show that if p is an invertible m m matrix, then rankpa d rank a. [hint: apply exercise 12 to pa and p 1 .pa/.]

∆MNO and ∆QRS are congruent with each other.

What are rigid motions in congruency of triangles?

Two plane figures are congruent if and only if one can be obtained from the other through a series of rigid motions (that is, reflections, translations, and/or rotations). A landscape architect designs the landscape around a mall using a grid. Trace the landscape elements to ensure that they are congruent.

For the given coordinates M(4, 7), N(5, 4), O(2, 3), Q(2, 5), R(3, 2), S(0, 1)​.

Let's draw the triangles on graph paper,

You can map MNO to QRS with a translation left 2 units and

down 2 units. The planters are congruent because there is a rigid

transformation that maps one to the other.

Hence,  ∆MNO and ∆QRS are congruent with each other.

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The statement if true, for 95% of the samples from the population, the confidence interval we compute will contain the true mean.

In the given question we have to check whether the given statement is TRUE or FALSE.

The given statement is:

For 95% of the samples from the population, the confidence interval we compute will contain the true mean.

Because the underlying approach succeeds on 95% of random samples, we have a 95% confidence that this confidence interval contains the population mean.

Approximately 95% of the estimated intervals will contain the actual value of the population mean if samples are taken frequently and 95% confidence intervals are generated.

So the given statement is true.

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If x and y are independent variables such that x has uniform distribution (0,1) and y has exponential distribution means 1 then e (X+Y) is 3/2, E(XY) is 1/2, E (x-y)2 is 4/3 and E x2 e24 is -1/3

[tex]2^{2}[/tex][tex]e^{ty}[/tex]x ≈ u (0,1) > Independent

y ≈ exp (1) > Independent

E (x) = 0+1/2 = 1/2

v (x) = [tex][1- 0 ] ^{2}[/tex] / 12 = 1/12

E [tex]x^{2}[/tex] = v (x) + [tex][ E x]^{2}[/tex]

       = 1/12 + 1/4 = 1+3/12 = 4/12 = 1/3

E (y) = 1  v(y)=1  E [tex]y^{2}[/tex]= 1+1= 2

E[tex]e^{ty}[/tex] = [tex]\int\limits^_0[/tex][tex]e^{ty}[/tex][tex]e^{-y} dy[/tex]

E[tex]e^{ty}[/tex]  = [tex]\int\limits^_0[/tex][tex]e^{-y} (1-t)[/tex] dy

a : E (x+y) = E (x) + E(y)

       E (x+y) = 1/2+1 = 3/2

b: E (xy) = E (x) E(y) = 1/2 x 1 = 1/2

c: E [tex][x-y]^2[/tex] = E ([tex]x^{2}[/tex]-2xy+ [tex]y^{2}[/tex]

   = E [tex]x^{2}[/tex] - 2 Exy + E [tex]y^{2}[/tex]

  =  1/3 - 2 x 1/2 + 2

   = 1/3 + 1 = 4/3

d. E [tex]x^{2}[/tex] [tex]e^{24}[/tex]

   E ([tex]x^{2}[/tex] ) E [tex]e^{24}[/tex] = 1/3 x -1 = - 1/3

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Answer:

the remaining mass is 7.3 g

Step-by-step explanation:

a=30g

t=200 years

h=98 years

f(98)=a([tex](\frac{1}{2})^ \frac{t}{h}[/tex]

f(98)=30([tex](\frac{1}{2})^ \frac{200}{98}[/tex]

f(98)=7.3

The length of Rocky Mountain Juniper tree will be 1.269 feet.

What is Proportional?

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

A tour guide for Yellowstone National Park is 5.1 feet tall and casts a shadow of 81.6 inches.

Now,

Let the height of Rocky Mountain Juniper tree = x feet

And, A tour guide for Yellowstone National Park is 5.1 feet tall and casts a shadow of 81.6 inches.

So, The height of a Rocky Mountain Juniper tree be if at the same time of day it casts a shadow of 20.3 feet will be find as;

⇒ 5.1 / 81.6 = x / 20.3

Solve for x as;

⇒ 5.1 × 20.3 / 81.6 = x

⇒ 103.53 / 81.6 = x

⇒ x = 1.269 feet

Thus, The length of Rocky Mountain Juniper tree will be 1.269 feet.

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The null hypothesis for the data will be 21.62 and the alternate hypothesis is 2.02 for the p-value for the data is 0.2253 .

The charge at which anything happens is referred to as the velocity at which it happens.

The required details for mean rate :

(a) H0: µ = 21.62

Ha: µ ≠ 21.62

(b) t = -1.231

p-value = 0.2253

(c) Stop rejecting H0 right now. No longer significantly different from the domestic water tariff in Tulsa, the suggested household water charge per five CCF for the entire USA.

(d) H0: µ = 21.62

Ha: µ ≠ 21.62

t = -1.231

check statistic ≥ 2.020

Don't dismiss H0 any longer. The suggested five CCF residential water charge for the entirety of the USA is no longer significantly different from the five CCF residential water tariff in Tulsa.

The P-value is higher at 0.05, the level of significance. The impact in this instance is negligible. The attempt to reject the null hypothesis failed.

The conclusion is that there is insufficient statistical support to determine whether other American cities have a different mortality rate than Tulsa.

The crucial values for t at this level of significance are t=2.019.

Given that the statistic t = -1.15 is inside the acceptance range in this case, the null hypothesis is not disproved.

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Answer:

Archimedes is known as the Father of Mathematics.

He was a Greek philosopher-mathematician who lived from around 287 BC to 212 BC in Syracuse, Sicily.

Answer:        philosopher Archimedes

Step-by-step explanation:

the great Greek mathematician and philosopher Archimedes.

and the  Father of mathematics in India?

Aryabhatta

But yes The Father of Math is the great Greek mathematician and philosopher Archimedes. Perhaps you have heard the name before–the Archimedes' Principle is widely studied in Physics and is named after the great philosopher.

The system of equation 2x + 6y = 10 , x = 8 - 3y has no solution.

System of equation can be solved using different method such as substitution method, elimination method and graphical method.

Let's use substitution method to solve the system of equation as follows:

2x + 6y = 10

x = 8 - 3y

substitute equation(ii) in equation(i)

2(8 - 3y) + 6y = 10

16 - 6y + 6y = 10

16 + 0 = 10

Therefore, the equation has no solution.

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The solution of the inequality 3(n - 6) > 2(n + 12) will be less than 42. Then the correct option is D.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The inequality is given below.

3(n - 6) < 2(n + 12)

Simplify the inequality, then we have

3(n - 6) < 2(n + 12)

3n - 18 < 2n + 24

3n - 2n < 24 + 18

n < 42

The solution of the inequality 3(n - 6) > 2(n + 12) will be less than 42. Then the correct option is D.

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The total after the discount would be $4,726.54

2/10 net 30 is a trade credit extended to the buyer from the seller. A buyer will get a 2% discount on the net amount if they pay in full within the first ten days of the invoice date

Given that: A retailer makes a purchase costing $4,823 from a vendor and then makes a payment in full within nine days of the purchase.

The bill is written with a 2/10 net 30, the buyer would get a two percent discount.

Since the payment is made within nine days, the discount is still valid. Thus:

Total = $4,823 - (2/100 × $4,823 )

Total = $4,823 - (0.02 × $4,823 )

Total = $4,726.54

Therefore, the total would be  $4,823-($4,823 x .02) = $4,726.54. The second option is the answer

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The letter A represents where the amount of $20 should be written .

The letter D, represents where the amount of $36 should be written.

The ending balance, e, is $ 154 .85

The ending balance would be the amount that is left in Mike's account at the end of the month. This amount would be:

= Balance on account after cash gift - ATM withdrawal + Transfer from savings

= 138.85 - 20 + 36

= $ 154 .85

The amount that Mike withdrew of $50 would be shown in letter A because it reduces his account balance and so will be debited.

The transfer from savings of $36 will be treated as a deposit which adds to the balance and so will be letter d.

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Answer:

A

Step-by-step explanation:

Eliminate B and C because they don't pass through (0,1).

Eliminate D because it doesn't decrease quickly enough.

The area of a 6m side polygon is c.) 61.9m².

In a two-dimensional plane, a polygon is a closed object formed of line segments rather than curves. Polygon is a word that combines the words poly (which meaning numerous) and gon (means sides). To create a closed figure, a minimum of three line segments must be connected end to end.

A two-dimensional closed figure with three or more straight sides is called a polygon. A polygon is any shape with straight edges, such as a triangle or rectangle. Figures with open sides or any curved sides are not considered to be polygons.

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The rewritten form of the given expression using the fewest possible terms as required is; 7/30t - 21.

It follows from the task content that the given expression is to be rewritten using the fewest terms.

Since the given expression is;

( 2/5t - 7 + 2/3t ) - (5/6t + 14)

By getting rid of the parentheses; we have;

2/5t - 7 + 2/3t - 5/6t - 14.

By collecting like terms; we have;

2/5t + 2/3t - 5/6t - 7 - 14

7/30t - 21.

Therefore, the required rewritten form of the given expression is; 7/30t - 21.

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By solving a linear equation we will see that DE = 22.67 units.

For the given square we know that EC = 7x - 3 and AE = 4x + 8, notice that both EC and AE are half of a diagonal of the square, so these measures must be the same one, then we can write the linear equation:

7x - 3 = 4x + 8

solving for x:

7x - 4x = 8 + 3

3x = 11

x = 11/3

And DE is also half of the diagonal, so the measure of DE is the same than the measure of EC, then it is:

DE = 7x - 3 = 7*11/3- 3 = 22.67

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[tex]Answer:\ f^{-1}(x)=\boxed{6^{-x}}[/tex]

Step-by-step explanation:

[tex]\displaystyle\\f(x)=6^x\\\\f^{-1}(x)=(6^x)^{-1}\\\\f^{-1}(x)=\frac{1}{6^x} \\\\f^{-1}(x)=6^{-x}[/tex]

Answer:

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

(−∞,∞)

Set-Builder Notation:

{x|x∈R}

Step-by-step explanation:

Answer:

Step-by-step explanation:

First of all let's look at the side lengths of both figures.

Let's see how the corresponding sides relate:-

[tex]\sf 6*\cfrac{1}{3} =3[/tex]

[tex]\sf 3*\cfrac{1}{3} =1[/tex]

We can see that all sides scale by the same factor of 1/3.

Therefore, YES A is a scaled copy of Figure B.

______________________

Hope this helps!

Have a great day!

The had to wait for the second flight for 40 mins.

We know that sometimes when a person is travelling there may be need to have a flight that connects a person from one place to another and at times you would have to wait for a connecting flight and this wait would add to the total time that is required for the journey.

Now we are told in the question that it takes 8 hours and 5 minutes to travel from Hong Kong to Dubai and that they left Dubai at 2250 hrs but landed in Hong King at  1405 hrs. The time in between must be;  2250 hrs - 1405 hrs = 8: 45 hrs thus the time of waiting is 40 minutes.

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Your monthly income after working 25 hours per week is 1400 dollars.

You are paid $14 an hour. You work 25 hours a week. Your tax rate is 17 % . Your monthly income can be calculated as follows:

4 weeks =  1 month

1 weeks = 25 hours

4 weeks  = ?

cross multiply

hours worked in a month = 100 hours

Therefore,

1 hours = 14 dollars

100 hours = ?

cross multiply

monthly income = 100 × 14

monthly income = 1400 dollars

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The Java code that follows inserts the code into the main function so that the result may be obtained. It incorporated the appropriate questions related to pet so that users could choose the data they should fill in.

Proper class naming and naming practises provide the following advantages:

Even if you aren't the person who developed it or if it was written a long time ago, you know what to anticipate from a specific class without looking at code or documentation.

A codebase is simple to find and traverse.

Speaking with your team about issues or improvements is simpler.

It facilitates newbie onboarding and reduces confusion.

A correctly utilised MVP with a defined name standard is generally a nice illustration of working name expectations. You would anticipate that a class named UseCase/Interactor would provide business logic.

How to solve?

import java.util.Scanner;

public class PetInformation {

 public static void main(String[] args) {

      Scanner scnr = new Scanner(System.in);

      String petName, dogName;

      String dogBreed = "null";

      int petAge, dogAge;

      Pet myPet = new Pet();

      System.out.println("Enter Pet Name:");

      petName = scnr.nextLine();

      System.out.println("Enter Pet Age:");

      petAge = scnr.nextInt();

      Dog myDog = new Dog();

      System.out.println("Enter Dog Name:");

      dogName = scnr.next();

      System.out.println("Enter Dog Age:");

      dogAge = scnr.nextInt();

      scnr.nextLine();

      System.out.println("Enter Dog Breed:");

      dogBreed = scnr.nextLine();

      System.out.println(" ");

      myPet.setName(petName);

      myPet.setAge(petAge);

      myPet.printInfo();

      myDog.setName(dogName);

      myDog.setAge(dogAge);

      myDog.setBreed(dogBreed);

      myDog.printInfo();

      System.out.println(" Breed: " + myDog.getBreed());

  }

}

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1) missing number is 7 (answer #2)

Each circles' numbers add up to 20. (the first one is 1 + 9 + 10, the second is 5 + 4 + 11.)

20 minus 10 minus 3 is 7, so that's the missing number.

2) missing number is 3 (answer #4)

This one's similar to the previous question. Each square's numbers have a sum of 10, this time. (First square is 2 + 7 + 1 + 0, second is 4 + 3 + 1 + 2.)

10 minus 6 minus 1 minus 0 is the same as 10 minus 7. This equals 3- so there's the number that's missing!

Hopefully this helps!

Answer:145,003 59

Step-by-step explanation:

he population 2016, this is more precise, will be 145116 people. If you just rounded the value of X to population growth rate to 1.176, then the population Uh in 2016 is 145,003 59.

Answer:

y=-2x+2: second graph

y=-2x-5: third graph

y= 3/2x+5: first graph

Step-by-step explanation:

we can just look at the y intercept since each equation has different ones

The graphs are left to right so I’ll call it by 1st graph 2nd graph and last graph

y=mx+b is slope intercept formula where big y intercept

The first equation b or the y intercept is 2 and the only graph where the Line intersects with the y axis at 2 is the second one

The second equation has a y intercept of -5 so the last graph is the only one that line intersects with the y axis at -5

the last equation has a y intercept of 5 so the first graph is the only one where the line intersects with 5

Hopes this helps please mark brainliest

Answer:

6115

Explanation:

[tex]70000(1-0.15)^{15} \approx 6115[/tex]

Answer:

98.6

Step-by-step explanation:

in photo!!

The expression of the radius is √3v/πx

The equation of the volume is given as

v = 1/3πr²x

Where

r= radius

x = height

So, we have

v = 1/3πr²x

Multiply both sides of the equation by 3

This gives

3v = πr²x

Divide both sides of the equation by πx

So, we have the following representation

3v/πx = r²

Take the square root of both sides

r = √3v/πx

Hence, the radius expression is √3v/πx

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