What is the sun (2/5 x + 5/8) + (1/5 x

The product of two consecutive odd integers is 99. If

bonufazy [111]

The equation in terms of x is x(x + 2) = 99 or $x^2 + 2x - 99 = 0$

The pairs of integers are -11 and -9 or 9 and 11

Solution:

Let the two consecutive odd integers be x and x + 2

Let "x" be the smallest integer

Given that product of two consecutive odd integers is 99

To find: an equation in terms of x

Product of x and x + 2 = 99

$x(x + 2) = 99\\\\x^2 + 2x = 99\\\\x^2 + 2x - 99 = 0$

Thus the equation in terms of x is found

Let us solve the above equation to find all pairs of integers

Solve the quadratic equation by grouping method

Middle term 2x can be written as 11x - 9x

$\rightarrow x^2 + 2x - 99 = 0\\\\\rightarrow x^2 + 11x - 9x -99 = 0$

Now group the terms,

$\rightarrow (x^2 + 11x) - (9x + 99) = 0$

Take "x" as common term from first group and 9 as common term from second group

$\rightarrow x(x + 11)-9(x+ 11) = 0$

Now take x + 11 as common term,

$\rightarrow (x + 11)(x - 9) = 0$

Equating to zero we get,

x + 11 = 0 or x - 9 = 0

x = -11 or x = 9

When x = -11 :

x + 2 = -11 + 2 = -9

Thus first set of two consecutive odd integers are -11 and -9

When x = 9 :

x + 2 = 9 + 2 = 11

Thus second set of two consecutive odd integers are 9 and 11

5 0

3 years ago

Suppose that insurance companies did a survey. They randomly surveyed 400 drivers and found that 320 claimed they always buckle

nirvana33 [79]

Answer:

i) $ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$

And replacing we got:

$ME= 1.96*\sqrt{\frac{0.8 (1-0.8)}{400}} =0.0392$

ii) $Lower = 0.8-0.0392= 0.7608$

$Upper = 0.8 +0.0392= 0.8392$

Step-by-step explanation:

Notation and definitions

$X=320$ number of people that claimed always buckle up.

$n=400$ random sample taken

$\hat p=\frac{320}{400}=0.8$ estimated proportion of people that claimed always buckle up

$p$ true population proportion of people that claimed always buckle up

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Solution to the problem

Part i

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96$

The confidence interval for the mean is given by the following formula:

$\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$

The margin of error is given by:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$

And replacing we got:

$ME= 1.96*\sqrt{\frac{0.8 (1-0.8)}{400}} =0.0392$

Part ii

And the confidence interval would be given by:

$Lower = 0.8-0.0392= 0.7608$

$Upper = 0.8 +0.0392= 0.8392$

6 0

3 years ago

Write an equation in point-slope form of the line having the given slope that contains the given point. m=5/6m=5/6m (30,12)(30,1

Eva8 [605]

Sorry, I don't clear the question

7 0

4 years ago

CAN SOMEONE PLS HELP

MA_775_DIABLO [31]

Answer:

B built many roads and temples

8 0

3 years ago

The ticket office at Orchestra Center estimates that if it charges x dollars for box seats for a concert, it will sell 50 - x bo

yan [13]

S=50x-x^2

dS/dx=50-2x

d2S/dx2=-2

Since acceleration is a constant negative, when velocity equals zero, it is at the absolute maximum point for S(x)...

dS/dx=0 only when 50-2x=0, 2x=50, x=25

So the price that will maximize income is $25.00 a seat.

And that maximum income is:

S(25)=50x-x^2

S(25)=$625.00

6 0

4 years ago

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What is the sun (2/5 x + 5/8) + (1/5 x - 1/4)