What’s equivalent to 6 to the -3 power

Answer:

A critical number can have different meanings depending on the context. In mathematics, a critical number is a value of x where the derivative of a function is zero or undefined. It helps to find the maximum and minimum of a function. In business, a critical number is a metric that represents a weakness or vulnerability that needs to be addressed and corrected to improve the performance and security of the company

Step-by-step explanation:

Answer:

D. 45 square feet

Step-by-step explanation:

To find the surface area of a square pyramid, we need to find the area of the base and the area of the four triangular lateral faces.

First, let's find the area of the base (square).

[tex]\boxed{\begin{minipage}{7 cm}Base area = side length $\times$ side length\\ \\Base area = 3 $\times$ 3 \\ \\Base area = 9 square feet\end{minipage}}[/tex]

Now, let's find the area of the triangular lateral faces.

As stated in the problem, the slant height of the triangle is 6 feet. We can find the area of one triangular lateral face:

[tex]\text{Triangle area = $\frac{1}{2}$ $\times$ base $\times$ height}\\\\\text{Triangle area = $\frac{1}{2}$ $\times$ 3 $\times$ 6} \\\\\text{Triangle area = 9 square feet}[/tex]

Since there are four triangular lateral faces, we need to multiply this area by 4:

[tex]\text{Total lateral area = 4 $\times$ 9}\\\\\text{Total lateral area = 36 square feet}[/tex]

Finally, we add the base area and the total lateral area to find the total surface area of the pyramid:

[tex]\text{Total surface area = base area + total lateral area}\\\\\text{Total surface area = 9 + 36}\\\\\text{Total surfacel area = 45 square feet}[/tex]

So, the area of the square pyramid is 45 square feet. Which is option D.

________________________________________________________

Answer:

  D.  45 square feet

Step-by-step explanation:

You want the surface area of a square base pyramid with a side length of 3 feet and a slant height of 6 feet.

The area of a triangular face is given by ...

  A = 1/2bh . . . . . base b and height h

The area of the square base is given by ...

  A = s²

The total surface area of the pyramid is the area of the base plus the areas of the 4 triangular faces:

  total area = s² +4(1/2bh) . . . . where b = s

This can be simplified to ...

  total area = s(s +2h) . . . . . area of a square pyramid with slant height h

For the pyramid with a square base 3 ft on a side, and a slant height of 6 ft, the total area is ...

  total area = (3 ft)(3 ft + 2·6 ft) = (3 ft)(15 ft) = 45 ft²

The area of the pyramid is 45 square feet.

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1. Using a calculator, we find that cos 10 ≈ 0.98.

2. Using a calculator, we find that sin 30 ≈ 0.50.

3. Using a calculator, we find that sin 20 ≈ 0.34.

4. Using a calculator, we find that tan 25 ≈ 0.47.

5. Using a calculator, we find that tan 48.5 ≈ 1.14.

Using a calculator to evaluate the given trigonometric functions, rounded to the nearest hundredth, we have:

Cos 10:

Using a calculator, we find that cos 10 ≈ 0.98.

Sin 30:

Using a calculator, we find that sin 30 ≈ 0.50.

Sin 20:

Using a calculator, we find that sin 20 ≈ 0.34.

Tan 25:

Using a calculator, we find that tan 25 ≈ 0.47.

Tan 48.5:

Using a calculator, we find that tan 48.5 ≈ 1.14.

These values represent the approximate decimal values of the trigonometric functions at the given angles, rounded to the nearest hundredth.

Just a reminder, when using a calculator, make sure it is set to the correct angle mode (degrees or radians) as per the given problem.

It's important to note that these values are approximate since they are rounded to the nearest hundredth. If you need more precise values, you can use a calculator that allows for a greater number of decimal places or use trigonometric tables.

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The sides of the rectangle that have the same length as the circumference of the circles are the sides parallel to the bases of the cylinder. The sides of the rectangle that have the same length as the height of the cylinder are the sides perpendicular to the bases. While the model provides a simplified representation, practical calculations might have slight differences due to real-world factors.

In a cylinder, the two circular bases are connected by a curved surface, forming a three-dimensional shape. The rectangular shape that wraps around the curved surface of the cylinder is called the lateral surface or the lateral area.

