According to a study, the salaries of registered nurses are normally distributed with a mean of 56310 dollars and a standard deviation of 5038 dollars. If X represents the salary of a randomly selected registered nurse find and interpret P(X< 45951).

\(~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$5000\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years\dotfill &3 \end{cases} \\\\\\ I = (5000)(0.05)(3) \implies I = 750\)

The dependent variable in this case would be the total number of hot dogs needed for the cookout.

In mathematics, a variable is a symbol, usually a letter, used to represent a quantity in an equation or in a mathematical expression. It can be thought of as a placeholder that can take on different values in a given equation or expression. Variables are essential for mathematics because they allow us to explore different scenarios and solve problems.

This is dependent on the number of guests attending, which is the independent variable. Depending on how many people show up, the individual will need to adjust the amount of hot dogs to accommodate the guests.

To know more about variables click-
https://brainly.com/question/25223322
#SPJ4

Answer:

Equation  :    y = 6

Explanation:

It is a straight line, cuts y axis and does not meet x axis.

Equation of the line is y = 6

\((\stackrel{x_1}{-3}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{-6}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-6}-\stackrel{y1}{(-4)}}}{\underset{run} {\underset{x_2}{-4}-\underset{x_1}{(-3)}}} \implies \cfrac{-6 +4}{-4 +3} \implies \cfrac{ -2 }{ -1 } \implies 2\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{ 2}(x-\stackrel{x_1}{(-3)}) \implies y +4 = 2 ( x +3) \\\\\\ y+4=2x+6\implies {\Large \begin{array}{llll} y=2x+2 \end{array}}\)

Answer: 8,064

Step-by-step explanation:

12 times 3 = 36

36 times 7 = 252

252 times 4 =1,008

1,008 times 8 = 8,064

Answer:

A) rectangle, 10 x 6

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

x2 + x = 42

Step-by-step explanation:

x = nhmber

x² = its square

then:

The sum of a number and its square is 42 is:

x² + x = 42

Answer:

1

Step-by-step explanation:

Anything (besides 0) to the 0 power is 1.

Answer:

a. Increases

Step-by-step explanation:

An exponential graph starts rising gradually and then starts to steeply incline.

In other terms, the derivative of an exponential function shows us that the slope of the exponential function increases as the inputs increase.

∴ our answer is A.

The money paid to the secretary is $14000 and the money paid to mathematician is $22000.

A mathematical statement that establishes the equality of two mathematical expressions is the called an equation.

Total money available for hiring = $36000

Let the money given to secretary = X

Money given to the mathematician = X + 8000

X + (X + 8000) = 36000

2X = 28000

X = 14000

Money given to secretary is $14000.

Money given to the mathematician is $22000.

Learn more about equations on:

https://brainly.com/question/2972832

#SPJ4

The area of the triangle is expressed as 2.718cm²

The formula for calculating the area of a triangle is expressed as:

A = 0.5absinФ

Given the following

Substitute the given parameters to have:

Area = 0.5(2.5)(2.3)sin71

Area = 2.718cm²

Hence the area of the triangle is expressed as 2.718cm²

Learn more on area of triangle here: https://brainly.com/question/17335144

[1] H 2.4

    Let us turn the pictures into equations, using the key given. Then, we will solve.

x + x + \(\frac{1}{4}\)x + 1 + 1 + 1 = x + x + x + \(\frac{1}{2}\)x

2x + \(\frac{1}{4}\)x + 3 = 3x + \(\frac{1}{2}\)x

\(\frac{9}{4}\)x + 3 =  \(\frac{7}{2}\)x

3 = \(\frac{5}{4}\)x

x = 2.4

[2] J

    We can tell the first two options are incorrect because there was a change in size, not position.

    Option H would make the shape bigger, but it becomes larger. This means the answer is option J.

Water pours into a fish tank at a rate of 0.3 cubic meters per minute, the water level is rising at a rate of 1/60 m/min

Given

Let, h is the height of the water level in the fish tank after t minutes. Then, the volume of the water in the fish tank after t minutes is given by \(V = Area of the base * height V = 6 * h m^3\)The rate at which water pours into the fish tank is 0.3 cubic meters per minute.

Therefore, the rate of change of volume of the water in the fish tank after t minutes is \(dV/dt = 0.3 m^3/min\). As per the chain rule of differentiation,\(dV/dt = dV/dh *dh/dt\) We have\(V = 6h^3m^3 \Rightarrow  dV/dh = 18h^2\Rightarrow  dV/dt = 18h^2 * dh/dt\) Given that,\(dV/dt = 0.3 m^3/min\). Therefore,\(0.3 = 18h^2 * dh/dt \Rightarrow  dh/dt = 0.3/18= 1/60 m/min\) Hence, the water level is rising at a rate of 1/60 m/min.

See more about volume at: https://brainly.com/question/463363

#SPJ11

The correct statement is: "A sample of size 30 is the smallest sample size that will have a sampling distribution that is approximately normal."

According to the central limit theorem, when the sample size is sufficiently large (typically around 30 or greater), the sampling distribution of the sample mean will approach a normal distribution regardless of the shape of the population distribution. This holds even if the population distribution is strongly skewed.

Therefore, in this case, a sample size of 30 is the smallest size that would ensure the sampling distribution of the sample mean is approximately normal, regardless of the right-skewness of the population distribution. Smaller sample sizes, such as a sample size of 10, may still provide useful information, but the sampling distribution may deviate more from a perfect normal distribution.

Learn more about sampling distribution here:

https://brainly.com/question/31465269

#SPJ11

Answer:

Width= 4.75

Step-by-step explanation:

Length x width = area

area / length = width

16.625/3.5 = 4.75

(a) To find the probability that the computer contains either a virus or a worm or both, we can use the inclusion-exclusion principle.

P(V or W) = P(V) + P(W) - P(V and W)

Given:

P(V) = 0.32

P(W) = 0.34

P(V and W) = 0.01

Substituting the values into the formula:

P(V or W) = 0.32 + 0.34 - 0.01

= 0.66

Therefore, the probability that the computer contains either a virus or a worm or both is 0.66.

(b) To find the probability that the computer does not contain a virus, we can subtract the probability of having a virus (P(V)) from 1.

P(not V) = 1 - P(V)

Given:

P(V) = 0.32

Substituting the value into the formula:

P(not V) = 1 - 0.32

= 0.68

Therefore, the probability that the computer does not contain a virus is 0.68.

Learn more about probability here:

https://brainly.com/question/31828911

#SPJ11

Here's the answer in C programming language to evaluate the given polynomial:

c

Copy code

#include <stdio.h>

#include <math.h>

double evaluatePolynomial(double x) {

   double term = (x - 1.0) / x; // Calculate the first term of the polynomial

   double result = term; // Initialize the result with the first term

   int i;

   for (i = 2; i <= 4; i++) {

       term = pow(term, i) * i; // Calculate the next term

       result += term; // Add the term to the result

   }

   return result;

}

int main() {

   double x;

   printf("Enter the value of x: ");

   scanf("%lf", &x);

   double y = evaluatePolynomial(x);

   printf("Y = %lf\n", y);

   return 0;

}

In this code, the evaluatePolynomial function takes a value x as input and calculates the polynomial expression. It uses a for loop to calculate each term of the polynomial and adds it to the result. Finally, the main function prompts the user to enter the value of x, calls the evaluatePolynomial function, and prints the result Y.

To know more about C programming language, visit:

https://brainly.com/question/28795101

#SPJ11

Answer:

B.

Step-by-step explanation:

Answer:

YO THE PICTURE DIFFRENT

Step-by-step explanation:

The  answer  is  if we roll the 20-sided dice many times, we can expect to get one of Antonio's favorite numbers about 15% of the time

probability of rolling one of Antonio's favorite numbers on a 20-sided dice can be calculated by dividing the number of favorable outcomes (rolling a 7, 3, or 11) by the total number of possible outcomes (rolling any number from 1 to 20).


The total number of possible outcomes on a 20-sided dice is 20 since there are 20 sides, each with a different number. However, out of these 20 numbers, only 3 of them (7, 3, and 11) are Antonio's favorite numbers.

