Subtract the following polynomials, then place the answer in the proper location on the grid.

Let A be a 5 × 4 matrix with a pivot in each column. Is A invertible? Why or why not?

erastova [34]

Answer:

Matrix A is not invertible.

Step-by-step explanation:

Invertible matrix are those matrix which are square matrix or non singular matrix.

For any matrix to be invertible, matrix should be non singular i.e. det(x) $\neq$ 0.

But for the question given above we cannot find determinant of matrix A as it is not square matrix. so inverse of given matrix does not exist. so it is not possible to have non trival solutions.

6 0

3 years ago

Suppose the daily customer volume at a call center has a normal distribution with mean 5,500 and standard deviation 1,000. What

lakkis [162]

Answer:

0.0665 = 6.65% probability that the call center will get between 4,800 and 5,000 calls in a day.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Mean 5,500 and standard deviation 1,000.

This means that $\mu = 5500, \sigma = 1000$

What is the probability that the call center will get between 4,800 and 5,000 calls in a day?

This is the p-value of Z when X = 5000 subtracted by the p-value of Z when X = 4800. So

X = 5000

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

$Z = \frac{5000 - 5500}{1000}$

$Z = -0.5$

$Z = -0.5$ has a p-value of 0.3085.

X = 4800

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

$Z = \frac{4800 - 5500}{1000}$

$Z = -0.7$

$Z = -0.7$ has a p-value of 0.2420.

0.3085 - 0.2420 = 0.0665

0.0665 = 6.65% probability that the call center will get between 4,800 and 5,000 calls in a day.

4 0

3 years ago

Evaluate the difference quotient for the given function.

kherson [118]

Assuming you mean f(t) = g(t) × h(t), notice that

f(t) = g(t) × h(t) = cos(t) sin(t) = 1/2 sin(2t)

Then the difference quotient of f is

$\dfrac{\frac12 \sin(2(t+h)) - \frac12 \sin(2t)}h = \dfrac{\sin(2t+2h) - \sin(2t)}{2h}$

Recall the angle sum identity for sine:

sin(x + y) = sin(x) cos(y) + cos(x) sin(y)

Then we can write the difference quotient as

$\dfrac{\sin(2t)\cos(2h) + \cos(2t)\sin(2h) - \sin(2t)}{2h}$

or

$\boxed{\sin(2t)\dfrac{\cos(2h)-1}{2h} + \cos(2t)\dfrac{\sin(2h)}{2h}}$

(As a bonus, notice that as h approaches 0, we have (cos(2h) - 1)/(2h) → 0 and sin(2h)/(2h) → 1, so we recover the derivative of f(t) as cos(2t).)

7 0

3 years ago

4(b+24)=(12b+8) pls help

vfiekz [6]

Answer:

b=11

Step-by-step explanation:

4(b+24)=(12b+8)

4b+96=12b+8

-4. -4

96=8b+8

-8. -8

88=8b

88÷8=11

8 0

3 years ago

Sally and Karl work at different jobs. Sally earns $7 per hour and Karl earns $5 per hour. They each earn the same amount per we

Lisa [10]

Answer:

Karl works 7 hours a week

Step-by-step explanation:

Step 1: Determine total amount that Sally earns

Total amount Sally earns=rate per hour×number of hours worked(h)

where;

Rate per hour=$7 per hour

Number of hours worked=h

Replacing;

Total amount Sally earns=(7×h)=7 h

Step 2: Determine total amount Karl earns

Total amount Karl earns=rate per hour×number of hours worked

where;

rate per hour=$5

number of hours worked=2 more than Sally=h+2

replacing;

Total amount Karl earns=5(h+2)

Step 3: Equate Sally's total earnings to Karl's total earnings and solve for h

7 h=5(h+2)

7 h=5 h+10

7 h-5 h=10

2 h=10

h=10/2

h=5

Karl works (h+2) hours=(5+2)= 7 hours

Karl works 7 hours a week

7 0

3 years ago