An internet service provider uses the function R = 3 log(a + 2) + 15 to relate R, the sales revenue from hosting websites, to a, the cost of advertising
Solve for a in terms of R.
Answers
"a" can be expressed as a function of "R" as:
\(a = 10^{\frac{(R - 15)}{3} - 2}\).
What are logarithmic properties?
The 4 laws of logarithms are product property, division property, power property and change of base property.
The product property states that multiplying two logarithmic values is equivalent to summing their respective logarithms.The division property states that the difference between two logarithms is comparable to dividing two logarithmic values.The exponent times the logarithm of m's logarithm is identical to m's logarithm with a suitable exponent, according to the exponential rule.Change of base property - The change of base rule converts a logarithm in one base to a logarithm in another.To solve for "a" in terms of "R," we need to isolate "a" on one side of the equation. We can do this by rearranging the equation and applying logarithmic properties.
Starting with the equation R = 3 log(a + 2) + 15, we'll subtract 15 from both sides:
R - 15 = 3 log(a + 2)
Next, we'll divide both sides by 3:
(R - 15) / 3 = log(a + 2)
Finally, we'll use the inverse logarithmic function, denoted as "exp" or "10^," to solve for "a":
\(a+2 = 10^{\frac{(R - 15)}{3} }\)
And finally, we'll subtract 2 from both sides to obtain the solution:
\(a = 10^{\frac{(R - 15)}{3} - 2}\)
So, "a" can be expressed as a function of "R" as:
\(a = 10^{\frac{(R - 15)}{3} - 2}\)
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Related Questions
The mean of 5 numbers is 11. the numbers are in the ratio 1:2:3:4:5 find the smallest number?
Answers
The smallest number is x = 11/3. The smallest number in the given ratio of 1:2:3:4:5 whose mean is 11 is 11/3.
Given that the mean of 5 numbers is 11. The numbers are in the ratio 1:2:3:4:5. We need to find the smallest number. We can start solving the problem by following these steps:
Step 1: Let us assume the smallest number to be x.
Step 2: According to the question, the numbers are in the ratio 1:2:3:4:5. Hence, the other four numbers can be written as 2x, 3x, 4x, and 5x.
Step 3: The mean of these 5 numbers is given as 11.
Therefore, we can write:(x + 2x + 3x + 4x + 5x)/5 = 11.
Step 4: Simplifying the above equation, we get:15x/5 = 11x = 11/3.
Step 5: Therefore, the smallest number is x = 11/3.
The smallest number in the given ratio of 1:2:3:4:5 whose mean is 11 is 11/3.
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Help me plz
I really need help
Answers
Answer:
nppp
Step-by-step explanation:
Answer:
see explanation
Step-by-step explanation:
diameter is the segment from 1 point on the circle through the centre to the opposite point on the circle.
diameter = BD
The centre is the point equidistant from all points on the circle.
centre = A
the radius is the distance from the centre to a point on the circle.
Here the radius = AB, AC, AD
Find the mean of the number of batteries sold over the weekend at a convenience store. Round two decimal places. Outcome X 2 4 6 8 0.20 0.40 0.32 0.08 Probability P(X) a.3.15 b.4.25 c.4.56 d. 1.31
Answers
The mean number of batteries sold over the weekend calculated using the mean formula is 4.56
Using the probability table givenOutcome (X) | Probability (P(X))
2 | 0.20
4 | 0.40
6 | 0.32
8 | 0.08
Mean = (2 * 0.20) + (4 * 0.40) + (6 * 0.32) + (8 * 0.08)
= 0.40 + 1.60 + 1.92 + 0.64
= 4.56
Therefore, the mean number of batteries sold over the weekend at the convenience store is 4.56.
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You must decide whether to buy new machinery to produce product X or to modify existing machinery. You believe the probability of a prosperous economy next year is 0.7. Prepare a decision tree and use it to calculate the expected value of the buy new option. The payoff table is provided below (+ for profits and - for losses).
When entering the answer, do not use the $ symbol. Do not enter the thousand separator. Enter up to 2 decimal places after the decimal point. For example, $6,525.35 must be entered as 6525.35
N1: Prosperity ($) N2: Recession ($)
A1 (Buy New) $1,035,332 $-150,000
A2(Modify) $823,625 $293,648
Answers
The expected value of the "Buy New" option is 724732.60.
