The cost of manufacturing a certain type of headphone varies inversely as the number of headphones increases. If 8000 headphones can be manufactured for $8. 00 each, find the cost to manufacture 2000 headphones

Answer:

Step-by-step explanation:

You want the measures of the angles where lines cross if the sum of three of them is 280°.

Angle b and c form a linear pair, so ...

  b + c = 180°

Substituting that into the given equation, we have ...

  b + c + d = 280°

  180° + d = 280°

  d = 100°

Angles in this figure that do not share a side are vertical angles, hence congruent.

  b = d = 100°

  c = 180° -b = 180° -100° = 80° . . . . using the linear pair relation

  a = c = 80°

It sounds like Leo will be using a specific type of random number generator that produces only five possible outcomes: 1, 2, 3, 4, or 555. It seems that the generator produces a repeating pattern of four numbers (1, 2, 3, 4) followed by a fifth number (555).

If Leo uses this generator 400400400 times, then he will get 100100100 repetitions of the pattern. This means that he will get 100100100 x 4 = 400400400 numbers 1, 2, 3, or 4, and 100100100 occurrences of the number 555.

It is important to note that this type of random number generator is not truly random, as it is not generating numbers with equal probability. Instead, it is producing a predetermined sequence of numbers. This means that if Leo knows the pattern, he could predict the next number that will be generated with certainty.

In general, it is important to use truly random number generators for many applications, such as cryptography or scientific simulations, where the results need to be unpredictable and unbiased.

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The simplified expression of 100-3(4. 25)-13-4(2. 99) is 48.29.

What is PEMDAS?

PEMDAS stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). It is a mnemonic or acronym used to remember the order of operations when simplifying mathematical expressions.

To simplify the expression 100-3(4.25)-13-4(2.99), you can follow the order of operations (PEMDAS) which is:

Parentheses

Exponents

Multiplication and Division (from left to right)

Addition and Subtraction (from left to right)

Using this order, you can simplify the expression as follows:

100 - 3(4.25) - 13 - 4(2.99)

= 100 - 12.75 - 13 - 11.96 // multiply 3 and 4 with their respective numbers

= 62.29 - 13 - 11.96 // perform subtraction within parentheses

= 48.29 // perform final subtraction

Therefore, the simplified expression is 48.29.

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To find the production level that will minimize the average cost, we need to differentiate the cost function with respect to x and set it equal to zero. So:

C'(x) = 0.005x^2 + 242x + 6000
0 = 0.005x^2 + 242x + 6000
Using the quadratic formula, we get:
x = (-242 ± sqrt(242^2 - 4(0.005)(6000))) / (2(0.005))
x = (-242 ± sqrt(146416)) / 0.01
x = (-242 ± 382) / 0.01
x = -14,000 or 27,000

Since the production level cannot be negative, we can discard the negative solution and conclude that the production level that will minimize the average cost is 27,000 units.

To find the minimal average cost, we need to plug the production level back into the cost function and divide by the production level. So:

C(27,000) = 6000 + 242(27,000) + 0.005(27,000)^2
C(27,000) = 6,594,000
Average cost = C(27,000) / 27,000
Average cost = 6,594,000 / 27,000
Average cost ≈ 244.22

Therefore, the minimal average cost is approximately $244.22.
To answer your question, first, let's correct the cost function, which should be in the form of C(x) = Fixed cost + Variable cost. Assuming it is C(x) = 6000 + 242x + 0.005x^2.

A) To find the production level that will minimize the average cost, we need to first determine the average cost function, which is AC(x) = C(x)/x. So, AC(x) = (6000 + 242x + 0.005x^2)/x.

Now, find the first derivative of AC(x) concerning x, and set it equal to zero to find the minimum point:

d(AC(x))/dx = 0

The first derivative of AC(x) is:

d(AC(x))/dx = (242 + 0.010x - 6000/x^2)

Setting this to zero and solving for x will give us the production level that minimizes the average cost:

242 + 0.010x - 6000/x^2 = 0

Now, you can solve for x using numerical methods, such as Newton-Raphson or others. After solving for x, you will get the production level that minimizes the average cost.

B) To find the minimal average cost, plug the production level x you found in part A into the average cost function, AC(x):

Minimal Average Cost = AC(production level)

This will give you the minimal average cost for the given cost function.

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Answer:

Step-by-step explanation:

Congruent triangles are triangles that are the same shape and same size.

So if they look the same and have the same dimension like area and perimeter then they are congruent.

Solving the equation, Boris needs to read 34 novels in 17 months.

Given that Boris needs to read 2 novels each month.

To relate the number of novels Boris needs to read (n) to the number of months he has to read them (m), we can use the equation:
n = 2m

This equation states that the number of novels (n) is equal to two times the number of months (m) since Boris needs to read 2 novels each month.

Now, to find the number of novels Boris needs to read in 17 months, we can substitute m = 17 into the equation:
n = 2m
n = 2(17)
n = 34

Therefore, Boris needs to read 34 novels in 17 months to meet his goal of reading 2 novels each month.

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Emir earned approximately $207.05 doing odd jobs.

Let x be the amount that Emir earned doing odd jobs. We can use the formula for compound interest, A = P(1+r/n)^(nt), where A is the final amount, P is the principal amount, r is the interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

In this case, we have P = x, r = 0.1, n = 12 (since interest is compounded monthly), t = 9, and A = 400. Solving for x, we get:

x = A/(1+r/n)^(nt) = 400/(1+0.1/12)^(12*9) ≈ $207.05

Therefore, Emir earned approximately $207.05 doing odd jobs.

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a) The table is completed as follows:

b) The graph is given by the image presented at the end of the answer.

To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.

The function for this problem is given as follows:

y=  x + 2.

Hence the numeric values of the function are given as follows:

Then the graph is constructed connecting two of these points and tracing a line through them.

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The distance between points E and B is (2/3)*AB, or (2/3)*(7+x) units.

Since the dotted line is the perpendicular bisector of side AB, it means that it cuts the line AB into two equal halves. Thus, the distance between points E and the dotted line is equal to the distance between point A and the dotted line.

We know that the distance between points E and A is 7 units, and since the dotted line bisects AB, the distance between point A and the dotted line is equal to the distance between point B and the dotted line. Let's call this distance 'x'.

Therefore, we have two equal distances (7 units and 'x') that add up to the length of AB. This means that:

AB = 7 units + x

However, we also know that the dotted line is the perpendicular bisector of AB, meaning that it forms right angles with both A and B. This creates two right-angled triangles, AED and BED, where DE is the perpendicular line from point E to AB.

Using Pythagoras' theorem, we can find the length of DE in terms of 'x':

(DE)² + (AE)² = (AD)²

(DE)² + (7)² = (AB/2)²

(DE)² + 49 = (AB²)/4

(DE)² = (AB²)/4 - 49

(DE)² = (AB² - 196)/4

(DE)² = (x²)/4

DE = x/2

Therefore, the distance between points E and B is equal to the length of DE plus the distance between point B and the dotted line, which is also equal to 'x'. Therefore, the distance between points E and B is:

EB = (x/2) + x = 1.5x

We can substitute this into the equation we found earlier:

AB = 7 units + x

AB = 7 units + (2/3)*EB

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The range of values for x in the triangle is 0 < x < 8

From the question, we have the following parameters that can be used in our computation:

AC = 3x + 32

BC = 7x + 16

Also, we know that

ADC is greater than BDC

This means that

AC > BC

So, we have

3x + 32 > 7x + 16

Evaluate the like terms

-4x > -32

Divide both sides by -4

x < 8

Also, the smallest value of x is greater than 0

So, we have

0 < x < 8

Hence, the range of values for x is 0 < x < 8

The steps to calculate the range is gotten from the theorem that implies that

The greater the angle opposite the side length of a triangle, the greater the side length itself

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The missing lengths of triangles are 5in, 5mi, 13.9km,13.3mi respectively.

What is triangle?

A triangle is a closed, two-dimensional geometric figure with three straight sides and three angles.

What is Pythagorean theorem?

The Pythagorean Theorem is a fundamental theorem in Euclidean geometry that relates to the three sides of a right-angled triangle.

Using the Pythagorean theorem [tex](a^2 + b^2 = c^2)[/tex], we can solve for the missing side in each triangle.

