The claim to be indicated is that there is enough evidence to reject the null hypothesis and the test statistic would be 21.75
What do you understand by Hypothesis testing?A type of statistical inference called hypothesis testing uses data from a sample to make inferences about a population parameter or population probability distribution. The parameter or distribution is initially assumed in a preliminary manner. The null hypothesis is also known as H0, because it is the default assumption. Then, the opposite of what the null hypothesis claims is characterized as an alternative hypothesis (designated Ha). Using sample data, the hypothesis-testing technique determines whether or not H0 may be rejected. If H0 is rejected, the statistical inference is that the alternative hypothesis Ha is correct.
How to solve?
If the die is fair, the probability of getting any of the six numbers is equal (1/6).
The test statistic (TS) is given as:
TS=∑(Oi−Ei)2Ei∼χ2n−1
TS=(4−8)^2/8+(13−8)^2/8+…(2−8)^2/8
TS=21.75
In conclusion, the die is unfair.
To learn more about Hypothesis Testing, visit:
https://brainly.com/question/14018613
#SPJ4
HELP PLEASE In MNO, M≈ O, NO = 10 and OM= 8. Find MN.
In the given triangle MNO, the length of MN is 10
Calculating the length of a side in a triangleFrom the question, we are to determine the length of the unknown side in the triangle
The side is MN
From the given information, we have that
In ΔMNO,
∠M ≅ ∠O
Thus,
ΔMNO is an isosceles triangle
Since angle M is congruent to angle O, the sides facing the two angles will also be congruent.
That is,
NO ≅ MN
From the given information,
NO = 10
Therefore,
MN = 10
Hence, the length of MN is 10
Learn more on Calculating triangle here: https://brainly.com/question/18995364
#SPJ1
need help quickly its due in 30
Answer: Alternate exterior angles --> 1,8 and 2,7
Vertical angles --> 2,3 and 5,8
Corresponding angles --> 1,5 and 2,6
Alternate interior angles --> 3,6 and 4,5
Morgan has an investment worth $13000 after 20 years if his original investment was for $15000 what must the interest rate have been
Answer:
8%
Step-by-step explanation:
pls mark brainliest
Answer : The interest rate have been 8 %
Step-by-step explanation :
First we have to calculate the simple interest.
As we know that:
Simple interest = Total amount - Principle
Simple interest = $130,000 - $50,000
Simple interest = $80,000
Now we have to calculate the interest rate.
Using simple interest formula:
where,
S.I = simple interest = $80,000
P = principle = $50,000
R = interest rate = ?
T = time = 20 years
Now put all the given values in the above formula, we get:
Therefore, the interest rate have been 8 %
Found answer from Alleei!
lacy draws a '10' from a standard deck of 52 cards. without replacing the first card, she then proceeds to draw a second card and gets a '4'. are these events independent? input yes or no
Determine the probability of drawing a spade and then a club without replacement.
Write your answer in decimal form, rounded to four decimal places as needed.
Answer =
The first two events are not independent, with a probability P = 0.00603
The second pair of events is independent, and the probability is P = 0.0625
First, all the cards on the deck have the same probability of being randomly drawn, which will be p = 1/52.
A) Now, if Lacy first draws a spade card, now the number of cards in the deck are less (now there are 51 cards on the deck). So the probability of drawing now a spade is larger than before. Then the first two events are not independent.
The probability of drawing a 10 card at first is:
P = 4/52 (because there are 4 10's and a total of 52 cards).
The probability of drawing a 4's after is:
Q = (4/51)
The joint probability is the product of the individual probabilities, this will give: p = P*Q = (4/52)*(4/51) = 0.00603
B) Now we replace the first card, then the events are now independent, as the probability of drawing a spade after the first draw is not changed (because the total number of cards will be 52).
The probability of drawing a spade is:
P = 13/52
Now we replace the spade card drawn.
