In a boxplot, potential outliers are data points that are more than 1.5 Interquartile Ranges (IQRs) from the edges of the box. A boxplot visually represents the distribution of a dataset, with the box containing the middle 50% of the data and the edges representing the lower and upper quartiles.
To answer your question, potential outliers in a boxplot are points that are more than 1.5 times the interquartile range (IQR) away from the edges of the box. The IQR is the difference between the third quartile (75th percentile) and the first quartile (25th percentile) of the data. The box in a boxplot represents the IQR, with the median (50th percentile) marked by a line inside the box. The whiskers of the boxplot extend to the minimum and maximum values that fall within 1.5 times the IQR from the edges of the box. Any points outside this range are considered potential outliers and are plotted as individual points beyond the whiskers. However, it is important to note that potential outliers do not necessarily indicate errors or incorrect data, and further investigation may be needed to determine their validity. Overall, boxplots are a useful tool for visualizing the spread and distribution of numerical data.
To know more about Interquartile Ranges visit:
https://brainly.com/question/29204101
#SPJ11
A person has agreed to participate in an ESP experiment. He is asked to randomly pick two numbers between 1 and 6. The second number must be different from the
first. Let
H = event the first number picked is a 4. K = event the second number picked exceeds 5
The probability that the person picks a 4 as the first number (event H) and the second number exceeds 5 (event K) is 1/30.
We can determine the probabilities of events H and K as follows:
P(H) = probability of picking a 4 as the first number = 1/6 (since there are 6 equally likely numbers to choose from and only 1 of them is a 4)
P(K) = probability of picking a number greater than 5 as the second number = 1/5 (since there are 5 remaining numbers to choose from and only 1 of them is greater than 5)
Now, we need to find the probability of both events H and K occurring, which is denoted as P(H ∩ K).
Since the person must randomly pick two numbers and the second number must be different from the first, the total number of equally likely outcomes is 6 * 5 = 30 (6 choices for the first number and 5 choices for the second number).
Out of these 30 equally likely outcomes, there is only 1 outcome where the first number is 4 and the second number exceeds 5, which is (4, 6). Therefore, P(H ∩ K) = 1/30.
Know more about probability here:
https://brainly.com/question/30034780
#SPJ11
Enter the number belongs in the green box. 78° 12 56° Round to the nearest hundredth.
10 is the number that belongs to the green box in the triangle.
Let us find the third interior angle in the triangle
By angle sum property the sum of three angles is 180 degrees
78+56+x=180
134 + x =180
Subtract 134 from both sides
x=180-134
x=46
So sin 56 /12 = sin 46/x
0.829/12=0.7193/x
0.069=0.7193/x
x=0.7193/0.069
The number in green box x=10.42
To learn more on trigonometry click:
https://brainly.com/question/25122835
#SPJ1
allison had two coins. she flipped the first coin, then flipped the second coin. what is the probability of getting a head, then another head?
The probability of getting a head on the first coin flip is 1/2. Assuming that the coins are fair and independent, the probability of getting another head on the second coin flip is also 1/2. By the multiplication rule of probability, we can find the probability of both events occurring by multiplying their individual probabilities:
P(head, then another head) = P(head on first flip) * P(head on second flip)
= (1/2) * (1/2)
= 1/4
Therefore, the probability of getting a head on the first coin flip and another head on the second coin flip is 1/4.
To learn more about probability : brainly.com/question/32004014
#SPJ11
Section 2
Go over the bank statement and answer the questions in detail. Use information from the statement to
support your answers.
Bank of Cascadia
Date
Pending
03/16
03/12
03/08
03/02
03/02
Description
Lucky Cat Fresh Ground Coffee
Car payment
Valkyrie Online Shopping
Southern Cascade Groceries
German Motors Garage
Chuck's Gas and Go
Total credit line: $3,000.00
Payment Due Date
Statement Balance
$ Amount
3.41
225.00
55.67
116.43
320.06
36.21
08/05
$756.37
Balance
756.78
753.37
528.37
472.70
356.27
36.21
Total credit available: $2,246.63
1. This bank statement is most likely for what kind of account? Provide at least two pieces of evidence from the statement that explain why. (2 points)
2. How much more can the owner of this account spend ? How do you know ? (1 point)
3. The owner of this account needs to make a $5,000 medical payment and doesn’t have enough in his or her other accounts. Describe at least one option available to the owner. (1 point)
4. What will be at least two consequences of letting the date, August 5, pass without making any payments ? (1 points)
This particular bank statement is likely assigned to a credit card account owing to the given credit line and statement balance of $3,000.00 and $756.37 respectively.
