Lena bought 2 CDs that were each the same price. Including sales tax, she paid a total of $23.40. Of that total, $1.80 was tax. What was the price of each CD
before tax?

Correct option is D. randomly sampling 50 batteries throughout the day and testing to see if they work would provide the most valid results.

A sample is described as a smaller, more manageable representation of a larger group. a smaller population with characteristics of a larger one. A sample is used in statistical analysis when the population size is too large to include all participants or observations in the test.

The sample may be biased if it is taken from the first 25 batteries made each day (option A) or the last 25 batteries made each day (option B).

The first and final batteries made each day could not be an accurate representation of the total quality of the batteries produced that day if the battery manufacturing process is not consistent throughout the day.

Although battery quality can change during the day, sampling the first 50 batteries produced each day (option C) may also add bias into the sample.

The ideal course of action is to randomly select 50 batteries throughout the day (option D), since this helps to ensure that the sample is reflective of the general caliber of batteries manufactured that day.

Random sampling reduces the possibility of bias into the sample.

A more accurate image of the quality of the batteries manufactured can be obtained using this method, which is also more likely to capture any variations in battery quality over the day.

Therefore, option D would provide the most valid results.

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The vοlume οf the pyramid is 64 cubic centimeters (cm^3).

The vοlume οf a pyramid is given by the fοrmula V = (1/3) Bh, where B is the area οf the base and h is the height.

In this case, the base οf the pyramid is a square with side length s = 8 cm, sο its area is [tex]B = s^2 = 8^2 = 64 cm^2[/tex].

The height οf the pyramid is h = 3 cm.

Therefοre, the vοlume οf the pyramid is:

[tex]V = (1/3) Bh = (1/3) (64 cm^2) (3 cm) = 64 cm^3[/tex]

Hence, the vοlume οf the pyramid is 64 cubic centimetres (cm^3).

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The first term in this sequence is 7 and the common ratio is -3, so the formula for the 7th term, a7, can be written as a7 = 7(-3)6.7 multiplied by -18 is equal to -126, so the 7th term in this geometric sequence is -126.

Geometric sequences are used to represent growth and decay. The common ratio determines whether the sequence is increasing (if r > 1) or decreasing (if 0 < r < 1). When the common ratio is a whole number, such as 2 or 3, the terms in the sequence are whole numbers as well.

Geometric sequences are sequences where each term is found by multiplying the previous term by a fixed number, called the common ratio. In this case, the first term is 7 and the common ratio is -3, so each term is found by multiplying the previous term by -3. This means that the second term is 7(-3) = -21, the third term is -21(-3) = 63, the fourth term is -63(-3) = -189, and so on. By using the formula a7 = ar6 and substituting in the first term and common ratio, the 7th term can be calculated as -126.

The 7th term of a geometric sequence is calculated by using the formula a7 = ar6, where a is the first term and r is the common ratio. The first term in this sequence is 7 and the common ratio is -3, so the formula for the 7th term, a7, can be written as a7 = 7(-3)6. To calculate this, the exponent 6 must be multiplied by -3, giving -18. 7 multiplied by -18 is equal to -126, so the 7th term in this geometric sequence is -126.

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Answer:  28/9  (choice D)

Explanation:

You don't need a calculator for this.

Each fraction involves 9 in the denominator. The numerators are the only thing that change. Let x be the numerator.

x/9 = 3.1 can be estimated to x/9 = 3 and that solves to x = 27

The numerator is around 27.

Choices A,B,C are ruled out since the numerators are smaller than 28. The only thing left is choice D.

You can use a calculator or long division to confirm that 28/9 = 3.1111... where the '1's go on forever.

Answer:

12723.5(cm^2)

Step-by-step explanation:

the area of the circle

S=Tur^2

The sems-circle is s.=1/2 s =1/2Tur^2

Answer:25

Step-by-step explanation: easy

The simplified forms are;

1) 2x[tex]y^2[/tex]

2) [tex]x^2y^3[/tex]

3) [tex]2xy^3z^5[/tex]

4)[tex]5p^2q[/tex]

5) [tex]5a^3b^5c^3/2[/tex]

6)[tex]4x^4y^5/3z^3[/tex]

7)[tex]7a^3b^3/2[/tex]

8) [tex]x^2y^3z^6[/tex]

9)-4a

10) [tex]3xy^5z^13/2[/tex]

To simplify a surd, you need to find the largest perfect square factor that divides the number under the square root symbol.

