Use the determinant function det(A) and rank function rank(A) to determine whether or not the following vectors are linearly dependent.
(a) (2, 4, 5, -3), (-3, 2, 7, 0), (9, 2, 4, 6), (3, 2, -6, 5)
(b) (1, -1, 3, 2), (-1, 2, 4, -5), (3, -4, 2, 9), (7, 2, 1, 3)

The equation that represents a non linear function is y = x²   , the correct option is (a) .

In the question ,

four functions are given ,

we have to select the option that is non linear ,

we know that ;

A Linear Function is an equation in which the the highest degree of the equation is 1 , and the graph is a straight line .    and

A Non Linear Function ,is an equation in which the highest degree of the equation is more than 1 , and the graph is not a straight line .

So , from the given options

we can see that all the options have degree 1 except the equation y = x² which has highest degree 2 .

Therefore , The Non Linear Function is (a) y = x² .

Learn more about Functions here

https://brainly.com/question/27405668

#SPJ4

The required equation for the variation of k is given as k = Fd² / xy.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
Newton's Law of Universal Gravitation states that the gravitational attraction, f, between two objects with masses x and y is proportional to the product of their masses and inversely proportional to the square of their distance, d.
So,

F ∝ x × y - - - - (1)
And
F ∝ 1 / d² - - - - - (2)

Combining equations 1 and 2
F ∝ xy / d²
Or
F = kxy / d²

Now,
Formulate the above expression with subject to constant k.
K = Fd² / xy

Thus, the required equation for the variation of k is given as k = Fd² / xy.

Learn more about simplification here:

https://brainly.com/question/12501526

#SPJ2

Answer:

43

Step-by-step explanation:

258 divided by 6 equals 43

Look below

Armando divided 6 and 258

258 is the bigger number, so we will keep that on the right, and then add the dividing symbol. Next, we will add the 6. That should look like this:

258÷6

then just put it on a calculator and you get the answer 43. hope that helps

The two events a and b are independent if and only if (a) Events a and b are independent  .

What are Independent Events ?

Two events A and B are said to be independents if the occurrence of event A does not affect the chance of occurrence of the other event B .

The probability of two independent events can be mathematically represented as  P(A and B) = P(A) × P(B) .

So, we can conclude that , Two events, a and b are independent if and only if Events a and b are independent  .

Therefore , the correct option is (a) .

The given question is incomplete , the complete question is

Two events, a and b are independent if and only if

Which of the following statements is true of a and b?

(a) Events a and b are independent

(b) Events a and b are not independent, but they are mutually exclusive

(c) Events a and b are not independent since and .

Learn more about Independent Events here

https://brainly.com/question/14106549

#SPJ4

By midpoint segment theorem DE=1/2BC for AD≅BD and AE≅EC of the triangle ABC.

A triangle is a three-sided polygon that consists of three edges and three vertices.

A line segment that connects two midpoints of the sides of a triangle is called a midsegment.

DE is the midsegment of AB and AC.

AD≅BD and AE≅EC.

The Midsegment Theorem states that the midsegment connecting the midpoints of two sides of a triangle is parallel to the third side of the triangle, and the length of this midsegment is half the length of the third side.

DE=1/2BC

5=1/2(10)

5=5

Hence, DE=1/2BC for AD≅BD and AE≅EC of the triangle ABC.

To learn more on Triangles click:

https://brainly.com/question/2773823

#SPJ1

Equation of the line parallel to the given line and passing through the given point = 2x+5y=18.

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. 

The meanings of the word equation and its cognates in various languages can vary slightly.

For instance, in French, an equation is defined as having one or more variables, whereas in English, an equation is any well-formed formula that consists of two expressions linked by the equals sign.

Finding the values of the variables that result in the equality is the first step in solving an equation with variables.

The unknown variables are also known as the variables for which the equation must be solved, and the unknown variable values that fulfill the equality are known as the equation's solutions.

Equations come in two varieties: identities and conditional equations.

According to our question-

Given line: 2x+5y−7=0

the mid - point of the line segment joining point (2,7) and (−4,1) is

( 2(2−4 )2(7+1))=(−1,4)

the equation of the line will be

y−y 1=m(x−x 1)y−4=( 5−2 )(x+1)

5y−20=−2x−2

2x+5y=18

Hence,  Equation of the line parallel to the given line and passing through the given point = 2x+5y=18.

learn more about equations click here:

https://brainly.com/question/2972832

#SPJ4

The statement "let c and d be disjoint compact subspaces of the Hausdorff space x and then there exist disjoint open sets u and v containing c and d, respectively." is proved.

Here we have given the let A and B be disjoint compact subspaces of the Hausdorff space X.

