If an article costs a store $7.45 and if it sells the article for $9.95, what percentage (to the nearest tenth) markup is it using?

The percentile scores for a distribution with a mean of 100 and a standard deviation of 15, the z-scores for 112 and 82 are 0.8 and -1.2, respectively.

Calculating Percentile Scores

To determine percentile scores for the values given in the original student question, we need to calculate the z-scores for 112 and 82 from a distribution with a mean of 100 and a standard deviation of 15.

To find the z-score, use the formula:

Z = (X - mu) / sigma

Where X is the raw score, \\mu is the mean, and \\sigma is the standard deviation.
For 112:

Z = (112 - 100) / 15

Z = 12 / 15

Z = 0.8
For 82:

Z = (82 - 100) / 15

Z = -18 / 15

Z = -1.2

Once the z-scores are calculated, we can look up the corresponding percentiles in a standard normal distribution table.

A z-score of 0.8 corresponds to approximately the 78.81st percentile, meaning about 78.81% of the scores are below 112.

A z-score of -1.2 corresponds to approximately the 11.54th percentile, meaning about 11.54% of the scores are below 82.

The solution is, By $.87 dollars has the price of gas changed from January to May

Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.

here, we have,

given that,

Starting price is 2.65, increased by .56

2.65+.56=3.21

Price is 3.21, decreased by .23

3.21-.23=2.98

Price is 2.98, increased by 1.02

2.98+1.02= 4

Price is 4, decreased by .48

4-.48=3.52

Now find the difference from the starting price (January) from the end price (May)

3.52-2.65=.87

The difference from gas prices is $.87.

Hence, The solution is, By $.87 dollars has the price of gas changed from January to May.

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The correct answer is C.

Jonathan’s answer is reasonable because 2 times 8 is 16, and 16 is close to 15.77.

Hope this helps.

To solve for the problem, the formula is:

n = [z*s/E]^2

where:

z is the z value for the confidence interval

s is the standard deviation

E is the number of units

So plugging that in our equation, will give us:

= [1.96*9.38/3]^2

= (18.3848/3)^2

= 6.1284^2

= 37.5 or 38

A G I = Adjustable Gross income,

1 exception = $ 8200,

A G I= Total Income (Gross Income + Amount earned through other means) - (Adjustments +Deduction)

= ($ 23670+$8200)-($ 0 + $0)

 = $ 31,870

1 exception = $ 8200, there may be many reasons for exception.

So, Taxable Income = Gross Income - 1 Exception

                                  = $ 23670 - $ 8200

                                  =  $ 15,470

The value of the expression -4²+(5-2)(-6) is -34 when following the standard rules of arithmetic.

The value of the expression −4²+(5−2)(−6) can be determined by first calculating the power and then performing the operations inside the parentheses, followed by the multiplication and addition/subtraction.

The power of −4² is 16 because the negative sign is not inside the parentheses, so it is not squared, and 16 will be considered as a negative number here (-16).

Next, we calculate the value within the parentheses (5−2), which gives us 3.

Then we multiply 3 by −6, which equates to −18. Finally, we add the two results: −16 + (−18) = −16 −18 = −(16 + 18) = −(34), resulting in the value −34.

Answer:

Hence, AB=12.

Step-by-step explanation:

We are given that the perpendicular bisector of side AB of ∆ABC intersects side BC at point D.

this means that side AE=BE.

Also we could clear;ly observe that

ΔBED≅ΔAED

( since AE=BE, side ED common, ∠BED=∠AED

so by SAS congruency the two triangles are congruent)

Now we are given that:

the perimeter of ∆ABC is 12 cm larger than the perimeter of ∆ACD.

i.e. AB+AC+BC=AC+AD+CD+12

AB+BC=AD+CD+12

as AD=BD

this means that AD+CD=BD+CD=BC

AB+BC=BC+12

AB=12

Hence AB=12

Answer:

The required length of [tex]AB[/tex] is [tex]12\rm\;{cm}[/tex].

Step-by-step explanation:

Given: The perpendicular bisector of side [tex]AB[/tex] of [tex]\bigtriangleup{ABC}[/tex] intersects side [tex]BC[/tex] at point [tex]D[/tex] and the perimeter of  [tex]\bigtriangleup{ACD}[/tex].

From the figure,

[tex]AE=BE[/tex]         .......(1)              (as [tex]DE[/tex] is perpendicular bisector of side [tex]AB[/tex])

Now, In [tex]\bigtriangleup{BED}[/tex] and [tex]\bigtriangleup{AED}[/tex]

     [tex]AE=BE[/tex]                                     ( from equation 1 )

[tex]\angle {BED} =\angle {AED}[/tex]                               ( Both [tex]90^\circ[/tex] )

    [tex]ED=ED[/tex]                                     ( Common side)

[tex]\bigtriangleup{BED}\cong\bigtriangleup{AED}[/tex]                              ( by SAS congruence rule)

      [tex]BD=AD[/tex]    .........(2)                   (by CPCT)

As per question,

The perimeter of ∆ABC is with 12 cm larger than the perimeter of ∆ACD.

