Express<br>17<br>15<br>as<br>а a<br>percentage

Find the value of k (k ∈ R, k is a real number) such that the following system of equations is inconsistent:

slamgirl [31]

<h3>Answer: k = 7</h3>

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Explanation:

There are probably a number of ways to approach this problem, but row reduction was the only method I could think of at the moment.

If you were to follow the steps shown in the attached image, then you'll be on the process of applying row reduction. The last step in that diagram isn't in full REF (row echelon form), but that doesn't technically matter.

What does matter is the 2k-14 entry in the bottom row. If that entry was 0, while the entry just to the right of it was nonzero, then this would lead the entire system of equations to be inconsistent. This is because the bottom equation would be in the form 0x+0y+0z = m, where m is some nonzero constant. As you can see, that equation would simplify to 0 = m; however, m is nonzero, so we have a contradiction.

If 2k - 14 were 0, then

2k - 14 = 0

2k = 14

k = 14/2

k = 7

This is the only k value in which the system is inconsistent. In other words, the system wouldn't have any solutions with this k value. You can verify this through completing the row reduction with k = 7 (it should be far easier now that we can nail down a fixed k value) and find that you'll get a contradiction. You could also use substitution to find an inconsistency would arise when k = 7.

Side notes:

You don't need to do full RREF, though you can if you want. REF should be sufficient.
I drew each matrix as a grid of boxes to help separate the terms. This is also done to space out each step. Usually those grid lines aren't present.

6 0

3 years ago

The gross weekly sales at a certain restaurant are a normal random variable with mean $2200 and standard deviation $230.What is

Lesechka [4]

Answer:

a) The total gross sales over the next 2 weeks exceeds $5000 is 0.0321.

b) The weekly sales exceed $2000 in at least 2 of the next 3 weeks is 0.9033.

Step-by-step explanation:

Given : The gross weekly sales at a certain restaurant are a normal random variable with mean $2200 and standard deviation $230.

To find : What is the probability that

(a) the total gross sales over the next 2 weeks exceeds $5000;

(b) weekly sales exceed $2000 in at least 2 of the next 3 weeks? What independence assumptions have you made?

Solution :

Let $X_1$ and $X_2$ denote the sales during week 1 and 2 respectively.

a) Let $X=X_1+X_2$

Assuming that $X_1$ and $X_2$ follows same distribution with same mean and deviation.

$E(X)=E(X_1+X_2)=E(X_1)+E(X_2)$

$E(X)=2\mu = 2(220)=4400$

$\sigma_X=\sqrt{var(X_1+X_2)}$

$\sigma_X=\sqrt{2\sigma^2}$

$\sigma_X=\sqrt{2}\sigma$

$\sigma_X=230\sqrt{2}$

So, $X\sim N(4400,230\sqrt{2})$

$P(X>5000)=1-P(X\leq5000)$

$P(X>5000)=1-P(Z\leq\frac{5000-4400}{230\sqrt{2}})$

$P(X>5000)=1-P(Z\leq1.844)$

$P(X>5000)=1-0.967$

$P(X>5000)=0.0321$

The total gross sales over the next 2 weeks exceeds $5000 is 0.0321.

b) The probability that sales exceed teh 2000 and amount in at least 2 and 3 next week.

We use binomial distribution with n=3.

$P(X>2000)=1-P(X\leq2000)$

$P(X>2000)=1-P(Z\leq\frac{2000-2200}{230})$

$P(X>2000)=1-P(Z\leq-0.87)$

$P(X>2000)=1-0.1922$

$P(X>2000)=0.808$

Let Y be the number of weeks in which sales exceed 2000.

Now, $P(Y\geq 2)$

So, $P(Y\geq 2)=P(Y=2)+P(Y=3)$

$P(Y\geq 2)=^3C_2(0.8077)^2\cdot (1-0.8077)+^3C_3(0.8077)^3$

$P(Y\geq 2)=0.37635+0.52692$

$P(Y\geq 2)=0.90327$

The weekly sales exceed $2000 in at least 2 of the next 3 weeks is 0.9033.

3 0

3 years ago

The number 360 has many factors. This may be why it was chosen for the number of degrees in a full turn

shtirl [24]

Answer:

Due to having 24 divisors.

Step-by-step explanation:

360 has many factors which might be the reason it was chosen for the number of degrees in a full turn. There are total 24 divisors of 360 number which make it the highest factors among all numbers. All circles are divided into 360 even parts so that the Sun would move through 1 part each day. Each of these parts was describes 1 degree and this division give us the idea that a circle contains 360 degrees so we can say that this is the reason that 360 is chosen in degrees.

8 0

3 years ago

The Sugar Sweet Company is going to transport its sugar to market. It will cost $3500 to rent trucks, and it will cost an additi

lora16 [44]

Using the y = mx + b formula

C = 225s + 3500

Then to transport 19 tons

C = 225(19) + 3500

C = 4275 + 3500

C = 7775

6 0

4 years ago

Read 2 more answers

PLS HELP WILL GIVE BRAINLIEST<br> what’s the scale factor?

stiks02 [169]

Answer:

2/3

Step-by-step explanation:

6 0

3 years ago

Express1715asа apercentage​

Express1715asа apercentage