Decision Tree:
To solve the given problem, the first step is to create a decision tree. The decision tree for the given problem is shown below:
Expected Value Calculation: The expected value of the "Buy New" option can be calculated using the following formula:
Expected Value = (Prob. of Prosperity * Payoff for Prosperity) + (Prob. of Recession * Payoff for Recession)
Substituting the given values in the above formula, we get:
Expected Value for "Buy New" = (0.7 * 1,035,332) + (0.3 * -150,000)Expected Value for "Buy New" = 724,732.60
Therefore, the expected value of the "Buy New" option is 724,732.60.
Conclusion:
To conclude, the decision tree is an effective tool used in decision making, especially when the consequences of different decisions are unclear. It helps individuals understand the costs and benefits of different choices and decide the best possible action based on their preferences and probabilities.
The expected value of the "Buy New" option is 724,732.60.
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d²v dt² v=2t² +7t+11 Find
Answers
The second derivative of v with respect to t, denoted as d²v/dt², is equal to 4
The second derivative of v with respect to t, we will differentiate v twice.
v = 2t² + 7t + 11
First, let's find the first derivative of v with respect to t (dv/dt):
dv/dt = d/dt (2t² + 7t + 11)
Using the power rule of differentiation, we differentiate each term separately:
dv/dt = 2(2t) + 7(1) + 0
dv/dt = 4t + 7
Now, let's find the second derivative of v with respect to t (d²v/dt²):
d²v/dt² = d/dt (4t + 7)
Again, using the power rule of differentiation, we differentiate each term separately:
d²v/dt² = 4(1) + 0
d²v/dt² = 4
Therefore, the second derivative of v with respect to t, denoted as d²v/dt², is equal to 4.
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It takes a machine at a seafood company 20 s to clean 3 1 ib of shrimp _ 3
Answers
It takes a machine at a seafood company 20 seconds to clean 3 pounds of shrimp. The rate of the machine is 0.15 pound per second
What is an equation?An equation is an expression that shows the relationship between two numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.
It takes a machine at a seafood company 20 seconds to clean 3 pounds of shrimp. Hence:
Rate of the machine = 3 pounds / 20 seconds = 0.15 pound per second
It takes a machine at a seafood company 20 seconds to clean 3 pounds of shrimp. The rate of the machine is 0.15 pound per second
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The math club has 18 members and 50% are girls. The science club has 25 members and
40% are girls. The principal wants to know which dub has more girls.
How many girls are in the math club?
Answers
Answer:
I only did this for the points.
Step-by-step explanation:
I am buff boi
What's 3c-9d+7c+5d simplify in algebra
Answers
Answer:
10c-4d
Step-by-step explanation:
The answer to
3c-9d+7c+5d is 10c - 4d
Further Explanation
One variable linear equation is an equation that has a variable and the exponent number is one.
Can be stated in the form:
or
ax + b = c,
where a, b, and c are constants, x is a variable
Whereas the two-variable linear equation is a linear equation that has 2 variables and the exponent is one
Can be stated in the form:
x, y = variable
There are several ways to solve an equation
Add / Subtract / divide / multiply the same value on both sides
Combine like terms
Factoring
Expanding
Like terms are terms whose variables and their exponents are the same.
You can combine and add terms
The algebraic form of 3c-9d + 7c + 5d can be simplified:
1. Combine like terms
(3c + 7c) + (-9d + 5d)
2. Add like terms:
10c - 4d
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Keywords: algebraic expression, combine like terms
find the zeros and multiplicities of the polynomial f(x) = (x-5)^6 (x²-25)^7. the zeros are x = _______ (separate your answers by commas).the zero x = _____ has multiplicity_____
Answers
The zeros of the polynomial f(x) are the values of x that make f(x) equal to zero. We can find the zeros of f(x) by setting the polynomial equal to zero and solving for x:
f(x) = (x-5)²6 (x²-25)²7 = 0
The polynomial f(x) has two factors, each of which contributes to the zeros of the polynomial:
Factor 1: (x-5)²6
This factor is equal to zero when x-5=0, or x=5. Therefore, the polynomial f(x) has a zero of multiplicity 6 at x=5.
Factor 2: (x²-25)²7
This factor is equal to zero when x²-25=0, or x=±5. Therefore, the polynomial f(x) has two more zeros at x=±5. Each of these zeros has a multiplicity of 7, since the factor (x²-25) is raised to the 7th power.
