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olga nikolaevna [1]
3 years ago
14

Hi:) I need help with 11(a) , thanks!:))

Mathematics
1 answer:
Irina-Kira [14]3 years ago
7 0

Answer:

18.95

Step-by-step explanation:

ln 2 x ln (4x) = 3

ln 4x = = 3 / ln 2

ln4x =  3 / 0.69315 = 4.3281

4x = e^4.328 = 75.80

x =  18.95.

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Vladimir79 [104]
Well, basically there are

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3 years ago
{(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4),
Rus_ich [418]

Answer:

  1/9

Step-by-step explanation:

Pairs that sum to 5 are (1,4), (2,3), (3,2), (4,1). There are 4 ways you can get that sum out of 36 possible outcomes. Assuming each outcome is equally likely, the probability of a sum of 5 is ...

  p(5) = 4/36 = 1/9

6 0
3 years ago
A certain geneticist is interested in the proportion of males and females in the population who have a minor blood disorder. In
lord [1]

Answer:

95% confidence interval for the difference between the proportions of males and females who have the blood disorder is [-0.064 , 0.014].

Step-by-step explanation:

We are given that a certain geneticist is interested in the proportion of males and females in the population who have a minor blood disorder.

A random sample of 1000 males, 250 are found to be afflicted, whereas 275 of 1000 females tested appear to have the disorder.

Firstly, the pivotal quantity for 95% confidence interval for the difference between population proportion is given by;

                        P.Q. = \frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+ \frac{\hat p_2(1-\hat p_2)}{n_2}} }  ~ N(0,1)

where, \hat p_1 = sample proportion of males having blood disorder= \frac{250}{1000} = 0.25

\hat p_2 = sample proportion of females having blood disorder = \frac{275}{1000} = 0.275

n_1 = sample of males = 1000

n_2 = sample of females = 1000

p_1 = population proportion of males having blood disorder

p_2 = population proportion of females having blood disorder

<em>Here for constructing 95% confidence interval we have used Two-sample z proportion statistics.</em>

<u>So, 95% confidence interval for the difference between the population proportions, </u><u>(</u>p_1-p_2<u>)</u><u> is ;</u>

P(-1.96 < N(0,1) < 1.96) = 0.95  {As the critical value of z at 2.5% level

                                             of significance are -1.96 & 1.96}  

P(-1.96 < \frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+ \frac{\hat p_2(1-\hat p_2)}{n_2}} } < 1.96) = 0.95

P( -1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+ \frac{\hat p_2(1-\hat p_2)}{n_2}} } < {(\hat p_1-\hat p_2)-(p_1-p_2)} < 1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+ \frac{\hat p_2(1-\hat p_2)}{n_2}} } ) = 0.95

P( (\hat p_1-\hat p_2)-1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+ \frac{\hat p_2(1-\hat p_2)}{n_2}} } < (p_1-p_2) < (\hat p_1-\hat p_2)+1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+ \frac{\hat p_2(1-\hat p_2)}{n_2}} } ) = 0.95

<u>95% confidence interval for</u> (p_1-p_2) =

[(\hat p_1-\hat p_2)-1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+ \frac{\hat p_2(1-\hat p_2)}{n_2}} }, (\hat p_1-\hat p_2)+1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+ \frac{\hat p_2(1-\hat p_2)}{n_2}} }]

= [ (0.25-0.275)-1.96 \times {\sqrt{\frac{0.25(1-0.25)}{1000}+ \frac{0.275(1-0.275)}{1000}} }, (0.25-0.275)+1.96 \times {\sqrt{\frac{0.25(1-0.25)}{1000}+ \frac{0.275(1-0.275)}{1000}} } ]

 = [-0.064 , 0.014]

Therefore, 95% confidence interval for the difference between the proportions of males and females who have the blood disorder is [-0.064 , 0.014].

8 0
3 years ago
Which expression is equivalent to 7a2b + 10a2b2 + 14a2b3?
Llana [10]
The given expression can be simplified in many ways by grouping like terms. The simplest form is obtained by factoring out a²b which gives us the following expression.

a²b(7 + 10b +14b²)
3 0
3 years ago
Read 2 more answers
The triangle on the grid will be translated two units left. On a coordinate plane, triangle A B C has points (negative 1, negati
nignag [31]

Answer:

Option B.

Step-by-step explanation:

The given vertices of triangle ABC are (-1, -1), (-1, -5) and (0.5, -5).

We need to find the coordinates of triangle when it is translated two units left.

So, the rule of translation is

(x,y)\rightarrow (x-2,y)

Using this rule, we get

A(-1,-1)\rightarrow A'(-1-2,-1)=A'(-3,-1)

B(-1,-5)\rightarrow B'(-1-2,-5)=B'(-3,-5)

C(0.5,-5)\rightarrow C'(0.5-2,-5)=C'(-1.5,-5)

The vertices of triangle A'B'C' are A'(-3,-1), B'(-3,-5) and C'(-1.5,-5).

Therefore, the correct option is B.

8 0
3 years ago
Read 2 more answers
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