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EleoNora [17]
3 years ago
11

Given the following matrices A and B, find an invertible matrix U such that UA = B:

Mathematics
1 answer:
Naddik [55]3 years ago
3 0

<span>A and B must be invertible, we have UA=B, since A is invertible.  A^-1 exists, by multiplying with A^-1, we have UA A^-1 =B A^-1. But AA^-1 = I (identity matrix) and XI=X, for all matrix X, we find UI= B A^-1, and U= B A^-1.</span>

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1.
Mama L [17]

Answer: x=25, y=19

Step-by-step explanation: Because the triangle is equilateral, all the angles must be equal to 60 degrees. So 2x+10=60. 2x=50 and x=25. Then the same thing: 3y+3=60. 3y=57, y=19.

3 0
3 years ago
Using the simple random sample of weights of women from a data​ set, we obtain these sample​ statistics: nequals45 and x overbar
Tomtit [17]

Answer: (141.1, 156.48)

Step-by-step explanation:

Given sample statistics : n=45

\overline{x}=148.79\text{ lb}

\sigma=31.37\text{ lb}

a) We know that the best point estimate of the population mean is the sample mean.

Therefore, the best point estimate of the mean weight of all women = \mu=148.79\text{ lb}

b) The confidence interval for the population mean is given by :-

\mu\ \pm E, where E is the margin of error.

Formula for Margin of error :-

z_{\alpha/2}\times\dfrac{\sigma}{\sqrt{n}}

Given : Significance level : \alpha=1-0.90=0.1

Critical value : z_{\alpha/2}=z_{0.05}=\pm1.645

Margin of error : E=1.645\times\dfrac{31.37}{\sqrt{45}}\approx 7.69

Now, the 90% confidence interval for the population mean will be :-

148.79\ \pm\ 7.69 =(148.79-7.69\ ,\ 148.79+7.69)=(141.1,\ 156.48)

Hence, the 90​% confidence interval estimate of the mean weight of all women= (141.1, 156.48)

3 0
3 years ago
Orlando invests $1000 at 6% annual interest compounded daily and Bernadette invests $1000 at 7%
Montano1993 [528]

Answer:

6 Years

Step-by-step explanation:

Orlando invests $1000 at 6% annual interest compounded daily.

Orlando's investment = A=1000(1+\frac{0.06}{365})^{(365\times t)}

Bernadette invests $1000 at 7% simple interest.

Bernadette's investment = A = 1000(1+0.07×t)

By trail and error method we will use t = 5

Bernadette's investment will be after 5 years

1000(1 + 0.07 × 5)

= 1000(1 + 0.35)

= 1000 × 1.35

= $1350

Orlando's investment after 5 years

A=1000(1+\frac{0.06}{365})^{(365\times 5)}

   = 1000(1+0.000164)^{1825}

  = 1000(1.000164)^{1825}

  = 1000(1.349826)

  = 1349.825527 ≈ $1349.83

After 5 years Orlando's investment will not be more than Bernadette's.

Therefore, when we use t = 6

After 6 years Orlando's investment will be = $1433.29

and Bernadette's investment will be = $1420

So, after 6 whole years Orlando's investment will be worth more than Bernadette's investment.

8 0
3 years ago
2x+y=5<br> -x+2y=4 <br><br> How do you solve this
d1i1m1o1n [39]
The answer to your problem is
x=5/2
y=5

x=-4
y=2
7 0
3 years ago
Please answer this correctly without making mistakes
HACTEHA [7]

Answer:

It would be the green chart

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
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