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3 years ago

One exterior angle of a regular pentagon has a measure of (2x). What is the value of x?

Mathematics

1 answer:

777dan777 [17]3 years ago

6 0

x = 36

pentagon has 5 sides . The formula n/360 gives you the measure of each angle in a regular polygon. So in this case n ( stands for number of sides) is 5. Sum of exterior angle of a any polygon is 360. The measure of 1 exterior angle is given. It is 2x.

Now using ALGEBRAIC EXPRESSIONS we can write it as 5/360 = 2x

which is 72=2x

which is 72/2 = x

which is 36 = x

so x = 36.

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3 years ago

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3 years ago

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3 years ago

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A bottle weighs 1.2 kg when it is 1/4 full of water. It weighs 2.4 kg when it is full. What is the weight of the empty bottle?

sweet [91]

Answer:

Weight of empty bottle = 0.8 kg

Weight of water = 1.6 kg

Step-by-step explanation:

As given , A bottle weighs 1.2 kg when it is 1/4 full of water. It weighs 2.4 kg when it is full.

Let us assume

Weight of empty bottle = x

Weight of water = y

Now,

when the bottle is 1/4 full of water

then,

weight of water = $\frac{1}{4}$ ×y

As given , Bottle weight = 1.2 , when it is 1/4 full of water

⇒ Weight of water + weight of bottle = 1.2

⇒ $\frac{1}{4}$ ×y + x = 1.2

⇒ y + 4x = 4.8 .......(1)

Also given, A bottle weight = 2.4 , when it is full of water

⇒ Weight of water + weight of bottle = 2.4

⇒ y + x = 2.4 ......(2)

Subtract equation (2) from equation (1) , we get

y + 4x - ( y+ x) = 4.8 - 2.4

⇒ y + 4x - y - x = 2.4

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⇒x = $\frac{2.4}{3}$ = 0.8 kg

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4 0

3 years ago

supervisor records the repair cost for 25 randomly selected dryers. A sample mean of $93.36 and standard deviation of $19.95 are

Simora [160]

<h2><u>Answer with explanation:</u></h2>

The confidence interval for population mean (when population standard deviation is unknown) is given by :-

$\overline{x}-t^*\dfrac{s}{\sqrt{n}}< \mu$

, where n= sample size

$\overline{x}$ = Sample mean

s= sample size

t* = Critical value.

Given : n= 25

Degree of freedom : $df=n-1=24$

$\overline{x}= \$93.36$

$s=\ $19.95$

Significance level for 98% confidence interval : $\alpha=1-0.98=0.02$

Using t-distribution table ,

Two-tailed critical value for 98% confidence interval :

$t^*=t_{\alpha/2,\ df}=t_{0.01,\ 24}=2.4922$

⇒ The critical value that should be used in constructing the confidence interval = 2.4922

Then, the 95% confidence interval would be :-

$93.36-(2.4922)\dfrac{19.95}{\sqrt{25}}< \mu$

$=93.36-9.943878< \mu$

$=83.416122< \mu$

Hence, the 98% confidence interval for the mean repair cost for the dryers. = $83.4161$

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3 years ago