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Naddik [55]
3 years ago
13

8 If u = 11i + 7j, v= -7i+ 11j find the dot product of u and v?

Mathematics
1 answer:
Harman [31]3 years ago
6 0

Let's solve for v.

v=−7i+11

Answer:v=−7i+11

Step-by-step explanation: Hope you understand. Hope this help :)

Let's simplify step-by-step.

11i+7j

There are no like terms.

Answer:=11i+7j

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An experiment was conducted to compare the wearing qualities of three types of paint (A, B, and C) when subjected to the abrasiv
MaRussiya [10]

Answer:

A) H0:  mean of A= mean of B= mean of C

   H1: all means are unequal

B) 3.48194

C) 0.04515

D) H0 is accepted. There is significant difference among mean hours after which visibile abrasion is observed for each type of paint

Step-by-step explanation:

A) Here Anova test will be used as we are comparing three groups

B) mean of A= 229.6, SD of A= 158.1962, SE of A= 50.026

   mean of B= 309.9 , SD of B= 147.8742, SE of B= 46.7619

   mean of C= 427.8, SD of C= 196.8179, SE of C= 62.2393

overall mean= 322.43

degrees of freedom between groups= 3-1=2

degrees of freeddom of error= total number of observations - number of groups= 30-3= 27

total degrees of freedom= total number of samples-1= 30-1 =29

Sum of squares between groups=∑ sample size of group×(individual group mean- over all mean)²

=198772.4667

mean of sum of squares between groups= sum of squares between groups/ (number of groups -1)

  = 198772.4667/2

sum of squares of error=∑∑ (individual observation of group- group mean)²

                                            = 770670.9223

mean sum of squares of erros= sum of squares of error/(total number of samples-number of groups)

                                                       = 770670.92/27

                                                         = 28543.38

F- stat= mean sum of squares between groups/ mean sum of squares of error

     F stat= 3.48194

C) p- value= 0.04515

D) since F-stat is greater than p- value, null hypothesis is rejected

from F distribution table

F(2,27)=

3 0
3 years ago
A study investigating the relationship between age and annual medical expenses randomly samples 400 individuals in a city. It is
ICE Princess25 [194]

Answer:

The probability is 0.789

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are 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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

\sigma = 16, n = 400, s = \frac{16}{\sqrt{400}} = 0.8

Find the probability that the mean age of the individuals sampled is within one year of the mean age for all individuals in the city.​

Using \mu = 30, this is the pvalue of Z when X = 31 subtracted by the pvalue of Z when X = 29. So

X = 31

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

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{31 - 30}{0.8}

Z = 1.25

Z = 1.25 has a pvalue of 0.8944

X = 29

Z = \frac{X - \mu}{s}

Z = \frac{29 - 30}{0.8}

Z = -1.25

Z = -1.25 has a pvalue of 0.1056

0.8944 - 0.1056 = 0.7888

Rounded to three decimal places, 0.789

The probability is 0.789

4 0
3 years ago
Read 2 more answers
Craig ran the first part of a race with an average speed of 8 miles per hour and biked the second part of a race with an average
lutik1710 [3]
Let the distance of the first part of the race be x, and that of the second part, 15 - x, then
x/8 + (15 - x)/20 = 1.125
5x + 2(15 - x) = 40 x 1.125
5x + 30 - 2x = 45
3x = 45 - 30 = 15
x = 15/3 = 5

Therefore, the distance of the first part of the race is 5 miles and the time is 5/8 = 0.625 hours or 37.5 minutes
The distance of the second part of the race is 15 - 5 = 10 miles and the time is 1.125 - 0.625 = 0.5 hours or 30 minutes.
4 0
2 years ago
Read 2 more answers
Write an equation of the graph:
katrin [286]
1. To translate to the left, add to x. 
The equation is: y = |x + 2|

2. To translate down, add to y. 
The equation is: y + 2 = |x| OR y = |x| - 2 (subtract 2 from each side)

Hope this helps!
5 0
3 years ago
5a + 18 < −27 pre algibra
Grace [21]

Answer:

X < -9

Step-by-step explanation:

5a +18 < -27

5a < -27 -18

5a < - 45

5a/5 < - 45/5

a < - 9

Answred by Gauthmath

5 0
2 years ago
Read 2 more answers
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