1/2b-9+8b-7-b+14
I need to combine like terms.

The ordered pairs (5, 0), (-15, -8) and (7, 11) are solutions to the linear inequality given by: 2x - 5y ≤ 10.

How to check if a given ordered pair is a solution to the given linear inequality?
Substitution of corresponding values of variables in a given linear equality and then assessing it to check the end condition of the linear inequality will help in checking if a given ordered pair is a solution to the given linear inequality.

Given, the linear inequality in question is 2x - 5y ≤ 10 --(i)
On substituting (-2, -4) in (i), we have: 2x - 5y = 2(-2) - 5(-4) = 16 > 10
On substituting (5, 0) in (i), we have: 2x - 5y = 2(5) - 5(0) = 10 ≤ 10
On substituting (-15, -8) in (i), we have: 2x - 5y = 2(-15) - 5(-8) = 10 ≤ 10
On substituting (7, 11) in (i), we have: 2x - 5y = 2(7) - 5(11) = -41 ≤ 10
Thus, the ordered pairs (5, 0), (-15, -8) and (7, 11) are solutions to the linear inequality given by: 2x - 5y ≤ 10.

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The expected value of the random variable y is computed to be 3.8.The variance of y is calculated to be 4.06, and the standard deviation is approximately 2.02.

To compute the expected value of the random variable y, we multiply each value of y by its corresponding probability and sum them up. In this case, we have:

E(y) = (2)(0.2) + (4)(0.1) + (5)(0.3) + (8)(0.2) + (10)(0.2) = 0.4 + 0.4 + 1.5 + 1.6 + 2 = 3.8.

To calculate the variance of y, we first need to compute the squared deviations from the expected value for each value of y, multiply them by their corresponding probabilities, and sum them up. Then, subtracting the squared expected value of y gives us the variance. Using the formula:

Var(y) = \(E[(y - E(y))^2],\)

we have:

Var(y) = \([(2 - 3.8)^2](0.2) + [(4 - 3.8)^2](0.1) + [(5 - 3.8)^2](0.3) + [(8 - 3.8)^2](0.2) + [(10 - 3.8)^2](0.2),\)

Var(y) = 0.36 + 0.04 + 0.36 + 4.84 + 36,

Var(y) = 4.06.

Finally, the standard deviation (σ) is the square root of the variance:

σ = √Var(y) ≈ √4.06 ≈ 2.02.

Therefore, the variance of y is 4.06, and the standard deviation is approximately 2.02.

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The statement "If v1,···,vk are vectors of Rn that do not span Rn, then v1,···,vk are linearly independent" is false. The counterexample provided is the two vectors v1 = [1, 0] and v2 = [0, 1] in R^2.

The statement is false. Here's a counterexample:

Consider the following two vectors in R^2:

v1 = [1, 0]

v2 = [0, 1]

These vectors do not span all of R^2 since any linear combination of them is of the form [a, b] where a, b ∈ R. Thus, they cannot generate, for example, the vector [1,1].

However, v1 and v2 are not linearly independent since there exists a nontrivial linear combination of them that yields the zero vector:

c1v1 + c2v2 = 0, where c1 = c2 = 0.

Therefore, the statement is false, and the given condition of not spanning Rn does not imply linear independence.

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Answer:

The distance betwen -4 and 5 is 9 spaces.

The distance betwen 4 and 3 is 1.

If you meant -4 and 3 then it is 7.

Step-by-step explanation:

   -5 -4 -3 -2 -1 0 1 2 3 4 5

Answer:

ur suppose to find how much it is after the discount so for example in question 1 the discount is 40% so subtract that from 100% to get 60% then multiply this 60% by the origanial vaule which is 120 so for the answer for question 1 would be 72. Also when multiplying 60% u dont multiply by 60 u multiply it by 0.6

Hope this help and sry for the bad grammar

If A and B are independent, then the correct statements are P(A and B) = 0.12 and P(A or B) = 0.58.