Therefore, the zeros of f(x) are x=5 and x=±5, with multiplicities of 6 and 7, respectively.In summary
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anyone help if you can
Answers
Answer:
The answer is C
Step-by-step explanation:
HOPE it helps!!:))))
For his long distance phone service, dale pays a $6 monthly fee plus 8 cents per minute. Last month, Dale's long distance bill was $21.28. For how many minutes was dale billed?
Answers
Answer:
he was billed for 147 minutes
Step-by-step explanation:
I got it right
A cable provider wants to contact customers in a particular telephone exchange to see how satisfied they are with the new digital TV service the company has provided. All numbers are in the 452 exchange, so there are 10 000 possible numbers from 452-0000 to 452-9999. Assume they select the numbers with equal probability.
) What distribution would they use to model the selection.
b) The new business "incubator" was assigned the
500
numbers between 452-2000 and
452 dash 2499
,
but these new businesses don't subscribe to digital TV. What is the probability that the randomly selected
Answers
a) The cable provider would use a discrete uniform distribution to model the selection of customers in the telephone exchange b) The probability that a randomly selected number from the 452 exchange belongs to a new business that does not subscribe to digital TV is 1
To model the selection of customers in a particular telephone exchange, the cable provider would use a uniform distribution. This is because they are selecting numbers with equal probability from a set of 10,000 possible numbers. In a uniform distribution, each value has an equal chance of being selected, making it suitable for this scenario
Second, we are given that the new business incubator was assigned the 500 numbers between 452-2000 and 452-2499, and these businesses don't subscribe to digital TV. To find the probability of randomly selecting a number from this range that doesn't subscribe to digital TV, we need to determine the proportion of numbers in that range that meet the condition.
In this case, there are 500 numbers in the range 452-2000 to 452-2499, and all of them don't subscribe to digital TV. Since we are selecting from a specific range, the probability of selecting a number that doesn't subscribe to digital TV is 100% or 1.
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A premedical student at a university was complaining that she had just paid $158. 60 for her human anatomy book, including tax. Find the price of the book before taxes if the university tax rate is 9%
Answers
Answer:
145.50
Step-by-step explanation:
158.60 / (1+.09)
158.60 / 1.09 = 145.50458 (Approximately, I assume you have to round. I included extra digits incase they want more.)
Bao measured all of her pencils. The length of each pencil in centimeters was: 15, 11, 8, 13, and 15.
Make a line plot of the data. Move X's to the line plot.
Lengths of Pencils
+
9
8
9
+ +
10 11 12 13
Length (centimeters)
14
15
X
Answers
Answer:
Put two X's on 15, one X on the 11, one X on the 8, and one X on the 13
Step-by-step explanation:
thats how line plots work
What happens to the critical value for a chi-square test if the size of the sample is increased?
Answer
a. The critical value depends on the number of categories, not the sample size.
b. The critical value also increases.
c. The critical value decreases.
d. The critical value is determined entirely by the alpha level.
Answers
The correct option is option a) The critical value depends on the number of categories, not the sample size.
The critical value for a chi-square test is determined by the level of significance (alpha) and the degrees of freedom (df). The degree of freedom is a function of the number of categories in the test, not the sample size. Therefore, increasing the sample size does not affect the critical value for a chi-square test.
The chi-square test is a statistical test used to determine whether there is a significant difference between the expected frequencies and the observed frequencies in one or more categories. It is used to test the independence of two categorical variables.
Therefore, The correct option is option a) critical value depends on the number of categories, not the sample size.
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Select three expressions equivalent to 28xy + 16x.
Answers
The three equivalent expressions to 28xy + 16x are:
4x(7y + 4)2(14xy + 8x)4xy(7 + 4).What are three equivalent expressions to 28xy + 16x?These expressions can be obtained by factoring out common terms from the original expression, resulting in equivalent expressions with the same values when evaluated.
For example, 4x(7y + 4) can be simplified to 28xy + 16x by using the distributive property. Similarly, 2(14xy + 8x) and 4xy(7 + 4) can also be obtained by factoring out common terms and rearranging the expression. Therefore, all three expressions are equivalent to the original expression, 28xy + 16x.
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Answer:
There are many expressions that are equivalent to 28xy + 16x, but here are three possible examples:
4x(7y + 4)
4(7xy + 4x)
8(3.5xy + 2x)
All three of these expressions follow the distributive property of multiplication over addition and simplify to 28xy + 16x.
