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3 years ago

Choose the solution set represented by the following graph.

Mathematics

1 answer:

Ivan3 years ago

3 0

Answer:

{x | x∈ R, x < -2}

Step-by-step explanation:

Given

See attachment for graph

Required

Determine the inequality

From the attachment, we can see that there is an open circle or -2.

This represents either < or >

Solving further:

The arrow points to the left of -2.

This means that the number line represents numbers less than -2. i.e. < -2

If the numbers are represented with x.

The inequality is: x < -2

So, we have: {x | x∈ R, x < -2}

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Which shows all the values of x that make the rational expression undefined? x = 6 x = 7 x = –6 or x = 6 x = –7 or x = 7

n200080 [17]

<h2>Explanation:</h2>

The rational expression is given by:

$E=\frac{2x^2-72}{5x^2-245} \\ \\ Factor \ out: \\ \\ E=\frac{2(x^2-36)}{5(x^2-49)} \\ \\ E=\frac{2(x-6)(x+36)}{5(x-7)(x+7)} : \ \ \ \ a^2-b^2=(a-b)(a+b)$

The denominator can't be zero, therefore:

$(x-7)(x+7)\neq 0 \\ \\ \\ Thus: \\ \\ \boxed{x\neq 7 \ and x \neq -7}$

Finally, the values of x that make the rational expression undefined are

x = 7 and x = -7

4 0

3 years ago

What is the length of AB with endpoints A (-1,0) and B (4,-3)

stepladder [879]

Answer:

√34

Step-by-step explanation:

it would be radical 34.

8 0

1 year 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

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

So, 95% confidence interval for the difference between the population proportions, ( $p_1-p_2$ ) is ;

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

95% confidence interval for ( $p_1-p_2$ ) =

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

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

= [-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].

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3 years ago

Helppppppppppppppp!!!!

alex41 [277]

Answer:

Step-by-step explanation:

i don’t see a picture?

8 0

3 years ago

Mai bank account is overdrawn by $125 which means her balance is negative 125 she gets $85 for her birthday and deposit into her

stira [4]

The answer is -125+85= -40 because she is adding -125 by 85 which equals-40

4 0

3 years ago