Triangle 1:

[tex]a = 12 in\\\\c = 13 in\\\\a^2 + b^2 = c^2\\\\12^2 + b^2 = 13^2\\\\144 + b^2 = 169\\\\b^2 = 25\\\\b = \sqrt{(25)}\\\\b = 5 in[/tex]

Therefore, the length of the missing side in Triangle 1 is 5 in.

Triangle 2:

[tex]a = 4 mi\\\\b = 3 mi\\\\c = x\\\\a^2 + b^2 = c^2\\\\4^2 + 3^2 = x^2\\\\16 + 9 = x^2\\\\25 = x^2\\\\x = \sqrt{(25)}\\\\x = 5 mi[/tex]

Therefore, the length of the hypotenuse in Triangle 2 is 5 mi.

Triangle 3:

[tex]a = x\\\\b = 11.9 km\\\\c = 14.7 km\\\\a^2 + b^2 = c^2\\\\x^2 + 11.9^2 = 14.7^2\\\\x^2 = 14.7^2 - 11.9^2\\\\x^2 = 192.36\\\\x = \sqrt{(192.36)}\\\\x = 13.9 km[/tex]

Therefore, the length of the height in Triangle 3 is 13.9 km.

Triangle 4:

[tex]a = x\\\\b = 6.3 mi\\\\c = 15.4 mi\\\\a^2 + b^2 = c^2\\\\x^2 + 6.3^2 = 15.4^2\\\\x^2 = 15.4^2 - 6.3^2\\\\x^2 = 178.09\\\\x = \sqrt{(178.09)}\\\\x = 13.3 mi[/tex]

Therefore, the length of the height in Triangle 4 is 13.3 mi.

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The area of the shaded sector of the given circle would be = 42,593.5 in²

To calculate the area of the given sector the formula that should be used is given as follows;

The area of a sector =( ∅/2π) × πr²

where;

π = 3.14

r = 12 in

∅ = 60°

Area of the sector = (60/2×3.14)b × 3.14× 12×12

= 94.2× 452.16

= 42,593.5 in²

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The probability of having NO rain for an entire week (7 days) is 0.9998

From the question, we have the following parameters that can be used in our computation:

P(Rain) = 30%

Given that the number of days is

n = 7

The probability of having no rain for an entire week is calculated as

P = 1 - P(Rain)ⁿ

Where

n = 7

Substitute the known values in the above equation, so, we have the following representation

P = 1 - (30%)⁷

Evaluate

P = 0.9998

Hence, the probability is 0.9998

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the Chain Rule to find Oz/as and Oz/ot for the expression sin(e) cos(6), we first need to break it down into its component parts.

Let u = sin(e) and v = cos(6), so that our expression becomes u*v.

Now we can find the partial derivative of Oz/as by using the Chain Rule:

Oz/as = (dOz/du) * (du/as) + (dOz/dv) * (dv/as)

Since Oz = st*, we have dOz/du = st and dOz/dv = t*, so we can substitute those values in:

Oz/as = (st) * (dcos(e)/das) + (t*) * (-sin(6)/das)

To simplify this expression, we need to find the partial derivative of u and v with respect to as:

du/as = (dcos(e)/das)

dv/as = (-sin(6)/das)

Substituting those values back into our original expression for Oz/as, we get:

Oz/as = st * du/as + t* * dv/as

Oz/as = st * (dcos(e)/das) + t* * (-sin(6)/das)

Finally, we can simplify this expression by factoring out the common factor of das:

Oz/as = (st * dcos(e) - t* * sin(6)) / das

To find Oz/ot, we can follow the same steps but with respect to ot instead of as:

Oz/ot = (dOz/du) * (du/ot) + (dOz/dv) * (dv/ot)

Since Oz = st*, we have dOz/du = st and dOz/dv = t*, so we can substitute those values in:

Oz/ot = (st) * (-sin(e)/dot) + (t*) * (-6sin(6)/dot)

To simplify this expression, we need to find the partial derivative of u and v with respect to ot:

du/ot = (-sin(e)/dot)

dv/ot = (-6sin(6)/dot)

Substituting those values back into our original expression for Oz/ot, we get:

