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Multiple choice answers:

A)14.7%
B)1187.5%
C)11.7%
D)26.4%

Using the properties of logarithm we get the value y = 100x⁻¹ in the exponential form axⁿ

The given logarithmic equation is :

log ₁₀y + log ₁₀x = 2

Now we know that: 1 = log₁₀10

∴log ₁₀y + log ₁₀x = 2× log₁₀10

or, log ₁₀y + log ₁₀x = log₁₀10² (10 raised to the power 2)

or,  log ₁₀y + log ₁₀x = log₁₀100

we know that log p+ log q = log pq

or, log ₁₀xy =  log₁₀100

Now we take antilog on both sides of the equation:

or, xy = 100

or, y = 100 / x

or, y = 100x⁻¹

Problems that cannot be solved using the concept of basic exponents alone can be solved with a logarithm. Simply said, a logarithm is another way to talk about exponents.

A relatively simple way to remember this is that base remains the base in both forms and base does not remain solely with exponent in log form. Be aware that "b" is the base on both the left and right sides of the implies symbol, and that when an equation is written in log form, the base b and exponent x do not necessarily stay on the same side of the equation.

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Answer:

será un posible gráfica de grado

Answer:

(h, k ) = (3, 1 )

Step-by-step explanation:

The coordinates of the vertex of a parabola are (h, k )

The vertex is the turning point of the graph and

(h, k ) = (3, 1 )

The mean score of the given three scores is approximately 26.6, which is not the mean score for all ninth graders in the city.

To find the mean score for all ninth graders in the city, we need more information than just three scores. Without additional data, we cannot accurately determine the mean score for all ninth graders in the city.

However, we can calculate the mean of the given scores to verify that it is not 79.7 as claimed by the PR manager:

Mean = (77 + 91 + 71) / 3 = 79.7/3 = 79.7 ÷ 3 ≈ 79.7/3 ≈ 26.6

So the mean score of the given three scores is approximately 26.6, which is not the mean score for all ninth graders in the city.

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The cost of the apples is 2.9 dollars.

The cost of the bananas is 5.7 dollars.

The total cost is 6 dollars, each apple cost $1.50 each banana cost $.30 and there’s two more bananas then apples.

Therefore,

let

x = number of apples

y = 2x

where

Therefore, using equations,

1.5(x) + y(0.30) = 6

Hence,

where

y = 2x

1.5(x) + 2x(0.30) = 6

1.5x + 0.6x = 6

2.1x = 6

divide both sides by 2.1

x = 6 / 2.1

x = 2.9 dollars

y = 2(2.9) = 5.7 dollars

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Answer:

353.25 miles.

Step-by-step explanation:
multiply 78.5 mph by 4.5 hours

15 and 67 degrees are the measure of x and m<ABK respectively.

The point where two lines meet is known as an angle. From the given diagram, the sum of the given angles is 180 degrees

4x + 7 + 8x - 7 = 180

12x = 180

Divide both sides by 12

12x/12 = 180/12

x = 15

For the measure of m<ABK

m<ABK = 4x + 7

m<ABK = 4(15) + 7

m<ABK = 67 degrees

Hence the measure of x and m<ABK is 15 and 67 degrees respectively.

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Answer:

Answer:

Revenue = 1.25x * (45-5x)

Revenue = 56.25x - 6.25x^2

Therefore, the answer is A) 56.25x - 6.25x^2.

Answer:

The pizza restaurant put 1/10 of the sauce on each pizza.

Step-by-step explanation:

Take the 3/5, and on a calculator divide the 3 by the 5:

0.6

Then, take the 0.6 and divide it by the 6 pizzas:

0.1, converted into a fraction equals 1/10.

The pizza restaurant put 1/10 of the sauce on each pizza.

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Answer:

17/3

Step-by-step explanation:

Answer:

If we divide 5 by any other integer, then the remainder will be a non-zero positive integer.

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

The  probability of event A is P(A) = 1/4 or 0.25.

The formula to find P(A) for a series of simple events is:

P(A) = (number of outcomes that satisfy the event A) / (total number of possible outcomes)

For example, if you are tossing a coin and selecting a number at the same time, and event A is defined as getting a head and an even number, then:

- The number of outcomes that satisfy event A is 1 (getting a head and an even number, i.e., H2)
- The total number of possible outcomes is 4 (H1, H2, T1, T2)
- Therefore, the probability of event A is P(A) = 1/4 or 0.25.

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Answer:

\(\sqrt{2}\)

Step-by-step explanation:

A rational number has the form

\(\frac{a}{b}\) , where a and b are integers

Given

- \(\sqrt{2}\) ( multiplying by \(\sqrt{2}\) gives )

- \(\sqrt{2}\) × \(\sqrt{2}\)

= - 2

= \(\frac{-2}{1}\) ← a rational number

The chance that the hospital will run out of sleeping pills on any given day is 0.5000 (or 0.5000 with four decimal places).

To calculate the chance that the hospital will run out of sleeping pills on any given day, we can use the normal distribution and Z-score.

First, let's calculate the Z-score using the formula:

Z = (X - μ) / σ

Where:

X = consumption rate per day (1,155 pills)

μ = average consumption rate per day (1,155 pills)

σ = standard deviation (81 pills)

Z = (1,155 - 1,155) / 81

Z = 0

Now, we need to find the probability associated with this Z-score. However, since the demand for sleeping pills can be considered continuous and not discrete, we need to calculate the area under the curve from negative infinity up to the Z-score. This represents the probability of not running out of sleeping pills.

We discover that the region to the left of a Z-score of 0 is 0.5000 using a basic normal distribution table or statistical software.

To find the probability of running out of sleeping pills, we subtract this probability from 1:

Probability of running out of sleeping pills = 1 - 0.5000

Probability of running out of sleeping pills = 0.5000

Therefore, on any given day, the hospital has a 0.5000 (or 0.5000 with four decimal places) chance of running out of sleeping tablets.

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Answer:

4 minutes

The amount of time spent on each problem must be ≤ 4 minutes

y ≤ 4

Step-by-step explanation:

let y be the amount of time spent on each problem

y = 24/6 ----> the total time divided by the amount of math problems

y = 24/6

y = 4

So to find any last digit of 3^2011 divide 2011 by 4 which comes to have 3 as remainder. Hence the number in units place is same as digit in units place of number 3^3. Hence answer is 7.

Alternatively, if you have 4 friends, then you would divide 5.6 by 4, giving each friend 1.4 pounds of meat.

If you have 5.6 pounds of meat and you want to give an equal amount to each of your friends, you will need to divide the total amount of meat by the number of friends you have. Let's say you have 4 friends, then you would need to divide 5.6 by 4, which would give you 1.4 pounds of meat per friend.

If you have more or fewer friends, you would need to adjust the amount of meat accordingly. For example, if you have 6 friends, then you would divide 5.6 by 6, giving each friend 0.93 pounds of meat.

It's important to make sure you have enough meat for everyone and to also consider any dietary restrictions or preferences your friends may have.

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Approximately 34% of American adults have a mobile phone but not a landline, based on the given proportions from the study conducted by the Centers for Disease Control.

The proportion of American adults who have a mobile phone but not a landline, we need to subtract the proportion of those who have both a mobile phone and a landline from the proportion of those who have a mobile phone.

Let's denote the proportion of American adults who have a mobile phone as P(M), the proportion who have a landline as P(L), and the proportion who have neither as P(N).

Given information:

P(M) = 89% (proportion with a mobile phone)

P(L) = 57% (proportion with a landline)

P(N) = 2% (proportion with neither)

We can now calculate the proportion of adults who have a mobile phone but not a landline using the following equation:

P(M and not L) = P(M) - P(M and L)

To find P(M and L), we can subtract P(N) from P(L) since those who have neither are not included in the group with a landline:

P(M and L) = P(L) - P(N)

P(M and L) = 57% - 2%

P(M and L) = 55%

Now we can substitute the values back into the equation to find P(M and not L):

P(M and not L) = P(M) - P(M and L)

P(M and not L) = 89% - 55%

P(M and not L) = 34%

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The candidate key for the relation schema R(A,B,C,D,E): A→B, C→B, D→A, D→B, D→C, C→D, D→E.

Candidate key for the given relation: To find the candidate key for the relation schema R(A,B,C,D,E), we need to follow the below steps:

Here, we have the following functional dependencies: A→B, C→B, D→ABC, AC→D, D→E.

