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krek1111 [17]
2 years ago
6

Is -9 3/8 a rational or irrational number

Mathematics
1 answer:
mel-nik [20]2 years ago
3 0

Answer:

Rational

Step-by-step explanation:

-9 ⅜ = -75/8

Every number which can be written in a fraction of integers is rational.

Integers can be negative too

You might be interested in
If a substance decays at a rate of 25% every 10 years, how long will it take 512 grams of the substance to decay to 121.5 grams
Juliette [100K]

Answer:

It will take 50 years to decay from 512 grams to 121.5 grams.

Step-by-step explanation:

The decay formula :

N=N_0e^{-\lambda t}

where

N= amount of substance after t time

N₀= initial of substance

t= time.

A substance decays at a rate 25% every 10 years.

So, remaining amount of the substance is = (100%-25%)= 75%

\frac{N}{N_0}=\frac{75\%}{100\%}=\frac{75}{100}=\frac34, t= 10

N=N_0e^{-\lambda t}

\Rightarrow \frac {N}{N_0}=e^{-\lambda t}

\Rightarrow \frac34 =e^{-\lambda .10}

Taking ln both sides

\Rightarrow ln|\frac34| =ln|e^{-\lambda .10}|

\Rightarrow ln|\frac34|=-10\lambda

\Rightarrow \lambda=\frac{ ln|\frac34|}{-10}

Now , N₀= 512 grams, N= 121.5 grams, t=?

N=N_0e^{-\lambda t}

\therefore 121.5=512e^{-\frac{ln|\frac34|}{-10}.t}

\Rightarrow 121.5=512e^{\frac{ln|\frac34|}{10}.t}

\Rightarrow \frac{121.5}{512}=e^{\frac{ln|\frac34|}{10}.t}

Taking ln both sides

\Rightarrow ln|\frac{121.5}{512}|=ln|e^{\frac{ln|\frac34|}{10}.t}|

\Rightarrow ln|\frac{121.5}{512}|={\frac{ln|\frac34|}{10}.t}

\Rightarrow t=\frac{ln|\frac{121.5}{512}|}{\frac{ln|\frac34|}{10}}

\Rightarrow t=\frac{10.ln|\frac{121.5}{512}|}{{ln|\frac34|}}

⇒t=50 years

It will take 50 years to decay from 512 grams to 121.5 grams.

8 0
3 years ago
Solve for r.<br> - 8x + 14 &gt; 60 OR<br> - 4r + 50 &lt; 58<br> Choose 1 answer:
hodyreva [135]
R would equal 2 i think
6 0
3 years ago
What facts are true for the graph of the function listed below? Please check all that apply.
lana [24]

Answer:

E, B, A,

Step-by-step explanation:

C is wrong because it isn't decreasing

D is wrong because if X=0 the 5 to the power of zero would be 1 and 2*1= 2 meaning y goes lower than 5

F is wrong because  if X=0 the 5 to the power of zero would be 1 and 2*1= 2 meaning the y intercept is 2 not 5

6 0
3 years ago
Read 2 more answers
(−4x <br> 4<br> +6x <br> 2<br> +3)−(5x <br> 2<br> −3)
LekaFEV [45]

Answer:

(-4x4+6x2+3)-(5x2-3)

ok.

-4x4+6x2=2x6

2x6          3

-(+5x2)      -(-3)

_____       _____

-3x4       +  6

i think, im not sure but i think its -3x4+6. i might be wrong

3 0
3 years ago
Suppose the expected tensile strength of type-A steel is 103 ksi and the standard deviation of tensile strength is 7 ksi. For ty
ExtremeBDS [4]

Answer:

a

i So  the approximate distribution of \= X is \mu_{\= X} =103 and  \sigma_{\= X} = 0.783

ii So the approximate distribution of \= Y is \mu_{\= Y} =105 and  \sigma_{\= Y} = 0.645

b

 the approximate distribution of  \=X  - \= Y is E (\= X - \= Y)  = -2 and  \sigma_{\= X  - \=Y}=1.029

Here we can see that the mean of the approximate distribution is negative which tell us that this negative value of the  data for  \=X  - \= Y sample   are more and their frequency occurrence is higher than the positive values  

c

the value of  P(-1 \le \=X - \= Y  \le 1) is = -0.1639    

Step-by-step explanation:

From the question we are given that

       The expected tensile strength of the type A steel is  \mu_A = 103 ksi

        The standard deviation of type A steel is  \sigma_A = 7ksi

         The expected tensile strength of the type B steel is \mu_B = 105\ ksi

            The standard deviation of type B steel is  \sigma_B = 5 \ ksi

Also the assumptions are

       Let \= X be the sample average tensile strength of a random sample of 80 type-A specimens

Here n_a =80

      Let \= Y be  the sample average tensile strength of a random sample of 60 type-B specimens.

  Here n_b = 60

Let the sampling distribution of the mean be

             \mu _ {\= X} = \mu

                   =103

 Let the sampling distribution of the standard deviation be

               \sigma _{\= X} = \frac{\sigma }{\sqrt{n_a} }

                     = \frac{7}{\sqrt{80} }

                    =0.783

So What this mean is that the approximate distribution of \= X is \mu_{\= X} =103 and  \sigma_{\= X} = 0.783

For \= Y

 The sampling distribution of the sample mean is

               \mu_{\= Y} = \mu

                    = 105

  The sampling distribution of the standard deviation is

               \sigma _{\= Y} = \frac{\sigma }{\sqrt{n_b} }

                    = \frac{5}{\sqrt{60} }

                    = 0.645

So What this mean is that the approximate distribution of \= Y is \mu_{\= Y} =105 and  \sigma_{\= Y} = 0.645                      

Now to obtain the approximate distribution for \=X  - \= Y

               E (\= X - \= Y) = E (\= X) - E(\= Y)

                                =  \mu_{\= X} - \mu_{\= Y}

                                = 103 -105

                                = -2

The standard deviation of \=X  - \= Y is

               \sigma_{\= X  - \=Y} = \sqrt{\sigma_{\= X}^2 - \sigma_{\= Y}^2}

                         = \sqrt{(0.783)^2 + (0.645)^2}

                         =1.029

Now to find the value of  P(-1 \le \=X - \= Y  \le 1)

  Let us assume that F = \= X - \= Y

    P(-1 \le F \le 1) = P [\frac{-1 -E (F)}{\sigma_F} \le Z \le  \frac{1-E(F)}{\sigma_F} ]

                             = P[\frac{-1-(-2)}{1.029}  \le  Z \le  \frac{1-(-2)}{1.029} ]

                             =  P[0.972 \le Z \le 2.95]

                             = P(Z \le 0.972) - P(Z \le 2.95)

Using the z-table to obtain their z-score

                             = 0.8345 - 0.9984

                             = -0.1639

                   

3 0
2 years ago
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