Two 5-year old girls, Alyse and Jocelyn, have been training to run a 1 mile race. Alyse’s 1 mile time A is approximately Normally distributed with a mean of 13. 5 minutes and a standard deviation of 2. 5 minutes.

Jocelyn’s 1 mile time J is approximately Normally distributed with a mean of 12 minutes and a standard deviation of 1. 5 minutes.

Assuming A and J are independent random variables, what is the probability that

Alyse has a smaller time than Jocelyn in a 1 mile race on a randomly selected day?


I'm more so looking for an explanation on how to find the answer, thanks :)

The correct statement regarding the null hypothesis is: the null hypothesis claims the opposite of what the researcher believes.

The null hypothesis is the claim that no relationship exists between two sets of data or variables being analyzed. The

null hypothesis is that any experimentally observed difference is due to chance alone, and an underlying causative

relationship does not exist, hence the term "null".

In research, the null hypothesis is a statement of no effect or no relationship between variables, while the alternative

hypothesis represents the effect or relationship the researcher is interested in demonstrating.

The purpose of statistical testing is to determine whether there is enough evidence to reject the null hypothesis in

favor of the alternative hypothesis.

for such more question on null hypothesis

https://brainly.com/question/25263462

#SPJ11

Here are the given expressions and their respective variables and coefficients:

12s + 4t | Variables: s, t | Coefficients: 12, 4

46rs + 10x | Variables: r, s, x | Coefficients: 46, 10

12q + 14x | Variables: q, x | Coefficients: 12, 14

10x + 10y | Variables: x, y | Coefficients: 10, 10

17rs + 32x | Variables: r, s, x | Coefficients: 17, 32

5x + 7y - 12z | Variables: x, y, z | Coefficients: 5, 7, -12

36ab + 70m | Variables: a, b, m | Coefficients: 36, 70

3r + 19a + 10m | Variables: r, a, m | Coefficients: 3, 19, 10

7k + 16m | Variables: k, m | Coefficients: 7, 16

8r + 5s | Variables: r, s | Coefficients: 8, 5

9h + 120m | Variables: h, m | Coefficients: 9, 120

12k + m | Variables: k, m | Coefficients: 12, 1

7g + 15h + w | Variables: g, h, w | Coefficients: 7, 15, 1

4c - 8d + 12f | Variables: c, d, f | Coefficients: 4, -8, 12

6t + 17r - 35j | Variables: t, r, j | Coefficients: 6, 17, -35

Read more about Coefficients here:

https://brainly.com/question/1038771

#SPJ1

the probability that an American man is 69.8 inches or taller is 0.5 (or 50%).

To solve this problem, we can use the properties of the normal distribution and the standard normal distribution.

First, we need to standardize the variable (the height of men) to a standard normal variable (with a mean of 0 and a standard deviation of 1). We can do this using the formula:

[tex]z = (x - mu) / sigma[/tex]

where z is the standard normal variable, x is the original variable, mu is the mean of the original variable, and sigma is the standard deviation of the original variable.

In this case, we want to find the probability that an American man is 69.8 inches or taller. So we need to calculate the z-score for x = 69.8:

[tex]z = (69.8 - 69.8) / 3.5 = 0[/tex]

The z-score is 0 because 69.8 is equal to the mean of the distribution.

Next, we can use a standard normal distribution table (or a calculator with a normal distribution function) to find the probability that a standard normal variable is less than or equal to 0. We can also use the fact that the area under the standard normal curve is 1.

Using a standard normal distribution table, we find that the probability that a standard normal variable is less than or equal to 0 is 0.5.

for such more questions on standard normal variable

https://brainly.com/question/4079902

#SPJ11

The value of C of is 49/4

Completing the square is a technique for converting a quadratic polynomial of the form to the form for some values of h and k. In other words, completing the square places a perfect square trinomial inside of a quadratic expression.

10k²+7k+C , to find the value of c that will make the expression a perfect square we divide b by 2 and Square it.