Oz/ot = st * du/ot + t* * dv/ot

Oz/ot = st * (-sin(e)/dot) + t* * (-6sin(6)/dot)

Finally, we can simplify this expression by factoring out the common factor of dot:

Oz/ot = (-sin(e)st - 6sin(6)t*) / dot
To find ∂z/∂s and ∂z/∂t using the Chain Rule, let's first define the given functions:

1. z = st (where s and t are variables)
2. s = sin(e) (where e is a variable)
3. t = cos(θ) (where θ is a variable)

Now, apply the Chain Rule to find ∂z/∂s and ∂z/∂t:

Chain Rule states: ∂z/∂x = (∂z/∂s) * (∂s/∂x) + (∂z/∂t) * (∂t/∂x)

1. Find ∂z/∂s:
Since z = st, ∂z/∂s = t

2. Find ∂z/∂t:
Since z = st, ∂z/∂t = s

Now we have ∂z/∂s and ∂z/∂t. You can use these expressions to find the desired derivatives by substituting the given functions for s and t.

∂z/∂s = t = cos(θ)
∂z/∂t = s = sin(e)

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The mean number of people in passenger cars on the highway is 1.7 (approximately 2).

The mean of a probability distribution function is also known as Expectation of the probability distribution function.

The mean number of people in passenger cars (or expectation of number of people in passenger cars ) on the highway can be denoted as E(x) where x is the number of people in passenger cars on the highway.

Thus E(x) can be calculated as,

E(x) = ∑ [tex]x_{i} p_{i}[/tex] ∀ i= 1,2,3,4,5

where, [tex]p_{i}[/tex] is the probability of number of people in passenger cars on the highway

⇒ E(x) = (1)(0.56) + (2)(0.28) + (3)(0.08) + (4)(0.06) + (5)(0.02)

⇒ E(x) = 1.7

Hence the mean number of people in passenger cars on the highway is 1.7, which is less than 2.

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Answer:

m<V=100.5°

u=84.86u

v=154.86u

Step-by-step explanation:

m<V= 180-46.9-32.6=100.5°

sin46.9°/115=sin32.6°/u

sin46.9°u=115sin32.6°

u=115sin32.6°/sin46.9°

u=84.86u

sin46.9°/115=sin100.5°/v

sin46.9°v=115sin100.5°

v=115sin100/5°/sin46.9°

v=154.86

The 99% confidence interval for the population mean is between 39.18 and 62.82, assuming that the population is normally distributed.

To construct a confidence interval for the population mean, we need to make certain assumptions about the distribution of the sample data and the population. In this case, we assume that the population is normally distributed, the sample size is small (less than 30), and the standard deviation of the population is unknown but can be estimated from the sample data.

Using these assumptions, we can calculate the confidence interval as:

CI = X ± tα/2 * (s/√n)

Where X is the sample mean, tα/2 is the critical value of the t-distribution with degrees of freedom (n-1) and a confidence level of 99%, s is the sample standard deviation, and n is the sample size.

Plugging in the values from the provided data, we get:

CI = 51 ± 2.898 * (17/√18)

CI = (39.18, 62.82)

Therefore, with 99% confidence, we can estimate that the population mean is between 39.18 and 62.82 based on the provided data.

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The area of the ring-shaped region with radii of 9m and 13m is approximately 276.32 square meters.

What is Area?

The area is the region defined by an object's shape. The area of a shape is the space covered by a figure or any two-dimensional geometric shape in a plane.

What is Perimeter?

The perimeter of a shape is defined as the total distance surrounding the shape. It is the length of any two-dimensional geometric shape's outline or boundary.

According to the given information:

The given shape is a two concentric circles with radii of 9m and 13m, we can calculate the area of this region using the formula for the area of a circle:

Area of shaded region = Area of outer circle - Area of inner circle

The area of a circle is given by the formula A = πr^2, where r is the radius of the circle.

Area of inner circle = π(9)^2 = 81π

Area of outer circle = π(13)^2 = 169π

Area of shaded region = 169π - 81π = 88π

Using the value of π = 3.14, we get:

Area of shaded region = 88π = 88(3.14) = 276.32 square meters (rounded to two decimal places)

Therefore, the area of the ring shaped region with radii of 9m and 13m is approximately 276.32 square meters.

