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Mashutka [201]
4 years ago
11

Solve the unknown variable: 5k/16 +2k/12 = (-25+k)/24

Mathematics
2 answers:
zvonat [6]4 years ago
8 0
5k/16+2k/12=(-25+k)/24
find common denomenator so we can cancel them
find GCM of 16,12, and 24

16=2*2*2*2
12=2*2*3
24=2*2*2*3
GCM=2*2*2*2*3=48

multiply everybody by 48

3(5k)+4(2k)=2(-25+k)
distribute
15k+8k=-50+2k
add like terms
23k=-50+2k
subtract 2k
21k=-50
divie both sides by 21
k=-50/21
k=-2 and 4/25
Goryan [66]4 years ago
6 0
Hello. (60k+32k)/192=(-25+k)/24 ; 92k/192=(-25+k)/24 ; 92k×24=192×(-25+k)/24 ; 2208k= -4800+192k ; 2208k-192k= -4800 ; 2016k= -4800 ; k= -4800/2016 ; k= -2,38. I hope to have helped you.
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Nadya [2.5K]

Answer: 58, 122

Step-by-step explanation:

x+2x+6=180\\\\3x+6=180\\\\x+2=60\\\\x=58\\\\\therefore 180-x=122

4 0
2 years ago
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The board of directors of a corporation has agreed to allow the human resources manager to move to the next step in planning day
denis-greek [22]

Answer:

Yes, at the 0.10 level of significance, there is enough interest in the service to move to the next planning stage.

Step-by-step explanation:

We are given that the board of directors of a corporation has agreed to allow the human resources manager to move to the next step in planning daycare service for employees' children if the manager can prove that at least 25% of the employees have interest in using the service.

The HR manager polls 300 employees and 90 say they would seriously consider utilizing the service.

<em />

<em>Let p = population proportion of employees who seriously consider utilizing the service</em>

SO, <u>Null Hypothesis,</u> H_0 : p \geq 25%   {means that the service will move to the next planning stage}

<u>Alternate Hypothesis</u>, H_a : p < 25%   {means that the service will not move to the next planning stage}

The test statistics that will be used here is <u>One-sample z proportion test statistics</u> because we don't know about the population standard deviation;

               T.S.  =  \frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }  ~  N(0,1)

where,  \hat p = sample proportion of employees who seriously consider

                   utilizing the service = \frac{90}{300} = 0.30

             n = sample of employees = 300

So, <u><em>test statistics</em></u>  =  \frac{0.30-0.25}{\sqrt{\frac{0.30(1-0.30)}{300} } }  

                               =  1.889

Now at 0.10 significance level, the z table gives critical value of -1.2816 for left-tailed test. Since our test statistics is more than the critical value of z so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.

Therefore, we conclude that there is enough interest in the service to move to the next planning stage.

8 0
4 years ago
5/8 plus 1/16 simplified
Mariana [72]
We want to make their denominators the same to add them, their common denominator is 16
So 5/8 will become 10/16
now we can add both fractions easily
10/16 + 1/16 = 11/16
4 0
3 years ago
Which of these sets of measurements represents the lengths of the sides of a right triangle?
mihalych1998 [28]

Answer: The answer is B, just had this answer today, teacher said it was correct.

6 0
3 years ago
Hans is planting a garden with snapdragons and daisies. The table shows some possible combinations of the two plants. If Hans pl
kow [346]
The equation is x+y=45

For 29 daisies, we have y=29
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6 0
4 years ago
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