(HELP, I’ll rank u brainliest?) Match each graph with the function that represents it, explain why you matched them that way
Answers
Answer:
\(A \Longrightarrow 1. \:\:f(x) = \log_2(x)\\\\B \Longrightarrow 4. \:\: j(x) = \ln(x)\\\\C \Longrightarrow 3. \:\: h(x) = \log_5(x)\\\\D \Longrightarrow 2. \:\: g(x) = \log_{10}(x)\\\\\)
Step-by-step explanation:
There are a few ways in which you can do this
1. By graphing
2. By comparing the bases of the logs
3. By determining the value of logₐ for some x
You have the right approach, comparing the values of logₐ(100) for a = 2, 10, 5 and e(e ≈ 2.7183) and your answers are correct
At x = 100 we get the following results
\(\log_2 (100) \approx 6.64\\\\\log_{10} (100) = 2\\\\\log_5 (100) \approx 2.86\\\\\ln (100) = \log_e (100) \approx \:4.61\)
Since 6.64 > 4.61 > 2.86 > 2 we get
\(\log_2 (100) > \ln (100) > \log_5 (100) > \log_{10} (100)\)
which means the following are the matches
\(A \Longrightarrow 1. \:\:f(x) = \log_2(x)\\\\B \Longrightarrow 4. \:\:fjx) = \ln(x)\\\\C \Longrightarrow 3. \:\: hfjx) = \log_5(x)\\\\D \Longrightarrow 2. \:\: gjx) = \log_{10}(x)\\\\\)\(A \Longrightarrow 1. \:\:f(x) = \log_2(x)\\\\B \Longrightarrow 4. \:\: j(x) = \ln(x)\\\\C \Longrightarrow 3. \:\: h(x) = \log_5(x)\\\\D \Longrightarrow 2. \:\: g(x) = \log_{10}(x)\\\\\)
A graph of the four functions shows this is so
Another method is to look at the bases of the logs
The smaller the base, the higher up the graph is
Since 2 < e < 5 < 10
\(\log_2 (100) > \ln (100) > \log_5 (100) > \log_{10} (100)\)
Related Questions
1/3 divided dy 7/9 diving fractions
Answers
Answer:
\(\frac{3}{7}\)Step-by-step explanation:
Find the reciprocal of the divisor
Reciprocal of \(\frac{7}{9} : \frac{9}{7}\)
Now, multiply it with the dividend
so, \(\frac{1}{3} ÷ \frac{7}{9} = \frac{1}{3} x \frac{9}{7} = \frac{1x9}{3x7} = \frac{9}{21}\)
after the reducing the fraction, the answer is \(\frac{3}{7}\)
Hope this help you!
Michael is 3 times as old as Brandon. 18 years ago, Michael was 9 times as old as Brandon
How old is Michael?
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Answer: 3b-18=9(b-18)
3b-18=9b-162
6b=144
b=24
3b=72
Brandon is 24, Michael is 72.
Step-by-step explanation:
please answer asap!!
Answers
Answer:
A
Step-by-step explanation:
6 is about halfway to 16
21 is about halfway to 56
they meet up, which makes the line the most accurate
Yw :D
solve by graphingggggggg
Answers
Answer:
Y can't i see the pic
Step-by-step explanation:
i hope you understand these lines
18x + 3y = 33 What is the y intercept form of this equation?
Answers
Answer: look at the picture
Step-by-step explanation: Hope this help:D
Answer: y=-6x+11
Step-by-step explanation:
Please Help
Find (f+g)(x)if f(x)=4x2-5x+8 and g(x)=2x2+x-2
Answers
Answer: (f+g)(x) = 6x²- 4x + 6
Step-by-step explanation:
We add f(x) and g(x) together, (4x²-5x+8) + (2x²+x-2)
Add like terms together, (4x²+2x²) + (-5x+x) +(8-2)
We are left with (f+g)(x) = 6x²- 4x + 6
1.) Solve the following equation for w: 3w-4(w-3) = 6
Answers
Answer: w=6
Step-by-step explanation: 1. Simplify. Distribute the -4 to the w and the -3. -4*w is -4w and -4*-3 is +12, so your left with 3w-4w+12=6.
2. simplify again. 3w-4w is -w.
3. -w+12=6. Subtract w to both sides, so its -w=-6. The negatives cancel out, so w just equals 6.
a water snake in a well is 30 M below the ground level its lights 20 m upward and then slips down 10 M how far it is from the ground level
\( - 30 - + 20 - - 10\)
Answers
If the water snake is initially 30 meters below the ground level and then climbs 20 meters upward, it will be 30 - 20 = 10 meters below the ground level. However, if it then slips down 10 meters, it will be 10 + 10 = 20 meters below the ground level.
Consider the following scores. (i) a score of 40 from a distribution with mean 50 and standard deviation 10 (ii) a score of 45 from a distribution with mean 50 and standard deviation 5 How do the two scores compare relative to their respective distributions
Answers
Answer:
The scores are equal
Step-by-step explanation:
The z-score for any normal distribution is:
\(z=\frac{X-\mu}{\sigma}\)
(i) Score (X) = 40
Mean (μ)= 50
Standard deviation (σ) = 10
\(z=\frac{40-50}{10}\\ z=-1\)
(ii) Score (X) = 45
Mean (μ)= 50
Standard deviation (σ) = 5
\(z=\frac{45-50}{5}\\ z=-1\)
Both scores have the same z-score, which means that, relative to their respective distributions, the scores are equal.
Charges for advertising on a TV show are based on the number of viewers, which is measured by the rating. The rating is a percentage of the population of 110 million TV households. The CBS television show 60 Minutes recently had a rating of 7.8, indicating that 7.8% of the households were tuned to that show. An advertiser conducts an independent survey of 100 households and finds that at least b+1 were tuned to 60 Minutes. Assuming that the 7.8 rating is correct, find the probability of surveying 100 randomly selected households and getting at least 5+1 tuned to
60 Minutes.
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The probability of surveying 100 randomly selected households and getting 4 or fewer tuned to 60 minutes is only 0.02%.
How to calculate the probabilityP(X <= 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)
P(X = k) = (100 choose k) * 0.078^k * (1 - 0.078)^(100-k)
P(X <= 4) = (100 choose 0) * 0.078^0 * (1 - 0.078)^(100-0) + (100 choose 1) * 0.078^1 * (1 - 0.078)^(100-1) + (100 choose 2) * 0.078^2 * (1 - 0.078)^(100-2) + (100 choose 3) * 0.078^3 * (1 - 0.078)^(100-3) + (100 choose 4) * 0.078^4 * (1 - 0.078)^(100-4)
Using a calculator or software, we can find that:
P(X <= 4) = 0.000203
This means that the probability is 0.02%.
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Charges for TV advertising on a TV show are based on the number of viewers, which is measured by the rating. The rating is the percentage of population of 110 million TV households.The CBS television show 60 minutes recently had a rating of 7.8, indicating that 7.8% of the household were tuned to that show.An advertiser conducts an independent survey of 100 households and finds that only 4 were tuned to 60 minutes. Assuming that the 7.8 rating is correct, find the probability of surveying 100 randomly selected households and getting 4 or fewer tuned to 60 minutes.Does the result suggest that the rating of 7.8 is too high?
help pls/////////////////
Answers
Answer:
It might be past the time, but I think the second one.
Step-by-step explanation:
Please help me, I am able to help but not solve on my own.
Answers
The distance traveled by a particle with velocity v(t) in the interval [3,13] is given by the following integral:
\(\int_3^{13}v(t)dt\)However, we can't calculate this integral since we don't have the equation of v(t). What we do have is a table with the value of v for several t's. We can use the values in this table to approximate the integral I wrote above with a trapezoidal sum.
