Select the correct answer. A new building in the shape of a square pyramid is to be constructed. The slant height will be five times the side length of the base. There will be between 20,000 square feet and 50,000 square feet of construction material used for the outside of the building. What would be the maximum possible side length of the base of the building? Round your answer to the nearest foot. Ο Α. 71 feet OB. 89 feet OC. OD. 45 feet 141 feet​

The angles of the triangle KHP are P ≈ 118.555°, H ≈ 34.614°, K ≈ 26.844°, respectively.

Here we have the case of a triangle where the lengths of three sides are known and measures of angles must be determined. The missing angles can be found by means of law of cosine, whose equations related to the triangle are introduced below;

p² = h² + k² - 2 · h · k · cos P

h² = p² + k² - 2 · p · k · cos H

k² = h² + p² - 2 · h · p · cos K

Given;

h, k, p - Sides

H, K, P - Angles

If we know that h = 16.1, p = 24.9 and k = 12.8, then the measures of the angles are;

cos P = (p² - h² - k²) / (- 2 · h · k)

cos P = (24.9² - 16.1² - 12.8²) / (- 2 · 16.1 · 12.8)

cos P = - 0.478

P ≈ 118.555°

cos H = (h² - p² - k²) / (- 2 · p · k)

cos H = (16.1² - 24.9² - 12.8²) / (- 2 · 24.9 · 12.8)

cos H = 0.823

H ≈ 34.614°

cos K = (k² - h² - p²) / (- 2 · h · p)

cos K = (12.8² - 16.1² - 24.9²) / (- 2 · 16.1 · 24.9)

cos K = 0.892

K ≈ 26.844°

Triangle KHP has the following missing angles: P ≈ 118.555°, H ≈ 34.614°, K ≈ 26.844°;

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The expression of the weight carried by x hikers is x (3.4 + 4.6 + 2.2).

The weight carried by each hiker is 10.2 lb.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Three items are given.

The weight of each items are 3.4 lb, 4.6 lb, and 2.2 lb.

Now,

The total weight of all the items.

= 3.4 + 4.6 + 2.2

= 10.2 lb

The weight carried by x hikers.

= x (3.4 + 4.6 + 2.2)

= 10.2x lb

The weight carried by each hikers.

= 3.4 + 4.6 + 2.2

= 10.2 lb

Thus,

Weight carried by x hikers is 10.2x lb.

Weight carried by each hiker is 10.2 lb.

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Answer:

see explanation

Step-by-step explanation:

to find the y- intercept, the point where the line crosses the y- axis.

Any point on the y- axis has an x- coordinate of zero.

let x = 0 in the equation and solve for y

- 4(0) + 7 = 2y - 3

0 + 7 = 2y - 3

7 = 2y - 3 ( add 3 to both sides )

10 = 2y ( divide both sides by 2 )

5 = y

then y- intercept = (0, 5 )

to find the x- intercept, the point where the line crosses the x- axis.

Any point on the x- axis has a y- coordinate of zero.

let y = 0 in the equation and solve for x

- 4x + 7 = 2(0) - 3

- 4x + 7 = 0 - 3

- 4x + 7 = - 3 ( subtract 7 from both sides )

- 4x = - 10 ( divide both sides by - 4 )

x = [tex]\frac{-10}{-4}[/tex] = [tex]\frac{10}{4}[/tex] = [tex]\frac{5}{2}[/tex]

then x- intercept = ( [tex]\frac{5}{2}[/tex], 0 ) or (2.5, 0 )

The proof of the given question is given in the solution as follows

A technique for factoring a number or a polynomial is called factorisation. The polynomials are divided into the sums of their component parts. As an illustration, x2 + 2x may be factored as x(x + 2), where x and x+2 are the factors that can be multiplied to obtain the original polynomial.

The six types of factoring are: greatest common factor, difference in two squares, grouping, sum or difference in two cubes, trinomials, and general trinomials.

In the given equation

we separate m2-1/n2 to (a+b)(a-b) form

and hence we get the answer as

(n+1/m)^m-n/(m-1/n)^m-n

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Answer:

Not a lot of information given but if you are looking for the difference in price it is 31 CHF

It is 31 more CHF in Manchester than in Switzerland.

