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SVEN [57.7K]
3 years ago
12

1. Solve: 6x - 12 < 6 2. Solve: 2(3x-8) >8

Mathematics
1 answer:
8090 [49]3 years ago
4 0

Answer:

Step-by-step explanation:

1. here you go mate

step 1

6x - 12 < 6  equation

step 2

6x - 12 < 6  simplify

6x-12+12<6+12

step 3

6x<18  Divide both sides

\frac{6x}{6}

answer

x<3

2. Here you go mate

step 1

2(3x-8) >8  equation

step 2

2(3x-8) >8  simplify

6x-16+16>8+16

step 3

6x>24  divide both sides

\frac{6x}{6} >\frac{24}{6}

answer

x>4

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A manufacturing company produces valves in various sizes and shapes. One particular valve plate is supposed to have a tensile st
maxonik [38]

Answer:

z=\frac{5.0611-5}{\frac{0.2803}{\sqrt{42}}}=1.413    

p_v =2*P(z>1.413)=0.158  

If we compare the p value and the significance level given \alpha=0.1 we see that p_v>\alpha so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the average tensile strength is different from 5lbs/mm at 10% of signficance

Step-by-step explanation:

Data given and notation  

\bar X=5.0611 represent the sample mean

\sigma=0.2803 represent the population standard deviation for the sample  

n=42 sample size  

\mu_o =5 represent the value that we want to test

\alpha=0.1 represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

p_v represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the true mean is different from 5, the system of hypothesis would be:  

Null hypothesis:\mu = 5  

Alternative hypothesis:\mu \neq 5  

If we analyze the size for the sample is > 30 but and we know the population deviation so is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:  

z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}  (1)  

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic

We can replace in formula (1) the info given like this:  

z=\frac{5.0611-5}{\frac{0.2803}{\sqrt{42}}}=1.413    

P-value

Since is a two sided test the p value would be:  

p_v =2*P(z>1.413)=0.158  

Conclusion  

If we compare the p value and the significance level given \alpha=0.1 we see that p_v>\alpha so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the average tensile strength is different from 5lbs/mm at 10% of signficance

8 0
3 years ago
PLZ HELP ASAP FEATURES OF A CIRCLE FROM ITS EXPANDED EQUATION LAST ONE
pantera1 [17]
We have the following equation:
 x2 + y2 + 6y - 72 = 0
 Rewriting we have:
 x2 + y2 + 6y = 72
 Complete squares we have:
 x2 + y2 + 6y + (6/2) ^ 2 = 72 + (6/2) ^ 2
 x2 + y2 + 6y + (3) ^ 2 = 72 + (3) ^ 2
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5 0
3 years ago
In a class of 54 students there are 6 more girls than boys. What is the ratio of the number of boys to the numbers of girls
OLEGan [10]

Answer:

6:54?

Step-by-step explanation:

Im really sorry if it's wrong but I'm pretty sure thats the answer since its a ratio

8 0
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18. During a clothing store's Bargain Days, the regular price for T-shirts is discounted to $8.25.
8090 [49]

Answer:

3.25

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Jack can text 180 words in 2 minutes and 45 seconds. What is his unit rate in texts per second?
grigory [225]

Answer: 1.091 which is approximately 1 word per second

Step-by-step explanation:

Jack can text 180 words in 2 minutes and 45 seconds. We would convert 2 minutes to seconds

60 seconds = 1 minute

x seconds = 2 minutes

x = 2×60 = 120 seconds

2 minutes 45seconds = 120+45 = 165 seconds

This means Jack can text 180 words in 165 seconds

Let's find his unit rate in texts per second

if jack texts 180 words in 165 seconds

Then jack texts y words in 1 second

165y = 180

y = 180/165= 1.091 words per second

This is approximately 1 word per second

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