With similar triangles the corresponding angles are equal.

The negative weight for the ant hill shows that two weeks ago there was no dirt on the ant hill .

Pounds of dirt add by ants on ant hill each day = 5 pounds

Pounds of dirt on ant hill = 68 pounds

To determine the number of pounds of dirt on the ant hill two weeks ago,

Calculate the amount of dirt added each day for two weeks and subtract that from the current weight of the ant hill.

There are 7 days in a week, so the ants add 5 pounds of dirt each day for 2 weeks,

which is a total of 5 pounds/day × 14 days = 70 pounds.

Subtracting the 70 pounds of dirt added in the past two weeks from the current weight of 68 pounds, we get,

=  68 pounds - 70 pounds

= -2 pounds.

Therefore, negative weight for the ant hill it is concluded that there was no dirt on the ant hill two weeks ago.

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Answer:

D

Step-by-step explanation:

3*(-7)=(-21)

A constant function is a function that has the same output with different inputs.

The value of f(-7) for the function f(x) = 3 is 3.

A constant function is a function that has the same output with different inputs.

It is a function having the same value of range for different values of the domain.

Example: f(x) = 9

f(1) = 0

f(2) = 6

Domain = inputs = 1, 2

Range = outputs = 9

We have,

f(x) = 3

This is a constant function.

So any value of x will always give the output as 3.

f(-7) = 3.

Thus the value of f(-7) for the function f(x) = 3 is 3.

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Answer:

the first one i think

Step-by-step explanation:

-3 is the y-intercept and that i all i got, sorry :(

Answer:

Its the first one! <3

Answer: A = 55* or 55 degrees

Step-by-step explanation:

The interior angles of a triangle always have a sum of 180 degrees.

75 + 50 + x = 180

Solve for x

FInal answer: 55 degrees

hope i explained it :)

-Q->P is proved from the contrapositive of 1.-P->Q.

What is Contrapostive ?

In logic, the contrapositive of a conditional statement of the form "if A, then B" is a statement of the form "if not B, then not A".

Here is a possible formal proof of the contrapositive of 1.-P->Q, which is -Q->P:

-P->Q Premise

Assume -Q Assume for sub proof

Assume -P Assume for subproof

From 2 and 1, we have P Modus tollens (MT)

From 4, we have P and -P Conjunction (CONJ)

From 3 and 5, we have # Contradiction (CONTR)

From 3-6, we have -Q-># Conditional proof (CP)

From 2 and 7, we have P Proof by contradiction (PC)

From 2-8, we have -Q->P Conditional proof (CP)

Therefore, -Q->P is proved from the contrapositive of 1.-P->Q.

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The values of a, b, c are 152°, 28°, 152° respectively.

Angles around a point describes the sum of angles that can be arranged together so that they form a full turn.

The sum of angles at a point will give 360°.

This means that a + b + c + 28 = 360

c +28 = 180° ( angle on a straight line)

c = 180 -28

c = 152°

c = a( alternate angles are equal)

therefore the value of a = 152°

b = 28( alternate angles are equal)

therefore the value of b is 28

therefore the values of a, b, c are 152°, 28°, 152° respectively

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\( \huge\underline\mathcal{Answer \: -} \)

We know that ,

exterior angle equals sum of two interior opposite angles.

therefore ,

\(\bold{x + x + 14 = 136\degree} \\ \\ \longrightarrow \: 2x + 14 = 136\degree \\ \\ \longrightarrow \: 2x = 136\degree - 14 \\ \\ \longrightarrow \: 2x = 122\degree \\ \\ \longrightarrow \: x = \cancel\frac{122}{2} \\ \\ \longrightarrow\boxed{ \: x = 61\degree}\)

hence , the first option is correct.

hope helpful ! ;-;

Answer:

First find the last angle of the triangle.

180 - 136 = 44° (sum of angles on a straight line=180)

Form an equation with the unknown angles with the knowledge that sum of angles in a triangle add up to 180°.

x + (x + 14) + 44 = 180

Simplify and solve for x.

2x + 58 = 180

2x = 122

x = 61

Answer: 1

Step-by-step explanation:

Bc 1 is match of P

Answer:

p = 5/2

Step-by-step explanation:

The function rule is:

y = -x/2 + 3

Plugging 1 in as x, we have:

y = -1/2 + 3

y = 5/2

Diversity in People can be seen in terms of:

In terms of Ethnicity,  people from various ethnic traditions bring a rich tapestry of sophistications, traditions, and outlooks to society. Access to Healthcare: Ensuring all has access to value healthcare improves the health and comfort of individuals, offspring, and communities.

In terms of Gender, embracing neutral diversity helps promote equal time for all genders in various fields and fights feminine-based bias. : Providing access to instruction for all members of society, although socio-economic rank, etc.

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See text below

Now we make a table and mention two examples of diversity in people and two examples of common good in society

Answer:

D. All whole numbers less than or equal to 31

Step-by-step explanation:

The x value in this situation is the number of years after 1970 and until 2001.

This means that the domain will be the number of years after 1970 and until 2001.

Since the situation calculates the value of land in years after 1970, the domain will start at 0. Since it is until 2001, which is 31 years after 1970, the domain will go up to 31.

So, the domain will include all whole numbers less than or equal to 31.

The correct answer is D. All whole numbers less than or equal to 31

The domain of the function is a real number from 1971 to 2001. Then the correct option is B.

Exponential notation is the form of mathematical shorthand which allows us to write complicated expressions more succinctly. An exponent is a number or letter is called the base. It indicates that the base is to raise to a certain power. X is the base and n is the power.

The value of a piece of land in a town is increasing every year.

Its value, in dollars, in t years after 1970 and until 2001 can be modeled by the function

\(\rm y = 31, 000(1.001) ^ t\)

Then the domain of the function will be

All real numbers are greater than or equal to 1971 and less than or equal to 2001.

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The Area of the composite figure = area of the rectangle + area of the triangle = 148.5 cm².

The figure formed by the arrow can be decomposed into a rectangle and a triangle.

The area of the composite figure = area of the rectangle + area of the triangle.

Find the area of the rectangle:

Length = 12 cm

Width = 11 cm

Area of the rectangle = (length)(width) = (12)(11)

Area of the rectangle = 132 cm²

Find the area of the triangle

Base = 11 cm

Height = 15 - 12 = 3 cm

Area of the triangle = 1/2(b)(h) = 1/2(11)(3)

Area of the triangle = 16.5 cm²

Area of the composite figure = area of the rectangle + area of the triangle = 132 + 16.5 = 148.5 cm².

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Answer:

The answer is Multiplication.

Step-by-step explanation:

The coefficient of the x term in f(x) is 2, and the coefficient of the x term in g(x) is 2. When we add or subtract the two functions, the coefficient of the x term remains 2. However, when we multiply the two functions, the coefficient of the x term becomes 4. Therefore, multiplication results in the largest coefficient on the x term.

Here is the solution for each of the operations:

Addition: f(x) + g(x) = (2x −1) + (2x + 4) = 4x + 3

Subtraction: f(x) - g(x) = (2x −1) - (2x + 4) = -5

Multiplication: f(x) * g(x) = (2x −1) * (2x + 4) = 4x^2 + 6x - 4

As you can see, the coefficient of the x term in f(x) * g(x) is 4, which is larger than the coefficients of the x terms in f(x) + g(x) and f(x) - g(x). Therefore, multiplication results in the largest coefficient on the x term.

To calculate the reliability of the bank loan processing system with backup components, we can use the concept of series-parallel system reliability.

In the original system, the three components are connected in series. To calculate the overall reliability of the system, we multiply the reliabilities of the individual components:

R_system = R_1 * R_2 * R_3 = 0.82 * 0.991 * 0.98 ≈ 0.801

So, the reliability of the bank loan processing system without backup components is approximately 0.801.

Now, if each of the three components has a backup with a reliability of 0.80, we have a parallel configuration between the original components and their backups. In a parallel system, the overall reliability is calculated as 1 minus the product of the complement of individual reliabilities.

Let's calculate the reliability of each component with the backup:

R_1_with_backup = 1 - (1 - R_1) * (1 - 0.80) = 1 - (1 - 0.82) * (1 - 0.80) ≈ 0.984

R_2_with_backup = 1 - (1 - R_2) * (1 - 0.80) = 1 - (1 - 0.991) * (1 - 0.80) ≈ 0.9988

R_3_with_backup = 1 - (1 - R_3) * (1 - 0.80) = 1 - (1 - 0.98) * (1 - 0.80) ≈ 0.9992

Now, we calculate the overall reliability of the system with the backups:

R_system_with_backup = R_1_with_backup * R_2_with_backup * R_3_with_backup ≈ 0.984 * 0.9988 * 0.9992 ≈ 0.981

Therefore, the reliability of the bank loan processing system with backup components is approximately 0.981.

Comparing the two scenarios, we can see that introducing backup components with a reliability of 0.80 has improved the overall reliability of the system. The total reliability increased from 0.801 (without backups) to 0.981 (with backups). Having backup components in a parallel configuration provides redundancy and increases the system's ability to withstand failures, resulting in higher reliability.

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Step-by-step explanation:

i hope i have been useful buddy.

good luck ♥️♥️♥️♥️♥️.

Answer:

\(1\frac{1}{9}\)

Step-by-step explanation:

Given the following question:

\(1\frac{2}{3} \times\frac{2}{3}\)

In order to multiply the two, we have to convert the mixed number into a improper fraction and then multiply the numerator by the numerator, the denominator by the denominator.

\(1\frac{2}{3} =3\times1=3+2=\frac{5}{3}\)
\(\frac{5}{3} \times\frac{2}{3}\)
\(5\times2=10\)
\(3\times3=9\)
\(=\frac{10}{9}\)

Convert the improper fraction into a mixed number:

\(\frac{10}{9}\)
\(\frac{10}{9} =10\div9=1\frac{1}{9}\)
\(=1\frac{1}{9}\)

Your answer is "1 1/9."

Hope this helps.

Answer:

12m

Step-by-step explanation:

B. The set is linearly independent describe the set. Given vectors are,{[ 1], [-2], [0], [ 0]}{[-5] [ 6] [0] [-7]}{[ 0] [ 0] [0] [ 4]}

To determine if the set of vectors shown to the right is a basis for R3 or not. We can check the rank of the matrix which is obtained by placing the given vectors as column vectors of a matrix and then taking the transpose of that matrix.

Then check the rank of that matrix and compare it with the number of given vectors, if rank is same as the number of vectors given then it forms a basis for R3.

To check the linearly independence and span, we can obtain the echelon form of the matrix and compare the pivot and non-pivot columns of that matrix.If the number of pivot columns is equal to the number of vectors, then they are linearly independent otherwise linearly dependent.Let A be the matrix obtained by placing given vectors as its column vectors and taking transpose of it. i.e

\[A = \begin{bmatrix}1 & -5 & 0\\-2 & 6 & 0\\0 & 0 & 0\\0 & -7 & 4\end{bmatrix}\]Let us obtain the echelon form of the matrix A,\[A = \begin{bmatrix}1 & -5 & 0\\-2 & 6 & 0\\0 & 0 & 0\\0 & -7 & 4\end{bmatrix}\mathop{\xrightarrow{{R_2}+2{R_1}}}\begin{bmatrix}1 & -5 & 0\\0 & -4 & 0\\0 & 0 & 0\\0 & -7 & 4\end{bmatrix}\]\[\mathop{\xrightarrow{-\frac{1}{4}R_2}}\begin{bmatrix}1 & -5 & 0\\0 & 1 & 0\\0 & 0 & 0\\0 & -7 & 4\end{bmatrix}\mathop{\xrightarrow{{R_1}+5{R_2}}}\begin{bmatrix}1 & 0 & 0\\0 & 1 & 0\\0 & 0 & 0\\0 & -7 & 4\end{bmatrix}\]

As the rank of matrix A is 2 and we have 3 vectors in the given set, so the given vectors do not form a basis for R3.Also, we can see that the first two columns of echelon form matrix contain pivot elements and the last column does not have a pivot element. Therefore, we can say that the given set of vectors are linearly independent but they do not span R3. The given options are,

A. The set is a basis for R3 (False)

B. The set is linearly independent (True)

C. The set spans R3 (False)

D. None of the above are true (False) Hence, the correct options is (B).

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a) The derivative of the function g(t) = 40t + 27t^2 is g'(t) = 40 + 54t.

b) The second derivative of g(t) is g''(t) = 54.

c) Evaluating g'(8) and g''(8), we find g'(8) = 472 and g''(8) = 54. These values represent the rate of change and the rate of acceleration, respectively, in millions of dollars per year.

a) To find the derivative of g(t), we differentiate each term separately using the power rule for differentiation. The derivative of 40t is 40, and the derivative of 27t^2 is 2 * 27t = 54t. Thus, the derivative of g(t) = 40t + 27t^2 is g'(t) = 40 + 54t.

b) To find the second derivative, we differentiate g'(t) with respect to t. Since g'(t) = 40 + 54t, the derivative of 40 is 0, and the derivative of 54t is 54. Therefore, the second derivative of g(t) is g''(t) = 54.

c) To evaluate g'(8) and g''(8), we substitute t = 8 into the expressions for g'(t) and g''(t). Plugging in t = 8, we get g'(8) = 40 + 54(8) = 472. This value represents the rate of change of the GNP at t = 8 years.

Similarly, g''(8) = 54, which represents the rate of acceleration of the GNP at t = 8 years. Both g'(8) and g''(8) are measured in millions of dollars per year and provide insights into how the GNP is changing and accelerating at that specific time point.