For the function v(t) we have:
\(\int_3^{13}v(t)dt=\frac{1}{2}\sum_{n\mathop{=}1}^4{}\lbrack v(t_{n-1})+v(t_n)\rbrack\cdot(\Delta t)_n\)Where the t's with subindices are the t values given by the table:
\(\begin{gathered} t_0=3 \\ t_1=7 \\ t_2=10 \\ t_3=12 \\ t_4=13 \end{gathered}\)And the Δt's are the lengths of the intervals defined by two consecutive t's. Let's find each Δt:
\(\begin{gathered} (\Delta t)_n=t_n-t_{n-1} \\ (\Delta t)_1=7-3=4 \\ (\Delta t)_2=10-7=3 \\ (\Delta t)_3=12-10=2 \\ (\Delta t)_4=13-12=1 \end{gathered}\)Now I'm going to write the full expression of the trapezoidal sum (expanding the sum):
\(\frac{1}{2}\lbrace\lbrack v(t_0)+v(t_1)\rbrack(\Delta t)_1+\lbrack v(t_1)+v(t_2)\rbrack(\Delta t)_2+\lbrack v(t_2)+v(t_3)\rbrack(\Delta t)_3+\lbrack v(t_3)+v(t_4)\rbrack(\Delta t)_4\rbrace\)Now we use the corresponding v(t) values from the table and we obtain:
\(\begin{gathered} \frac{1}{2}\lbrack(5+9)\cdot4+(9+14)\cdot3+(14+18)\cdot2+18+24\rbrack=\frac{1}{2}\cdot(14\cdot4+23\cdot3+32\cdot2+18+24) \\ =\frac{1}{2}\cdot231=115.5\approx\int_3^{13}v(t)dt \end{gathered}\)AnswerThen the answer is the third option, 115.50.
Can anyone explain why this two is being added before the integral? Does it have something to do with integral symmetry?
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Yes it's exactly due to symmetry. Specifically, symmetry about the x axis.
Simply writing \(\displaystyle \int_{-8}^{-4}\left[\sqrt{x+8} \ \right]dx\), without the 2 out front, will only get you the area of the portion shown in red (see diagram below).
The blue region has equal area of the red region due to symmetry.
So,
\(\displaystyle 2\int_{-8}^{-4}\left[\sqrt{x+8} \ \right]dx\)
represents the red and blue regions combined.
The portion in green is \(\displaystyle \int_{-4}^{8}\left[\sqrt{x+8} - \frac{x}{2} \ \right]dx\) which is the integral of the difference of the upper and lower curves over the interval \(-4 \le x \le 8\)
---------------
In all honesty, it's probably easier to integrate with respect to y since the given functions are in terms of y initially. Also, there isn't a junction point in which the curves swap places in terms of which one is larger. However, it doesn't hurt to have practice in integrating with respect to x.
If you're curious about what the y integral looks like, then it would be
\(\displaystyle \int_{-2}^{4} \bigg[ (2y) - (y^2-8)\bigg] dy\)
You can use a tool like WolframAlpha to check that both integral expressions result in 36 to help confirm that they represent the same overall area (just in different ways of course).
Answer:
Yes - see attached sketch and explanation
Step-by-step explanation:
As you have a sideways parabola, you would need to split the integral into 3 parts.
Find the x coordinate where the parabola first intersects the line: x = - 4.
Now you should be able to see that the parabola between where it intersects the x-axis (x = -8) and the line x = -4 can be split into 2 equal parts (above and below the x-axis). I have shaded these parts as blue and red on my attached sketch.
As the areas above and below the x-axis and the parabola are equal, this can be written as 2 x the area ABOVE the x-axis (the positive integral). So yes, this is why the 2 has been added before the integral, as without the 2 the integral is finding the area ABOVE the x-axis and the parabola curve ONLY.
Then you would find the area between the parabola and the line between x = -4 and x = 8 (shaded grey on my sketch), and as it's only the positive part of the parabola, a normal "integral between 2 curves" can be applied, i.e.
\(\int\limits^a_b {(top-bottom)} \, dx \)
The probability of winning a two-spot Keno game is 0.0601. A win occurs whenever both of the numbers picked by the player are pulled out of the hopper. What is the
probability of losing this game? Round to four decimal places. Put a leading zero on your answer; for example 0.0601.
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The probability of losing the game is 0.9399. So, the answer is 0.9399.
The probability of losing the game is 0.9399. To determine the probability of losing, we must subtract the probability of winning from 1.
The probability of losing is equal to the complement of the probability of winning, and the complement of an event is the probability of the event not occurring.
Therefore, we will calculate the probability of the event not winning.
We know that the probability of winning a two-spot Keno game is 0.0601.
This means that the probability of not winning is 1 - 0.0601 = 0.9399.
Therefore, the probability of losing the game is 0.9399. So, the answer is 0.9399.
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If you were to reflect the coordinates (4,6), (12,2), and (-1,0) about the y-axis, what would
then be your new coordinates?
