filled with nuts 13 with caramel and 10 are solid chocolate you randomly select one piece eat it and then select a second piece find the probability of selecting to solid in a row
Answers
The probability of selecting two solid chocolates in a row is 0.0607 .
In the question ,
it is given that
there are total 39 chocolates in the box .
number of chocolates filled with nuts = 16
number of chocolates filled with caramel = 13
number of chocolates filled with solid = 10
Probability of selecting first chocolate as a solid is 10/39.
Now , there are 38 chocolates , with 9 solid chocolates ,
hence the probability of selecting second chocolate as a nut is = 9/38
So, the probability of selecting two solid chocolates in a row = 10/39×9/38
= 90/1482
= 0.0607
Therefore , the probability of selecting two solid chocolates in a row is 0.0607 .
The given question is incomplete , the complete question is
There are 39 chocolates in a box, all identically shaped. There 16 are filled with nuts, 13 with caramel, and 10 are solid chocolate. You randomly select one piece, eat it, and then select a second piece. Find the probability of selecting 2 solid chocolates in a row.
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Write an equation of the line that passes through (4, 3) and is parallel to the line defined by 5x-2y-3. Write the answer in slope-intercept form (if possible)
and in standard form (Ax+By-C) with smallest integer coefficients. Use the "Cannot be written" button, if applicable.
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The final answer to the question is highlighted in the box
The area of Bryce is 71.5 sq units.what is the area of abcd?
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Solution
Step 1:
Area of BXYC = 71.5 square units
Step 2:
The area of ABCD is twice the area of BXYC
Step 3:
[tex]\begin{gathered} \text{Area of ABCD = 2 }\times\text{ Area of BXYC} \\ Area\text{ of ABCD = 2 }\times\text{ 71.5} \\ Area\text{ of ABCD = 143 square units} \end{gathered}[/tex]How many angles and sides are there in a Heptagon?ANGLES:SIDES:
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The heptagon is a polygon of 7 sides and 7 angles
The heptagon is a closed figure formed from 7 sides
Since every 2 sides connected to form an angle, then
It contains also 7 angles
Then the answer is :
Angles: 7
Sides: 7
15. x=m<1=I'll upload a picture of my HW
Answers
Opposite angles are the same
Then:
[tex]\begin{gathered} 6x+4=8x\text{ - }18 \\ 18+4=8x\text{ -}6x \\ 22=\text{ 2x} \\ x=\text{ 22/2} \\ x=11 \end{gathered}[/tex]So: (Remember the line has a 180º degrees
using the converse of the same-side interior angles postulate what equation shows that g∥h
Answers
Answer: [tex]\angle 2+\angle 4=180^{\circ}[/tex] or [tex]\angle 1+\angle 3=180^{\circ}[/tex]