Let's evaluate each statement:

P(B/A) = 0.4:

This statement is incorrect. If events A and B are independent, the occurrence of event A does not affect the probability of event B.

Therefore, P(B/A) would still be equal to the probability of B, which is 0.4 in this case.

P(A and B) = 0.12:

This statement is correct. The probability of the intersection of independent events A and B is calculated by multiplying their individual probabilities. In this case, P(A and B) = P(A) * P(B) = 0.3 * 0.4 = 0.12.

P(A/B) = 0.3:

This statement is incorrect. If events A and B are independent, the occurrence of event B does not affect the probability of event A. Therefore, P(A/B) would still be equal to the probability of A, which is 0.3 in this case.

P(A or B) = 0.58:

This statement is incorrect. To calculate the probability of the union of two events, we need to consider whether the events are mutually exclusive or not.

If events A and B are independent, but not mutually exclusive, we can calculate P(A or B) as P(A) + P(B) - P(A and B). In this case, P(A or B) = 0.3 + 0.4 - 0.12 = 0.58.

Therefore, the correct statements are:

The statements regarding P(B/A) = 0.4 and P(A/B) = 0.3 are incorrect in the context of independent events A and B.

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Answer:

Wait what?

Step-by-step explanation:

The amount of discount on the jacket is Birr 144.

We can use the following formula :

Discount amount = Original price - Discounted price

We must determine the original pricing of the jacket given that it has a discounted price of Birr 576 and the discount is 20%.

Assume "x" stands in for the original price.

The information provided indicates that the discounted price is 80% (100% - 20%) of the original cost:

Discounted price = 80% of the original price

576 = 0.8x

To find the original price, we can divide both sides of the equation by 0.8:

x = 576 / 0.8

x = 720

Now that we have the original price, we can calculate the amount of discount:

Discount amount = Original price - Discounted price

Discount amount = 720 - 576

Discount amount = Birr 144

Therefore, the amount of discount on the jacket is Birr 144.

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Answer:

Hey there!

Step-by-step explanation:

This is ur answer...

Hope it helps!

Brainliest pls!

Have a good day!^^

The capability index that is most desirable is a. 1.00.

The capability index, often represented by Cp, is a measure of the capability of a process to consistently produce output within specified limits. It compares the spread of the process output to the width of the specification limits.

A capability index of 1.00 indicates that the process spread is equal to the width of the specification limits, indicating a high level of capability. This means that the process is able to consistently produce output that meets the desired specifications without significant deviation.

On the other hand, a capability index below 1.00 indicates that the process spread is wider than the specification limits, indicating a lower level of capability. In such cases, the process may have difficulty consistently meeting the desired specifications.

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The function \(B(t) = 182(1.065)^t\) represents the annual population of bees in a county park, the growth rate is 6.5%.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.

An exponential function is in the form:

y = abˣ

Where a is the initial value and b is the multiplication factor.

From the function \(B(t) = 182(1.065)^t\):

b = 1.065

Growth rate = 1.065 - 1 = 0.065 = 6.5%

The function \(B(t) = 182(1.065)^t\) represents the annual population of bees in a county park, the growth rate is 6.5%.

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The simplified expression is \(\tan x+\sec x\), we arrive at this after performing mathematical calculations using basic identities.

Basic mathematical identities refer to fundamental equations or relationships between mathematical functions that are true for all values of the variables involved.

For example,  a + b = b, a x 0 = 0 are basic identities. Applying the same principle we can simply the mathematical expression with the basic identities provided below:

\(= \frac{\tan^2x-\sec^2x}{\cos x}\)

= \(\frac{\sin^2x-\cos^2x}{\cos x\cdot\cos^2x} \quad\text\)

\(=\frac{\sin^2x}{\cos^2x}\text{ and }\sec^2x\)

= \(\frac{1}{\cos^2x} \ =\frac{(\sin x+\cos x)(\sin x-\cos x)}{\cos^3x}\)

factoring the numerator using the difference of squares.

\(=\frac{\sin x}{\cos^2x}+\frac{\cos x}{\cos^2x} \\)

\(&=\tan x+\sec x\)

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After putting the value of y into the eq. (ii) ,

\( \sf 3x + 2 \times 5x = 52\)

\( \sf ⇒ \: 3x + 10x = 52\)

\(⇒ \sf13x = 52\)

\( \sf ⇒x = 4\)

After putting the value of x into the eq. (1)

\( \sf \: y = 5 \times 4\)

\(⇒ \sf y = 20\)

Hence, the value of x is 4

& the value of y is 20.

If Ojemba is sitting on a sled on the side of a hill inclined at 60° and  weight of Ojemba and sled is 160 pounds , then magnitude of force needed for Mandisa to keep sled from sliding down the hill is 355.59 N   .

the inclination angle of the the side of the hill is = 60° ;

the compound mass of Ojemba and Sled is = 160 pounds ,

On conversion we get the mass in Kg is = 72.57 Kg .

the acceleration due to gravity is , \(g = 9.8 m/s^{2}\) ;

The force required for Mandisa to keep sled from sliding down the hill can be calculated by the formula ;

\(F = mgSin\theta\) , Substituting the values ,

we get ;

\(F = 72.57\times 9.8\times Sin(30\textdegree)\)

\(F = 72.57\times 9.8\times \frac{1}{2}\) ;

So , \(F = 355.59 N\) .

The required magnitude of the force is 355.59 N .

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Answer: (-0.5, 3)

Step-by-step explanation:

     The solution of two graphed linear functions is the point of intersection, also known as the point the lines cross each other. See attached for a visual. These lines intersect at point (-0.5, 3) which means our answer is;

                (-0.5, 3)

Answer:

all 3 options are true : A, B, C

Step-by-step explanation:

warning : it has come to my attention that some testing systems have an incorrect answer stored as right answer for this problem.

they say that A and C are correct.

but I am going to show you that if A and C are correct, then also B must be correct.

therefore, my given answer above is the actual correct answer (no matter what the test systems say).

originally the information about the alignment of the point F in relation to point E was missing.

therefore, I considered both options :

1. F is on the same vertical line as E.

2. F is not on the same vertical line as E.

because of optical reasons (and the - incomplete - expected correct answers of A and C confirm that) I used the 1. assumption for the provided answer :

the vertical line of EF is like a mirror between the left and the right half of the picture.

A is mirrored across the vertical line resulting in B. and vice versa.

the same for C and D.

this leads to the effect that all 3 given congruence relationships are true.

if we consider assumption 2, none of the 3 answer options could be true.

but if the assumptions are true, then all 3 options have to be true.

now, for the "why" :

remember what congruence means :

both shapes, after turning and rotating, can be laid on top of each other, and nothing "sticks out", they are covering each other perfectly.

for that to be possible, both shapes must have the same basic structure (like number of sides and vertices), both shapes must have the same side lengths and also equally sized angles.

so, when EF is a mirror, then each side is an exact copy of the other, just left/right being turned.

therefore, yes absolutely, CAD is congruent with CBD. and ACB is congruent to ADB.

but do you notice something ?

both mentioned triangles on the left side contain the side AC, and both triangles in the right side contain the side BD.

now, if the triangles are congruent, that means that each of the 3 sides must have an equally long corresponding side in the other triangle.

therefore, AC must be equal to BD.

and that means that AC is congruent to BD.

because lines have no other congruent criteria - only the lengths must be identical.

Answer: 1/9

Step-by-step explanation:

You have 3 possible options. The probablility of the spinner landing on 3 is 1/3. The probability of it landing on 2 is also 1/3. For them to happen together, you multiply them. 1/3 * 1/3 = 1/9.

The probability of landing on a 3 and then landing on a 2 is,

⇒ 1/9

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one

Given that;

You spin the spinner twice.

Now, The probability of the spinner landing on 3 is,

⇒ 1/3.

And, The probability of it landing on 2 is,

⇒ 1/3.

Hence, The probability of landing on a 3 and then landing on a 2 is,

⇒ 1/3 × 1/3

⇒ 1/9.

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Explanation:

Concept:

The zero of a function is any replacement for the variable that will produce an answer of zero. Graphically, the real zero of a function is where the graph of the function crosses the x‐axis; that is, the real zero of a function is the x‐intercept(s) of the graph of the function.

Hence,

From the graph below,

We can see that the graph cuts the x-axis at two points

Therefore,

The zeroes of the graph are

Answer:

Step-by-step explanation:

The first step would be to determine if there are any common factors of 9 and 12. In this case, the factors of 9 are 1, 3, and 9; and the factors of 12 are 1, 2, 3, 4, 6, and 12. We want to pull out or divide each of the numbers in the equation by the largest common factor. In this instance, the largest common factor is 3.Therefore, the equation can be rewritten as 3(3s + 4). To check our work, multiply the 3x3s and add 3x4; you get back to the original statement of 9s + 12.

2x+y-3 = 0 iS a linear function with coefficient as 2 and 1 with constant part c = 3.

In a graph, a linear function is one that generates a straight line. The degree of the polynomial function is often either maximum 1 or minimum 0. Despite the fact that both calculus and linear algebra can be used to express linear functions. The function notation is the only thing that differs. Also required is the ability to read an ordered pair expressed in function notation. A function is denoted by the notation f(a), where an is an independent variable on which the function depends. The straight line on the linear function graph contains the expression or formula;

Linear function can be always represented in the format of ax + by + c = 0.

Here,

a € ( -∞, +∞)

b € ( -∞, +∞)

c € ( -∞, +∞)

Hence, Linear expression always contains y¹ and x¹.

and can always be represented in the form of y = mx.

So it always represents the straight line.

For example: 2x+y-3 = 0 ia a linear expression with coefficient as 2 and 1 with constant part c = 3.

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Answer:

x=-1

Step-by-step explanation:

f (x)= -x + 8

Let f(x) = 9

9 = -x+8

Subtract 8 from each side

9-8 = -x+8-8

1 = -x

Multiply each side by -1

-1 = x

The largest possible error you could make in approximating P(a < M < b) by e is when a = 0 and b = 1. The error would be |P(0 < M < 1) - e|.

You are given an approximation of P(a < M < b) by e, where M is an integer between a and b. You want to find the largest possible error in this approximation. The range of values for M is between a and b, and both a and b are integers between 0 and 100. The largest possible error would occur when the difference between the true value and the approximation is at its maximum. Since e is an approximation of P(a < M < b), the largest error would occur when the difference between the actual probability and the approximation is at its maximum.

This would happen when the actual probability is either very close to 0 or 1, and the approximation is far from the actual value. Since a and b are integers between 0 and 100, the largest possible error would occur when the range of possible values for M is at its smallest. This means that a and b should be as close together as possible. The smallest range for M would be 1, which would occur when a = 0 and b = 1.

In this case, the largest possible error in the approximation would be |P(0 < M < 1) - e|, where P(0 < M < 1) is the true probability and e is the approximation. In summary, the largest possible error you could make in approximating P(a < M < b) by e is when a = 0 and b = 1. The error would be |P(0 < M < 1) - e|.

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Carlos buy 35 number of angelfish and 360 number of parrotfish.

What is solving an equation?

Unifying Principle for Equation Solving

By deleting parenthesis and grouping like terms, each side of the equation can be made simpler.

The variable term on one side of the equation can be separated using addition or subtraction.

To find the variable, use multiplication or division.

x represents the number of angelfish Carlos bought and the variable y represents the number of parrotfish he bought.

Carlos bought 405 tropical fish for a museum display.

x + y = 405            ..(1)

As he bought 8 times as many parrotfish as angelfish.