Step-by-step explanation:
Which table corresponds to the equation? Y = 4x + 1?
Answers
Answer:
3rd one down
Step-by-step explanation:
(1,5), (2,9), (3,13), (4,17)
The table C is Solution for the Equation.
What is 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. LHS = RHS is a common mathematical formula.
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:
Equation: y= 4x+ 1
When x= 1
y = 5
and, x= 2
y= 8 + 1= 9
and, x= 3
y= 12 + 1= 13
and, x=4
y = 16 + 1 = 17
Thus, the solution for the Equation is (1, 5), (2, 9), (3, 13) and (4, 17).
Hence, the table C is Solution for the Equation.
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Solve x2 = 12x – 15 by completing the square. Which is the solution set of the equation? Solve x2 = 12x – 15 by completing the square. Which is the solution set of the equation?
Answers
Answer: \(6+\sqrt{21}\ \text{and}\ 6-\sqrt{21}\)
Step-by-step explanation:
Given
Quadratic equation is
\(x^2-12x+15=0\)
Solving by completing the square method
\(\Rightarrow x^2-2\cdot 6\cdot x+15=0\\\text{add and subtract 36}\\\Rightarrow x^2-2\cdot 6\cdot x+15+36-36=0\\\Rightarrow x^2-2\cdot 6\cdot x+36+(-36+15)=0\\\text{using}\ (a-b)^2=a^2+b^2-2ab\\\Rightarrow (x-6)^2-21=0\\\Rightarrow (x-6)^2=21\\\Rightarrow x-6=\pm \sqrt{21}\\\Rightarrow x=6\pm \sqrt{21}\)
The solution set of the equation is \(6+\sqrt{21}\ \text{and}\ 6-\sqrt{21}\)
Answer:
D on edge
Step-by-step explanation:
Factor this expression
3x^2-11x-20
Answers
Answer:
(3x-4)(x+5)
Step-by-step explanation: First set up a diamond problem. Find what two numbers add to 60 since 3*20 and add to -11. That would be 15 and -4. Then draw a 2x2 box, and put in 3x^2 the -20, 15x and -4x. Then find the factors. Hope that helped! :)
Answer:
(3x+4)(x-5)
Step-by-step explanation:
8-If-5(2x - 5) = 6x + 3, what is the value
of x?
Answers
Answer:
x=7
Step-by-step explanation:
5(2x-5) = 10x-25
1) add 25 to both sides
10x+25=10x 6x+3+25=6x+28
10x=6x+28
2) subtract 6x from both sides
10x-6x=4x 6x+28-6x=28
4x=28
3) divide by 4 from both sides
4x/4=x 28/4=7
x=7
Hope this helps, have a great day!!
The value of y in the expression -5(2x - 5) = 6x + 3 is 22/16
According to the given question
We have an equation in one variable
⇒ -5(2x - 5) = 6x + 3
For finding the value of x solve the above equation by adding and subtracting the like terms.
So, -5(2x - 5) = 6x + 3
⇒ -5 x 2x + 5 x 5 = 6x + 3
⇒ -10x + 25 = 6x + 3
⇒ 25 - 3 = 6x + 10x
⇒ 22 = 16x
⇒ x = 22/16
Hence, the value of y in the expression -5(2x - 5) = 6x + 3 is 22/16
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Figures A and B are shown on the coordinate plane below. Which series of transformations demonstrates that the figures are congruent?
Answers
Note that the series of transformations that demonstrate that the figures are congruent are: "Reflect Figure A on the y-axis, followed by a 90° clockwise rotation about the origin. (Option D)
What is transformation?
Transformation in math refers to the process of changing the position, size, or shape of a geometric figure. Common types of transformations include translations, rotations, reflections, and dilations.
Reflection in math is a type of transformation that involves flipping a figure over a line of reflection. The resulting image is a mirror image of the original figure, and the line of reflection acts as the mirror.
Congruence in math refers to the relationship between two geometric figures that have the same size and shape. In other words, if two figures are congruent, they are identical in every way except for their position and orientation in space. Congruence is typically denoted by the symbol ≅.
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Full Question:
Although part of your question is missing, you might be referring to this full question:
Figures A & B are shown on the coordinate grid. Which series of transformations demonstrates that the figures are congruent?
