The coordinates of the endpoints of MP are
M(-3,-2) and P (2,3).
Which measurement is closest to the length of MP in
units?

Answer:

6x-5

Step-by-step explanation:

Alright let's begin.

6 times a number means 6 times x. So 6x.

Then when it says decreased by 5 it means you subtract 5!

Your expression would look like this:

6x-5

Hope it helps! Mark brainliest if possible

The sample space for the experiment of tossing a pair of dice consists of all possible outcomes of the two dice rolls. Using a rule method, we can represent the sample space as S = {(1,1), (1,2), (1,3), ..., (6,5), (6,6)}.

(a) The event A corresponds to the sum of the outcomes being greater than 8. The elements of event A are (3,6), (4,5), (4,6), (5,4), (5,5), (5,6), (6,3), (6,4), (6,5), (6,6).
(b) The event B corresponds to a 2 occurring on either die. The elements of event B are (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (1,2), (3,2), (4,2), (5,2), (6,2).
(c) The event C corresponds to a number greater than 4 appearing on the green die. The elements of event C are (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6).
(d) The event A∩C corresponds to the outcomes where both the sum is greater than 8 and a number greater than 4 appears on the green die. The elements of event A∩C are (5,4), (5,5), (5,6), (6,3), (6,4), (6,5), (6,6).
(e) The event A∩B corresponds to the outcomes where both the sum is greater than 8 and a 2 occurs on either die. There are no elements in this event.
(f) The event B∩C corresponds to the outcomes where both a 2 occurs on either die and a number greater than 4 appears on the green die. The elements of event B∩C are (5,2), (6,2).
(g) The Venn diagram illustrating the intersections and unions of the events A, B, and C would have three overlapping circles representing each event. The area where all three circles intersect represents the event A∩B∩C, which is empty in this case. The area where circles A and C intersect represents the event A∩C, and the area where circles B and C intersect represents the event B∩C. The unions of the events can also be represented by the combinations of overlapping areas.

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2.4

(a) Sample space S: {(1, 1), (1, 2), ... (6, 5), (6, 6)}

(b) Rule method: S = {(x, y) | x, y ∈ {1, 2, 3, 4, 5, 6}}

2.8

(a) A: {(3, 6), (4, 5), ... (6, 6)}

(b) B: {(1, 2), (2, 1), (2, 2)}

(c) C: {(5, 1), (5, 2), ... (6, 6)}

(d) A∩C: {(5, 4), ... (6, 6)}

(e) A∩B: {}

(f) B∩C: {}

2.4

(a) Sample space S by listing the elements (x, y):

S = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),

(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),

(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),

(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),

(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6),

(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

(b) Sample space S using the rule method:

S = {(x, y) | x, y ∈ {1, 2, 3, 4, 5, 6}}

2.8

(a) Elements corresponding to event A (the sum is greater than 8):

A = {(3, 6), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 3), (6, 4), (6, 5), (6, 6)}

(b) Elements corresponding to event B (a 2 occurs on either die):

B = {(1, 2), (2, 1), (2, 2)}

(c) Elements corresponding to event C (a number greater than 4 on the green die):

C = {(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6),

(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

(d) Elements corresponding to event A∩C:

A∩C = {(5, 4), (5, 5), (5, 6), (6, 3), (6, 4), (6, 5), (6, 6)}

(e) Elements corresponding to event A∩B:

A∩B = {} (No common elements between A and B)

(f) Elements corresponding to event B∩C:

B∩C = {} (No common elements between B and C)

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Carl can select red marbles most likely.

Probability is a measure of the likelihood of an event occurring. The probability formula is defined as the possibility of an event happening is equal to the ratio of the number of favorable outcomes and the total number of outcomes. Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.

Given Carl is going to select 1 marble,

total marbles in bag = 12

number of red marbles = 6

probability of red marbles = 6/12

number of blue marbles = 3

probability of blue marbles = 3/12

number of green marbles = 1

probability of green marbles = 1/12

number of yellow marbles = 2

probability of yellow marbles = 2/12

since the chances of red marble is more as compared than others.

Hence there of chances of selecting red marble.

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the image of bag is attached.

At a standard deviation of $15,000, the probability that the condominium will sell at a price below $200,000 is 0.2525 and above $240,000 is 0.02. At a standard deviation of $20,000, the probability that the condominium will sell at a price below $200,000 is 0.3085 and above $240,000 is 0.0668.

From the given question;

Let the average sale price(μ)=210,000

Standard Deviation(σ)=$15,000

(a) We have to find the probability that the condominium will sell at a price.

