1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
horsena [70]
3 years ago
15

Which calculation correctly uses prism factorization to write the square root of 420 in simplest form?

Mathematics
1 answer:
IRISSAK [1]3 years ago
7 0

Answer:

\sqrt{420}=\sqrt{2\times2\times3\times5\times7}  =2\sqrt{105}

Step-by-step explanation:

We need to write prime factorisation to solve \sqrt{420}

Prime factorisation: We need to find only those prime factors that are divisible

So, Prime factors of 420 are: 2x2x3x5x7

Now replacing 420 with its prime factors

\sqrt{420}\\=\sqrt{2\times2\times3\times5\times7}  \\=\sqrt{2^2\times3\times5\times7}  \\=\sqrt{2^2}\sqrt{3\times5\times7}\\=2  \sqrt{105}

Since the options are incomplete, kindly verify the options.

So, \sqrt{420}=\sqrt{2\times2\times3\times5\times7}  =2\sqrt{105}

You might be interested in
Find the soluations to (x+3)^2=49
Jobisdone [24]

Answer:

x = 4 , − 10

Step-by-step explanation:

3 0
3 years ago
Dwight has $124, with which he can buy at most 2 video games that are the same price. Use an inequality to find the maximum pric
Hunter-Best [27]

Answer:

$124 divided by 2 = $62

Step-by-step explanation:

4 0
2 years ago
A rectangular pan has a length that is 4/3 the width. The total area of the pan is 432 in.2. What is the width of the cake pan?
Maru [420]
<span>the width of the cake pan can be found with the following formula
area = W x L=</span>432 in.2<span>
but L= 4/3W
so we have </span>
area = W x 4/3W=4/3W²=<span>432 in.2, and </span><span>W²=<span>(3/4)x 432 in.2, and W=18 in</span> </span>


3 0
3 years ago
I need help in my math homework
IRINA_888 [86]
All you do is subtract the two numbers
4 0
3 years ago
Part I - To help consumers assess the risks they are taking, the Food and Drug Administration (FDA) publishes the amount of nico
IRINA_888 [86]

Answer:

(I) 99% confidence interval for the mean nicotine content of this brand of cigarette is [24.169 mg , 30.431 mg].

(II) No, since the value 28.4 does not fall in the 98% confidence interval.

Step-by-step explanation:

We are given that a new cigarette has recently been marketed.

The FDA tests on this cigarette gave a mean nicotine content of 27.3 milligrams and standard deviation of 2.8 milligrams for a sample of 9 cigarettes.

Firstly, the Pivotal quantity for 99% confidence interval for the population mean is given by;

                                  P.Q. =  \frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }  ~ t_n_-_1

where, \bar X = sample mean nicotine content = 27.3 milligrams

            s = sample standard deviation = 2.8 milligrams

            n = sample of cigarettes = 9

            \mu = true mean nicotine content

<em>Here for constructing 99% confidence interval we have used One-sample t test statistics as we don't know about population standard deviation.</em>

<u>Part I</u> : So, 99% confidence interval for the population mean, \mu is ;

P(-3.355 < t_8 < 3.355) = 0.99  {As the critical value of t at 8 degree

                                      of freedom are -3.355 & 3.355 with P = 0.5%}  

P(-3.355 < \frac{\bar X-\mu}{\frac{s}{\sqrt{n} } } < 3.355) = 0.99

P( -3.355 \times {\frac{s}{\sqrt{n} } } < {\bar X-\mu} < 3.355 \times {\frac{s}{\sqrt{n} } } ) = 0.99

P( \bar X-3.355 \times {\frac{s}{\sqrt{n} } } < \mu < \bar X+3.355 \times {\frac{s}{\sqrt{n} } } ) = 0.99

<u />

<u>99% confidence interval for</u> \mu = [ \bar X-3.355 \times {\frac{s}{\sqrt{n} } } , \bar X+3.355 \times {\frac{s}{\sqrt{n} } } ]

                                          = [ 27.3-3.355 \times {\frac{2.8}{\sqrt{9} } } , 27.3+3.355 \times {\frac{2.8}{\sqrt{9} } } ]

                                          = [27.3 \pm 3.131]

                                          = [24.169 mg , 30.431 mg]

Therefore, 99% confidence interval for the mean nicotine content of this brand of cigarette is [24.169 mg , 30.431 mg].

<u>Part II</u> : We are given that the FDA tests on this cigarette gave a mean nicotine content of 24.9 milligrams and standard deviation of 2.6 milligrams for a sample of n = 9 cigarettes.

The FDA claims that the mean nicotine content exceeds 28.4 milligrams for this brand of cigarette, and their stated reliability is 98%.

The Pivotal quantity for 98% confidence interval for the population mean is given by;

                                  P.Q. =  \frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }  ~ t_n_-_1

where, \bar X = sample mean nicotine content = 24.9 milligrams

            s = sample standard deviation = 2.6 milligrams

            n = sample of cigarettes = 9

            \mu = true mean nicotine content

<em>Here for constructing 98% confidence interval we have used One-sample t test statistics as we don't know about population standard deviation.</em>

So, 98% confidence interval for the population mean, \mu is ;

P(-2.896 < t_8 < 2.896) = 0.98  {As the critical value of t at 8 degree

                                       of freedom are -2.896 & 2.896 with P = 1%}  

P(-2.896 < \frac{\bar X-\mu}{\frac{s}{\sqrt{n} } } < 2.896) = 0.98

P( -2.896 \times {\frac{s}{\sqrt{n} } } < {\bar X-\mu} < 2.896 \times {\frac{s}{\sqrt{n} } } ) = 0.98

P( \bar X-2.896 \times {\frac{s}{\sqrt{n} } } < \mu < \bar X+2.896 \times {\frac{s}{\sqrt{n} } } ) = 0.98

<u />

<u>98% confidence interval for</u> \mu = [ \bar X-2.896 \times {\frac{s}{\sqrt{n} } } , \bar X+2.896 \times {\frac{s}{\sqrt{n} } } ]

                                          = [ 24.9-2.896 \times {\frac{2.6}{\sqrt{9} } } , 24.9+2.896 \times {\frac{2.6}{\sqrt{9} } } ]

                                          = [22.4 mg , 27.4 mg]

Therefore, 98% confidence interval for the mean nicotine content of this brand of cigarette is [22.4 mg , 27.4 mg].

No, we don't agree on the claim of FDA that the mean nicotine content exceeds 28.4 milligrams for this brand of cigarette because as we can see in the above confidence interval that the value 28.4 does not fall in the 98% confidence interval.

5 0
2 years ago
Other questions:
  • to visit a magic show ,sam will have to purchase tickets for himself ,his wife and his child. if an adult ticket cost AED 32 and
    10·1 answer
  • A system of equations is shown below: x + 3y = 5 (equation 1) 7x − 8y = 6 (equation 2) A student wants to prove that if equation
    13·2 answers
  • You have a picture that is 5 inches by 7 inches. You want to make a frame for the picture that is of uniform width. Together, th
    15·1 answer
  • 12. I don’t know how to do it
    12·1 answer
  • Please help!
    14·2 answers
  • Help please <br><br><br> On the number line below length AB=
    13·1 answer
  • How do I solve this for x?
    13·1 answer
  • 7 of 8
    6·2 answers
  • I need help eeeeeeeeeeeeeeeeee
    8·2 answers
  • How fast was a plane flying if it traveled 400 mile in 0.5 hours
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!