5a-5b. What is wrong with these systems.
5a. x - 3y = 0 y= 1/3x - 4
5b. x + 4y = 8
y = -1/4x + 2

Answer:

Step-by-step explanation:

The steps are in the photo above

I hope that is useful for you :)

Explanation:

Let's go over the possible choices to see which statements are true and which are false.

To summarize, only choice B is true. The rest are false.

Answer:

The third one

Step-by-step explanation:

Answer:

Graph B.

Step-by-step explanation:

The algebraic expression for the verbal expression 7 divided by the product of 9 and x is 7/9x.

Given verbal expression is 7 divided by the product of 9 and x.

Hence, the required algebraic expression for given verbal expression is 7/9x.

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For a Poisson process with rate λ, the interarrival times between events are exponentially distributed with parameter μ = 1/λ. So, the time between the (n-1)-th and n-th event, denoted as Tn, follows an exponential distribution with parameter μ = 1/3 minutes.

Since Sn is the sum of the first n interarrival times, we have:

Sn = T1 + T2 + ... + Tn

The sum of n exponential random variables with parameter μ is a gamma random variable with shape parameter n and scale parameter μ. Therefore, Sn follows a gamma distribution with shape parameter n and scale parameter μ.

In this case, n = 10 and μ = 1/3. So, E[S10] can be calculated as:

E[S10] = n * μ = 10 * (1/3)

= 10/3 minutes.

Therefore, E[S10] = 10/3 minutes.

b. E[S4|N(1) = 3]:

Given that N(1) = 3, we know that there are 3 events in the first minute. Therefore, the time of the 4th event, S4, will be the sum of the first 3 interarrival times plus the time between the 3rd and 4th event.

Using the same reasoning as in part a, we know that the sum of the first 3 interarrival times follows a gamma distribution with shape parameter 3 and scale parameter 1/3. The time between the 3rd and 4th event, denoted as T4, follows an exponential distribution with parameter 1/3.

So, S4 = T1 + T2 + T3 + T4.

Since T1, T2, T3 are independent of T4, we can calculate E[S4|N(1) = 3] as:

E[S4|N(1) = 3] = E[T1 + T2 + T3 + T4]

= E[T1 + T2 + T3] + E[T4]

= (3/3) + (1/3)

= 4/3 minutes.

Therefore, E[S4|N(1) = 3] = 4/3 minutes.

c. Var(S10):

The variance of Sn, Var(Sn), for a Poisson process with rate λ, is given by:

Var(Sn) = n * σ^2,

where σ^2 is the variance of the interarrival times.

In this case, n = 10 and the interarrival times are exponentially distributed with parameter μ = 1/3. The variance of an exponential distribution is \(\mu^2\)So, \(\sigma^2 = \left(\frac{1}{3}\right)^2\)

= 1/9.

Substituting the values into the formula, we have:

Var(S10) = 10 * (1/9)

= 10/9.

Therefore, Var(S10) = 10/9.

d. E[N(4) − N(2)|N(1) = 3]:

Given that N(1) = 3, we know that there are 3 events in the first minute. Therefore, at time t = 2 minutes, there will be 3 - 1 = 2 events that have already occurred.

Now, we need to find the expected value of the difference in the number of events between time t = 4 minutes and t = 2 minutes, given that there were 3 events at t = 1 minute.

Since the number of events in a Poisson process follows a Poisson distribution with rate λt, where t is

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Answer:

49th term = 225

Step-by-step explanation:

The following sequence: -15, -10, -5, 0, -5... is an example of an arithmetic progression.

An arithmetic progression or AP for short, is a sequence in which the difference between successive terms is constant. This difference is known as the common difference, and can be found by subtracting a term by its preceding term.

The general formula, for the nth term of an arithmetic progression, is thus:

Tn = a + (n - 1)d, where a = first term, and d = common difference.

In the sequence: -15, -10, -5, 0, 5...,

a = -15, and d = -10--15 = 5

T49 = -15 + (49 - 1)5 = 225

∴ 49th term = 225

The probability from the odds is 3/7

The value of the odds is given as

Odds = 3 to 4

Represent the odds as a fraction

So, we have the following representation

Odds = 3/4

To convert the odds to probability, we make use of the following equation

Probability = Odds/(1 + Odds)

Substitute the known values in the above equation, so, we have the following representation

Probability = (3/4)/(3/4 + 1)

Evaluate the sum

Probability = (3/4)/(7/4)

Evaluate the quotient

Probability = 3/7

Hence, the probability is 3/7

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Answer:

64 + (-15) + (-5)= 44

Stella is 24ft above the ground.

