The simplified exponential expression for this problem is given as follows:
(3² x 5)³ = 3^6 x 5³.
How to simplify the expression?The exponential expression for this problem is defined as follows:
(3² x 5)³.
As we have a product applied to the exponent, the exponent can be applied to each factor of the exponent, as follows:
(3²)³ x 5³.
Applying the power of power rule, we have that:
(3²)³ = 3^(2 x 3) = 3^6.
Hence the simplified exponential expression for this problem is given as follows:
(3² x 5)³ = 3^6 x 5³.
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Select the inequality that models the problem.
The sum of two consecutive odd integers is at least 76. Find the least possible pair of integers.
A) n + n + 2 > 76
B) n + n + 1 ≥ 76
C) n + n + 2 ≥ 76
D) n + n + 1 > 76
By resolving the inequality, we discovered that the least possible pair of numbers is (37,39) if the total of two consecutive odd integers is at least 76.
The sum of two consecutive odd integers is at least 76.
First we let the two consecutive odd integers.
The first consecutive odd integer = n
The second consecutive odd integer = n + 2
The sum is at least 76. So the inequality that models the problem is
n + n + 2 ≥ 76
Now we determine the least possible pair of integers by solving the inequality.
2n + 2 ≥ 76
Subtract 2 on both side, we get
2n ≥ 74
Divide by 2 on both side, we get
n ≥ 37
If the least value of x is 37. So
The second odd integer = x + 2 = 37 + 2 = 39
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Basil has 5 numbered cards. Two of the numbers are hidden. The mode of the 5 is 8. The mean of the 5 is 6. Work out the two hidden numbers
Two hidden cards out of five numbered cards with 8 as mode and 6 as mean of five numbers is equal to 8 and 1.
Total number of numbered cards is equal to 5
Number of hidden cards are two.
Let us consider two hidden cards be 'a' and 'b'.
Mode of the five numbered cards is 8
Three numbers are 4 , 9 , a, b, 8.
Mode represents the number with higher frequency.
4, 9, 8 only one time as 8 is the mode one of the number should be equal to 8.
let b = 8
Mean of five numbers is 6
Mean = ( Sum of all the numbers ) / total numbers
⇒ 6 = ( 4 + 9 + a + 8 + 8 ) / 5
⇒ 30 = 29 + a
⇒ a = 30 -29
⇒ a = 1
Therefore, two hidden numbers for the given mode and mean is equal to 8 and 1.
The above question is incomplete , the compete question is:
Basil has five numbered cards.
Two of the numbers are hidden. 4 9 ? ? 8
The mode of the five numbers is 8.
The mean of the five numbers is 6
c) Work out the two hidden numbers.
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Use logarithms to solve: 9x=4
The value of given expression 9x=4 equals to 4/9.
What is Algebraic expression ?
Algebraic expressions are the concept of expressing numbers the usage of letters or alphabets without specifying their real values. The basics of algebra taught us how to express an unknown fee using letters which includes x, y, z, and so forth. these letters are known as here as variables. An algebraic expression can be a aggregate of both variables and constants. Any price that is placed before and accelerated through a variable is a coefficient.
Given expression ,
log 9x = log 4
log 9 + log x = log 4
log x = log 4 - log 9
log x = log 4 / 9
x = 4 /9.
Hence, The value of given expression 9x=4 equals to 4/9.
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What is the intermediate step in the form (x+a)^2=b as a result of completing the square for the following equation?
-6x^{2}-582=−60x
The result of completing the square for the equation -6x² - 582 = −60x will be (x - 5)² = - 72.
What is a quadratic equation?The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2.
The equation is given below.
-6x² - 582 = −60x
Simplify the equation, then we have
-6x² - 582 = −60x
-6(x² + 97) = - 60x
x² + 97 = 10x
x² - 10x = - 97
x² - 10 + 25 = 25 - 97
(x - 5)² = - 72
The result of completing the square for the equation -6x² - 582 = −60x will be (x - 5)² = - 72.
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Question B is where I am confused
Dan should leave his house at least on 08.33 am.
What is Addition?Addition is one of the basic mathematical operations where two or more numbers is added to get a bigger number.
The process of doing addition is also called as finding the sum.
We have,
Dan has to get to work at 10.30 am.
There is a 20 minute walk from the bus stop in Coventry to work.
Dan should arrive at the bus stop in Coventry at 10.10 am.
The latest time of the bus that reaches Coventry closest to the time that Dan should reach at the bus stop in Coventry is 10.06.
The bus which reaches at Coventry at 10.06 depart from Birmingham at 08.38.
There is a 5 minutes to walk from his house to Birmingham bus stop.
Dan should leave the house at 08.33 am.
The latest time that Dan should leave the house is 08.33 am.
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Convert. Simplify your answer and write it as a proper fraction or as a whole or mixed
number.
? Teaspoons = 7 1/3 tablespoons
Based on the conversion of tablespoon to teaspoon, 7 1/3 tablespoons is equal to 22 teaspoons.
What is a conversion factor?In Science, a conversion factor is a number that is used to convert a number in one set of units to another, either by dividing or multiplying.
Generally speaking, there are three (3) teaspoons in one (1) tablespoon. This ultimately implies that, a proportion or ratio for the conversion of tablespoon to teaspoon would be written as follows;
Conversion:
3 teaspoons (tsp) = 1 tablespoon (tbsp)
X teaspoons (tsp) = 7 1/3 tablespoons (tbsp)
Cross-multiplying, we have:
X teaspoons (tsp) = 7 1/3 × 3
X teaspoons (tsp) = 22/3 × 3
X teaspoons (tsp) = 22 teaspoons.
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a particular professor is known for his arbitrary grading policies. each paper receives a grade from the set {a, a-, b . b, b-, c }, with equal probability, independent of other papers. how many papers do you expect to hand in before you receive each possible grade at least once?
Papers do you expect to hand in before you receive each possible grade at least once is 14.7.
given,
Total number of grades= 6
Imagine Y to be number of papers till we get all grades once. Hence
Yi= Number of papers till we get i th newer grades
Expected value of Y₆= ?
The difference between getting a new grade maybe represented as
Xi= Yi+1 - Yi
Using above equation for Y₆, we get
[Y₆]= ∑⁵i=o Xi
which means, we need to get 5 different grades from the first grade.
Number of tries to see second new grade maybe represented as
X₁= {(6-1)/6}, which, for generalization is written as Xi=geo{(6-i)/6}
Xi represents the success probability of seeing further new grade.
Expected value of Xi is inverse of parameter of geometric distribution, which is,
[Xi] = 6/(6-i) = 6.{1/(6-i)}
Expected value of Y₆= [∑⁵ i=0 Xi] = ∑⁵ i=0 [Xi]
Substituting value of [Xi] in the above expression
6.∑⁵i=0 {1/(6-i)} = 6. ∑⁶i=1 (1/i)
Now solving for 6 grades
Y₆ = 6[(1/6) + (2/6) + (3/6) + (4/6) + (5/6) + (6/6)]
Y₆ = 6 x 2.45 = 14.7
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Mr. Snow keeps a list of vocabulary terms that he wants his students to memorize from the textbook.
He began the year with 15 terms on the list. Of the 35 new terms in each chapter, Mr. Snow puts the definitions of 10 terms on the wall and adds the remaining terms to the vocabulary list to be memorized.
.Write an equation in slope-intercept form to represent the situation. Use x for the independent variable and y for the dependent variable. Identify what both variables represent.
The linear function in slope-intercept form that represents the equation is given as follows:
y = 15 + 25x.
The variables are given as follows:
Variable x: number of chapters read.Variable y: number of terms on the list.How to define the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
For which:
The slope m represents the number of words added to the list for each chapter.The intercept b represents the initial number of words in the list.He began the year with 15 terms on the list, hence the parameter b is given as follows:
b = 15.
Of the 35 new terms in each chapter, Mr. Snow puts the definitions of 10 terms on the wall and adds the remaining terms to the vocabulary list to be memorized, hence the slope m is obtained as follows:
m = 35 - 10
m = 25.
Then the function is:
y = 25x + 15.
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What is a asymptote?
Answer:
It is a line that continually approaches a given curve but does not meet it at any finite distance.
Step-by-step explanation:
Answer:
See below
Step-by-step explanation:
An asymptote is a line that continually approaches a given curve but does not meet it at any finite distance.
For example, for the rational function [tex]f(x)=\frac{1}{x}[/tex], there's a horizontal asymptote at y=0 because as x approaches infinity, y gets increasingly closer to 0.
Same goes for the vertical asymptote of x=0 where as y approaches infinity, x gets increasingly closer to 0.
a spherical snowball is melting in such a manner that its radius is changing at a constant rate, decreasing from 34 cm to 18 cm in 30 minutes. at what rate, in cubic cm per minute, is the volume of the snowball changing at the instant the radius is 6 cm?
The rate at which the volume of the snowball is changing at the instant the radius is 6 cm is -241.27 cm³/min.
The volume of a sphere is given by the formula V = 4/3πr³, where r is the radius of the sphere. To find the rate at which the volume is changing, we need to take the derivative of this equation with respect to time, using the chain rule.
dV/dt = 4/3π(3r²) dr/dt
We know that the radius of the snowball is decreasing at a constant rate, so we can find the value of dr/dt by using the information given in the problem. The radius is decreasing from 34 cm to 18 cm in 30 minutes, which means that:
dr/dt = (34 - 18) cm / 30 minutes = -0.5333 cm/min
Now that we know the rate at which the radius is changing, we can substitute it into the equation for dV/dt and find the rate at which the volume is changing.
We know that the radius is 6 cm at the instant the volume is changing, so we can substitute that into the equation:
dV/dt = 4/3π(3r²) dr/dt = 4/3(π)(3)(6 cm)²(-0.5333 cm/min) = -241.27 cm³/min
So, the rate at which the volume of the snowball is changing at the instant the radius is 6 cm is -241.27 cm³/min.
Note that the negative sign indicates that the volume is decreasing.
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a fire station is to be located along a road of length a, where a is a fixed positive real number. if fires will occur at points uniformly chosen on (0, a), where should the station be located so as to minimize the expected distance from the fire?
If fires occur at points uniformly chosen on (0, A), then [tex]a = \frac{A}{2}[/tex] is the second derivative where should the station be located so as to minimize the expected distance from the fire.
From the question, a fire station is to be located along a road of length A, A < ∞.
If fires occur at points uniformly chosen on (0, A), then we have to find where should the station be located so as to minimize the expected distance from the fire.
E∣X−a∣ = [tex]\int^{A}_{0}|x-a| \frac{1}{A} dx[/tex]
E∣X−a∣ = [tex]\int^{a}_{0}|a-x| \frac{1}{A} dx+\int^{A}_{a}|x-a| \frac{1}{A} dx[/tex]
Now integrating.
E∣X−a∣ = [tex]\frac{1}{A}\left(\frac{a^2}{2}+\frac{A^2}{2}-aA-\left(\frac{a^2}{2}-a^2\right)\right)[/tex]
E∣X−a∣ = [tex]\frac{a^2}{A}-a+\frac{A}{2}[/tex]
If we set the derivative to zero, we get [tex]\frac{2a}{A}-1=0[/tex], where [tex]a = \frac{A}{2}[/tex] is the derivative. One can look at the second derivative, which is always positive, to see if this is the minimizer.
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The complete question is:
A fire station is to be located along a road of length A, A < ∞. If fires occur at points uniformly chosen on (0, A), where should the station be located so as to minimize the expected distance from the fire? That is, choose a so as to minimize E[∣X−a∣] when X is uniformly distributed over (0, A).
In a recent student government election, the ratio of students who voted for the winner to all the students who voted was 0.85. The number of students who voted was 60. How many votes did the winner get?
In a recent student government election, the number of vote of the winner is 51
How to determine the ratioAn ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0.
In a proportion, two ratios are specified to be equal to one another in an equation.
The number of votes of the winner is calculated by writing the ratio
= number of the students who voted / total number of students
let x be the number of students that voted the winner
85 / 100 = x / 60
100x = 60 * 85
x = 5100 / 100
x = 51
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You buy a 562. 75 mL of dish soap. You already have some at home. How many mL do you have? 224. 14 at home
The total amount of dish soap added to both amounts will be 786.89 ml.
Describe addition.
In math, addition is the process of adding two or more integers together.
Since you currently have 224.14 mL of dish soap at home, you decide to buy a 562.75 ml container of it.
We will combine the two amounts together to get the total amount of dish soap.
Dish soap is 786.89 ml total (562.75 ml plus 224.14 ml).
Consequently, there is 786.89 ml of dish soap in total.
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See screenshot below.
By polar form properties, the product of complex numbers (5 · cos 225° + i 5 · sin 225°) and (2 · cos 135° + i r₂ · sin 135°).
How to multiply complex numbers
In this question we find the case of the product of two complex numbers in rectangular form but including features of polar form (magnitude, direction). Then, we have the following situation:
(r₁ · cos θ₁ + i r₁ · sin θ₁) · (r₂ · cos θ₂ + i r₂ · sin θ₂)
Result can be found easily by transforming the expression into polar form:
(r₁, θ₁) · (r₂, θ₂) = (r₁ · r₂, θ₁ + θ₂)
[r₁ · r₂ · cos (θ₁ + θ₂) + i r₁ · r₂ · sin (θ₁ + θ₂)]
If we know that r₁ = 5, r₂ = 2, θ₁ = 225° and θ₂ = 135°, then the product of the complex number is:
10 · [cos 360° + i sin 360°]
10 · (1 + i 0)
10
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According to the 2010 U. S. Census, 11. 7% of the people in the state of Oregon were Hispanic or Latino. A political party wants to know how much impact the Hispanic and Latino vote will have, so they wonder if the percentage has changed since then. They take a random sample of 853 adults in Oregon and ask, among other things, their race. 110 of the people surveyed were Hispanic or Latino. Can the party conclude that the Hispanic or Latino proportion of the population has changed since 2010
The test hypothesis for the 2010 U. S. Census is H0 = Oregon < Latino.
In math the term called hypothesis is defined as an idea that is suggested as the possible explanation for something but has not yet been found to be true or correct.
Here we know that in 2010 U. S. Census, 11. 7% of the people in the state of Oregon were Hispanic or Latino.
And here we have also know that random sample of 853 adults in Oregon and 110 of the people surveyed were Hispanic or Latino.
Then the sample proportion is calculated as,
=> sample proportion=113/853=0.1325
And the value of Test statistic is,
=> z = (0.1325-0.117)/√(0.117*(1-0.117)/853)
=> z = 1.41
So, the hypothesis is written as,
=> H0 = Oregon < Latino.
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Amal can run 1/8 mile in 1/12 minutes. If Amal can maintain that pace, how long will it take him to run 1 mile?
It will take 2/3 minutes to run 1 mile.
What is division?
The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.
Given:
Amal can run 1/8 mile in 1/12 minutes.
If Amal can maintain that pace,
it will take him to run 1 mile,
= 1/12 ÷ 1/8
= 1/12 x 8/1
= 8/12
= 2/3 minutes.
Therefore, the required time is 2/3 minutes.
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The mean weight of adult man is US is 190 lb and SD 59lb. An elevator in our building has a weight limit of 2500lb. what is the probability that if 10 men on the elevator, they will overload its weight limit
Answer: no it will not overload it's weight limit
Step-by-step explanation: 190 x 10 = 1900
i'm sorry if i am wrong
then i think i do/ 59 x 10 = 590 so then 1900 + 590 = 2490
Solve for x:
1/4 |x + 1| ≥ 4
Please show how its done
Answer:
x ≤ - 17 or x ≥ 15
Step-by-step explanation:
[tex]\frac{1}{4}[/tex] | x + 1 | ≥ 4 ( multiply both sides by 4 to clear the fraction )
| x + 1 | ≥ 16
Inequalities of the type | ax + b | ≥ c , have solutions of the form
ax + b ≤ - c or ax + b ≥ c , then
x + 1 ≤ - 16 ( subtract 1 from both sides )
x ≤ - 17
or
x + 1 ≥ 16 ( subtract 1 from both sides )
x ≥ 15
solution is x ≤ - 17 or x ≥ 16
Banana Inc. is producing batches of smartphones. The company's quality control department randomly picks a sample phone from each batch for testing. Which of the following percentages is possible as the percentage of the samples that pass?
Answer:
It is not possible to determine the percentage of samples that pass without additional information.
Twenty percent of US adults have some type of mental illness. You randomly select six US adults. Find the
probability that the number of US adults who have some type of mental illness is (a) exactly two, (b) at
least one, and (c) less than three.
This is a Binomial
distribution
a.
b.
C.
a. The probability of exactly two US adults having a mental illness in a sample of six is 0.235904
B. The probability of at least one US adult having a mental illness is >=21
C. The probability of less than three US adults having a mental illness is <=3
How do we find the values of the probabilities?a. The probability of exactly two US adults having a mental illness in a sample of six is given by the binomial probability formula:
P(X = 2) = (6 choose 2) * (0.2)^2 * (0.8)^4 = 0.235904
b. To find the probability of at least one US adult having a mental illness, we need to find the probability of zero or one or two or three or four or five or six US adults having a mental illness.
This can be found by summing the probabilities of each event:
P(X >= 1) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)
c. To find the probability of less than three US adults having a mental illness, we need to find the probability of zero or one or two US adults having a mental illness.
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)
Note that the binomial probability formula can be used to find the individual probabilities as well.
Therefore, the correct answer is as given above
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tickets number one 1 to 20 are mixed up and then a ticket is drawn at random what's the probability that the ticket drawn at random has a multiple of four or five
The probability that the ticket drawn at random has a multiple of four or five is 2/5.
We have to determine the probability that the ticket drawn at random has a multiple of four or five.
Tickets number 1 to 20 are mixed up and then a ticket is drawn at random.
Total number of tickets = 20
The possible numbers of tickets that are multiple of four or five = 4, 5, 8, 10, 12, 15, 16, 20
So total number of outcome that are multiple of four or five = 8
So, the probability that the ticket drawn at random has a multiple of four or five = Total number of outcome that are multiple of four or five/Total number of tickets
The probability that the ticket drawn at random has a multiple of four or five = 8/20
The probability that the ticket drawn at random has a multiple of four or five = 2/5
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3/4 x +3-2x = -1/4 +1/2x+5
step by step pleasz lets me know what to add sub etc...
The value of x from the expression 3/4 x +3-2x = -1/4 +1/2x+5 can be simplified as 45/29.
What is simplification?The concept that will be used is simplification. To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue.
3/4x +3-2x = -1/4 +1/2x+5
We can simplify by collecting the like terms,
3/4x - 1/2x - 2x = -1/4 + 5 -3
Then we can simplify further as:
-29x/20 = - 9/4
29x = (20*9)/4
29x= 45
x= 45/29
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megan collects stamps.she keeps her stamps ina abook that can hold 17 on each page. she has 56 pages full of stamps, and 14 pages that are only half full.how many stamps does megan have?
Megan have total 1,071 stamps.
The concept used in this problem is multiplication, specifically using it to find the total number of stamps by multiplying the number of pages by the number of stamps per page. Additionally, it also uses the concept of addition to find the total number of stamps by adding the number of stamps on full pages to the number of stamps on half-full pages.
as given, Megan keeps her stamps in a book that can hold 17 on each page. she has 56 pages full of stamps. So,
Megan has 56 pages * 17 stamps per page = 952 stamps on full pages.
and 14 pages that are only half full. So,
She has 14 pages * (half of 17 stamps per page) = 14 pages * 8.5 stamps per page = 119 stamps on half-full pages.
Therefore, Megan has 952 stamps + 119 stamps = 1,071 stamps in total.
hence, Megan have total 1,071 stamps.
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Henry Heavyfoot was just arrested for speeding by Officer O'Rourke for traveling 65 mph in a 55 mph zone. Henry claimed his speedometer said 55 mph not 65 mph. What could Henry claim as his percent error?
Henry can claim 15.38% as his percent error.
We know that the formula for the percent error is:
Percent Error = (Absolute Error ÷ Actual Value) × 100
where, Absolute Error = ∣Actual Value - Estimated Value|
In this situation, the actual value is 65 mph and the Estimated value is 55 mph.
So, using above formula for absolute error,
Absolute Error = ∣Actual Value - Estimated Value|
Absolute Error = ∣65 - 55|
Absolute Error = 10
Now we find the percent error using above formula for the percent error.
Percent Error = (10 ÷ 65) × 100
Percent error = 15.38%
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true or false: if the median of a data set is larger than the mean, then the histogram of the data will likely have a longer right tail.
The given statement about Histogram that , " if median of a data set is larger than mean, then the histogram of data will likely have a longer right tail" is FALSE .
A histogram is a graph in which most of data falls to the right of graph's peak and is known as a right-skewed histogram. This type of histogram is also known as a positively skewed histogram.
The relation between the mean , median and mode in a right-skewed histogram is denoted as : mean > median > mode .
A distribution is called skewed Right if, in histogram , the right tail (smaller values) is much longer than the left tail (larger values).
Therefore , For histogram to have longer right tail , the median should be less than the mean .
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what is the vaulue of |6| - | -6| - (-6)
Answer:
I think it is just 6
Step-by-step explanation:
I hope it helped!
Solve the system of equations x+3y=5 and -3x-2y=20 by combining the equations
Answer:
-2x + y = 25
Step-by-step explanation:
just add them together by columns. X-3x = -2x
3y-2y = y
5+20 =25.
done.
Please help me find the value and what kind of angle is this?
Answer: consecutive interior angles and x=66°
Step-by-step explanation:
The angles are consecutive interior angles. The property is consecutive interior angles are supplementary.
2x+24+24=180 [combine like terms]
2x+48=180 [subtract both sides by 48]
2x=132 [divide both sides by 2]
x=66
Therefore, the angle is consecutive interior angles and x=66°.
What’s a system of equations that can be entered into a graphing calculator to solve 16.9x-2.3=3.2x+18
The system of equations that can be entered is y = 16.9x - 2.3 and y = 3.2x + 18
How to determine the system of equationsFrom the question, we have the following parameters that can be used in our computation:
16.9x-2.3=3.2x+18
Express the equation properly
So, we have the following representation
16.9x - 2.3 = 3.2x + 18
Next, we split the equation and introduce the variable y
So, we have
y = 16.9x - 2.3
y = 3.2x + 18
The above is the system of equations
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Solve log x = 4. (5 points) 10,000 1,000 40 4
log(x) = 4 can be restated as an exponential statement: 10^4 = x
x = 10000