Ana's manager is trying to figure out how much to charge for a chair that just arrived. If the wholesale price of the chair is $135 and Ana's store marks up all the furniture by 85%, at what price should the manager sell the chair? Round your answer to the nearest cent.

These types of questions are categorized under exponential equations which involve addition, subtraction, multiplication, and division of exponents.

Exponents is the term used to describe a way to represent huge numbers using powers. In other words, the exponential describes how many times a number has been multiplied by itself. Various rules of exponents are presented according to the capacities they possess.

The following rule governs multiplication: Add the exponents while maintaining the base's consistency.

When bases are raised by a power of two or more, multiply the exponents while maintaining the original base.

Division Rule: When dividing like bases, take the exponent of the denominator and divide it by the exponent of the numerator, keeping the exponential base constant.

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Answer:

most appropriate is y=3x - 13 but it is not the correct one.comparing y=3x-13 with y=mx+c the we get,m(slope)=3 whereas comparing y=X+4 with y=mx +c,we get m(slope)=1.But the slopes of parallel lines are always equal.

The correct equation for the line is y=X -1.

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The equation formed by the sentence is 9b - 7 = 8.

What is equation ?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used.

Let the variable be b

By the given sentence we get the equation

9b - 7 = 8

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An Experimental study is used. As subjects were randomly assigned to two groups, and one group was given an herb and the other group a placebo. after months, the numbers of respiratory tract infections each group had were compared.

Experimental investigations or study involve introducing an intervention and observing its results. Typically, volunteers in experimental research are grouped randomly, or by chance.

During a randomized controlled trial (RCT), participants are divided into two or more groups at random. While the control group is given nothing or a placebo, the intervention group is given the new drug, for example. The outcome of each group is then investigated by the researchers. The intervention can thus be blamed for any variations in the results.

Whereas, Observational study is the Studies in which researchers look at how a risk factor, diagnostic test, treatment, or other intervention affects a population without attempting to alter who is or is not exposed to it.

Hence, it is experimental study.

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The equation of the line that passes through the point (5, 3) and has a slope of - 6/5 is y = -6/5x - 3.

What is Slope?

A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).

What is Equation of line?

The equation for a straight line is y=mx+c where c is the height at which the line intersects the y-axis, often known as the y-intercept, and m is the gradient.

Given that ;

point passes through is (5,3)

and has slope of (-6/5)

We have equation of line;

y = mx+c

3 = -6/5(-5)+b

3 = 6 + b

Eliminate 6 by using the equality's subtraction property, then isolate b. (subtract 6 from 6 to cancel it out and to 3).

b = -3

So, the equation of the line that passes through the point (5, 3) and has a slope of - 6/5 is y = -6/5x - 3.

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The evaluation of the arithmetic series  gives 4545

An arithmetic progression ( AP ) is a sequence of numbers such that the difference between the consecutive terms is constant.

From the given information, we can get the first term (a) and  last term (l) of the sequence by substituting n = 1  and n = 45 respectively into the given expression, (4n + 9). That is:

a = 4(1) + 9 = 13

l = 4(45) + 9 = 189

Sum of all terms in a finite AP with the first term (a) and last term (l) is given by:

S = n/2(a + l)

S = 45/2 (13+189) = 4545

Thus, the arithmetic series evaluates to

[tex]\sum_{n}^{45}(4n + 9) = 4545[/tex]

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Answer:

54

Step-by-step explanation:

[tex]f(x)=x^2+10x+29 \\ \\ f(x)=(x^2+10x+25)+29+25 \\ \\ f(x)=(x+5)^2+54 \\ \\ \therefore (x+5)^2 \geq 0 \implies (x+5)^2+54=f(x) \geq 54[/tex]

The histogram for the stickers from the small package is distributed as follows:

Normally.

To obtain the distribution of the histogram, we must correctly identify the mean and the median of the distribution.

Hence the distribution is defined as follows:

The ordered distribution is given as follows:

13, 15, 18, 19, 22, 24.

Hence the median is of:

(18 + 19)/2 = 18.5.

The mean is of:

(13 + 15 + 18 + 19 + 22 + 24)/6 = 18.5.

They are equal, hence the histogram is normal = symmetric;

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This is $20,330.08 more than the total cost of the bank loan.

Payment is the transfer of money from one party to another in exchange for goods, services, or to fulfill a legal obligation. Payment is an important part of any transaction, as it is the final step that completes the exchange of goods or services.

Therefore, the lowest monthly payment would be the credit card payment of $511.11. Paying with a credit card at 15% compounded monthly would be the least expensive option for Genesis. With this option,  would pay a total of $36,330.08 over the 7 years, including the interest. This is $20,330.08 more than the total cost of the bank loan.

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The value of sum of squared deviations is 12.

The given population is 1,1,1,5

First find the mean:

Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.

Mean = (Sum of all the observations/Total number of observations)

Mean=[tex]\frac{1+1+15}{4}=\frac{8}{4}=2[/tex]

The Mean is 2.

The symbol of mean is usually given by the symbol [tex]\bar x[/tex]. The bar above the letter x, represents the mean of x number of values.

[tex]\bar X[/tex] = (Sum of values ÷ Number of values)

Subtract the mean from each observation and square the resulting difference. Then add the differences to get SS:

SS=[tex](1-2)^{2}+ (1-2)^{2}+ (1-2)^{2}+ (5-2)^{2}[/tex]

[tex]=1+1+1+(3)^{2} \\=3+9\\=12[/tex]

Therefore, the value of SS is 12.

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263,187.70 rad / hour is the angular velocity of the nail in radians per hour.

The equation relating angular velocity and linear velocity is:

w = v / r

where,

w = angular velocity, v = linear velocity, and r = radius

Since r is in inches, convert v to inches:

v = (54 miles per hour) * (63360 inches / mile)

v = 3,421,440 inches / hour

Solving for w:

w = (3,421,440 inches / hour) / 13 inches

w = 263,187.70 rad / hour

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The system of equations that can be used to find the price in dollars of each pencil, x, and each folder, y that Sally and Henry bought is D.

6x + 3y = 3.90

2x + 5y = 3.30.

A system of equations is also known as a simultaneous equation.

Simultaneous equations are equations solved concurrently.

                            Sally     Henry

Units of pencils     6            3

Units of folders     3            2

Total costs         $3.90    $3.30

Let pencils = x and folders = y

Sally's total cost = 6x + 3y = $3.90

Henry's total cost = 3 x + 2y = $3.30

In this situation, to find the price of each pencil and each folder, the system of equations that can be used is from Option D.

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Answer:

How many couples bought tickets?

50

Step-by-step explanation:

s + 2c  = 196              Eq. 1

6s + 10c = 1076          Eq, 2

s = single tickets

c = couple tickets

From Eq. 1:

s = 196 - 2c                 Eq. 3

Replacing Eq. 3 in Eq. 2:

6(196-2c) + 10c = 1076

(6*196 + 6*-2c) + 10c = 1076

(1176 - 12c) + 10c = 1076

1176 - 2c = 1076

1176 - 1076 = 2c

100 = 2c

c = 100/2

c = 50

From Eq. 3:

s = 196 - 2c

s = 196 - 2*50

s = 196 - 100

s = 96

Check:

From Eq. 2:

6s + 10c = 1076

6*96 + 10*50 = 1076

576 + 500 = 1076

On solving the provided question, we can say that  the given function, f(6)=26.

 where a, b, and c are numbers and an is not equal to zero, is  quadratic function. A parabola is the shape of a quadratic function's graph. Although the "width" or "steepness" of a parabola can vary as well as its direction of opening, they all share the same fundamental "U" shape.

f(n^2) = f(n) + 6

On putting n=2,

we get,

f(4) = f(2^2)  = f(2) + 6 = 8 + 6 = 14

On putting n=4, we get

f(16) = f(4^2) = f(4) + 6 = 14 + 6 = 20

On putting n=16, we get

f(256) = f(16^2) = f(16) + 6 = 20 + 6 = 26

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The original value for the first angle so that the angle measures form a triangle is 39.5°

For any triangle to be formed, its three interior angles must sum up to 180°. Thus the sum of the interior angles of a triangle is 180°

Considering, the angles: 115.1°, 47.5° and 93°, their sum which is 255.6° is not equal to 180° so they cannot form a triangle.

but a new value represented by x for the first angle 115.1° can be derived as follows;

x + 47.5° + 93° = 180°

x + 140.5 = 180° {subtract 140.5° from both sides}

x = 180° - 140.5°

x = 39.5°

Therefore, the new value for the first angle 115.1° that will make the angle measures form a triangle is 39.5°

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Therefore , the solution to the given problem of unitary method comes out to be Henry uses the scooter for 143 minutes after that.

In order to solve an issue, one can use the unit technique, which involves first multiplying the worth of one unit by the number of units needed. Simply said, the unit function is used to extract a single entity number from a given many. 40 needle would cost 400 rupees, or the price of one pen. There may be a standard method for checking this out. one country only. anything has a distinctive element. Mathematical analysis, algebra, matrix logic, and its interpellation and inverse are all equivalent.

Here,

Start the scooter for $7.00

$0.07 for each minute

$17.01 in total.

1. Subtract the cost of starting the scooter from the total bill:

The price for Henry's entire ride is $10.01.

2. Subtract the price for each minute to get the price per minute:

=> 10.01/0.07 * 100/100

=> 1001/7

=> 143

Henry uses the scooter for 143 minutes after that.

Therefore , the solution to the given problem of unitary method comes out to be Henry uses the scooter for 143 minutes after that.

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Based on whether the function is increasing or decreasing, the slope values are calculated. Then, the required slope values of A, B, C, D, E, and F are 1/2, 0, 1, 3, -3, and -1.

We match the slopes with the points in the given graph. For this, we must know that,

We may determine the rate at which the function is increasing or decreasing by measuring the slope's magnitude. Here, in this graph, first, the slope is zero at B. Therefore, the value of the slope in B is zero (0).

We can determine from the graph that the slope is descending at points E and F. Additionally, the slope is ascending at points A, C, and D.

Therefore, slope D> slope C> slope A> slope B. So, the slope values for D, C, and A are 3, 1, and 1/2 respectively.

Also, slope F> slope E. So, the slope values for F and E are -1 and -3.

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The inequalities that represent the situation can be presented as follows;

x + y ≤ 13

16·x + 6·y ≥ 120

Please find attached the graph of the inequality created with MS Excel

An inequality is a non equal comparison between expressions, quantities, or numbers.

The specified information are;

The amount Gabriella makes lifeguarding = $16 per hour

The amount she makes walking dogs = $6 per hour

The maximum number of hours Gabriella can work in a week = 13 hours

The minimum amount Gabriella must earn in a week = $120

Let x represent the number of hours Gabriella spends lifeguarding, and let y represent the number of hours Gabriella spends walking dogs.

The system of inequalities that can be obtained based on the above details are;

The graph of the above inequalities can be obtained by making y the subject of the inequalities as follows;

y ≤ 13 - x

y ≥ (120 - 16·x)/6 = 20 - (8/3)·x

y ≥ 20 - (8/3)·x

The feasible region is in the triangle with vertices (13, 0), (7.5, 0), (4.2, 8.8)

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Answer:

The "solution" is the intersection point of the two lines when drawn on a graph plot.

Explanation:

If a graphical plot is made with sufficient resolution linear equations may be solved by observing the solution point(s) on the graph coordinates.

Answer:

A) 10

Step-by-step explanation:

3(8)(5) / 6(2) = 120/12 which equals 10

Answer: A = 10

Step-by-step explanation:

substitute the value of the variable into the equation and simplify

Hope this helps !

By comparing the population range to the mean of the sample ranges, the answer will be D) The population range equal the youngest official at the time of death and the mean of the sample ranges is equal to the oldest official at the time of death.

Creating a tonne of random numbers between 40 and 70 points so that we can see that the population range is equal to 70. That is presumably the oldest value that is still valid. The population range is the sum of the data generated at the highest level and the lowest level. The population range is now 30 points. by taking a handful of random samples.

We want a sample table containing random samples of the data so we don't have to worry about this. Going through the samples with the new table that will be generated here and want to find this range by taking the max of each sample. Subtracting the mean from each sample from the range samples from 1 to 10. The range for the initial data was 30 points because the entire range was 40 to 70 points; nevertheless, we can observe that this range varies from 64 to 70 points.

We made the table because we wanted the mean of the average of our separate ranges to be 21.7. The mean value of the ranges in 100 samples will be discovered if the sample size is increased. A sample's range is not representative of the population. We can infer that we do it since the samples' range and average range are greatly dissimilar.

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Answer: The monthly payment on a bank loan would be $480, which is lower than the monthly credit card payment.

To calculate the monthly payment on the bank loan, we can use the formula:

monthly payment = P * (r / (1 - (1 + r)^(-n)))

where P is the total loan amount, r is the annual interest rate as a decimal, and n is the number of months of the loan.

For a loan of $16,000 at 8% interest for 3 years (36 months)

r = 0.08/12 = 0.0067

n = 36

P = 16000

So, the monthly payment = 16000 * (0.0067 / (1 - (1 + 0.0067)^(-36))) = 480

To calculate the monthly credit card payment, we can use the formula:

M = P * r * (1 + r)^n / [(1 + r)^n - 1]

where P is the total loan amount, r is the monthly interest rate, and n is the number of months of the loan.

For a credit card with an annual rate of 15% for 7 years (84 months)

r = 0.15/12 = 0.0125

n = 84

P = 16000

So, the monthly payment = 16000 * 0.0125 * (1 + 0.0125)^84 / [(1 + 0.0125)^84 - 1] = 511.11

As we can see the monthly payment on the bank loan is lower than the monthly credit card payment. So, the correct answer is "The monthly payment on a bank loan would be $480, which is lower than the monthly credit card payment."

Answer: 0.25 30% 1/3  

Step-by-step explanation:

1/3 is the largest because when made in a decimal it would be 3.3 reapeting, 30 % is 0.3 and 0.25 . So the order will be 0.25 30% and 1/3.

Answer:

Step-by-step explanation:

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Suzanne pays $21.03 in sales tax for the computer upgrades.

Tax in math is a type of mathematical problem that involves the distribution of a certain amount of money among several parties. The problem is solved by calculating the amount of money each party needs to pay in order to make the distribution fair and equitable. This type of math problem is often used to determine the amount of taxes that need to be paid by individuals or businesses. Tax problems can also be used to analyze the effects of different tax policies on the economy.

This amount is rounded to the nearest cent and is calculated by multiplying the pre-tax cost of the upgrades ($311.60) by the sales tax rate (6.75%). Thus, the equation would be: $311.60 x 6.75% = $21.03.

Suzanne must pay an additional $21.03 for the sales tax on her purchase, making the total cost of the upgrades $331.60.

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The answers to each part of the labelled graph is given below.

A function describes a relationship between a dependent and independent variable. Example -

y = f(x) = 5x + 9

Given are the distance - time (x{t}) and the velocity - time, (v{t}) graphs as shown in the image.

We can conclude for each part of the graph as -

The object is moving in the forward direction at a constant velocity.

The object is not moving.

The object is slowing down in the backward direction.

The object is changing directions.

The object is speeding up in the forward direction.

Therefore, the answers to each part of the labelled graph is given above.

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The amount in sale tax, Suzanne paid for the computer upgrades is 21.03 dollars.

Suzanne buys upgrades for her computer . The upgrades cost $311.60 before taxes. The sales tax rate is 6.75%.

Therefore, the amount of sales tax Suzanne paid for the computer upgrades can be calculated as follows;

A sales tax is a tax paid to a governing body for the sales of certain goods and services.

amount of the sale tax = 6.75% of 311.60

amount of the sale tax = 6.75 / 100 × 311.60

amount of the sale tax = 2103.3 / 100

Therefore,

amount of the sale tax = 21.033

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Yes, for every 6 duck decoys big lake bob carves he must give up 20 fishing lures.

Production possibility schedule:-

Fish lures:

Fish lures in one week = 100

lures in a day = 20

So, 100-20 = 80

80 - 20 = 60

60 - 20 = 40

40 - 20 = 20

20 - 20 = 0

Duck decoys:

Duck in one day = 0

So, 0 + 6 = 6

6 + 6 = 12

12 + 6 = 18

18 + 6 = 24

24 + 6 = 30

number of duck decoy in a week = 30

Hence, For every 6 duck decoys Bob carves 20 lures.

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