Find the value of the logarithm.
log 110
Round your answer to the nearest thousandth.

Answer:

(a) Probability that at most 3 cars per year will experience a catastrophe is 0.2650.

(b) Probability that more than 1 car per year will experience a catastrophe is 0.9596.

Step-by-step explanation:

We are given that the distribution of the number of cars per year that will experience the catastrophe is a Poisson random variable with variance = 5.

Let X = the number of cars per year that will experience the catastrophe

SO, X ~ Poisson([tex]\lambda = 5[/tex])

The probability distribution for Poisson random variable is given by;

               [tex]P(X=x) = \frac{e^{-\lambda} \times \lambda^{x} }{x!} ; \text{ where} \text{ x} = 0,1,2,3,...[/tex]

where, [tex]\lambda[/tex] = Poisson parameter = 5  {because variance of Poisson distribution is [tex]\lambda[/tex] only}

(a) Probability that at most 3 cars per year will experience a catastrophe is given by = P(X [tex]\leq[/tex] 3)

    P(X [tex]\leq[/tex] 3)  =  P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

                   =  [tex]\frac{e^{-5} \times 5^{0} }{0!} +\frac{e^{-5} \times 5^{1} }{1!} +\frac{e^{-5} \times 5^{2} }{2!} +\frac{e^{-5} \times 5^{3} }{3!}[/tex]

                   =  [tex]e^{-5} +(e^{-5} \times 5) +\frac{e^{-5} \times 25 }{2} +\frac{e^{-5} \times 125}{6}[/tex]      

                   =  0.2650

(b) Probability that more than 1 car per year will experience a catastrophe is given by = P(X > 1)

               P(X > 1)  =  1 - P(X [tex]\leq[/tex] 1)

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

                             =  [tex]1-\frac{e^{-5} \times 5^{0} }{0!} -\frac{e^{-5} \times 5^{1} }{1!}[/tex]

                             =  1 - 0.00674 - 0.03369

                             =  0.9596

Answer:

Step-by-step explanation:

a circle will satisfy the conditions of Green's Theorem since it is closed and simple.

Let's identify P and Q from the integral

[tex]P=x^2 y[/tex], and [tex]Q= xy^2[/tex]

Now, using Green's theorem on the line integral gives,

[tex]\oint\limits_C {x^2ydx-xy^2dy } =\iint\limits_D {y^2-x^2} \, dA\\\\[/tex]

Answer:

your answer is 127596 because you would take (45+2) first then you would take (55^2+10s+3) then you multiply them

Step-by-step explanation:

Answer: THE SOLUTION IS B

x=4  gives the linear factor x-4

x=6 gives the linear factor x-6

Step-by-step explanation:

Answer:

For a 45 45 90 triangle

leg = hypotenuse / (square root of 2)

leg = 128 / 1.4142135624

leg = 90.5096679902 cm

Step-by-step explanation:

Answer:

answer is B   64 root 2

Step-by-step explanation:

got it right on edg 2020-2021

Answer:

Step-by-step explanation:

x

2

+

4

x

+

3

x

2

+

4

x

+

3

The dimensions of the rectangle are given as 4cm and 1cm respectively.

A rectangle is a type of parallelogram having equal diagonals.

All the interior angles of a rectangle are equal to the right angle.

The diagonals of a rectangle do not bisect each other.

Suppose the length of rectangle be x.

And, the width be y.

Then, the following equations can be written as per the information given as,

2x - 3y = 1               (1)

And, 1/3(x - y) = 1

⇒ x - y = 3              (2)

Multiply equation (2) by 2 and subtract from (1) to get,

2x - 3y - 2(x - y) = 1 - 2 × 3

⇒ -5y = -5

⇒ y = 1

Substitute y = 1 in equation (2) to get,

x - 1 = 3

⇒ x = 4

Hence, the dimensions are 4cm and 1cm respectively.

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Answer:

His total is $269

Step-by-step explanation:

8x19 = 152

6x19.50 = 117

152+117 = 269

Answer:

the total number is 104756

Step-by-step explanation:

You need to add 56437 with 48319 which equals 104756

Awnser is 104,756 if you add the 2 numbers

D because Caleb had swam 8 more after swimming 13

Answer:

d. That order is taken into account (consider rearrangements of the same items to be different sequences).

Step-by-step explanation:

Given the combination rule:

[tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]

A major difference between permutation and combination is the order of the items in the selection. If the order does not matter then we have a combination. If on the other hand, the order of the items matter, then it is a permutation.

Therefore, that which is not a rule for combination is Option D since, in combination, we do not consider rearrangements of the same items to be different sequences.

Answer:

the base is 5 meters long.

Step-by-step explanation:

To find the a missing side when given the area you have to multiply the area by 2 which in this case would be 50 so 50/10 would be 5m which is your answer.

So the right answer is 5m

Please see the attached picture for full solution

Hope it helps

Good luck on your assignment..

Answer:

Search Results

Featured snippet from the web

Which means that the first number is 104, the second number is 104 + 1 and the third number is 104 + 2. Therefore, three consecutive integers that add up to 315 are 104, 105, and 106.

Step-by-step explanation:

This type of blinding is used to prevent what is referred to as placebo effect in this scenario.

