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1 year ago

Matrix a is a 6 × 5 matrix. which order of matrix can be multiplied by matrix a to create matrix ab?

Mathematics

1 answer:

mezya [45]1 year ago

7 0

Order (B) 5 × 6 of the matrix can be multiplied by matrix a to create matrix ab.

<h3>What is a matrix?</h3>

A matrix is a rectangular array or table of numbers, symbols, or expressions that are organized in rows and columns to represent a mathematical object or an attribute of such an object in mathematics.
For instance, consider a matrix with two rows and three columns.

To find the order of matrix:

We must first check the dimension of two matrices, say matrix A by matrix B, before we may multiply them.
Multiplication is achievable if the number of columns in the first matrix, A, equals the number of rows in the second matrix.
Dimension is assigned to the provided matrix: 6 × 5
This means the given matrix contains six rows and five columns.
As a result, the second matrix MUST have 5 rows in order for multiplication to be POSSIBLE.
The only matrix with 5 rows among the above alternatives is the matrix with dimension (B) 5 × 6.

To prove:

In other words, the inner products of the dimensions should be equal.
That is; (a × b)(b × a) is possible but (a ×b)(c × b) is impossible.
The dimensions of the matrix are given by, row × column.

Therefore, order (B) 5 × 6 of the matrix can be multiplied by matrix a to create matrix ab.

Know more about matrix here:

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In a large on-the-job training program, half of the participants are female and half are male. In a random sample of six partici

Radda [10]

Answer: 0.9844

Step-by-step explanation:

given data:

sample size n = 6

It’s assumed that half the population are male and the remaining half are females

F = 1/2

M = 1/2

the probability that the investigator would draw altleats one male

P ( x ≥ 1 ) =

= 1 - ( 0.5 ) ^ 6

= ( 0.5 )^6

= 0.9844

5 0

3 years ago

kicyunya [14]

Answer:

8.69% probability that at least 285 rooms will be occupied.

Step-by-step explanation:

For each booked hotel room, there are only two possible outcomes. Either there is a cancelation, or there is not. So we use concepts of the binomial probability distribution to solve this question.

However, we are working with a big sample. So i am going to aproximate this binomial distribution to the normal.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

A popular resort hotel has 300 rooms and is usually fully booked. This means that $n = 300$

About 7% of the time a reservation is canceled before the 6:00 p.m. deadline with no pen-alty. What is the probability that at least 285 rooms will be occupied?

Here a success is a reservation not being canceled. There is a 7% probability that a reservation is canceled, and a 100 - 7 = 93% probability that a reservation is not canceled, that is, a room is occupied. So we use $p = 0.93$

Approximating the binomial to the normal.

$E(X) = np = 300*0.93 = 279$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{300*0.93*0.07} = 4.42$

The probability that at least 285 rooms will be occupied is 1 subtracted by the pvalue of Z when X = 285. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{285- 279}{4.42}$

$Z = 1.36$

$Z = 1.36$ has a pvalue of 0.9131.

So there is a 1-0.9131 = 0.0869 = 8.69% probability that at least 285 rooms will be occupied.

8 0

3 years ago

A truck is used to transport gravel. The box on the truck is a rectangular prism 11 ft long, 7 ft wide and 4 ft high. The box do

chubhunter [2.5K]

Answer:

308 cubic feet

Step-by-step explanation:

The box on the truck has dimensions 11 ft by 7 ft by 4 ft.

The volume of the box is:

V = L * W * H

V = 11 * 7 * 4

V = 308 cubic feet

The truck can transport 308 cubic feet of gravel.

8 0

3 years ago

Which line is perpendicular to the line y=-1/3x-2 and passes through point (1,4)

xxMikexx [17]

Answer:

Option 3) y = 3x+1

Step-by-step explanation:

Given equation is:

y = $-\frac{1}{3} x -2$

Perpendicular => It will have a slope of negative reciprocal to this slope

So the ⊥ line has a slope = m = 3

Now,

Point = (x,y) = (1,4)

So, x = 1, y = 4

Putting this in slope intercept form to get b

=> $y = mx+b$

=> 4 = (3)(1) + b

=> b = 4-3

=> b = 1

Now, Putting m and b in the slope intercept form to get the required equation:

=> y = 3x+1

4 0

3 years ago

Read 2 more answers

HELP ME PLEASE! Vector's map has the scaling missing.he knows from the lake to the youth center is 8 miles. on the map, they are

Naddik [55]

Hey there!

Since 2 goes into 8, you would simplify. You would get 1 inch and 4 miles. Next, set up a ratio. The ratio is 1 inch: 4 miles. So for every inch on the map, there is 4 miles.

I hope this helps!

7 0

3 years ago