Since b = 7

therefore c =( b/2)²

c = (7/2)² = 49/4

therefore the value of C is 49/4.

The expression can now be written as;

10k²+7k +49/4

and it can be simplified as;

40k²+28k +49

learn more about completing the square from

https://brainly.com/question/13981588

#SPJ1

In a standard additions method workup the information from the linear regression that is most closely related to the unknown concentration is this:  the intercept of the linear regression line.

In the standard additions method workup, the information that is most closely related to the unknown concentration is the intercept of the linear regression line.

The reason why this is the case is that the intercept represents the y-value of the regression line where the line crosses the y-axis. This y-axis is the value of the dependent variable when the independent variable or concentration is zero. So, by solving for the intercept, we can determine the concentration of the unknown sample.

Learn more about linear regression here:

https://brainly.com/question/25987747

#SPJ1

The explanation of how to convert a general form equation to a standard form equation is given below:

Let's first look at how to convert a general form equation to a standard form equation. Given a general form equation:

x^2 + y^2 + Dx + Ey + F = 0

Complete the square for both x and y:

a. Divide the coefficients D and E by 2, and square the results. Let's call these values Cx and Cy:

Cx = (D/2)^2

Cy = (E/2)^2

b. Add and subtract Cx and Cy on both sides of the equation:

x^2 + Dx + Cx + y^2 + Ey + Cy = -F + Cx + Cy

Rearrange the equation to form the standard form equation:

a. Group the x and y terms and rewrite as perfect squares:

(x + D/2)^2 + (y + E/2)^2 = -F + Cx + Cy

b. Now, compare this to the standard form equation:

(x - h)^2 + (y - k)^2 = r^2

c. Identify the values of h, k, and r:

h = -D/2

k = -E/2

r^2 = -F + Cx + Cy

Now let's see how to convert a standard form equation to a general form equation. Given a standard form equation:

(x - h)^2 + (y - k)^2 = r^2

Expand the squares:

(x^2 - 2hx + h^2) + (y^2 - 2ky + k^2) = r^2

Rearrange the equation to form the general form equation:

x^2 + y^2 - 2hx - 2ky + h^2 + k^2 - r^2 = 0

Compare this to the general form equation:

x^2 + y^2 + Dx + Ey + F = 0

Identify the values of D, E, and F:

D = -2h

E = -2k

F = h^2 + k^2 - r^2

Now you can convert equations between the general form and the standard form. If you're missing some variables in the general form equation, just treat them as zero and proceed with the same steps.

Read more about standard forms here:

https://brainly.com/question/19169731

#SPJ1

Answer: 3 additional men are needed to reduce the work by 1 hour.

Step-by-step explanation: There is a relationship between working men and the hours needed to complete the work, both are inversely proportional to each other.

Let, x represent the number of men required to complete the work in :

5-1 = 4 hours

then,

4x = 5 * 12 = 60

Hence,

x = 60/4 = 15

There are 12 men, who are working currently on the job and 15 men are required to complete the work in 1 hour less time.

Then,

15 - 12 = 3

3 additional men are required to reduce work by 1 hour.

To learn more about Time and work :

brainly.com/question/28881781

brainly.com/question/14464103

Answer:

To determine which ratio is proportional to 80:60, we need to simplify the ratio by dividing both terms by their greatest common factor. In this case, the greatest common factor of 80 and 60 is 20, so:

80/20 = 4

60/20 = 3

Therefore, the simplified ratio is 4:3.

Now we can compare this ratio to the given options to see which one is proportional to 4:3:

16:15 is not proportional

16:12 is proportional (since 16/4 = 4 and 12/3 = 4)

18:15 is not proportional

18:12 is proportional (since 18/3 = 6 and 12/2 = 6)

Therefore, the ratio that is proportional to 80:60 is 16:12.

Since they can't rent for a fraction of a day, the maximum number of days they can rent the small car with insurance is 10 days.

