If x, y, z be in HP prove that (y+x)/(y-x)+(y+z)/(y-z) = 2 ​

Answer:

2) DE = 25

4) LN = 27

Solve for x:

\(x=17\)

Step-by-step explanation:

2) \(41-16=25\)

4) \(x+10 = 3x-24; x=17\); \((17)+1=18; 18+9 = LN; LN=27\)

Tip:

DE + EF = DF

LM + MN = LN

Answer: 130, 43, 55, 27

Step-by-step explanation:

9) 130 / it's supplementary to 180

10) 43 / its vertical to 43 meaning its 43

11) 55 / will add up to 360 meaning b = 55

12) 27 / its a 90-degree angle with 63 degrees needing 27

Answer:

11 /13 = t

Step-by-step explanation:

5/13  = t -6/13

Add 6/13 to each side

5/13 + 6/13  = t -6/13+ 6/13

11 /13 = t

Answer:

\(t=\frac{11}{13}\)

Step-by-step explanation:

\(\frac{5}{13} = t -\frac{6}{13}\)

Add \(\frac{6}{13}\) to both sides.

\(\frac{5}{13} + \frac{6}{13} = t -\frac{6}{13} + \frac{6}{13}\)

\(\frac{11}{13} =t\)

Answer:

Suppose that the batch has N liters of paint.

we know that the recipe is:

1/2 of red paint

1/3 of yellow paint

1/6 of white paint.

Then, out of the N liters, 1/2 is red.

This means that we must use:

N/2 liters of red paint.

And the same for the other two colors:

N/3 liters of yellow paint

N/6 liters of white paint.

When we add those 3, we have:

(N/2 + N/3 + N/6)  = (3*N/6 + 2*N/6 + N/6) = N.

Now, if for example N = 2

Then the batch has 2 liters of paint, this would mean that we must use:

2/2 liters of red paint

2/3 liters of yellow paint

2/6 liters of white paint.

Answer:

A

Step-by-step explanation:

-4 is the y-intercept, so there will always be an arrow that crosses over that point. And for the slope (2x) you need to go up two places from the y-intercept and then one to the right :)

Answer:

A

Step-by-step explanation:

The 2 in 2x-4 tells us that the line is rising, so that disqualifies answer B and C.

The -4 tells us the line passes the y axis at -4, so that disqualifies C and D.

Leaves A!

Piecewise linear functions, f(x) as common core algebra, Evaluate each of the following :

(1) f(-3) = 12

(2) f(4) = 2

(3) f(0)= 8

(4) f(3)= 8

A piecewise linear function is a function defined on the interval [xₘᵢₙ ,xₘₐₓ]. A piecewise linear function is a function that consists of straight line segments. This is a piecewise function whose pieces are affine (linear) functions. Graphs of piecewise linear functions consist of line segments and rays.

We have given that,

f(x) = 5x - 3 ; x< -2

= x+8 ; -2≤x< 3

= 1/3(x) + 7 ; x ≥3

we see here that , f(x) is a piecewise linear function defined on interval [-2,3).

Now, we solve the following

(1) f(-3) , here x = -3< -2 i.e we take f(x) =5 x -3

=> f(-3) = 15 - 3 = 12

(2) f(4) , x= 4 >3 so, f(x) = 1/3(x) + 7

=> f(4) = 1/3(4) + 7 = 14/7 = 2

(3) f(3) , x = 3 so, f(x) = 1/3(x) + 7

=> f(3) = 1/3(3) + 7 = 8

(4) f(0) , x = 0 or -2 < x < 3 so, f(x) = x+8

=> f(0) = 0+8 = 8

Hence, we evaluate the given functions.

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Complete question:

piecewise linear functions common core algebra 2 homework answers

5x - 3 x&lt;-2 1. For f (x) = x+8 -25x&lt;3 answer the following questions. -x+7 x23 (a) Evaluate each of the following by carefully applying the correct formula: (1) f ( -3 ) (ii) f (4) (iii ) f ( 3 ) (iv ) f (0 )

To maximize the seating area while using 45π + 60 meters of light strips, the radius of the semicircular stage should be approximately 29π/3 - 5 meters.

To maximize the seating area, we need to determine the dimensions of the rectangular auditorium that will give us the largest possible area while using the given length of light strips.

Let the length of the rectangular auditorium be L, and its width be W.

The seating area consists of the rectangular portion minus the semicircular stage. So, the seating area's length is L - 2r (subtracting the semicircle's diameter) and the seating area's width is W - 2r.

The perimeter of the seating area is the sum of the lengths of its four sides, excluding the semicircular stage. The perimeter is given as 45π + 60 meters.