What is the extra amount the owner can spend?Thereby allowing the account holder to utilize an unused credit provision of $2,246.63 available for expenditures.
Should the owner need to settle a medical payment amounting to $5,000, an increase in the credit limit could be requested as one option.
But if this due date passes, on August 5th, they may face potential penalty charges such as late fees, interest fees, or even cause harm to their credit score.
Read more about credit limit here:
https://brainly.com/question/26867415
#SPJ1
A central bank like the Federal Reserve in the United States can help banks survive a bank run by A. increasing the required reserve ratio. B. acting as a lender of last resortſ C. raising the discount rate. D. printing money
Answer: B. Acting as a lender of last resort.
A bank run occurs when a large number of depositors withdraw their funds from a bank, which can lead to a bank's insolvency.
A central bank like the Federal Reserve can help banks survive a bank run by acting as a lender of last resort.
This means that the central bank will provide funds to the bank in the form of loans or other financial assistance to ensure that it has enough cash on hand to meet the demands of depositors who are withdrawing their funds.
By doing so, the central bank can prevent the bank from going bankrupt and restore confidence in the banking system.
Other measures such as increasing the required reserve ratio or raising the discount rate may also be used to control the money supply and stabilize the economy, but they may not directly address the issue of a bank run.
To learn more about central bank refer below
https://brainly.com/question/31871579
#SPJ11
Ana vai fazer pulseiras de miçangas para presentear alguns amigos. para fazer cada uma dessas pulseiras, ela precisa de 16 miçangas. ana tem 4 potes com quantidades diferentes de miçangas e quer escolher, para utilizar na confecção dessas pulseiras, aquele que tem uma quantidade de miçangas que permite fazer uma determinada quantidade de pulseiras sem sobrar nenhuma miçanga no pote. observe, no quadro abaixo, as quantidades de miçangas disponíveis em cada um dos potes que ana tem.
Para escolher o pote de miçangas que permitirá fazer uma quantidade exata de pulseiras sem sobrar nenhuma miçanga no pote, precisamos encontrar um número que seja divisível por 16 em cada um dos valores apresentados nos potes.
Analisando as opções apresentadas no quadro, podemos ver que apenas a quantidade de miçangas no pote B é divisível por 16, já que 16 x 9 = 144. Portanto, Ana deve escolher o pote B com 144 miçangas para confeccionar as pulseiras de seus amigos. Dessa forma, ela poderá fazer 9 pulseiras utilizando todas as miçangas disponíveis no pote. As outras opções apresentam quantidades de miçangas que não são divisíveis por 16, o que resultaria em sobras de miçangas no processo de confecção das pulseiras.
Learn more about escolher here
https://brainly.com/question/16607567
#SPJ11
Given that 1 /1−x =[infinity]∑n=0 x^n with convergence in (−1, 1), find the power series for 1/x with center 3.
[infinity]∑n=0 =
Identify its interval of convergence. The series is convergent from
x= , left end included (enter Y or N):
to x= , right end included (enter Y or N):
Answer: The interval of convergence is: x ∈ (2, 4) and the series is convergent from x=2, left end included, to x=4, right end included.
Step-by-step explanation:
To get the power series for 1/x with center 3, we can use the fact that:
1/x = (1/(x-3)) / (1/3)
Then, we can use the formula for the geometric series:
1/(1-r) = ∑n=0^∞ r^n, for |r| < 1
to obtain:
1/(x-3) = -1/(3(1-(x-3)/3)) = -1/3 ∑n=0^∞ ((x-3)/3)^n, for |(x-3)/3| < 1
Multiplying both sides by 1/3, we get:
1/x = -1/9 ∑n=0^∞ ((x-3)/3)^n, for |(x-3)/3| < 1
So, the power series for 1/x with center 3 is:[infinity]∑n=0 (-1/9) ((x-3)/3)^n
To obtain its interval of convergence, we note that the series converges if:|(x-3)/3| < 1 which is equivalent to:
-1 < (x-3)/3 < 1
Solving for x, we get:
2 < x < 4
Therefore, the interval of convergence is: x ∈ (2, 4)
And the series is convergent from x=2, left end included, to x=4, right end included.
Learn more about power series here, https://brainly.com/question/14300219
#SPJ11
Which of the following statements correctly describe the graph of the function above? select all that apply
F(x)=x^4-2x^2+1
a. As x approaches positive infinity, f(x) approaches negative infinity.
b. As x approaches negative infinity, f(x) approaches negative infinity.
c. When x = -2, f(x) = 0.
d. As x approaches negative infinity, f(x) approaches positive infinity.
e. As x approaches positive infinity, f(x) approaches positive infinity.
f. When x = -1, f(x) = 0
IMAGE ADDED
The correct statements that describe the graph of the function
f(x) = x^4 - 2x² + 1 are:
c. When x = -2, f(x) = 0.
f. When x = -1, f(x) = 0.
e. As x approaches positive infinity, f(x) approaches positive infinity.
b. As x approaches negative infinity, f(x) approaches negative infinity.
We have,
Statement (a) is incorrect because as x approaches positive infinity, f(x) approaches positive infinity, not negative infinity.
Statement (d) is incorrect because as x approaches negative infinity, f(x) approaches negative infinity, not positive infinity.
The graph of the function f(x) = x^4 - 2x² + 1 is a parabola that opens upwards, which means that as x approaches positive infinity, the value of f(x) also approaches positive infinity.
This makes statement (e) true.
Similarly, as x approaches negative infinity, the value of f(x) also approaches negative infinity because the polynomial function contains even powers of x. This makes statement (b) true.
The function f(x) has two real roots, which occur when f(x) = 0. These roots are x = -2 and x = -1.
At these values, the function crosses the x-axis and changes sign from positive to negative.
This makes statements (c) and (f) true.
Thus,
The correct statements that describe the graph of the function
f(x) = x^4 - 2x² + 1 are:
c. When x = -2, f(x) = 0.
f. When x = -1, f(x) = 0.
e. As x approaches positive infinity, f(x) approaches positive infinity.
b. As x approaches negative infinity, f(x) approaches negative infinity.
Learn more about functions here:
https://brainly.com/question/28533782
#SPJ1
Answer: The correct statements are: As x approaches negative infinity, f(x) approaches positive infinity; When x = -1, f(x) = 0; and As x approaches positive infinity, f(x) approaches positive infinity.
Step-by-step explanation:
Step 1: Analyze the function
The given function is f(x) = x^4 - 2x^2 + 1.
Step 2: Determine the behavior as x approaches infinity
Since the highest degree term is x^4, as x approaches positive or negative infinity, the x^4 term will dominate the function. Since x^4 is always positive for any real value of x, f(x) will approach positive infinity as x approaches both positive and negative infinity.
Step 3: Check for zeros of the function
To find the zeros of the function, we need to solve the equation f(x) = 0.
x^4 - 2x^2 + 1 = 0
This is a quadratic equation in terms of x^2. Let y = x^2, then the equation becomes:
y^2 - 2y + 1 = 0
(y - 1)^2 = 0
y = 1
Now, substitute back x^2 for y:
x^2 = 1
x = ±1
Step 4: Check the given statements
1. As x approaches negative infinity, f(x) approaches positive infinity. (True)
2. As x approaches negative infinity, f(x) approaches negative infinity. (False)
3. As x approaches positive infinity, f(x) approaches negative infinity. (False)
4. When x = -1, f(x) = 0. (True)
5. As x approaches positive infinity, f(x) approaches positive infinity. (True)
6. When x = -2, f(x) = 0. (False)
a student used 545 milliliters of a solution in a science experiment how many more liters of the solution did the student use in the experiment
The student used 0.545 liters of the solution in the experiment.
We have,
To convert the unit milliliters to liters, you need to divide by 1000 since there are 1000 milliliters in 1 liter.
So, to find how many liters were used, you can divide 545 milliliters by 1000.
= 545 mL ÷ 1000
= 0.545 L
Therefore,
The student used 0.545 liters of the solution in the experiment.
Learn more about unit conversion here:
https://brainly.com/question/13899873
#SPJ1
If x = −3 and y = −6, what is the value of 3x + 4y + 15?