The probability of drawing a club will be:
Q = 13/52
The joint probability is:
p = P×Q = (13/52)² = 0.0625
To Learn more about similar probability questions:
https://brainly.com/question/12721990
#SPJ4
Enlarge the triangle by scale factor -3 with centre (3,3)
The triangles when enlarged by a scale factor of 3 the final image is at the coordinates: (7, 3), (5, 3), and (7, 7)
How to find the coordinates of the imageThe coordinates of the preimage are
(5, 3), (4, 3), and (5, 5)
translate to the origin
= (5 - 3, 3 - 3), (4 - 3, 3 - 3), and (5 - 3, 5 - 3)
= (2, 0), (1, 0), and (2, 2)
dilate about the origin
2 * { (2, 0), (1, 0), and (2, 2) }
(4, 0), (2, 0), and (4, 4)
translate back to usual position
(4 + 3, 0 + 3), (2 + 3, 0 + 3), and (4 + 3, 4 + 3)
(7, 3), (5, 3), and (7, 7)
Therefore the image is at (7, 3), (5, 3), and (7, 7)
Learn more about dilation at:
https://brainly.com/question/10253650
#SPJ1
Madelyn is a high school basketball player. In a particular game, she made some free throws (worth one point each) and some two point shots. Madelyn made a total of 13 shots altogether and scored a total of 21 points. Determine the number of free throws Madelyn made and the number of two point shots she made.
The number of free throws = 5
The number of two point shots = 8
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the number of free throws be = x
Let the number of two point shots be = y
The total number of shots made by Madelyn is = 13
So , the equation is
x + y = 13 be equation (1)
The total number of points scored by Madelyn is = 21
So , the equation is
x + 2y = be equation (2)
On simplifying the equation , we get
Subtracting equation (1) from equation (2) , we get
2y - y = 8
y = 8
Therefore , the value of y is 8
And , The number of two points be = 8
Substituting the value for y in equation (1) , we get
x + y = 13
x + 8 = 13
Subtracting 8 on both sides of the equation , we get
x = 5
Therefore , the value of x is 5
And , the number of free throws is 5
Hence , The number of free throws = 5
The number of two point shots = 8
To learn more about equations click :
https://brainly.com/question/10413253
#SPJ1
automobile repair costs continue to rise with the average cost now at $367 per repair.† assume that the cost for an automobile repair is normally distributed with a standard deviation of $88. answer the following questions about the cost of automobile repairs. what is the probability that the cost will be between $250 and $470?
The probability that the cost will be between $250 and $470 is 0.7354.
What is probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Given:
Automobile repair costs continue to rise with the average cost now at $367 per repair.†
Assume that the cost for an automobile repair is normally distributed with a standard deviation of $88.
We have to find the probability that the cost will be between $250 and $470.
P( 250 < x < 470 ) = P( x <470 ) - P( x < 250 )
P( x < 470 ) = NORMDIST( 470 , 367, 88, 1 ) = 0.8272
P( x < 250 ) = NORMDIST( 250 , 367, 88, 1 ) = 0.09183
P( 250 < x < 470 ) = 0.8272 - 0.09183 = 0.7354
P( 250 < x < 470 ) = 0.7354
Hence, the probability that the cost will be between $250 and $470 is 0.7354.
To know more about probability, click on the link
https://brainly.com/question/24756209
#SPJ4
the homework consists of 36 independent problems. if the time taken to answer each question is a random variable with mean 6 minutes and a standard deviation 3 minutes. suppose we want to find the probability that all 36 problems in the homework will be completed in less than 180 minutes. which of the following is incorrect?
the probability that all 36 problems in the homework will be completed in less than 180 minutes
P(∑[tex]\left \{ {{i=36} \atop {i=1}} \right.[/tex] [tex]X_{i}[/tex] < 180) = P(X<5) = P(Z<-1) = ∅(-1)
given that
there are 36 independent problems
mean(μ) = 6minutes
standard deviation(σ) = 3 minutes
sample standard deviation = σ/[tex]\sqrt{n}[/tex]
= 3/[tex]\sqrt{36}[/tex]
=3/6
=0.5
the sample mean x of 36 questions answering time approximately follows a normal distribution with mean 6 minutes and sample standard deviation is 0.5 minutes
now we need to find the probability that all 36 problems in the homework will be completed in less than 180 minutes
P(∑[tex]\left \{ {{i=36} \atop {i=1}} \right.[/tex] [tex]X_{i}[/tex] < 180) = P(X<5) = P(Z<-1) = ∅(-1)
To learn more about standard deviation:
https://brainly.com/question/13905583
#SPJ4
A high school. Asket ball team is selling 10$ dollar raffle tickets as part of a fund raising program the first prize is a trip to the bahamas find the average amount per game
The Expected Value to the player for one play of the game is - 7.784.