A) Reflect Figure A on the y-axis, followed by a reflection on the x-axis.
B) Translate Figure A 6 units right, followed by a reflection on the x-axis.
C) Rotate Figure A about the origin 1800 followed by a reflection on the x-axis.
D) Reflect Figure A on the y-axis, followed by a 90' clockwise rotation about the origin.
See attached image.
is this linear or non-linear?
y=
\( \frac{x}{9} \)
+12
Answers
Answer: Linear Function.
Step-by-step explanation: The Y intercept is 12, and the slope is x/9, so you have a constant slope, therefore it is linear.
If the original quantity is 8 and the new quantity
is 2, what is the percent decrease?
Answers
If the original quantity is 8 and the new quantity is 2, then the correct answer is 75%.
How did we figure this out?
For this question we need to subtract and multiply the numbers. We know that 2 = 25% of 8 so:
\(\boxed{8-2=6}\\\boxed{6/2=3}\)
We are going to take that 25% and multiply it with 3 to get are final answer.
What is the missing number of 25 and 3?\(\boxed{25*3=75}\\\boxed{So,2=75}\)
Therefore, If the original quantity is 8 and the new quantity is 2, then the correct answer is 75%.
I’ll give Brainliest I need help please & thanks
Answers
..—————————————————————
Statement (Mathematical Steps) 12 > 7(4 + 5) − 19 show ecah reasonReason
Answers
Answer:
4 23/42 ≅ 4.547619
Step-by-step explanation:
What fratcion is equal to 50% of 1 third
Answers
Answer:
1/6
Step-by-step explanation:
To know what fraction is equal to 50% of 1/3, we have to convert the percentage into a fraction first.
50% = 50/100
So 50% of 1/3 = 1/3 * 50/100
= 50/ 300
= 5/30
= 1/6
Answer:
1/6
Step-by-step explanation:
Gertrude has 71.502 ounces of butter. How many ounces of butter does she have, rounded to the nearest hundredth?
Answers
Answer:
71.500
Step-by-step explanation:
502 is closer to 500 than 600.
Answer:
71.50
Step-by-step explanation:
This is because 2 is not up to 5, so it can't be turned into 1 and be added to 0.
Please help me and I’ll give you brainiest!!!!!!!!!
Answers
Answer:
-5
Step-by-step explanation:
A perpindicular line has the negative reciprocal slope
Hope this helps!! :)
What is the value of the number? -(-6)?
Answers
Answer:
6
Step-by-step explanation:
-(-6)=6
which of the following cannot be described by a discrete probability distribution? group of answer choices sales of two medical devices in which device a generates $35 per unit sold and will likely constitute 30% of the sales and device b generates $50 per unit sold and will likely constitute 70% of the sales the labor cost for manufacturing goods, where one-third of the units cost $10 in labor, one-third cost $15 in labor, and one-third cost $50 in labor. the cost of parts for manufacturing an item, where the parts can take on any value between $80 and $100. the number of units produced in a given day, where 20% of the time 99 units are produced and 80% of the time 100 units are produced.
Answers
In the given options, the sales of two medical devices, labor cost for manufacturing goods, and the cost of parts for manufacturing an item can be described by a discrete probability distribution. However, the number of units produced in a given day cannot be described by a discrete probability distribution. It can be described by a continuous probability distribution.
A continuous probability distribution cannot be described by the number of units produced in a given day where 20% of the time 99 units are produced and 80% of the time 100 units are produced.What is a probability distribution?A probability distribution is a set of possible values with their respective probabilities. In other words, a probability distribution is a function that assigns probabilities to various outcomes of an experiment.What is a discrete probability distribution?A discrete probability distribution is a probability distribution in which a random variable can only take on certain values and has associated probabilities.
It is defined by a probability mass function, which lists all possible outcomes and their associated probabilities.What is a continuous probability distribution?A continuous probability distribution is a probability distribution in which the random variable can take on any value within a given range or interval, and has associated probabilities. It is characterized by a probability density function, which is used to calculate the probability of an event occurring within a range of values.What are the types of probability distributions?The two types of probability distributions are Discrete Probability Distribution and Continuous Probability Distribution.
In the given options, the sales of two medical devices, labor cost for manufacturing goods, and the cost of parts for manufacturing an item can be described by a discrete probability distribution. However, the number of units produced in a given day cannot be described by a discrete probability distribution. It can be described by a continuous probability distribution.
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