A 48
B 35
C -18
D -48
Answer:
C. -18
Step-by-step explanation:
3(-3)+4(-6)+15=
-9+-24+15
-33+15=-18
Answer:
Step-by-step explanation:
x=-3 and y=-6 ⇒
3*x=3*(-3)=-94*y=4*(-6)=-2415so if we add these numbers together, we will have :
-9 + (-24) + 15 = -18
and it is C .
Jannick biked to his friend milos house to play video games. He made two stops on his way there. From his house, jannixk travelled 2 miles north to the recycle station he then travelled 5 miles east to the hardware store finally he went 4. 5 miles south to milos house. What is the distance between
Answer: To find the distance between Jannick's house and Milos' house, we can use the Pythagorean theorem. We first need to find the total distance travelled by Jannick:
Distance north + Distance east + Distance south =
√(2^2 + 5^2) + 4.5 = √29 + 4.5 ≈ 8.74 miles
Therefore, the distance between Jannick's house and Milos' house is approximately 8.74 miles.
Please help fast 50 points
Answer:
38
Step-by-step explanation:
it is generally believed that the average population age is 50. you claim that the population average age is less than 50. perform a statistical test on the sample to see if the average age for the sample is consistent with your hypothesis (use a margin of error of 5%). what is the p-value from the test? group of answer choices 0.05 0.0179 0.9911 0.0089
To perform a statistical test on the sample and determine if the average age is consistent with your hypothesis that it is less than 50, we can use a one-sample t-test. The null hypothesis (H0) is that the population average age is equal to or greater than 50, and the alternative hypothesis (Ha) is that the population average age is less than 50.
Using the sample data, we calculate the t-test statistic by subtracting the assumed population mean (50) from the sample mean, dividing it by the standard error of the mean, and considering the sample size.
Next, we compare the t-test statistic with the critical t-value at a significance level of 5%. If the t-test statistic is smaller than the critical t-value, we reject the null hypothesis and conclude that the average age is consistent with being less than 50.
The p-value from the test represents the probability of obtaining a t-test statistic as extreme as the observed value, assuming the null hypothesis is true. We compare the p-value with the significance level to make our decision.
Unfortunately, the p-value was not provided in the answer choices. The p-value obtained from the test would need to be calculated separately to determine the correct answer option.
To learn more Probability - brainly.com/question/30034780
#SPJ11
Brain Hirt started business on January 1, 2000. Every year he plans to deposit Rs. 2500 in his bank account, which earns 8 percent annually. First payment will start at the end of year 2000. On December 31, 2005, he used the entire balance in his bank account to invest in a certificate of deposit at 12 percent annually. How much will he have on December 31, 2010?
Answer:
He would have 20,00
Step-by-step explanation:
You first have to calculate the profit them add it to your original price and since he put 2,500 in for five years you multiply 2,500 by five to get your original price before you add your interest to it
50 POINTS A circular cookie cake is 153.86 square inches. What is the diameter of the cookie cake? Approximate using π = 3.14.
49 inches
28 inches
14 inches
7 inches
The solution is : 14 inches is the diameter of the cookie cake.
We know that,
area of a circle = πr²
We know the area = 153.86
So substitute and solve for radius.
153.86 = (3.14) * r^2
153.86/3.14 = r^2
49 = r^2
take square root of both sides
7 = r
The diameter is double the radius.
Diameter = 2r
So 2 * r = 2 * 7 = 14 inches
Hence, The solution is : 14 inches is the diameter of the cookie cake.
To learn more on area of circle click:
brainly.com/question/22964077
#SPJ1
tori is getting ready to run a marathon. she kept track of the lengths of her last few training runs. training runs (mi.) 11 8 15 16 8 20 16 12 6 13 7 which box plot represents the data?
The box plot would show the distribution of Tori's training runs and provide insights into the Central tendency and variability of the data.
A box plot, also known as a box-and-whisker plot, is a visual representation of the distribution of a dataset. It shows the median, quartiles, and range of the data. The median is the middle value of the dataset, the first quartile is the value that separates the lowest 25% of the data from the rest, and the third quartile is the value that separates the lowest 75% of the data from the rest. The range is the distance between the minimum and maximum values of the data.
To create a box plot for Tori's training runs, you would first order the data from smallest to largest: 6, 7, 8, 8, 11, 12, 13, 15, 16, 16, 20. Then, you would find the median (the middle value), which is 12.5. Next, you would find the first quartile (the value that separates the lowest 25% of the data from the rest), which is 8, and the third quartile (the value that separates the lowest 75% of the data from the rest), which is 16. Finally, you would calculate the range (the distance between the minimum and maximum values), which is 14 (20 - 6).