(i) below $200,000, i.e. P(x<200,000)

Z=(x−μ)/σ

Z=(200,000−210,000)/15,000

Z= −10,000/15000

Z= −0.67

Now finding P(x<200,000) is same as finding P(Z<−0.67) using the standard table of z.

P(Z<−0.67) = 0.2525

(ii) above $240,000, i.e. P(x>240,000)

Z=(x−μ)/σ

Z=(240,000−210,000)/15,000

Z= 30,000/15000

Z= 2

Now finding P(x>240,000) is same as finding P(Z>2) using the standard table of z.

P(Z>240,000)=P(Z>2)

P(Z>240,000)=1−P(Z<2)

P(z>240,000)=1−0.98

P(z>240,000)=0.02

(b) Now the average sale price(μ)=210,000

Standard Deviation(σ)=$20,000

We have to find the probability that the condominium will sell at a price.

(i) below $200,000, i.e. P(x<200,000)

Z=(x−μ)/σ

Z=(200,000−210,000)/20,000

Z= −10,000/20000

Z= −0.5

Now finding P(x<200,000) is same as finding P(Z<−0.5) using the standard table of z.

P(Z<−0.5) = 0.2085

(ii) above $240,000, i.e. P(x>240,000)

Z=(x−μ)/σ

Z=(240,000−210,000)/20,000

Z= 30,000/20000

Z= 1.5

Now finding P(x>240,000) is same as finding P(Z>1.5) using the standard table of z.

P(Z>240,000)=P(Z>1.5)

P(Z>240,000)=1−P(Z<1.5)

P(z>240,000)=1−0.93319

P(z>240,000)=0.0668

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Answer:

120

Step-by-step explanation:

Answer:

If solved by using quadratic formula, you would need to solve the rational equation by combining expressions and isolating the variable  y .

y ≈ 2.45043159

Step-by-step explanation:

The expression (y⁴ - 81) / (y - 3) simplifies to (y + 3)(y² + 9) after factoring and canceling common terms.

expression (y⁴ - 81) / (y - 3)

by simplification

factoring the numerator

y⁴ - 81 = (y²)² - 9² = (y² - 9)(y² + 9)

factoring the denominator

y - 3

we get, (y² - 9)(y² + 9) / (y - 3)

simplifying

(y² - 9) = (y - 3)(y + 3)

(y - 3)(y + 3)(y² + 9) / (y - 3)

(y + 3)(y² + 9)

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The roots of the quadratic equation x² - 8x + 16 = 0 are real and equal which is 4.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

The quadratic equation is given below.

x² - 8x + 16 = 0

The value of the discriminant is given as,

D = b² - 4ac

D = (-8)² - 4(1)(16)

D = 64 - 64

D = 0

The roots of the equation are calculated as,

x² - 8x + 16 = 0

x² - 4x - 4x + 16 = 0

x(x - 4) - 4(x - 4) = 0

(x - 4)(x - 4) = 0

x = 4, 4

The roots of the quadratic equation x² - 8x + 16 = 0 are real and equal which is 4.

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The angle, θ, at which the chair is currently reclined is approximately 31.4 degrees. Thus, the correct option is a. 31.4.

To determine the reclined angle, θ, of the patio lounge chair, we can use trigonometry and the given measurements.

In the diagram, we can see that the chair's reclined position forms a right triangle. The length of the side opposite the angle θ is given as 1.2 meters, and the length of the adjacent side is given as 2.3 meters.

The tangent function can be used to find the angle θ:

tan(θ) = opposite/adjacent

tan(θ) = 1.2/2.3

θ = arctan(1.2/2.3)

Using a calculator, we can find the arctan of 1.2/2.3, which is approximately 31.4 degrees.

Therefore, the angle, θ, at which the chair is currently reclined is approximately 31.4 degrees. Thus, the correct option is a. 31.4.

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The variance of the return on a portfolio with many securities is more dependent on the covariances between the individual securities than on the variances of the individual securities.

The variance of a portfolio measures the variability or dispersion of the portfolio's returns. When a portfolio consists of multiple securities, the overall variance is influenced by the interrelationships among the returns of those individual securities.

The covariance between individual securities in a portfolio has a significant impact on the portfolio's variance.

The diversification benefits arise from the fact that covariances tend to offset each other, potentially leading to a lower overall portfolio variance compared to the sum of individual variances.

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The population is growing as the births are more than deaths in an year.

Increases in a population's or a dispersed group's membership are referred to as population growth.

Given:

To find: Is population growing or shrinking?

Finding:

Hence the population is growing as the births are more than deaths in an year.

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Answer:

The value of x = 20.

Step-by-step explanation:

Figure B is the scale image of A.

It is clear that:

which can be obtained by multiplying 10 with 1.25

i.e.

so the side 16 of figure A must have to be multiplied by 1.25 to get the image the figure B.

so

Therefore, the value of x = 20.