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The volume of this cone is approximately 127.2 cubic inches

Hi! To calculate the volume of the Styrofoam cone used by Dylan to make a floral arrangement, we can use the formula for the volume of a cone: V = (1/3)πr²h. The cone had a radius of 4.5 inches and a height of 6 inches.

Substituting these values into the formula, we have:
V = (1/3)π(4.5)²(6)

V ≈ 127.2 cubic inches (rounded to the nearest tenth).

So, the volume of this cone is approximately 127.2 cubic inches.

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The answer is option C) A total of 25.2 percent passed both tests. The events are not independent.

To solve this problem, we can use a Venn diagram. Let P(A) be the probability of passing the first test, P(B) be the probability of passing the second test, and P(A and B) be the probability of passing both tests.

From the problem, we know:

P(A) = 0.42

P(B) = 0.50

P(B | A) = 0.60 (the probability of passing the second test given that the student passed the first test)

We can use the formula P(B | A) = P(A and B) / P(A) to find P(A and B):

0.60 = P(A and B) / 0.42

P(A and B) = 0.60 x 0.42

P(A and B) = 0.252

Therefore, 25.2% of the class passed both tests.

To determine if the events are independent, we can compare P(B) to P(B | A). If they are equal, the events are independent. If they are not equal, the events are dependent.

P(B) = 0.50

P(B | A) = 0.60

Since P(B) is not equal to P(B | A), the events are dependent.

Therefore, the answer is option C) A total of 25.2 percent passed both tests. The events are not independent.

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The measure of angles a and b is 36 degrees if they are alternate interior angles formed by a transversal intersecting two parallel lines.

To find the measure of angles a and b when angle b has a measure of 36 degrees, we need additional information.

If we assume that angles a and b are adjacent angles formed by two intersecting lines, then we can use the fact that adjacent angles are supplementary, meaning their measures add up to 180 degrees. Since angle b has a measure of 36 degrees, we subtract it from 180 to find angle a.

Thus, angle a = 180 - 36 = 144 degrees. Therefore, angle a has a measure of 144 degrees when angle b has a measure of 36 degrees.

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Answer:

24.1 feet

Step-by-step explanation:

We can represent these 3 points as a triangle:

- place in the water fountain line

- where her lab partner is

- where her friend is

We know that the distance from the water fountain to the lab partner is 6.6 ft, and the distance from the water fountain to the friend is 7.5 ft.

These are the legs (shorter sides) of the right triangle. Now, we need to find the hypotenuse, which is the distance from the lab partner to the friend. We can solve for this using the Pythagorean Theorem.

[tex]a^2 + b^2 = c^2[/tex]

[tex]6.6^2 + 7.5^2 = c^2[/tex]

[tex]43.56 + 56.25 = c^2[/tex]

[tex]99.81 = c^2[/tex]

[tex]c = \sqrt{99.81}[/tex]

[tex]c \approx 10.0 \text{ ft}[/tex]

To finally answer this question, we need to find the perimeter of the triangle (i.e., the distance that will be walked).

[tex]P = 6.6 + 7.5 + 10.0[/tex]

[tex]\boxed{P = 24.1 \text{ ft}}[/tex]

Answer:

x = 13

Step-by-step explanation:

We Know

(5x - 6) + (8x + 17) must equal 180°

Find the value of x.

Let's solve

5x - 6 + 8x + 17 = 180

13x + 11 = 180

13x = 169

x = 13

So, the value of x is 13.

The triangle theorems will be:

Side-Side-Side (SSS) Congruence Theorem: If the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.

Side-Angle-Side (SAS) Congruence Theorem: If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

Angle-Side-Angle (ASA) Congruence Theorem: If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

Angle-Angle-Side (AAS) Congruence Theorem: If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the two triangles are congruent.

Hypotenuse-Leg (HL) Congruence Theorem: If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle, then the two triangles are congruent.

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5 or more Xs

To complete the activities based on the given data:

Compare the sizes: By looking at the shooting star lengths, we can determine the number of Xs that would appear on the line plot. The shooting star lengths "10" and "8" appear more than 5 times, so they would be placed in the "More than 5 Xs" box. The shooting star lengths "6" and "4" appear fewer than 5 times, so they would be placed in the "Fewer than 5 Xs" box.

Complete the line plot: Using the given set of data, we can create a line plot to represent the lengths of shooting stars. We mark each measurement on the number line and place an X above the corresponding value.

The line plot would have an X above the number 10, 8, 6, and 4, each representing the occurrence of shooting stars with those lengths.

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The variance of the given data set is 18603.39.

To find the variance of the given data set {4, 44, 404, 244, 4, 74, 84, 64}, follow these steps:

Step 1: First, we need to find the mean of the data set:

Mean = (4 + 44 + 404 + 244 + 4 + 74 + 84 + 64) / 8 = 120.5

Step 2: Next, we calculate the deviation of each data point from the mean:

(4 - 120.5) = -116.5

(44 - 120.5) = -76.5

(404 - 120.5) = 283.5

(244 - 120.5) = 123.5

(4 - 120.5) = -116.5

(74 - 120.5) = -46.5

(84 - 120.5) = -36.5

(64 - 120.5) = -56.5

Step 3: Now, we square each deviation:

[tex](-116.5)^2 = 13556.25\\(-76.5)^2 = 5852.25\\(283.5)^2 = 80322.25\\(123.5)^2 = 15252.25\\(-116.5)^2 = 13556.25\\(-46.5)^2 = 2162.25 \\(-36.5)^2 = 1332.25\\(-56.5)^2 = 3192.25[/tex](-116.5)^2 = 13556.25

Step 4: We add up all the squared deviations:

13556.25 + 5852.25 + 80322.25 + 15252.25 + 13556.25 + 2162.25 + 1332.25 + 3192.25 = 130223.75

Step 5: We divide the sum of the squared deviations by the number of data points minus 1 to get the variance:

Variance = 130223.75 / 7 = 18603.39 (rounded to two decimal places)

Therefore, the variance of the data set is 18603.39.

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The line y=10x will in this instance pass through most of the data points, demonstrating that it is a good fit for the data.

A good line of fit should travel across the greatest number of data points and exhibit a positive connection.

A relationship between two variables in which rising values of one cause rising values of the other. On a scatter plot, it is shown as a positive slope.

The line y=10x will in this instance pass through most of the data points, demonstrating that it is a good fit for the data.

The line will be favourably sloped, so as the duration of an accessible bike rental increases, so does the total cost charged.

The scatterplot confirms this, proving that the line y=10x is a good match for the data.  

This indicates that the data points are nearly aligned with the line but not exactly so.

A good line of fit should travel across the greatest number of data points and exhibit a positive connection.

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The unique solution, y(x), to the given differential equation with initial condition y(0) = 4 is

:
y(x) = [-(6x⁸ - 64)]¹/³

Determine the unique solution?

To determine the unique solution, y(x), to the given differential equation with initial condition y(0) = 4, we first need to separate the variables and integrate both sides with respect to x and y, respectively.

dy/y⁴ = 8x⁷ dx

Integrating both sides, we get:

-1/3y³ = 2x⁸ + C

where C is the constant of integration.

Now we can use the initial condition y(0) = 4 to solve for C:

-1/3(4)³ = 2(0)⁸ + C

C = -64/3

Substituting C back into the previous equation, we get:

-1/3y³ = 2x⁸ - 64/3

Multiplying both sides by -3 and taking the cube root, we get:

y(x) = [-(6x⁸ - 64)]¹/³

Therefore, the unique solution, y(x), to the given differential equation with initial condition y(0) = 4 is:

y(x) = [-(6x⁸ - 64)]¹/³

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The length of side b for the triangle is equal to 21.8 to the nearest tenth using the sine rule.

The sine rule is a relationship between the size of an angle in a triangle and the opposing side.

Using the sine rule;

18/sin22° = b/sin27°

b = (18 × sin27°)/sin22° {cross multiplication}

b = 21.8144

Therefore, the length of side b for the triangle is equal to 21.8 to the nearest tenth using the sine rule.

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Answer:12.4

Step-by-step explanation:

18^2-13^2=155
Square root of 155 to the nearest tenth is 12.4