To draw the box plot, you would draw a rectangle with the bottom edge at the first quartile and the top edge at the third quartile. Inside the rectangle, draw a line at the median. Then, draw whiskers (lines) from the edges of the rectangle to the minimum and maximum values of the data (6 and 20). Any outliers (values that are more than 1.5 times the interquartile range away from the nearest quartile) can be plotted as individual points outside of the whiskers.
Without a visual representation of the data, it is difficult to say which box plot represents the data. However, the box plot would show the distribution of Tori's training runs and provide insights into the central tendency and variability of the data.
To know more about Central tendency.
https://brainly.com/question/1288901
#SPJ11
Solve for x
2x-3/3 + 5-x /2 = 3
the answer to your question is X= -1
the fox population in rocky mountain national forest is decreasing at a rate of 2% each year. there are currently 76,000 foxes in the forest. write a function that models the number of foxes in the rocky mountain national forest after x years.
The function that models the number of foxes in Rocky Mountain National Forest after x years is N(x) = [tex]76,000 \times (0.98)^x[/tex]
To model the number of foxes in Rocky Mountain National Forest after x years, we can use exponential decay since the fox population is decreasing at a rate of 2% each year.
Let N(x) represent the number of foxes after x years.
We can write the function as:
N(x) = [tex]N_0 \times (1 - r)^x[/tex]
Where:
N₀ is the initial number of foxes (76,000 in this case),
r is the decay rate (2% or 0.02), and
x is the number of years.
Plugging in the values, we get:
N(x) = [tex]76,000 \times (1 - 0.02)^x[/tex]
Simplifying further, we have:
N(x) = [tex]76,000 \times (0.98)^x[/tex]
This function models the number of foxes in Rocky Mountain National Forest after x years.
By substituting different values of x, we can calculate the estimated number of foxes in the forest for any given year.
It's important to note that this model assumes a continuous exponential decay and does not account for other factors that may affect the fox population.
For such more questions on function
https://brainly.com/question/25638609
#SPJ11
A, B & C form the vertices of a triangle, where
∠CAB = 90°.
AB = 4.7 m and BC = 11.3m.
Evaluate
∠ABC, giving your answer rounded to 3 SF.
A triangle is a shape with 3 sides and angles. The measure of angle ∠ABC is 57.6 degrees
Here, we have,
Application of trigonometry identity
A triangle is a shape with 3 sides and angles. Given the following parameters
∠CAB = 90°.
AB = 5.9 m and;
BC = 11.1m.
Determine the measure of ∠ABC
cos∠ABC = AB/BC
cos∠ABC = 5.9/11
cos∠ABC = 0.5363
∠ABC = arccos0.5363
∠ABC = 57.6 degrees
Hence the measure of angle ∠ABC is 57.6 degrees
Learn more on angles here:
brainly.com/question/25716982
#SPJ1
which amounts of money can be formed using just twodollar bills and five-dollar bills? prove your answer using strong induction.
by strong induction, we can form any amount of money that is a multiple of $2$ greater than or equal to $2$.To prove this using strong induction, we need to show two things:
1. That we can form the amounts $2$ and $5$ using just $2$-dollar bills and $5$-dollar bills.
2. That if we can form any amount $n$ using just $2$-dollar bills and $5$-dollar bills, we can also form the amount $n+2$.
For the base case, it's clear that we can form the amounts $2$ and $5$.
For the inductive step, assume that we can form any amount $k$ using just $2$-dollar bills and $5$-dollar bills, where $k \geq 5$. We want to show that we can also form the amount $k+2$.
There are two cases to consider:
1. If we have at least one $5$-dollar bill, then we can form the amount $(k+2)$ by adding a $5$-dollar bill to the amount $(k-3)$, which we know we can form using just $2$-dollar bills and $5$-dollar bills.
2. If we don't have any $5$-dollar bills, then we must have at least two $2$-dollar bills. We can form the amount $(k+2)$ by using one of the $2$-dollar bills to form the amount $(k-3)$, which we know we can form, and then adding three more $2$-dollar bills.
Therefore, by strong induction, we can form any amount of money that is a multiple of $2$ greater than or equal to $2$.