Step-by-step explanation:

1.55(145) = 224.75

224.75-193.75 = 31

Answer:5441 is the population increase per year and 123,000 is when we start added the population increase. to get this equation i found the population increase between 2007 and 1990 which is 215,500-123,000 which is 92,500. to find the population increase per year you divide that by 17 which is the difference between 2007 and 1990 and you would get 5441.176. but since you can have part of a person i rounded it to 5441.

Step-by-step explanation:

Answer:

The linear equation representing the population growth since 1990 is p = 92t + 123000.

Where p is the population, 92 is the growth rate (215500-123000)/(2007-1990), and t is the years after 1990.

Step-by-step explanation:

The inequality h ≤ 8 represents the number of hours, Carmen works on the job.  

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

Given:

On Saturday, Carmen works no more than 8 hours at her job.

Let h be the number of hours, he works on the job.

According to the question,

h ≤ 8.

That means,

Carmen works less than or equals to 8 hours.

Therefore, the inequality is h ≤ 8.

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Answer: 1/2

Step-by-step explanation:

Slope = Δy/Δx = -3/-6 = 1/2

The value of information is directly related to how it assists decision makers in achieving the goals of the company. -Differentiate data from information and define the features used to assess data quality.

The value of information in decision analysis is the improvement in the consequences of our actions that we would expect if we could minimise or remove uncertainty before making a choice.

The value of information is determined by the influence of a choice on achieving the organization's goals and enhancing its profit-ability.

Management information systems give information on the organization's relative position and the underlying factors at work. It offers the necessary information for decision making and assists businesses in carrying out their control, planning, and operational activities successfully.

The interaction between information systems and decision making is a major problem in the subject of information systems (IS).

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a. The probability that the sample proportion will be within ±0.03 of the population proportion is 0.6456.
b. The probability that the sample proportion will be within ±0.03 of the population proportion is 1.985.

What is population proportion?
The probability that a specific event will occur in the population is known as the population proportion. It is a parameter, and the sample proportion statistic is used to estimate it. The percentage of occurrences that occur in the sample is known as the sample proportion.

a. The probability that the sample proportion will be within ±0.03 of the population proportion is P(-0.03 < p‌ - P < 0.003).
We Know that z-score of sample proportion is given by:
z = (p‌ - P)/SE(p‌), where SE(p‌) represents standard error.
⇒SE(p‌) = √(0.3 * 0.7)/200
⇒SE(p‌) = √0.00105
⇒SE(p‌) = 0.0324

Now, using the z score, the probability P(-0.03 < p‌ - P < 0.003) is computed as follows:
P(-0.03 < p‌ - P < 0.003) = P(-0.03/SE(p‌) < p‌ - P/SE(p‌) < 0.003/SE(p‌))
= P(-0.03/0.0324 < Z < 0.003/0.0324)
= P(−0.925926 < Z < 0.925926)
= 2P(0 < Z < 0.925926)


P(0 < Z < 0.925926) = 0.3228   (Using standard table)
So,
2P(0 < Z < 0.925926) = 2*0.3228 = 0.6456
Hence, the probability that the sample proportion will be within ±0.03 the population proportion is 0.6456.


b. The probability that the sample proportion will be within ±0.03 of the population proportion is P(-0.08 < p‌ - P < 0.008).
Also, SE(p‌) = 0.0324
Now, using z score,
P(-0.08 < p‌ - P < 0.008) = P(-0.08/SE(p‌) < p‌ - P/SE(p‌) < 0.008/SE(p‌))
= P(-0.08/0.0324 < Z < 0.008/0.0324)
= P(−2.469135 < Z < 2.469135)
= 2P(0 < Z < 2.469135)

P(0 < Z < 2.469135) = 0.9925   (Using standard table)
So,
2P(0 < Z < 2.469135) = 2*0.9925 = 1.985

Hence, the probability that the sample proportion will be within ±0.03 of the population proportion is 1.985.