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Answer:

Liam has 10/3 pizza

Step-by-step explanation:

step one:

given that Martin has 5/6 pizza and Liam has 4 times as much

we can solve for the amount of Liams Pizza by multiplying Martins pizza by 4 we have

step two:

=5/6*4

=20/6

we can reduce the fraction by dividing the numerator and denominator by 2

=10/3

Hence Liam has 10/3 pizza

The expected value of the square of the distance of the knight after 2016 moves is approximately 462.05.

The expected value of the square of the distance of the knight from the origin after n moves can be calculated using the following formula:

E(d²) = (1/8) * (2 * (E(d²) - 1) + 5)

where d is the distance from the origin, and E(d²) is the expected value of d².

Using this formula, the expected value of the square of the distance after 2016 moves can be calculated iteratively.

Starting with an initial estimate of E(d²), we can use the formula to calculate a better estimate in each iteration. This process can be repeated until the estimate converges to a value within a desired accuracy.

Using this approach, the expected value of the square of the distance after 2016 moves can be approximated to be 462.05.

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The number of one-to-one functions from a set with five elements to sets with one, two, three, four, and five elements are 1, 20, 60, 120, and 1, respectively.To answer this question, we need to use the concept of one-to-one functions.

A one-to-one function is a function where each element in the domain corresponds to a unique element in the range. In other words, no two elements in the domain can have the same image in the range.

Let's consider each case separately.

1. Set with one element: In this case, there is only one possible function since there is only one element in the range that needs to be mapped to.

2. Set with two elements: There are a total of 20 possible one-to-one functions from a set with five elements to a set with two elements. To see why, we can think of it as choosing two distinct elements from the domain to map to the two elements in the range. There are 5 choices for the first element, and 4 choices for the second element (since we can't choose the same element twice). So the total number of possible functions is 5 x 4 = 20.

3. Set with three elements: There are a total of 60 possible one-to-one functions from a set with five elements to a set with three elements. To see why, we can think of it as choosing three distinct elements from the domain to map to the three elements in the range. There are 5 choices for the first element, 4 choices for the second element, and 3 choices for the third element. So the total number of possible functions is 5 x 4 x 3 = 60.

4. Set with four elements: There are a total of 120 possible one-to-one functions from a set with five elements to a set with four elements. To see why, we can think of it as choosing four distinct elements from the domain to map to the four elements in the range. There are 5 choices for the first element, 4 choices for the second element, 3 choices for the third element, and 2 choices for the fourth element. So the total number of possible functions is 5 x 4 x 3 x 2 = 120.

5. Set with five elements: In this case, there is only one possible function since there are five elements in both the domain and the range, and every element in the domain must be mapped to a unique element in the range.

In summary, the number of one-to-one functions from a set with five elements to sets with one, two, three, four, and five elements are 1, 20, 60, 120, and 1, respectively.

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Answer:

-4

Step-by-step explanation:

Parallel lines have the same slope

If the green line has a slope of -4, then the red line has a slope of -4

Answer: 4

Step-by-step explanation:

Answer:

18.0 (use 18 if 18.0 is not an answer choice)

Step-by-step explanation:

15²+10²=225+100 = 325

√325 = 18.028 or 18.0 (use 18 if 18.0 is not an answer choice)

Answer:

the 2nd one

Step-by-step explanation:

all the other ones don't make 6

The hair color of the players on a tennis team would be considered nominal data. Therefore, the most appropriate answer is option (c): Nominal data.

In data classification, there are four main levels of measurement: nominal, ordinal, interval, and ratio. Nominal data is the lowest level of measurement and represents categories or labels that cannot be ranked or ordered. Hair color falls into this category as it represents different categories or labels such as blonde, brunette, red, etc. Nominal data does not have any inherent numerical value or order.

On the other hand, ordinal data represents categories that can be ordered or ranked but do not have a consistent interval between them. Interval and ratio data involve numerical values with a consistent interval and a true zero point, with ratio data having a meaningful zero point.

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The statements that are true to determine whether x=10 is unusually high number of defective items on the next run of 100 products are given by the following option:

I and III.

Unusual values in the normal distribution are found using the range rule of thumb, which states that if a value is more than two standard deviations from the mean, the measure is unusual.

The measures for the binomial distribution are given as follows:

The parameters for this problem are given as follows:

n = 100, p = 0.04.

Then the mean and the standard deviation are given as follows:

Thus the upper bound for usual values is of:

4 + 2 x 1.96 = 7.92.

Which is less than 10, hence 10 is an unusual measure and statement I is correct.

Statement III is also correct, as:

P(X >= 10) < 0.05.

While statement II is false, as we do not look at the exact measure, but an interval of measures.

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

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