This refers to a situation where some individuals feel improvement in their health when dummy treatment is used.

The subjects not being unaware of the treatment helps to prevent the placebo effect thereby making it the most appropriate choice.

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Answer:

Top right

Step-by-step explanation:

The solution to a system of equation is where the two graphs cross

The top right lines cross at (5,-3)

Answer:

(A)[tex]2^n[/tex]

Step-by-step explanation:

Given a set with "n" number of elements, the collection of all subsets of the set is referred to as the Power set of the given set.

To find the  number of possible subsets of any set, we use the formula: [tex]2^n[/tex]

Take for example the set: A={2,3,4)

A has 3 elements, therefore n=3

The number of possible subsets of A is: [tex]2^3=8$ subsets[/tex]

Answer: B

Step-by-step explanation:

Answer:

x<12

Step-by-step explanation:

subtract both sides by -3 because you need to isolate x. then you have x/4<3. now you need to get rid of the 4. so you do the opposite of division and multiply 4 by both sides so you get x<12

Answer:

A, B and C

Step-by-step explanation:

1) After reflecting the circle over line g, we would come to know that Both are same in size

OR

2) we can also rotate the circle 180° around point C

OR

3) we can also translate the dilated circle so that it's centre is at point b

Answer:  0.0003

Step-by-step explanation:  Solution for fraction 3/10000 to decimal conversion

In the given, we want to convert 3 / 10000 to decimal form, we can compute this by dividing numerator 3 by denominator 10000

3/10000 = 0.0003

Answer:

it is b

Step-by-step explanation:

the answer is b because

Answer:

96

Step-by-step explanation:

Rectangle area:

(8)(10)=80

Triangle area:

(1/2)(4)(8)=16

Total area:

16+80=96

Answer:

[tex]96 {ft}^{2} [/tex]

Step-by-step explanation:

[tex]area = \frac{1}{2} (a + b)h \\ = \frac{1}{2} \times (10 + 14) \times 8 \\ = \frac{1}{2} \times 24 \times 8 \\ = 96 {ft}^{2} [/tex]

Answer:

80%

Step-by-step explanation:

rate=100×Interest/ principal × time

Interest= 40

principal= 600

time= 1 month=1/12

100%×$40×12/$600×1=80%

Answer:

I should take 10.44 tablets in a day, approximately 10.5 tablets.

Step-by-step explanation:

In order to solve this problem we need to convert the weight from pounds to kilograms, to do that we need to divide it by 2.205.

[tex]w = \frac{128}{2.205}\\w = 58.05 \text{ kg}[/tex]

Since I need to take 7.5 mg per kg of body weight, then in order to find the dosage we need to multiply the weight in kg by 7.5.

[tex]\text{dosage} = 58*7.5 = 435 \text{ mg}[/tex]

Since I need to take it every six hours and there are 24 hours in a day, we will have to take 4 dosages in a day, therefore we need:

[tex]\text{dosage(day)} = 435*6 = 2,610 \text{ mg}[/tex]

The antibiotic comes in 250 mg in tablets, therefore the number of tablets is:

[tex]tablets = \frac{2610}{250} = 10.44[/tex]

I should take 10.44 tablets in a day, approximately 10.5 tablets.

Answer:

68°

Step-by-step explanation:

Angle IJK is 112

Opposite angles of a quadrilateral inscribed in a circle add up to 180°

So

m<IHK = 180-112

m<IHK = 68°

Answer:

10  miles

Step-by-step explanation:

tree points form a right triangle with sides 8, 6 and x

x is the hypotenuse of the triangle

x²=8²+6²=100

x=√100=10  miles

Answer:

0.62% probability that the mean of our sample is greater than $70.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

[tex]\mu = 65, \sigma = 20, n = 100, s = \frac{20}{\sqrt{100}} = 2[/tex]

What is the probability mean of our sample is greater than $70.

This is 1 subtracted by the pvalue of Z when X = 70. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{70 - 65}{2}[/tex]

[tex]Z = 2.5[/tex]

[tex]Z = 2.5[/tex] has a pvalue of 0.9938

1 - 0.9938 = 0.0062

0.62% probability that the mean of our sample is greater than $70.

Answer:

Probabilty= 4.171. *10^-4

Step-by-step explanation:

bridge is made up of 13 cards

probability that a bridge chosen at random contains

6 of one suit, 4 of another, and 3 of another

Probabilty of 6 = 13C6

Probabilty of 4 = 13C4

Probabilty of 3 = 13C3

Then total= 53C13

Probabilty =( 13C6*13C4*13C3)/53C13

Probabilty=( 1716*715*286)/53C13

Probabilty= 4.171. *10^-4

Answer:

7/2 x 52/3

Step-by-step explanation:

Steps:

Since 1 year = 52 weeks

52*7/2*3= 7/2*52/3

Since 1 year equal 52 weeks meaning we have to times 52 by 7/2 then times by 3 the weeks. The answer is below.

Answer: 7/2 x 52/3

Please mark brainliest

Hope this helps.

Answer:

5q + 9

Step-by-step explanation:

Combine like terms to simplify the expression.

Have a blessed day!

Answer:

7q+9

Step-by-step explanation:

6q+4+q+5

6q+q+4+5

=7q+9