Define Expected Value.In probability theory, the weighted average is expanded upon by the expected value. The arithmetic mean of a sizable number of outcomes of a random variable that were independently selected is, informally, the anticipated value.
Price of raffle ticket= $10
First price= $5460
Second prize= $496
Remaining 18 prize= $100
$0 for the remaining tickets= 3500-20=3480 tickets
When winning the 1st prize, the winnings = $5460−$10=$5450.
When winning the 2nd prize, the profit= $496−$10=$486.
When winning the other 18 prizes, the profit= $100−$10=$90.
When there is no winning, the loss= $0
The probability is calculated by dividing the number of likely outcomes by the total number of outcomes:
P(X=5450)= 1/3500
P(X= 486)= 1/3500
P(X= 90)= 18/3500
P(X= -10)= 3480/3500
The product of each alternative and its probability equals the expected value, which is added up:
E(X)= ∑ xP(x)
= 5450 * [tex]\frac{1}{3500}[/tex] + 486 * [tex]\frac{1}{3500}[/tex] + 90 * [tex]\frac{18}{3500}[/tex] + (-10) * [tex]\frac{3480}{3500}[/tex]
= [tex]\frac{-27224}{3500}[/tex]
= - 7.784
To know more about expected value, visit:
https://brainly.com/question/29574962
#SPJ1
One diagonal of a rhombus is decreasing at a rate of 777 centimeters per minute and the other diagonal of the rhombus is increasing at a rate of 101010 centimeters per minute. At a certain instant, the decreasing diagonal is 444 centimeters and the increasing diagonal is 666 centimeters. What is the rate of change of the area of the rhombus at that instant (in square centimeters per minute)?.
At that point, the area of the rhombus is changing at a rate of -1 cm²/min (measured in square centimeters per minute).
What is rhombus?A quadrilateral with all equal sides is a rhombus. Rhombuses are a particular kind of parallelogram in which all of the sides are equal since the opposing sides of a parallelogram are equal. A quadrilateral with four equal sides that has the form of a diamond is called a rhombus. In everyday life, rhombus-shaped objects can be seen. The graphic below illustrates some examples of rhombuses in everyday objects, like a diamond, a kite, an earring, etc.
Here,
The area of a rhombus is given in terms of its diagonal lengths x and y,
A = (1/2)xy
A' = (1/2)(x'y +xy')
A' = (1/2)((-7 cm/min)(6 cm) +(4 cm)(10 cm/min))
A' = (1/2)(-42 cm²/min +40 cm²/min)
A' = -1 cm²/min
The rate of change of the area of the rhombus at that instant (in square centimeters per minute) is -1 cm²/min.
To know more about rhombus,
https://brainly.com/question/12783973
#SPJ4
#3 Mia has $50 on a gift card to her favorite *
coffee shop. Each time she visits the coffee
shop she spends $3.75 on her favorite drink.
Write an equation to represent the relationship
between n, the number of times she visits the
coffee shop, and b, the total balance on her
gift card
type 1500 words in 30 minutes __ words per minute
Answer:
50
Step-by-step explanation:
1500/30=50
Answer:
50 words per minute
brainliest plss
water is pouring at a constant rate into a tank that is a 4-foot-high rectangular solid. if the warer was turned on at 11:00 and if at 11:25 the depth of the water in the tank was 4 inches, at what time was the pool full
The time at which the pool was full is 4:00 when the water is in the 4 inches tank .
What is multiplication?In mathematics, multiplication is one of the four basic arithmetic operations. It represents the basic idea of repeated addition of the same number.
Equating the time when pool be full :The height of the tank is 4 feet water pouring is turned on at 11:00 at 11:25 the depth of the water in the tank is 4 inches.
which means,
To fill 4 inches it takes = 25 min
To fill 1 inch it takes = 25/4 min 4 feet = 4×2.54 = 48 inches
To fill 48 inches it takes = 48 × 25/4
= 300 min
= 5 hours
So, 5 hours after 11:00 will be 4:00
Hence, the time at which the pool was full is 4:00
Read more about multiplication :
brainly.com/question/1135170
#SPJ4
Subtract.
(2/9v) − (−1/3v + 5/9)
Answer:
5(v-1)/9
Step-by-step explanation:
(2/9v) - (-1/3v + 5/9)
To find the opposite of -1/3v + 5/9, find the opposite of each term.
2/9v - (-1/3v) - 5/9
The opposite of -1/3v is 1/3v.
2/9v + 1/3v - 5/9
Combine 2/9v and 1/3v to get 5/9v
5/9v - 5/9
decrease £16855.21 by 3.5% rounded to 2 dp
The lowered value will thus be £16265.28.
What is the percentage?
A percentage that represents a tenth of a quantity. One percent, denoted by the symbol 1%, is equal to one-hundredth of something; hence, 100 percent denotes the full thing, and 200 percent designates twice the amount specified. A portion per hundred is what the percentage denotes. The percentage refers to one in a hundred. The % sign is used to denote it.
Therefore, the decreased sum is: 16265.2777 = 16855.21 - (16855.21 3.5/100) = (16855.21 - 589.93235).
Next, we'll round the number to two decimal places: 16265.2777, 16265.278, and 16265.28
Hence, The lowered value will thus be £16265.28.
Learn more about percentage, by the following link.
https://brainly.com/question/24304697
#SPJ4
Plot the points (6, 4) and (3, 2) and find the slope.
Answer:
Slope is 2/3.
Step-by-step explanation:
I can't help you plot the points, but the slope formula is y2-y1/x2-x1.
2-4/3-6. -2/-3. This simplifies to 2/3.
Find the value of x in the following equation:
2.5(5x + 2) = 12.5x + 5
A: x = 0
B: x = 1.5
C: No solution
D: Infinite solutions
[tex] \Large{\boxed{\sf Option \ D) \ \ Infinite \ solutions }} [/tex]
[tex] \\ [/tex]
Explanation:We will solve this equation by isolating x.
[tex] \\ [/tex]
Given equation:
[tex] \sf 2.5(5x + 2) = 12.5x + 5 [/tex]
[tex] \\ [/tex]
Expand the left side of the equation using the following distributive property:
[tex] \blue{\begin{gathered}\begin{gathered} \\ \boxed { \begin{array}{c c} \\ \green { \boxed{ \sf Distributive \: property \text{:}}} \\ \\ \sf A(B + C) = AB + BC \\ \end{array}}\\\end{gathered} \end{gathered}} [/tex]
[tex] \\ [/tex]
[tex] \sf \overbrace{\sf 2.5}^{A} (\underbrace{\sf 5x}_{B} + \overbrace{\sf 2}^{C}) = 12.5x + 5 \\ \\ \sf 2.5 \times 5x + 2.5 \times 2 = 12.5x + 5 \\ \\ \sf 12.5x + 5 = 12.5x + 5 [/tex]
[tex] \\ [/tex]
Now, subtract 5 from both sides of the equation:
[tex] \sf 12.5x +5 - 5 = 12.5x + 5 - 5 \\ \\ \sf 12.5x = 12.5x [/tex]
[tex] \\ [/tex]
Finally, divide both sides of the equation by 12.5:
[tex] \sf \dfrac{12.5x}{12.5} = \dfrac{12.5x}{12.5} \\ \\ \\ \boxed{\boxed{\sf x = x}} [/tex]
[tex] \\ [/tex]
Since any value is equal to itself, the equation has infinite solutions.
[tex] \\ [/tex]
[tex] \hrulefill [/tex]
[tex] \\ [/tex]
▪️Learn more about equations here:
↣https://brainly.com/question/27404966
Farmer John has cows and chickens on his farm. His farm animals have 120 legs and 48 heads total. How many cows and how many chickens are on the farm?
a. Explain what 120 represents, and how it relates to the cows and chickens.
b. Explain what 48 represents, and how it relates to the cows and chickens.
c. Setup a system, of two equations, to help you solve this riddle.
d. Solve this system using either Elimination or Substitution, show your work, and state your answer as a complete sentence.
Answer:
a. 120 represents the total number of cow legs and chicken legs
b. 48 represents the total number of cow heads and chicken heads
c. System:
Let x = number of cows
Let y = number of chickens
1. 2x + 4y = 120
2. x + y = 48
d. I am going to use substitution for this problem
Step 1: Solve for y in the equation x + y = 48
1. x + y = 48 → y = -x + 48
Step 2: Substitute -x + 48 for y in 2x + 4y = 120
2. 2x + 4(-x + 48) = 120
Step 3: Solve for x
3. 2x - 4x + 184 = 120 → -2x + 184 = 120 → -2x = -64 → x = 32
Step 4: Sustitute 32 for x in x + y = 48
4. (32) + y = 48
Step 5: Solve for y
5. y = 16
Number of chickens on the farm (y) = 16
Number of cows on the farm (x) = 32
Step-by-step explanation:
All of it is above :)
Find the determinant of the following matrix A by *only* using the 3 basic properties in Treil section 3 paragraph 3.1 (page 79), the determinant formula for triangular and diagonal matrices, and row or column operations. Explain your work. A= (1 0 2 0 3 0 1 2 3 4 1 0 3 0 5
0 0 0 2 4
1 0 3 0 8)
We must first transform matrix A into a triangular or diagonal matrix in order to determine its determinant.
Using the row operations to change the matrix, having three rows and five columns, in a triangular matrix, having three rows and three columns.
combining the first and second rows, then the first and third rows:
(1 0 2 0 3 0 1 2 3 4 1 0 3 0 5 (1 0 0 2 4 (1 0 3 0 8 (3 0 5 2 11
0 0 0 2 4 + 0 0 0 2 4) + 1 0 3 0 8) = 0 0 0 2 4
1 0 3 0 8) 2 0 6 0 16)
subtracting the second and third rows from the first row
We get a triangular matrix
(3 0 5 2 11 (0 0 0 2 4 (2 0 6 0 16 (1 0 5 0 3
0 0 0 2 4 - 0 0 0 2 4) - 2 0 6 0 16) = 0 0 0 2 4
2 0 6 0 16) 0 0 0 0 0)
Now that the matrix is triangular, we can use the determinant formula for triangular matrices, which states that the determinant of a triangular matrix is equal to the product of the diagonal elements. The diagonal elements of matrix A are 1, 0, and 0, so the determinant of matrix A is 0.
Therefore, the determinant of matrix A is 0, and we can find it by only using the three basic properties in Treil section the determinant formula for triangular and diagonal matrices, and row or column operations.
To learn more about determinants: https://brainly.com/question/24254106
#SPJ4
help me out please
answers:
-2/3
3/2
-3/2
2/3
Answer:
Step-by-step explanation:
Chose 2 points (-3,6) and (0,8)
Using slope formula; m=( y2 - y1 ). / ( x2 -x1)
m=(8-6)/(0+3) = 2/3
slope 2/3 and y intercept is 8 because the line cuts the y axis at (0,8)
the equation of the line is: y=2/3(x) + 8
to log on to a certain computer account, the user must type in a -letter password. in such a password, no letter may be repeated, and only the lower case of a letter may be used. how many such -letter passwords are possible? (there are letters in the alphabet.)
There are 358,800 different ways that a 4-letter password might be used.
Explain the term permutation?The number of possible arrangements for a given set is calculated mathematically, and this process is known as permutation.For the stated question-
To make a four-letter password with no repeating letters and just lowercase letters;Every letter from A -Z (or 26) can be used as the initial letter for the computer account.Apart from the first letter again for second letter, we can select any letter between A and Z.Whatever letter from A to Z is available for selection, with the exception of the first and second letters again for third letter.For the fourth letter, we might select any letter between A and Z besides the first, second, and third letters.
SO;
Number of possible combinations for 4-letter passwords
= 26 × 25 × 24 × 23
= 358,800
Thus, there are 358,800 different ways that a 4-letter password might be used.
To know more about the permutation, here
https://brainly.com/question/1216161
#SPJ4
The complete question is-
To log on to a certain computer account, the user must type in a 4-letter password. In such a password, no letter may be repeated, and only the lower case of a letter may be used. How many such 4-letter passwords are possible.
A rectangular pan has a length that is the width. The total area of the pan is 432 in. 2. What is the width of the cake pan?.
Using the area formula, we know that the width of the pan is 18 inches.
What is the area?An area is a unit of measurement used to describe a region's size on a flat or curved surface.
While a plane region or area refers to the area of a shape or planar lamina, a surface region or plane area refers to the area of an open surface or the boundary of a three-dimensional object.
So, the width of the pan will be:
We know that:
The length of a rectangular pan is exactly 4/3 the width.
The pan's total surface area is 432in².
Formula: Area = 432 = length*width = w*4w/3
Now, calculate the width as follows:
Formula: Area = 432 = length*width = w*4w/3
4w^2/3 = 432
w^2 = 432*3/4 = 324
w = 18
Therefore, using the area formula, we know that the width of the pan is 18 inches.
Know more about the area here:
https://brainly.com/question/25292087
#SPJ4
Complete question:
A rectangular pan has a length that is 4/3 the width. The total area of the pan is 432 in.2. What is the width of the cake pan
Answer: B. 18 in
Step-by-step explanation:
You will get this answer using the Area formula, which is A-lw
describe the sampling distribution for the sample mean by naming the model and telling its mean and standard deviation.
Mean and standard deviation for the sample distribution is in the main body.
What is standard deviation?
Standard Deviation is a measure that shows what quantity variation (such as unfold, dispersion, spread,) from the mean exists. the quality deviation indicates a “typical” deviation from the mean. it's a well-liked live of variability as a result of it returns to the first units of live of the info set.
Main body:
sample Mean
Population mean =mu = ∑ xi /N
Mu represents pop mean
∑xi = the sum of all scores in the dataset
sample mean is the average score of a sample on a given variable and is represented by
x bar = ∑ xi /N
SE.M(Sample error of the Mean) is
=σ/√n
standard deviation is
σ = √∑(xi - υ)²/N
hence the formula for each of terms is as follows.
To know more about standard deviation , click on the link below
brainly.com/question/475676
#SPJ4
a test for a certain drug has a 0.1% probability of producing a false positive. if a company hired 500 drug-free employees, what is the probability of obtaining at least 1 false positive?
The probability of obtaining at least 1 false positive if the number of employees is 500 is 0.5
Probability
In the statistics concept, the probability refers the possible number of way of happening the particular event.
Given,
A test for a certain drug has a 0.1% probability of producing a false positive.
Here we need to find the probability of obtaining at least 1 false positive if a company hired 500 drug-free employees.
In the given question, we have the following values,
=> number of employees = 500
=> Probability of false positive = 0.1%
So, the probability of obtaining at least 1 false positive is calculated as,
=> 500 x 0.1/100
=> 5 x 0.1
=> 0.5
Therefore, the probability of obtaining at least 1 false positive is 0.5.
To know more about Probability here.
https://brainly.com/question/11234923
#SPJ4
assume that the helium porosity level (measured in percentage) of coal samples taken from any particular seam is normally distributed with true standard deviation 0.75. how large a sample size is necessary if the width of the 95% interval for the true average porosity level is to be 0.40
A large sample size of 15 is necessary if the width of the 95% interval is to be 0.40
Sample size determination is the act of choosing the number of observations or replicates to include in a statistical sample. The sample size is an important feature of any empirical study in which the goal is to make inferences about a population from a sample. In practice, the sample size used in a study is usually determined based on the cost, time, or convenience of collecting the data, and the need for it to offer sufficient statistical power. In complicated studies there may be several different sample sizes.
Sample sizes may be chosen in several ways:
Using experience – small samples, though sometimes unavoidable, can result in wide confidence intervals and risk of errors in statistical hypothesis testing.Using a target variance for an estimate to be derived from the sample eventually obtained, i.e., if a high precision is required this translates to a low target variance of the estimator.Using a target for the power of a statistical test to be applied once the sample is collected.Using a confidence level, i.e. the larger the required confidence level, the larger the sample size.Given in the question:
A sample size of n is needed.
n is found when M = 0.4.
95% Central interval
Z = 1.96
M = z × σ /√n
⇒ 0.40 = 1.96 × 0.75 /√n
⇒ 0.40√n = 1.96 ×0.75
⇒ √n = 1.96 ×0.75/0.40
⇒ (√n)² = (1.96 ×0.75 / 0.40 )²
⇒ n = 14.6
Rounding up 14.6
n = 15
The sample size of 15 is needed.
Thus, A large sample size of 15 is necessary if the width of the 95% interval is to be 0.40
Learn more about Sample Size:
https://brainly.com/question/25894237
#SPJ4
let x represent the sum of the first 25 positive odd integers. let $y$ represent the sum of the next 25 positive odd integers. what is the value of y-x?
By using the concept of arithmetic series, it can be calculated that
y - x = 1250
What is arithmetic series?
Arithmetic series are those series whose difference between two consecutive terms are same.
The odd integers forms an arithmetic series
For the sum of first 25 odd integer
First odd integer = 1
25th odd integer = 49
Sum of first 25 odd integers = [tex]\frac{25}{2}(1 + 49)[/tex] = 625
x = 625
For the sum of first 50 odd integers
First odd integer = 1
50th odd integer = 99
Sum of first 50 odd integers = [tex]\frac{50}{2}(1 + 99)[/tex] = 2500
Sum of next 25 odd integers = 2500 - 625 = 1875
y = 1875
y - x = 1875 - 625 = 1250
To learn more about arithmetic series, refer to the link-
https://brainly.com/question/6561461
#SPJ4
y=-7x-1
Can you help me please, I need to graph it
thank you in advance
Answer:
The dots shown in the graph are the answers.
Step-by-step explanation:
Answer: (-0.25, .75)
A family buys a studio apartment for $200,000. They pay a down payment of $20,000. a. Their down payment is what percent of the purchase price? b. What percent of the purchase price would a $90,000 down payment be?
Answer:
A. 20,000 is 10% of 200,000, so the percentage of the purchase price is 10%.
B. 90,000 is 45% of 200,000, so the percentage of the 90,000 down payment is 45%.
a jury pool consists of 30 people, 16 men and 14 women. compute the probability that a randomly selected jury of 12 people is all male.
The probability that a randomly selected jury of 12 people is all male is 2.01 × 10⁻⁵ .
In the question ,
it is given that ,
total number of people in the jury pool is 30 people ,
the total number of men in the jury pool is = 16 ,
total number of women in the jury pool is = 14 ,
So , 12 members can be selected from 30 people in ³⁰C₁₂ ways ,
So , total number of ways = ³⁰C₁₂ = 86493225 ways
and 12 male can be selected from 16 men in ¹⁶C₁₂ ways
= ¹⁶C₁₂ = 1820.
So , the probability of selecting 12 men is = 1820/86493225
= 0.00002104211
≈ 2.01 × 10⁻⁵
Therefore , the required probability is 2.01 × 10⁻⁵ .
Learn more about Probability here
https://brainly.com/question/29651724
#SPJ4
i have 5 marbles numbered 1 through 5 in a bag. suppose i take out two different marbles at random. what is the expected value of the product of the numbers on the marbles? answer as a decimal to the nearest tenth.
The expected value of the product of the numbers on the marbles is
6.
Given:
There are 5 marbles numbered 1 through 5 in a bag.
Suppose if two different marbles are taken out at random.
what is the expected value of the product of the numbers on the marbles = ?
5C 2 = 10
So we have ten possible sums
1 + 2 = 3 2 + 3 = 5 3 + 4 = 7 4 + 5 = 9
1+ 3 = 4 2 + 4 = 6 3 + 5 = 8
1 + 4 = 5 2 + 5 = 7
1 + 5 = 6
Expected value =
3 * Prob of occurence + 4 * Prob of occurence + 5*Prob of occurence + 6 * Prob of occuence +7 * Prob of occurence + 8 * Prob of occurence + 8 * Prob of occurence
3 (1/10) + 4(1/10) + 5(2/10) + 6(2/10) + 7 (2/10) + 8 (1/10) + 9(1/10) =
3/10 + 4/10 + 10/10 + 12/10 + 14/10 + 8/10 + 9/10 =
60/10
= 6
Hence we get the required answer.
Learn more about Probability here:
https://brainly.com/question/24756209
#SPJ4