⇒ y = 8x                ..(2)

Plug y = 8x in equation (1)

x + 8x = 405

     9x = 405

       x = 45

Plug x = 45 in equation (2)

y = 8(45)

y = 360

Hence, Carlos bought 35 number of angelfish and 360 number of parrotfish.

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Therefore, Assuming that approximately 20% of the lake's trout population was marked, we can estimate that the lake contains approximately 250 trout.

To find the probability L(N) that 16 trout are marked in a sample of 80, we need to use the hypergeometric distribution formula. The formula is P(X=k) = [C(M,k) * C(N-M,n-k)] / C(N,n), where M is the total number of trout in the lake, N is the number of trout in the sample (80), k is the number of marked trout in the sample (16), and n is the sample size (50). Plugging in the values, we get P(X=16) = [C(M,16) * C(M-50,34)] / C(M,80). We don't know the exact value of N, but we can estimate it using the fact that 16 out of 80 trout were marked, which means that approximately 20% of the lake's trout population was marked. Therefore, we can estimate that the lake contains approximately 250 trout (i.e., 50 / 0.2). Writing the main answer in 2 lines: The probability L(N) that 16 trout are marked in a sample of 80 can be estimated using the hypergeometric distribution formula.

Therefore, Assuming that approximately 20% of the lake's trout population was marked, we can estimate that the lake contains approximately 250 trout.

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Answer:

Answer: The third equation

Step-by-step explanation:

From the general equation of a line:

\( \hookrightarrow \: { \boxed{ \tt{y = mx + b}}}\)

• m is the slope

\({ \tt{slope = \frac{y _{2} - y _{1} }{x _{2} - x _{1}} }} \\ \\ m = { \tt{ \frac{ - 1- ( - 2)}{4 - 0} = \frac{1}{4} }}\)

• b is the y-intercept:

\({ \tt{y = mx + b}}\)

consider point (0, -2):

\({ \tt{ - 2 = (0 \times \frac{1}{4} ) + b }} \\ \\ { \tt{b = - 2}}\)

• Therefore, equation is;

\( \dashrightarrow \: { \boxed{ \tt{y = \frac{1}{4}x - 2 }}}\)

The value of l is either 2 or 3, depending on whether the second letter drawn is b or not, respectively.The problem can be solved using the pigeonhole principle. We can draw letters one by one until we have seen any two of a, b, and c, but not all of them.

To minimize the number of letters drawn, we want to draw as few letters as possible before seeing any two of a, b, and c. We can start by assuming that the first letter drawn is a. Then, there are two cases to consider:

Case 1: The second letter drawn is b.

In this case, we have seen both a and b, so we stop drawing letters. The value of l is 2.

Case 2: The second letter drawn is not b (i.e., it is either a or c).

In this case, we need to draw one more letter to ensure that we have seen any two of a, b, and c. If the third letter is the same as the second letter, then we keep drawing letters until we see a different letter. Therefore, the maximum number of letters we need to draw in this case is 3.

Therefore, the value of l is either 2 or 3, depending on whether the second letter drawn is b or not, respectively.

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Answer:

6.5 inches

Step-by-step explanation:

Divide 26 by 4

26/4=6.5

The length of one side of the poster to the nearest tenth of an inch is 5.1 inches.

The area of a square can be calculated as the square of the sides of a given figure.

The area of a square = side x side

Given; The area of a square poster 26 inch

We need to find the length of one side of the poster to the nearest tenth of an inch.

The area of a square would be S^2

26 = S^2

s = sqrt(26) = 5.099

Then rounded to nearest tenth = 5.1 inches

Hence, the length of one side of the poster to the nearest tenth of an inch is 5.1 inches.

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Answer:For 19 to 250 odds against winning;

Probability of:

Winning = (0.9294) or 92.9368%

Losing = (0.0706) or 7.0632%

"Odds for" winning: 250:19

"Odds against" winning: 19:250

Step-by-step explanation: