Explain why 20 is not a square number.

Answer:

HYPOTHESIS

Step-by-step explanation:

Answer:

Step-by-step explanation:

Yes it does

10 and 15

Answer:

A. the independent and dependent variables are the number of miles and total fee (y = 2.8 + 3.5x)

B. the domain is 0 <= x <= 20 and  range is 2.8≤x≤20

Step-by-step explanation:

Answer:

Radius = 1.02493

Answer: C. y=1/5x+1

Step-by-step explanation:

The region is bounded by the x-axis x=0, x=2pi*/3 and y= 3sin(x/2)   is pi/3.

To find the area of region r, we first need to sketch the region on the x-y plane. From the given information, we know that the region is bounded by the x-axis, the line x=0, the line x=2pi/3, and the curve y=3sin(x/2). To sketch the curve, we can start by noting that sin(x/2) is a periodic function with period 2pi. This means that the curve will repeat itself every 2pi units on the x-axis. We can also note that sin(x/2) is non-negative for x in the interval [0, 2pi], which means that the curve will lie above the x-axis in this interval. To sketch the curve in the interval [0, 2pi/3], we can use the fact that sin(x/2) is increasing on this interval. This means that the curve will start at the point (0,0) and increase until it reaches its maximum value of 3sin(pi/6) = 3/2 at x=pi/3. The curve will then decrease until it reaches the x-axis at x=2pi/3.
Using this information, we can sketch the region r as a triangle with base 2pi/3 and height 3/2. The area of this triangle is given by:
area = 1/2 * base * height = 1/2 * (2pi/3) * (3/2) = pi/3
Therefore, the area of region r is pi/3.

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The first and the third statements are false and second and fourth statements are true. The solution has been obtained by using arithmetic operations.

What are arithmetic operations?

Any real number can be represented using one of four basic mathematical operations, which are as follows:

1. The addition operator ('+') is used to calculate the sum of the numbers.

2. Using the "-" sign to subtract, which yields the difference between the integers.

3. When the result is the product of the numbers, multiply (×) it.

4. Division (÷), which results in the quotient of the numbers.

We are given that Jorge biked a total of 42 miles in 5 days.

The number of miles, m, Tim biked is represented by m = 8.75d for d days.

So, the number of miles, m, Tim biked in 5 days is

m = 8.75(5)

m = 43.75

Statement 1: Jorge biked more miles per day than Tim biked.

Miles per day of Jorge = 42/5 = 8.4 miles

Miles per day of Tim = 8.75 miles

The statement is false because Tim biked more miles per day than Jorge.

Statement 2: The difference between the number of miles jorge and Tim biked is 0.35 mile per day.

Difference = 8.75 - 8.4 = 0.35 miles

So, the statement is true.

Statement 3: In 5 days, the difference between the number of miles Jorge and Tim biked is 1.25 miles.

Difference = 43.75 - 42 = 1.75 miles

So, the statement is false.

Statement 4: In 7 days, the difference between the number of miles Jorge and Tim would bike would be 2.45 miles.

Miles biked in 7 days by Jorge = 8.4*7 = 58.8 miles

Miles biked in 7 days by Tim = 8.75*7 = 61.25 miles

Difference = 61.25 - 58.8 = 2.45 miles

So, the statement is true.

Hence, the first and the third statements are false and second and fourth statements are true.

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Answer:

2,1,4,3,6,5,8,7

Step-by-step explanation:

Given:

2,1,4,3,6,5,8,___

Pairing the sequence in twos

2,1

4,3

6,5

It can be seen that each pair of the sequence is arranged in descending order (from highest to lowest)

1, 2 is written as 2,1

3, 4 is written as 4,3

5, 6 is written as 6, 5

Then the next two numbers

7, 8 will be written as 8,7

2,1,4,3,6,5,8,7

a.)Gross pay = $400

b.) Total deductions = $89.25

c .) Net pay = $310.75

For question a.) The gross pay of Omark is calculated as thus:

The number of days per week = 7 days

The of working hours per week = 50 hours.

The amount paid per hour = $10

Therefore gross payment for a week = 40×10 = $400

For question b.)

The total deductions = 9.25+15.25+48.50+9.50+2.75+4.00 = $89.25

For question c )

Omark net payment = gross payment - total deductions = 400- 89.25 = $310.75

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The projected error of this sample would be an understatement of $2,000.

Hence, the correct option is A.

Step 1. In a probability-proportional-to-size sample, the projected error can be determined by calculating the difference between the recorded amount and the audit amount, and then scaling it up to the population using the sampling interval.

Step 2. Given:

Sampling interval = $5,000

Recorded amount = $10,000

Audit amount = $8,000

Step 3. Projected error = (Audit amount - Recorded amount) * (Population size / Sample size)

Step 4. In this case, since it is mentioned that this is the only error discovered by the auditor, the sample size can be assumed to be 1.

Projected error = ($8,000 - $10,000) * (Population size / 1)

Step 5. Since the error is the difference between the recorded amount and the audit amount, and the audit amount is lower than the recorded amount, it indicates an understatement.

Therefore, the projected error of this sample would be an understatement of $2,000.

Hence, the correct option is A.

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Answer:

$2.50

Step-by-step explanation:

Answer:

$25 per ft2

Step-by-step explanation:

you have to calculate the area  (20x8=160sq ft) and then get 4000/160 which is $25.

Dr. Feng's test lacks reliability.

Given,

Dr. Feng devises a questionnaire to measure adults' extraversion, a stable personality trait. Dr. Feng computes the questionnaire scores of a large sample of adults. six months later, he gives the same sample and the same test. the correlation between the two sets of scores is 0.10.

Now,

We can conclude regarding Dr. Feng's test,

The test lacks reliability.

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Answer:

9.44444

Step-by-step explanation:

Answer:

two red chips and one blue would equal 15, three red chips and two blue would equal 26

Step-by-step explanation:

The value of sin(A+B) is 32/25. We can use the trigonometric identities to find the value of sin(A+B). First, we need to determine the value of cos(B) using the given information about sin(B) and the quadrant of angle B.

Since sin(B) is negative and B is in Quadrant III, we can deduce that cos(B) must be positive. Using the Pythagorean identity sin^2(B) + cos^2(B) = 1, we can find cos(B) as follows:

sin^2(B) + cos^2(B) = 1

(-24/25)^2 + cos^2(B) = 1

576/625 + cos^2(B) = 1

cos^2(B) = 1 - 576/625

cos^2(B) = 49/625

cos(B) = √(49/625) = 7/25

Next, we can use the sum-to-product identity for sine:

sin(A + B) = sin(A) * cos(B) + cos(A) * sin(B)

Substituting the given values:

sin(A + B) = (−4/5) * (7/25) + (−24/25) * (−4/5)

sin(A + B) = −28/125 + 96/125

sin(A + B) = 68/125

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Answer:

−2.

Step-by-step explanation:

y = 4 − 2x? b is the y -intercept. Here, 4 is b and −2 is m. Therefore, the slope is −2.

There were 60 jelly beans in the unopened bag of jelly beans.

Let's work through the problem step by step to find the original number of jelly beans in the bag.

John ate three-fourths of the jelly beans.

This means that he consumed 3/4 of the total number of jelly beans, leaving 1/4 of the original amount.

Mike then ate two-thirds of the remaining jelly beans.

Since 1/4 of the original amount was left after John, Mike ate 2/3 of this remaining 1/4.

To find out how much is left, we need to calculate \((\frac{1}{4} )\times (\frac{2}{3} )\).

\((\frac{1}{4} )\times(\frac{2}{3} )=\frac{2}{12} =\frac{1}{6}\)

Mike ate 1/6 of the original amount, leaving 1/6 of the original amount.

Finally, Fred ate the ten jelly beans that were left.

We know that these ten jelly beans represent 1/6 of the original amount.

Let's calculate how many jelly beans are equal to 1/6.

\(\frac{1}{6} = 10\) jelly beans

Now, we can determine how many jelly beans are equal to 6/6 (the whole).

\(\frac{1}{6} \times6=10\times6=60\) jelly beans

Therefore, there were 60 jelly beans in the unopened bag of jelly beans.

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Answer:

x≤2

Step-by-step explanation:

-6(4 - x) ≤-4(x + 1)

Distribute

-24 +6x≤ -4x-4

Add 4x to each side

-24 +6x+4x≤-4x-4+4x

-24 +10x≤ -4

add 24 to each side

-24+10x+24≤-4+24

10x≤20

Divide by 10

10x/10 ≤20/10

x≤2

Answer:

D. x ≤ 2

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Distributive Property

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

-6(4 - x) ≤ -4(x + 1)

Step 2: Solve for x

Answer:

Explanation:

A number is said to be in standard form when it is written as a product of a number between 1 and 10 and a power of 10.

The given length is:

This number is already in standard form.

Answer:

x + 2

Step-by-step explanation:

An algebraic expression is an expression made of algebraic operations, variables, and constants that are integers. Algebraic expressions DO NOT have an equal or inequality sign.

Since options 2-4 have either an equal or inequality sign, option A, x + 2, is the correct answer.

Answer:

300 students

Step-by-step explanation:

We can infer from the information given that 35% = 105 students. To find 100%, we can first find 5%, divide 105 by 7. 105 ÷ 7 = 15. We can now multiply by 20 to get 100%; 15 × 20 = 300.

Answer: 300 students

Hope this helps!

The area of rectangle ABCD would be,

⇒ Area = 6x² + 15x

Since, A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Since, We have to given that;

In a rectangle,

Lenght of rectangle (L)= 3x

And, Width of rectangle (B) = (2x + 5)

We know that;

Area of rectangle is,

⇒ A = length x width

Substitute given values, we get;

⇒ A = 3x (2x + 5)

Multiply we get;

⇒ A = 3x × 2x + 3x × 5

⇒ A = 6x² + 15x

Therefore, The area of rectangle ABCD would be,

⇒ Area = 6x² + 15x

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The value is 24 square units is parallel to the face of the right rectangular prism.

We can see that the face of the given rectangular prism shows a width 4 and a height of 6. If we cut the figure at any point along the length 20, such that the cross-section is parallel to the face, the cross-section, which occurs at x length, will always have the same dimensions, which are 4 and 6.

So the area of the cross-section which is parallel to the face of the given rectangular prism is given by:

A = 6 × 4

A = 24

Thus, the value is 24 square units is parallel to the face of the right rectangular prism.

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A = 6 × 4

A = 24

Thus, the value is 24 square units is parallel to the face of the right rectangular prism.

The expected loss without the generator ($495,000) is less than the cost of installing the generator ($800,000), it would not be economically justifiable for the bank to install the new power generator based on this decision tree analysis.

The management of First American Bank faces a decision regarding the installation of an emergency power generator to mitigate potential losses from physical catastrophes such as power failures or fires.

To evaluate this decision, we can use decision tree analysis.

Without the generator, there is a 10% chance of a power outage. In the event of an outage, there is a 0.05 probability of very large losses ($80 million) and a 0.95 probability of slight losses ($1 million). To calculate the expected loss from not installing the generator, we can use the following formula:

Expected loss = (probability of outage) x [(probability of large loss x large loss amount) + (probability of slight loss x slight loss amount)]

Expected loss = 0.1 x [(0.05 x $80 million) + (0.95 x $1 million)]
Expected loss = 0.1 x [$4 million + $950,000]
Expected loss = 0.1 x $4.95 million
Expected loss = $495,000

Now let's compare this expected loss to the cost of installing the emergency power generator, which is $800,000. Since the expected loss without the generator ($495,000) is less than the cost of installing the generator ($800,000), it would not be economically justifiable for the bank to install the new power generator based on this decision tree analysis.

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While implementing the bubble sort algorithm, the maximum number of comparisons that can take place for n elements are \(\frac{n(n -1)}{2}\)

When an array or list of items has to be rearranged, a sorting algorithm is used to compare the elements and sort the elements in the array or list. In each data structure, the new order of the items is determined using the comparison operator.

The simplest sorting method is called Bubble Sort, and it involves periodically exchanging nearby components if they are arranged incorrectly. Since the average and worst-case time complexity of this approach is relatively high, it is not appropriate for huge data sets.

According to the condition the maximum number of comparison can be found as follows:

Number of elemnts = n

Number of passes required by bubble sort of n elements will be = n-1

Therefore for the maximum number of comparisons that can take place for n elements will be = \(\frac{n(n -1)}{2}\)

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The  two ways to compute the bill we can either calculate the cost of sandwiches and drinks separately and then add them, or calculate the cost of one friend's order and multiply it by the number of friends. The property of real numbers known as the distributive property.

To compute the bill for the five friends at the restaurant, there are two ways we can approach it.

Firstly, we can multiply the cost of one sandwich by the number of friends, and then add the cost of one drink multiplied by the number of friends.

Let's say each sandwich costs $5 and each drink costs $2.

Total cost of sandwiches = $5 x 5 = $25
Total cost of drinks = $2 x 5 = $10
Total bill = $25 + $10 = $35

Secondly, we can calculate the total cost of one friend's order (sandwich + drink), and then multiply it by the number of friends.

Total cost of one friend's order = $5 (sandwich) + $2 (drink) = $7
Total bill = $7 x 5 = $35

Both methods yield the same result, illustrating the property of real numbers known as the distributive property.

This property states that when multiplying a number by a sum, we can distribute the multiplication to each term in the sum. In this case, we distributed the multiplication to each friend's order, resulting in the same total bill.

In summary, to compute the bill for the five friends, we can either calculate the cost of sandwiches and drinks separately and then add them, or calculate the cost of one friend's order and multiply it by the number of friends. Both methods illustrate the distributive property of real numbers.

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Answer:a = 9 r^2

Step-by-step explanation:

We need to make a subject of the formula given r = square root a / 3

Given r = √a / 3 -------------1

Now we can find a.

Squaring the given equation 1 we get

So r^2 = (√a / 3)^2

So r^2 = a / 9

The equation for the line with a slope of 2 and a y-intercept of 8 is y = 2x + 8.

The equation of a line can be written in the form y = mx + b, where m represents the slope of the line and b represents the y-intercept. In this case, the given slope is 2, which means that for every unit increase in x, the corresponding y-value increases by 2 units. The y-intercept is 8, which is the value of y when x is equal to 0. By substituting these values into the equation, we get y = 2x + 8.

This equation represents a line that has a slope of 2, indicating that the line is increasing at a constant rate. The y-intercept of 8 means that the line intersects the y-axis at the point (0, 8). By plotting points on this line, we can observe that for every unit increase in x, the corresponding y-value increases by 2 units. For example, when x = 1, y = 2(1) + 8 = 10, and when x = 2, y = 2(2) + 8 = 12. This linear equation can be used to determine the y-values for any given x-value and can help represent various real-world scenarios or mathematical relationships.

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Explanation:

We replace every copy of x with -2. From there, use PEMDAS to simplify

y = 3x^2 + 17

y = 3(-2)^2 + 17

y = 3(4) + 17

y = 12 + 17

y = 29

Therefore, x = -2 pairs up with y = 29.

Put another way, the point (x,y) = (-2, 29) is on the function curve.