To write the equation in exponential form we must follow certain rules:
1. Logarithm product rule - log b ( x ∙ y) = log b ( x) + log b ( y)
2. Logarithm quotient rule - log b ( x / y) = log b ( x) - log b ( y)
3. Logarithm power rule - log b ( x y) = y ∙ log b ( x)
4. Logarithm base switch rule - log b ( c) = 1 / log c ( b)
1. ㏒z(w) = p
Here all constants are taken to be positive and not equal to 1
z = base of the logarithmic function
z^p = w --------> (1)
This z^p = w is the exponential form of ㏒z(w) = p
2. ㏒(s) = r
Here all constants are taken to be positive and not equal to 1
e = base of the logarithmic function
e^r = s --------> (2)
This e^r = s is the exponential form of ㏒(s) = r
3. 7m = a
Here we have to write the equation in logarithmic form
㏒(7m) = log r
log(7m) - log r = 0
We know quotient rule :-
log b ( x / y) = log b ( x) - log b ( y) --------(A)
Applying that same principle to our question by using this equation we have:
log (7m/r)
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Kanoi can weed a garden in 40 minutes. Ale'a can weed the same garden in 50 minutes. How long would it take for Kanoi and Ale'a to weed the same garden together? (Round to the nearest hundredth)
Kanoi and Ale'a can weed the same garden together in 22.22 minutes
How to find the time it will take to weed the garden togetherRate of work refers to amount to of work completed at a given time
Information from the question include
Kanoi can weed a garden in 40 minutes
Kanoi's rate = 1/40 per minute
Ale'a can weed the same garden in 50 minutes
Ale'a rate = 1/50 per minute
When both are working together the rate will be
1/40 per minute + 1/50 per minute
= 9/200 per minute
The time is solved
1 / 9/200
= 200/9
= 22.2222 minutes
= 22.22 minutes to the nearest hundredth
The time it will take both of them to weed is 22.22 minute
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Given m
|| n, find the value of x and y.
(8x+1)°
Z
(4y+3)
(9x-16)°
m
72
Use photo for better explanation PLEASE HELP
Answer:
(x, y) = (17, 10)
Step-by-step explanation:
You want the values of x and y given three angles written in terms of x and y at a transversal crossing parallel lines.
Corresponding anglesAngles at lower right of the points of intersection are corresponding angles, and are congruent:
(9x -16)° = (8x +1)°
x = 17 . . . . . . . . . . . . . divide by °, add 16-8x
Linear pairThe marked angles at the bottom form a linear pair, so are supplementary.
(4y +3)° = 180° -(9x -16)°
4y +3 = 180 -9(17) +16 = 43 . . . . . . use 17 for x and simplify
4y = 40 . . . . . . subtract 3
y = 10 . . . . . . divide by 4
Use Elimination for the answer on both :)
The value of x and y after solving the equation -5x - 10y = 30 and - 3x + 3y = 27 by elimination method is -6 and 3 respectively.
What is the equation?A formula known as an equation uses the equals sign to denote the equality of two expressions.
Given:
-5x - 10y = 30 and - 3x + 3y = 27
Solve by using the elimination method,
Divide the equation - 3x + 3y = 27 by 3 and equation -5x - 10y = 30 by 5 on both sides,
(- 3x + 3y) / 3 = 27 / 3 and (-5x - 10y) / 5 = 30 / 5
-x + y = 9 and -x - 2y = 6
Subtract equation
-x + y = 9 - (-x - 2y = 6)
-x + y - 9 = x - 2y - 6
y = 3
and - x + 3 = 9, x = -6
Therefore, the value of x and y after solving the equation -5x - 10y = 30 and - 3x + 3y = 27 by elimination method is -6 and 3 respectively.