To learn more about induction click here:brainly.com/question/31848775
#SPJ11
Which state is true by the segment addition postulate
Answer:
D is the correct answer.
ZY + YX = ZX
please help and i’ll give u brainliest
Answer:
Set your calculator to degree mode.
Using the Law of Cosines:
c = √(27^2 + 13^2 - 2(27)(13)(cos 106°))
= 33.0378
Now use the Law of Sines:
sin A/13 = sin 106°/33.0378
sin A = 13 sin 106°/33.0378
A = 22.2°
The measure of angle ∠A will be 22.1°. Then the correct option is B.
Given that:
a = 13 in
b = 27 in
∠C = 106°
Let the triangle ΔABC, then the cosine law is given as,
c² = a² + b² - 2 a·b cos C
The length AB of the triangle is calculated as,
c² = 13² + 27² - 2 · 13 · 27 · cos 106°
c² = 169 + 729 - (-196.5)
c² = 1094.5
c = 33.08 inches
The measure of ∠A is calculated as,
a² = b² + c² - 2 b·c cos A
13² = 27² + 33.08² - 2 x 27 x 33.08 x cos A
cos A = 0.9262
A = 22.1°
The measure of angle ∠A will be 22.1°. Then the correct option is B.
More about the cosine law link is given below.
https://brainly.com/question/17289163
#SPJ1
The triangle on the grid will be translated two units left. On a coordinate plane, triangle A B C has points (negative 1, negative 1), (negative 1, negative 5), (0.5, negative 5). Which shows the triangle when it is translated two units left? Group of answer choices On a coordinate plane, triangle A prime B prime C prime has points (1, negative 1), (1, negative 5), (2.5, negative 5). On a coordinate plane, triangle A prime B prime C prime has points (negative 3, negative 1), (negative 3, negative 5), (negative 1.5, negative 5). On a coordinate plane, triangle A prime B prime C prime has points (negative 1, 1), (negative 1, negative 3), (0.5, negative 3). On a coordinate plane, triangle A prime B prime C prime has points (negative 1, negative 3), (negative 1, negative 7), (0.5, negative 7)
The translated triangle is A'B'C', and its vertices are (-3, -1), (-3, -5), and (-1.5, -5). (option b)
To translate the triangle two units to the left, we need to subtract 2 from the x-coordinates of each vertex, while leaving the y-coordinates unchanged. This is because moving the triangle left means we're decreasing its x-values.
So, let's apply this transformation to each point.
The first point, (-1, -1), becomes (-1 - 2, -1), which simplifies to (-3, -1).
The second point, (-1, -5), becomes (-1 - 2, -5), or (-3, -5).
The third point, (0.5, -5), becomes (0.5 - 2, -5), or (-1.5, -5).
These new coordinates give us the vertices of the triangle after it has been translated two units to the left.
Now that we have the new vertices, we can label them A', B', and C' to distinguish them from the original vertices. So, the translated triangle is A'B'C', and its vertices are (-3, -1), (-3, -5), and (-1.5, -5).
This is the second option in the answer choices given.
To know more about triangle here
https://brainly.com/question/8587906
#SPJ1
What is 2+1000-789+12-2x10-2
Answer:
203
Step-by-step explanation:
We have to solve this according to BODMAS THEOREM to solve this.
That is,
B ⇒ Brackets
O ⇒ Orders.
D ⇒ Division
M ⇒ Multiplication
A ⇒ Addition
S ⇒ Subtraction
Let us solve it now.
2 + 1000 - 789 + 12 - 2 x 10 - 2
2 + 1000 - 789 + 12 - 20 - 2
1002 - 789 + 12 -20 - 2
213 + 12 - 20 - 2
225 - 20 - 2
205 - 2
203
The solution of 2+1000-789+12-2x10-2 using BODMAS is 203.