Answer:

y = 21

Step-by-step explanation:

(3y-8) = 55 (corresponding angles are equal)

3y-8 = 55 (add 8 from both sides)

3y = 63 (divide 3 from both sides to isolate the y variable)

y = 21 (final answer)

Answer:

y = 21

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

\((3x-y)(x+y)^2\)

Step-by-step explanation:

\(3x^3-x^2y+6x^2y-2xy^2+3xy^2-y^3\)

Multiply and combine like terms.

\(3x^3+xy^2-y^3+5xy^3\)

Consider \(3x^3+xy^2-y^3+5xy^3\) as a polynomial over variable x.

\(3x^3+5xy^2+y^2x-y^3\)

Find one factor of the form kx^m +n, where kx^m  divides the monomial with the highest power 3x^3  and n divides the constant factor −y^3 . One such factor is 3x−y. Factor the polynomial by dividing it by this factor.

\((3x-y)(x^2+2xy+y^2)\)

Consider \(x^2+2xy+y^2\). Use the perfect square formula, \(a^2+2ab+b^2\) = \((a+b)^2\), where a=x and b=y.

\((x+y)^2\)

Rewrite the complete factored expression.

\((3x-y)(x+y)^2\)

Answer:

see explanation

Step-by-step explanation:

(a)

calculate the lengths using the distance formula

d = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)

with (x₁, y₁ ) = J (- 3, - 7 ) and (x₂, y₂ ) = K (3, - 8 )

JK = \(\sqrt{(3-(-3))^2+(-8-(-7))^2}\)

    = \(\sqrt{(3+3)^2+(-8+7)^2}\)

    = \(\sqrt{6^2+(-1)^2}\)

    = \(\sqrt{36+1}\)

    = \(\sqrt{37}\)

repeat with (x₁, y₁ ) = M (8, 3 ) and (x₂, y₂ ) = N (7, - 3 )

MN = \(\sqrt{(7-8)^2+(-3-3)^2}\)

      = \(\sqrt{(-1)^2+(-6)^2}\)

     = \(\sqrt{1+36}\)

     = \(\sqrt{37}\)

repeat with (x₁, y₁ ) = P (- 8, 1 ) and (x₂, y₂ ) = Q (- 2, 2 )

PQ = \(\sqrt{-2-(-8))^2+(2-1)^2}\)

      = \(\sqrt{(-2+8)^2+1^2}\)

      = \(\sqrt{6^2+1}\)

      = \(\sqrt{36+1}\)

      = \(\sqrt{37}\)

(b)

JK ≅ MN ← true

JK ≅ PQ ← true

MN ≅ PQ ← true

Answer:

36 years old

Step-by-step explanation:

48 divided by 4 equalls 12 (Emily's age)

12 times 3 equalls 36 (Denise's age)

Checking

36+12=48

According to the given statement , the value of "b" in the equation cos(22.6°) = b/13 is approximately 12.

To solve for "b" in the equation cos(22.6°) = b/13, we can use trigonometric functions.

Step 1:

Rewrite the equation as cos(22.6°) = b/13.

Step 2:

Multiply both sides of the equation by 13 to isolate "b". This gives us:

b = 13 * cos(22.6°).

Step 3:

Use a calculator to find the cosine of 22.6°. The value of cos(22.6°) is approximately 0.9239.

Step 4:

Substitute this value back into the equation to find "b". b = 13 * 0.9239.

Step 5:

Calculate the value of "b" by multiplying 13 by 0.9239. The result is approximately 11.999.

Step 6:

Round the value of "b" to the nearest whole number. Since 11.999 is closer to 12, we round up to 12.

Therefore, the value of "b" in the equation cos(22.6°) = b/13 is approximately 12.

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The row numbers along the left side of the worksheet are 1, 2, 4, 5, 6. We can observe that there is a missing number in the sequence, specifically the number 3. Therefore, based on the pattern, we can deduce that row 3 is missing from the worksheet.

Based on the given information, the row numbers along the left side of the worksheet are 1, 2, 4, 5, 6, with a missing number in the sequence, which is the number 3.

The presence of the numbers 1, 2, 4, 5, and 6 indicates that rows corresponding to those numbers exist in the worksheet. However, there is no row with the number 3 mentioned in the sequence. Thus, we can conclude that row 3 is missing from the worksheet.

It is important to note that the missing row could be intentional or accidental, but based on the given information, we can deduce that there is a discontinuity in the row numbering, specifically the absence of row 3.

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The area needed to cover is 89.6 square feet.

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

Area = 256

Area covered = 65%

The area of the floor that Vinnie has already covered is calculated as

Covered = 256 x 65%

Evaluate

Covered = 166.4 square feet.

The area that he still needs to cover is:

Remaining = 256 - 166.4

Remaining  = 89.6 square feet.

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Answer:

Step-by-step explanation:

12/15 or simplified: 4/5

Answer:

8 is the maximum he can get.

Step-by-step explanation:

Good luck!

The area of the described larger loop and smaller loop is pi+3root3

Given by is the area of one half of the outer loop..

One-half of the inside loop's area is calculated using

Now, to account for symmetry, we multiply by 2 and subtract the outer loop from the inner loop:

To take shape, coordinate, or meld into an effective or cohesive whole: To combine with something else; to incorporate into a larger entity. 3. Differentiation is the antithesis of integration. In other words, integration results if the differentiation process is reversed. The example below exemplifies it: dy/dx = 2x when y = x2 As a result, dx and dy go hand in hand and signify the integration of the function with regard to x. Integration of races and cultures is a successful joining or mingling with a different set of people.

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Step-by-step explanation:

-x²-8x=15

=> -x²-8x-15= 0

<=> x2+8x+15=0

(x+5)(x+3)=0

x= -5 or x = -3

The required probabilities are

a. P(X < 75) = 0.29, b. P(X < 28) = 0, and c. P(X = 75) = 0

A continuous probability distribution is a type of probability distribution that describes the probabilities of all possible values that a continuous random variable can take within a specific range.

In contrast to discrete probability distributions, which describe the probabilities of discrete outcomes, continuous probability distributions describe the probabilities of continuous outcomes.

Here we have

For a continuous random variable X,

P(28 ≤ X ≤ 75) = 0.15 and P(X > 75) = 0.14

Given probabilities can be calculated as follows

a. P(X < 75)

P(X < 75) = P(X ≤ 75) - P(X = 75)

= 0.15 + 0.14

= 0.29

b. P(X < 28)

P(X < 28) = P(X ≤ 28) = 0,

[ since X cannot be less than 28 if P(28 ≤ X ≤ 75) = 0.15 ]

c. P(X = 75)

P(X = 75) = P(X ≤ 75) - P(X < 75)

= 0.15 - 0.29

= -0.14.

However, this is not a valid probability since probabilities cannot be negative.

Therefore, P(X = 75) = 0.

Therefore,

The required probabilities are

a. P(X < 75) = 0.29, b. P(X < 28) = 0, and c. P(X = 75) = 0

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Answer:

Step-by-step explanation:

To solve the given equation \(\sf x - y = 4 \\\), we can perform the following calculations:

a) To find the value of \(\sf 3(x - y) \\\):

\(\sf 3(x - y) = 3 \cdot 4 = 12 \\\)

b) To find the value of \(\sf 6x - 6y \\\):

\(\sf 6x - 6y = 6(x - y) = 6 \cdot 4 = 24 \\\)

c) To find the value of \(\sf y - x \\\):

\(\sf y - x = - (x - y) = -4 \\\)

Therefore:

a) The value of \(\sf 3(x - y) \\\) is 12.

b) The value of \(\sf 6x - 6y \\\) is 24.

c) The value of \(\sf y - x \\\) is -4.

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

A. x ≤ - 9 or x ≥ 9

x² ≥ 81

| x | ≥ 9

x ≥ 0 => x ≥ 9 => x ∈ [ 9 ; + oo)

x < 0 => x ≤ - 9 => x ∈ ( -oo ; - 9 ]

x ∈  ( -oo ; - 9 ] ∪ [ 9 ; + oo)

Answer:

3. D

4. I

5. E

6. G

7. J

8. B

9. A

10. H

Answer:

65

Step-by-step explanation:

I promise as i got the answer wrong from the other person on this question and then it said the right answer was 65 degrees

The series Σan = (4n^3)/(2n^2 + 9) can be analyzed using the limit comparison test to determine its convergence or divergence.

By selecting a series Žbn with terms of the form bn = 1/n, we can apply the limit comparison test. Taking the limit as n approaches infinity of the ratio of the two series, we have:

lim(n→∞) (an/bn) = lim(n→∞) [(4n^3)/(2n^2 + 9)] / (1/n)

Simplifying the expression, we get:

lim(n→∞) [(4n^3)/(2n^2 + 9)] * n

Further simplification yields:

lim(n→∞) [(4n^4)/(2n^2 + 9)]

Since the degree of the numerator is greater than the degree of the denominator, the limit approaches infinity. Therefore, the series Σan diverges.

In summary, the series Σan = (4n^3)/(2n^2 + 9) diverges based on the limit comparison test with the series Žbn = 1/n.

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