To determine which sides of the rectangle have the same length as the circumference of the circles, we need to understand the geometry of a cylinder. The circumference of a circle is calculated using the formula:

Circumference = 2πr,

where r is the radius of the circle. In a cylinder, the bases are identical circles, so the circumference of each base is equal. Therefore, the sides of the rectangle that are parallel to the bases have the same length as the circumference of the circles.

Now, let's consider the height of the cylinder. The height is the distance between the two bases and is perpendicular to the bases. In the rectangular representation of the cylinder, the sides that are perpendicular to the bases represent the height. Hence, the sides of the rectangle that are perpendicular to the bases have the same length as the height of the cylinder.

When comparing the model (rectangular representation) with practical calculations, we may notice some differences. The model provides a simplified representation of the cylinder, assuming that the lateral surface is perfectly wrapped around the curved surface. However, in practical calculations, there might be slight variations due to factors like material thickness, manufacturing processes, or measuring precision. These variations can result in minor deviations between the model and the practical calculations.

It's important to consider that the model is an approximation and serves as a visual aid to understand the basic properties of the cylinder. In real-life applications or engineering calculations, precise measurements and considerations of tolerances are crucial.

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Step-by-step explanation:

Part A: The first step where Margie made an error is Step 1:

−2.67b + 11 + (−5.38b) + 15

The error lies in the addition of the two terms: (−5.38b) + 15. Margie incorrectly added the two terms together instead of subtracting them.

Part B: To correctly write the expression in the fewest terms, we need to correct the error from Part A. The correct step-by-step process is as follows:

Given: (−2.67b + 11) − (5.38b − 15)

Step 1: Distribute the negative sign to the terms inside the second parentheses:

−2.67b + 11 − 5.38b + 15

Step 2: Combine like terms:

(−2.67b − 5.38b) + (11 + 15)

Step 3: Simplify:

−7.05b + 26

Therefore, the correct expression, written in the fewest terms, is −7.05b + 26.

Answer: A,

Step-by-step explanation:

8 people, times whatever each person payed will equal to 55$ in total

Answer:

Step-by-step explanation:

To find the equation of a line that is perpendicular to a given line and passes through a specific point, we need to follow a few steps:

Find the slope of the provided line.

The point-slope form of a line is given by: y - y1 = m(x - x1), where (x1, y1) represents the given point.

Substituting the values, the equation of the perpendicular line becomes:

y - 5 = (-1/m)(x - 2)

Simplifying the equation further, we can rewrite it in point-slope form:

y - 5 = (-1/m)x + (2/m)

Using basic inference rules, we can establish the validity of the argument: p ⟹ ¬q, q V r, p V u, ¬r ├ u.

1. We are given the following premises:

  - p ⟹ ¬q (Premise 1)

  - q V r (Premise 2)

  - p V u (Premise 3)

  - ¬r (Premise 4)

2. To prove the conclusion, u, we need to use the premises and apply inference rules.

3. From Premise 4 (¬r) and the Disjunctive Syllogism rule, we can deduce ¬q: (¬r, q V r) ⟹ ¬q.

4. From Premise 1 (p ⟹ ¬q) and Modus Ponens, we can conclude ¬p: (p ⟹ ¬q, ¬q) ⟹ ¬p.

5. From Premise 3 (p V u) and Disjunctive Syllogism, we obtain ¬p V u.

6. Using Disjunctive Syllogism with ¬p V u and ¬p, we can derive u: (¬p V u, ¬p) ⟹ u.

7. From Premise 2 (q V r) and Disjunctive Syllogism, we have q.

8. Finally, using Modus Tollens with q and ¬q, we can deduce ¬p: (q, p ⟹ ¬q) ⟹ ¬p.

9. Therefore, combining ¬p and u, we can conclude the desired result: ¬p ∧ u.

10. Since ¬p ∧ u is logically equivalent to u, we have established the validity of the argument: p ⟹ ¬q, q V r, p V u, ¬r ├ u.

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If all the values in the series are the same, the A.M, G.M, and H.M are all equal and can be represented as A.M = G.M = H.M = x.

If all the values in the series are the same, the arithmetic mean (A.M), geometric mean (G.M), and harmonic mean (H.M) will all be equal.

Let's consider a series with the same value repeated n times, denoted as x:

Series: x, x, x, ..., x (n times)

Arithmetic Mean (A.M):

The arithmetic mean is calculated by summing all the values in the series and dividing by the total number of values. In this case, the sum of all the values is nx, and since there are n values, the arithmetic mean is (nx) / n = x. So, A.M = x.

Geometric Mean (G.M):

The geometric mean is calculated by taking the nth root of the product of all the values in the series. In this case, the product of all the values is x^n, and since there are n values, the nth root of x^n is x. So, G.M = x.

Harmonic Mean (H.M):

The harmonic mean is calculated by taking the reciprocal of the arithmetic mean of the reciprocals of all the values in the series. Since all the values are the same, the reciprocal of each value is 1/x. The arithmetic mean of the reciprocals is (1/x + 1/x + ... + 1/x) / n = (n/x) / n = 1/x. Taking the reciprocal of 1/x gives x. So, H.M = x.

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Circle 1 (-6, 2) with a radius of 8 cm can be transformed into Circle 2 (-1, -4) with a radius of 6 cm through translation, scaling, and translation, proving their similarity.

To prove that two circles are similar, we need to find a sequence of transformations that maps one circle to another circle. In this case, we need to find a sequence of transformations that map Circle 1 to Circle 2. Circle 1 has a center (-6, 2) and a radius of 8 cm. Circle 2 has a center (-1,-4) and a radius of 6 cm.

Let's write the equations of the two circles:C1: (x + 6)² + (y - 2)² = 64C2: (x + 1)² + (y + 4)² = 36Step 1: TranslationWe can translate Circle 1 by (-5,-6) to obtain a new circle with center at the origin. The equation of the translated circle is C1': (x + 11)² + (y - 4)² = 64Step 2: Scale

We can scale the translated Circle 1' by a factor of 3/4 to obtain a circle with a radius of 6.

The equation of the scaled circle is C1'': (x + 11)² + (y - 4)² = 36Step 3: TranslationWe can translate the scaled Circle 1'' by (2,-4) to obtain a new circle with center at (-1,-4). The equation of the translated circle is C1''': (x - 1)² + (y + 4)² = 36The transformations applied to Circle 1 to obtain Circle 2 are:

Translation by (-5,-6)

Scale by 3/4

Translation by (2,-4)

Therefore, we can say that Circle 1 and Circle 2 are similar. Circle 1 can be transformed into Circle 2 by translation, scale, and translation.

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Answer:

Step-by-step explanation:To determine which of the given numbers is closest to 7, we can calculate the absolute difference between each number and 7 and choose the number with the smallest absolute difference.

Let's calculate the absolute differences:

Absolute difference between √51 and 7:

|√51 - 7| ≈ 7.13 - 7 ≈ 0.13

Absolute difference between 50 and 7:

|50 - 7| = 43

Absolute difference between 46 and 7:

|46 - 7| = 39

Comparing the absolute differences, we can see that the number closest to 7 is √51. The absolute difference between √51 and 7 is the smallest among the given options.

Therefore, √51 is the number closest to 7.

The correct statement is C. The mean of East Hills HS is greater than the mean of Southview HS. So, option C is the correct answer.

To compare the centers of the distributions, we need to consider the measures of central tendency such as the median and the mean.

Looking at the given information about the class sizes at East Hills HS and Southview HS:

East Hills HS class sizes: 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44

Southview HS class sizes: 0, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44

Let's compare the measures of central tendency:

Median: The median is the middle value of a dataset when arranged in ascending or descending order. In this case, both datasets have an odd number of values, so the median is the middle value.

For East Hills HS: Median = 34

For Southview HS: Median = 34

Therefore, the medians of both distributions are the same.

Mean: The mean is calculated by summing all the values in the dataset and dividing by the total number of values.

For East Hills HS: Mean = (24 + 26 + 28 + 30 + 32 + 34 + 36 + 38 + 40 + 42 + 44) / 11 ≈ 35.727

For Southview HS: Mean = (0 + 24 + 26 + 28 + 30 + 32 + 34 + 36 + 38 + 40 + 42 + 44) / 12 ≈ 33.667

Therefore, the mean of East Hills HS is greater than the mean of Southview HS.

Based on the comparisons, the correct statement is:

C. The mean of East Hills HS is greater than the mean of Southview HS.

So, option C is the correct answer.

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The question is asking for comparison of the centers and range of two data sets - the class sizes at two different high schools. Because no specific numeric data given for the mean and median of both school sizes, it's not possible to definitively choose an answer. Theoretically, if Southview has a higher concentration at larger class sizes, its median and mean might be larger.

This question refers to comparing the statistical centers (mean and median) and range of two data sets, which are the class sizes at East Hills High School and Southview High School. The centers and range of a data distribution tell us about the typical values, variety, and spread in the data set.

Without actual numbers (i.e., mean and median) for both the East Hills HS and Southview HS distributions, we can't definitively answer this question. However, let's assume that the representations provided suggest that Southview HS has a higher concentration of students in larger class sizes. In that case, the mean and median for Southview HS could be greater than those for East Hills HS, which would suggest option A and D. With regards to the range, if the minimum and maximum values of class sizes are the same in both schools, then the range, which is the difference between the maximum and minimum, would be the same. Therefore, option B wouldn't be accurate. However, as previously mentioned, this can only be suggestive as actual numbers are required for a definite answer.

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Incremental cash flows associated with the donation of a valuable painting from a corporation's private collection may include It's important to note that any direct costs associated with the donation.

Tax benefits: The corporation may be eligible for tax deductions or credits for charitable donations, which could result in a reduction in its tax liability and generate cash flow savings.

Opportunity cost: If the corporation could have sold the painting instead of donating it, the incremental cash flow would be the potential proceeds from the sale.

Storage and maintenance cost savings: By donating the painting to the art museum, the corporation no longer has to incur expenses for storing, insuring, and maintaining the artwork, resulting in cost savings.

Public relations and marketing benefits: Donating the painting can enhance the corporation's reputation and generate positive publicity, potentially leading to increased customer goodwill and brand value, which can translate into future cash flows.

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The correct statement regarding the relative extremas of F(x) is given as follows:

F(x) has a relative maximum at x = -1 and a relative minimum at x = -0.8.

Hence the extremas for this problem are given as follows:

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The scale factor used to create the image of polygon ABCD is 4.

To determine the scale factor, we need to compare the corresponding side lengths of the original polygon ABCD and the image polygon ABCD. Let's denote the scale factor as k.

Original polygon ABCD:

Side AB: length = 3 - 1 = 2

Side BC: length = -2 - (-1) = -1

Side CD: length = 1 - 3 = -2

Side DA: length = -2 - (-1) = -1

Image polygon ABCD:

Side AB: length = 12 - 4 = 8

Side BC: length = -3 - (-4) = 1

Side CD: length = 4 - 12 = -8

Side DA: length = -3 - (-4) = 1

Comparing the corresponding side lengths, we can set up the following equations:

k * 2 = 8 (for side AB)

k * (-1) = 1 (for side BC)

k * (-2) = -8 (for side CD)

k * (-1) = 1 (for side DA)

From the equations, we can see that k = 4 satisfies all of them.

Therefore, the scale factor used to create the image of polygon ABCD is 4.

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a) The mean of the data-set is of 2.

b) The range of the data-set is of 4 units, which is of around 4.3 MADs.

The mean of a data-set is obtained as the sum of all observations in the data-set divided by the number of observations in the data-set, which is also called the cardinality of the data-set.

The dot plot shows how often each observation appears in the data-set, hence the mean of the data-set is obtained as follows:

Mean = (1 x 0 + 5 x 1 + 3 x 2 + 5 x 3 + 1 x 4)/(1 + 5 + 3 + 5 + 1)

Mean = 2.

The range is the difference between the largest observation and the smallest, hence:

4 - 0 = 4.

4/0.93 = 4.3 MADs.

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Answer:

(3, -2) is the correct choice.

Answer:the answer is 15 units

Step-by-step explanation:

just took the test

There are no positive or negative zeros, and the number of complex zeros cannot be determined without further information.

To determine the number of positive, negative, and complex zeros of the given polynomial [tex]6 + 9x^2 + 3x^3 + 2x^4 - 12x,[/tex] we need to analyze its behavior and apply the properties of polynomial functions.

Positive Zeros:

Positive zeros are the values of x for which the polynomial evaluates to zero.

To find positive zeros, we set the polynomial equal to zero and solve for x.

However, in this case, we can see that all the coefficients of the terms in the polynomial are positive.

Therefore, there are no positive zeros.

Negative Zeros:

Negative zeros are the values of x for which the polynomial evaluates to zero.

Similar to positive zeros, we set the polynomial equal to zero and solve for x.

However, in this case, we can see that all the coefficients of the terms in the polynomial are positive.

