The smaller triangle is dilated to create the larger triangle. The center of
dilation is plotted, but not labeled

only option (c) satisfies the criteria of a probability distribution.

Among the options given, only (c) represents a probability distribution. A probability distribution is a function that assigns probabilities to each possible value of a random variable, ensuring that the probabilities sum to 1. In option (c), the random variable Z takes values 1, 2, 3, 4, and 5, and the corresponding probabilities assigned to these values are 0.1, 0.2, 0.3, 0.4, and 0.0, respectively. These probabilities satisfy the requirement that they sum to 1, making it a valid probability distribution.

In option (a), the random variable X has repeated values, which violates the requirement that each value should have a unique probability. For example, X takes the value 2 with a probability of 0.1 twice, which is not a valid probability distribution.

In option (b), the probabilities assigned to the values of the random variable Y are not non-negative, as there is a negative probability (-1.25). Negative probabilities are not allowed in probability distributions.

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To prove that if $S = \{v_1, v_2, \ldots, v_n\}$ is a basis for a vector space $V$ and $c$ is a nonzero scalar, then the set $S_1 = \{cv_1, cv_2, \ldots, cv_n\}$ is also a basis for $V$, we need to show two things:

1. $S_1$ spans $V$: Every vector in $V$ can be expressed as a linear combination of vectors in $S_1$.

2. $S_1$ is linearly independent: The only way to obtain the zero vector by forming a linear combination of vectors in $S_1$ is by setting all the scalars to zero.

Proof:

1. $S_1$ spans $V$:

Let $v$ be an arbitrary vector in $V$. Since $S$ is a basis for $V$, $v$ can be expressed as a linear combination of vectors in $S$. Therefore, there exist scalars $a_1, a_2, \ldots, a_n$ such that:

\(\sf\:v = a_1v_1 + a_2v_2 + \ldots + a_nv_n \\\)

Now, consider the vector $cv$:

\(\sf\:cv = c(a_1v_1 + a_2v_2 + \ldots + a_nv_n) = a_1(cv_1) + a_2(cv_2) + \ldots + a_n(cv_n) \\\)

Thus, $cv$ can be expressed as a linear combination of vectors in $S_1$. This shows that $S_1$ spans $V$.

2. $S_1$ is linearly independent:

To show that $S_1$ is linearly independent, we need to prove that the only solution to the equation:

\(\sf\:x_1(cv_1) + x_2(cv_2) + \ldots + x_n(cv_n) = 0 \\\)

is $x_1 = x_2 = \ldots = x_n = 0$. Suppose there exists a nontrivial solution to the equation, where at least one $x_i$ is nonzero. Without loss of generality, assume $x_1 \neq 0$. Then we have:

\(\sf\:x_1(cv_1) + x_2(cv_2) + \ldots + x_n(cv_n) = x_1(cv_1) + 0 + \ldots + 0 = cx_1v_1 \\\)

Since $c$ is a nonzero scalar, and $x_1 \neq 0$, we have $cx_1v_1 \neq 0$. However, the equation states that the left side is equal to $0$, which contradicts the assumption. Therefore, the only solution to the equation is $x_1 = x_2 = \ldots = x_n = 0$, confirming that $S_1$ is linearly independent.

Based on the above proofs, we can conclude that if $S = \{v_1, v_2, \ldots, v_n\}$ is a basis for a vector space $V$ and $c$ is a nonzero scalar, then the set $S_1 = \{cv_1, cv_2, \ldots, cv_n\}$ is also a basis for $V$.

Answer: -(-3)

Step-by-step explanation:

a double negative would equal to a positive :)

Using the information provided in the table, The total holding cost is  $547.50, the total setup cost is $600 and the total cost is  $1,147.50.

To develop a POQ (Periodic Order Quantity) solution use a lot-for-lot solution, which means that we will order exactly what we need for each period.

The missing values can be found on the attached table.

From the table, the total holding cost which is the sum of the holding costs for all periods is $547.50 while the total setup cost which is the sum of the setup costs for all periods is $600.

