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4 years ago

Solve the equation (x - 4) - (x + 7) = 8x

Mathematics

1 answer:

siniylev [52]4 years ago

7 0

For this case we have the following equation:

$(x-4) - (x + 7) = 8x$

We have to:

$- * + = -$

So, rewriting the expression we have:

$x-4-x-7 = 8x$

We add similar terms from the left side:

Equal signs are added and the same sign is placed.

Different signs are subtracted and the major sign is placed.

$-11 = 8x$

We divide between 8 on both sides:

So:

$x = - \frac {11} {8}$

ANswer:

$x = - \frac {11} {8}$

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A manufacturer of small appliances purchases plastic handles for coffeepots from an outside vendor. If a handle is cracked, it i

Rus_ich [418]

Answer:

$n=\frac{0.5(1-0.5)}{(\frac{0.1}{1.96})^2}=96.04$

And rounded up we got:

$n\approx 97$

Step-by-step explanation:

Data given and previous concepts

ME=0.1 represent the margin of error desired

Confidence =0.95 or 95%

$\alpha=0.05$ represent the significance level

z represent the quantile from the normal standard distribution

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

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

Solution to the problem

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 for the proportion interval is given by this formula:

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

And on this case we have that $ME =\pm 0.1$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

Since we don't have a prior estimate for the proportion $\hat p$ we can use as estimator 0.5 and replacing into equation (b) the values from part a we got:

$n=\frac{0.5(1-0.5)}{(\frac{0.1}{1.96})^2}=96.04$

And rounded up we have that n=97

5 0

4 years ago

Find the numerical value of the log expression

Setler79 [48]

Answer:

Step-by-step explanation:

I'm going to solve this question by expanding the logarithm (note that you can also solve this equation by solving for a, b, and c)

We know the following

$log(ab)=log(a)+log(b)$

Which means we can split the numerator into

$log(b^{1/2})+log(c^{3/2})$

We also know that

$log(a^{x})=x*log(a)$

Which means that we can rewrite the following as

$\frac{log(b)}{2}+\frac{3log(c)}{2}$

We can evaulate this and get

-1+12= 11

for the numerator

Now we need to take care of the denominator

we know the following

$log(\frac{x}{y})=log(x)-log(y)$

which means that we have

11-2log(a)

solve and get

11-2

7 0

3 years ago

HELLO EVERYONE IT WOULD BE GREAT IF YOU CAN HELP ME IM ABOUT TO FAIL MY CLASS

MrMuchimi

Well we first need to add up all the purchases, 2 sandwiches are 6.86 each so by multiplying that we get 13.72. Next are the burgers, 3.44 x 4 is 13.76. We don’t need to multiply fries since there’s only one, so that’s just 3.19. Finally there are 4 drinks for 1.52 which gives us 6.08. We need to add these prices all together to get the total. 13.72 + 13.76 + 3.19 + 6.08 = 36.75. In order to find ten percent we multiply 36.75 by .10 which gives us 3.675. Double of 3.675 is 7.35. The price 13.72 (14 rounded) needs to be added with the tax 3.675 (4 rounded) and once again add 7.35. All together we get 25. Are there no other answer choices? Unless I did something wrong I’m sure this is right

8 0

3 years ago

Please help, due today!!

GalinKa [24]

Answer:

4h+7 $\leq$ 20,

Step-by-step explanation:

Because it says that he has to pay $4 for an hour and we don't know how many hours he will be there so it will 4h, and he just has to pay $7 and we know that he has $20 so he can't have a price that will be higher or equal to 20!

Hope this helps!

8 0

3 years ago

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Find an equation of a line that is parallel to 2x+3y=6 and passes through the point (4, 4)

wariber [46]

Answer:

Answer:

Step-by-step explanation:

Slope of a line 2x+3y=6 is -2/3

So line passing through (0,4) has same slope because both are parallel

From slope intercept form we have

Y-y1 =m(x-1)

Y-4= -2/3(x-0)

3Y-12 = -2x

3Y+2x = 12

Which is required equation of a line.

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers