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sladkih [1.3K]
2 years ago
7

Find the area of the triangle with the given measurements. Round the solution to the nearest hundredth if necessary. B = 105°, a

= 12 cm, c = 19 cm

Mathematics
1 answer:
Akimi4 [234]2 years ago
4 0

Answer:

The area of triangle is 110.10cm^{2}

Step-by-step explanation:

It is given that AB=19cm, BC=12cm and ∠B=105°

Now, Area of the triangle ABC=\frac{1}{2}acsinB

=\frac{1}{2}{\times}12{\times}19{\times}sin105^{\circ}

=6{\times}19{\times}(0.965)

=110.10cm^{2}

Thus, the area of triangle is 110.10cm^{2}

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Seventy percent of a town's population voted in an election. If 1,589 people voted, what is the population of the town?
Crank
The total population of the town is 2270 people.
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2 years ago
Volume of a cylinder pi 3.14 d=2r h=6cm d=12cm
alex41 [277]

Answer:

V = 678.24cubic cm

Step-by-step explanation:

Volume of a cylinder

V = πr^2h

V - volume of a cylinder

π - pie

r - radius of a cylinder

h - height of a cylinder

Given:

π - 3.14

h - 6

d = 12

d = 2r

Divide both sides by 2

d/2 = 2r/2

d/2 = r

r = d/2

r = 12/2

r = 6

Insert the values into the formula

V = πr^2h

V = 3.14 * 6^2 * 6

= 3.14 * 36 * 6

= 678.24cubic cm

5 0
2 years ago
The average weight of a chicken egg is 2.25 ounces with a standard deviation of 0.2 ounces. You take a random sample of a dozen
n200080 [17]

Answer:

P(\bar X

P(\bar X

Step-by-step explanation:

Previous concepts

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 Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Let X the random variable that represent interest on this case, and for this case we know the distribution for X is given by:

X \sim N(\mu,\sigma)  

And let \bar X represent the sample mean, the distribution for the sample mean is given by:

\bar X \sim N(\mu,\frac{\sigma}{\sqrt{n}})

On this case  \bar X \sim N(2.25,\frac{0.2}{\sqrt{12}})

Solution to the problem

We want this probability:

P(\bar X

The best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}

If we apply this formula to our probability we got this:

P(\bar X

P(\bar X

5 0
2 years ago
In a lecture demonstration, an object is suspended from a spring scale which reads 8N when the object is in air. The object is t
katovenus [111]

Answer:

a) density of the object is 3995.01, b) the weight scale reads 22N c) the sum individually will be the same with when added together.

Step-by-step explanation:

The weight of the object in air is 8N,

and weight = Mass * acceleration due to gravity = m * 9.81

8/9.81 = 0.815,

upthrust( force acting on the body from the liquid impeding the immersion) on the body when fully submerged = weight in air - weight in water = 8N - 6N =2N

Upthrust = weight of water displaced = 2N = mass * acceleration

2/9.81 = 0.204kg

density of water(1000kg/m^3) = mass of water / volume of water

volume of water displaced = 0.204/1000 = 0.000204m^3 (204cm^3)

volume of water displaced = volume of the solid

density of solid = mass/ volume = 0.815/0.000204 = 3995.01kg/m^3

b) when fully submerge in water the the scale experience according to newton third law of motion ( equal and opposite reaction of forces) additional 2N push so that total weight with the fully submerge solid = 20N + upthrust = 20N + 2N =22N

c) the of two scale reading is before (8N + 20N = 28N) and after (6N + 22N = 28) since there is no loss of matter; the demonstration was in equilibrium.

6 0
2 years ago
Data from 14 cities were combined for a​ 20-year period, and the total 280 ​city-years included a total of 107 homicides. After
leonid [27]

Answer:

P(0) =  0.6825

P(1) = 0.2607

Step-by-step explanation:

From the given information, the number of homicide is 107 and the total number of homicides per city –year is 280.

Let us denote the number of homicides per city-year as X.

The mean value, X is calculated as:

\begin{array}{c}\\{\rm{Mean}} = \frac{{107}}{{280}}\\\\ = 0.382\\\end{array}  

Mean=   107/280 = 0.382  

The mean number of homicides per city- year \left( {\lambda = \mu } \right)(λ=μ) is 0.382.

a. The probability that zero homicides is obtained is as below:

\begin{array}{c}\\P\left( {X = 0} \right) = \frac{{{e^{ -0.382}}{{\left( {0.382} \right)}^0}}}{{0!}}\\\\ = \frac{{\left( {0.6825 \right)\left( {\rm{1}} \right)}}{1}\\\\ = 0.6825\\\end{array}  

P(X=0) =  e  −0.382  (0.382)⁰​/1  

= (0.6825)(1) /1  

P(X=0) = 0.6825

Thus, the probability that zero homicides P(0) is 0.6825.

b. The probability that one homicides is obtained is as below:

\begin{array}{c}\\P\left( {X = 0} \right) = \frac{{{e^{ -0.382}}{{\left( {0.382} \right)}^0}}}{{0!}}\\\\ = \frac{{\left( {0.6825 \right)\left( {\rm{1}} \right)}}{1}\\\\ = 0.6825\\\end{array}  

P(X=1) =  e  −0.382  (0.382)¹​/1  

= (0.6825)(0.382)/1  

P(X=1) = 0.2607

Thus, the probability that zero homicides P(0) is 0.2607.

​

5 0
2 years ago
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