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GenaCL600 [577]
2 years ago
10

Determine whether each set equipped with the given operations is avector space. For those that are not vector spaces identify th

e vector space axioms that fail.a). The set of all pairs of real numbers of the form (x,y), where x ≥ 0, with the standard operations on R^2.b). The set of all triples of real numbers with the standard vectoraddition but with scalar multiplication defined by k(x,y,z) = (k^2x,k^2y,k^2z)c). The set of all 2 x 2 invertible matrices with the standard matrix addition and scalar multiplication
Mathematics
1 answer:
castortr0y [4]2 years ago
6 0

Answer: Determine whether each set equipped with the given operations is avector space. For those that are not vector spaces identify the vector space axioms that fail.a). The set of all pairs of real numbers of the form (x,y), where x ≥ 0, with the standard operations on R^2.b). The set of all triples of real numbers with the standard vectoraddition but with scalar multiplication defined by k(x,y,z) = (k^2x,k^2y,k^2z)c). The set of all 2 x 2 invertible matrices with the standard matrix addition and scalar multiplication

Step-by-step explanation:

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The area of the rectangle is 64.8 square centimeters. What is the perimeter of the rectangle? One group of ten tenths and one gr
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Answer:

(a) Perimeter = 32.2\ cm

(b) 100

Step-by-step explanation:

Solving (a):

Given

Shape: Rectangle

Area = 64.8

Required

Calculate the perimeter.

Area is calculated as:

Area = L * W

Where

L = Length and W = Width

Substitute 64.8 for Area

64.8 = L * W

Make L the subject:

L = \frac{64.8}{W}

Perimeter is calculated as:

P = 2 * (L + W)

Substitute 64.8/W for L

P = 2 * (\frac{64.8}{W} + W)

P = \frac{129.6}{W} + 2W

To solve further, we take the derivative of P and set it to 0, afterwards.

dP = -\frac{129.6}{W^2} + 2

Set to 0

0 = -\frac{129.6}{W^2} + 2

Collect Like Terms

\frac{129.6}{W^2} = 2

Cross Multiply:

2W^2= 129.6

Divide through by 2

W^2 = 64.8

Take square roots

W = \sqrt{64.8

W = 8.05

Recall that:

L = \frac{64.8}{W}

So:

L= \frac{64.8}{8.05}\\

L= 8.05

The perimeter is:

Perimeter = 2 * (8.05 + 8.05)

Perimeter = 2 * (16.10)

Perimeter = 32.2\ cm

Solving (b):

Given

((1 Group of 10 tenths) and (1 group of 8 tenths))/(6 groups of 3 tenths)

Required

Solve

Tenths = \frac{1}{10}

So, the expression becomes:

((1 Group of 10 * \frac{1}{10}) and (1 group of 8 * \frac{1}{10}))/(6 groups of 3 * \frac{1}{10})

This gives:

((1 Group of \frac{10}{10}) and (1 group of \frac{8}{10}))/(6 groups of \frac{3}{10})

Group means product, so the expression becomes:

\frac{(1 * \frac{10}{10} \ and\ 1 * \frac{8}{10})}{6 * \frac{3}{10}}

And, as used here means addition

\frac{(1 * \frac{10}{10} +  1 * \frac{8}{10})}{6 * \frac{3}{10}}

Simplify:

\frac{(1 * 1 +  1 * 0.80)}{6 *0.30}

\frac{(1 +  0.80)}{1.80}

\frac{1.80}{1.80}

= 1.00

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1 year ago
If Emily made 75% of the baskets that she attempted if she made nine baskets how many attempt did she make
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Twelve attempts were made at making a basket
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1 year ago
A deli has a special one-day event to celebrate its anniversary. On the day of the event, every eighth customer receives a free
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Answer:

the number of common customers are 8 in number

4 0
2 years ago
Read 2 more answers
Express x in term of y:x/7+2y=6​
lions [1.4K]

Answer:

You have to multiply the denorminator to both sides in order to make x the subject :

\frac{x}{7 + 2y}  = 6

x = 6(7 + 2y)

8 0
1 year ago
The distribution of the amount of a customer’s purchase at a convenience store is approximately normal, with mean $15.50 and sta
viktelen [127]

Answer:

0.42 is closest to the proportion of customer purchase amounts between $14.00 and $16.00

Step-by-step explanation:

Mean = \mu = 15.50

Standard deviation = \sigma = 1.72

We are supposed to find the proportion of customer purchase amounts between $14.00 and $16.00

P(14<x<16)

Formula : z=\frac{x-\mu}{\sigma}

At x = 14

z=\frac{14-15.50}{1.72}

z=-0.8720

Refer the  z table for p value

P(x<14)=0.1922

At x = 16

z=\frac{16-15.50}{1.72}

z=0.290

Refer the  z table for p value

P(x<16)=0.6141

P(14<x<16)=P(x<16)-P(x<14)=0.6141-0.1922=0.42

So, Option C is true

Hence 0.42 is closest to the proportion of customer purchase amounts between $14.00 and $16.00

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