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Find the equation of a line that passes through the points (-4,-3) and (4,-1)
Answer:
y=x/4 - 2
Step-by-step explanation:
First, find the slope:
m=(y2-y1)/(x2-x1) ==> slope formula where m=slope
(x1, y1), (x2, y2) ==> (x1=-4, y1=-3) and (x2=4, y2=-1)
Now plug in known values back into the slope formula:
m=(-1-(-3))/(4-(-4))
m=(-1+3)/(4+4)
m=2/8 ==> simplify
m=1/4
y=mx+b ==> slope-intercept equaiton form
-1=(1/4)(4)+b ==> plug in the slope, m=1/4, and a known coordinate: (4,-1)
-1=1+b ==> simplify
-1-1=1-1+b ==> solve for b
b=-2
y=(1/4)x+(-2) ==> plug in b=-2 and m=1/4 back into y=mx+b
y=x/4 - 2
Determine the value of x that makes Triangle ABC congruent to Triangle XYZ
Which inequality matches the graph?
is this right?
Answer:
Your Answer is A.
Step-by-step explanation:
First look at the inequality graph.
We can note that its a variable is greater than 2. (p >2)
Then looking at our options.
Option A can be.
Option B can't be it since its greater than or equal to.
Option C can be.
Option D can't be since dividing or multiplying by a negative switches the signs greater than to less than or vice versa.
Leaving only option A or C.
Solve A and C.
Option A5p + 4 > 14
5p > 10
p > 2
Option C.5p - 4 > 14
5p > 18
p > 18/5
Simplify each algebraic expression by combining like terms.
2x+ (9+x) -6
Answer:
3x +3
Step-by-step explanation:
You want to simplify 2x+ (9+x) -6.
Like termsLike terms have the same constellation of variables. Here, there are terms containing x, and terms not containing x.
2x+ (9+x) -6 = (2 +1)x +(9 -6) = 3x +3
The simplified expression is 3x +3.
Answer:3x+3
Step-by-step explanation:
First we remove the parenthesis because they are not needed in an addition problem to make it 2x+9+x-6
Then we sort and combine like terms, [2x+x]+[9-6]
After that, you add the coefficients of the the first term, which makes 3x and subtract 6 from 9 to get 3
This then leads you to 3x+3
Next, you select the basic statistics that can help your team better understand the ratings system in your data. Assume the first part of your code is: trimmed_flavors_df %>% You want to use the summarize() and mean() functions to find the mean rating for your data. Add the code chunk that lets you find the mean value for the variable Rating.
Based on the rating system and the summarize() and mean() functions, the code chunk to add is summarize(mean(Rating)) and the mean rating is 3.185933.
To determine the mean value for the variable Rating, you must add the code chunk summarize(mean(Rating)). Trimmed flavors df%>% summarize(mean(Rating)) is the right code. In this section of the code:
You can display summary statistics using the summarize() method. To generate specific statistics, you can combine the summarize() method with others like mean(), sd(), and max().
In this instance, you compute the mean value for the variable Rating using the mean() function.
The average score is 3.185933.
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Choose the correct solution graph for the inequality.
7x+2≥30 or 2x-3≤-11 PLEASE HELP I HAVE 2 HOURS
Answer:
Therefore, the correct solution graph for the inequality is a line with no solution. This means that there is no value of x that satisfies both inequalities at the same time.
Step-by-step explanation:
To solve this inequality, we need to consider the two separate cases of 7x+2≥30 and 2x-3≤-11 separately.For the first case, 7x+2≥30, we can rewrite the inequality as 7x≥28, which simplifies to x≥4. This means that the solution for this inequality is x≥4.For the second case, 2x-3≤-11, we can rewrite the inequality as 2x≤-8, which simplifies to x≤-4. This means that the solution for this inequality is x≤-4.To find the combined solution for both inequalities, we need to take the intersection of these two solutions. The intersection of x≥4 and x≤-4 is the empty set, which means that there is no solution that satisfies both inequalities
find the dimensions of a rectangle with area 64000 m2 whose perimeter is as small as possible. (give your answers in increasing order, to the nearest meter.)
the dimensions of a rectangle with area 64000 m2 whose perimeter is as small as possible. (give your answers in increasing order, to the nearest meter.)Length: 200 m and Width: 320 m
The area of a rectangle is given by the formula A = lw, where l is the length and w is the width. To find the dimensions of a rectangle with an area of 64000 m2 and a perimeter that is as small as possible, we can use the formula P = 2l + 2w. We can use this to create an equation with the area and solve for l and w: 64000 = lw, and 2l + 2w = P (min). Solving for l and w, we get l = 200 m and w = 320 m. Thus, the dimensions of the rectangle with an area of 64000 m2 and a perimeter that is as small as possible are 200 m by 320 m.
