The annual rainfall in Springfield is approximately distributed as a normal random variable with mean 36 inches and variance 70 inches. a. What is the probability that the next year's rainfall will exceed 40 inches? b. What is the probability that in exactly three of the next six years will exceed 40 inches? (Hint: Start with defining the event Eị that the rainfall exceeds 40 inches in the year i.)

Answer:

5 hours

Step-by-step explanation:

217+43+43+43+43+43=432

Answer:

Each child will receive 22 cookies.

6 tins of cookies x 88 cookies per tin = 528 total cookies

528 total cookies / 4 children = 132 cookies per child

132 cookies per child / 6 cookies in a tin = 22 cookies per child

Answer:

Step-by-step explanation:

25 × 4.5= 112.5 and that is you answer

The probability that the sample mean will be greater than 57.95 is 0.0495.

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. This is the basic probability theory, which is also used in the probability distribution.

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

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z=\dfrac{X-\mu}{\sigma}\)

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 p-value, we get the probability that the value of the measure is greater than X.

The Central Limit Theorem establishes that, for a random variable X, with mean \(\mu\) and standard deviation \(\sigma\), a large sample size can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(\frac{\sigma}{\sqrt{\text{n}} }\).

In this problem, we have that:

The probability that the sample mean will be greater than 57.95

This is 1 subtracted by the p-value of Z when X = 57.95. So

\(Z=\dfrac{X-\mu}{\sigma}\)

By the Central Limit Theorem

\(Z=\dfrac{X-\mu}{\text{s}}\)

\(Z=\dfrac{57.95-53}{3}\)

\(Z=1.65\)

\(Z=1.65\) has a p-value of 0.9505.

Therefore, the probability that the sample mean will be greater than 57.95 is 1-0.9505 = 0.0495

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Answer:

?

Step-by-step explanation:

The value of x is 3/7 because the angles of the two intersecting lines at point c, a c e and e c b, have specific values that can be used to solve for x.

Step 1: Calculate the angle of intersection between lines de and ab at point c.

Step 2: Calculate the angle of intersection between lines de and ab at point c.

Step 3: Subtract the angle of intersection between lines de and ab from the angle of intersection between lines d e and a b.

Step 4: Divide the difference in angles by 7 to get the value of x.

To calculate the value of x, first calculate the angle of intersection between lines de and ab at point c. This angle is (2x +2) degrees. Then calculate the angle of intersection between lines d e and a b at point c, which is (5x +3) degrees. Subtract the angle of intersection between lines de and ab from the angle of intersection between lines d e and a b, which is

(5x + 3) - (2x + 2) = 3x + 1

Divide the difference in angles by 7 to get the value of x, which is

x = (3x + 1)/7 = 3/7.

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The two angles measure 90 degrees are called as complementary angles.

What are  complementary angles?

In geometry, complementary angles are defined as two angles whose sum is 90 degrees.

The two angles' complement and supplement are determined by the sum of their measurements. The two angles are said to be complimentary if their combined measurement equals that of a straight angle.

In other words, a right angle results from the combination of two complimentary angles (90 degrees). Angles 1 and 2 are said to be complementary if their sum of angles equals 90 degrees (i.e., 1 + 2 = 90°), and as a result, they are referred to as each other's partners.

two angles that add up to 90 degrees are known as complementary angles. For example, 60° and 30°.

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Answer:

$1,800

Step-by-step explanation:

We know that Tamara invested $15,000 and gets %4 of it each year, She plans to withdraw all the money by the end of 3 years.

4 percent of 15,000 is 600

So we can multiply 600 by three and add it to the 15,000

That gives us 16,800

So Tamara will make a $1,800 interest

Answer:

-72

Workout:
= -3(5)^2-(-3)

= -3(25)+3

= -75+3

= -72 (answer)

The given statement "The this pointer is not automatically passed to static member functions of a class." is false as static member functions can be called without creating an object of the class, and the "this" pointer is used to refer to the current instance of the class. Since no instance is required for static member functions, the "this" pointer is not applicable in this case.

In object-oriented programming, a class is a blueprint for creating objects, and member functions are functions defined within a class that can be called on objects of that class.

Static member functions, also known as class methods, are special member functions that are associated with the class itself rather than any specific object or instance of the class. They are declared using the "static" keyword.

Since static member functions do not operate on specific instances of the class, they do not have access to the "this" pointer. The "this" pointer is a hidden pointer that points to the current object instance, allowing non-static member functions to access the data members and other member functions of the object. However, static member functions do not have this pointer because they are not tied to any specific object.

Static member functions can only access static members of the class, which include static variables and other static member functions. They can be called using the class name itself, without creating an instance of the class. This is because they are not associated with any particular object but rather with the class as a whole.

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Answer:

4

Step-by-step explanation:

The Author - Shakespeare introduces the theme of unrequited love by indicating the refusal of Olivia regarding Duke Orsino's affections.

The play opens with the Duke listening trying to drown his feeling with music. He so openly and unashamedly professes his love for one whose consent he had yet to gauge or decipher.

The bouts of refusal begins with Valentines message declining him from delivering the Dukes message.

9514 1404 393

Answer:

  (b)  DCE is congruent to triangle D'C'E'

Step-by-step explanation:

The congruency statement must list the vertices in the same order.

  DCE ≅ D'C'E'

Its A on edge........

Amelia was at camp for 6 days. The equation used to determine how many days(D) she was at camp is C x D = 6D and S - (C x D) = E

Given data:

S = initial amount = $54

D = the number of days

C = the cost per day = $6

E: the ending amount = $18

Amelia started with S=$54 and spent C=$6 each day at camp.

Therefore, the total amount she spent at camp is given in an algebraic expression that states the product of two variables:

C x D = 6D

Next, she ended with E=$18. So, the equation can be written in algebraic expression that states the difference between the variable:

S - (C x D) = E

Substituting the values in the equation we get:

54 - 6D = 18

54 - 18 = 6D

36 = 6D

D = 6

Therefore, Amelia was at camp for 6 days.

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Answer:

10x+2

Step-by-step explanation:

(3x+5)+(7x-3)

Combine like terms

3x+7x +5-3

10x+2

Answer:

12

Step-by-step explanation:

Because if you do the equation right and take out the x the answer will be 12

Answer:

1. 20

2. 34

3. 14

Step-by-step explanation:

20 is smallest number

34 is biggest number

34-20=14

range is 34-20

Answer:

Hence he will be 4 large containers and 4 small containers

Step-by-step explanation:

Given data

Let the number of small containers be x

and the number of large containers be y

x+y= 8---------1

also

2x+4y= 24-----2

the system of equation to solve the problem is

x+y= 8

2x+4y= 24

from 1

x=8-y

put this in 2

2(8-y)+4y= 24

16-2y+4y= 24

2y= 24-16

2y= 8

y= 8/2

y= 4

put y= 4 in 1

x+4=8

x= 8-4

x= 4

Hence he will be 4 large containers and 4 small containers

The equivalent expression of  (r/s)(6) is determined as (3 (6) - 1 ) / ( 2(6) + 1).

Option A.

The equivalent expression that represents (r/s)(6) is calculated by substituting the given values of r and s as follows;

The given expression;

r = 3x - 1

s = 2x + 1

Now, we are going to find the value of the expression [r/s] (6) as follows;

( 3x - 1 ) / (2x + 1) ( 6 )

Simplify further and we will have;

So we will replace, x with 6, to obtain the desired expression;

(3 (6) - 1 ) / ( 2(6) + 1)

This expression corresponds to the solution in option A.

Thus, the equivalent expression of  (r/s)(6) is determined as (3 (6) - 1 ) / ( 2(6) + 1) as shown in option A.

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Answer:

0.2%

Step-by-step explanation:

6                x

------   =   ----------

3000         100

Answer:

Step-by-step explanation:

if we have 3000 who tried the shampoo but only 6 had an allergic reaction,

3000/100=30

30 represent one percent

we have only 6 people

30/6=0.2 %

only 0.2 % of people had an allergic reaction

To calculate the cash balance at the end of the period, we need to consider the cash inflows and outflows.

Starting cash balance: $4,520

Cash inflows: $1,654 (receivables collected)

Cash outflows: $1,961 (payments to suppliers) + $500 (cash expenses)

Total cash inflows: $1,654

Total cash outflows: $1,961 + $500 = $2,461

To calculate the cash balance at the end of the period, we subtract the total cash outflows from the starting cash balance and add the total cash inflows:

Cash balance at the end of the period = Starting cash balance + Total cash inflows - Total cash outflows

Cash balance at the end of the period = $4,520 + $1,654 - $2,461

Cash balance at the end of the period = $4,520 - $807

Cash balance at the end of the period = $3,713

Therefore, the cash balance at the end of the period is $3,713.

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Answer:

8*(g-5)

Step-by-step explanation:

To determine your weight on the surface of a neutron star with the same mass as our sun and a diameter of 16.0 km, we need to calculate the gravitational force exerted on you.