Therefore, there are no negative zeros.

Complex Zeros:

Complex zeros occur when the polynomial has complex roots. Since the given polynomial has only real coefficients, complex zeros will occur in conjugate pairs.

To determine the number of complex zeros, we need to examine the degree of the polynomial.

In this case, the highest power of x is [tex]4 (x^4),[/tex]  indicating a fourth-degree polynomial.

A fourth-degree polynomial can have at most four complex zeros. However, we cannot determine the exact number of complex zeros without further information or solving the polynomial explicitly.

In conclusion, the given polynomial has no positive or negative zeros due to all coefficients being positive.

The number of complex zeros cannot be determined without additional information.

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In order to achieve a profit of $123,525, the Vilas County News would require a subscriber base of 6,355,500 individuals.

Let's break down the problem step by step to find the number of subscribers needed to bring a total profit of $123,525.

First, we know that the Vilas County News earns a profit of $20 per year for each of its 3,000 subscribers. This means that the current profit from the 3,000 subscribers is $20 x 3,000 = $60,000.

Management projects that the profit per subscriber would increase by 1¢ for each additional subscriber over the current 3,000. This means that for every additional subscriber, the profit increases by $0.01. Therefore, we need to find how many additional subscribers are required to reach a total profit of $123,525 - $60,000 = $63,525.

To find the number of additional subscribers needed, we divide the additional profit required by the increase in profit per subscriber: $63,525 / $0.01 = 6,352,500.

However, we need to remember that this number represents the total number of additional subscribers needed, not the final total number of subscribers. To find the final total number of subscribers, we add the additional subscribers to the current number of subscribers: 6,352,500 + 3,000 = 6,355,500.

Therefore, to bring a total profit of $123,525, the Vilas County News would need a total of 6,355,500 subscribers.

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Answer:

[tex]5a2b2/4[/tex]

Step-by-step explanation:

The probability of rolling a 6 with this die would be = 1/15.

To determine the possibility of the given event, the formula for probability should be used and it's given below as follows:

Probability= Possible outcome/sample space

where;

possible outcome= 1

sample space= 15

Probability = 1/15

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Answer:

The fish tank holds 40,000 ml of water.

Step-by-step explanation:

Volume = Length x Width x Height

Volume = 50 x 40 x 20

Volume = 40,000

The percentile of 6.2 in the given dataset is 30%. This means that 30% of the values in the dataset are lower than or equal to 6.2.

To determine the percentile of 6.2 in the given dataset, we need to calculate the percentage of values in the dataset that are lower than or equal to 6.2.

First, we arrange the dataset in ascending order: 4.2, 4.6, 5.1, 6.2, 6.3, 6.6, 6.7, 6.8, 7.1, 7.2.

Next, we count the number of values that are lower than or equal to 6.2. In this case, there are three values: 4.2, 4.6, and 5.1.

The next step is to calculate the percentage. We divide the count (3) by the total number of values in the dataset (10) and multiply by 100.

(3/10) * 100 = 0.3 * 100 = 30%

Percentiles are used to understand the relative position of a particular value within a dataset. In this case, 6.2 is higher than 30% of the values in the dataset and lower than the remaining 70%.

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Answer:

Number of Females in Class = x Given: Ratio of Males to Females = 2:3 Given: Number of Males in Class = 12 Assume the total number of people in class = y 2/3 of y = x 2x = 3y 12 + x = y y - 12 = x y - 12 = 2x 3y - 36 = 2x 3y = 2x + 36 y = (2x + 36) / 3 y = (2(12) + 36)/3 y = 24 x = y - 12 x = 24 - 12 x = 12 Answer: There are 12 females in the class.

Step-by-step explanation:

Answer:

4.
A regular polygon is a polygon in which all sides are equal in length and all angles are equal in measure.

5.

a. The measure of a single interior angle in a regular pentagon is:
[(n – 2)*180°]/n = 540°/5 = 108°.

b. The measure of a single exterior angle in a regular pentagon is:
360°/n = 360°/5 = 72°.

6.
This can be found using the following formula:

[(n – 2)*180°]/n = Interior angle

(n-2)*180=162°*n

180n-360=162n

180n-162n=360

18n=360

n=360/18

n=20

where n is the number of sides in the regular polygon.

A regular polygon with an interior angle of 162° has 20 sides.