Determine whether b can be written as a linear combination of a1 and a2. In other words, determine whether weights x1a1 + x2a2 = b. Determine the weights x1 and x2 if possible. Let a1 = [2 6 -4], a2 = [-2 6 6], and b = [0 36 6]. A. x1 = 3, x2 = 4 B. x1 = 3, x2 = 3 C. x1 = 4, x2 = 2 D. There is no solution.

Answer:

y=19.625

Step-by-step explanation:

30+1.4

31.4÷1.6

To check your answer plug in your answer for y

Hope this helps! :)

Answer:

1.6y = 30 + 1.4 both sides multiply by 10x

16y = 314 both sides devide by 2x

8y = 157

y = 157/8 = 19.625

Answer: 21

Step-by-step explanation:

since 19 is the breadth and the perimeter is 80m, so 19*2=38 and 80-38= 42 so 42/2=21. The answer is 21

Answer:

Step-by-step explanation:

Since the sides are in the ratio 5:12:13 and the perimeter is 90 cm, we can determine the length of the sides as follows:

5x + 12x + 13x = 90 cm

30x = 90 cm

x = 3 cm

So the sides of the triangle are 15 cm, 36 cm, and 39 cm.  The 39 cm side is the hypotenuse, so the area is:

Area = (1/2)*Base*Height = (1/2)*(15)*(36) = 270 cm2

The simplified equation is y = 10,312.50 + 0.25x - 18,672.50

What is the linear equation?

Linear equations are the equations of degree 1. It is the equation for the straight line. The standard form of linear equation is ax+by+c =0, where a ≠ 0 and b ≠ 0.

(a) The $10,312.50 represents the fixed amount of income tax owed for the range of incomes between $74,900 and $151,200.

(b) The 0.25(x - 74,900) represents the additional amount of income tax owed based on a tax rate of 0.25 (25%) of the income above $74,900. The x-74,900 term represents the amount of income that is above $74,900, and multiplying by 0.25 calculates the additional tax owed for this portion of the income.

(c) To simplify the equation:

y = 10,312.50 + 0.25(x - 74,900)

y = 10,312.50 + 0.25x - 74,900 * 0.25

y = 10,312.50 + 0.25x - 18,672.50

Hence, the simplified equation is y = 10,312.50 + 0.25x - 18,672.50

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The given mathematical expression is evaluated for the input values (2, 4). The result of the expression is calculated using various operations such as addition, multiplication, square root, natural logarithm, minimum, maximum, and function composition.

The expression f(x1, x2) involves several mathematical operations. Let's evaluate each part of the expression step by step:

1. The first term is 421 + 222, which equals 643.

2. The second term is 3x² + 213. Plugging in x1 = 2 and x2 = 4, we get 3(2)² + 213 = 3(4) + 213 = 12 + 213 = 225.

3. The third term is 5x11². Substituting x1 = 2 and x2 = 4, we have 5(2)(11)² = 5(2)(121) = 1210.

4. The fourth term is (√₁+√₂)². Replacing x1 = 2 and x2 = 4, we obtain (√2 + √4)² = (1 + 2)² = 3² = 9.

5. The fifth term is 10ln(₁). Plugging in x1 = 2, we have 10ln(2) = 10 * 0.69314718 ≈ 6.9314718.

6. The sixth term is (x₁+x₂)(x² + x3). Substituting x1 = 2 and x2 = 4, we get (2 + 4)(2² + 4³) = 6(4 + 64) = 6(68) = 408.

7. The seventh term is min(3r1, 10√2). As we don't have the value of r1, we cannot determine the minimum between 3r1 and 10√2.

8. The eighth term is max{5x1,2r2}. Since we don't know the value of r2, we cannot find the maximum between 5x1 and 2r2.

9. Finally, we have MP1(x1, x2), MP2(X1, X2), and TRS(x1, x2), which are not defined or given.

Considering the given expression, the evaluated terms for the input values (2, 4) are as follows:

- 421 + 222 = 643

- 3x² + 213 = 225

- 5x11² = 1210

- (√₁+√₂)² = 9

- 10ln(₁) ≈ 6.9314718

- (x₁+x₂)(x² + x3) = 408

The terms involving min() and max() cannot be calculated without knowing the values of r1 and r2, respectively. Additionally, MP1(x1, x2), MP2(X1, X2), and TRS(x1, x2) are not defined.

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Random variable

a. E (X+ Y) = 14.10

   E|(X – Y)| = 5.1

b. E[max(X ,Y )] = 9.60

   E[min(x, y)] = 4.5

Conversely, once Y=y is observed, we would more likely be interested in the quantity E(X∣Y=y)=ρy which is a scalar.

