let A and B be nxn matrices such that AB is singular prove that either A or Bis singular

Answer: 6 sq. units

Step-by-step explanation:

The formula to find the circumference of a circle is given by :-

[tex]C=2\pi r[/tex], where r is the radius of the circle.

Given : Circumference = 10 units

Then , [tex]10=2\pi r[/tex]

[tex]\\\\\Rightarrow\ r=\dfrac{10}{2\pi}\approx1.59[/tex]

The area of a circle is given by :-

[tex]A=\pi r^2=\pi(1.59)^2=7.9422603875\approx7.94\text{ sq. units}[/tex]

Now, the 75 % of the area is given by :-

[tex]0.75\times7.94=5.955\approx6\text{ sq. units}[/tex]

Hence, 75% of the area of a circle with a circumference of 10 units = 6 sq. units

The irrational number among the options is root 3 + 8.486. option C.

An irrational number is a number that cannot be expressed as a fraction of two integers and has a non-repeating, non-terminating decimal expansion.

Let's examine each option:

A. [tex]\(7.51\ldots \times -4\)[/tex]

This is a rational number because it's the product of a rational number [tex](\(7.51\ldots\)) and \(-4\),[/tex] which is also rational. So, option A is not irrational.

B. [tex]\(\sqrt{16} + \frac{3}{4}\)[/tex]

[tex]\(\sqrt{16} = 4\)[/tex], so this expression simplifies to [tex]\(4 + \frac{3}{4}\)[/tex], which is a rational number. So, option B is not irrational.

C. [tex]\(\sqrt{3} + 8.486\)[/tex]

If [tex]\(\sqrt{3}\)[/tex] is not exactly equal to 8.486 , then this expression is irrational because it's the sum of an irrational number and a rational number. However, if [tex]\(\sqrt{3}\)[/tex] does happen to be exactly 8.486, then this expression would be rational. To determine if [tex]\(\sqrt{3}\)[/tex] is exactly 8.486, we need to compute [tex]\(\sqrt{3}\).[/tex] Since [tex]\(\sqrt{3}\)[/tex] is irrational (it's not a perfect square), 8.486 is not [tex]\(\sqrt{3}\)[/tex], so this expression is irrational. Therefore, option C is the correct answer.

D.[tex]\(8 \frac{2}{3} \times 17.75\)[/tex]

This is a rational number because it's the product of a rational number [tex](\(8 \frac{2}{3}\)) and \(17.75\),[/tex] which is also rational. So, option D is not irrational.

Complete question: Which of the following is irrational?

A. 7.51... x -4

B. root 16 + 3/4

C. root 3 + 8.486

D. 8 2/3 x 17.75

Answer:

Option 3 - 45 tens

Step-by-step explanation:

Given : Expression 45 ones times 10.

To find : What is the expression?

Solution :

We know that,

"one" means "  1

We  have 45 ones means multiply 45 by 1.

[tex]45\text{ ones}=45\times 1=45[/tex]

Now, 45 ones times 10 means

[tex]45\times 10=450[/tex]

450 means 45 tens as tens is 10.

So, The correct choice is 45 tens.

Therefore, Option 3 is correct.

Final answer:

The small business owner's profit for a ten-day period is $4,675, calculated by determining the total daily revenue from pizza slices and sandwiches, subtracting daily expenses, and then multiplying the result by ten.

Explanation:

The question pertains to calculating the profit for a small business over a ten-day period. To do this, we first calculate the daily revenue from selling pizza slices and sandwiches and then subtract the daily expenses. After that, we multiply the daily profit by ten.

The owner's profit for the ten-day period would then be $4,675.

there are 4 Aces and 4 8's for a total of 8 cards

52 cards in a deck

 so probability of picking an Ace or 8 = 8/52

Final answer:

The probability of being dealt an ace or an 8 from a standard 52-card deck is 2/13, which is approximately 15.38%.

Explanation:

The question asks for the probability of being dealt an ace or an 8 from a standard 52-card deck. There are 4 aces and 4 eights in a 52-card deck. To calculate the probability of getting either an ace or an 8, we add the probability of getting an ace to the probability of getting an 8. The probability of drawing an ace (P(Ace)) is 4/52 and the probability of drawing an 8 (P(8)) is also 4/52. Since these are mutually exclusive events (you cannot draw an ace and an 8 simultaneously with one card), we can simply add these probabilities together:

P(Ace or 8) = P(Ace) + P(8)
= (4/52) + (4/52)
= 8/52
= 2/13

Therefore, the probability of being dealt an ace or an 8 is 2/13, which is approximately 0.1538 or 15.38%.

To calculate the total fraction of tickets sold for the movie Fist Bump by Thursday, we find the least common denominator for the fractions (21), convert each fraction, and then sum them up to get 16/21 of the tickets sold.

The question is asking how much of the tickets were sold by Thursday for the movie Fist Bump. To find the total fraction of tickets sold from Monday to Wednesday, we need to add up the fractions:

First, let's find a common denominator for the fractions. The least common multiple of 7 and 3 is 21, so we'll convert all fractions to have a denominator of 21:

Now we can add the fractions:

3/21 + 7/21 + 6/21 = 16/21

Therefore, by Thursday, a total of 16/21 of the tickets have been sold.

Answer:

[tex]N=0[/tex]

Step-by-step explanation:

We have been given that a number N is multiplied by 3. So our number would be [tex]3\cdot N[/tex].

We are also told that N is divided by 3. So our number would be [tex]\frac{N}{3}[/tex].

As we are told that the both results are same, so we can equate both expressions as:

[tex]3\cdot N=\frac{N}{3}[/tex]

[tex]3*3\cdot N=\frac{N}{3}*3[/tex]

[tex]9N=N[/tex]

[tex]9N-N=N-N[/tex]

[tex]8N=0[/tex]

[tex]\frac{8N}{N}=\frac{0}{N}[/tex]

[tex]N=0[/tex]

Therefore, the value of N is 0.

Based on the pattern observed in the given equations, 13 + 13 would equal 8.

The given equations seem to follow a pattern where the sum of two numbers is not their arithmetic sum but rather a result derived from some other relationship. Let's try to decipher the pattern:

For the equation 11 + 11 = 4:

  The word "eleven" has 6 letters, so it becomes 6 + 6 = 4, which is true.

For the equation 12 + 12 = 9:

  The word "twelve" has 6 letters, so it becomes 6 + 6 = 9, which is true.

Following the same pattern:

For 13 + 13:

  The word "thirteen" has 8 letters, so it becomes 8 + 8 = ?

Thus, 13 + 13 = 8.

Therefore, based on the pattern observed in the given equations, 13 + 13 would equal 8.

The probable question maybe:

If 11 + 11 = 4 and 12 + 12 = 9 then what is 13 + 13 = ?

Final answer:

To find the binary equivalent of the decimal number 97, one divides it by 2 repeatedly and records the remainders in reverse order, resulting in the binary number 1100001.

Explanation:

The binary equivalent of the decimal value 97 can be found using a process of dividing by 2 and keeping track of the remainders. Firstly, divide 97 by 2, which gives a quotient of 48 and a remainder of 1. We write down the remainder. Continuing this process:

After collecting all the remainders in reverse order, the binary equivalent of decimal 97 is 1100001.

The solution of expression is, 7/2.

A mathematical expression is a group of numerical variables and functions that have been combined using operations like addition, subtraction, multiplication, and division.

We have to give that,

An expression is,

⇒ x¹ + x⁻¹ + x⁰

Now, Substitute x = 2 in the above expression and find the value,

⇒ x¹ + x⁻¹ + x⁰

⇒ 2¹ + 2⁻¹ + 2⁰

⇒ 2 + 1/2 + 1

⇒ 3 + 1/2

⇒ (6 + 1)/2

⇒ 7/2

Therefore, The solution is, 7/2

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To solve this problem, first we have to plot the vertices in a Cartesian plane to know the plot. This would also give us an idea of which points are adjacent or interconnected forming a hexagon.

The plot is shown below. Now we can see which points are adjacent to each other. Let us take points (-6.5, 5) and (6.5, 5) for our calculation.

The distance formula given two points is:

d^2 = (x2 – x1)^2 + (y^2 – y^1)^2

Now we calculate the distance between 2 points:

d^2 = (6.5 – (-6.5))^2 + (5 – 5)^2

d^2 = 169

d = 13

Therefore the length of each side of the park is 13 units.

Answer:

13 units

To find the length of each side of the hexagon, you can use the distance formula. The distance formula is derived from the Pythagorean theorem for finding the length of the hypotenuse of a right triangle. By following the steps outlined, you can determine the length of each side of the hexagon.

To find the length of each side of the hexagon, you can use the distance formula. The distance formula is derived from the Pythagorean theorem for finding the length of the hypotenuse of a right triangle. In this case, the coordinates of the vertices of the hexagon form a regular hexagon, meaning all sides are equal in length. Here's how you can find the length of one side:

By following these steps, you should be able to determine the length of each side of the hexagon.

Hence, it will take 4.71 minutes  for all the liquid in the funnel to pass through the nozzle.

A cone shaped funnel has a radius(r) of 3 inches and a height(h) of 7 inches.

Now, the volume(V) of the cone is given as:

[tex]V=\dfrac{1}{3}\times (\pi r^2h)[/tex]

Hence, on putting the value of r and h in the formula of volume we obtain the volume of cone funnel as:

[tex]V=\dfrac{1}{3}\times (3.14\times (3)^2\times 7)\\\\\\V=\dfrac{1}{3}\times (197.82)\\\\V=65.94 \ in^3[/tex]

If the liquid drips at the rate of 14 cubic inches per minute.

i.e. for 14 cubic inches it takes 1 minutes.

Now for 1 cubic inches it will take:

[tex]\dfrac{1}{14} \ min.[/tex]

Hence, for all the liquid ( i.e. 65.94 cubic inches) to pass the nozzle is the time taken is:

[tex]\dfrac{65.94}{14}\ min.\\\\=4.71\ min.[/tex]

Hence, it will take 4.71 minutes  for all the liquid in the funnel to pass through the nozzle.

The probability that at least one of the four randomly chosen items will be defective is 34.39%. This is calculated by subtracting the probability that all items are not defective from 1.

The subject of the question relates to the field of Probability. This problem pertains to the concept known as 'probability of at least one' event. In this case, we are considering the probability that at least one item will have a defect.

To calculate this, it's easier to find the probability that none of the items have a defect and then subtract that from 1. Since the machine has a 10% defect rate, it means there's a 90% chance that any item chosen will NOT be defective. If we choose 4 items, the probability that all are good is 0.9 * 0.9 * 0.9 * 0.9 = 0.6561.

So, the probability that at least one defective item will be chosen is 1 - 0.6561 = 0.3439 or 34.39%.

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