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3 years ago

Are the two cylinders similar? The diagrams are not drawn to scale.

Mathematics

1 answer:

vovangra [49]3 years ago

5 0

Answer:

a) no

Step-by-step explanation:

-The diagrams can be said to be mathematically similar if the dimensions of their corresponding sides enlarge or reduce by the same factor.

-We therefore determine the enlargement factor for both the radius and height as below:

-Let k be the scale factor

$k_r=\frac{R}{r}\\\\=\frac{3.64}{2.6}\\\\=1.4\\\\k_h=\frac{H}{h}\\\\=\frac{10.192}{8.32}\\\\=1.225\\\\k_r\neq k_h$

Hence, the cylinders are not mathematically similar since the enlargment factors for the radius and height are not equal.

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10. Two plots of land, one square and other rectangle have same perimeter. If the rectangular field is of size 90 m by 70 m, whi

masya89 [10]

Answer:

Here is your answer.

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2 years ago

Which reason justifies the following statement?

amid [387]

Answer:

(A) Complements of the same angle are congruent.

Step-by-step explanation:

Since, ∠CEF is complementary to ∠DCF, therefore

∠CEF+∠DCF=90° (1)

Also, ∠CEG=∠CEF+∠FEG

⇒90°=∠CEF+∠FEG (2)

Therefore, from(1) and (2), we get

∠CEF+∠DCF=90°

∠CEF+∠FEG=90°

Subtracting both the equations, we get

∠DCF-∠FEG=0

∠DCF=∠FEG.

Hence, ∠DCF≅∠FEG by the rule: Complements of the same angle are congruent.

3 0

3 years ago

Read 2 more answers

The current process has a mean of 2.50 and a std deviation of 0.05. A new process has been suggested by research. What sample si

Novay_Z [31]

Answer:

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

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

The critical value for 95% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.025,0,1)", and we got $z_{\alpha/2}=1.96$ , replacing into formula (2) we got:

$n=(\frac{1.96(0.05)}{0.02})^2 =24.01$

So the answer for this case would be n=25 rounded up to the nearest integer

Step-by-step explanation:

Previous concepts

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".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

$\sigma=0.05$ represent the population standard deviation

n represent the sample size (variable of interest)

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

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$

The margin of error is given by this formula:

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

And on this case we have that ME =0.02 and we are interested in order to find the value of n, if we solve n from equation (1) we got:

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

$n=(\frac{1.96(0.05)}{0.02})^2 =24.01$

So the answer for this case would be n=25 rounded up to the nearest integer

7 0

2 years ago

Explain how solving -4t < 32 is different from solving 4t <-32.

stiv31 [10]

Thanks for the question!

When you multiply or divide both sides of an inequality, you flip the sign. "Flip," meaning greater than becomes less than and less that becomes greater than.

Hope this helps!

3 0

3 years ago

Daniel is a very good television salesperson. His annual sales average at $187,400. His commission on sales is 30% and his annua

BaLLatris [955]

Answer: $96,220

Step-by-step explanation:

From the questionwe are we informed that Daniel is a very good television salesperson and that his annual sales average at $187,400 and his commission on sales is 30% while his annual base salary is $40,000.

His annual gross income will be his annual base salary plus commission annually. This will be:

= $40,000 + (30% × $187,400)

= $40,000 + (0.3 × $187,400)

= $40,000 + $56,220

= $96,220

7 0

2 years ago