Therefore, the total cost is the sum of the holding cost and the setup cost and it is calculated as $1,147.50.

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Yes , the integer k is divisible by 4 and statement (1) alone is sufficient to determine that k is divisible by 4.

Given data ,

Let the equation be represented as A

Now , the value of A is

a)

To determine if the integer k is divisible by 4, let's analyze the given statements:

Statement (1): 8k is divisible by 16.

This means that 8k is a multiple of 16. Since 16 is divisible by 4, we can conclude that k must be divisible by 4 as well. Therefore, statement (1) alone is sufficient to determine that k is divisible by 4.

8k = 16

k = 2

b)

This statement does not provide direct information about the divisibility of k by 4. While 12 is divisible by 4, the fact that 9k is divisible by 12 does not guarantee that k itself is divisible by 4.

9k = 12

k = 12/9

k = 4/3

So , it is not an integer

In conclusion, statement (1) alone is sufficient to determine that k is divisible by 4. Statement (2) is not sufficient on its own.

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Answer:

dude its 1

Step-by-step explanation:

Select all that apply

Question options :

The median height of the sample must be between 59 and 63 inches.

Another random sample of 20 trees is likely to have a mean between 57 and 65 inches.

The mean height of these 20 trees is likely to be the same as the mean height of all trees in the back field .

The mean height of these 20 trees is likely to be the same as the mean height of a second random sample of 20 trees.

Shawn would be more likely to get an accurate estimate of the mean height of the population by sampling 40 trees instead of sampling 20 trees.

Answer:

The median height of the sample must be between 59 and 63 inches.

The mean height of these 20 trees is likely to be the same as the mean height of all trees in the back field .

The mean height of these 20 trees is likely to be the same as the mean height of a second random sample of 20 trees.

Shawn would be more likely to get an accurate estimate of the mean height of the population by sampling 40 trees instead of sampling 20 trees

Explanation:

The mean absolute deviation is the summary of absolute deviations from the central point or average of a data set. The central point measurement can be the mean, median or mode of the data set. An average absolute deviation can be used instead of a standard deviation to measure dispersion from central point.

In the above case, a sample is taken of 20 trees and there is a mean absolute deviation of 2, hence, median can be between 59 and 63. Also sample represents population, therefore mean of another sample taken is likely to be same as the previous one taken. Mean invariably gets more accurate as sample size increases too.

The type of correlation not associated with scatterplots is called; an indefinite correlation

Correlation is also called dependence and is defined as any statistical relationship, whether causal or not, between two random variables or bivariate data.

Correlation can only be between -1 and 1 but not outside these values.

The types of correlation that we have to include:

no correlation

positive correlation

negative correlation

Hence the type of correlation not associated with scatterplots is an indefinite correlation

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Complete question is;

Which of the following is not a type of correlation associated with scatterplots?

A. no correlation

B. positive correlation

C. negative correlation

D. indefinite correlation

Answer:

Below

Step-by-step explanation:

.014 g / .0022 cm^3   = 6.364  gm / cc   = 6364 kg/m^3

    density is too low to be pure gold  

Answer: 1,000,000,000

Answer:

x<-3

Step-by-step explanation

2x+5<x-1/4

in x-1/4 you should remove 4 so you should multiply 4 from both side

8x+20<x-1

subtract x from both side

8x-x<-1-20

7x<-21

divided by 7 from both side

x<-3 answer is x<-3

The possible rational zeros are:  ±1/1, ±2/1, ±3/1, ±4/1, ±6/1, ±8/1, ±12/1, ±24/1, ±1/2, ±2/2, ±3/2, ±4/2, ±6/2, ±8/2, ±12/2, ±24/2, which can be simplified as follows:  ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24, ±1/2, ±2, ±3/2, ±4, ±6, ±8, ±12, ±24.

To find the list of all possible rational zeros of the given function f(x) = 2x⁴ + x³ - 12x² + 2x + 24, you need to apply the Rational Root Theorem. The Rational Root Theorem states that if a polynomial equation has integer coefficients, then any rational zero of the equation must have a numerator that is a factor of the constant term and a denominator that is a factor of the leading coefficient of the polynomial.