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For the Given Parallelogram: AC¯≅BD¯;AC¯⊥BD¯

The parallelogram is not a square because the statement "AC¯≅BD¯;AC¯⊥BD¯" means that opposite sides of the parallelogram are congruent and perpendicular but it's not enough to say that the parallelogram is a square, In a square, all four sides are congruent, and the diagonal bisect each other at right angles.

For the first Theorem, AC¯≅BD¯, congruent figures' corresponding sides are congruent(CPCTC) while the AC¯⊥BD¯ Theorem have opposite angles of a parallelogram that is useful (Parallelogram Opposite angles Theorem).

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The actual length of the train is calculated to be 18.33 feet

Scale factors are used to increase or decrease image. The situation of increment is usually called enlargement, and it is case for the problem.

solving for the factor, assuming the factor is k, using the ratio 1 : 40.  the scale factor is 40 / 1 = 40

Solving for the actual length

actual length =  scale facto * model length

actual length = k * 5.5 in

actual length = 40 * 5.5 in

actual length = 220 in

converting to feet

12 in = 1 foot

220 in = ?

cross multiplying

12 * ? = 220

? = 220 / 12

? = 18.33 feet

the actual length of the train is 18.33 feet

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The requried ratio of boys in the club to girls is given as 7/9 or 7:9. Option A is correct.

The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.

Here,
The conservation club has 32 members. There are 18 girls in the club.
Number of boys = 32 - 18 = 14
Ratio of boys to girls = number of boys / number of girls
                                = 14 / 18 = 7/9

Thus, the requried ratio of boys in the club to girls is given as 7/9 or 7:9. Option A is correct.

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Answer:

Tabitha's commission would be 6% of the total sales from the three cars

Step-by-step explanation:

which is $(23,000 + 13,800 + 25,760) * 0.06 = $3,638.40

There are 192 pennies in a stack that is 1 ft high.

A measurement unit is a standard quality used to express a physical quantity. Also it refers to the comparison between the unknown quantity with the known quantity.

Given that;

Stack is 1 feet high.

Now, We know that;

⇒ 1 inch = 16 pennies

And, 1 feet = 12 inches

So, We get;

⇒ 1 ft = 12 inches

         = 12 × 16 pennies

         = 192 pennies

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Answer: 4 1/3

Step-by-step explanation:

(12 + 1) 3 = 12 3 + 1 3 = 4 + 1 3 = 4 1 3 13 3 = 4 1 3 Hence, 13/3 as a mixed number is 4 1/3

a. To subtract like terms, subtract the coefficients, not the variables b. Like terms are terms that contain the same variable e. Negative (negative x) is equivalent to Negative x, so Negative 5 x minus x = negative 6 x.

The expression can be made simpler by using these facts.

We may take the coefficients of the similar terms, which are x and -x, out using fact a. In this instance, the expression is simplified to read as Negative 5 x minus x = Negative 6 x.

According to fact b, terms that have the same variable raised to the same power are referred to as being like terms. As we can see, there are two like terms—Negative y and -2y—in this situation that can be joined. The similar terms' coefficients, which are -1 and -2, can be added. The total is y-3.

Negative (negative x) is equal to negative x, according to Fact e. We can see that Negative 5 x is Negative (negative x) in this situation and can be reduced to Negative 6 x.

Therefore, Negative 6 x -3 y + 3 z would be the abbreviated expression.

Due to the fact that fact C's computation does not use the same simplified formulation as the other facts, it is important to note that fact C is incorrect.

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IQ scores are normally distributed with mean mu equals 100 and standard deviation sigma equals 15. the standard deviation of the sampling distribution is 3.

Generally, The standard deviation of the sampling distribution, also known as the standard error, can be calculated using the formula:

standard error = (standard deviation of population) / (sqrt(sample size)).

In this case, the standard deviation of the population is 15, and the sample size is 25. So the standard error would be:

15 / sqrt(25) = 15 / 5 = 3

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Answer:

-18

Step-by-step explanation:

-3-15=-18

The expression that is different from "Add −4.5 and 3.5" will be "What is the distance between negative 4 point 5 and 3 point 5?"