Answers
Answer:
Step-by-step explanation:
When reflecting coordinates about the y-axis, we change the sign of the x-coordinate while keeping the y-coordinate the same.
So, for the point (4, 6), the new coordinates after reflection about the y-axis would be (-4, 6).
For the point (12, 2), the new coordinates would be (-12, 2).
For the point (-1, 0), the new coordinates would be (1, 0).
Therefore, the new coordinates after reflecting these points about the y-axis are (-4, 6), (-12, 2), and (1, 0).
Find the value of x, 6,4, 3x, 4x+1
Answers
Answer:
If two chords intersect in a circle, then the product of the segments of one chord equals the product of the segments of the other chord.
6(3x) = 4(4x + 1)
18x = 16x + 4
2x = 4
x = 2
Ann 's car can go 132 miles on 4 gallons of gas. During a drive last weekend, Ann used 5 gallons of gas. How far did she drive? Use pencil and paper. Explain how the problem changes if you were given the distance Ann drove last weekend instead of how much gas she used.
Answers
Answer:
Ann traveled 165 miles on 5 gallons of gas
Step-by-step explanation:
First we must know how many miles are in a gallon (in this situation). Last weekend Ann drove 132 miles with 4 gallons of gas, we can divide to find out how many miles she drove on 1 gallon. 132/4 = 33. This means Ann drove 33 miles on 1 gallon of gas. To get your answer, simply multiply 5 and 33. 5 times 33 = 165.
am I right for part A. And please help me with B
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a) The radius of the sphere is given as follows: 27.13 ft.
b) The surface area can be checked as follows: S = 4 x 3.14 x 27.13² = 9244.
How to obtain the surface area?The surface area for a sphere of radius r is given by the equation presented as follows:
S = 4πr².
The surface area for this problem is given as follows:
9244 ft².
Hence the radius is given as follows:
\(r = \sqrt{\frac{9244}{4 \times 3.14}}\)
r = 27.13 ft.
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What is the value of y?
3
4
5
6
Answers
Answer:
y = 3
Step-by-step explanation:
2y + 4 = 10
2y = 6
y = 3
Answer:
Its A- 3
Step-by-step explanation:
I did the quiz
Guided Practice
Find the balance in the account.
$4000 principal earning 6% compounded annually, after 5 years
A.
$5352.90
B.
$6872.20
C.
$4240
Answers
Answer:
A.
$5352.90
Step-by-step explanation:
A=p(1+r)^t
A=4,000×(1+0.06)^(5)
A=5,352.90
.........................................................
Answer:
The Final Investment Value is
Step-by-step explanation:
we know that
The compound interest formula is equal to
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
substitute in the formula above
Ejemplo: catalina compro una piscina para
ponerla en el jardín de su casa.
-Piscina cilíndrica 206cm de diámetro y 60cm
de profundidad además construirá una zona de
cemento y cerco de seguridad alrededor de la
piscina.
¿Cuál es el volumen máximo de agua que
puede contener la piscina? (considere T=3)
¿cuál es la extensión del cerco de seguridad?
(considere П=3)
Answers
The length of the fence must be 618cm
The volume that it can hold is 1,909,620 cm³
How to find the volume and the length of the fence?First, the fence is just equal to the circumference of the cylinder, remember that the circumfernce of a circle of diameter D is:
C = П*D
Here we use П = 3, then:
C = П*206cm
C = 3*206cm = 618cm
Now the volume, for a cylinder of diameter D and height H, the volume is:
V = П*(D/2)²*H
Replacing the values that we know we will get:
V = 3*(206cm/2)²*60cm = 1,909,620 cm³
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I need help with this!
Answers
The length AC in the kite is 8.7 cm.
How to find the side AC in the kite?A kite is a quadrilateral that has two pairs of consecutive equal sides and
perpendicular diagonals. Therefore, let's find the length AC in the kite.
Hence, using Pythagoras's theorem, let's find CE.
Therefore,
7² - 4² = CE²
CE = √49 - 16
CE = √33
CE = √33
Let's find AE as follows:
5²- 4² = AE²
AE = √25 - 16
AE = √9
AE = 3 units
Therefore,
AC = √33 + 3
AC = 5.74456264654 + 3
AC = 8.74456264654
AC = 8.7 units
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The length of a rectangle is twice its width. Find its lenght and width, if its perimeter is 7 1/3 cm.
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The length of the rectangle is twice its width. If its perimeter is 7 1/3 cm, its length will be 22/9 cm, and the width is 11/9 cm.
Let's assume the width of the rectangle is "b" cm.
According to the given information, the length of the rectangle is twice its width, so the length would be "2b" cm.
The formula for the perimeter of a rectangle is given by:
Perimeter = 2 * (length + width)
Substituting the given perimeter value, we have:
7 1/3 cm = 2 * (2b + b)
To simplify the calculation, let's convert 7 1/3 to an improper fraction:
7 1/3 = (3*7 + 1)/3 = 22/3
Rewriting the equation:
22/3 = 2 * (3b)
Simplifying further:
22/3 = 6b
To solve for "b," we can divide both sides by 6:
b = (22/3) / 6 = 22/18 = 11/9 cm
Therefore, the width of the rectangle is 11/9 cm.
To find the length, we can substitute the width back into the equation:
Length = 2b = 2 * (11/9) = 22/9 cm
So, the length of the rectangle is 22/9 cm, and the width is 11/9 cm.
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A cake mix calls for these ingredients 3 cups of milk 6 cups of flour 2 cups of sugar 1 cup of oil Which is the lowest ratio?
Answers
Answer:
3:6:2:1
Step-by-step explanation:
You can't divide any of them with a common denominator anymore, this is the lowest ratio.
In 2011 Staci invested $14,000 in a savings account for her newborn son. The account pays 3.4% interest each year. Determine the accrued value of the account in the year 2029, when her son will go to college. Round your answer the nearest cent.In the year 2029, the accrued value will be $
Answers
EXPLANATION
We need to use the Compounding Interest Equation as shown as follows:
\(A=P(1+\frac{r}{n})^{nt}\)Where P=Principal = 14,000 r=rate in decimal form = 3.4/100 = 0.034 n=number of times interest is compounded per unit 't' = 1 t= time = 2029 - 2011 = 18 years
Plugging in the terms into the expression:
\(A=14,000(1+\frac{0.034}{18})^{1\cdot18}\)Adding numbers:
\(A=14,000(\frac{9017}{9000})^{1\cdot18}\)Computing the power:
\(A=14,000(1.034)\)Multiplying numbers:
\(A=14,476\)In conclusion, in the year 2029 the value will be $14,476
The perimeter of the triangle shown is 225 feet, find the length of each side
X feet = How many Feet?
5x feet = how many feet?
(6x - 3) feet = for many feet?
Answers
Answer:
I have solved it and attached in the explanation.
Step-by-step explanation:
F(x)=(x+2)^2 (x-3) graph the function
Answers
The value of the equation f ( x ) is
f ( x ) = x³ + x² - 8x - 12
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
f ( x ) = ( x + 2 )²( x -3 ) be equation (1)
Now , on simplifying the equation , we get
f ( x ) = ( x + 2 )²( x -3 )
f ( x ) = ( x² + 4x + 4 ) ( x - 3 )
Now , multiplying each term with ( x - 3 ) , we get
f ( x ) = ( x - 3 ) x² + ( x - 3 ) 4x + ( x - 3 ) 4
f ( x ) = x³ - 3x² + 4x² - 12x + 4x - 12
On simplifying the equation ,we get
f ( x ) = x³ + x² - 8x - 12
Now , the value of the equation f ( x ) = x³ + x² - 8x - 12
On graphing the equation , we get
The graph of the equation f ( x ) = x³ + x² - 8x - 12 is shown below
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Herman took out a loan for $8,500 at a rate of 8% for a term of 10 years. How much interest will he pay on the loan?
Answers
Answer:
Monthly loan payment is $400.76 for 60 payments at 7.5%.
Step-by-step explanation:
YA'LL ARE SMART!! PLEASE HELP!!
Answers
Answer:
Its C
Step-by-step explanation:
Substitute in 3 for x and check. The equation doesn't work.
Substitute 2 in for y. The equation still doesn't work.
So its right.
lol are u using edguenity
rip
A trough is an open container that is used to hold food or water for animals. The figure below shows a water trough.
1 4. How much ground is covered by the trough?
15. How much metal is needed to make the trough?
16. How much water can the trough hold?
Answers
Answer:
8 ft², 21.8ft², and 11.2ft²
Step-by-step explanation: