Answer:
I =2000(0.075)4= $600
Step-by-step explanation:
A Weather Forecaster, predicts that there is a 30% chance of rain on Saturday and a 40% chance of rain on Sunday. If these probabilities are correct, what is the probability that it will rain both days?
35%
10%
12%
70%
"The correct answer is C. The statement If these probabilities are correct, 12%is the probability that it will rain both days
To find the probability that it will rain both days, we need to multiply the probability of rain on Saturday by the probability of rain on Sunday, assuming that the events are independent.
The probability of rain on Saturday is 30%, which can be expressed as 0.30 or[tex]\(\frac{30}{100}\)[/tex].
The probability of rain on Sunday is 40%, which can be expressed as 0.40 or[tex]\(\frac{40}{100}\)[/tex].
Now, we multiply these two probabilities to find the probability of both events occurring:
[tex]\[ P(\text{Rain on Saturday}) \times P(\text{Rain on Sunday}) = \frac{30}{100} \times \frac{40}{100} \][/tex]
[tex]\[ \frac{30}{100} \times \frac{40}{100} = \frac{30 \times 40}{100 \times 100} \] \[ \frac{30 \times 40}{100 \times 100} = \frac{1200}{10000} \] \[ \frac{1200}{10000} = \frac{12}{100} \] \[ \frac{12}{100} = 0.12 \][/tex]
Converting this decimal to a percentage, we get 12%.
Therefore, the probability that it will rain both days is 12%."
According to the diagram, which way is the magnetic
field pointing?
O into the screen
O out of the screen
O left
Oright
Answer:
The answer is left
Step-by-step explanation:
Answer:
Left
Step-by-step explanation:
Took it on edg
1024 players in a tennis tournament in each round half the players are eliminated which function can be used to find the number of players remaining in the tournament at the end of x rounds
Answer:
Option B. 1024(0.5)^x
Step-by-step explanation:
From the question given, we were told that half (1/2) the players are eliminated at the end of each round.
If T is the total number players, then after round one it becomes:
T x (1/2)^1 = T x 0.5
After round x, the the numbers of player remaining will be:
T x (1/2)^x = T x (0.5)^x
From the question given, the total number of players are 1024. Therefore, the above expression can be written as:
T x (0.5)^x => 1024(0.5)^x
I need help please???
Answer:
i think it is E
Step-by-step explanation:
if you have 2 cookies and split them between 3 friends including you how much cookie will each person get?
Answer:
[tex]\frac{2}{3}[/tex] or [tex].666666666[/tex] or [tex]\%66.66[/tex]
Step-by-step explanation:
Answer:
Each person would get 2/3
Step-by-step explanation:
Split the two circles and each person gets one portion of it.
What is the surface area of the triangular prism?
a
2,001 square feet
b
2,376 square feet
c
2,592 square feet
d
4,320 square feet
Answer:
BStep-by-step explanation:
2376
Debbie bought 8 1/2 lb of ground turkey. She packed the turkey in 1/2 lb containers and put them in the freezer. How many containers of ground turkey did she pack?
Answer: 17 containers
Step-by-step explanation:
Debbie bought 8 1/2 lb of ground turkey and she packed the turkey in 1/2 lb containers before put the turkeys in the freezer.
To calculate the number of containers she used for packing the turkey, we divide 8 1/2lb by 1/2 lb.
= 8 1/2 ÷ 1/2
We change 8 1/2 to improper fraction
= 17/2 ÷ 1/2
= 17/2 × 2/1
= 17
Debbie would need 17 containers to pack the turkey.
Answer:
Debbie will need 17 containers to pack the turkey.
Step-by-step explanation:
Debbie bought 8 1/2 lb of ground turkey
she packed the turkey in 1/2 lb containers
To know the number of containers she used for packing the turkey,
we divide 8 1/2lb of ground turkey by 1/2 lb containers.
[tex]=8\frac{1}{2} \div \frac{1}{2}[/tex]
[tex]= \frac{17}{2} \div \frac{1}{2}[/tex]
[tex]= \frac{17}{2} \times \frac{2}{1}[/tex]
[tex]=\frac{34}{2} \\\\= 17[/tex]
Debbie will need 17 containers to pack the turkey.
What is the answer and how you solved it plz I need help
Answer:
3/6
Step-by-step explanation:
there are 3 white slice, two grey slice and 1 black slice. in total there are six slices. so the answer is 3/6.
hope it helps
An electronic tuning aid is often used by a piano tuner to properly tune a piano. The frequency of the 64th key on a standard 88-key piano is 1046.5 hertz. Write a sine model that gives the Tone, T, as a function of time, t, for this key.
Answer:
T = sin(6572t)
Step-by-step explanation:
A pure tone is a sine-wave and sine-waves are defined by ω (omega) and t (time)
For a sine model:
Amplitude of wave form = sin(ωt)
A sine model that gives the Tone, T, as a function of time, t, for this key:
T = sin(ωt)
Sin is a mathematical operator in trigonometry
ω = 2πf
π = 3.14
The frequency of the 64th key on a standard 88-key piano is 1046.5 hertz.
f = 1046.5 hertz
ω = 2×3.14×1046.5
ω = 6572.02
T = sin(6572t)
The sine model for the 64th key on a standard 88-key piano with a frequency of 1046.5 Hz is represented as T(t) = A sin(2π(1046.5)t + φ), where A is the amplitude, φ is the phase shift, and t is the time.
The student has asked for a sine model that represents the Tone, T, as a function of time, t, for the 64th key on a standard 88-key piano, which has a frequency of 1046.5 hertz. A sine function that models the tone can be written as:
T(t) = A sin(2πft + φ)
For this example, since frequency (f) is given as 1046.5 Hz and we don't have information about amplitude (A) and phase shift (φ), we can write the model as:
T(t) = A sin(2π(1046.5)t + φ)
This model can be used by piano tuners to ensure that the piano is properly tuned by comparing the accurate frequency with the sound coming from the piano and making adjustments as needed.
Activity
Patricia and her brother Ian help themselves to a pitcher of lemonade on the kitchen counter. Patricia takes a glass and fills it with p ounces of lemonade. Ian takes a bigger glass and pours himself 20% more lemonade than Patricia poured in her glass. Write an expression to represent the quantity of lemonade (in ounces) in Ian’s glass in terms of the quantity in Patricia’s glass (p).
Complete the steps below to solve the problem.
Part A
Write an expression in terms of p that shows how many more ounces Ian poured in his glass than Patricia poured in hers.
a = (1+0.2)p
This equation is used to calculate the quantity of lemonade.
Step-by-step explanation:
Let the quality of lemonade in lans glass be 'a'
Quantity of lemonade in patricias glass = p ounces
Lan pours 20% more than Patricia
a = (1+0.2)p
This equation is used to calculate the quantity of lemonade
Answer:
Patricia poured P ounces of lemonade in her glass. Ian poured 20% more than P ounces in his glass; that is, he poured 0.20p or .2p ounces more than Patricia.
ANSWER: 0.20p
Step-by-step explanation:
You're ordering a one-topping pizza. You can choose from 3 different toppings and 2 types of crust. If you randomly pick the topping and crust, which of these diagrams can be used to find all of the different kinds of pizza you can order?
Answer:
Table A
Step-by-step explanation:
It's only Table A because if you look at Table B at the top it says
Topping 1 and Topping 2
You're only supposed to have Crust and Topping, not 2 toppings
Answer:
Table A
Step-by-step explanation:
Khan
It's believed that as many as 24% of adults over 50 never graduated from high school. We wish to see if this percentage is the same among the 25 to 30 age group. What sample size would allow us to increase our confidence level to 95% while reducing the margin of error to only 4%?
Answer:
n=438
Step-by-step explanation:
-Given the sample proportion [tex]\hat p=0.24[/tex] and the confidence level is 95%.
-The sample size can be calculated using the formula;
[tex]ME=z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
#Substitute parameters in the formula and make n the subject of the formula;
[tex]ME=z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}\\\\=z_{0.025}\sqrt{\frac{\hat p(1-\hat p)}{n}}\\\\n=(\frac{z_{0.025}}{ME})^2\hat p(1-\hat p)\\\\\\=(\frac{1.96}{0.04})^2\times 0.24\times 0.76\\\\=437.94\approx 438[/tex]
Hence, the desired sample size is n=438
15 kilograms of rice are separated equally into 4 containers. How many kilograms of rice are in each container? Express your answer as a decimal and as a fraction. Hint: Use the remainder to form fractions
We needa use fractions to solve this so help
Answer: Fraction= 3 3/4kg
Decimal= 3.75kg
Step-by-step explanation:
15 kilograms of rice are separated equally into 4 containers. To get the number of kilograms of rice are in each container, we divide the total kilograms of rice by the number of containers. This will be:
Kilograms of rice in each container=
15/4 =3 3/4kg as a fraction.
To convert the fraction to decimal, we divide 3 by 4 and add to 3. 3/4 equals 0.75. We then add 3 to 0.75. This will be:
Decimal of 3 3/4 = 3+0.75 = 3.75kg
Lily model car covers 250 m in 5 minutes. what is the average speed of her car?
please show all work, thanks
Answer:
50m per 1 minute
Step-by-step explanation:
250m/5 min=50/1
pls mark brainliest!! i only need one more!
Jorge watches cars that pass in front of his house. He counts 25 red cars and 40 cars that are not red. What is the approximate probability that the next car Jorge sees is red?
A) 62.5 %
B) 8/5
C) 0.33
D) 5/13
Step-by-step explanation:
firstly you will add
the red cars and non red cars together and which is 65
probability of the red car = 25/65
to the lowest form is the 5/13(D)
Answer:
its D
Step-by-step explanation:
On the spring an entire field of flowering trees blossoms. The population of focusts consuming these Flowers rapidly increases as the trees blossom The relationship between the elapsed time in weekssince the beginning of spring, and the total number of focusts N(t) is modeled the following function N(t) = 300 * (49/16) ^ t Complete the following sentence about the rate of change of the locust population. Round your answer to two decimal places. On the spring an entire field of flowering trees blossoms. The population of focusts consuming these Flowers rapidly increases as the trees blossom The relationship between the elapsed time in weekssince the beginning of spring, and the total number of focusts N(t) is modeled the following function N(t) = 300 * (49/16) ^t Complete the following sentence about the rate of change of the locust population. Round your answer to two decimal places.
Answer:.5
Step-by-step explanation:
.5
If there are 192 students in 4 buses, then how many students are in each bus
Answer:
48 in each bus
Step-by-step explanation:
divide 192 by 4
Answer: 48
Step-by-step explanation:
If there are 4 buses and 192 students you divide 192 by 4 and get 48
The rectangle below has an area of x2 - 4x - 12 square meters and a length of x + 2 meters.
What expression represents the width of the rectangle?
X+2
Width
x² - 4x – 12
Width =
meters
Answer:
w=(x-6)
Step-by-step explanation:
x^2-4x-12=(x + 2)(w)
a=wl (area equals width times length)
x^2-4x-12=(x + 2)(w)
(x-6)(x+2)=(x + 2)(w)
(x-6)=w
Convert the unit mass . Enter your answer in the box
6.75 kg = _____ g
Answer:
6750
Step-by-step explanation:
There are 1000g in a single kilogram. Therefore, [tex]\frac{6.75kg}{1}\cdot \frac{1000}{1kg}=6750g[/tex]. Hope this helps!
Answer:
6750
Step-by-step explanation:
Lukas plotted these points on the number line. Point A: −12 3 Point B: −2 3 Point C: −11 3 Point D: −22 3 Which point did he plot incorrectly? Point
Answer:
The answer is A.
Answer: The Answer is A
Step-by-step explanation:
Hector invests $800 in an account that earns 6.96% annual interest compounded semiannually. Rebecca invests $1,000 in an account that earns 5.44% annual interest compounded monthly. Find when the value of Rebecca's investment equals the value of Hector's investment and find the common value of the investments at that time. If necessary, enter the year to the nearest tenth and the value to the nearest cent. The value of Rebecca's investment equals the value of Hector's investment after approximately ________ years to the nearest tenth. The common value of the investments is approximately $_________ .
Answer:
The value of Rebecca's investment equals the value of Hector's investment after approximately 15.8 years to the nearest tenth
The common value of the investments is approximately $2358.05
Step-by-step explanation:
The formula of the compound interest including the principal is
[tex]A=P(1+\frac{r}{n})^{nt}[/tex] , where
A is the future value of the investment/loan, including interestP is the principal investment amountr is the annual interest rate (decimal)n is the number of times that interest is compounded per unit tt is the time the money is invested or borrowed forHector invests $800 in an account that earns 6.96% annual interest compounded semiannually
∵ P = 800
∵ r = 6.96 = [tex]\frac{6.96}{100}[/tex] = 0.0696
∵ n = 2 ⇒ semiannually
- Substitute all these values in the formula to find future value
∴ [tex]A=800(1+\frac{0.0696}{2})^{2t}[/tex]
∴ [tex]A=800(1.0348)^{2t}[/tex]
Rebecca invests $1,000 in an account that earns 5.44% annual interest compounded monthly
∵ P = 1,000
∵ r = 5.44 = [tex]\frac{5.44}{100}[/tex] = 0.0544
∵ n = 12 ⇒ monthly
- Substitute all these values in the formula to find future value
∴ [tex]A=1000(1+\frac{0.0544}{12})^{12t}[/tex]
∴ [tex]A=1000(1.004533333)^{12t}[/tex]
∵ Rebecca's investment equals the value of Hector's investment
- Equate the two equations
∵ [tex]1000(1.004533333)^{12t}[/tex] = [tex]800(1.0348)^{2t}[/tex]
- Insert ㏑ in both sides and remember ㏑(ab) = ㏑(a) + ㏑(b)
∴ ㏑( [tex]1000(1.004533333)^{12t}[/tex] ) = ㏑( [tex]800(1.0348)^{2t}[/tex] )
∴ ㏑(1000) + ㏑( [tex](1.004533333)^{12t}[/tex] ) = ㏑(800) + ㏑( [tex](1.0348)^{2t}[/tex] )
- Remember [tex]ln(a)^{n}[/tex] = n ㏑(a)
∴ ㏑(1000) + 12t [㏑(1.004533333)] = ㏑(800) + 2t [㏑(1.0348)]
- Subtract ㏑(800) and 12t [㏑(1.004533333)] from both sides
∴ ㏑(1000) - ㏑(800) = 2t [㏑(1.0348)] - 12t [㏑(1.004533333)]
- Take t as a common factor from the right hand side
∴ ㏑(1000) - ㏑(800) = t(2[㏑(1.0348)] - 12[㏑(1.004533333)])
- Divide both sides by (2[㏑(1.0348)] - 12[㏑(1.004533333)])
∴ 15.8 = t
The value of Rebecca's investment equals the value of Hector's investment after approximately 15.8 years to the nearest tenth
Let us find this value using Hector or Rebecca equations
∵ [tex]A=800(1.0348)^{2t}[/tex]
- Substitute t by 15.8
∴ [tex]A=800(1.0348)^{2(15.8)}[/tex]
∴ A = 2358.05
The common value of the investments is approximately $2358.05
A travel mug of 87∘C coffee is left on the roof of a parked car on a cold winter day. The temperature of the coffee after t minutes is given by H=87(2)−t/14. After how many minutes will the coffee be only lukewarm (30∘C)?
Answer:
After 21.28 minutes will the coffee be only lukewarm (30∘C)
Step-by-step explanation:
Given -
A travel mug of 87∘C coffee is left on the roof of a parked car on a cold winter day . The temperature of the coffee after t minutes is given by
[tex]H = 87(2)^{\frac{-t}{14}}[/tex]
Let after [tex]t_{1}[/tex] time H will be [tex]$30^\circ$[/tex]C
put t = [tex]t_{1}[/tex] , H = [tex]$30^\circ$[/tex]C
[tex]30 = 87(2)^{\frac{-t_{1}}{14}}[/tex]
[tex]\frac{30}{87} = (2)^{\frac{-t_{1}}{14}}[/tex]
.3448275 = [tex](2)^{\frac{-t_{1}}{14}}[/tex]
Taking logarithm both side
[ [tex]log(2^{x}) = xlog2[/tex] ]
log.3448275 = [tex]{\frac{-t_{1}}{14}}[/tex] log 2
-.4581 = [tex]{\frac{-t_{1}}{14}} \times.3010[/tex]
[tex]{\frac{-t_{1}}{14}}[/tex] = -1.52
[tex]t_{1}[/tex] = 21.28 minutes
To find the time it will take for the coffee to cool to 30 degrees Celsius, we need to solve the equation 30=87(2)−t/14 for the variable 't', which represents time.
Explanation:The subject of this problem is a mathematical application of heat transfer. To answer this question thoroughly, we need to solve the given equation H=87(2)−t/14 for 't' when H (the temperature of the coffee) is 30 degrees Celsius.
When we set H equal to 30, we can rearrange the equation to solve for 't':
Set H=30. The new equation becomes 30=87(2)−t/14. By simplifying the equation, we find t=(87(2)-30)*14.The solution of 't' will give the time it will take the coffee to reach 30 degrees Celsius.While this equation primarily pertains to heat transfer, it is also fundamentally about solving algebraic expressions, the core focus of high school Mathematics.
Learn more about Solving Algebraic Expressions here:https://brainly.com/question/39818720
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Students were surveyed about their preference between dogs and cats. The following two-way table displays
data for the sample of students who responded to the survey.
Approximately what percent of students in the sample prefer cats?
Round your answer to the nearest percent.
X
D
Male
Female
TOTAL
Preference
Prefers dogs
N
Prefers cats
No preference
TOTAL
2
The 36% of the students in the sample prefer cats. Hence, 36% is correct answer.
The step-by-step calculation to determine what percent of students in sample prefer cats:
1) Find the total number of students who prefer cats:
Add the number of male students who prefer cats (10) to the number of female students who prefer cats (26). 10 + 26 = 36
2) Find the total number of students surveyed:
Add the number of students who prefer dogs (36 + 20), the number of students who prefer cats (36), and the number of students with no preference (2 + 6). 36 + 20 + 36 + 2 + 6 = 100
3) Calculate the percentage of students who prefer cats:
Divide number of students who prefer cats (36) by the total number of students surveyed (100) and multiply by 100%. 36 / 100 * 100% = 36%
4) Round the answer to the nearest percent:
36% rounded to nearest percent is 36%.
Complete and correct question is in the image:
According to the given sample, 36% of students in the sample prefer cats.
To find the percentage of students in the sample who prefer cats, we need to sum up the number of students who prefer cats, which is 26 for females and 10 for males.
Total number of students who prefer cats = 26 (females) + 10 (males) = 36.
Now, let's find the total number of students in the sample:
Total number of students = 36 (males who prefer dogs) + 20 (females who prefer dogs) + 10 (males who prefer cats) + 26 (females who prefer cats) + 2 (males with no preference) + 6 (females with no preference)
= 36 + 20 + 10 + 26 + 2 + 6
= 100.
Now, we can calculate the percentage of students who prefer cats:
Percentage of students who prefer cats = [tex]\frac{Number \ of \ students \ who \ prefer \ cats}{Total \ number \ of \ students}[/tex] × 100
= ([tex]\frac{36}{100}[/tex]) × 100 = 36%.
So, approximately 36% of students in the sample prefer cats.
The question is:
Students were surveyed about their preference between dogs and cats. The following two-way table displays data for the sample of students who responded to the survey.
Preference Male Female
Prefers dogs 36 20
Prefers cats 10 26
No preference 2 6
Approximately what per cent of students in the sample prefer cats?
ABC is translated onto A’B’C’. The coordinates of point A are (3, 7) and the coordinates of
point A’ are (1, 12). If the coordinates of point B are (7, 2), what are the coordinates of point
B’?
The horizontal shift from point A to point A’ is _______. The vertical shift from point A to
point A’ is _______. Since in a translation all points shift the same distance, the coordinates of
point B’ are ( ____, ____ ).
Answer:
The horizontal shift from point A to point A’ is -2. The vertical shift from point A to point A’ is 5. Since in a translation all points shift the same distance, the coordinates of point B’ are (5, 7 ).
Step-by-step explanation:
A moved two units to the left.
1 - 3 = -2
A also moved 5 units up.
12 - 7 = 5
The translation rule is: [tex](x,y) -> (x - 2, y + 5)[/tex]
Apply the translation rule to point B.
[tex](7 -2, 2+5) = (5,7)[/tex]
B' should be (5,7).
Answers and Step-by-step explanations:
1. The horizontal shift from point A to point A' will simply be the difference in the x-coordinates. The x-coordinate of A is 3 and the x-coordinate of A' is 1. So, we take 1 - 3 = -2. The horizontal shift is 2 units to the left.
2. The vertical shift is the difference in the y-coordinates. The y-coordinate of A is 7 and the y-coordinate of A' is 12. So, we take 12 - 7 = 5. The vertical shift is 5 units up.
3. Basically, we want to move the coordinates of B 2 units to the left and 5 units up. B is currently (7, 2). When we move 2 units to the left, we subtract 2 from the x-coordinate 7, and when we move 5 units up, we add 5 to the y-coordinate 2: B' = (7 - 2, 2 + 5) = (5, 7)
Hope this helps!
Shameeka sold her hamsters to a pet store. This doubled the number of hamsters in the store. Then the store got six more hamsters. If the pet store has 46 hamsters now, how many did shameeka sell to the store
Answer: shameeka sold 20 hamsters to the store.
Step-by-step explanation:
Let x represent the number of hamsters that shameeka sold to the store.
Let y represent the number of hamsters that the pet store had initially.
Shameeka sold her hamsters to a pet store. This doubled the number of hamsters in the store. It means that
x + y = 2y
x = 2y - y
x = y
Then the store got six more hamsters. If the pet store has 46 hamsters now, it means that
2y + 6 = 46
2y = 46 - 6
2y = 40
y = 40/2
y = 20
Since x = y, then
x = 20
When trying to find the probability of rolling an even number on a number cube with numbers 1 through 6, how many desired outcomes are there?
Answer:
3
Step-by-step explanation:
3 even numbers 2,4,6
or 1/2
or 50%
The graph of a quadratic function has a vertex at the point (8,6). It passes through the point (-4,-5). Which of the following equations
represents this function?
Answer:
y= -11/144(x-8)^2+6
Step-by-step explanation:
This equation can be represented in vertex form, which is:
y=a(x-h)^2+k
If we plug in 8 as h and 6 as k we get the following equation:
y=a(x-8)^2+6
Now we have to plug in x and y. We can use the other point (-4,-5) and plug it into the equation and get:
-5=a(-4-8)^2+6
Once we solve this we get a= -11/144
Now we have to plug in -11/144 into the original equation to get
y = -11/144 (x-8)^2 + 6
A circle graph titled Education Level. 13 percent is some high school, 26 percent is completed high school, 27 percent is some college, 34 percent is completed college. This graph shows the results of 150 people surveyed. How many people completed college? people
Answer:
51
Step-by-step explanation:
Just did it on edgu
Final answer:
Based on the circle graph, 34 percent of the 150 surveyed people completed college, which translates to 51 individuals.
Explanation:
The question asks how many people completed college based on a circle graph showing the education levels of 150 surveyed individuals. To answer this, we use the percentage given for those who completed college and apply it to the total number surveyed. With 34 percent having completed college, we calculate the number of people by multiplying 34 percent (or 0.34 as a decimal) by the total survey number, 150 people.
The calculation is as follows: 0.34 × 150 = 51. Therefore, 51 people surveyed completed college.
Mrs. Lia has 19 pounds of modeling clay. She divides the clay into 1/2
pound blocks.
If Mrs. Lla sets aside 9 of the blocks and gives the rest to the students in her art class, how many 1/2 pound
blocks of clay does Mrs. Lia glve to her class?
Consider the equation below. log Subscript 4 Baseline (x + 3) = log Subscript 2 Baseline (2 + x) Which system of equations can represent the equation? y 1 = StartFraction log (x + 3) Over log 4 EndFraction, y 2 = StartFraction log (2 + x) Over log 2 EndFraction y 1 = StartFraction log x + 3 Over log 4 EndFraction, y 2 = StartFraction log 2 + x Over log 2 EndFraction y 1 = StartFraction log 4 Over log 2 EndFraction, y 2 = StartFraction log (x + 3) Over log (2 + x) EndFraction y 1 = StartFraction log x + 3 Over 4 EndFraction, y 2 = StartFraction log 2 + x Over 2 EndFraction
Answer:
A
Step-by-step explanation:
just took the quiz on edgen
The system of equations that can represent the equation is,[tex]\rm y_1 = \frac{log(x+3)}{log 4} , y_2 = \frac{log(2+x)}{log 2}[/tex].Option A is correct.
What is the definition of a logarithm?Exponents can also be written as logarithms. The other number is equal to a logarithm with a number base. It's the exact inverse of the exponent function.
The property of the logarithm is found as;
[tex]\rm log_b(a) = \frac{log_x(a)}{log_x(b)}[/tex]
Given equation;
[tex]\rm log_4(x+3) = log_2(2+x)[/tex]
LHS;
[tex]\rm log_b(a) = \frac{log_x(a)}{log_x(b)} \\\\ \rm log_4(x+3) \\\\ y_1 = \rm y_1 = \frac{log(x+3)}{log 4}[/tex]
RHS;
[tex]\rm log_b(a) = \frac{log_x(a)}{log_x(b)} \\\\ \rm log_2(2+x) \\\\ y_2 = \frac{log(2+x)}{log 2}[/tex]
The system of equations that can represent the equation is,[tex]\rm y_1 = \frac{log(x+3)}{log 4} , y_2 = \frac{log(2+x)}{log 2}[/tex].Option A is correct.
Hence, option A is correct.
To learn more about the logarithm refer ;
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