A. 64 + (-15) = 49

B. -121 + (-34) = -155

C. -86 + 92= 6

D. 109 + (-162)= -53

After 4 hours of discharging, the volume left in the tank would be 500 liters. The correct option is C.

Initially, the tank has a water capacity of 1500 liters.

After three hours of discharging, half of the water is discharged, which means 1500/2 = 750 liters have been removed from the tank.

To find the volume left after 4 hours of discharging, we need to subtract the additional amount discharged in the fourth hour.

Since the discharge rate remains the same, we can calculate the amount discharged in one hour as 750/3 = 250 liters.

Therefore, in the fourth hour, 250 liters would be discharged. Subtracting this from the remaining water after three hours (750 liters), we get 750 - 250 = 500 liters.

Therefore, the correct answer is c. 500 liters.

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Answer:

Step-by-step explanation:

The meaning of the translation (x + 6, y + 10) is that all points in a coordinate plane are moved 6 units to the right and 10 units up.

In other words, for any point (x, y) in the original position, after the translation, the new coordinates would be (x + 6, y + 10). This means that the x-coordinate of each point is increased by 6 units, resulting in a shift to the right, and the y-coordinate is increased by 10 units, resulting in a shift upwards.

The equivalent function in the form \(R(t) = ab^t\) is: \(R(t) = 4001 * 0.9^t.\)

What is an equivalent function?

The domain and range of an equivalent function are the same. In mathematics, the phrases equivalent and equal do not have the same meaning.

The equation R(t) = 4000(0.9)^t + 1 can be rewritten in the form \(R(t) = ab^t\)by separating the constant factor and the exponential factor. We can do this by defining a = 4000 and b = 0.9:

 \(R(t) = 4000 * (0.9)^t + 1\\\\= 4000 * b^t + 1\\\\= (4000 + 1) * b^t\\\\= 4001 * b^t\\\\= ab^t\)

where, a = 4001 and b = 0.9.

So, the equivalent function in the form \(R(t) = ab^t\) is:

\(R(t) = 4001 * 0.9^t.\)

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Answer:

690.50

Step-by-step explanation:

Answer:

The area of rectangle is "31 units²".

Step-by-step explanation:

The given values are:

Length of rectangle,

= \(\frac{21}{7}\)

Width of rectangle,

= \(\frac{31}{3}\)

As we know,

The area of rectangle is:

=  \(Length\times width\)

On substituting the values, we get

=  \(\frac{21}{7}\times \frac{31}{3}\)

=  \(\frac{217}{7}\)

=  \(31 \ units^2\)

Answer:

-8/1 or just -8

Step-by-step explanation:

Answer:

Answer is 1.6

Step-by-step explanation:

I hope it's helpful!

Answer:

1 3/5    or 1.6

Step-by-step explanation:

8/5 = 1 3/5   or   1.6

Using the proportional rule of Similar Triangles, the length of SD is 12 m.

Given a truss bridge.

From it,

The triangles BCD and RSD are similar.

For similar triangles, corresponding sides are proportional.

Corresponding sides are,

BC and RS, CD and SD, BD and RD.

BC / RS = CD / SD = BD / RD.

Consider BC / RS = CD / SD.

2 / 1 = 24 / SD

2 (SD) = 24

SD = 12

Hence the length of SD is 12 m.

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Answer:

8 grams

Step-by-step explanation:

a triangle is half a square

Answer: only x=3 is a solution and only x=1 is an extraneous root

For the given expression (x/x-1) - (3/x) = 1/x-1 both x=3 and x=1 are solutions. The correct option is B.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression is  (x/x-1) - (3/x) = 1/x-1. Check the solution of the expression,

(x/x-1) - (3/x) = 1/x-1

( 3 / 3 - 1 ) - ( 3 / 3 ) = 1 ( 3 - 1 )

( 3 / 2 - 1 ) = 1 / 2

1 / 2 = 1/2

For x = 1 the value is the same.

Therefore, both 3 and 1 are solutions to the given formula (x/x-1) - (3/x) = 1/x-1.

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Answer:

there's nothing there

Step-by-step explanation:

Answer:

\(pr(x=6)=\frac{17}{28}\)

Step-by-step explanation:

Well the probabilities should all up to 1. This means pr(x<6) + pr(x=6) + pr(x>6) = 1.

So plugging in the known values we get: \(\frac{1}{7} + pr(x=6) + \frac{1}{4}=1\)

To make things easier, let's multiply the 1/7 by 4/4 and 1/4 by 7/7

\(\frac{4}{28}+pr(x=6)+\frac{7}{28}=1\)

Now combine like terms: \(pr(x=6)+\frac{11}{28}=1\)

Subtract 11/28 from both sides

\(pr(x=6)=\frac{17}{28}\)

Answer:

?, the value does not exist because you can't square root a negative value.

Step-by-step explanation:

root 8 can be simplified but in this case, its negative so answer D.N.E.

= 3 x √-8

= D.N.E.

Answer:-2

-2 times -2 times -2 = -8

Answer:.2 grams per year

Step-by-step explanation:you divide 6 by 30 and thats what you get:)

Answer:5

Step-by-step explanation:30/6=5

A graph of polygon GREAT and its image after a counterclockwise rotation of 90° around the origin is shown in the image attached below.

In Mathematics and Geometry, the rotation of a point 90° about the center (origin) in a counterclockwise (anticlockwise) direction would produce a point that has these coordinates (-y, x).

By applying a rotation of 90° counterclockwise around the origin to vertices W, the coordinates of the vertices of the image ΔA'B'C' are as follows:

(x, y)                               →            (-y, x)

Ordered pair G = (-3, -2) → Ordered pair G' = (2, -3)

Ordered pair R = (-4, 4) → Ordered pair R' = (-4, -4)

Ordered pair E = (0, 1) → Ordered pair E' = (-1, 0)

Ordered pair A = (1, -2) → Ordered pair A' = (2, 1)

Ordered pair T = (-1, -3) → Ordered pair T' = (3, -1)

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After considering the given data we conclude that there truth table is possible and is placed in the given figures concerning every sub question.

A truth table is a overview that projects  the truth-value of one or more compound propositions for each possible combination of truth-values of the propositions starting up the compound ones.
Every row of the table represents a possible combination of truth-values for the component propositions of the compound, and the count of rows is described by the range of possible combinations.
For instance, if the compound has just two component propositions, it comprises  four possibilities and then four rows to the table. The truth-value of the compound is projected on each row comprising the truth functional operator.
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The linear functions for each graph are given as follows:

6. y = -1/3x + 3.

7. y = 1/3x + 1.

8. y = x + 3.

10. y = -2x.

The definition of a linear function is presented as follows:

y = mx + b.

In which the coefficients of the function are given as follows:

For item 6, we have that:

Then the equation is:

y = -1/3x + 3.

For item 7, we have that:

Then the equation is:

y = 1/3x + 1.

For item 8, we have that:

Then the equation is:

y = x + 3.

For item 10, we have that:

Then the equation is:

y = -2x.

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Answer:

-36, -34, -32, -30, -28, -26

Step-by-step explanation:

The surface area of the right rectangular prism is 652 ft²

The surface area of a right rectangular prism is expressed as;

SA = 2( wl + hl + hw )

From the diagram;

Plug the values into the above formula and solve for the surface area.

SA = 2( wl + hl + hw )

SA = 2( (7×8) + (18×8) + 18×7 )

Simplify

SA = 2( 56 + 144 + 126 )

SA = 2( 326 )

SA = 652 ft²

Therefore, the surface area of the prsim is 652 ft².

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The correct option is :

A package that weighs 7 pounds will cost $17 for both options.

The declaration that shows that the provided variables exist is a mathematical equation. When describing the scenario in this circumstance, two or more factors are taken into account.

The equation can be used to symbolize the price, y: Y is equal to 3 plus 2 times the weight of the package, x.

Another choice is for the buyer to pay a one-time price of $17, which is represented by the equation y = 17, in order to send the package.

We'll compare the equation as a whole.

In this case,

3 + 2x = 17

Compile similar terms

2x = 17 - 3

2x = 14

x = 14 divided by 2x = 7

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We should reject the null hypothesis, and we have enough evidence to support the claim.

What is the test statistic ?

Identify the null Hypothesis -

The null hypothesis contains “equal” sign (“=” or “≥” or “≤”),  the  alternative  hypothesis  is the complement to the null hypothesis. The claim is “professional pilots have IQ scores with a standard deviation less than 15”. As the claim contains the “<” sign, it is an alternative hypothesis. Thus, the null hypothesis is the complement: “professional pilots have  IQ  scores  with  a  standard deviation at least 15”.

H0: s ≥ 15

Alternative hypothesis:

“Professional pilots have IQ scores with a standard deviation less than 15.”

H0: s<15

Test statistic:

As the alternative hypothesis contains “<” sign, the test is left - tailed. α = 0.05

The sample standard deviation:

s = 9.5

The test statistic is:

x2 = (n - 1) * s22

= (12 - 1) * s2152

=4.412

P - Value or critical value(s):

For α = 0.05 and d.f. = (12 – 1) * (2 – 1) = 11 the critical value is 4.575 (determined by the table for chi - squared distribution).

As 4.412 < 4.575,

we should reject the null hypothesis, and we have enough evidence to support the claim.

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