[tex]AB+BC+AC=AC+CD+AD+12[/tex]

         [tex]AB+BC=AD+CD+12\\AD+CD=BD+CD\\AB+BC=BC+12\\[/tex]

                   [tex]AB=12\rm\;{cm}[/tex]

Hence, the length of [tex]AB[/tex] is [tex]12\rm\;{cm}[/tex].

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(a) The function describes a parabola that opens downward. The value of A(x) is zero when x=0 and when x=100. The vertex (maximum) is halfway between those zeros, at x=50. The dimensions are 50 and 100-50 = 50. The maximum area pen will be 50 ft square.

(b) A(50) = (50 ft)² = 2500 ft² . . . the maximum area

(c) A(x) will be negative if x < 0 or x > 100, so the domain is 0 ≤ x ≤ 100.

The value of A(x) ranges from 0 to its maximum, 2500. Hence the range is 0 ≤ A(x) ≤ 2500.

For a rectangular fenced area, the dimensions that maximize the area are 50 feet by 50 feet, given a total of 200 feet of fence. The maximum possible area is 2500 square feet. The domain for this function is [0, 100] and the range is [0, 2500].

This problem deals with maximizing an area given a certain length of fencing. It is a part of optimization problems often encountered in calculus. Firstly, we understand that a rectangle will give maximum area for a fixed perimeter. Considering a rectangle, the dimensions would be x and 100-x, where x is one of the sides of the rectangle.

(a) To find the dimension that maximizes the area, we first need to find the derivative A'(x) of A(x), which equals to -2x + 100. Setting A'(x) to zero gives us x = 50. That means the dimensions that will give us maximum area are 50 feet by 50 feet.

(b) Substituting x = 50 back into the original function, we find that the maximum area is A(50)=50(100-50)=50*50=2500 square feet.

(c) For the domain of A in this application, it would be all possible values of x. So, x could be any number from 0 to 100 (both inclusive). The range of A would be from 0 to the maximum value, 2500 square feet.

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The zeros of the function y = -3(x - 2)² + 6 are x = 2 + √2 and x = 2 - √2, which represent the hot dog prices at which the hot dog stand makes $0.00 profit.

The zeros of a function are the values of x that make the y-coordinate equal to zero. In this case, the function y = -3(x - 2)² + 6 represents the daily profit, and we need to find the x-values that result in a profit of $0.00. Setting the profit, y, to zero and solving for x, we get:

0 = -3(x - 2)² + 6

Adding 3(x - 2)² to both sides and simplifying the equation gives:

3(x - 2)² = 6

Dividing both sides by 3, we have:

(x - 2)² = 2

Take the square root of both sides, remembering to consider both the positive and negative square roots:

x - 2 = ±√2

Adding 2 to both sides gives us the final solutions:

x = 2 ± √2

So, the zeros of this function are x = 2 + √2 and x = 2 - √2. These are the hot dog prices at which the hot dog stand makes $0.00 profit.

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The answer provides an expression for the course average and a compound inequality to earn a B in a wellness course.

Expression representing the course average: 1/5(70 + 86 + 81 + 83 + x)

Compound inequality for earning a B: 80 ≤ 1/5(70 + 86 + 81 + 83 + x) < 90

The expression [tex]180+15x[/tex] consists of ONE CONSTANT [180] and another VARIABLE EXPRESSION [15x].

Since the coach purchased ONE GOAL, this corresponds to the CONSTANT, which is 180. 180 is the price of the goal.

Since coach purchased several soccer balls, but doesn't say how many, it is the variable part, 15x, where

ANSWER:

180 represents the price of the goal

15x represents the total price of the soccer balls

Answer:

180 represents the price of the goal

15x represents the total price of the soccer balls

Step-by-step explanation:

Answer:

19 members voted.

Step-by-step explanation:

Percentage problems can be solved by a rule of three.

25% of the 76 members of the club voted in the election. How many members voted?

So 76 is 100% = 1. How much is 0.25?

76 - 1

x - 0.25

[tex]x = 76*0.25[/tex]

[tex]x = 19[/tex]

19 members voted.

Final answer:

To find the derivative of f(x) = 3√x at a nonzero point, use the definition of the derivative with limits. The derivative at x=0 does not exist because the function has an infinite slope at this point, demonstrated by the absence of a limit, signifying a vertical tangent line at (0,0).

Explanation:

To find f'(a) for f(x) = 3√x when a ≠ 0, we can use the given definition of the derivative:
f'(a) = limh→0 (f(a+h) – f(a)) / h.
To show that f'(0) does not exist and that f has a vertical tangent line at (0,0), we need to evaluate the limit as h tends to zero for the derivative definition applied at a = 0. Since the square root function is not differentiable at 0 (due to the function having an infinite slope at this point), the limit will not exist, indicating that the derivative at 0 does not exist, and the graph of f exhibits a vertical tangent at that point.

Answer:

$48

Step-by-step explanation:

List price = $60.00

Discount = 20% .

Hence the new price is (100-20)% = 80% of original price .

=> price = $ 60* 80/100

=> price = $ 48