FIND THE SUM:
FIND THE DIFFERENCE:

The probability that the mean number of raisins in the Happy Trail Mix is more than the mean number of raisins in the generic mix is 9.7%.

To solve this problem, we need to use the central limit theorem, which states that the distribution of the sample means approaches a normal distribution as the sample size increases. With a sample size of 17, we can approximate the distribution of the sample means as normal.

Let's call the mean of the Happy Trail Mix sample x and the mean of the generic mix sample y.

Using the formula for the mean of a normal distribution, we can find the mean of x and y:

μx = μ = 33.6

μy = μ = 28.8

Using the formula for the standard deviation of the sample mean, we can find the standard deviation of x and y:

σx = σ/√n = 8.4/√17 = 2.04

σy = σ/√n = 12.7/√17 = 3.08

Now that we have the mean and standard deviation of x and y, we can use a normal distribution calculator or a z-score table to find the probability that x > y.

The z-score is given by:

z = (x - y - μ)/σ = (33.6 - 28.8)/(√(2.04^2 + 3.08^2)) = 1.30

Using a standard normal table, we find that the probability of a z-score being greater than 1.30 is 0.097, or 9.7%.

To know more on central limit theorem

https://brainly.com/question/18403552

#SPJ4

Answer:

only one triangle can be formed ...

Answer: 17 m/s

Step-by-step explanation:  

Answer:

only one solution

Step-by-step explanation:

4x - 8 = 3x + 13

x = 21

Hey there!

Given:

[tex]4x-8=3x+13[/tex]

Solution(s):

One Solution; [tex]x=21[/tex]

Hope this helps!

According to the given information in the question rounded to the nearest hundredth, the probability is 0.14.

Probability is a measure of how likely something is to occur. The probability is computed by dividing the total possible outcomes by the number of possible ways the event could occur.

Adding the probabilities together will yield the chance of a simple event occurring. Your total chances of acquiring something are 10% + 25% = 35%, for instance, if you have an 10% opportunity to win $10 and a 25 percentage chance of getting $20.

The probability of a student studied for exactly 5 hours can be calculated using the formula for probability of a discrete event:

P(X = 5) = (number of ways to get a 5) / (total number of outcomes)

From the data provided, we know that 5 students studied for 5 hours. And there were a total of 35 students surveyed. So the probability is:

P(X = 5) = 5/35 = 0.14

Rounded to the nearest hundredth, the probability is 0.14.

To know more about probability visit:

https://brainly.com/question/30034780

#SPJ1

One technique to write numbers such that you can see the mathematical significance of each individual digit is in expanded form or expanded notation. So the expanded form of (3x-5)³ is 27x³-135x²+225x-125.

One technique to write numbers such that you can see the mathematical significance of each individual digit is in expanded form or expanded notation.

It is also possible to create a mathematical expression using integers that have been divided into distinct place values and decimal places.

5,000 + 300 + 20 + 5 = 5,325 is the expanded notation for the number.

Expanded form of the given expression.

1) We can expand the given term by the direct formula of the algebra

(A-B)³ = A³-B³-3AB(A-B)2)

We have (3x-5)³on comparing with the formula:

A = 3x

B = 5

(3x-5)³

(3x)³-5³-3×3x×5(3x-5)

27x³-125-45x(3x-5)  27x³-125-135x²+225x

So the expanded form of (3x-5)³ is 27x³-135x²+225x-125.

To learn more about expanded form refer

https://brainly.com/question/19989422

#SPJ1

Exercise can be beneficial for academic performance in a variety of ways.

Improved cardiovascular health, for example, can lead to improved blood flow to the brain, providing a better environment for learning and memory formation. Exercise can also improve mental health, reduce stress, and increase energy levels, helping to better prepare for tests and exams. Finally, exercise can help to improve concentration, focus, and overall cognitive function.