Using this theorem, we can obtain the list of all possible rational zeros of the given function by finding all the possible combinations of factors of 24 (constant term) and 2 (leading coefficient).The possible factors of 24 are ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24.The possible factors of 2 are ±1, ±2.So,

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Answer:

the 4th and 6th one

Step-by-step explanation:

A function is when there are x- and y-values but each x value has only 1      y-value

Simple: If the x-value is repeated its not a function

Answer:

Step-by-step explanation:

1,2,3

The answer to the given question is the angular acceleration of the wheel is 0.7742 rad/s².

We can use the formula for rotational dynamics:

τ = Iα

where τ is the torque applied, I is the moment of inertia, and α is the angular acceleration.

Rearranging this equation, we get:

α = τ / I

Plugging in the given values, we have:

α = 48 Nm / 62 kg⋅m²

Simplifying, we get:

α = 0.7742 rad/s²

Rotational dynamics deals with the motion of objects that are rotating around an axis. The key concept in rotational dynamics is torque, which is a measure of how much a force can cause an object to rotate. The moment of inertia is another important quantity in rotational dynamics, and it describes an object's resistance to rotational motion. The moment of inertia depends on the distribution of mass around the axis of rotation. The angular acceleration of a rotating object is directly proportional to the torque applied and inversely proportional to the moment of inertia. Therefore, a greater torque or a smaller moment of inertia will result in a greater angular acceleration. These concepts are used in a variety of applications, from the motion of planets to the operation of engines and turbines.

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Answer:

true

Step-by-step explanation:

if you rewrite \(sec\left(\frac{\pi }{2}\:-x\right)\) with trigonometric identities:

\(sec\left(\frac{\pi }{2}\:-x\right)\)    \(=\frac{1}{\sin \left(x\right)}\)

\(\frac{1}{\sin \left(x\right)}\)  \(=\csc \left(x\right)\)

so, yes,  \(sec\left(\frac{\pi }{2}\:-x\right)\)  \(=\csc \left(x\right)\)

hope this helps!!

The set of vectors {x, cos(x)} is linearly independent as per the concept of linearity of vectors.

To determine if the set of vectors {x, cos(x)} in F(-∞, ∞) is linearly dependent, we need to check if there exist scalars c1 and c2, not all zero, such that c1x + c2cos(x) = 0 for all values of x in the given interval.

Let's consider a specific value of x, say x = 0.

Plugging this value into the equation, we have c1(0) + c2cos(0) = 0. Since cos(0) = 1, the equation simplifies to c2 = 0.

Now, considering another specific value of x, say x = π/2, we have c1(π/2) + c2cos(π/2) = 0. Again, cos(π/2) = 0, so the equation simplifies to c1(π/2) = 0. This implies that c1 = 0.

Since c1 = c2 = 0, the only solution to the equation c1x + c2cos(x) = 0 for all x in F(-∞, ∞) is the trivial solution. Therefore, the set of vectors {x, cos(x)} is linearly independent.

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The complete question:

By using appropriate identities, where required, determine which of the following sets of vectors in F(-∞, ∞) are linearly dependent.

a. x, cosx

Using the law of cosines, it is found that the measure of angle Y is of 64º.

The problem is incomplete, hence we research it on a search engine, and we have that we have a triangle in which:

The law of cosines states that we can find the side c of a triangle as follows:

c² = a² + b² - 2abcos(C)

In which:

For this problem, the parameters are given as follows:

a = 12, b = 17, c = 16, C = Y.

Hence:

c² = a² + b² - 2abcos(Y)

16² = 12² + 17² - 2(12)(17)cos(Y)

408cos(Y) = 177

cos(Y) = 177/408

Y = arccos(177/408)

Y = 64º.

The measure of angle Y is of 64º.

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If the perimeter of the parallelogram is 102 feet, then the value of m is 12.75

The perimeter of the parallelogram = 102 feet

The perimeter of the parallelogram = 2(l + w)

Where l is the length and w is the width of the parallelogram

The length of the parallelogram = 3m

The width of the parallelogram = m

Substitute the values in the equation of the perimeter

102 = 2(3m + m)

102 = 2(4m)

102 = 8m

m = 102 / 8

Divide the terms

m = 12.75

Hence, if the perimeter of the parallelogram is 102 feet, then the value of m is 12.75

The complete question is:

The perimeter of the parallelogram is 102 feet. Find m. Write your answer as a decimal or mixed number.

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Answer:

y=mx+c

Step-by-step explanation:

noice

Answer:

Less than a right angle.

Step-by-step explanation:

If you really think about it, a right angle is 90 degrees, and from the looks of it, that angle shown is an acute angle. Acute angles are always smaller than a right angle, so your answer is less than a right angle. :)

Answer:

16 - 3x5

Step-by-step explanation:

In the expression -2x4+16+2x4+9-3x5

-2x4 will eliminate +2x4 so we have 16 - 3x5 these two are not like terms so we can't add or subtract them

Answer:

See below.

Step-by-step explanation:

\(-2x^4+16+2x^4+9-3x^5\)

A helpful thing to do is to rearrange them in descending order:

\(=-3x^5-2x^4+2x^4+16+9\)

We can see that the second and third term cancel. The fourth and fifth term are able to be added:

\(-3x^5+25\)

Note: If you're confused on why \(-2x^4+2x^4\) cancel, use the distributive property:

\(-2x^4+2x^4=x^4(-2+2)=x^4(0)=0\)

The probability that a salesperson selected at random will have an excellent potential for advancement given they have above average sales ability is 0.3.

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we might discuss the likelihood or likelihood of several outcomes. Statistics is the study of occurrences that follow a probability distribution. Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has included probability to forecast the likelihood of certain events. Information about the possibility that something will happen is provided by probability. For instance, meteorologists utilize weather patterns to forecast the likelihood of rain. Probability theory is used in epidemiology to comprehend the connection between exposures and the risk of health effects.

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Time taken by Matilda on each project is \(5\frac{7}{12}\) hours.

According to the question we have been given that,

Total time taken by Matilda to complete the consulting projects = \(16\frac{3}{4}\) hours

First we will convert it into simple fraction which is

         \(16\frac{3}{4} = \frac{67}{4} \\\) hours

Number of consulting projects = 3

And Matilda spends same amount of time to each of the project.

To find the time she spend on each project is by using unitary method

that is,            3 projects = \(\frac{67}{4}\) hours

                      1 project = \(\frac{67}{4} / 3\)

                                     = 67/12

                                     = \(5\frac{7}{12}\) hours

Hence time taken by Matilda on each project is \(5\frac{7}{12}\) hours.

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Answer:

PAIN

Step-by-step explanation:

If f(x) is a linear function, then

f(x) = ax + b

for some constants a and b.

Given that f (1) = 4 and f (4) = 1, these constants are such that

f (1) = a + b = 4

f (4) = 4a + b = 1

Solve for a and b : eliminate b by subtracting the two equations,

(a + b) - (4a + b) = 4 - 1

-3a = 3

a = -1

Then

-1 + b = 4

b = 5

So we have

f(x) = -x + 5

Answer:

d)

Step-by-step explanation:

a - b = 10

a = 4 + 3b

The number of subs in the order is 8 or 9

Let's call the number of subs in the order "x".

Since the cost of 3 subs is $20, the cost per sub is $20 / 3 = $6.67.

And since the cost of 4 subs is $26, the cost per sub is $26 / 4 = $6.50.

So the cost per sub is between $6.50 and $6.67.

If the total cost is $56, then the cost per sub must be $56 / x.

So:

x = 56/6.5 or x = 56/6.67

Evalutate

x = 8.6 or x = 8.4

Approximate

x = 9 or 8

Hence, the subs is 8 to 9

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Answer:

H<18

Step-by-step explanation:

Step-by-step explanation:

the answer is number A for ur q