Perimeter = 2(L - 2r) + 2(W - 2r) + πr = 45π + 60

Simplifying: 2L + 2W - 8r + πr = 45π + 60

Rearranging: 2L + 2W = 8r + 44π + 60

The area of the seating area is given by A = (L - 2r)(W - 2r).

We want to maximize A, so we need to express it in terms of a single variable. Since we have an equation with two variables (L and W), we can rewrite one of the variables in terms of the other.

Rearranging the perimeter equation: 2L + 2W = 8r + 44π + 60

Solving for L: L = (8r + 44π + 60 - 2W) / 2

Substituting L in terms of W into the area equation: A = [(8r + 44π + 60 - 2W) / 2 - 2r] (W - 2r)

Simplifying: A = (4r + 22π + 30 - W) (W - 2r)

Now we have the area equation in terms of a single variable, W. To maximize A, we can take the derivative of A with respect to W, set it equal to zero, and solve for W.

dA/dW = 2(4r + 22π + 30 - W) - (W - 2r) = 0

Solving for W: 8r + 44π + 60 - W = W - 2r

Simplifying: 10r + 44π + 60 = 2W

W = 5r + 22π + 30

Now that we have W in terms of r, we can substitute this expression back into the area equation to get the area in terms of r only.

A = (4r + 22π + 30 - (5r + 22π + 30)) ((5r + 22π + 30) - 2r)

Simplifying: A = (r - 22π) (3r + 22π + 30)

Expanding: A = 3r² + 8rπ + 30r - 66πr - 660π

Now, to find the maximum area, we can take the derivative of A with respect to r, set it equal to zero, and solve for r.

dA/dr = 6r + 8π + 30 - 66π = 0

Simplifying: 6r - 58π + 30 = 0

6r = 58π - 30

r = (58π - 30) / 6

r ≈ 29π/3 - 5

Therefore, to maximize the seating area while using 45π + 60 meters of light strips, the radius of the semicircular stage should be approximately 29π/3 - 5 meters.

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Answer:

He would need to walk the dog 6 more times because 8 times 11 is 88 and if he has already walked the dog 5 times you would subtract that from 11 to get 6. So the answer would be 6

Step-by-step explanation:

8·11= 88

11-5= 6

Answer:

Obtuse triangle

Step-by-step explanation:

Given the side lengths :

3, 9, 10

Let :

a = 3 ; b = 9 ; c = 10 (longest side)

If a² + b² = c² (right angle)

If a² + b² > c² (acute angle)

If a² + b² < c² (obtuse angle)

a² + b²

3² + 9²

9 + 81 = 90

c² = 10² = 100

90 < 100

Hence,

a² + b² < c² (then we have an obtuse triangle)

Answer:

D

Step-by-step explanation:

"Solution to the system" means when the two lines intersect. As seen in the graph, you can see that the two lines intersect at (3,-4). This was for Question 11

The probability of getting someone in the 18-21 age bracket or someone who refused to respond is approximately 0.34 or 34%.

To find the probability of getting someone in the 18-21 age bracket or someone who refused to respond, we need to add the probabilities of these two events happening.

First, let's find the probability of getting someone in the 18-21 age bracket. Out of the total 374 people contacted, 88 are in this age bracket. So the probability of getting someone in this age bracket is 88/374.

Next, let's find the probability of getting someone who refused to respond. Out of the total 374 people contacted, 13 in the 18-21 age bracket and 26 in the 22-29 age bracket refused to respond. So the total number of people who refused to respond is 13+26=39. Therefore, the probability of getting someone who refused to respond is 39/374.

Finally, we add these two probabilities to get the probability of getting someone in the 18-21 age bracket or someone who refused to respond:

88/374 + 39/374 = 127/374

total is 0.34% or 34%

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Answer:

1. Not necessarily congruent.

There is SAS in one triangle and SSA in the other.

2. Triangle ABC and triangle BCD are congruent by SAS.

3. Triangles GHI and KLJ congruent by ASA.

Steve spent 2/3 of $15, to find how much this 2/3 of $15 is, we have to multiply $15 by 2/3, as follows:

Therefore, we have found that Steve already spent $10 .

Answer:

12 * 1.07 = 12.84

Step-by-step explanation:

You an can pick any number to express another number in this example we find  0.84 = 7% and 12 = 1 as 12 represents 1 whole.

Answer:

A. 7

Step-by-step explanation:

The 10th term of the sequence is -1, which is not one of the answer choices. Therefore, the answer is (C) 1/32.

What is geometric sequence?

A geometric sequence is one where each phrase is discovered by multiplying the term before it by the same number.

The given sequence is a geometric sequence with a first term of 16 and a common ratio of -1/2. We can use the formula for the nth term of a geometric sequence to find the 10th term:

where a1 = 16, r = -1/2, and n = 10

Therefore, the 10th term of the sequence is -1, which is not one of the answer choices. Therefore, we can also express the 10th term as the negative of the absolute value of the 10th term (i.e., |-1| = 1 and -1 = -|1|).

So, the answer is (C) 1/32.

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The statement is true. The timing of observations is crucial for time series data, while it is not significant for cross-sectional data.

For time series data sets, the time at which each observation is made is crucial. Time series data involves collecting observations over a specific time period, where the order and timing of the observations hold significance. Time series data allows for the analysis of trends, patterns, and changes over time.

On the other hand, for cross-sectional data, the time at which each observation is made is not important. Cross-sectional data involves collecting observations at a single point in time, capturing a snapshot of different entities or individuals at that particular moment. The focus is on comparing different entities or variables, rather than analyzing changes over time.

Therefore, the statement is true. The timing of observations is crucial for time series data, while it is not significant for cross-sectional data.

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Answer:

x :      35

x +5 : 48

35x+175=48x

175= 48x-35x

13x=175

x=175/13

x=13 students

Therefore, the three consecutive odd integers are 17, 19, and 21.

An equation is a statement that shows the equality of two expressions, typically separated by an equal sign. An equation can contain variables, constants, coefficients, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. The goal of solving an equation is to find the value(s) of the variable(s) that satisfy the equality.

Here,

Let x be the first odd integer, then the second and third odd integers are x+2 and x+4, respectively, since the difference between consecutive odd integers is 2.

The sum of the three consecutive odd integers is 57, so we can write:

x + (x+2) + (x+4) = 57

Simplifying and solving for x, we get:

3x + 6 = 57

3x = 51

x = 17

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Answer:

I'm assuming we're solving for the hypotenuse, which is 21.5

Step-by-step explanation:

If a^2+b^2=c^2

Then 19^2+10^2 =461

This is c^2 so we must find the square root of 461

the square root of 461 is 21.47, or 21.5 rounded to the nearest tenth

Answer:

\( \sf \: a) \: 27 = 9p \: ; p = 3\)

Step-by-step explanation:

Given information,

→ Simon have 27 pieces of candy.

→ Each person will get 9 pieces.

Now we have to,

→ Find the required equation.

The equation will be,

→ 27 = 9p

→ 9p = 27

=> As each person (p) gets 9 pieces.

Then the value of p will be,

→ 9p = 27

→ p = 27 ÷ 9

→ [ p = 3 ]

Hence, option (a) is correct.

Answer:

Step-by-step explanation:

Hope this Helps ;)

Answer:

Step 2 is incorrect. It should be -4x +2= -12

Step-by-step explanation:

The pair (m, n) for which the nullity of T must be greater than or equal to two is (4, 6).Nullity is the dimension of the kernel of a linear transformation, which is the set of all vectors in the domain that map to the zero vector in the codomain. Let T be a linear transformation from an n-dimensional vector space V to an m-dimensional space W. If the nullity of T is greater than or equal to two, then dim(Ker T) ≥ 2.Since Ker T is a subspace of V, its dimension cannot be greater than n. Thus, dim(Ker T) ≤ n. Similarly, the dimension of the image space cannot be greater than m, so dim(Im T) ≤ m. The rank-nullity theorem states that dim(Ker T) + dim(Im T) = n.

Therefore, we have: m - dim(Ker T) = dim(Im T) ≤ mt hus:dim(Ker T) ≥ m - mdim(Ker T) ≥ 2m - n. If the nullity of T is greater than or equal to two, then dim(Ker T) ≥ 2. Thus, we have:2 ≤ dim(Ker T) ≥ 2m - n2 ≤ 2m - n2 + n ≤ 2m(n, m) must satisfy the inequality 2 + n ≤ 2m.

The only pair of numbers that satisfies this condition is (4, 6).Therefore, the correct answer is (4, 6).

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Answer:

-------------------------

Each coordinate of the midpoint is the average of endpoints:

Therefore M is (13, 14).

a.  The probability is approximately \(0.1847\).

b. The probability of exactly 2 times falling between 1 and 5 seconds is approximately \(0.3038\).

(a) To find the probability that between 1 and 5 seconds elapse between emits, we can use the Poisson distribution. Given a mean rate of 3 emits per second, the parameter \($\lambda$\) for the Poisson distribution is also 3.

Let \($X$\) be the random variable representing the waiting time between emits. We want to find \($P(1 \leq X \leq 5)$\).

Using the Poisson distribution formula, we can calculate this probability:

\($P(1 \leq X \leq 5) = P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)$\)

\(P(X = k) = \frac{e^{-\lambda} \lambda^k}{k!}\)

Substituting \($\lambda = 3$ and $k = 1, 2, 3, 4, 5$\), we have:

\($P(1 \leq X \leq 5) = \frac{e^{-3} 3^1}{1!} + \frac{e^{-3} 3^2}{2!} + \frac{e^{-3} 3^3}{3!} + \frac{e^{-3} 3^4}{4!} + \frac{e^{-3} 3^5}{5!}$\)

Calculating this expression, we find that the probability is approximately \(0.1847\).

(b) When selecting 10 times between emissions randomly, the number of times falling between 1 and 5 seconds follows a binomial distribution. The probability of exactly 2 times falling in this range can be calculated using the binomial distribution formula:

\($P(X = 2) = \binom{10}{2} \cdot (P(1 \leq X \leq 5))^2 \cdot (1 - P(1 \leq X \leq 5))^{(10 - 2)}$\)

Substituting the probability from part (a), we have:

\($P(X = 2) = \binom{10}{2} \cdot (0.1847)^2 \cdot (1 - 0.1847)^{(10 - 2)}$\)

Calculating this expression, we find that the probability of exactly 2 times falling between 1 and 5 seconds is approximately 0.3038.

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As per the given statement a.) The probability that between 1 and 5 seconds elapse between emits is 5.26%. b.) The probability that exactly 2 of the emissions are between 1 and 5 seconds is 27.05%.

a. To find the probability that between 1 and 5 seconds elapse between emits in a Poisson process with a mean rate of 3 per second, we can use the exponential distribution.

The exponential distribution is characterized by the parameter lambda \((\(\lambda\))\), which is equal to the mean rate of the process. In this case, \(\(\lambda = 3\).\) The probability density function (PDF) of the exponential distribution is given by:

\(\[ f(t) = \lambda e^{-\lambda t} \]\)

To find the probability that between 1 and 5 seconds elapse between emits, we need to calculate the integral of the PDF from 1 to 5 seconds:

\(\[ P(1 \leq t \leq 5) = \int_{1}^{5} \lambda e^{-\lambda t} dt \]\)

Integrating the PDF, we have:

\(\[ P(1 \leq t \leq 5) = \left[ -e^{-\lambda t} \right]_{1}^{5} \]\)

\(\[ P(1 \leq t \leq 5) = -e^{-3 \cdot 5} - (-e^{-3 \cdot 1}) \]\)

\(\[ P(1 \leq t \leq 5) = -e^{-15} + e^{-3} \]\)

\(\[ P(1 \leq t \leq 5) \approx 0.0526 \]\)

Therefore, the probability that between 1 and 5 seconds elapse between emits is approximately 0.0526, or 5.26%.

b. If we randomly select 10 times between emissions, and we assume they are independent, we can model the situation as a binomial distribution.

The probability of having exactly 2 times between emissions between 1 and 5 seconds can be calculated using the binomial probability formula:

\(\[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \]\)

where \(\( n \)\) is the number of trials (10), \(\( k \)\) is the number of successful trials (2), and \(\( p \)\) is the probability of success (probability that between 1 and 5 seconds elapse between emits).

From part a, we know that \(\( P(1 \leq t \leq 5) \approx 0.0526 \).\)

Plugging in these values into the formula:

\(\[ P(X = 2) = \binom{10}{2} (0.0526)^2 (1 - 0.0526)^{10 - 2} \]\)

\(\[ P(X = 2) = 45 \cdot (0.0526)^2 \cdot (0.9474)^8 \]\)

\(\[ P(X = 2) \approx 0.2705 \]\)

Therefore, the probability that exactly 2 of the times between emissions are between 1 and 5 seconds is approximately 0.2705, or 27.05%.

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15/19 + 14/19 = 29/19

Step-by-step explanation:

Add the number of balls in the basket together.

Subtract the number of white balls from the sample space ( the total amount of balls) your answer is written over the sample space and the same process is done for the green ball

The value of x is x = 9/4. The equation 2xc = d as follows: 2xc = d2x * 1/2 = 9/22x = 9/2 * 2x = 9/4

The equation 2xc = d and 2x + 1 = 9 are similar in that they are both linear equations and involve the variable x.

However, they are different in that they have different constants and coefficients.

How to use 2xc = d to solve 2x + 1 = 9? To use 2xc = d to solve 2x + 1 = 9, you first need to rewrite 2x + 1 = 9 in the form 2xc = d.

To do this, you need to isolate x on one side of the equation. 2x + 1 = 9

Subtract 1 from both sides2x = 8. Divide both sides by 2x = 4Now, we can write 2x + 1 = 9 as 2x * 1/2 = 9/2.

Therefore, we can see that this equation is similar to 2xc = d, where c = 1/2 and d = 9/2.

We can use this relationship to solve for x in the equation 2xc = d as follows: 2xc = d2x * 1/2 = 9/22x = 9/2 * 2x = 9/4 Therefore, x = 9/4.

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