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3 years ago

6

A fort had enough provisions for 100 men for 8 days. If 60 more men were joined then how many days the provisions will last for?

1 answer:

Grace [21]3 years ago

8 0

Answer:

It would last for 3.2 days.

Step-by-step explanation:

100 men = 8 days

10 men = 0.8 days

60 men = 0.8 x 6 = 4.8 days

Now you subtract the days of 100 men and 60 men

8 - 4.8 = 3.2 days

Hope this helps!

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If m angle GEF is thirteen less than five times m angle DEG and m angle DEF = 149º, find m angle GEF.

Nina [5.8K]

Answer:

122*

122 degrees

Step-by-step explanation:

m∠GEF is 13 less than 5 times m∠DEG and m∠DEF = 149*

Solution:

As per given data,

m∠GEF = 5m∠DEG - 13* … (i)

m∠DEF = 149* -> m∠GEF + m∠DEG = 149* .. (ii)

Substituting value of m∠GEF in (ii)

We get,

(5m ∠DEG - 13*) + m∠DEG = 149*

6m ∠DEG - 13* = 149*

6m ∠DEG = 149* + 13* = 162*

m∠DEG = * = 27*

Substituting value of m∠DEG in (i)

We get,

m∠GEF = 5(27*) - 13*

m∠GEF = 135* - 13* = 122*

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The sum of the lengths of two opposite sides of the circumscribed quadrilateral is 10 cm, and its area is 12 cm2. Find the radiu

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Answer:

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Step-by-step explanation:

The area of sircumscribed quadrilateral over a circle is equal to

$A=s\cdot r,$

where s is semi-perimeter of the quadrilateral and r is the radius of the circle.

Use property of circumscribed quadrilateral: The sums of the opposite sides are equal.

So, if the sum of two opposite sides of the circumscribed quadrilateral is 10 cm, then the sum of another two sides is also 10 cm and the perimeter of the quadrilateral is 20 cm. Hence,

$s=\dfrac{20}{2}=10\ cm$

Now,

$A=s\cdot r\\ \\12=10r\\ \\r=\dfrac{12}{10}=1.2\ cm$

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Step-by-step explanation:

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3 years ago

Watching tv: in 2012, the general social survey asked a sample of 1310 people how much time they spend\t watching tv each day. T

gayaneshka [121]

Answer:

a) Null hypothesis: $\mu \geq 3$

Alternative hypothesis: $\mu < 3$

This hypothesis test is a left tailed test.

b) $t=\frac{2.8-3}{\frac{2.6}{\sqrt{1310}}}=-2.784$

The p value for this case can be calculated with this probability:

$p_v =P(z$

We can conduct the test with the Ti84 using the following steps:

STAT>TESTS>T-test>Stats

We input the value $\mu_o =3, \bar X= 2.8, s_x = 2.6, n=1310$ and for the alternative we select $< \mu_o$ . Then press Calculate.

And we got the same results.

Step-by-step explanation:

Information given

$\bar X=2.8$ represent the sample mean

$s=2.6$ represent the population standard deviation

$n=1310$ sample size

$\mu_o =3$ represent the value to test

$\alpha=0.5$ represent the significance level for the hypothesis test.

t would represent the statistic

$p_v$ represent the p value for the test

Part a) System of hypothesis

We want to test if the true mean is less than 3, the system of hypothesis would be:

Null hypothesis: $\mu \geq 3$

Alternative hypothesis: $\mu < 3$

This hypothesis test is a left tailed test.

Part b

The statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

Replacing the info given we got:

$t=\frac{2.8-3}{\frac{2.6}{\sqrt{1310}}}=-2.784$

The p value for this case can be calculated with this probability:

$p_v =P(z$

We can conduct the test with the Ti84 using the following steps:

STAT>TESTS>T-test>Stats

We input the value $\mu_o =3, \bar X= 2.8, s_x = 2.6, n=1310$ and for the alternative we select $< \mu_o$ . Then press Calculate.

And we got the same results.

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3 years ago