Find the surface area of a square pyramid with a side length of 2m and slant height of 3m.

Using ratio, the number of children that are in the village is 264.

In mathematics, a ratio is a comparison of two or more numbers that indicates their sizes in relation to each other.

The ratio of farmers to children in a village is 13: 11. There were 312 farmers in the village.

The number of children on the village can be computed as follows;

let

x = total number of people in the village

Hence,

312 = 13 / 24 x

cross multiply

13x = 24 × 312

13x = 7488

x = 7488 / 13

x = 576

Therefore, total number of people = 576.

Hence,

The number of children in the village = 576 - 312

The number of children in the village = 264.

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Answer:

Volume, \(V=169.56\ \text{units}^3\)

Step-by-step explanation:

We have,

Radius of cylinder is 3 units

Height of the cylinder is 6 units

It is assumed to find the volume of the cylinder. The formula of the volume of cylinder is given by :

\(V=\pi r^2 h \\\\V=3.14\times 3^2 \times 6\\\\V=169.56\ \text{units}^3\)

So, the volume of the cylinder is \(169.56\ \text{units}^3\).

The forecast for May using a five-month moving average is 39 (Option E).

Moving average is used for smoothing out time series data to find any trends or cycles within the data. A five-month moving average is the average of the past five months. To calculate the moving average, add up the sales for the previous five months and divide it by five.

According to the question, the sales for the previous five months are: Nov. 39 Dec. 27 Jan. 40 Feb. 42 Mar. 41 April 47

We have to add the sales of these five months, which gives:

27 + 40 + 42 + 41 + 47 = 197

To find the moving average for May, we divide this sum by 5:

197 / 5 = 39.4

Since we have to round the answer to the nearest whole number, we round 39.4 to 39, which is option E.

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The chance of observing Mississippi after permuting the letters of it and randomly picking a word from that set is 1 in 34032.

The number of words that can be constructed from the letters of the word "Mississippi" is given by the number of permutations of those letters. Since the letters are not unique, we use the formula for permutations with repetition:

n! / (n₁! ×  n₂! ×  ... × nk!)

where n is the total number of letters, and n₁, n₂, ..., nk are the number of times each letter is repeated.

In this case, n = 11 and n₁ = 4, n₂ = 4, n₃ = 2, n₄ = 1.

So, the number of words that can be constructed is 11! / (4! × 4! × 2! × 1!) = 34, 032.

Thus, the chance of observing "Mississippi" is 1 in 34, 032 or approximately 1/34.

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The population of bacteria after 4 hours will be 10342400.

Equations with exponent variables are known as exponential equations. For example, exponential equations are in the form ax=by . Use the equality of exponential functions property to solve exponential equations with the same base. Only if x=y does bx=by apply if b is a positive number other than 1 and other than 1. In the biological sciences, exponential functions are frequently employed to simulate the evolution of a certain quantity over time, such as population number. Experimental data graphs are often created with the quantity on the y-axis and the time on the x-axis.

Given,

The initial population count was 2525 bacteria.

Culture of bacteria that doubles in size every 30 minutes.

The exponential equation accurately captures the scenario.

p = 2525×2^(t/20) t in minutes; p is the number of people.

The population is at its peak after 4 hours (240 minutes).

Population after three hours:

p = 2525×2^(240/20)

p = 2525×2¹²

p = 10342400

The population of bacteria after 4 hours will be 10342400.

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Based on the given data, the line of best fit equation is g = 9m - 0.17, where "g" represents the number of gallons of water in the tank and "m" represents the number of minutes the tank was being filled.

To find the approximate number of gallons of water in the tank after 45 minutes of being filled, we need to substitute "m=45" in the equation and solve for "g".

g = 9(45) - 0.17

g = 405.83

Therefore, approximately 405 gallons of water would be in the tank after 45 minutes of being filled. The closest option to this answer is option B, which states 405 gallons. Therefore, option B is the correct answer.

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Answer:

a cycle is a sequence of non-repeated vertices and the degree of a graph is the number of neighbors the vertex has.

The Mean, Variance, Standard Deviation, and Coefficient of Variation for the given sample of the number of severe car accidents in 1-90 from 2015 to 2020 are:

Mean = 224.833

Variance = 1956.0667

Standard Deviation (SD) = 108.319

Coefficient of Variation (CV) = 48.163%

From the question above, Given data is: 256, 189, 172, 220, 320, 192

Mean, variance, standard deviation and coefficient of variation for the given sample of the number of severe car accidents in 1-90 from 2015 to 2020 are given below:

The mean of data is equal to the sum of all data points divided by the total number of data points.

N = 6

Sum of data = 256 + 189 + 172 + 220 + 320 + 192 = 1349 ∴ Mean = 1349 / 6= 224.833

Calculation of Variance: The variance of data is the average of the squared differences from the mean.

Variance is calculated by dividing the sum of squared deviations by N-1, where N is the number of data points and then find the average.

Calculation of standard deviation: The standard deviation of data is the square root of the variance.SD = √11736.4 = 108.319

Coefficient of variation (CV): The coefficient of variation (CV) is a normalized measure of the dispersion of the data points. It is the ratio of the standard deviation to the mean.