An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator

In this case, the expression that is different from "Add −4.5 and 3.5" will be "What is the distance between negative 4 point 5 and 3 point 5?" This is because finding the distance simply means:

= -4.5 - 3.5

= -8.0

This is different from the initial value.

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Answer: 4.5

Step-by-step explanation: Those bars are absolute value. Hope it helps, please mark brainliest and give your thanks.

The proportion for y is the value 6.9 to the nearest tenth value.

Proportions are defined as the concept where two or more ratios are set to be equal to each other.

Suppose we have two ratio p : q and r : s. If both these ratios are proportional, then we can write it as p: q : : r : s.

This is same as p : q = r : s or p/q = r/s

Given the proportional relation,

11 / y = 8 / 5

Doing the cross multiplication,

11 × 5 = 8y

55 = 8y

8y = 55

y = 6.875

To the nearest tenth, the value is 6.9.

Hence the y value to the nearest tenth is 6.9

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Answer:

6p + 3s = 500

p + s = 120

Step-by-step explanation:

p represents the parents and s represents the students

the total amount of tickets should be p and s, hence why they equal 120

The total cost should be 500, and each parent ticket is $6 while each student ticket is $3 hence the 6p and 3s

Answer:

Out of all possible choices you've shown, I'd say the best answer would be A

Step-by-step explanation:

No, because the data values are the time spend in training, and are not points in time. (Option - A is correct )

Weather records, economic indicators and patient health evolution metrics — all are time series data. Time series data could also be server metrics, application performance monitoring, network data, sensor data, events, clicks and many other types of analytics data.

variance is NOT a time series component, it refers to the spread of a data set.

The three main types of time series models are moving average, exponential smoothing, and ARIMA. The crucial thing is to choose the right forecasting method as per the characteristics of the time series data.

y(t) = x(t)β + ε(t), where y(t) = {yt;t = 0,±1,±2,...} is a sequence, indexed by the time subscript t, which is a combination of an observable signal sequence x(t) = {xt} and an unobservable white-noise sequence ε(t) = {εt} of independently and identically distributed random variables.

Therefore,

No, because the data values are the time spend in training, and are not points in time. (Option - A is correct )

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Answer:

the growth factor of the initial amount is correct

Answer:

Option A or 1 or   |-11.2 -4.7|

Step-by-step explanation:

Calculate the distance :

distance =

| 4.7 - (- 11.2) | =

| 4.7 + 11.2 | =

| 15.9 | =

15.9.

Should help

Answer:

  |-11.2 -4.7|

Step-by-step explanation:

You want the expression that represents the distance between 4.7 and -11.2 on a number line.

The distance on a number line is the positive difference between the coordinates of the points. Here, that would be either of ...

  |4.7 -(-11.2)|

or

  |-11.2 -4.7| . . . . . . matches an answer choice

__

Additional comment

Note that when we subtract the left coordinate from the right coordinate, the difference is already positive, so no absolute value function is needed.

The lines are perpendicular

What is slope-intercept?

The slope-intercept form of a linear equation is a way of writing the equation of a line in the form y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis).

the equation of a line in slope-intercept form is

y = mx + c ( m is the slope and c the y- intercept )

3x + 5y = 10 ( subtract 3x from both sides )

5y = - 3x + 10 ( divide through by 5 )

y = -  x + 2 ← in slope- intercept form

with slope m = -

---------------------------

5x - 3y = - 6 ( subtract 5x from both sides )

- 3y = - 5x - 6 ( divide through by - 3 )

y =  x + 2 ← in slope-intercept form

with slope m =

---------------------------

• Parallel lines have equal slopes

clearly, the lines are not parallel

• the product of the slopes of perpendicular lines equals - 1

-  ×  = - 1

thus the 2 lines are perpendicular to each other

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Answer:

27 cm^2

Step-by-step explanation:

The formula for finding area of trapezoid:

[tex] \frac{a + b}{2} \times h[/tex]

[tex] \frac{6 + 12}{2} \times 3 = 27[/tex]

So the answer is 27 cm^2