Maybe this seems like needless complication, but regarding E(X∣Y) as a random variable in its own right is what makes things like the tower-law E(X)=E[E(X∣Y)] make sense - the thing on the inside of the braces is random, so we can ask what its expectation is, whereas there is nothing random about E(X∣Y=y).

a. E (X+ Y)

=∑∑( x +y)p(x ,y)

= (0+0)(0+2) + (0 + 5)(.06) + … + (10 + 15)(.01)

= 14.10

E|(X – Y)| = ∑∑ |x – y| p(x,y)

= |(0-0)|(0.02) + |(0-5)|(0.06) + ……+ |(10-15)|(0.01)

= 5.1

b.

E[max(X ,Y )] = ∑∑max(x+y).p (x ,y)

= (0)(.02) + (5)(.06) +…+(15)(.01)

= 9.60

E[min(x, y)] = ∑∑ min (x,y) p(x,y)

= 0(0.02) + 0(0.06) + ……+ 10(0.14) + 10(0.01)

= 4.5

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Answer:

answer is 282

Step-by-step explanation:

im smart

Answer:

A.

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

doesnt have an equals sign

Answer:

The second one, there is not = sign

2(4m+6)

Step-by-step explanation:

An equation is a mathematical statement that two things are equal. It consists of two expressions, one on each side of an 'equals' sign.

for it to be an equation there needs to be an equal sign

Answer:

n < 3

Step-by-step explanation:

6n + 9n < 50

15n < 50

n < 50/15

n < 3.33

Approximately

n < 3

The greatest Number of tickets penny can buy is children 3 tickets; adults 3 tickets making a total of 6 tickets

Answer:

V = 343

Step-by-step explanation:

V = lwh

= 7(7)(7)

= 49(7)

= 343

Answer:

thhe answer would only be 3 feet

Step-by-step explanation:

Answer:

2 bus

Step-by-step explanation:

The expected value of y is larger than the expected value of x. This is because y takes into account the number of students on all 4 buses, while x only takes into account the students on the bus with the randomly selected student.

The expected value of a random variable represents the average value of that variable over multiple trials. In this case, x is a random variable representing the number of students on the bus carrying the randomly selected student, and y is a random variable representing the number of students on the randomly selected bus.

The expected value of x can be calculated as follows:

E[x] = (10/100)×10 + (20/100)×20 + (30/100)×30 + (40/100)×40

= 16 + 12 + 9 + 16

= 53/4

= 13.25

This means that, on average, the bus carrying the randomly selected student would have 13.25 students.

The expected value of y can be calculated as follows:

E[y] = (1/4)×10 + (1/4)×20 + (1/4)×30 + (1/4)×40

= 25

This means that, on average, the randomly selected bus would have 25 students.

As expected, the expected value of y is larger than the expected value of x. This is because y takes into account the number of students on all 4 buses, while x only takes into account the students on the bus with the randomly selected student. Since the number of students on the other 3 buses can vary widely, y has a higher expected value than x.

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The expected number of pairs of professors in conflict is given by (m choose 2) * 1/n.

It can be calculated using the principle of linearity of expectation. We can first calculate the probability that any two professors pick the same time slot, which is 1/n. Then, we can count the number of pairs of professors, which is given by the binomial coefficient (m choose 2) = m(m-1)/2. Therefore, the expected number of pairs of professors in conflict is:

Expected number of pairs in conflict = (m choose 2) * 1/n

This formula holds when the selection of time slots by each professor is independent of the choices made by all other professors. Note that this formula assumes that each professor selects only one time slot, and does not consider the possibility of a professor selecting multiple time slots. If professors are allowed to select multiple time slots, then the formula would need to be modified accordingly.

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The integral test is used to find whether the given series is converged or not. The convergence of series is more significant in many situations when the integral function has the sum of a series of functions.

∫1+∞f(x)dx exists finite ⇒ ∑+∞ (n=1) an coverges.

we know ∫1+∞ 1/x^5dx= (-1/4x^4)1+∞ = 1/4, which is finite, so the series converges.

(If this is wrong you have every right to report me)

I hoped this helped <3333

Answer:

a. x² + 6x + 9 = -22 + 9

Step-by-step explanation:

they moved the 22 to the right by subtracting it. this leaves a binomial on the left side, which if what you want to solve it.

then they completed the square by dividing b (6) by 2 = 3. then squaring 3 to get 9.

if you added 9 to the left, then you have to add 9 to the right, therefore resulting in -22 + 9.

Answer:

In TTM/Imagine Math it is top left or a.

Step-by-step explanation:

the probability of transitioning from state 1 to state 2 after the first transition is:

P(X(t) enters state 2 after the first transition | X(0) = 1) = 1 / 3

To write the system of ordinary differential equations (ODEs) for the transition probabilities Pᵢⱼ(t) of the given continuous-time Markov chain, we need to consider the rate at which the system transitions between different states.

Let Pᵢⱼ(t) represent the probability that the Markov chain is in state j at time t, given that it started in state i at time 0.

The ODEs for the transition probabilities can be written as follows:

dP₁₂(t)/dt = q₁₂ * P₁(t) - q₂₁ * P₂(t)

dP₁₃(t)/dt = q₁₃ * P₁(t) - q₃₁ * P₃(t)

dP₂₁(t)/dt = q₂₁ * P₂(t) - q₁₂ * P₁(t)

dP₂₃(t)/dt = q₂₃ * P₂(t) - q₃₂ * P₃(t)

dP₃₁(t)/dt = q₃₁ * P₃(t) - q₁₃ * P₁(t)

dP₃₂(t)/dt = q₃₂ * P₃(t) - q₂₃ * P₂(t)

where P₁(t), P₂(t), and P₃(t) represent the probabilities of being in states 1, 2, and 3 at time t, respectively.

Now, let's consider the second part of the question: Suppose that the initial state is 1. We want to find the probability that after the first transition, the process X(t) enters state 2.

To calculate this probability, we need to find the transition rate from state 1 to state 2 (q₁₂) and normalize it by the total rate of leaving state 1.

The total rate of leaving state 1 can be calculated as the sum of the rates to transition from state 1 to other states:

total_rate = q₁₂ + q₁₃

Therefore, the probability of transitioning from state 1 to state 2 after the first transition can be calculated as:

P(X(t) enters state 2 after the first transition | X(0) = 1) = q₁₂ / total_rate

In this case, the transition rate q₁₂ is 1, and the total rate q₁₂ + q₁₃ is 1 + 2 = 3.

Therefore, the probability of transitioning from state 1 to state 2 after the first transition is:

P(X(t) enters state 2 after the first transition | X(0) = 1) = 1 / 3

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Answer: The plane traveled 15838.5 feet from point A to point B.

The value of the boolean variable x is 0

The boolean equation is given as:

x . 1 = 0

The above means that:

x and 1 = 0

The law of the and operator is that;

The output is 0 if both inputs are different.

One of the inputs is 1.

So, the other input is 0

Hence, the value of x is 0

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==========================================================

Rule:

If A+B = 90, then tan(A) = 1/( tan(B) ) and tan(B) = 1/( tan(A) )

-------

Since C = 90, this must mean the other two angles A and B are acute and complementary. So A+B = 90 must be the case. This allows us to use that rule above.

So,

tan(B) = 1/( tan(A) )

tan(B) = 1/( 0.25 )

tan(B) = 4

-------

Here's another way to think about it.

If tan(A) = 0.25, then we could have BC = 1 and AC = 4 as the opposite and adjacent sides respectively. That leads to tan(A) = opposite/adjacent = BC/AC = 1/4 = 0.25

When computing tan(B), the BC and AC sides swap roles in terms of opposite and adjacent,

tan(B) = opposite/adjacent = AC/BC = 4/1 = 4.

For any of these cases, we don't involve the hypotenuse AB.

If the random sample of 10 bags is taken to check the working ; then the average amount of candy dispensed by the machine is less than 16 ounces .

In the question ,

it is given that ,

a random sample of 10 bags is taken to verify that the machine is working fine ,

the mean amount of candy dispensed is = 15.887 oz ,

the standard deviation of the sample is = 0.1304 oz .

we have to check whether the average amount of candy dispensed by machine is different from 16.0 oz .

So , H₀ : μ = 16 v/s  H₁ : μ < 16

the test statistic(t) will be =

t = (mean - average)/(σ/√n)

= (15.887 - 16)/(0.1304/√10)

= -0.113/0.0412361

Simplifying further ,

we get ;

= -2.7403  .

|t| = 2.7403

Now t(critical value) at n - 1= 9 degree of freedom and α = 0.05 .

So , t₉,₀.₀₅ = 1.833

Now , Since the t value calculated (2.7403) is greater than t critical (1.833)

we reject the H₀ and accept H₁ .

Therefore , The average amount of candy dispensed by the machine is less than 16 ounces .

The given question is incomplete , the complete question is

A packing machine in a candy factory is supposed to put 16.0 ounces of chocolate-covered raisins in each bag. to verify that the machine is working correctly, a random sample of 10 bags is taken, and found to contain an average of 15.887 oz. of candy, with sample standard deviation 0.1304 oz. does this indicate that the average amount of candy dispensed by the machine is different (either way) from 16.0 ounces ?