The formula for calculating the potential benefits of exercise on academic performance is:

Academic Performance = Exercise + Improved Cardiovascular Health + Mental Health + Stress Reduction + Energy + Concentration + Focus + Cognitive Function

By increasing the amount of exercise, the individual can increase their academic performance. This is done by improving cardiovascular health, mental health, stress levels, energy, concentration, focus, and cognitive function. All of these factors play a role in academic performance, and increasing any one of them can lead to an overall improvement in academic performance.

Learn more about factors  here:

https://brainly.com/question/29128446

#SPJ4

She could only solve 24 * 25 if the array has 24 rows and 25 columns or vice versa

From the question, we have the following parameters that can be used in our computation:

Product expression = 24 * 25

An array is a set of items that has rows and columns

The array is not given

However, the true statement is that: for Rosie to evaluate the expression using an array, then the array must be a 24 x 25 array or 25 x 24 array

Read more about array at

https://brainly.com/question/13134820

#SPJ1

Perimeter (P) = AB + BC + CD + DA.

The perimeter of a trapezoid is the sum of the lengths of each side of the trapezoid. A trapezoid is a quadrilateral that has two sides parallel to each other and two non-parallel sides termed as bases and legs respectively. Let us learn how to calculate the perimeter of the trapezoid in this article.

perimeter of the trapezoid=sum of 4 side

                                            =AB+BC+CD+DA

Perimeter (P) = AB + BC + CD + DA.

It can also be written as a sum of lengths of parallel sides and the sum of lengths of non-parallel sides where AB and CD are the parallel sides and AD and BC are the non-parallel sides.

To learn more about perimeter of the trapezoid refers to;

https://brainly.com/question/19036195

#SPJ1

There are several different sampling methods that could be employed for this study, including:

Simple random sampling: This method involves randomly selecting a certain number of students from each campus and measuring the distance between their hometowns and their campuses.

Stratified random sampling: This method involves dividing the student population at each campus into different strata (e.g. by major or year in school) and then randomly selecting a certain number of students from each stratum.

Cluster sampling: This method involves randomly selecting a certain number of campuses and then measuring the distance between the hometowns of all students at those campuses and their respective campuses.

Multi-stage sampling: This method involves using a combination of the above methods, such as first using cluster sampling to select a certain number of campuses and then using stratified random sampling to select a certain number of students from each campus.

This study would be an enumerative study because it seeks to measure the characteristics of a population, in this case, the average distance between the hometowns of students and their campuses, by counting and measuring them.

It is not an analytic study because it doesn't involve testing a hypothesis or making causal inferences.

To know more about types of sampling visit :

https://brainly.com/question/12902833?referrer=searchResults

#SPJ4

Answer:

B. [tex]\frac{1}{6}[/tex]

Step-by-step explanation:

imma human calculator and no one can stop me

No, that i not a ucce, the electric bill need to be  amount $1530 or le to be conidered a ucce.

To calculate the electric bill after the 11% decrease, simply multiply the current electric bill by 0.89, which is 1-11%. This will give you the new electric bill.

$1700 x 0.89 = $1530

Therefore, if the company's electric bill for next month is amount $1530 or less, then that would be considered a success.

The company must reduce their electric bill to $1530 or less in order to be considered successful in decreasing their energy usage by 11%.

Learn more about amount here

https://brainly.com/question/8082054

#SPJ4

The required volume of the prism when area of cross section of the prism and the length of the prism are given is calculated to be 750 cm³.

Area of cross section of the prism = 30 cm²

Length of the prism = 25 cm

Volume of the prism = ?

A prism is a polyhedron consisting of an n-sided polygon base. The relation between volume, base area and height of the prism is mathematically given as,

V = B H

where, B is Base area

H is Height of prism

V = 30 × 25 = 750 cm³

Thus, the required volume of the prism when area of cross section of the prism and the length of the prism are given is calculated to be 750 cm³.

To know more about volume:

https://brainly.com/question/12643532

#SPJ4

The comparable word in Bryan's pattern is 28 whereas the number in Liam's pattern is 49.

