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Molodets [167]
2 years ago
8

Simplify the problem.

Mathematics
1 answer:
lesya [120]2 years ago
7 0

Answer:

Option 4: 4¹¹

Step-by-step explanation:

Looking at the problem, I need to work out 4⁴ squared first, which is the same as 4⁸. Then multiply that by 4³ to get 4¹¹. What I did was simply add 3 + (4 * 2), which is 11.

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Describe the transformation done to y=1/x to get y=1/4x-12.<br><br> Please Show Work.
goldenfox [79]
These are the steps for transforming y=1/x to y=1/4x -12:

Step 1: Compress the original function by 4 in x direction. This will yield,

y= 1/4x

Step 2: The resulting function in step 1 is moved down by 12 spaces. The resulting function will be;

y= 1/4x -12
3 0
3 years ago
A retired math teacher takes his niece shopping. He tells his niece that they can spend x dollars and x minus 49.5 equals 15. Wh
kakasveta [241]
X - 49.5 = 15
x = 15 + 49.5
x = 64.5
8 0
3 years ago
3. A new process has been developed for applying pho­ toresist to 125-mm silicon wafers used in manufac­ turing integrated circu
dlinn [17]

Answer:

a

The null hypothesis is  H_o : \mu  =  13.4000

The alternative hypothesis is  H_a :  \mu \ne  13.4000

The null hypothesis is rejected

b

The  99% confidence level is   13.3930  < \mu  < 13.3994

Step-by-step explanation:

From the question we are told that

  The sample size is  n =  10

   The  population mean is  \mu =  13.4 000 \  angstroms

   The level of significance is  \alpha =  0.05

   The  sample data is  

13.3987, 13.3957, 13.3902, 13.4015, 13.4001, 13.3918, 13.3965, 13.3925, 13.3946, and 13.4002

Generally the sample mean is mathematically represented as

        \= x =  \frac{13.3987+ 13.3957\cdots +13.4002 }{10}

=>     \= x = 13.3962

Generally the sample standard deviation  is mathematically represented as

    \sigma = \sqrt{\frac{\sum (x_i - \= x)^2}{n} }

=> \sigma = \sqrt{\frac{ (13.3987 - 13.3962)^2 +  (13.3987 - 13.3962)^2 + \cdots + (13.3987 -13.4002)^2  }{10} }

=>  \sigma =0.0039

The null hypothesis is  H_o : \mu  =  13.4000

The alternative hypothesis is  H_a :  \mu \ne  13.4000

Generally the test statistics is mathematically represented as

      z  =  \frac{\= x - \mu}{\frac{\sigma}{\sqrt{n} } }

=>    z  =  \frac{13.3962 -  13.4000}{\frac{0.0039}{\sqrt{10} } }

=>   z =  3.08

Generally the p-value is mathematically represented as

       p-value  = 2P( z   >  3.08)

From the z-table  P(z >  3.08)= 0.001035

So

       p-value  = 2* 0.001035

      p-value  = 0.00207

So from the obtained value we see that

     p-value  < \alpha

Hence the null hypothesis is rejected

Consider the b question

Given that the confidence level is  99%  then the level of significance is

    \alpha =  (100 -99)\%

=> \alpha =  0.01

Generally from the normal distribution table critical value  of  \frac{\alpha }{2} is  

    Z_{\frac{\alpha }{2} } =  2.58

Generally the margin of error is mathematically represented as  

     E =  Z_{\frac{\alpha }{2} } *  \frac{\sigma}{\sqrt{n} }

=>   E = 2.58  *  \frac{0.0039}{\sqrt{10} }

=>    E = 0.00318

Generally the 99% confidence interval is mathematically represented as

     13.3962   - 0.00318  < \mu  < 13.3962   +  0.00318

=>   13.3930  < \mu  < 13.3994

 

7 0
3 years ago
To rent a boat, you pay for an initial fee plus. John rented a boat for 3 hours and paid $41. Jessica rented a boat for 6 hours
8090 [49]

Answer:

The intial fee is $5

The equation to represent this is: y=12x+5

12 is the cost per hour    x=hours  y=total cost  

Step-by-step explanation:

77-41=36

36/3=12

12*6=72

77-72=5

6 0
3 years ago
Jacob made a banner for a sporting event in the shape of a parallelogram the area of the banner is 127 1/2 square centimeters th
Firlakuza [10]
For a parallelogram, the area is calculated by the equation,
                                            A = bh
where A is area, b is base, and h is height. From this equation, we can solve for the base of the banner by dividing the area by the height. 
                        base of the banner = 127.5 cm² / 4.25 cm
                         base of the banner = 30 cm
Thus, the measure of the base of the banner is equal to 30 cm. 
8 0
3 years ago
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