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Misha Larkins [42]
3 years ago
14

Nine identical cakes weigh a total of 20¼ pounds. How much does each cake weigh? Simplify.

Mathematics
1 answer:
KATRIN_1 [288]3 years ago
4 0

Answer:

2\frac{1}{4}

Step-by-step explanation:

20 1/4 = 20.25

20.25/9 = 2.25

2.25 = 2\frac{1}{4}

Each cake weighs 2.25 pounds.

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In Buffalo, New York, the temperature was "14 °F in the morning. If the temperature drops 7°F, and then rose 9°F, what is the te
elena55 [62]

Answer:

16 Degrees

Step-by-step explanation:

14-7=7     7+9=16

7 0
2 years ago
Find the area of the figure. (Sides meet at right angles.)
kvasek [131]

Answer:

The area of the figure is 48 cm^2

Step-by-step explanation:

Break it into 3 different quadrilaterals and find the area of each one.

8 0
3 years ago
The amount of money spent on textbooks per year for students is approximately normal.
Ostrovityanka [42]

Answer:a

a

   336.04    <  \mu < 443.96

b

  The  margin of error will increase

c

The  margin of error will decreases

d

The 99% confidence interval is  0.4107 <  p  < 0.4293

Step-by-step explanation:

From the question we are  told that

   The sample size  n =  19

    The sample mean is  \= x  = \$\  390

    The  standard deviation is  \sigma =  \$ \  120

 

Given that the confidence level is  95% then the level of significance is mathematically represented as

           \alpha = 100 -  95

          \alpha  =  5 \%

          \alpha  =  0.05

Next we obtain the critical value of \frac{\alpha }{2} from the normal distribution table

    So  

         Z_{\frac{\alpha }{2} } =  1.96

The  margin of error is mathematically represented as

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

=>    E = 1.96 *  \frac{120}{\sqrt{19} }

=>   E = 53.96

The 95% confidence interval is  

     \= x  -  E  <  \mu < \= x  +  E

=>   390  -   53.96   <  \mu < 390  -   53.96

=>  336.04    <  \mu < 443.96

When the confidence level increases the Z_{\frac{\alpha }{2} } also increases which increases the margin of error hence the confidence level becomes wider

Generally the sample size mathematically varies with margin of error as follows

         n  \  \ \alpha  \ \  \frac{1}{E^2 }

So if the sample size increases the margin of error decrease

The  sample proportion is mathematically represented as

       \r p  =  \frac{210}{500}

       \r p  = 0.42

Given that the confidence level is 0.99 the level of significance is  \alpha =  0.01

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

      Z_{\frac{\alpha }{2} }  =  2.58

  Generally the margin of error is mathematically represented as

       E =  Z_{\frac{\alpha }{2} }*  \sqrt{ \frac{\r p (1- \r p )}{n} }

=>   E =  0.42 *  \sqrt{ \frac{0.42 (1- 0.42 )}{ 500} }

=>     E =  0.0093

The 99% confidence interval  is

     \r p  -  E <  p  < \r p  +  E

     0.42  -  0.0093 <  p  < 0.42  +  0.0093

     0.4107 <  p  < 0.4293

 

4 0
3 years ago
Alice, Bertie and Cara like to spend time outdoors. One of them is an avid
sergij07 [2.7K]

Answer:

Cara.

Step-by-step explanation:

Cara went to an Island.

8 0
3 years ago
What 2 numbers multiply to -100 and add to -21 ​
mylen [45]

Answer:

-25 and 4

Step-by-step explanation:

-25×4=-100 and -25+4=-21

6 0
3 years ago
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