By using the formula for gravitational force and considering the difference in distance from the center of the neutron star compared to the Earth's center, we can determine the weight. However, due to the extreme density and gravitational pull of a neutron star, your weight on its surface would be significantly higher than on Earth.

The weight of an object is determined by the gravitational force acting on it. On Earth, the weight can be calculated using the formula W = mg, where W is the weight, m is the mass of the object, and g is the acceleration due to gravity. In this case, if your weight on Earth is 670 N, it means that the gravitational force acting on you is 670 N.

To calculate the weight on the surface of a neutron star, we need to consider the gravitational force exerted by the neutron star. The formula for gravitational force is F = G(m1m2)/r^2, where F is the force, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between their centers.

Given that the neutron star has the same mass as our sun and a diameter of 16.0 km, we can calculate the distance from the center of the neutron star to its surface. By using the formula for the circumference of a circle, C = 2πr, we can find the radius of the neutron star. Using the obtained radius value, we can then calculate the weight on the surface of the neutron star by plugging the values into the formula for gravitational force.

Due to the extreme density and gravitational pull of a neutron star, the weight on its surface would be much higher than on Earth. The exact weight value can be calculated by substituting the known values into the formula and evaluating the expression.

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The process for classifying or predicting the value of the target variable of a new observation for given values of predictor variables called is called scoring a card.

In the given question we have to explain what is the process for classifying or predicting the value of the target variable of a new observation for given values of predictor variables called.

As we know that, a score a card is a statistical model generated using information about the portfolio's past performance. The main advantage of categorizing clients using a statistical scorecard is that it gives the client an accurate numerical forecast of their future behavior.

So, the process for classifying or predicting the value of the target variable of a new observation for given values of predictor variables called is called scoring a card.

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The right question is:

What is the process for classifying or predicting the value of the target variable of a new observation for given values of predictor variables called?

Answer:

68.26

Step-by-step explanation:

The symbol σ represents standard deviation. 1 standard deviation (in both directions) under a normal distribution= 68.26

Answer:

68%.

Step-by-step explanation:

The 68-95-99.7 rule (also know as the Empirical Rule) states that 68% of the data lies within 1 standard deviation of the mean. 95% of the data lies within 2 standard deviations of the mean. 99.7% of the data lies within 3 standard deviations of the mean.

According to the diagram, the area shaded shows data within 1 standard deviation of the mean (one standard deviation to the left, and one to the right). That means that 68% of the data is within the shaded area.

Hope this helps!

The integral ∫10x^p * ln(x) dx converges for all values of p except p = -1.

To determine the values of p for which the integral ∫10x^p * ln(x) dx converges, we need to consider the convergence of the integrand for different values of p. The integral will converge if the integrand is well-behaved and does not exhibit any divergence.

Let's analyze the integrand in two separate cases:

Case 1: p ≠ -1

When p ≠ -1, the integrand is well-defined for all x > 0. We can proceed with evaluating the integral.

∫10x^p * ln(x) dx = [x^(p+1) * ln(x)] / (p+1) + C

To calculate the value of the integral for a specific value of p, we can substitute the limits of integration into the antiderivative expression and evaluate the resulting expression.

Case 2: p = -1

When p = -1, the integrand becomes 10x^(-1) * ln(x), which poses a potential issue at x = 0. To determine if the integral converges for this case, we need to examine the behavior of the integrand near x = 0.

As x approaches 0, the expression ln(x) approaches negative infinity, which would cause the integrand to diverge. Therefore, for p = -1, the integral does not converge.

In summary, the integral ∫10x^p * ln(x) dx converges for all values of p except p = -1.

Please note that when evaluating the definite integral for specific limits of integration, you should substitute the limits into the antiderivative expression and then calculate the difference of the resulting expressions evaluated at the upper and lower limits.

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The scale of the drawing is given as follows:

1 : 4.5.

The scale of the drawing is obtained applying the proportions in the context of this problem.

The scale is defined as the division of the drawn length by the actual length.

The lengths are given as follows:

90/20 = 4.5, hence the scale of the drawing is given as follows:

1 : 4.5.

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If two angles are complementary, it means that their sum is 90 degrees. This means that

angle FGJ + angle JGH = 90

From the diagram, angle JGH = 24.4

Thus,

angle FGJ + 24.4 = 90

angle FGJ = 90 - 24.4

angle FGJ = 65.6 degrees

Answer:

c>9

Step-by-step explanation:

c-3>6

+3   +3

c>9

Answer: 6 candies

Step-by-step explanation:

So if the teacher buys 12 packs of 8 candies she will have 96 candies in total giving each of the 30 students 3 candies. That leaves her with 6 candies to enjoy by herself.