We can see that the surds here can be reduced to the simplest forms when we apply the basics of the rules of exponent which have been used to show the simplified forms as shown here.

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3/8 or .375

You can find slope by doing rise/run (in fraction form) Rise is counting up or down spaces from one point until you hit the line of the next point. And then the run is counting over to the next point on the line. the number of spaces you counted up or down is the numerator and the run is the denominator.

Therefore , the solution of the given problem of area comes out to be

option B 864 sq. centimetres is the correct response.

The amount of area it takes to cover the outside is a good indicator of its overall size. When calculating a trapezoidal shape surface, the immediate environs are taken into account. The surface area of something determines its overall measurements. The internal water capacity of a cuboid is the sum of the limits for each of its six rectangular edges. Utilize the following technique to determine the box's dimensions: The area is the same in 2lh, 2lw, but also 2hw (SA). The area is represented by the adaptable shape's face.

Here,

The following algorithm determines a cube's surface area:

=> SA = 6s²

where s represents the cube's edge lengths.

=> S =12 cm in this instance.

The result of substituting into the algorithm is:

=> SA = 6 (12)²

=> 6 (144 )²

=> 864 square centimetres.

The cube's surface size is 864 sq. cm as a result.

B) 864 sq. centimetres is the correct response.

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The roots of the function y = 2x^3+ 8x^2 - 32x - 128, considering it's graph, are given as follows:

The roots of a function can be obtained from the graph of the function, as they also represent the x-intercepts of the function.

The x-intercepts of a function are given by the values of x at which the graph of the function crosses the x-axis, which is the horizontal axis.

The multiplicities of each root are given as follows:

From the graph given by the image presented at the end of the answer, the roots of the function are given as follows:

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Answer:

Step-by-step explanation:

The cable company offers Erik 3 free months of cable if he signs a contract with them for $40 per month. This means that Erik will pay for (m - 3) months of cable service, since he will get 3 months for free. So the cost of the cable service for (m - 3) months is:

Cost = $40 per month x (m - 3) months

Cost = $40m - $120

We know that Erik spent $680 for the cable television service. So we can set up an equation to relate the cost to the number of months:

$40m - $120 = $680

To solve for m, we can isolate the variable on one side of the equation:

$40m = $800

m = 20

Therefore, Erik will have cable television service for 20 months with this deal.

Answer: I believe the answer would be 53.85%

Step-by-step explanation:

6+8=14

14+7+5=26

14/26=.53846

Move decimal and round up.

The area of the circle is 78.5m² And when the radius is doubled, the area will be 314m².

The ratio of the larger circle to the smaller circle is 4 : 1

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object. The area is measured in squared units.

The area of a circle is expressed as :

A = πr²

A = 3.14 × 5²

A = 3.14 × 25

A = 78.5m²

When the radius is doubled, i.e

r = 5×2 = 10m

A = πr²

A = 3.14 × 100

A = 314m²

Therefore the area of the new circle is 314m²

The ratio of the area of the larger circle to the area of the smaller circle is ;

314/78.5 = 4/1 = 4 : 1

therefore the ratio of the larger circle to the smaller circle is 4 : 1

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Answer:

6

Step-by-step explanation:

radius is 1/2 the diamiter

Answer:

Step-by-step explanation:

Answer: 6 inches.

Explanation:

Since the radius is 3 inches, the diameter will be twice the size of the radius. The radius is half the width of a circular object. The diameter is the full width. Therefore Omar's lollipop has a diameter of 6 inches.

Therefore, the z-score of a data value x = 21 is 0.

Answer: 0.

Data are pieces of information that have undergone modifications to make them transferable or computer-processable. For usage with modern computers and communication networks, data is information that has been converted into binary digital form. The topic of the data is admissible in both its singular and plural variants.

To find the z-score of a data value x, we use the formula:

z = (x - μ) / σ

where:

x is the data value

μ is the mean

σ is the standard deviation

In this case, we are given the mean μ = 21 and the standard deviation σ = 1.2. The data value x is also equal to 21.

Substituting the values into the formula, we get:

z = (21 - 21) / 1.2 = 0 / 1.2 = 0

Therefore, the z-score of a data value x = 21 is 0.

Answer: 0.

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the answer is 42 will be 42 because i answer that before

As a result, the variable x is 9 which is the correct answer.

By combining two expressions, the equation generates a mathematical expression, similar to an expression. A typical equation would have been 3x - 5 = 16. The solution to this equation reveals that the value assigned to the variable x is 7.

We'll refer to the number we're looking for as "x" for the time being.

The problem states that the result of "x" and -6.5 is -58.5:

-6.5x = -58.5

We can divide all of the equation's components by -6.5 to find the answer to "x":

x = -58.5 ÷ -6.5

x = 9

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The given piecewise function is not continuous.

Continuous function is a function such that a continuous variation of the argument induces a continuous variation of the value of the function.

Given is the piecewise function as -

f(x) = {(x² - 2x - 8)/(x + 2)}              x ≠ -2

f(x) = {k}                        x = - 2

At {x} = - 2, the function is not defined and we get -

k = {(-2)² - 2(-2) - 8)/(- 2 + 2)} = {(-2)² - 2(-2) - 8)/0} = ∞

So, the function is not continuous.

Therefore, the given piecewise function is not continuous.

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Answer:

Rounding 395,621 to the nearest ten thousand is 400,000.

Step-by-step explanation:

Answer:

the nearest 10 thousand is 400,000.

Step-by-step explanation:

hope this helps!

The point after 30, 000 km will they first have to change the oil, rotate the tires and replace the wiper blades all at once.

Arithmetic Progression (AP) is a numerical series in which the difference between any two consecutive numbers is a constant value. Arithmetic Sequence is another name for it.

The First term is an "oil change" with a step d = 3000 km;

and, the second term is tire rotation = 10, 000 Km

and, the third term is replacement of wiper blades = 15, 000 Km

Now, we know from the formula of Arithmetic Progression is

= + d(n-1)

So, 15,000 = 10,000 + 10,000 (n-1)

15, 000 = 10,000 + 10, 000n- 10,000

150000 = 10000n

n = 1.5

This means that at the point 15 000 km and all three progressions will not intersect.

Now, We take the second term of the progression as  = 30,000 km

So, 30,000 = 10,000 + 10,000 (n-1)

20,000 = 10,000n - 10,000

30, 000 = 10,000n

n= 3

Similarly, check this intersection point for the first progression with a step of d = 3 000 km we get n =9.

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The complete question is :-

Peter's parents follow a regular schedule for taking care of the car. They change the plugs every 30 000km, rotate the tyres every 10 000km and replace the brake pads blades every 15 000km. After how many kilometers will they have to change the plugs, rotate the tyres and replace the brake pads all at once for the first time?

The length of the line of sight from the ship to Nicole is approximately 2046.1 feet, rounded to the nearest tenth.

Trigonometry is a branch of mathematics that studies the relationships between triangle sides and angles.

The term trigonometry is derived from the Latin derivative of the Greek words for triangle (trigonon) and measurement (measur) (metron).

Trigonometry is a branch of mathematics concerned with angle relationships and length ratios.

Let's assume that the distance between Nicole's window and Nick's position is "x" feet. Then, we can use trigonometry to set up the following equation:

tan(5) = (175 + 10) / x

Simplifying and solving for "x", we get:

x = (185) / tan(5)

x ≈ 2046.1 feet

Therefore, the length of the line of sight from the ship to Nicole is approximately 2046.1 feet, rounded to the nearest tenth.

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Answer:

h'(1) = 19

Step-by-step explanation:

if h(x) = f(x) + g(x), and f(x) = x³ and g(x) = 4x⁴,

then h(x) = (x³) + (4x⁴)

h(x) = x³ + 4x⁴

h'(x) is the derivative of h(x), which = 3x² + 16x³. Thus, h'(1) = 3(1)² + 16(1)³ = 19

Answer:

The team was penalized 10 yards on each play.

Answer:

If Input is 150, then Output is 25.

Step-by-step explanation:

The rule is to divide 6.

IF: You input 72 & the output is 12:

72/6 = 12

IF: You input 54 & the output is 9:

54/6 = 9

IF: You input 120 & the output is 20:

120/6 = 20

etc.

Therefore, you are dividing 6 each time. The given input is 150. Divide 150 with 6 to find your output:

150/6 = 25

25 would be your output.