We know about BODMAS which shows the correct order to solve mathematical expression as
B ⇒ Brackets
O ⇒ Of
D ⇒ Division
M ⇒ Multiplication
A ⇒ Addition
S ⇒ Subtraction
Now, we have to solve 2+1000-789+12-2x10-2 using BODMAS
= 2 + 1000 - 789 + 12 - 2 x 10 - 2
= 2 + 1000 - 789 + 12 - 20 - 2
= 1002 - 789 + 12 -20 - 2
= 213 + 12 - 20 - 2
= 225 - 20 - 2
= 205 - 2
= 203
Learn more about BODMAS here:
https://brainly.com/question/29795897
#SPJ1
a comparison between species: biologists comparing the gestation period of two newly discovered species of frog collected data from 16 frogs of species a and 23 frogs of species b. species a exhibited an average gestation period of 13 days with a standard deviation of 3.4 days while species b had a gestation period of 18 days and a standard deviation of 2.6 days. the researchers want to know whether the average lengths of the gestational periods differ between the two species. conduct a hypothesis test at a significance level of .
To conduct a hypothesis test to compare the gestation periods of the two frog species, we can use a two-sample t-test assuming equal variances.
State the hypotheses:
The null hypothesis (H0) is that there is no difference in the mean gestation periods between species A and B.
H0: μA = μB
The alternative hypothesis (Ha) is that there is a difference in the mean gestation periods between species A and B.
Ha: μA ≠ μB
Set the significance level:
The significance level, denoted as α represents the probability of making a Type I error (rejecting the null hypothesis when it is actually true). In this case, the significance level is given as 0.05.
Calculate the test statistic:
We can use the two-sample t-test formula to calculate the t-statistic.
Where A and B are the sample means of gestation periods for species A and B, respectively, s is the pooled standard deviation and nA and nB are the sample sizes for species A and B, respectively.
The pooled standard deviation can be calculated as:
t = -6.28
Determine the critical value:
The critical value of t can be found using a t-distribution table with degrees of freedom (df) equal to nA + nB - 2.
At a significance level of 0.05 with df = 16 + 23 - 2 = 37 the critical values are -2.02 and 2.02 (two-tailed test).
Make a decision and interpret the results:
The absolute value of the calculated t-statistic (6.28) is greater than the critical value (2.02).
Indicating that we can reject the null hypothesis.
Thus, we can conclude that there is a statistically significant difference in the mean gestation periods between species A and B.
Calculate the p-value:
The p-value is the probability of obtaining a t-statistic as extreme as the one calculated or more extreme, assuming the null hypothesis is true.
We can use a t-distribution table or a statistical software package to find the p-value.
For this example,
The p-value is very small (p < 0.0001), indicating strong evidence against the null hypothesis.
Therefore, we can conclude that the average lengths of the gestational periods differ significantly between the two newly discovered frog species, with species B having a longer gestation period than species A.
For similar question on t-test:
https://brainly.com/question/15870238
#SPJ11
PLEASE HELP!!! I NEED TO REVIEW THIS FOR AN EXAM!!! 25 POINTS FOR WHOEVER ANSWERS IN DETAILS!!!!!
The sum of the given finite geometric series is approximately 0.6640625.
How to find the sum of the finite geometric series[tex]S_n= \frac{ a(1 - r^n)}{(1 - r)}[/tex]
Substituting the values, we get:
[tex]S_n =\frac{ 1(1 - (-1/2)^n) }{1 - (-1/2)}[/tex]
= [tex]\frac{1(1 - (-1/2)^n)}{(3/2)}[/tex]
= [tex]2/3(1 - (-1/2)^n)[/tex]
To find the sum of the given series, we need to evaluate S_8, since there are 8 terms in the series:
[tex]S_8 = 2/3(1 - (-1/2)^8)[/tex]
= 2/3(1 - 0.00390625)
= 2/3(0.99609375)
= 0.6640625
Therefore, the sum of the given finite geometric series is approximately 0.6640625.
Read more on finite geometric series here:https://brainly.com/question/30264021
#SPJ1
Determine whether the geometric series is convergent or divergent. if it is convergent, find its sum. (if the quantity diverges, enter diverges.) 7 + 6 + 36/7 216/49+ ...
convergent divergent If it is convergent, find its sum. (If the quantity diverges, enter DIVERGES.)
The given geometric series is divergent.
To determine whether the geometric series is convergent or divergent, we need to first identify the common ratio (r). Let's analyze the given series:
7, 6, 36/7, 216/49, ...
To find the common ratio, divide the second term by the first term, and the third term by the second term:
r1 = 6 / 7
r2 = (36/7) / 6 = 6 / 7
Since r1 = r2, the common ratio (r) is 6/7.
Now we can determine if the series is convergent or divergent. A geometric series converges if the absolute value of the common ratio (|r|) is less than 1, and diverges otherwise.
In this case, |r| = |6/7| = 6/7, which is less than 1. However, the first term of the given series is 7, which doesn't belong to the geometric sequence with a common ratio of 6/7. The correct geometric sequence should be:
6, 36/7, 216/49, ...
So, the given series is not a geometric series, and thus we cannot determine if it's convergent or divergent using the geometric series test. Since it doesn't form a proper geometric sequence, we can conclude that it is divergent.
To know more geometric series visit:
brainly.com/question/4617980
#SPJ11
Miguel collected data modeling a company's costs versus its profits. the data are shown in the table: x g(x) −3 17 −1 −3 0 −4 2 13 which of the following is a true statement for this function? the function is increasing from x = −3 to x = −1. the function is decreasing from x = −3 to x = −1. the function is increasing from x = −1 to x = 0. the function is decreasing from x = 0 to x = 2.
The statement "the function is decreasing from x = −3 to x = −1" is true for this function.
To determine whether the function is increasing or decreasing on a particular interval, we need to compare the values of g(x) for the endpoints of the interval. In this case, we are asked to consider the interval from x = −3 to x = −1. At x = −3, g(x) = 17. At x = −1, g(x) = −3. Since g(x) is decreasing from 17 to −3 as we move from left to right along the interval, we can conclude that the function is decreasing on this interval.
Learn more about function here
https://brainly.com/question/10439235
#SPJ11
Answer:
"the function is decreasing from x = −3 to x = −1"
Step-by-step explanation:
i took the test :)
Restaurants often slip takeout menus under britney's apartment door. britney counted how many menus there were from each type of restaurant.chinese 2japanese 9mediterranean 1thai 2italian 6what is the experimental probability that the next menu slipped under britney's door will be from a chinese restaurant?
The experimental probability that the next menu slipped under Britney's door will be from a Chinese restaurant is 0.1 or 10%.
To find the experimental probability that the next menu slipped under Britney's door will be from a Chinese restaurant, we need to determine the number of Chinese restaurant menus in relation to the total number of menus.
The total number of menus is the sum of menus from all types of restaurants:
Total number of menus = Chinese + Japanese + Mediterranean + Thai + Italian
= 2 + 9 + 1 + 2 + 6
= 20
The number of Chinese restaurant menus is 2.
Now we can calculate the experimental probability:
Experimental probability of getting a Chinese restaurant menu = Number of Chinese restaurant menus / Total number of menus
= 2 / 20
= 0.1
Know more about experimental probability here:
https://brainly.com/question/23343260
#SPJ11
A sample of 41 observations yielded a sample standard deviation of 5. If we want to test H0: σ2 = 20, the test statistic is a. 100.75. b. 10. c. 51.25. d. 50.
The answer to this question is the test statistic is a. option a. 100.75.
To arrive at this answer, we need to use the chi-square distribution to test the null hypothesis that the population variance (σ2) is equal to 20. The test statistic for this hypothesis test is given by:
χ2 = (n - 1) * s² / σ2
where n is the sample size, s is the sample standard deviation, and σ is the population standard deviation (which is assumed to be equal to the hypothesized value of 20).
Substituting the given values, we get:
χ2 = (41 - 1) * 5² / 20
χ2 = 40 * 25 / 20
χ2 = 50
Therefore, the test statistic is 50.
However, to determine the p-value (i.e. the probability of obtaining a test statistic as extreme or more extreme than the observed one, assuming the null hypothesis is true), we need to consult a chi-square distribution table with (n - 1) degrees of freedom. For this problem, the degrees of freedom is 40 (i.e. 41 - 1).
Using the chi-square distribution table, we find that the p-value for a test statistic of 50 with 40 degrees of freedom is less than 0.001. This means that the probability of obtaining a sample with a variance as extreme or more extreme than 20 (assuming the null hypothesis is true) is less than 0.001.
Therefore, we can reject the null hypothesis at a significance level of 0.001 or lower. This leads us to the conclusion that the population variance is unlikely to be 20, based on the given sample of 41 observations with a sample standard deviation of 5.
finding the p-value using a chi-square distribution table, and making a conclusion based on the significance level. The main answer is option a. 100.75, which corresponds to the test statistic calculated using the formula χ2 = (n - 1) * s² / σ2.
To know more about sample standard deviation visit:
brainly.com/question/24277447
#SPJ11
