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3 years ago

U = 6i – 10j g= -81 – 11j Find: -3u + 5g

Mathematics

1 answer:

VARVARA [1.3K]3 years ago

6 0

Answer:

$-3u + 5g =-58i -25j$

Step-by-step explanation:

Given

$u = 6i - 10j$

$g=-8i - 11j$

Required

$-3u + 5g$

We have:

$-3u + 5g$

This gives:

$-3u + 5g = -3(6i - 10j) + 5(-8i - 11j)$

Open bracket

$-3u + 5g = -18i + 30j - 40i - 55j$

Collect like terms

$-3u + 5g = -18i - 40i+ 30j - 55j$

$-3u + 5g =-58i -25j$

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3 years ago

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you are racing your friend and he has traveled 200 meters and you friend has traveled 30 kilometers . who has traveled the furth

stepan [7]

Answer:

The one who traveled 30km

Step-by-step explanation:

In order to compare the two lengths, we first need to convert them both into the same units so we can compare them properly. To avoid decimal points, it would be easier in this case to convert the km to meters, which is the unit of the 200. 1km = 1000 meters, so 30km x 1000 = 30,000m

Out of 30,000m and 200m, the 30,000 is clearly greater so the one who traveled 30km is the one who has traveled further.

Hope this helped!

3 0

3 years ago

Create a vector named iq of 100 elements of N(100,20) (normal with a mean of 100 and std dev of 20) data. 6. add 10 to every ele

DaniilM [7]

Answer:

See code and explanation below.

Step-by-step explanation:

For this case we can use the following R code to create a vector of 100 elements from a normal distribution given by:

$X \sim N (\mu = 100. \sigma= 20)$

The function rnorm creates a sample data from the normla distribution with the mean and deviation provided

> normal<-rnorm(100,mean = 100,sd=20)

We can visualize the data like this

> normal

[1] 87.47092 103.67287 83.28743 131.90562 106.59016 83.59063 109.74858 114.76649 111.51563

[10] 93.89223 130.23562 107.79686 87.57519 55.70600 122.49862 99.10133 99.67619 118.87672

[19] 116.42442 111.87803 118.37955 115.64273 101.49130 60.21297 112.39651 98.87743 96.88409

[28] 70.58495 90.43700 108.35883 127.17359 97.94425 107.75343 98.92390 72.45881 91.70011

[37] 92.11420 98.81373 122.00051 115.26351 96.70953 94.93277 113.93927 111.13326 86.22489

[46] 85.85010 107.29164 115.37066 97.75308 117.62215 107.96212 87.75947 106.82239 77.41274

[55] 128.66047 139.60800 92.65557 79.11731 111.39439 97.29891 148.03236 99.21520 113.79479

[64] 100.56004 85.13454 103.77585 63.90083 129.31110 103.06507 143.45223 109.51019 85.80107

[73] 112.21453 81.31805 74.92733 105.82892 91.13416 100.02211 101.48683 88.20958 88.62663

[82] 97.29643 123.56174 69.52866 111.87892 106.65901 121.26200 93.91632 107.40038 105.34198

[91] 89.14960 124.15736 123.20805 114.00427 131.73667 111.16973 74.46816 88.53469 75.50775

[100] 90.53199

Then we can add 10 to each element of the vector like this:

> normal1<-normal+10

And we can visualize the results like this

> normal1

[1] 97.47092 113.67287 93.28743 141.90562 116.59016 93.59063 119.74858 124.76649 121.51563

[10] 103.89223 140.23562 117.79686 97.57519 65.70600 132.49862 109.10133 109.67619 128.87672

[19] 126.42442 121.87803 128.37955 125.64273 111.49130 70.21297 122.39651 108.87743 106.88409

[28] 80.58495 100.43700 118.35883 137.17359 107.94425 117.75343 108.92390 82.45881 101.70011

[37] 102.11420 108.81373 132.00051 125.26351 106.70953 104.93277 123.93927 121.13326 96.22489

[46] 95.85010 117.29164 125.37066 107.75308 127.62215 117.96212 97.75947 116.82239 87.41274

[55] 138.66047 149.60800 102.65557 89.11731 121.39439 107.29891 158.03236 109.21520 123.79479

[64] 110.56004 95.13454 113.77585 73.90083 139.31110 113.06507 153.45223 119.51019 95.80107

[73] 122.21453 91.31805 84.92733 115.82892 101.13416 110.02211 111.48683 98.20958 98.62663

[82] 107.29643 133.56174 79.52866 121.87892 116.65901 131.26200 103.91632 117.40038 115.34198

[91] 99.14960 134.15736 133.20805 124.00427 141.73667 121.16973 84.46816 98.53469 85.50775

[100] 100.53199

The sample mean is given by:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

And the sample deviation by:

$s =\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

If we want to calculate the mean and standard deviation for the original data we can do this:

> mean(normal)

[1] 102.1777

And the standard deviation with:

> sd(normal)

[1] 17.96399

Other way to calculate the deviation is:

> sqrt(sum((normal-mean(normal))^2/(length(normal)-1)))

[1] 17.96399

7 0

3 years ago

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3 years ago

Workout the lowest integer

V125BC [204]

Answer:

x ≥ 9/2

Step-by-step explanation:

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2x ≥ 9

x ≥ 9/2

5 0

2 years ago