~

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If a water sample shows 0.37 grams of some trace element for every cubic centimeter of water.  Terrence has collected 841.51 grams of the trace element.

First, we need to find the volume of the cylinder container:

Volume of cylinder = π(radius)² height)

= π(7.9cm)²(11.6cm)

= 2,274.37 cm³

Amount of trace element = concentration x volume

= 0.37 grams/cm³ x  2,274.37 cm²

= 841. 51 grams

Therefore, Terrence has collected  841.51 grams of the trace element.

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The requried it cannot conclude whether the variable is normally distributed or skewed based on the given data. None of the options are correct.

The statistic is the study of mathematics that deals with relations between comprehensive data.

It is not possible to determine if the variable "footprint" is normally distributed or skewed based on the given data.

The data represents the measurements of shoe prints for 5 males, but it is not enough to determine the distribution of the variable without additional information such as a larger sample size, the mean and standard deviation of the variable, or a histogram or frequency plot of the data.

Therefore, we cannot conclude whether the variable is normally distributed or skewed based on the given data.

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The factoring of the polynomial expression is presented as follows;

Part A; The greatest common factor is; 5

Part B; 15·x² + 25·x - 10 = 5·(3·x - 1)·(x + 2)

Part C; 5 × (3·x - 1) × (x + 2) = 15·x² + 25·x - 10

A polynomial is an expression containing algebraic terms that consists of variables and coefficients, joined together by operators.

The expression is 15·x² + 25·x - 10

Part A; The greatest common factor of the polynomial is the value that divides each of the terms of the polynomial, therefore;

The greatest common factor of 15·x² + 25·x - 10 is obtained as follows;

The largest number that divides each term of he polynomial expression is 5

15·x² + 25·x - 10 = 5·(3·x² + 5·x - 2)

Part B; The expression, 15·x² + 25·x - 10, can be factored as follows;

15·x² + 25·x - 10 = 5·(3·x² + 5·x - 2)

3·x² + 5·x - 2 = 3·x² + 6·x - x - 2

3·x² + 6·x - x - 2 = 3·x·(x + 2) - 1·(x + 2) = (3·x - 1)·(x + 2)

3·x² + 5·x - 2  = (3·x - 1)·(x + 2)

15·x² + 25·x - 10 = 5·(3·x² + 5·x - 2) = 5·(3·x - 1)·(x + 2)

Factoring the expression completely, we get;

15·x² + 25·x - 10 = 5·(3·x - 1)·(x + 2)

Part C: The factoring of the expression, 15·x² + 25·x - 10, can be checked as follows;

The factored expression is; 5·(3·x - 1)·(x + 2)

5 × (3·x - 1) × (x + 2) = 5 × (3·x² + 6·x - x - 2) = 5 × (3·x² + 5·x - 2)

5 × (3·x² + 5·x - 2) = 15·x² + 25·x - 10, which is the original expression

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Assuming the trend continues, the next 12 animals will include 4 sheep.

Number is a mathematical concept that represents a quantity or amount. It is usually used to identify a specific value or set of values that can be used for calculation and measurement. Numbers are used in many different fields, including mathematics, science, engineering, and economics. They help us to keep track of quantity and count objects, measure distances and time, and even help to solve problems. Numbers are an essential part of our everyday lives and are essential for understanding the world around us.

This is calculated by taking 2 sheep from the initial group of 8 animals and then multiplying that number by the additional 12 animals for a total of 4 sheep.

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(I) Break even sales: S = 40,000

(ii) Sales needed to earn a profit  Rs 6000 per period: S = Rs. 45,000.

The formula for the Break even sales is:

(S‐v) /S= F + P  

s x P/V Ratio = Contribution

First calculate P/V Ratio:

P/V Ratio = Contribution/sales x 100

P/V Ratio = (40‐24)/40 x 100

P/V Ratio= 16/40 x 100

P/V Ratio = 40%

(I) Break even sales  

S x P/V Ratio = Fixed Cost

For break even sales, deposition equals fixed cost.

Thus,

Put the values:

S x 40/100 = 16,000

S = 16,000 x 100 / 40

S = 40,000

S = 1000 units

(II) Sales to gain a profit of Rs. 6,000

S x P/V Ratio = F + P

Put the values:

S x 40/100 = 16000 + 2000

S = 18,000 x 100/40  

S = Rs. 45,000

S =  1125 units

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