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3 years ago

Plse help so confused

Mathematics

1 answer:

anzhelika [568]3 years ago

3 0

Answer:

Step-by-step explanation:

As we can see that Line WL is a straight line that the angles that make up it like Angle HJW and Angle GJH and Angle LJG all equal to 180 degrees

Angle HJW = 18 degrees

ANGLE GLH = 90 degrees (we know that because there is a little square)

Angle LJG = 9x

Now lets set up the equation:

Angle HJW + Angle GLH + ANGLE LJG = 180 degrees

18 + 90 + 9x = 180

108 + 9x = 180

9x = 72

x = 8

So x = 8

Hope that helps!

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Of all the registered automobiles in a city, 12% fail the emissions test. Fourteen automobiles are selected at random to undergo

postnew [5]

Answer:

a) 0.1542

b) 0.7685

c) 0.2315

d) No, it is not unusual

Explanation:

The procedure to make the test meets the requirements of binomial experiments because:

there are two possible mutually exclusive outputs: fail the test, or pass the test.
the probability of each event remains constant during all the test (p=12% = 0.12, for failing the test, and 1-p = 88% = 0.88, for passing the test)
each trial (test) is independent of other trial.

Solution

(a) Find the probability that exactly three of them fail the test.

You want P(X=3)

Using the equation for discrete binomial experiments, the probability of exactly x successes is:

$P(X=x)=C(n,x)\cdot p^x\cdot (1-p)^{(n-x)}$

Substituting C(n,x) with its developed form, that is:

$P(X=x)=\dfrac{n!}{x!\cdot (n-x)!}\cdot p^x\cdot (1-p)^{(n-x)}$

Thus, you must use:

x = 3 (number of automobiles that fail the emissions test)
n = 14 (the number of automobiles selected to undergo the emissions test),
p = 0.12 (probability of failing the test; this is the success of the variable on our binomial experiment)
1 - p = 0.88 (probability of passing the test; this is the fail of the variable on our binomial experiment)

$P(X=3)=\dfrac{14!}{3!\cdot (14-3)!}\cdot 0.12^3\cdot 0.88^{11}=0.1542$

(b) Find the probability that fewer than three of them fail the test.

The probability that fewer than three of them fail the test is the probability that exactly 0, or exactly 1, or exactly 2 fail the test.

That is: P(X=0) + P(X=1) + P(X=2)

Using the same formula:

$P(X=0)=\dfrac{14!}{0!\cdot 14!}\times 0.12^0\cdot 0.88^{14}$

$P(X=0)=0.1670$

$P(X=1)=\dfrac{14!}{1!\cdot 13!}\cdot 0.12^1\cdot 0.88^{13}$

$P(X=1)=0.3188$

$P(X=2)=\dfrac{14!}{2!\cdot 12!}\codt0.12^2\cdot 0.88^{12}$

$P(X=2)=0.2826$

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.7685

(c) Find the probability that more than two of them fail the test.

The probability that more than two of them fail the test is equal to 1 less the probability that exactly 0, or exactly 1, or exactly 2 fail the test:

P( X > 2) = 1 - P( X = 0) - P(X = 1) - P(X = 2)

P X > 2) = 1 - [P(X=0) + P(X = 1) + P(X = 2)]

P (X > 2) = 1 - [0.7685]

P (X > 2) = 0.2315

(d) Would it be unusual for none of them to fail the test?

Remember that not failing the test is the fail of the binomial distribution. Thus, none of them failing the test is the same as all of them passing the test.

You can find the probability that all the automibles pass the emission tests by multiplying the probability of passing the test (0.88) 14 times.

Then, the probability that none of them to fail the test is equal to:

$(1-p)^{14}\\\\(0.88)^{14}=0.1671$

That means that the probability than none of the automobiles of the sample fail the test is 16.71%.

Unusual events are usually taken as events with a probability less than 5%. Thus, this event should not be considered as unusual.

5 0

3 years ago

the white rabbit has an appointment to see the red queen at 4pm every day of the week except weekends. On Monday he arrives 16 m

lakkis [162]

Answer:friday

Step-by-step explanation:

6 0

3 years ago

GIVING BRAINLIESST PPL

GrogVix [38]

You need to split the shape into simpler shapes so you would get a rectangular prism and a triangular prism finding the volume is pretty straightforward the formula is

Volume of a triangular prism = area of base triangle × height

The formula for finding the volume of a rectangular prism is the following: Volume = Length * Height * Width, or V = L * H * W.
After solving for this you would just have to add the 2 shapes volume together tie get the volume of the composite figure
Finding the surface area is also pretty simple since it would only require you to know the formulas

S = 2(lw + lh + wh) to find the surface area of a rectangle or prism

A=12bh is used to find the area of the top and bases triangular faces, where A = area, b = base, and h = height.
And by adding the two surface areas of the shapes you can get the surface area of the composite figure but remember to subtract the top face of the rectangular prism and the bottom face of the triangular prism
Hope this helps <3

4 0

3 years ago

Convert 4,300 inches into miles.

tatuchka [14]

Answer:

0.06786616

Step-by-step explanation:

To convert an inch measurement to a mile measurement, divide the length by the conversion ratio. The length in miles is equal to the inches divided by 63,360.

6 0

2 years ago

Read 2 more answers

A new hard drive costs $225, plus $40 per hour for

allsm [11]

Answer:

4 hours

Step-by-step explanation:

y= 40x +225

$385 money to spend - $225 that go for hard drive = $160

40* x can be maximum 160 so x= 160 /40= 4

5 0

3 years ago