The total cost of renting a small car with insurance is:

$465 = $25x + $21x

Simplifying and solving for x, we get:

$465 = $46x

x = 10.11

Since they can't rent for a fraction of a day, the maximum number of days they can rent the small car with insurance is 10 days.

Learn more about insurance below.

https://brainly.com/question/25221455

#SPJ1

[tex]\begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ log_a a^x = x\qquad \qquad \stackrel{ \textit{we'll use this one} }{a^{log_a (x)}=x} \end{array} \\\\[-0.35em] ~\dotfill\\\\ \log_2(16x)=4\implies 2^{\log_2(16x)}=2^4\implies 16x=2^4\implies x=\cfrac{2^4}{16}\implies x=1[/tex]

The goal of the data analysis stage is to figure out how information is currently flowing and why it isn't flowing properly. The statement is True.

The basic purpose of data analysis is to obtain meaningful insights and information from data by examining it. While knowing how information progresses is an important part of this process, the ultimate goal is to get a better knowledge of the data itself, as well as any patterns or correlations that may exist within it.

The process of troubleshooting and problem-solving is more directly tied to determining why information is not flowing properly. This may entail examining the data to discover any abnormalities, mistakes, or inconsistencies that may be interfering with information flow. Once these concerns have been recognized, efforts may be made to fix them and enhance information flow.

Therefore, the statement is true, the goal of the data analysis stage is to figure out how information is currently flowing and why it isn't flowing properly.

Learn more about Data Analysis:

https://brainly.com/question/29214006

#SPJ4

TRUE. In the data analysis step, the focus is on examining and evaluating data to identify patterns, trends, and insights. The goal is to pinpoint any issues or inefficiencies in the way information flows and to determine the root cause of these problems.

By analyzing the data, organizations can gain a better understanding of their processes and identify areas for improvement.
 In the data analysis step, the goal is to examine and understand the current flow of information. This involves analyzing the data to identify patterns, trends, and any potential issues. By pinpointing the reasons why the information is not flowing properly, you can then work towards implementing solutions to improve the efficiency and effectiveness of the data management process.

To learn more about Analysis - brainly.com/question/29926939

#SPJ11

Answer:

[tex]36x^{3}a+45xa^{2}=9xa(4x^{2} +5a)[/tex]

Step-by-step explanation:

You can factor out both 9, x, and a, as all the terms can be divided by 9xa.

Hope this helped!

Hong rode the scooter for approximately 86 minutes.

Let's start by using algebra to solve for the number of minutes Hong rode the scooter.

Let's say the number of minutes Hong rode the scooter is "m". Then, we can set up the following equation:

Total cost = $5 fee + 9 cents per minute x m minutes

$12.74 = $5 + $0.09m

Next, we'll solve for "m" by isolating it on one side of the equation:

$12.74 - $5 = $0.09m

$7.74 = $0.09m

m = $7.74 ÷ $0.09

m ≈ 86

Therefore, Hong rode the scooter for approximately 86 minutes.

To know more about cost related question visit:

https://brainly.com/question/30045916

#SPJ1

Answer:

-3

Step-by-step explanation:

To find the slope (m) of the line that passes through Point A(3, -9) and the origin (0, 0), we can use the formula:m = rise/run = (change in y)/(change in x)We can calculate the change in y and change in x as follows:

Change in y = y2 - y1 = 0 - (-9) = 9

Change in x = x2 - x1 = 0 - 3 = -3

Substituting these values into the formula, we get:

m = rise/run = 9/-3 = -3

Therefore, the slope of the line that passes through Point A(3, -9) and the origin is -3.

The expression that represents the total price of buying g pounds of grapes, b pounds of bananas, and p pounds of pears is Total cost = $2.19g + $0.59b + $1.49p

In this case, we need to use the given prices per pound of each fruit to calculate the total cost of purchasing a certain amount of each fruit. We can do this by multiplying the price per pound by the number of pounds of each fruit we want to buy, and then adding up these values.