The difference between every two successive terms in an arithmetic series is always the same. The number "a" is the first term, and "d" is the common difference between the. sequence. The nth term of an arithmetic sequence is given by. aₙ = a + (n – 1)d

Given this, we must first determine what is the position of 49 in Liam's pattern. Since Liam's pattern starts at 7 and increases by 7 each time, we can say that

d = 7

a₁ = 7

Substituting these values, we will get

49 = 7 + (n - 1) * 7

49 = 7 + 7n - 7

49 = 7n

n = 7

we are asked what is the corresponding term in Bryan's pattern when the number in Liam's pattern is 49. Since 49 is the 7th term in Liam's pattern, we need to find the 7th term in Bryan's pattern. As stated in the problem, Bryan's pattern starts at 4 and increases by 4 each time. This means that

d = 4

a₁ = 4 n = 7

Substituting these values, we will get

a₇= 4 + (7 - 1) * 4

a₇ = 4 + (6) * 4

a₇ = 4 + 24

a₇ = 28

Therefore, when the number in Liam's pattern is 49, the corresponding term in Bryan's pattern is 28.

Learn more about arithmetic sequence here:

https://brainly.com/question/15412619

#SPJ1

X intercept is none , y intercept is (0,1)

The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis.

the distance from the origin to a point where a graph crosses a coordinate axis. : interception.

The x- and y-intercepts of a line, or linear equation intercepts, are often used in problems involving lines and their graphs. Linear equation intercepts are important points to be able to understand and decipher in applications of linear equations problems and can also be used when graphing lines.

f(x)=x^2+1=0

so the x intercept is none and y intercept is (0,1)

To learn more about intercept refers to;

https://brainly.com/question/10715722

#SPJ1

Answer:

the answer is

c = 4

and h = √2/10

The percentage change is by 30% and it indicates percentage increase due to increase in new quantity.

The percent change will be calculated using the formula -

Percentage change = difference in quantity ÷ original quantity × 100

Difference in quantity will further be expressed by the formula -

Difference in quantity = New quantity - original quantity

Keep the values in formula for calculation. Firstly finding the difference in quantity.

Difference in quantity = 39 - 30

Performing subtraction

Difference in quantity = $9

Percentage change = 9/30×100

Performing division and cancelling zero

Percentage change = 30%

The mentioned scenario represents percentage increase.

Learn more about percentage -

https://brainly.com/question/11360390

#SPJ4

Check the picture below.

Answer:

x=−3⋅−6+4=x=22

Step-by-step explanation:

The probability of spinning an odd number first then spinning an even number is 3/8 x 4/8 = 12/64.

This can be expressed as a fraction, decimal, or percentage. As a fraction, this probability is 12/64. As a decimal, this probability is 0.1875. As a percentage, this probability is 18.75%.

To calculate this probability, we first need to calculate the probability of spinning an odd number first. Since there are eight sections and four of them are odd numbers (1, 3, 5, 7), the probability of spinning an odd number is 4/8. We then need to calculate the probability of spinning an even number. Since there are four even numbers (2, 4, 6, 8), the probability of spinning an even number is 4/8. Finally, we multiply these two probabilities together to get the probability of spinning an odd number first then spinning an even number, which is 3/8 x 4/8 = 12/64.

Learn more about probability here:

https://brainly.com/question/30034780

#SPJ4

The runner's average speed in kilometers per hour is 24.257 km.

The total distance covered by the runner is 1 mile. The relation between kilometers and miles is given as 1 km = 0.62 mi. Converting 1 mile to km by using the given relation, we get-

Distance = 1 mile

 = 1 mile × [1 km/0.62 mile]

= 1.6129 km

The time taken to complete a 1-mile run is 3 minutes and 59.37 seconds. The relation between hours and minutes is given below.

1 hour = 60 minutes ……(1)

Converting 3 minutes to hours using equation (1), we get-

3 minutes = 3 minutes × [1 hour/60 minutes]

= 0.05 hours

The relation between hours and seconds is given below.

1 hour = 3600 second …….(2)

Converting 59.37 seconds to hours using equation (2), we get-

59.37 seconds = 59.37 seconds × [1 hour/3600 seconds]

= 0.016492 hours

Total time to cover 1 mile = (0.05 + 0.016491) hours = 0.066492 hours

The average speed of the runner is calculated by the following relation-

Average Speed = Distance (km)/time (hours)

= 1.6129 km/0.066492 hours

= 24.257 km/hour

Therefore, the average speed in kilometers per hour is 24.257km.

For more such questions on average speed

https://brainly.com/question/12322912

#SPJ4

Answer:

#1 is 2.56

#2 is 2374.32

#3 is 19

#4 is 2,007.62

Step-by-step explanation:

3.2 x 0.8 = 2.56

Solve 22.83 x 104 =2374.32

The aquarium in Key West has a display of 486 fish. How many fish would be in 25 displays=12150

542.6 x 3.7 =2007.62

6,325 x 48 =303600

Answer: Infinite, or unsolvable

Step-by-step explanation:

6x + 12 = 2(3x+6)

6x + 12 = 6x + 12 <-- opening up the bracket

Because both sides of the equation are the same, the answer is either that there are an infinite amount of solutions for x, or that the equation is unsolvable.

Answer: 2.4 x 10^-2

Step-by-step explanation:

6 x 4 = 24 (you can do this because powers are the same)
24 x 10^-3
2.4 x 10^-2

The required solution of the given quadratic equation are 2 or -2.

A quadratic equation is a second-order polynomial equation in a single variable x ax² +bx+c=0. with a ≠ 0 . Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution.

We have,

b² -4=0

Here we will use identity a² - b² = (a+b)(a-b)

Then,

b² -4=0

b² - (2)² = 0

(b + 2)(b - 2) = 0

b + 2 = 0

b = -2

Or b - 2 = 0

b = 2

Thus,required solution of the quadratic function are 2 or -2.

To know more about quadratic function visit:

brainly.com/question/27958964

#SPJ1

Answer: This is a geometric sequence, because each term is obtained by multiplying the previous term by a constant ratio. In this case, the ratio is -2.

To find the 9th term, we can use the formula for the nth term of a geometric sequence:

a_n = a_1 * r^(n-1)

where:

a_n is the nth term of the sequence

a_1 is the first term of the sequence (9)

r is the common ratio (-2)

n is the term number (9)

Plugging in the values:

a_9 = 9 * (-2)^(9-1) = 9 * (-2)^8 = 9 * -256 = -2304

So the 9th term of the sequence is -2304

All of the statements that are true include the following:

II. The hypothesis was supported with the results of the experiment.

III. It can be concluded that every time 8 wraps are added to the nail, the total number of paper clips lifted doubles.

Therefore, the correct answer option is: A. II and III only.

In Science, a hypothesis is primarily considered to be a tentative or an educated guess and it can be defined as a testable explanation for an observation, result, or a specific experimentation (scientific) problem, especially through the use of the "if . . . then . . . because" format.

Based on the information provided about this experiment, we can reasonably infer and logically deduce that the hypothesis developed about the steel nail is true because when eight (8) wraps of an insulated copper wire are added to the steel nail, the total number of paper clips that would be lifted is twice as many paper clips.

Read more on hypothesis here: brainly.com/question/146342

#SPJ1

Answer:  D. percentages only for each line item.

Horizontal analysis, also known as trend analysis, is a method of financial statement analysis that compares line items over time by expressing them as a percentage of a base year. The base year is typically the most recent year, and the comparison is typically made to the prior year. In horizontal analysis, the increases and decreases are shown as percentages for each line item, so that the changes in the line items can be easily compared and analyzed. This is different from vertical analysis, which shows the line items as a percentage of a total, such as total assets or total revenue.

Step-by-step explanation: