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3 years ago

What inequality represents the verbal expression? all real numbers less than 69

1 answer:

6 0

I think the correct answer from the choices listed above is option C. The inequality that represents the verbal expression that states that all real numbers less than 69 would be <span>x > 69. Hope this answers the question. Have a nice day.</span>

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the area of a square floor on a scale drawing is 100 square centimeters, and the scale of the drawing is 1 cm: 2 ft. what is the

kondaur [170]

The square root of 100 is 10. The drawing must be 10 cm by 10 cm.

1 cm = 2 ft, so 10 cm must equal 20 feet.

20 * 20 = 400 square feet :)

3 0

3 years ago

Triangle J K L is shown. Angle J L K is 105 degrees. The length of J K is 4.7 and the length of J L is 2.7.

cluponka [151]

Answer:

The approximate measure of angle K is 34°

Step-by-step explanation:

In ΔJKL

∠L = 105°

JK = 4.7

JL = 2.7

Sine Rule:

$\frac{SinA}{a} = \frac{SinB}{b}= \frac{SinC}{c}$

So, $\frac{SinL}{JK} = \frac{SinK}{JL}\\\frac{SinL}{4.7} = \frac{SinK}{2.7}\\\frac{Sin 105}{4.7} = \frac{SinK}{2.7}\\\frac{Sin 105 \times 2.7}{4.7} = SinK\\\frac{(0.9659 \times 2.7)}{4.7} = Sin K\\\frac{2.60793}{4.7} = Sin K\\0.5549 = Sin K\\Sin^{-1}(0.5549)= K\\K = 33.70$

K ≈ 34°

So, Option B is true

Hence The approximate measure of angle K is 34°

5 0

3 years ago

Suppose we are interested in analyzing the weights of NFL players. We know that on average, NFL players weigh 247 pounds with a

tigry1 [53]

Answer:

$SE= \frac{\sigma}{\sqrt{n}} = \frac{47}{\sqrt{30}}= 8.58$

$ME= 1.64 *\frac{\sigma}{\sqrt{n}} = 1.64*\frac{47}{\sqrt{30}}= 14.073$

$\bar X - ME = 237- 14.073 = 222.927$

$\bar X + ME = 237+ 14.073 = 251.073$

$n=(\frac{1.640(47)}{5})^2 =237.65 \approx 238$

So the answer for this case would be n=238 rounded up to the nearest integer

Null hypothesis: $\mu \geq 247$

Alternative hypothesis: $\mu$

$z=\frac{237-247}{\frac{47}{\sqrt{30}}}=-1.165$

$p_v =P(z$

If we compare the p value and the significance level given $\alpha=0.1$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can't conclude that the true mean is lower than 247 at 10% of significance.

Step-by-step explanation:

For this case we have the following data given:

$\bar X =237$ represent the sample mean

$\sigma = 47$ represent the population deviation

$n =30$ represent the sample size selected

$\mu_0 = 247$ represent the value that we want to test.

The standard error for this case is given by:

$SE= \frac{\sigma}{\sqrt{n}} = \frac{47}{\sqrt{30}}= 8.58$

For the 90% confidence the value of the significance is given by $\alpha=1-0.9 = 0.1$ and $\alpha/2 = 0.05$ so we can find in the normal standard distribution a quantile that accumulates 0.05 of the area on each tail and we got:

$z_{\alpha/2}= 1.64$

And the margin of error would be:

$ME= 1.64 *\frac{\sigma}{\sqrt{n}} = 1.64*\frac{47}{\sqrt{30}}= 14.073$

The confidence interval for this case would be given by:

$\bar X - ME = 237- 14.073 = 222.927$

$\bar X + ME = 237+ 14.073 = 251.073$

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (a)

And on this case we have that ME =5 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (b)

Replacing into formula (b) we got:

$n=(\frac{1.640(47)}{5})^2 =237.65 \approx 238$

So the answer for this case would be n=238 rounded up to the nearest integer

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the true mean is lower than 247 pounds, the system of hypothesis would be:

Null hypothesis: $\mu \geq 247$

Alternative hypothesis: $\mu$

Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$z=\frac{237-247}{\frac{47}{\sqrt{30}}}=-1.165$

P-value

Since is a left tailed test the p value would be:

$p_v =P(z$

Conclusion

5 0

3 years ago

Cual es la derivada de ()=√x sin

fgiga [73]

Answer:

$f(x) =\sqrt{x} sin (x)$

And on this case we can use the product rule for a derivate given by:

$\frac{d}{dx} (f(x)* g(x)) = f'(x) g(x) +f(x) g'(x)$

Where $f(x) =\sqrt{x}$ and $g(x) =sin (x)$

And replacing we have this:

$f'(x)= \frac{1}{2\sqrt{x}} sin (x) + \sqrt{x}cos(x)$

Step-by-step explanation:

We assume that the function of interest is:

$f(x) =\sqrt{x} sin (x)$

And on this case we can use the product rule for a derivate given by:

$\frac{d}{dx} (f(x)* g(x)) = f'(x) g(x) +f(x) g'(x)$

Where $f(x) =\sqrt{x}$ and $g(x) =sin (x)$

And replacing we have this:

$f'(x)= \frac{1}{2\sqrt{x}} sin (x) + \sqrt{x}cos(x)$

3 0

3 years ago

The owner of an apartment complex is preparing a report about the property. he wants to show how the number of available apartme

Stella [2.4K]

B - line graph. A line graph should be added because he wants to know how many of available apartments there were during the time of the year and line graphs are usually up and down on the info.

3 0

3 years ago

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