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Answer:

The maximum is when both X and y = 1.The maximum value of the function is 3.When both X and YY are equal to 0, the minimum value is 0

The absolute maximum value is 3 and the absolute minimum value is 0.

To find the absolute maximum and minimum values of f(x,y) = x^2 + 2y^2 on the square [0,1] x [0,1], we need to consider both the interior and the boundary of the square.

First, check for critical points in the interior by finding the partial derivatives and setting them equal to zero:

fx = 2x and fy = 4y

Setting them equal to zero, we have:
2x = 0 => x = 0
4y = 0 => y = 0

The only critical point in the interior is (0,0).

Next, evaluate f(x,y) on the boundary of the square [0,1] x [0,1]. The boundary consists of four segments: x=0, x=1, y=0, and y=1.

1. x=0: f(0,y) = 2y^2 (for y in [0,1])
2. x=1: f(1,y) = 1 + 2y^2 (for y in [0,1])
3. y=0: f(x,0) = x^2 (for x in [0,1])
4. y=1: f(x,1) = x^2 + 2 (for x in [0,1])

Now, compare the values of f at the critical point and boundary points to find the absolute maximum and minimum:

Absolute minimum: f(0,0) = 0
Absolute maximum: f(1,1) = 3

So the absolute maximum value is 3 and the absolute minimum value is 0.

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Answer:

x = 4.08

Step-by-step explanation:

3x = 12.25

3/3x = 12.25/3

x = 4.0833..

x is about 4.08

Answer:

4.08

Step-by-step explanation:

12.25 / 3 = 4.0833333333333 and round

If there were 1000 births in 1995 in a given community and of these 90 died before Jan. 1, 1996 and 50 died after Jan. 1, 1996 but before reaching their first birthday then, the cohort probability of death before age 1 for 1995 is 0.140.

To calculate the cohort probability of death before age 1, we need to determine the proportion of infants who died before their first birthday relative to the total number of births. This proportion represents the likelihood of an infant in the given community dying before reaching the age of 1.

Given, Birth in 1995 = 1000

Died before Jan. 1, 1996= 90

Died after Jan. 1, 1996= 50

We need to find the cohort probability of death before age 1.

The total number of births in 1995 = 1000

The number of infants who died before Jan. 1, 1996= 90

Therefore, the number of infants who survived up to Jan. 1, 1996= 1000 - 90 = 910

Number of infants who died after Jan. 1, 1996, but before their first birthday = 50

Therefore, the number of infants who survived up to their first birthday = 910 - 50 = 860

The cohort probability of death before age 1 for 1995 can be calculated as follows:

\text{Cohort probability of death before age 1 }= \frac{\text{Number of infants died before their first birthday}}{\text{Number of births in 1995}}

\text{Cohort probability of death before age 1 }= \frac{90 + 50}{1000}

\text{Cohort probability of death before age 1 }= 0.14

Therefore, the cohort probability of death before age 1 for 1995 is 0.140.

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Answer:

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

Step-by-step explanation:

Assuming you require the expression factorised.

4x² - 9y² ← is a difference of squares and factors in general as

a² - b² = (a - b)(a + b)

4x² - 9y²

= (2x)² - (3y)²

= (2x - 3y)(2x + 3y)

Answer:

59

Step-by-step explanation:

all triangles add up to 180 degrees.

add 87+34=121

do 180-121=59 because you want to find the value of x

to check your work add up all of the degrees together and when you get 180 you will be correct!

Answer:

x=59

Step-by-step explanation:

87+x+34=180 because its a straight line

121+x=180

x=59

Answer:

-3

Step-by-step explanation:

in minus number the smallest number is the biggest

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The dimensions of the rectangular pen should be 15 by 20 feet and the maximum area is 1200 square feet.

Let the area be y .

Area = (base) × (height)

Base = 2x

Height = h

Let the area of the rectangular pens be y .

∴ y = 2xh

Perimeter of all the fencing = 4x+3h

∴ 4x+3h = 120

now we solve for h

3h = 120-4x

h = 40 - 4/3 x

Now we will substitute this value in the above first equation:

y = 2xh

or, y = 2x (40 - 4/3 x)

or, y = 80x - 8/3 x²

Now for the maximum area we have to find the first order differentiation of y

now,

dy /dx = 80 - 16/3 x

At dy/dx = 0 we get the value of x for which y is maximum.

80 - 16/3 x = 0

or, - 16/3 x = -80

or, x = 15 feet

Hence height =  40 - 4/3 x = 40 - 20 = 20feet

Maximum area = 2xh = 2×15×40 = 1200 square feet

The dimensions of the rectangular pen should be 15 by 20 feet and the maximum area is 1200 square feet.

Disclaimer : The missing figure for the question is attached below.

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