Mrs. Chin paid a 20 percent tip on the bill for lunch. Percents Total 20% 20% 20% 20% 20% 100% $2.75 $2.75 $2.75 $2.75 $2.75 If the tip amount was $2.75, what was the bill for lunch before the tip was added to it?

The amount of interest earned on a deposit of $60.00 at a rate of 9% per annum for 2 years is $108.

As per the given problem:

Amount deposited = $60.00

Interest rate per year = 9%

The formula for calculating the interest is given by:

Interest = (Principal × Rate × Time)/100

Where Principal is the initial amount invested or deposited

Rate is the percentage of interest that you earn per annum

Time is the duration for which you want to calculate the interest

Putting the values in the above formula, we get:

Interest = (60 × 9 × 2)/100= (108 × 1)/1= $108

So, the amount of interest earned on a deposit of $60.00 at a rate of 9% per annum for 2 years is $108.

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Answer:

x=7

Step-by-step explanation:

5-2 is 3

21 divided by 3 is 7

therefore 7 is x

Answer: 5x = 5 times 5. 2x = 2 times 2

AKA 25-4=21

Answer:

x=15

Step-by-step explanation:

Since 13+6+2x-18= 4x-29, use this equation.

Combine like terms:

1+2x= 4x-29

-1            -1

2x= 4x-30

-4x     -4x

\(\frac{-2x=-30}{-2}\)

x=15

Hope this helps! :)

Step-by-step explanation:

if the solution has "nice" numbers, we can split the expression into 2 factors in the form

(x + a)(x + b) = x² + (a+b)x + ab

as this is equal to x² + 4x - 21.

ab = -21

so, one is positive and one is negative.

and 4 = a + b

we know the typical factors of 21 : 3×7

and then we see easily : 7-3 = 4

so,

we have

(x + 7)(x - 3) >= 0

this has 2 x-intercepts (x-values when y = 0) :

x = -7

x = 3

because the coefficient of x² is positive (1), we know that the parabola (or quadratic equation) is opening upwards.

that means the y-values for x-values between -7 and +3 are negative (< 0), but the y-values for everything else are positive.

so, the solution are the intervals

x <= -7 and x >= 3

in these areas is the expression x² + 4x - 21 >= 0.

Answer:

#4

When the figures are similar, their perimeters and their corresponding sides will have same ratio.

#5

When the figures are similar, their areas will have the ratio equal to the square of ratio of corresponding sides.

Answer:

10

Step-by-step explanation:

1/12 times 2 would be 1/6 miles per minute, so times that by 6 and it takes 6 minutes to run 1 mile. 60 minutes divided by 6 equals 10 miles per hour. Sorry if thats confusing

Based on the transformation of the given parent function f(x), the function g(x) is: C. g(x) = ∛(x) + 2

In Mathematics, the translation of a geometric figure to the right is a type of transformation which simply means adding a digit to the value on the x-coordinate (x-axis) of the pre-image while translating a geometric figure up is a type of transformation that simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image.

Translating the parent function f(x) = ∛(x) two (2) units up, would produce an image of function f(x):

g(x) = f(x) + 2

g(x) = ∛(x) + 2

In this context, we can reasonably infer and logically deduce that the parent function f(x) was shifted 2 units up to produce function g(x).

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If Janet provides 4 waiting spaces, the expected fraction of potential customers that will be lost due to inadequate waiting space is 0.0042, or about 0.42%.

What is the fraction?

A fraction is a mathematical representation of a part of a whole, where the whole is divided into equal parts. A fraction consists of two numbers, one written above the other and separated by a horizontal line, which is called the fraction bar or the vinculum.

To determine the expected fraction of potential customers that will be lost due to inadequate waiting space, we need to use queuing theory to model the car wash operation.

Let's consider the two scenarios:

(a) 2 waiting spaces:

In this case, we can model the system as an M/M/2 queue, where arrivals follow a Poisson process with a rate λ = 1/5 customers per minute and service times follow an exponential distribution with rate μ = 1/4 cars per minute.

The utilization factor of the system is ρ = λ/2μ = (1/5)/(2*(1/4)) = 0.4, which is less than 1, so the system is stable.

Using Little's Law, we can calculate the expected number of customers in the system:

L = λ * W

where L is the expected number of customers in the system, λ is the arrival rate, and W is the expected time a customer spends in the system (i.e., waiting time plus service time).

The expected waiting time in an M/M/2 queue can be calculated as:

Wq = (2ρ)/(2 - ρ) * (1/λ)

where Wq is the expected waiting time in the queue.

The expected time in the system can be calculated as:

W = Wq + (1/μ)

Substituting the values, we get:

Wq = (2*0.4)/(2-0.4) * (1/1/5) = 1 minute

W = 1 + 1/4 = 1.25 minutes

The expected fraction of potential customers that will be lost due to inadequate waiting space can be calculated as:

P(lost) = ρ² / (1 - ρ) * (1 - 2ρ⁽ⁿ⁻¹⁾ + ρⁿ)

where n is the number of waiting spaces. In this case, we have n = 2, so:

P(lost) = 0.4² / (1 - 0.4) * (1 - 2*0.4⁽²⁻¹⁾+ 0.4²) = 0.196

Therefore, if Janet provides 2 waiting spaces, the expected fraction of potential customers that will be lost due to inadequate waiting space is 0.196, or about 19.6%.

(b) 4 waiting spaces:

In this case, we can model the system as an M/M/4 queue, where arrivals follow a Poisson process with rate λ = 1/5 customers per minute and service times follow an exponential distribution with rate μ = 1/4 cars per minute.

The utilization factor of the system is ρ = λ/4μ = (1/5)/(4*(1/4)) = 0.25, which is less than 1, so the system is stable.

Using the same formulas as before, we can calculate:

Wq = (4*0.25)/(4-0.25) * (1/1/5) = 0.625 minute

W = 0.625 + 1/4 = 0.875 minutes

P(lost) = 0.25² / (1 - 0.25) * (1 - 2*0.25⁽⁴⁻¹⁾ 0.25⁴) = 0.0042

Therefore, if Janet provides 4 waiting spaces, the expected fraction of potential customers that will be lost due to inadequate waiting space is 0.0042, or about 0.42%.

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To find a quadratic equation with the y-intercept and vertex, follow these steps: identify the coordinates of the y-intercept and vertex, substitute them into the general form of the quadratic equation, solve for the coefficients, and substitute the coefficients back into the equation. For example, if the y-intercept is (0, 3) and the vertex is (-2, 1), the quadratic equation would be y = x^2 + x + 3.

To find a quadratic equation with the y-intercept and vertex, we can follow these steps:

For example, let's say the y-intercept is (0, 3) and the vertex is (-2, 1). We can substitute these coordinates into the general form of the quadratic equation:

3 = a(0)^2 + b(0) + c

1 = a(-2)^2 + b(-2) + c

Simplifying these equations, we get:

c = 3

4a - 2b + c = 1

By substituting c = 3 into the second equation, we can solve for a and b:

4a - 2b + 3 = 1

4a - 2b = -2

2a - b = -1

By solving this system of equations, we find a = 1 and b = 1. Substituting these values back into the general form of the quadratic equation, we obtain the final equation:

y = x^2 + x + 3

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To find a quadratic equation with a given y-intercept and vertex, you need the coordinates of the vertex and one additional point on the curve.

Example:

Suppose we want to find a quadratic equation with a y-intercept of (0, 4) and a vertex at (2, -1).

To find a quadratic equation with a given y-intercept and vertex, you can use the vertex form of a quadratic equation and substitute the coordinates to obtain the equation. Then, use the y-intercept to find an additional point on the curve and solve a system of equations to determine the coefficients. Finally, substitute the coefficients into the standard form of the quadratic equation to get the final equation.

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True, to calculate the average of numeric values in the list, the first step is to get the total of values in the list.

Steps to calculate the Average:

Let’s assume there are 4 numbers having values of 2,8,22,48 respectively.

To find the average we first have to take the total of all values.

2+8+22+48=80.

Our next step will be to divide this total by the number we have in our question i.e., 4.

so, our average will be 80/4= 20.

So, 20 will be our average.

So yes, it is true that to calculate the average of numeric values in the list, the first step is to get the total of all values in the list.

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The linear equation that can be used to find the height considering all the information is h2 = h1 + (-0.5)(t2 - t1)

The height of a candle can be modeled by a linear function with a slope of -0.5 cm/hour.

If the height of the candle after t1 hours is h1 centimeters, then the height of the candle after t2 hours is given by h2 = h1 + (-0.5)(t2 - t1).

So, if the height of the candle after t1 hours is h1 centimetres, and after t2 hours is h2 centimeters, we have:

h2 = h1 + (-0.5)(t2 - t1)

We can use the given information to find the value of h1, and then use the equation above to find the value of h2.

However, the information given in the question is not enough to solve for h1 and h2. We need more information such as the height of the candle after a certain number of hours.

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Remember to refer to your own course materials or textbooks to identify the specific end-of-chapter correlations that you have learned.

but as an AI language model, I don't have personal experiences or the ability to recall specific information that I have learned this term. However, I can explain how to interpret end-of-chapter correlations.

An end-of-chapter correlation is a statistical measure that indicates the relationship between two variables. It shows whether there is a positive or negative association between the variables, as well as the strength of that relationship.

To answer your question, you would need to review the end-of-chapter correlations that you have learned this term. Identify seven correlations where one variable is either "performance" or "commitment" and specify the direction (positive or negative) and strength (.3 or .5) of the relationship.

For example:
1. Performance and Commitment: Positive correlation, strength .3
2. Commitment and Performance: Negative correlation, strength .5
3. Performance and Productivity: Positive correlation, strength .5
4. Commitment and Job Satisfaction: Positive correlation, strength .3
5. Performance and Engagement: Negative correlation, strength .3
6. Commitment and Turnover Intention: Negative correlation, strength .5
7. Performance and Teamwork: Positive correlation, strength .3

Remember to refer to your own course materials or textbooks to identify the specific end-of-chapter correlations that you have learned.

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The complete factorization of the polynomial x³ + 2x² -x - 2 is equal to (x + 2)(x + 1)(x - 1)

An equation is an expression that shows how numbers and variables are related to each other using mathematical operators.

A polynomial is an expression consisting of coefficients and variables forming an equation.

Given the polynomial:

x³ + 2x² -x - 2

Factorizing:

= (x + 2)(x² - 1)

= (x + 2)(x + 1)(x - 1)

The polynomial x³ + 2x² -x - 2 is equal to (x + 2)(x + 1)(x - 1)

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Answer:

Step-by-step explanation:

If m and n are both 1 then

Minimum value = 10^(1+1) * 3^(1-1) * 225

= 325.

If m and n have to be different, then m = 2 and n = 1

Minimum value = 10^3 * 3^1 * 15^2

= 675,000.

Answer:

Total surface area=228cm²

Step-by-step explanation:

Area of bottom(parallelogram)=12×12=144cm²

area of 1 triangle=1/2×8×12=48cm²

area of 3triangles=48×3=144cm²

Total surface area=144+144=228cm²

The area of circle A to the area of circle B ratio is 100: 64, and the ratio of e: f is 13: 10.

The area of the circle is equal to the multiplication of the square of the circle's radius and π.

A = πr²

where 'r' is the radius

Circumference of circle A × 0.8 = circumference of circle B

So, taking r as the radius of A,

2πr =  circumference of circle A

2πr × 0.8 = circumference of circle B

So the radius of B is r × 0.8.

Now we can substitute that in the area equations :

Area of A = π×r²

Area of B = π × (r × 0.8)² = π × r² × 0.64

The circumferences of the A to B ratio is

Circumference of A : Circumference of B = (2 × π × r)/(2 × π × r × 0.8)

= 1: 0.8 = 100: 80,

The areas of circle A to circle B ratio is

Area of A : Area of B = (π × r²)/(π × r² × 0.64) = 1: 0.64 = 100: 64

e² = f² × 1.69

69% larger shows that f² is the 100% to which we must add 69% to obtain e². 100% + 69% Equals 169%, obtaining a factor of 1.69.

We have this equation:

e² = f² × 1.69

Apply the square root on both sides.

e = f × √(1.69) = f × 1.3

e/f = 1.3 = 1.3/1 = 13/10

the ratio e:f = 13: 10

Thus, the ratio of circle A's area to circle B's area is 100: 64 and the ratio of e: f is 13: 10.

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Answer:

see explanation

Step-by-step explanation:

Given

5y + 4 = 10 ( subtract 4 from both sides )

5y = 10 - 4 , that is

5y = 6

Thus 5y + 4 = 10 is equivalent to 5y = 6

Answer: y=  9x+6y=15

Step-by-step explanation:

As similarity theorem, the value of x that will make the triangles similar by SSS similarity theorem is 77.

Similarity theorem:

In math, similarity theorem refers the line segment splits two sides of a triangle into proportional segments if and only if the segment is parallel to the triangle's third side.

Given,

Here we need to find the t value of will make the triangles similar by the similarity theorem.

For example, we are told that the 2 triangles are similar by SSS theorem.

Here we know that, SSS means Side - Side -Side and it is a congruence theorem which states that the 3 corresponding sides of two triangles have same ratio, then we can say that the two triangles are congruent by SSS theorem

Therefore, in the triangles ,applying the SSS postulate gives;

=> x/35 = 44/20

Then by applying the multiplication property of equality, let us multiply both sides by 35 to get;

=> x = (44 * 35)/20

When we simplify this one then we get,

=> x = 77

Therefore, the value of x is 77.

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There are two main subtypes of quantitative data, which are discrete data and continuous data. Each subtype has different techniques for analysis.

1. Discrete data: This type of data represents whole numbers or counts that can only take specific values. Examples include the number of students in a class or the number of cars in a parking lot. Techniques used to analyze discrete data include:
  a. Frequency distribution: A summary of the number of times each value appears in the dataset.

 b. Measures of central tendency: Calculating the mean, median, and mode of the dataset to understand its central point.

 c. Measures of dispersion: Assessing the range, variance, and standard deviation to understand the spread of the data.

2. Continuous data: This type of data represents measurements that can take any value within a range, such as height, weight, or temperature. Techniques used to analyze continuous data include:

 a. Histogram: A graphical representation of the distribution of the data, using bars to represent the frequency of values within specific intervals.

  b. Probability density function: A mathematical function that describes the probability of a continuous random variable falling within a specific range.

  c. Regression analysis: A statistical method for analyzing the relationship between a dependent variable and one or more independent variables.

Both discrete and continuous data can also be analyzed using inferential statistics, such as hypothesis testing and confidence intervals, to make inferences about a population based on a sample of the data.

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Answer:

its 0.5 I took the test and it was correct

Step-by-step explanation:

Thus , multiplication factor answer is water desalination plant can produce 2.8 x 10⁶ gallons per day. Thus, it can produce 1.4 x 10⁷gallons in 5 days.

A multiple is a number that can be divided by another number a certain number of times without a remainder. A factor is one of two or more numbers that divides a given number without a remainder. Multiplication is one of the four basic arithmetic operations, alongside addition, subtraction, and division. In math, multiply means the repeated addition of groups of equal sizes. To understand better, let us take a multiplication example of the ice creams. Each group has ice creams, and there are two such groups.

Here,

So if there was 5 days, it would produce 5 times the amount above.

So 5 × (2.8 × 10⁶) = 14 × 10⁶

We must rewrite in scientific notation, so:

14 x 10⁶ = 1.4 x 10⁷

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Thus , multiplication factor answer is water desalination plant can produce 2.8 x 10⁶ gallons per day. Thus, it can produce 1.4 x 10⁷gallons in 5 days.

A multiple is a number that can be divided by another number a certain number of times without a remainder. A factor is one of two or more numbers that divides a given number without a remainder. Multiplication is one of the four basic arithmetic operations, alongside addition, subtraction, and division. In math, multiply means the repeated addition of groups of equal sizes. To understand better, let us take a multiplication example of the ice creams. Each group has ice creams, and there are two such groups.

Here,

So if there was 5 days, it would produce 5 times the amount above.

So 5 × (2.8 × 10⁶) = 14 × 10⁶

We must rewrite in scientific notation, so:

14 x 10⁶ = 1.4 x 10⁷

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Answer:

\(\mathrm{No\:Solution}\)

Step-by-step explanation:

\(\begin{bmatrix}Y=3x-2\\ Y-3x=4\end{bmatrix}\)

\(\mathrm{Substitute\:}Y=3x-2\)

\(\begin{bmatrix}3x-2-3x=4\end{bmatrix}\)

\(\mathrm\:{Combine\:like\:terms:\)

\(\begin{bmatrix}-2=4\end{bmatrix}\)

\(-2=4\:\mathrm{\:is\:false,\:therefore\:the\:system\:of\:equations\:has\:no\:solution}\)

\(\mathrm{No\:Solution}\)

Answer:

umm ok

Step-by-step explanation:

Answer:

z = 23/12

Step-by-step explanation:

13(z+4)−6=23(5−z)

Distribute

13z + 52 -6 = 115 - 23z

Combine like term

13z+46 = 115 -23z

Add 23z to each side

13z+23z+46 = 115-23z+23z

36z +46 = 115

Subtract 46 from each side

36z+46-46 = 115-46

36z=69

Divide each side by 36

36z/36 = 69/36

z = 23/12

Answer:

\(z=\frac{23}{12}\)

Step-by-step explanation:

Example that demonstrates the contrapositive of the limit comparison test. Let's consider a pair of series an and bn with positive terms, where lim(n→∞)(an/bn) = 0, bn diverges, but an converges.

Let's define the series an and bn as follows:
- an = 1/\(n^2\)
- bn = 1/n

Now, let's examine the limit:
lim(n→∞)(an/bn) = lim(n→∞)((1/\(n^2\)) / (1/n))

To simplify the limit expression, we multiply both numerator and denominator by \(n^2\):
lim(n→∞)(\(n^2\)(1/\(n^2\)) / \(n^2\)(1/n)) = lim(n→∞)(n/\(n^2\)) = lim(n→∞)(1/n)

As n approaches infinity, the limit becomes:
lim(n→∞)(1/n) = 0

Now, let's check the convergence of the series an and bn:
- an = Σ(1/\(n^2\)) is a convergent p-series with p = 2 > 1.
- bn = Σ(1/n) is a divergent p-series with p = 1.

Thus, we have provided an example of a pair of series an and bn with positive terms, where lim(n→∞)(an/bn) = 0, bn diverges, but an converges. This demonstrates the contrapositive of the limit comparison test, as requested.

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T is an exponential random variable with expected value 0.02 and B = { T > 0.04 }

a. Then  the conditional expected value of T given B is E[T|B] = 0.06

b. Then the conditional variance of T given B is Var[T|B] = 0.0004

We are given that T is an exponential random variable with an expected value of 0.02, and B = { T > 0.04 }.

a. To find the conditional expected value of T given B, we need to calculate E[T|B]. For an exponential random variable, the conditional expectation E[T|B] can be calculated as:

E[T|B] = E[T] + t, where t is the lower limit of the conditional range (in this case, t = 0.04).

Given the expected value of T (E[T]) is 0.02, we can plug in the values:

E[T|B] = 0.02 + 0.04 = 0.06

b. For the conditional variance of T given B, Var[T|B], it remains the same as the original variance for an exponential random variable. To find the variance, we first need to calculate the rate parameter, λ:

λ = 1 / E[T] = 1 / 0.02 = 50

The variance of an exponential random variable is given by Var[T] = 1 / λ²:

Var[T|B] = Var[T] = 1 / (50²) = 1 / 2500 = 0.0004

Your answer:
a. E[T|B] = 0.06
b. Var[T|B] = 0.0004

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Answer:

First one

Step-by-step explanation:

FIRST pair of triangles is congruent by Angle - Side - Angle

The pair of triangles in option 1 is congruent by Angle Side Angle.

For the given question,

In option one,

one pair of angles is given equal.

One side is also given equal.

As both triangles are formed due to intersection of the two lines.

They have equal vertical angles.

Thus, by angle side angle property pair of triangles are congruent.

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