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3 years ago

6

Kendra has a painting canvas that is 29 inches wide by 37 inches high. She painted a red rose, which covered 60% of the canvas.

What was the area of the canvas which was covered by the red rose? A. 386.28 in2 B. 32.19 in2 C. 1,073 in2 D. 643.8 in2

1 answer:

grigory [225]3 years ago

3 0

$0,60*(37*29)=643.8$
D. 643.8

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find the sum of the first 20 terms of an arithmetic sequence with a first term of -14 and a comman difference of 4

timama [110]

Answer:

480

Step-by-step explanation:

Sn = n÷2 × (2a + (n-1)d)

n = 20 a = -14 d = 4

S20 = 10 × (-28 + 19 × 4) = 480

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3 years ago

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

postnew [5]

Answer:

<u>a) 0.1542</u>

<u>b) 0.7685</u>

<u>c) 0.2315</u>

<u>d) No, it is not unusual</u>

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.

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aksik [14]

Answer:

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Step-by-step explanation:

I have a lot to do so there won't be a step by step

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3 years ago

Write an expression so that the product of a whole number and a decimal is.0.28

Butoxors [25]

Let

x-------> the whole number

y------> the decimal number

we know that

$x*y=0.28$ ------> equation 1

assume the value of x and then calculate the value of y

Let

x=280

solve for y in the equation 1

$y= \frac{0.28}{x}$

substitute the value of x

$y= \frac{0.28}{280}$

$y=0.001$

therefore

<u>the expression is equal to</u>

280*0.001=0.28

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3 years ago

What is the solution or solutions to the the equation x+2=2^x

Rainbow [258]

Answer:

x=2

Step-by-step explanation:

2^2=4

2+2=4

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3 years ago