So, to create the expression, we can start by using the given prices to calculate the cost of each fruit:

Grapes: $2.19/pound

Bananas: $0.59/pound

Pears: $1.49/pound

Next, we can use the variables g, b, and p to represent the number of pounds of each fruit we want to buy. We then multiply each price by its respective variable to get the cost of each type of fruit:

Cost of grapes: $2.19/g x g = $2.19g

Cost of bananas: $0.59/b x b = $0.59b

Cost of pears: $1.49/p x p = $1.49p

Finally, we can add up the costs of all three types of fruit to get the total cost:

Total cost = $2.19g + $0.59b + $1.49p

To know more about expression here

https://brainly.com/question/14083225

#SPJ4

Given statement: The rule of thumb for estimating the time of completion is 1.5 times what you originally think it will be.

Given statement is True.

The reason for this rule of thumb is that tasks often take longer than initially estimated due to unforeseen challenges, dependencies, and other factors that can cause delays.

By estimating the time of completion as 1.5 times the original estimate, you are accounting for these potential delays and allowing for a more realistic timeline.

This rule of thumb is not a hard and fast rule, and there will be cases where tasks take less or more time than 1.5 times the original estimate. However, it can be a helpful guideline for project planning and resource allocation, as it helps to ensure that sufficient time and resources are allocated to complete tasks within a realistic timeframe.

For similar question on estimating.

https://brainly.com/question/597381

#SPJ11

The scientist used 0.786 liters of the liquid for the experiment.

Unit conversion is the process of converting a quantity expressed in one unit of measurement to an equivalent quantity expressed in a different unit of measurement.

To convert between different units of measurement, we need to use conversion factors, which relate to the two units.

In this case, the conversion factor is 1 liter = 1000 milliliters, which allows us to convert from milliliters to liters by dividing by 1000.

Here we have

A scientist used 786 millimeters  

To convert milliliters to liters, we need to divide by 1000 since there are 1000 milliliters in one liter.

So, to convert 786 milliliters to liters, we divide by 1000:

786 milliliters ÷ 1000 = 0.786 liters

Therefore,

The scientist used 0.786 liters of the liquid for the experiment.

Learn more about Unit conversion at

https://brainly.com/question/19420601

#SPJ1

Complete Question:

A scientist used 786 milliliters of a liquid for an experiment. How many liters of the liquid did the scientist use for this experiment?

For events A and B to be independent, the condition that must be true is:
P(A ∩ B) = x * y

The correct condition that must be true if events A and B are independent is:

P(A ∩ B) = P(A) x P(B).

where P(A) is the probability of event A, P(B) is the probability of event B, and P(A ∩ B) is the probability of both events A and B occurring together.

In other words, if events A and B are independent, then the probability of both events occurring together is equal to the product of their individual probabilities.

When two events A and B are independent, the following condition must be true:
P(A ∩ B) = P(A) * P(B)
In your case, the probability of event A is x, and the probability of event B is y.

Therefore, the correct answer is:

P(A ∩ B) = x*y

For similar question on condition.

https://brainly.com/question/10739947

#SPJ11

The total area of the figure with of the semicircle and triangle is 12.27 sq. ft.

Half of a circle is known as a semicircle, and the diameter of the circle is equal to the length of the semicircle's straight edge. A sector of a circle is a section of a circle that is bounded by an arc, two radii, and both. A semicircle is always half of a circle and has a constant central angle of 180 degrees, but a sector can be any part of a circle and has a central angle that can vary from 0 to 360 degrees. This is the major distinction between the two.

Given, the diameter of the semicircle is 3 ft, so its radius is 1.5 ft.

Now, area of the semicircle is given as:

A = 1/2 * pi * (1.5)² = 1.77 sq ft

The area of the triangle is:

A = 1/2 * 3 ft * 7 ft = 10.5 sq ft

Adding the areas we have the total area of the figure:

1.77 sq ft + 10.5 sq ft = 12.27 sq ft

Hence, the total area of the figure is 12.27 sq. ft.

Learn more about area of semicircle here:

https://brainly.com/question/16952186

#SPJ1

Answer:

6x² + 19x + 15

Step-by-step explanation:

(2x+3)(3x + 5)

= 6x² + 10x + 9x + 15

= 6x² + 19x + 15

So, the answer is 6x² + 19x + 15

Three trigonometric ratios are Sin C=21/29,Cos C=20/29, Tan C=21/20.

Trigonometric ratios, also known as trigonometric functions, are mathematical functions that relate the angles of a right triangle to the lengths of its sides. The three primary trigonometric ratios are sine (sin), cosine (cos), and tangent (tan), which are defined as follows:

In the given triangle;

AB=21

BC=20

AC=29

Calculating trigonometric ratios;

Sin C=Perpendicular/Hypotenuse

=AB/AC

=21/29

Cos C=Base/Hypotenuse

=BC/AC

=20/29

Tan C=Perpendicular/Base

=AB/BC

=21/20.

To know more about hypotenuse, visit:

https://brainly.com/question/29407794

#SPJ1

1) The name of the shape is rectangle

2) The name of the shape is trapezoid

3) The name of the shape is rhombus

4) The name of the shape is rectangle

From the question, we are to state the most specific name for each of the given figures

1.

We have a quadrilateral

Opposite sides are parallel and equal

Each interior angle is a right angle

The name of the shape is rectangle

2.

We have a quadrilateral

Only a pair of opposite sides are parallel

The name of the shape is trapezoid

3.

We have a quadrilateral

Opposite sides are parallel and equal

All sides are equal

None of the angle is a right angle

The name of the shape is rhombus

4.

We have a quadrilateral

Opposite sides are parallel and equal

Each interior angle is a right angle

The name of the shape is rectangle

Learn more on Naming plane shapes here: https://brainly.com/question/1710621

#SPJ1

The slope of the linear regression prediction equation is 1,600, which means that for each additional year of

schooling, the expected increase in salary is 1,600.

The slope of the linear regression prediction equation can be calculated by using the formula:

slope = (y2 - y1) / (x2 - x1)

where y2 is the second data point (in this case, 28,600),

y1 is the first data point (in this case, 27,000),

x2 is the second value of the independent variable (in this case, 13 years of schooling), and

x1 is the first value of the independent variable (in this case, 12 years of schooling).

Plugging in the values, we get:

slope = (28,600 - 27,000) / (13 - 12)

slope = 1,600 / 1

slope = 1,600

Therefore, the slope of the linear regression prediction equation is 1,600, which means that for each additional year of

schooling, the expected increase in salary is 1,600.

for such more question on linear regression

https://brainly.com/question/26755306

#SPJ11

The distance of the base of the tower and the airplane is 348.5 ft,  and the right option is 4. 348.5 ft.

Distance is the length between two points.

To calculate the distance of the base of the tower and the airplane, we use the formula below.

Formula:

Where:

From the diagram,

Given:

SUbstitute these values into equation 1 and solve for A

Hence, the right option is 4. 348.5 ft.

Learn more about Distance here: https://brainly.com/question/26046491

#SPJ1

The radius of the water bottle which is in cylindrical shape is approximately 2.12 cm.

A cylinder is a three-dimensional shape that consists of two congruent, parallel circular bases that are connected by a curved lateral surface. The lateral surface of the cylinder is formed by a rectangle that is wrapped around the circular bases.

A cylinder can be thought of as a circular prism, where the bases are circles and the lateral surface is curved. The height of a cylinder is the perpendicular distance between the two bases, and the radius is the distance from the center of the base to the edge of the circular base.

The formula for the volume of a cylinder is V = πr^2h, where V is the volume, r is the radius, and h is the height. We can rearrange this formula to solve for the radius:

r = √(V/πh)

Substituting the given values, we have:

r = √(150/π(8.9))

r ≈ 2.12 cm (rounded to two decimal places)

Therefore, the radius of the water bottle is approximately 2.12 cm.

To know more about the Cylinder visit:

brainly.com/question/15891031

#SPJ1

The equation (x + 6)^2 + (y + 4)^2 = 36 is in the standard form of the equation of a circle:

(x - h)^2 + (y - k)^2 = r^2

where (h, k) is the center of the circle, and r is the radius of the circle. Comparing this with the given equation, we see that the center of the circle is (-6, -4), and the radius of the circle is 6.

Therefore, the signal is located at the point (-6, -4), which is the center of the circle. This is the point from which the radio signal is transmitted.

The range of the signal is the distance from the center of the circle to any point on the circumference of the circle, which is equal to the radius of the circle.

In this case, the radius is 6, which means that the range of the signal is 6 units in all directions from the center. This means that any receiver within 6 units of the center can pick up the radio signal transmitted from this source.

More on equation of circles can be found here: https://brainly.com/question/23799314

#SPJ1

The relative frequency of the given students surveyed and prefer to go to Cook Middle School and Energy Flow is equal to 0.4 or 40%.

The relative frequency of all students surveyed who go to Cook Middle School and prefer Energy Flow

= (Number of students go to Cook Middle School and prefer Energy Flow) /( total number of students surveyed)

From the given table,

The number of students who go to Cook Middle School and prefer Energy Flow is  equal to 20.

The total number of students surveyed is equal to 50.

The relative frequency of all students surveyed who go to Cook Middle School and prefer Energy Flow is,

= 20/50

= 0.4

Therefore, the relative frequency of all students surveyed going to the Cook Middle School and prefer Energy Flow is equal to 0.4 or 40%.

learn more about relative frequency here

brainly.com/question/20399450

#SPJ4

The above question is incomplete, the complete question is :

Some students at Cook Middle School and Elm Middle School participated in a survey. They were asked which sports drink they prefer: Gym Juice or Energy Flow. The two-way table shows the results.

                       Gym Juice        Energy Flow   Total

Cook                   15                     20                    35

Elm                       5                     10                     15

Total                    20                     30                     50

What is the relative frequency of all students surveyed who go to Cook Middle School and prefer Energy Flow?

Therefore, the simplified expression is (c).-5.05u - 6.

To simplify an expression, you typically want to combine like terms and perform any necessary operations in the correct order. Here are the steps you can follow:

Identify any like terms in the expression. Like terms are terms that have the same variables raised to the same powers.

Combine the coefficients of like terms. If there are no like terms, leave the expression as is.

Simplify any operations in the expression, such as multiplication, division, addition, or subtraction, according to the order of operations.

Check if the expression can be simplified further. If it can, repeat steps 1-3 until the expression cannot be simplified further.

Here's an example of how to simplify the expression. [tex]3x + 2x^2 - 5x - x^2[/tex]:

Identify like terms: 3x and -5x are like terms, as are [tex]2x^2[/tex] and [tex]-x^2[/tex].

Combine the coefficients of like terms: [tex]3x - 5x = -2x[/tex], and [tex]2x^2 - x^2[/tex]= x^2. So, the expression becomes:

[tex]-2x + x^2[/tex]

The expression is already simplified in terms of like terms, so there are no further operations to perform.

The expression cannot be simplified further, so the final answer is [tex]-2x + x^2.[/tex]

(3.65u − 11) − (−5 + 8.7u) can be simplified as follows:

First, distribute the negative sign in the second parenthesis:

[tex](3.65u -11) + (5 -8.7u)[/tex]

Next, combine like terms:

[tex]3.65u - 8.7u - 11 + 5[/tex]

Simplify:

[tex]-5.05u - 6[/tex]

Therefore, the simplified expression is -5.05u - 6.

To know more about variables, visit:

https://brainly.com/question/17344045

#SPJ1

the complete question: Simplify the expression.

(3.65u − 11) − (−5 + 8.7u)

(a).12.35u + (−6)

(b). −5.05u + (−16)

(c). −5.05u + (−6)

(d).12.35u + (−16)