CV is used to analyze and compare data of different sizes.

So, CV = (SD / Mean) × 100%CV = (108.319 / 224.833) × 100%= 48.163%∴

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If there are 100 cows in this dairy, it requires a total of 32000 L of water daily to operate the dairy. According to the U.S. Department of Agriculture, the average dairy cow can consume up to 200 L of water daily.

An additional 120 L per cow per day is required to wash the milking equipment and milking area. So, in total, a single cow requires 320 L of water per day. For instance, suppose there are 100 cows in this dairy.

To determine the total quantity of water required for the day, multiply the amount of water needed per cow by the number of cows:100 cows × 320 L/cow = 32000 L

Therefore, if there are 100 cows in this dairy, it requires a total of 32000 L of water daily to operate the dairy.

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one mole of NaOH dissociates into one mole of Na⁺ ions and one mole of OH⁻ ions in aqueous solution.

a) Aqueous solutions of HClO₄ and LiOH are mixed:

The balanced chemical equation for the reaction between HClO₄ (perchloric acid) and LiOH (lithium hydroxide) is:

2 HClO₄ + 2 LiOH → 2 LiClO₄ + 2 H₂O

In this reaction, two moles of HClO₄ react with two moles of LiOH to produce two moles of LiClO₄ and two moles of water.

b) Aqueous NaOH:

The balanced chemical equation for the dissociation of NaOH (sodium hydroxide) in water is:

NaOH(aq) → Na⁺(aq) + OH⁻(aq)

In this reaction, one mole of NaOH dissociates into one mole of Na⁺ ions and one mole of OH⁻ ions in aqueous solution.

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Answer:

(0, -1)

Step-by-step explanation:

hope this helps :)

a) Sample mean is arithmetic average of data values. The sample mean of provide data values is 10.

b) The five-number summary of the sample is minimum = 4, Q1 = 4.5, median = 9 , Q3 = 15.5 and maximum= 16.

The population mean is denoted by greek letter, μ and sample mean is a random variable; which is written as x-bar and x-bar stands for individual values it takes. The sample mean is a statistic measure obtained by calculating the arithmetic mean of sample values ( values of variable in sample). The sample mean formula is: x-bar = ( Σxᵢ) / n

Now, we have to calculate sample mean of following data values, 12,8,15,16,5,4.

Sum of values, Σ xi = 12 + 8 + 15 + 5 + 4 + 16 = 60

Number of values = 6

So, Sample mean, = ( Σ xi ) / n = 60/6 = 10

The five-number summary includes following :

So, Steps to determine the five-number summary:

Now, the sample set is 12,8,15,16,5,4. Arrange the data values in ascending order, 4,5,6,12,15,16. So, Minimum value

= 4 , Maximum value = 16 ,Median = mean of 6 and 12 = (6 + 12)/2 = 9. The vales written as(4, 5, ) 6, 12, (15, 16 ). The value of first quartile, Q₁ = median of lower ( 4,5) = (4+5)/2

= 9/2 = 4.5. Similarly, Third quartile, Q₃

= (15+16)/2= 31/2 = 15.5. Thus, the five-numer summary is minimum = 4, Q₁

= 4.5, median = 9 , Q₃ = 15.5 and

maximum = 16.

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Complete question:

Consider the sample set 12,8,15,16,5,4 and answer the below questions:

(a)[2 pts] what is the notation of the sample mean? find the sample mean.

(b)[3 pts] find the five-number summary of the sample.

Answer: A

Step-by-step explanation:

Answer:

A

Just do it Step By Step

As per the concept of average rate of change, the best estimate for the number of miles Michele would cycle in 2 hours is 24 miles

Here we have given the scatter plot shows the relationship between the number of hours Michele cycles on different days and numbers of miles traveled each day.

Then the average rate of change is calculated as,

=> (5 - 2) / (0.50 - 0.25)

=> 3/0.25

=> 12.

Then the best estimate for the number of miles Michele would cycle in 2 hours is calculated as,

=> 2 x 12

=> 24.

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Answer:

option 1

Step-by-step explanation:

the square root of 6 is 2.44949, rounded it's 2.4

the square root of 42 is 6.48074, rounded it's 6.5

in option 1 the 6 is placed after the 2 because it is point 4, not quite 2 but a bit bigger than 2 but less than 3.

same thing for 42, it is placed after 6 because it is not quite 6 but not over 7. i hope this helped

The volume V of solid S is e - 1 cubic unit.

What is Volume?

Volume refers to the measure of three-dimensional space occupied by an object or a region. It quantifies the amount of space enclosed by the boundaries of an object or contained within a given region. In mathematical terms, volume is often calculated by integrating the cross-sectional areas of the object or region along a particular axis. Volume is typically expressed in cubic units, such as cubic meters (m^3) or cubic centimeters (cm^3). It is an essential concept in geometry, physics, engineering, and other scientific fields where the measurement of three-dimensional space is involved.

To find the volume of solid S, we need to integrate the areas of the cross sections perpendicular to the x-axis along the interval \([e, \infty).\)

The area of each square cross-section is equal to the square of the side length, which in this case is \(y = \sqrt{\ln(x)}.\)

Therefore, the volume V of solid S can be calculated as:

\(V = \int_{e}^{\infty} (\sqrt{\ln(x)})^2 dx\)

To evaluate this integral, we can simplify the expression:

\(V = \int_{e}^{\infty} \ln(x) dx\)

Using integration by parts, we let \(u = \ln(x)\)and dv = dx:

\(du = \frac{1}{x} dx\\v = x\)

Applying the integration by parts formula:

\(V = [uv] - \int v du= [x \ln(x)] - \int x \left(\frac{1}{x}\right) dx= x \ln(x) - \int dx= x \ln(x) - x + C\)

Evaluating the definite integral:

\(V = [x \ln(x) - x]_{e}^{\infty}= (\infty \cdot \ln(\infty) - \infty) - (e \cdot \ln(e) - e)= \infty - 0 - (1 - e)= e - 1\)

Therefore, the volume V of solid S is e - 1 cubic unit.

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Answer:

5(x+8)

5x+8x

5x+40

6q+2+3q+5

9q+7

Answer:

1. 5x + 40

to get this answer i multiplied the 5 to the variables in the parenthesis

2. 9q +7

to get this answer i added the variables that were similar., one pair has q at the end and the other does not.

The perimeter of triangle ABC is 240 units. Using the given information, we determined the lengths of the remaining sides using the angle bisector theorem and the Pythagorean theorem. The lengths of AB, BC, and AC are 45, 75, and 120 units, respectively.

To find the perimeter of triangle ABC, we need to determine the lengths of the remaining sides.

Given that BD = 15 and BE = 20, we can use the properties of the angle bisectors to find the lengths of the other sides.

Let's denote the length of AB as a, BC as b, and AC as c.

Using the Angle Bisector Theorem, we know that the ratios of the lengths of the sides are equal. Therefore, we have

BD/DC = AB/AC => 15/(AC-15) = a/c ----(1)

BE/EC = AB/AC => 20/(AC+20) = a/c ----(2)

Setting the right sides of equations (1) and (2) equal to each other, we can solve for AC:

15/(AC-15) = 20/(AC+20)

Cross-multiplying and simplifying, we get

15(AC+20) = 20(AC-15)

15AC + 300 = 20AC - 300

5AC = 600

AC = 120

Now that we have the length of AC, we can find the lengths of AB and BC using the Pythagorean theorem:

AB² + BC² = AC²

a² + b² = c²

a² + b² = 120²

We also know that the sum of the lengths of the two legs (AB and BC) will be equal to the hypotenuse (AC):

a + b = 120

We have two equations with two unknowns, so we can solve this system of equations to find the values of a and b.

By solving these equations, we find that a = 45 and b = 75.

Finally, the perimeter of triangle ABC is

Perimeter = AB + BC + AC = a + b + c = 45 + 75 + 120 = 240 units.

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Answer:

The value of x is 12.

Step-by-step explanation:

Given equation,

→ (4x + 2)/5 = 10

Now the value of x will be,

→ (4x + 2)/5 = 10

→ 4x + 2 = 10 × 5

→ 4x = 50 - 2

→ 4x = 48

→ x = 48 ÷ 4

→ [ x = 12 ]

Hence, the value of x is 12.

The ratio of dividends to the average number of common shares outstanding is known as the dividend yield. It is a measure of the return on an investment in the form of dividends received relative to the number of shares held.

To calculate the dividend yield, you need to divide the annual dividends per share by the average number of common shares outstanding during a specific period. The annual dividends per share can be obtained by dividing the total dividends paid by the number of outstanding shares. The average number of common shares outstanding can be calculated by adding the beginning and ending shares outstanding and dividing by 2.

For example, let's say a company paid total dividends of $10,000 and had 1,000 common shares outstanding at the beginning of the year and 1,500 shares at the end. The average number of common shares outstanding would be (1,000 + 1,500) / 2 = 1,250. If the annual dividends per share is $2, the dividend yield would be $2 / 1,250 = 0.0016 or 0.16%.

In summary, the ratio of dividends to the average number of common shares outstanding is the dividend yield, which measures the return on an investment in terms of dividends received per share held.

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The area of the triangle is 4.5 square unit.

We have, y= 4x/ (1 + x³)

Now, differentiating the above equation wrt to x we get

y' = 4(1 + x³)- 4x . 3x² / (1+ x³)²

y'= -8x³ + 4/ (1+x³)²

When x = 1 then y' = -4/4 = -1

so, y -2 = -1 (x-1)

y= -x+ 3

Here the x intercept is (3, 0) and y intercept is (0, 3).

so, Area of Triangle is

= 1/2 x 3 x 3

= 9/2

= 4.5 square unit

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Answer:

k = 66

Step-by-step explanation:

To solve this problem, subtract 301 from 367.

369 - 301 = 66

Therefore, k is equal to 66.

Hope this helps!

Answer:  -2

Explanation: The coefficient is the number to the left of the variable.

Another example would be that 10xy has the coefficient 10.

Something like x^2 has coefficient 1 because x^2 = 1x^2.