Find the area of a rectangular blackboard whose length and breadth are 120 cm and 100 cm, respectively.​

The lower bound for the function f(n) = 4n^3 + 2n^2 + n is Ω(n^3).


To find the lower bound, we need to determine the term with the highest growth rate in the function f(n). In this case, the highest growth rate is determined by the cubic term 4n^3. The other terms, 2n^2 and n, have a lower growth rate, and therefore, their impact on the overall growth of the function becomes less significant as n increases.

As a result, we can say that the lower bound for the function f(n) is dominated by the cubic term 4n^3, which means that the function f(n) grows at least as fast as Ω(n^3).


The lower bound for the function f(n) = 4n^3 + 2n^2 + n is Ω(n^3). This means that the function grows at least as fast as a cubic function, and the other terms have a lesser impact on the overall growth rate as n increases.

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Answer:

$2.93

Step-by-step explanation:

Divide 58.65 by 20 and you get your answer :)

Option C best describes the limiting values of T and a under the conditions given. In this case, T represents tension and a represents acceleration.

Without the specific conditions mentioned, it is impossible to determine the exact limiting values of T and a. However, certain options can be ruled out based on common sense and physical laws. For example, option C (T=mg and a=0) is not possible as the tension in a string cannot be equal to the weight of an object. Option E (T=0 and a=[infinity]) is also not possible as a mass cannot have zero tension and infinite acceleration.

Based on these eliminations, the most reasonable options are A (T=0 and a=0) and D (T=[infinity] and a=g). In the former case, the object is not moving and there is no tension in the string. In the latter case, the object is in free fall and the tension in the string is negligible compared to the weight of the object.

However, it is important to note that the exact limiting values of T and a will depend on the specific conditions of the scenario, such as the mass of the object and the angle of the string.

Option C best describes the limiting values of T and a under the conditions given. In this case, T represents tension and a represents acceleration. When T=mg and a=0, it means that the tension in the system is equal to the gravitational force acting on the mass (mg) and the system is in equilibrium with no acceleration. This is a common scenario when an object is hanging from a rope or cable and not moving. The other options do not represent stable or realistic conditions for a physical system.

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Geometrically, S represents a plane in ℝ^3 that is orthogonal (perpendicular) to the vector m.

To establish that S is a subspace of ℝ^3, we must confirm that S is closed under vector summation and scalar multiplication.

A pertinent theorem from linear algebra that can be applied here is the "Subspace Criterion" theorem. This principle states that a non-empty subset S of a vector space V is a subspace if and only if it fulfills the following conditions:

For any vectors a, b ∈ S, their addition a + b ∈ S.

For any vector a ∈ S and any scalar k, the product ka ∈ S.

Now, let's define a vector m = v - e.

Observe that for any y in S, we have:

m • y = (v - e) • y = (v • y) - (e • y) = 0.

This implies that y is orthogonal to the vector m.

Geometrically, S represents a plane in ℝ^3 that is orthogonal (perpendicular) to the vector m.

As the plane is closed under vector summation and scalar multiplication, S is indeed a subspace of ℝ^3.

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Suppose v = (2, 4, 5) and e = (6, 7, 3) are a pair of vectors in ℝ^3. Let S be the collection of all y in ℝ^3 such that the inner product of v and y equals the inner product of e and y (i.e., v • y = e • y).

What principle can be utilized to demonstrate that S is a subspace of ℝ^3? Describe S in geometric terms.

The n 1/2 of the se 1/4 of the sw 1/4 and the ne 1/4 of the sw 1/4 of Section 19 contains 40 acres.

The method used for land surveying is called the government rectangular survey system.

This system is commonly known as the Public Land Survey System (PLSS) of the United States. It is based on a grid network. The grid is formed with meridians and baselines.

The meridians are the imaginary lines running north to south, and the baselines are the imaginary lines running east to west. The meridians and baselines are named as ranges and townships, respectively.

Each range is 6 miles wide and numbered consecutively, beginning with the one on the far west side of the state. The townships are numbered from 1 to 36, in sequence, beginning at the southeast corner of the state. The government rectangular survey system divides the land into smaller units as follows:

Each township is further divided into 36 sections, each section is one square mile, or 640 acres.

Each section is further divided into halves, or 320 acres, and each half is divided into quarters, or 160 acres, and each quarter is divided into quarters again, or 40 acres.

Finally, each 40-acre parcel is divided into quarters, or 10 acres.

Therefore, the n 1/2 of the se 1/4 of the sw 1/4 and the ne 1/4 of the sw 1/4 of section 19 contains 40 acres.

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In a triangle one side that lies on an extended line segment,  statement about x is true, x = 62 because 147−85=62 and 85 + 62 = 147. So Option B is correct

In mathematics, the triangle is a type of polygon which has three sides and three vertices. the sum of all the interior angles of the triangle is 180°

Given that,

A triangle, which has one interior angle 85° and one exterior angle 147°

Another exterior angle x = ?

It is already known that,

Sum of complementary angles are 180

So,

⇒  Y + 147 = 180

⇒  Y  = 180 - 147

⇒  Y = 33

sum of all the interior angles of the triangle is 180°

X + Y + 85 = 180

X = 180 - 85 - 33

X = 62

Hence, the value of x is 62

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The dependent variable of interest in examining whether the degree of parental involvement differs based on students' grade in school is the degree of parental involvement.

In this scenario, the independent variable is the students' grade in school (i.e., first, second, third, etc.). The dependent variable is the variable that is expected to be influenced by the independent variable. In this case, the dependent variable of interest is the degree of parental involvement.

The degree of parental involvement refers to the level or extent to which parents are engaged in their child's education and school-related activities. It can encompass various aspects, such as attending parent-teacher meetings, volunteering at school, helping with homework, and participating in school events.

By examining whether the degree of parental involvement differs based on students' grade in school, researchers or educators aim to explore any potential patterns or differences in parental involvement as children progress through different grade levels. This investigation can provide insights into how parental involvement may vary across grade levels and inform strategies to enhance parental engagement in education at specific stages of a child's schooling. Thus, the dependent variable of interest is the degree of parental involvement.

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The binary expanded form of 19 is 1×2⁴ + 0×2³ + 0×2² +1×2¹ + 1×2⁰

To convert 19 to binary expanded form, we need to convert 19 into a base two number by dividing 19 by 2 and taking into the reminder. Thus:

Dividend   Remainder

19/2 = 9          1      ∧

9/2 = 4           1       |

4/2 = 2          0       |

2/2 = 1           0       |

1/2 = 0            1       |

Then we will write the remainder from bottom to top following the direction of the arrow. Thus, 19 in base 2 is:

19₁₀ = 10011₂

To write binary expanded form, multiply the binary number obtained by 2 and raise them to a power starting from 0 by counting from the right. That is:

19₁₀ = 1×2⁴ + 0×2³ + 0×2² +1×2¹ + 1×2⁰

Therefore, 19 in binary expanded form is 1×2⁴ + 0×2³ + 0×2² +1×2¹ + 1×2⁰

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Answer:

3/4 or 1/4 are easy ones

Step-by-step explanation:

For the professor's randomized controlled trial (RCT) to be valid, the following must be true: the average age of students in group B should be similar to group A, the average characteristics of the students in both groups should be statistically similar

In order for the professor's experiment to be a valid RCT, several conditions must be met. First, the average age of students in group B should be similar to group A, meaning that there should not be a significant statistical difference between the average ages of the two groups. While the actual average age may differ slightly, it should not be significantly different.

Second, the average characteristics of the students in both groups should be statistically similar. This ensures that any differences observed between the groups can be attributed to the treatment or intervention being tested, rather than inherent differences in the characteristics of the students.

Third, the professor must have randomly assigned students to the groups. Random assignment helps minimize selection bias and ensures that any differences observed between the groups are not due to systematic differences in the individuals assigned to each group.

Regarding the type of data collected in the RCT, the professor likely collected experimental data. An RCT involves intentionally manipulating an independent variable (in this case, group assignment) to observe its effect on a dependent variable (the outcome being measured). This differs from other types of data such as panel data (data collected from the same individuals over time), time series data (data collected over regular intervals), and observational data (data collected without intervention or control).

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A correlational result can be used to infer causality, but only if the value of r is greater than 0.

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Answer:

18

Step-by-step explanation:

an angle subtended by a chord to the center is twice to that subtended by the same chord to the circumference

The probability that all three selected students are boys is approximately 0.3929 or 39.29%.

To calculate the probability that all three selected students are boys, we need to consider the total number of possible outcomes and the number of favorable outcomes.

In this case, there are 12 boys and 4 girls in the class, making a total of 16 students. We want to select three students, and we want all three of them to be boys.

The total number of ways to select three students from the class is given by the combination formula, which can be represented as:

Total Possible Outcomes = nCr(16, 3) = (16!)/((16-3)! * 3!) = 560

Now, let's consider the number of favorable outcomes where all three selected students are boys. Since there are 12 boys, we can choose three of them using the combination formula:

Favorable Outcomes = nCr(12, 3) = (12!)/((12-3)! * 3!) = 220

Therefore, the probability that all three selected students are boys is:

Probability = Favorable Outcomes / Total Possible Outcomes = 220 / 560 ≈ 0.3929, or approximately 39.29%.

Hence, the probability that all three selected students are boys is approximately 0.3929 or 39.29%.

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The total cost of the siding material is given as follows:

B. $292.50.

To obtain the cost of material, the first step is obtaining the area that will be covered, which is given as follows:

The rectangular area of 8 feet by 24 feet will be covered, with these following exceptions:

The triangular area with base 24 feet and height 6 feet will also be covered.

Then the total area to be covered is given as follows:

Area = 8 x 24 - (2 x 6 x 4) - (3 x 7) + 0.5 x 24 x 6

Area = 195 ft².

The total cost is of $1.5 per ft², hence it is calculated as follows:

Total cost = 195 x 1.5 = $292.50.

Meaning that option B is correct.

The problem is given by the image shown at the end of the answer.

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Answer:

2m+3r-2x-2y

Step-by-step explanation:

2m+3r=2m+3r

-2×x=-2x

-2×y=-2y

answer=2m+3r-2x-2y

Answer:

  (a)  (3, -1)

Step-by-step explanation:

You want the graphical solution to the system ...

A graphing calculator plots these equations easily, and will give you the coordinates of the point where the lines intersect. That point is the solution to the system of equations:

  (x, y) = (3, -1)

__

Additional comment

Here, the offered choices are the y-intercepts (clearly wrong), and points in the first and fourth quadrants. You can choose the correct point by thinking about the x-intercepts.

The line with positive slope has an x-intercept of 7/2 = 3.5. For positive x-values less than this, the line is in the 4th quadrant.

The line with negative slope has an x-intercept of -8/-3 ≈ 2.7. For positive x-values greater than this, the line will be in the 4th quadrant.

The point of intersection must be in the 4th quadrant with an x-value between 2.7 and 3.5. Only one answer choice is like this: (3, -1).

The term that describes an event that increases the likelihood of a response being repeated is known as reinforcement.

Reinforcement can be defined as any consequence that strengthens or increases the probability of a behavior occurring again in the future. This can include positive reinforcement, which involves adding a desirable consequence after a behavior, or negative reinforcement, which involves removing an aversive consequence after a behavior. Both types of reinforcement have been shown to be effective in increasing the likelihood of a behavior being repeated.

Overall, understanding the concept of reinforcement is essential in the field of psychology, particularly in the areas of behaviorism and behavior modification. By providing positive consequences after desired behaviors, individuals can be motivated to continue engaging in those behaviors, which can lead to long-term positive changes. Reinforcement can also be used to shape new behaviors or replace unwanted behaviors with more desirable ones.

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Applying the properties of similar triangles, the other side lengths of ΔDEF are: B. 9 and 12

Properties of Similar Triangles:

Given that ΔABC and ΔDEF are similar triangles, therefore:

Thus:

a/x = b/y = c/z

6/x = 8/y = 12/18

Find x using 6/x = 12/18:

6/x = 12/18

x = \(\frac{18 \times 6}{12}\)

x = 9

Find x using 8/y = 12/18:

8/y = 12/18

x = \(\frac{18 \times 8}{12}\)

x = 12

Therefore, applying the properties of similar triangles, the other side lengths of ΔDEF are: B. 9 and 12

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Answer:

23 parts

Step-by-step explanation:

4 minutes 92 parts

1 minute 92/2 parts

= 23 parts

Answer:

$3.72

Step-by-step explanation:

7.75*2=15.5

15.5+0.78=16.28

20-16.28=3.72

The average sales quantities for the year before and after the given year, for all existing customer, product, quarter, and year combinations, have been computed.

To calculate the average sales quantities for the year before and after the given year, we need the following information: customer names, product names, quarters (1-4), and years. Let's assume we have a dataset containing this information.

1. Year before: To calculate the average sales quantity for the year before the given year, we subtract 1 from the given year and consider all customer, product, and quarter combinations for that year. We calculate the average sales quantity for each combination and store the results.

2. Year after: Similarly, to calculate the average sales quantity for the year after the given year, we add 1 to the given year and consider all customer, product, and quarter combinations for that year. We calculate the average sales quantity for each combination and store the results.

By following the above steps, we have computed the average sales quantities for the year before and after the given year, for all existing customer, product, quarter, and year combinations. This information can provide valuable insights into sales trends and help businesses make informed decisions regarding inventory management, customer targeting, and forecasting.

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A) The interval(s) on which f is increasing is; (1,3) ∪ (4,6).

B) The interval(s) on which f is decreasing is; (0,1) ∪ (3,4).

(C) The interval(s) on which f is concave upward is; (0,2) ∪ (3,5).

A) A function is said to be increasing on an interval if for every point on that interval we see that the first derivative is positive. Thus, from the attached graph, we see that the function is increasing on the intervals (1,3) and (4,6).

B) If the value of the derivative f' (x) ≤ 0 of the function, then we can say that the interval is a decreasing interval. From the graph, we can say that the function is decreasing on intervals (0,1) and (3,4).

C) The graph is concave upward on the intervals (0,2) and (3,5).

D) The graph is concave downward which means convex on the interval (3,4).

e) The points of inflection are defined as the points located on a smooth plane curve that the curvature changes sign. In this graph, the points of inflection are x=3 and x=5.

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The fractional equivalent of the repeating decimal 0.2 is 2/9

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

Repeating decimal = 0.2

Represent properly

So, we have

Repeating decimal = 0.2222

Express as fraction

So, we have

Fraction = 2/(10 - n)

In this case

n = 1

So, we have

Fraction = 2/(10 - 1)

Evaluate

Fraction = 2/9

Hence, the fractional equivalent is 2/9

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Answer:

7x

Step-by-step explanation:

We know

\(\boxed{\sf Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}}\)

ATQ

\(\\ \sf\longmapsto \sqrt{(-1-2)^2+(x+2)^2}=5\)

\(\\ \sf\longmapsto \sqrt{(-3)^2+x^2+4x+4}=5\)

\(\\ \sf\longmapsto \sqrt{9+x^2+4x+4}=5\)

\(\\ \sf\longmapsto \sqrt{x^2+4x+13}=5\)

\(\\ \sf\longmapsto x^2+4x+13=5^2=25\)

\(\\ \sf\longmapsto x^2+4x+13-25=0\)

\(\\ \sf\longmapsto x^2+4x-12=0\)

\(\\ \sf\longmapsto x^2+6x-2x-12=0\)

\(\\ \sf\longmapsto x(x+6)-2(x+6)=0\)

\(\\ \sf\longmapsto (x-2)(x+6)=0\)

\(\\ \sf\longmapsto x=2\:or\:x=-6\)

Answer:

$22.48 for 4 pairs of jeans is a better deal.

Step-by-step explanation:

To find the price of one pair of jeans, you divide.

39.55 ÷ 7 = price of 1 pair of jeans

39.55 ÷ 7 = $5.65

22.48 ÷ 4 = price of 1 pair of jeans

22.48 ÷ 4 = $5.62

The price difference between the two prices is 3 cents. So, $22.48 for 4 pairs is a better deal that $39.55 for 7 pairs of jeans.

Hope this helps!

Answer:

1/3

Step-by-step explanation:

differentiate first equation to get t , then replace t with 1/3

Answer:

-10/7

Step-by-step explanation:

Use slope formula

\(\frac{y2-y1} {x2-x1}\)

x1= -3

y1 = 5

x2 = 4

y2 = -5

\(\frac{-5-5}{4--3}\)

\(\frac{-10}{7}\)

Answer:

c = 80 ÷ 5

Or

5c = 80

Step-by-step explanation:

It's pretty self explanatory. All you have to do is convert the words into an equation.

The perpendicular linear equation that passes through (8, 2) is:

y = x - 6

A general linear equation is of the form:

y = m*x + b

Where m is the slope.

Two lines are perpendicular only if the product between the slopes is equal to -1.

Here we start with the line:

y = -x

So the slope is -1.

Then the slope of the perpendicular line m must be:

-1*m = -1

m = -1/-1 = 1

Then the perpendicular line is something like:

y = x + b

And we want this to pass through (8, 2), replacing these values we get:

2 = 8 + b

2 - 8 = b

-6  =b

The linear equation is:

y = x - 6

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