Step 1: To normalize the given dependencies, we have the following dependencies:

A→B, C→B, D→ABC, AC→D, D→E becomes

A→B, C→B, D→A, D→B, D→C, D→E.

Step 2: To check for the minimal dependency, we can eliminate the redundancy by eliminating D→ABC. Therefore, we have the following dependency:

A→B, C→B, D→A, D→B, D→C, D→E.

Step 3: Find the closure on each attribute, which is as follows:

1. A+ = {A,B}

2. B+ = {B}

3. C+ = {B}

4. D+ = {A,B,C,D,E}

5. E+ = {E}

Step 4: The combination of attributes that have all attributes of the relation schema, and it will be a candidate key is AD. Therefore, the candidate key is AD.

Compute the minimal cover of F:

Minimal Cover: The minimal set of dependencies that is equivalent to the given set of dependencies is the minimal cover.

We have the following functional dependencies:

A→B, C→B, D→ABC, AC→D, D→E.

The process to compute the minimal cover of F is as follows:

Step 1: To find the redundant dependencies, we need to split the dependencies. We have the following dependencies:

A→B, C→B, D→ABC, AC→D, D→E  becomes

A→B, C→B, D→A, D→B, D→C, D→E.

Step 2: To eliminate the dependencies with three attributes, we can use the following steps:

If X→YZ, then X→Y and X→Z.

Therefore, we have the following dependency:

D→A, D→B, D→C.

Step 3: To eliminate the dependency with two attributes, we can use the following steps:

If X→Y and Y→Z, then X→Z.

We have the following dependency: AC→D, C→D.

Step 4: Therefore, the minimal cover of F is A→B, C→B, D→A, D→B, D→C, C→D, D→E.

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Answer:

C(x) = 15            0 ≤ x ≤ 2

C(x) = 5x + 10    2 < x ≤ 6

C(x) = 50           x > 6

Step-by-step explanation:

Its A

Answer:

c

Step-by-step explanation:

Answer:

98 yd²

Step-by-step explanation:

From the diagram attached, The polygon is a square with the distance from the edge of the square to the center of the square = 7 yd.

The distance from the edge of the square to the center of the square is half of the diagonal. Therefore length of the diagonal = (7 yd * 2) = 14 yd

The diagonal and two sides of the triangle form a right angle triangle. Let the side of the triangle be a. Therefore the hypotenuse is the diagonal, using Pythagoras theorem:

a² + a² = 14²

2a² = 196

a² = 98

a = √98 = 7√2

The length of the side of the triangle = a = 7√2 yd

The area of the rectangle = length × length = 7√2 × 7√2  = 98 yd²

Answer:

21 minutes

Step-by-step explanation:

Ms.Keller is speed reading a book that has 342 pages, she has already completed 300 of them and can read 2 pages per minute. The question is asking how long it'll take her to finish this book.

So we know the vital information that Keller reads two pages per minute and she only has 42 pages left of the book, this is all we need to answer the question.

All we need to do is divide 42 by 2 :

42 / 2

21

Therefore, it'll take Ms.Keller 21 minutes to finish the book at the constant speed

The Wronskian of y1 = e^(3x) and y2 = e^(-7x) on the interval (-∞, ∞) is W(y1, y2) = 10.

To find the Wronskian of y1 = e^(3x) and y2 = e^(-7x), we can use the formula for calculating the Wronskian of two functions. Let's denote the Wronskian as W(y1, y2).

The formula for calculating the Wronskian of two functions y1(x) and y2(x) is given by:

W(y1, y2) = y1(x) * y2'(x) - y1'(x) * y2(x)

Let's calculate the derivatives of y1 and y2:

y1(x) = e^(3x)

y1'(x) = 3e^(3x)

y2(x) = e^(-7x)

y2'(x) = -7e^(-7x)

Now, substitute these values into the Wronskian formula:

W(y1, y2) = e^(3x) * (-7e^(-7x)) - (3e^(3x)) * e^(-7x)

= -7e^(3x - 7x) - 3e^(3x - 7x)

= -7e^(-4x) - 3e^(-4x)

= (-7 - 3)e^(-4x)

= -10e^(-4x)

So, the Wronskian of y1 = e^(3x) and y2 = e^(-7x) is W(y1, y2) = -10e^(-4x).

Note that the order of the functions matters in the Wronskian calculation. If we were to reverse the order and calculate W(y2, y1), the result would be the negative of the previous Wronskian:

W(y2, y1) = -W(y1, y2) = 10e^(-4x).

Since the Wronskian is a constant value regardless of the interval (-∞, ∞) in this case, we can evaluate it at any point. For simplicity, let's evaluate it at x = 0:

W(y1, y2) = 10e^(0)

= 10

Therefore, the Wronskian of y1 = e^(3x) and y2 = e^(-7x) on the interval (-∞, ∞) is W(y1, y2) = 10.

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The statement that correctly shows the relationship between both expressions is

f(2) >  g(2)

The given equation is

f(x) = 2x⁴  and

g(x) = 4 x 2ˣ

plugging in 2 for x in both expressions

f(x) = 2x⁴  

f(2) = 2 * (2)⁴  

f(2) = 2 * 16

f(2) = 32

Also

g(x) = 4 x 2ˣ

g(2) = 4 x 2²

g(2) = 4 * 4

g(2) = 16

hence comparing both we can say that

f(2) = 32 is greater than g(2) = 16

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Answer:

-5/2

Step-by-step explanation:

Answer:

5/2

Step-by-step explanation:

Rise / run

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Two values have frequency 2, so both are modes. They are 5 and 6. Therefore, the mode is 5 and 6.

Given measure: 3, 5, 4, 6, 10, 5, 6, 9, 2, 13.(D) To calculate \(x_2\), first we need to sort the data in ascending order: 2, 3, 4, 5, 5, 6, 6, 9, 10, 13

Now, we need to find the median, which is the middle value of the data. Since the data has even number of values, we will calculate the mean of middle two values, that is:(5+6)/2 = 5.5 Therefore, \(x_2 = 5.5\).\( \frac{2}{x}= \) To find the value of x, we will first cross-multiply and then take the reciprocal of both sides:\[\frac{2}{x} = y \Rightarrow 2 = xy \Rightarrow x = \frac{2}{y}\] Therefore, \( \frac{2}{x}= \frac{2}{y}\).

(b) To calculate Fried m, we will use the formula: \[f_m = L + \frac{(n/2 - F)}{f} \times c\]where L is the lower limit of the modal class, F is the cumulative frequency of the class preceding the modal class, f is the frequency of the modal class, c is the class interval, and n is the total number of values.

First, we will calculate the class interval:c = (upper limit of class - lower limit of class) = (7-6) = 1 Next, we will construct a frequency table to find the modal class:| Class Interval | Frequency ||-------------------|------------|| 2-3 | 1 || 3-4 | 1 || 4-5 | 1 || 5-6 | 2 || 6-7 | 2 || 7-8 | 1 || 9-10 | 1 || 10-11 | 1 || 13-14 | 1 |The modal class is the class with highest frequency.

Here, two classes have frequency 2, so both are modes. They are 5-6 and 6-7.

Therefore, L = 5, F = 2, f = 2, n = 10, and c = 1. Substituting the values, we get:\[f_m = L + \frac{(n/2 - F)}{f} \times c = 5 + \frac{(10/2 - 2)}{2} \times 1 = 7\] Therefore, Fried m = 7.

(c) To find the mode, we look for the value(s) with highest frequency. Here, two values have frequency 2, so both are modes. They are 5 and 6. Therefore, the mode is 5 and 6.

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Step 1: To calculate the cost of 5kg of breakfast cereal, we need to multiply the cost of 1kg by 5.

Step 2: R36 x 5 = R180

Step 3: Therefore, 5kg of breakfast cereal will cost R180.

An exponential function is a mathematical function of the following form: f(x) = a^(x), where a is the base of the function, and x is the exponent. The general form of an exponential function is f(x) = ab^x, where a and b are constants.

The exponential function can be used to model a variety of phenomena, such as population growth, radioactive decay, and compound interest. For example, the growth of a population can be modeled using the equation P = P0e^(rt), where P0 is the initial population, r is the growth rate, t is time, and e is the mathematical constant approximately equal to 2.71828.

In this equation, the exponential function e^(rt) represents the growth of the population over time. Similarly, the decay of a radioactive substance can be modeled using the equation N = N0e^(-λt), where N0 is the initial quantity of the substance, λ is the decay constant, and t is time. In this equation, the exponential function e^(-λt) represents the decay of the substance over time.

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