Therefore, the number of favorable outcomes is 3.

To calculate the probability of rolling one of Antonio's favorite numbers, we divide the number of favorable outcomes (3) by the total number of possible outcomes (20):

Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 3/20

So the probability of rolling one of Antonio's favorite numbers on a 20-sided dice is 3/20.


The probability of an event is the measure of how likely it is to occur. It can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

In this case, we are interested in the probability of rolling one of Antonio's favorite numbers on a 20-sided dice. To calculate this probability, we need to first determine the number of favorable outcomes and the total number of possible outcomes.

The total number of possible outcomes on a 20-sided dice is 20, since there are 20 sides, each with a different number. However, only 3 of these numbers (7, 3, and 11) are Antonio's favorite numbers.

Therefore, the number of favorable outcomes is 3. We can now use the formula for probability to calculate the probability of rolling one of Antonio's favorite numbers:

Probability = Number of favorable outcomes / Total number of possible outcomes

Substituting the values, we get:

Probability = 3/20

So the probability of rolling one of Antonio's favorite numbers on a 20-sided dice is 3/20 or 0.15 (15%). This means that if we roll the 20-sided dice many times, we can expect to get one of Antonio's favorite numbers about 15% of the time.

To know more about probability visit:

brainly.com/question/10544271

#SPJ11

The area of the window is 1440 square inches. Given that the ratio of the length of the base to the height will be 5 to 2 and the base will have a length of 60 inches. We are to determine the area of the window.

Solution:

Let's first calculate the height of the window.

If the ratio of the length of the base to the height will be 5 to 2,

Then we can assume the length of the base is 5x, where x is some constant of proportionality.

And we can also assume the height is 2x.

So we know,

Length of the base = 60 inches

5x = 60x

= 60/5

= 12 inches

Height of the window = 2x

= 2 × 12

= 24 inches

Now we can calculate the area of the window.

Area of the window = Length × Width

Area of the window = 60 × 24

Area of the window = 1440 square inches

To leran more about length, refer:-

https://brainly.com/question/32060888

#SPJ11

Answer:

There is no picture, my sweetheart.

Step-by-step explanation:

Answer: The answer is 81m + 27t

Step-by-step explanation:

Answer: (3t)^t+3 and 3^t^2 x 27^t are both equivalent to the expression while 9^t x 27^t is not equivalent.

Step-by-step explanation:

Answer:

4q + 16

Step-by-step explanation:

4 × q = 4q

4 × 4 = 16

4q + 16

Answer:

2(2x+19) would be your answer

The soda left in the bottle is 0.4 liters in a 2-liter bottle.

Let’s understand this with the concept of Ratio.

How does ratio work?

When two objects are related using numbers or amounts, the relationship is known as a ratio.

Initially, we are given that the bottle is 2 liters. From that, Sergio poured ⅘ of the soda.

So, the soda left is the initial quantity- the final quantity

= 2(initial quantity) - ⅘*2(final quantity)

=2 - 1.6= 0.4 liter

So finally, the soda left in the 2-liter bottle is 0.4 liter.

To know more about Ratios, visit: https://brainly.com/question/1706633

#SPJ4

Answer:

D

Step-by-step explanation:

Multiply everything on the bottom by -2 and then they are the same so infinite answers

The measure of angle B is 107°.

What do similar triangles mean?

If two triangles have an equal number of corresponding sides and an equal number of corresponding angles, then they are comparable. Similar figures are described as items with the same shape but varying sizes, such as two or more figures.

Given a triangle, NPZ is similar to triangle HBZ.

Which can also be written as ΔNPZ ≈ ΔHBZ

So, by equating the corresponding angles that are angle P = angle B:

8x-37°=180-(2x-5+42)°

10x=180

x=18°

So, H=36-5=31°

Since the sum of all angles in a triangle is 180°, angle B can be calculated  as

B= 180°-(42+31)°

B=107°

Therefore the measure of angle B is 107 degrees

To learn more about similar triangles, refer to the link below:

https://brainly.com/question/14285697

#SPJ1