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Use the given values of n and p to find the minimum usual value u - 20 and the maximum usual value u + 20. Round your answer to the nearest hundredth unless otherwise noted. n = 108 p = 0.24
The minimum usual value, μ-2σ is 17.8 and the maximum usual value, μ+2σ is 54.04
How to find the minimum and maximum usual values?From the information, n = 108, p = 0.24
minimum usual value μ-2σ
maximum usual value μ+2σ
Find the mean, μ:
μ = np = 108 × 0.24 = 35.92
Find the variance, n(1-p):
n(1-p) = 108 ×( 1-0.24) = 82.08
Find the standard deviation, σ:
σ = √82.08 = 9.06
minimum usual value, μ-2σ:
μ-2σ = 35.92 - (2×9.06) = 17.8
maximum usual value, μ+2σ:
μ+2σ = 35.92 + (2×9.06) = 54.04
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Rewrite
17/5
as a mixed number.
How much do you have after investing $1000 at 9% compounded continuously for 2 years and nine months
Answer:
$1,127.49
Step-by-step explanation:
Compound interest formulas
Hence, if a two-year savings account containing $1,000 pays a 9% interest rate compounded daily, it will grow to $1,127.49 at the end of two years
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Perform the following mathematical operation and report the answer to the appropriate number of significant figures.
We know the least precise place value is in the 10's place.
67.4 +43 +30 + 42.10 = [?]
it's not 182.5 / 137.9 / 182
Answer:
200
Step-by-step explanation:
The sum is 182.5, which is 200 to 1 significant figure.
-28 = -4x
What value of x makes this equation true?
A -7
B 24
C-32
D 7
Select each expression that has a sum of 4 4/12 A 3 1/5 + 1 3/7. B 1 11/12 + 2 1/4. C 1 3/6 + 1 1/2 + 1 3/4. D 1 1/3 + 1 1/2 + 2 1/3. E 3/6 + 1 2/4 + 2 1/3
assume victoria's indifference curves are bowed outward but her indifference curves satisfy the other three properties of indifference curves. as victoria moves from right to left along the horizontal axis, her marginal rate of substitution
The marginal rate of substitution (MRS) is a measure of how much of one good an individual is willing to give up in exchange for another good. In other words, it represents the slope of the indifference curve at a given point.
If Victoria's indifference curves are bowed outward, it means that as she moves from right to left along the horizontal axis, the MRS will decrease. This is because as she consumes more of one good, she becomes less willing to give up units of the other good in exchange. The MRS will continue to decrease until it reaches its minimum value at the point where the indifference curve is tangent to the budget line.
It's important to note that the MRS will only decrease if Victoria's indifference curves satisfy the other three properties of indifference curves:
Higher indifference curves represent a higher level of utility.Indifference curves do not intersect.Indifference curves are downward sloping.If Victoria's indifference curves do not satisfy these properties, it is not possible to accurately determine the behavior of her MRS as she moves from right to left along the horizontal axis.
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a linear equation is graphed to the left. which of the following equations combines with the graphed equation to create a system of equations whose solution set is comprised of the points
To get the equation which combines with the graphed equation to create a system of equations whose solution set is comprised of the points (−1,−5) and (3,3) we need to plug the points into each equation choice.
Therefore , this is the first step to solve this equation.
The equations of degree 1 are known as linear equations.
These are the equations which are defined for a straight line in a coordinate system.
A linear equation is one that describes a straight line. The general form of a linear equation is y= mx + b, where m denotes the slope and b its y-intercept.
Note:
The complete question is ,
A linear equation is graphed to the left. Which of the following equations combines with the graphed equation to create a system of equations whose solution set is comprised of the points (−1,−5) and (3,3)?
WHAT IS THE FIRST STEP IN SOLVING THIS PROBLEM?
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Solve for f.
f 3 = 8
f =
Determine whether the system of equations is consistent or inconsistent and if it is independent or dependent.
3x+y=−5
3y+15=−9x
Multiple choice question.
A)
consistent and dependent
B)
consistent and independent
C)
inconsistent
D)
inconsistent and dependent
Answer:
C) inconsistent
Step-by-step explanation:
3x+y=−5
3y+15=−9x
3x + y = -5
9x + 3y = 15
3x + y = -5
3x + y = 5
The system graphs as two parallel lines.
Answer: C) inconsistent
Find the distance between the two points.
(-4,-5)
(4,2)
√ [?]
Enter the number that
goes beneath the
radical symbol.
Enter
By using distance formula, it can be calculated that-
Distance between (-4, -5) and (4, 2) is [tex]\sqrt{113}[/tex] units
What is distance formula?
Distance formula is used to find the distance between two coordinates.
If the points are [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex], then distance is calculated by the formula
d = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
The points are (-4, -5) and (4, 2)
Distance between (-4, -5) and (4, 2) = [tex]\sqrt{(-4-4)^2+(-5-2)^2}[/tex]
= [tex]\sqrt{64 + 49}\\\sqrt{113}[/tex]units
Distance between (-4, -5) and (4, 2) is [tex]\sqrt{113}[/tex] units
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Match each data set with its range.
The range of the data set are
{10.2, 3.8, 21.9, 33.4, 31.8, 17.2} = 29.6
{0.5, 0.65, 0.22, 0.11, 0.47, 0.55, 0.55, 0.71} = 0.6
{6, 2, 14, 11, 28, 10, 19, 15, 11} = 26
The first data set is
{10.2, 3.8, 21.9, 33.4, 31.8, 17.2}
The range is the difference between the highest value and the smallest value
The highest value = 33.4
Lowest value = 3.8
The range = 33.4 - 3.8
= 29.6
The second data set is
{0.5, 0.65, 0.22, 0.11, 0.47, 0.55, 0.55, 0.71}
The highest value = 0.71
Lowest value = 0.11
The range = 0.71 - 0.11
= 0.6
The third data set is
{6, 2, 14, 11, 28, 10, 19, 15, 11}
Highest value = 28
Lowest value = 2
The range = 28 - 2
= 26
Therefore, the range of the each data set has been found
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Akin's salary is 20% less than Shola's and Shola spent 45% of his salary on accommodation leaving him with #550. How much is Akin's salary?
Answer:
$800
Step-by-step explanation:
Let's say that Shola's salary is x dollars. This means that Akin's salary is 0.8x dollars, because his salary is 20% less than Shola's salary.
Since Shola spent 45% of his salary on accommodation, he had 0.55x dollars left, or $550. This means that we can write the equation 0.55x = 550.
To solve for x, we can divide both sides of the equation by 0.55 to get x = 1000. This means that Shola's salary is $1000, and since Akin's salary is 20% less than Shola's, his salary is 0.8 * 1000 = $800. Therefore, Akin's salary is $800.
Diane has quarters, dimes, and
pennies in her pocket. The value of her
money is $1.55. There are 4 more
dimes than quarters and the number of
pennies equals the sum of the number
of quarters and dimes.
How many pennies does Diane have?
Answer: The solution here is found by establishing a system of linear equations.
A system of equations with x unknowns can be evaluated for an exact solution if the system has x equations.
Within the question, we are asked to discover the values of two different unknowns - dimes and nickels.
Therefore, we'll need two equations to obtain an exact solution, both of these will come directly from the problem itself.
Let d represent the number of dimes Diane has and let n represent the number of nickels.
Equation 1
We know from the given information that the total number of coins (both dimes and nickels) is equal to 19.
Subsequently, we can generate the equation d + n = 19.
Equation 2
We know that the individual value of a dime is $0.10 or 0.1 dollars, therefore the total value of the dimes is equal to the individual value of a dime multiplied by the total number of dimes.
The resultant expression for the total value of the dimes is (0.1)*d
We know that the individual value of a nickel is $0.05 or 0.05 dollars, therefore the total value of the nickels is equal to the individual value of a nickel multiplied by the total number of nickels.
The resultant expression for the total value of the nickels is (0.05)*n
We know that Diane only has dimes and nickels, and the total value of all her coins must be equal to the total value of the dimes plus the total value of the nickels. This value is given within the problem to be $1.55 or 1.55 dollars.
Subsequently, our second equation within the system is (0.1)*d + (0.05)*n = 1.55.
Now, we can solve the system of equations using whichever means is most convenient. For this example, I will solve the system by substitution
First, solve for one of the variables —> Equation 1 —> d + n = 19 —> d = 19 - n
Second, substitute the value of d into Equation 2 —> (0.1)*(19 - n) + (0.05)*n = 1.55
Recall that 0.1 = 1/10 and 0.05 = 1/20
Equation 2 —> (1/10)*19 - (1/10)*n + (1/20)*n = (31/20) —> (19/10) - (n/10) + (n/20) = (31/20)
Find the least common denominator of all fractions in the equation (20 in this case), convert the fractions to have like denominators, and solve.
(19/10)*(2/2) - (n/10)*(2/2) + (n/20) = (31/20) —> (38/20) - (2n/20) + (n/20) = (31/20) —> (38/20) - (n/20) = (31/20) —> (n/20) =(38/20) - (31/20) =(7/20) —>n = 7
Substitute solution into Equation 1 to solve for d
d + 7 = 19 —> d = 12
q+4+q + 10q+40 + 25q = 155
37q + 44 = 155
37q = 111
q = 3 (# of quarters)
d = q+4 = 7 (# of dimes)
p = d+q = 7+3 = 10 (# of pennies)
Step-by-step explanation:
a stack of books is 61 inches high. how high is it in feet and inchess
Answer: 5.08333 repeating three
How do you know that segment AD is congruent to segment BC ? Lesson (2-1)
Two line segments are said to be congruent if, regardless of their orientation or position, their lengths are the same.
What are congruent Triangles ?If the matching sides and angles of two triangles are the same length, then the triangles are said to be congruent.
What are Two congruent Sides ?Two sides that are the same length make up an isosceles triangle .In addition, it contains two equal-sized angles located across from the two sides of equal length. A triangle with three identical sides is called an equilateral triangle.
So
According to the given information
Segment AD = Segment BC
Two line segments are said to be congruent if, regardless of their orientation or position, their lengths are the same.
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3) Suppose you finance a car in the amount of $28,550. The loan is for 7 years with an APR of
8%. What will be the payoff balance of this car loan after 4 years?
The
Answer:
So the payoff balance of the car loan after 4 years will be approximately $22,169.73.
Step-by-step explanation:
payoff balance after 4 years can be calculated using the following formula:
Payoff balance = Principal * (1 + APR/n)^(nt) - [(Principal * (1 + APR/n)^(nt) * (APR/n)) / (1 + APR/n - 1)]
Where:
Principal is the loan amount, which is $28,550 in this case.
APR is the annual percentage rate, which is 8% in this case.n is the number of times per year that interest is compounded, which is usually 12 for monthly compounding.t is the number of years for which the loan is taken, which is 4 years in this case.
Plugging in the values, we get:
Payoff balance = $28,550 * (1 + 0.08/12)^(124) - [($28,550 * (1 + 0.08/12)^(124) * (0.08/12)) / (1 + 0.08/12 - 1)]
Payoff balance = $28,550 * 1.006669^48 - [$28,550 * 1.006669^48 * 0.006669] / 0.006669Payoff balance = $22,169.73
Hope one of y’all help me with this question.. because i was struggling!!
Please and thank you.
a) The value in four years is 2,207,626
b) The growth rate percent is 102.5 %
c) It would attain the value in 11 years.
What is a function?We know that a function has to do with a mathematical rule that is used for the establishment of a fact. We have from the question that the function that models the car is; V = 2000000(1.025)^n
Let us recall that n has to do with the number of years.
a) In four years, the value of the car would be;
V = 2000000(1.025)^4
V = 2,207,626
b) The growth rate percent of the function can be obtained as;
1.025 * 100 = 102.5 %
c) To obtain the year in which the value of the car would reach 2624173.32, we have;
2624173.32 = 2000000(1.025)^n
2624173.32/2000000 = (1.025)^n
1.312 = (1.025)^n
ln1.312 = n ln (1.025)
n = ln1.312 /ln (1.025)
n = 0.272/0.025
n = 11
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suppose baby kittens' weights are normally distributed with a mean of 12.3 and a standard deviation of 2.2. the z-score tells you how many units above the average (if z-score is positive) or below the average (if z-score is negative) any particular baby kitten's weight is. find the baby kitten weight that corresponds to the following z-scores given below. hint: use the formula x
X-μ Use the formula Z where is the mean, o is the standard deviation, and X is the baby kitten σ weight. a. Z= 1.98, X = b. Z-2.87, X =
X-μ Use the formula Z where is the mean, o is the standard deviation, and X is the baby kitten σ weight. a. Z= 1.98, X = b. Z-2.87, X ,,a. X = 16.786 , b. X = 8.014
To find the baby kitten weight corresponding to the given z-scores, we use the formula X = μ + Zσ, where μ is the mean, σ is the standard deviation, and Z is the z-score. For the first z-score of 1.98, we substitute the values and solve for X. X = 12.3 + (1.98)(2.2) = 16.786. For the second z-score of 2.87, we substitute the values and solve for X. X = 12.3 + (2.87)(2.2) = 8.014. Therefore, the baby kitten weights corresponding to the given z-scores are 16.786 and 8.014, respectively.
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Blue Skies Inc. is a retail gardening company that is piloting a new strategic initiative aimed at increasing gross profit. Currently, the company’s gross profit is 25% of sales, and its target gross profit percentage is 30%. The company’s current monthly sales revenue is $600,000. The new initiative being piloted is to produce goods in-house instead of buying them from wholesale suppliers. Its in-house production process has two procedures. The makeup of the costs of production for Procedure 1 is 40% direct labor, 45% direct materials, and 15% overhead. The makeup of the costs of production for Procedure 2 is 60% direct labor, 30% direct materials, and 10% overhead. Assume that Procedure 1 costs twice as much as Procedure 2.
The Cost make up of procedure 1 is $280000.
Cost make up of procedure 2 is 140000
What is the cost make up?The cost makeup will be calculated thus:
Cost make up of procedure 1
Labour (40%) 112000
Materials (45%) 126000
Overhead (15%) 42000
Total =[280000
Cost make up of procedure 2
Labour ( 60%) 84000
Materials (30%) 42000
Over head (10%) 14000
Total 140000
Working note:
Sales $600000
Less: Gross profit (sale *30%) $ 180000
COGS $420000
Procedure 1 ( COGS *2/3) $ 280000
Procedure 2 (COGS * 1/3) $ 140000
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Complete question
Blue Skies Inc. is a retail gardening company that is piloting a new strategic initiative aimed at increasing gross profit. Currently, the company’s gross profit is 25% of sales, and its target gross profit percentage is 30%. The company’s current monthly sales revenue is $600,000. The new initiative being piloted is to produce goods in-house instead of buying them from wholesale suppliers. Its in-house production process has two procedures. The makeup of the costs of production for Procedure 1 is 40% direct labor, 45% direct materials, and 15% overhead. The makeup of the costs of production for Procedure 2 is 60% direct labor, 30% direct materials, and 10% overhead. Assume that Procedure 1 costs twice as much as Procedure 2.
Determine what the cost of labor, materials, and overhead for both Procedures 1 and 2 would need to be for the company to meet its target gross profit.