And we have to prove the statement.

According to the given question, let us consider that x be an arbitrary coordinate of A and here the points of x isn't in Y because A and B are disjoint.

Then according to Lemma 26.4 disjoint open sets Ux and Vx such that x Î Ux and Ux contain B.

Here the collection {Ux} is a covering of A by sets open in X.

And the finite collection of them {U1, ..,Un} covers A because A is compact.

Here the open set U = U1 U....U Un contains A and it is disjoint from

V = V1 I.....I Vn that contains B because it's the finite intersection of the corresponding open sets containing.

Therefore, here there exists disjoint open sets U and V containing A and B, respectively.

To know more about coordinate here.

https://brainly.com/question/27749090

#SPJ4

Answer:

The equation that accurately represents Liam's balance, y, after x days is y = -12.75 - 10x.

This equation takes into account the fact that Liam's balance is already -$12.75 and that he is charged a $10 overdraft fee each day his balance is below $0. As the number of days, x, increases, the total amount of overdraft fees he is charged will also increase, resulting in a decrease in his balance.

For example, if Liam's balance is -$12.75 after 0 days, his balance will be -$22.75 after 1 day (y = -12.75 - 10(1) = -22.75), and his balance will be -$32.75 after 2 days (y = -12.75 - 10(2) = -32.75).

The data are statistically significant at level = 0.05, but not at level = 0.01.

Given-

H0: μ = 115

HA: μ ≠ 115

The sample mean = 120

The standard deviation = 25

Standard error of mean 2.5

Solution-

If  z = (xbar- μ ) / SE

Then the solution would be

z = (120-115) / 2.5

z = 2

P of the value = 2 P( z > 2) = 2(0.0228) = 0.0456 is the statistically significant level.

Therefore the answer is technically at .05 level of significance.

To learn more about the  hypothesis test refer here

https://brainly.com/question/15414435

#SPJ4

Answer:

1) $468

2) 7668

Step-by-step explanation:

1) 6.5% of 7200 is 468. Therefore, this is the amount it had increased.

2) 7200+468=7668 Total for the end of the year

Since our test statistics ( 8.96 ) is less than the critical value ( 29.141 ),

there is no strong evidence to indicate that the standard deviation of hole diameter exceeds 0.02 millimeters.

Given that;

H₀ : σ = 0.02

H₁ : σ > 0.02

The test statistics is;

X² = ( n-1 )s² / σ²  = ( 15 - 1)(0.016)² / (0.02)²

= 0.003584 / 0.0004

= 8.96

degree of freedom

df = n - 1 = 15 - 1 = 14

For right tailed test, critical value at 0.01 level of significance is 29.141.

Now since our test statistics ( 8.96 ) is less than the critical value (29.141 ),

Therefore, there is no strong evidence to indicate that the standard deviation of hole diameter exceeds 0.02 millimeters.

To learn more about p value refer here

https://brainly.com/question/4621112

#SPJ4

The value of the x is 3.26556.

What is the Intersecting Chord Theorem?

When two chords intersect each other inside a circle, the products of their segments are equal.

We have,

It is a little easier to see this in the diagram, each chord is cut into two segments at the point where they intersect.

One chord is cut into two line segments A(x+10) and B(x+1). The other is into segments C(x) and D(5x+1).

According to Intersecting Chord Theorem:

This theorem states that A×B is always equal to C×D no matter where the chords are.

A.B = C.D

(x+10) * (x+1) = (x) * (5x+1).

x² + x + 10x + 10 = 5x² + x

x² + x + 10x + 10 - 5x² - x = 0

-4x² + 10x + 10  = 0

using the Quadratic Formula where, a = -4, b = 10, and c = 10, we get

x=−0.765564

x = 3.26556

Hence, the value of the x is 3.26556.

To learn more about Intersecting Chord Theorem visit,

https://brainly.com/question/13950364

#SPJ1

Answer:

19.9 m

Step-by-step explanation:

Cone: r= 1m Height= 2m (You will use the radius for the Cylinder)

1/3 x π x 1^2 × 2 = 2.0943951023932

2.0943951023932 x 2 = 4.1887902047864 (Just use the hundreths place if writing down.)

Cylinder: r= 1m Height= 5m

π x 1^2 x 5 = 5π = 15.707963267949

Now add both together then round to tenths.

4.1887902047864 + 15.707963267949 = 19.8967534727354

(Remember use hundreths place if writing down)

19.8967534727354 --> 19.9 m

Answer:

R = 0≤ y ≤ 800

D = 0≤ x ≤ 16

.

.

.

.

Answer:

sorry new don't understand the app

The value of the amount will be $721.40.

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

500 dollar deposit for 20 years with a interest rate of 2%.

Now,

We know that;

The formula for amount is,

⇒ [tex]A = P (1 + r)^n^t[/tex]

Where, A is total amount, P is principle amount, r is interest rate.

Here, We have;

P = $500

t = 20 years

r = 2%

Substitute all the values, we get;

⇒  [tex]A = P (1 + r)^n^t[/tex]

⇒ [tex]A = 500 (1 + 0.02)^2^0[/tex]

⇒ A = 500 × 1.02²⁰

⇒ A = 500 × 1.44

⇒ A = $721.40

Thus, The value of the amount = $721.40

Learn more about the percent visit:

https://brainly.com/question/24877689

#SPJ1

Ma'am there is nothing to solve...

:<

Answer:

Step-by-step explanation:

Yes there is literally nothing to solve:(

a) The probability that they actually use drugs, if an employee tests positive for drug use is 69%

b) The probability that a nondrug user will test positive for drug use twice in a row is 0.25%

c) The probability that someone who tests positive twice in a row is not a drug user is 23%

Based on past knowledge of circumstances that might be relevant to the event, Bayes' theorem estimates the likelihood of an event.

The theorem explains how a degree of belief, stated as a probability, should logically alter to account for the presence of relevant data using Bayesian probability interpretation.

The question state that

Pr(D) = 0.10

Pr(D') = 0.90

Pr (P/D) = 0.98 ( (2% False negatives means for drug users, 2% will get a negative result, so 98% will get positive result)

Pr(P/D') = 0.05

a) The probability that they actually use drugs, if an employee tests positive for drug use Pr(D/P) = Pr(D)*Pr (P/D) / Pr(D)*Pr (P/D)+Pr(D')*Pr(P/D')

⇒ Pr(D/P) = (0.10*0.98)/(0.10*0.98 + 0.90*0.05)

⇒ Pr(D/P) = 0.098/(0.098+0.045)

⇒ Pr(D/P) = 0.098/0.143

⇒ Pr(D/P) ≈ 0.6853

⇒ Pr(D/P) ≈ 69%

b) The probability that a nondrug user will test positive for drug use twice in a row Pr (P*2/D') = Pr(P/D')*Pr(P/D')

⇒ Pr (P*2/D') = 0.05*0.05

⇒ Pr (P*2/D') = 0.0025

⇒ Pr (P*2/D') = 0.25%

c) The probability that someone who tests positive twice in a row is not a drug user Pr (D'/P*2) = Pr(D')*Pr (P*2/D') / Pr(D')*Pr (P*2/D')+Pr(D)*Pr (P*2/D)

⇒ Pr (D'/P*2) = (0.90*.0.05²)/(0.90*0.05²+0.10*0.98²)

⇒ Pr (D'/P*2) = 0.00225/ 0.00225+0.09604

⇒ Pr (D'/P*2) = 0.00225/0.09829

⇒ Pr (D'/P*2) ≈ 0.2289

⇒ Pr (D'/P*2) ≈ 23%

To learn more about Bayer's theorem visit:

brainly.com/question/28096770

#SPJ4

The statement given in the question holds true . We get this result after analyzing the given data set .

Given , hypothesis is ,

Let d be any positive integer not equal to2 , 5 or 13 .

Show that one can find distinct a , b  in the set {2,5,13,d} such that ab-1 is not a perfect square.

Using the modular way to solve this question we get ,

d = 0 , 3 = | 4 |

Then , we get the result as ,

13d - 1 , which is not a perfect square.

d = 2|4|

we get , 2d -1

which again is not a perfect square.

Similarly after checking the value for all the possible cases , we will get the result that the hypothesis is correct.

To learn more about hypothesis

brainly.com/question/29519577

#SPJ4

In a study where the least squares estimates were based on 34 sets of sample observations, the total sum of squares and regression sum of squares were found to be: SST = 4.35 and SSR = 4.18. What is the error sum of squares is 0.17.

To learn more about square refer to:

https://brainly.com/question/25092270

#SPJ1

Answer:

Need more info please

Step-by-step explanation:

Let D be the region bounded by the lines y = 0, y = x, x = 1, and x = 2. In order to express the double integral as an iterated integral with reversed order of integration, we first need to sketch the region D.

The double integral could be expressed as an iterated integral with reversed order of integration as follows:

[tex]$\int_{1}^{2}\int_{0}^{x}f(x,y)dydx$[/tex]

The region is bounded by the lines y = 0, y = x, x = 1, and x = 2. This forms a triangle-like shape with 1 and 2 being the x-coordinates of the vertices and y = 0 being the base of the triangle. Then, we can express the double integral as: [tex]$\int_{1}^{2}\int_{0}^{x}f(x,y)dydx$[/tex], where the order of integration is reversed from the original double integral. This means that first we are integrating with respect to y from 0 to x, and then we are integrating with respect to x from 1 to 2.

Learn more about integral here

https://brainly.com/question/18125359

#SPJ4

The upper control limit is 16.4 if our desired confidence interval is 99.73%.

In statistics, a confidence interval describes the likelihood that a population parameter will fall between a set of values for a given percentage of the time.

Given 131 population

Standard deviation = 5

sample size = 11.

mean   = 131/11 = 11.9.

Determine the upper control limit if desired confidence interval is 99.73%

Confidence interval = sample mean ± margin of error

Upper limit  = sample mean + margin of error.

Margin of error = z* * population of standard deviation/[tex]\sqrt{n}[/tex]

Margin of error = 3.00 * 5/[tex]\sqrt{11}[/tex].

Value of z* for 99.73% confidence interval  is 3.00.

So margin of error = 4.5.

Upper limit  = 11.9 + 4.5

Upper limit  = 16.4

If we want a confidence level of 99.73%, the top control limit is 16.4.

To know more about confidence interval here

brainly.com/question/24131141

#SPJ4.

Answer:

e

Step-by-step explanation:

because it's number is common

Answer:

81.74 cm²

Step-by-step explanation:

Use tan(x) to find x

tanθ = opposite/adjacent

tan(36) = x/15

15tan(36) = x

area of triangle = [tex]\frac{1}{2}[/tex]*b*h

[tex]\frac{1}{2}[/tex]*15tan(36)*15 = 81.74 cm² (2 d.p.)

the 25th, 50th, and 75th percentile from the following list of 32 data are 25th percentile: 13 , 50th percentile: 21 , 75th percentile: 29.

To find the 25th percentile:

25th percentile: 25% of 32 = 8th number = 13

Count the total number of values in the data set, which is 32

Calculate 25% of 32, which is 8

Count 8 numbers from the beginning of the list and the 25th percentile is the 8th number, which is 13

To find the 50th percentile:

50th percentile: 50% of 32 = 16th number = 21

Count the total number of values in the data set, which is 32

Calculate 50% of 32, which is 16

Count 16 numbers from the beginning of the list and the 50th percentile is the 16th number, which is 21

To find the 75th percentile:

75th percentile: 75% of 32 = 24th number = 29

Count the total number of values in the data set, which is 32

Calculate 75% of 32, which is 24

Count 24 numbers from the beginning of the list and the 75th percentile is the 24th number, which is 29

Learn more about percentile here

https://brainly.com/question/1594020

#SPJ4

To calculate the volume of a cylindrical tank, you will need to use the formula for the volume of a cylinder, which is:

V = πr^2h

Where V is the volume, r is the radius of the base of the cylinder, and h is the height of the cylinder.

To use this formula, you will need to first calculate the radius of the base of the tank. To do this, you will need to divide the diameter of the tank (170 feet) by 2.

Once you have calculated the radius, you can plug the value into the formula along with the height of the tank (60 feet) to find the volume of the tank.

Answer:

Step-by-step explanation:

height of the tank= 60 feet

diameter = 170 feet.

as we know, radius = 2 *diameter

therefore radius = diameter /2

                            =  170/2

                             =85 feet

volume of cylinder =  πr²h

 π =3.14    

                               = 3.14 ×85×60

                                =10927.2 feet²  

The probability generating function of a discrete nonnegative integer valued random variable X is defined by ø(s) = E[s] = Σp;si j=0, where pj is the probability mass function of X. P{XY} = P{X=i,Y=j} = P{X=i}P{Y=j} = pi pj sij,Therefore, ø(s) = Σ pi pj sij = P{XY}

In this problem, we are also given a geometric random variable Y with parameter p 1 s, where 0 < s < 1. Y is independent of X. To show that ø(s) = P{XY}, we must show that the two expressions are equal.

First, we note that the probability of X and Y being equal to i and j, respectively, is given by P{X=i,Y=j} = P{X=i}P{Y=j} = pi pj sij. This is because the probability of X being equal to i is pi, and the probability of Y being equal to j is pj (where p is the parameter of the geometric distribution). Since sij is the product of i and j, the probability of both X and Y being equal to i and j, respectively, is pi pj sij.

We can now substitute this expression into the probability generating function for X. We have that ø(s)

= E[s] = Σp;si j=0

= Σ pi pj sij

= P{XY}

Learn more about probability here

https://brainly.com/question/11234923

#SPJ4