Answer:
[tex]\bar X =\frac{2.3+3.1+2.8+1.7+0.9+4+2.1+1.2+3.6+0.2+2.4+3.2}{12}=2.29[/tex]
[tex] s=1.09[/tex]
Step-by-step explanation:
For this case we have the following data given:
2.3 3.1 2.8
1.7 0.9 4.0
2.1 1.2 3.6
0.2 2.4 3.2
Since the data are assumedn normally distributed we can find the standard deviation with the following formula:
[tex]\sigma =\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n}}[/tex]
And we need to find the mean first with the following formula:
[tex]\bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]
And replacing we got:
[tex]\bar X =\frac{2.3+3.1+2.8+1.7+0.9+4+2.1+1.2+3.6+0.2+2.4+3.2}{12}=2.29[/tex]
And then we can calculate the deviation and we got:
[tex] s=1.09[/tex]
Answer:
X ~ Norm ( 2.29167 , 1.09045^2 )
Step-by-step explanation:
Solution:-
- The (GPA) for 12 randomly selected college students are given as follows:
2.3 , 3.1 , 2.8 , 1.7 , 0.9 , 4.0 , 2.1 , 1.2 , 3.6 , 0.2 , 2.4 , 3.2
- We are to assume the ( GPA ) for the college students are normally distributed.
- Denote a random variable X: The GPA secured by the college student.
- The normal distribution is categorized by two parameters:
- The mean ( u ) - the average GPA of the sample of n = 12. Also called the central tendency:
[tex]Mean ( u ) = \frac{\sum _{i=1}^{\ 12 }\: Xi }{n}[/tex]
Where,
Xi : The GPA of the ith student from the sample
n: The sample size = 12
[tex]Mean ( u ) = \frac{2.3 + 3.1 + 2.8 + 1.7 + 0.9 + 4.0 + 2.1 + 1.2 + 3.6 + 0.2 + 2.4 + 3.2}{12} \\\\Mean ( u ) = \frac{27.5}{12} \\\\Mean ( u ) = 2.29167[/tex]
- The other parameter denotes the variability of GPA secured by the students about the mean value ( u ) - called standard deviation ( s ):
[tex]s = \sqrt{\frac{\sum _{i=1}^{\ 12 }\: [ Xi - u]^2}{n} } \\\\\\\sum _{i=1}^{\ 12 }\: [ Xi - u]^2 = ( 2.3 - 2.29167)^2 + ( 3.1 - 2.29167)^2 + ( 2.8 - 2.29167)^2 + ( 1.7\\\\ - 2.29167)^2+ ( 0.9 - 2.29167)^2 + ( 4 - 2.29167)^2 + ( 2.1 - 2.29167)^2 + ( 1.2 - 2.29167)^2 +\\\\ ( 3.6 - 2.29167)^2 + ( 0.2 - 2.29167)^2 + ( 2.4 - 2.29167)^2 + ( 3.2 - 2.29167)^2 \\\\\\\sum _{i=1}^{\ 12 }\: [ Xi - u]^2 = 14.26916 \\\\\\s = \sqrt{\frac{ 14.26916 }{12} } \\\\s = \sqrt{1.18909 } \\\\s = 1.09045[/tex]
- The normal distribution for random variable X can be written as:
X ~ Norm ( 2.29167 , 1.09045^2 )
Answer the question bellow
Answer:
D
Step-by-step explanation:
All of the other functions are functions that are just multiplicative. When we substitute any x for A, B,or C, y/x will be the same. In D y/x will vary.
Find the complete solution of the linear system, or show that it is inconsistent. (If the system has infinitely many solutions, express your answer in terms of t, where x = x(t), y = y(t), and z = t. If there is no solution, enter NO SOLUTION.) 2x + 3y − z = −1 x + 2y = 5 x + 3y + z = 12
Answer:
inconsistent
Step-by-step explanation:
The sum of the first and last equations is ...
(2x +3y -z) +(x +3y +z) = (-1) +(12)
3x +6y = 11
Three times the second equation is ...
3(x +2y) = 3(5)
3x +6y = 15
There are no values of x, y, or z that can make both of these equations true. They are inconsistent.
A spinner has 8
equal-sized sections. Two
of the sections are yellow
.
a. What is the probability that the spinner will land on yellow
?
b. Use words to describe the probability.
Answer:
1/4
Step-by-step explanation:
The probability that the spinner will land on yellow is 2/8 because 2 is how many of the sections are yellow and 8 is how many sections there are in total. However, you need to simplify this to 1/4 and that is your answer
Final answer:
The probability that a spinner with 8 equal sections will land on yellow is 2 out of 8, which simplifies to 1/4 or a 25% chance.
Explanation:
The question asks about the probability of a spinner with 8 equal-sized sections landing on yellow, where 2 of the sections are yellow. To calculate the probability:
Count the number of favorable outcomes (the yellow sections): 2 sections.Count the total number of possible outcomes (all sections of the spinner): 8 sections.Divide the number of favorable outcomes by the total number of possible outcomes to get the probability.a. The probability that the spinner will land on yellow is 2 out of 8, or 1/4.
b. In words, the probability can be described as having a one in four chance or a 25% chance of landing on yellow when the spinner is spun.
How many black cherry trees have a height of 80 or more feet?
(Group of answer choices)
A) 7
B) 5
C) 10
D) 17
1. In a study on the likability of comedians, 10 participants observed one of two comedians (one who was humorous and one who was not humorous), and rated how likeable these comedians were on a 9-point scale from 1 (not likeable at all) to 9 (very likeable). The ratings are the data below. Test to see if the humorous comedian was liked more or less than the nonhumorous comedian, using alpha = .05 and four steps. Also calculate and interpret effect size and explained variance if appropriate.]
Answer:
a. 84 < n + (n + 2) + (n + 4) < 96
b. 26 < n < 30
step-by-step explanation:
using 'n' to represent the smallest even number, the next even number would be 'n + 2' and the next even number would be 'n + 4'. so, the expression to represent three consecutive even numbers is: n + (n + 2) + (n + 4).
since the sum of the these numbers needs to be between 84 and 96, we can set up the following inequality:
84 < n + (n + 2) + (n + 4) < 96
in order to solve for 'n', we must first combine like terms:
84 < 3n + 6 < 96
subtract 6 from all sides: 84 - 6 < 3n + 6 - 6 < 96 - 6 or 78 < 3n < 90
divide 3 by all sides: 78/3 < 3n/3 < 90/3 or 26 < n < 30.
The number of cell phone accounts in a certain country has increased exponentially for the last decade. The number of cell phone accounts (in millions) in this country can be approximated by the following function. Estimate the number of cell phone accounts in 2003.
f(x)= 114.8e.125x (0
What was the approximate number of cell phone accounts in 2003?
Answer:
See Below
Step-by-step explanation:
The equation estimating the number of cellphones in the country is:
[tex]f(x)=114.8 e^{0.125x}[/tex]
Where x = 0 corresponds to year 2000
thus,
x = 1 is year 2001
x = 2 is year 2002
x = 3 is year 2003
and so on...
We want approx. number of cellphones in the country in 2003. This corresponds to x = 3. So substituting in the equation we get:
[tex]f(x)=114.8 e^{0.125x}\\f(3)=114.8 e^{0.125(3)}\\f(3)= 167.03[/tex]
So, approximately there were 167.03 million cellphones in the country in 2003
ILL GIVE BRAINLIEST please please help (only help if u know the right answer)
Okay, to find the answer,
All we need to do it multiply !
[tex]\frac{f}{-3.2}[/tex] = 0.01
f = (0.01) × (-3.2)
f = -.032
I hope I helped :) Just comment if you have any questions and remember to vote me "brainliest" if you like my answer !!!
What is the area of the triangle below?
Answer:
9 square units
Step-by-step explanation:
Draw a rectangle around the triangle. The rectangle is 4 units tall by 6 units wide. The area of the triangle equals the area of the rectangle minus the triangles in the corners.
A = (4)(6) − ½(2)(4) − ½(1)(4) − ½(3)(6)
A = 24 − 4 − 2 − 9
A = 9
Maximum height___feet
Answer:
you are not aloud to cheat on tests please don't do that sorry can't answer to a cheater
Step-by-step explanation:
What is the density of an object with a mass of 20 g and volume of 10 cm3?
Answer:
2 g/cm^3
Step-by-step explanation:
D=m/V
=20g/10cm^3
=2g/cm^3
Density calculation based on mass and volume of an object is 2 g/cm³.
The density of an object is calculated by dividing its mass by its volume. In this case, with a mass of 20 g and volume of 10 cm³, the density can be calculated as:
Density = Mass / Volume = 20 g / 10 cm³ = 2 g/cm³
Immediately after a ban on using hand-held cell phones while driving was implemented, compliance with the law was measured. A random sample of 1,250 drivers found that 98.9% were in compliance. A year after the implementation, compliance was again measured to see if compliance was the same (or not) as previously measured. A different random sample of 1,100 drivers found 96.9% compliance.
(2 Points) State an appropriate null and alternative hypothesis for testing whether or not there is any statistical difference (i.e., a two-sided test) in these two proportions measured initially and then one year later. Conduct the test of hypothesis using a significance level of α= 0.05. Be sure to check the assumptions and conditions for your test. State the P-value of your test and also state your conclusion. (Feel free to use R in showing your work - and show your commands and output if using R.)
(2 points) Develop a 95% confidence interval for the true difference in proportions between the first survey and the second survey and explain what this confidence interval means in context of this problem. (Feel free to use R in showing your work - and show your commands and output if using R.
Answer:
Step-by-step explanation:
* The Null hypothesis was rejected.
* The confidence interval for the true difference in proportions between the first and second survey are:
0.008238357 and 0.003176164 respectively in 95% situations.
Please kindly go through the attached files for a step by step explanation of how these answer are gotten.
The price of a movie ticket after a 16% increase is $8.99. What was the price before increase?
Answer:
The price before the increase was $7.75.
Step-by-step explanation:
This question can be solved using a rule of three.
The price of a movie ticket after a 16% increase is $8.99.
This means that the current price, of $8.99, is 100+16 = 116% = 1.16 of the original
x, the original price, is 100% = 1. So
8.99 - 1.16
x - 1
[tex]1.16x = 8.99[/tex]
[tex]x = \frac{8.99}{1.16}[/tex]
[tex]x = 7.75[/tex]
The price before the increase was $7.75
Answer:
$7.75
Step-by-step explanation:
When a number is increased by a certain percentage, it means that the product of the percentage and the number is added to the number. The result is the increase of the original number by the given percentage.
As such, if the original number is x and it is increased by 16%, to get $8.99, this may be expressed mathematically as
16% * x + x = 8.99
1.16x = 8.99
x = 8.99/1.16
= $7.75
The price before the increase was $7.75
What is the ratio of our solar system's radius to the Milky Way's radius given that the distance from Pluto to the sun is 5.9 * 10^12 meters; and the Milky Way's disk radius is 3.9 * 10^20 meters. Round the coefficient to the nearest tenth.
Answer:
Just divide the sun-pluto distance by the milky way radius and you get the following ratio:
6.6 x 10^7 : 1
The Tauroto region contains 31 different species of IceCream-type small monsters. Each capture of an IceCream-type small monster has an equal chance of being any of the 31 species. If a collector captures five of these small monsters, what is the probability that they have captured at least two small monsters of the same species?
Answer:
0.28
Explanation:
You can determine the probability of the collector has captured at least two small monsters of the same species is the complent of that all the monsters captured are of different species, i.e. none are of the same species.
The probability than none of the five captured small monsters are of the same species are:
1. Probability than the one monster is of the species One, and the others are not of the species One:
(1/32) × (31/32) × (30/32) × (29/32) × (28/32)2. Probability that the first monster is of the species Two, and the others are not of the species Two:
(1/32) × (31/32) × (30/32) × (29/32) × (28/32)3. Probability that the first monster is of the species Three and the others are not of the same species:
(1/32) × (31/32) × (30/32) × (29/32) × (28/32)4. Inference
As you see you have to do this 32 times, and then add all the equal 32 probabilities, which is
32 × (1/32) × (31/32) × (30/32) × (29/32) × (28/32) = 0.72That is the probability that none of the five small monsters are of the same species. Then, the probability that at leas two small monsters are of the same species is 1 - 0.72 = 0.28
If $5958 is invested in an account at 5.9% annual interest compounded quarterly, how much will be in the account in 7 years if no money is withdrawn (Round your answer to the nearest hundredth)?
Answer:
Pretty sure in 7 years with no money withdrawn it would be $8,418.65
Step-by-step explanation:
because you would find out what 5.9% of $5958 which would be $351.522 you get that by multiplying [5958*5.9%=351.522]
Then multiply 351.522 by 7 and you get 2460.654 [351.522*7=2460.654]
Finally you add 2460.654 and 5958 and you get 8418.654 [5958+2460.522=8418.654]
Then you round down .654 and you get [8418.65]
The length of life (in days) of an alkaline battery has an exponential distribution with an average life of 340 days. (Round your answers to three decimal places.) (a) What is the probability that an alkaline battery will fail before 185 days? (b) What is the probability that an alkaline battery will last beyond 2 years? (Use the fact that there are 365 days in one year.)
The probability that an alkaline battery will fail before 185 days is approximately 0.457, or 45.7%. The probability that an alkaline battery will last beyond 2 years is approximately 0.228, or 22.8%.
Explanation:To answer part (a), we need to find the probability that an alkaline battery will fail before 185 days. Since the length of life of an alkaline battery follows an exponential distribution with an average life of 340 days, we can use the formula for the exponential distribution to calculate the probability. The formula is:
P(X < t) = 1 - e^(-t/μ)
Where X is the random variable representing the length of life of the battery, t is the time (in days) we are interested in, and μ is the average life of the battery. Plugging in the values, we have:
P(X < 185) = 1 - e^(-185/340)
Solving this equation gives us a probability of approximately 0.457, or 45.7%.
For part (b), we want to find the probability that an alkaline battery will last beyond 2 years. Since there are 365 days in a year, 2 years is equal to 730 days. Using the same formula as before, we have:
P(X > 730) = 1 - P(X < 730) = 1 - (1 - e^(-730/340))
Solving this equation gives us a probability of approximately 0.228, or 22.8%.
A nonlinear function with at least one term raised to the power of two is known as a a. logarithmic function. b. quadratic function. c. hyperbolic function. d. cubic function.
Answer:
The option b) quadratic function is correctA nonlinear function with at least one term raised to the power of two is known as a quadratic functionStep-by-step explanation:
A nonlinear function with at least one term raised to the power of two is known as a quadratic function
FOR :
A non-linear system of equations is a set of equations where one or more terms have a variable of power two or higher .
In Algebra, linear functions are polynomials with highest exponent equal to 1 or of the form y = c where c is constant. Non-linear functions are all other rest functions with exponent atleast 2.
Hence A nonlinear function with at least one term raised to the power of two is known as a quadratic function
Therefore the option b) quadratic function is correctBethany sells roses and petunias. The expression
3
r
+
2.5
p
3r+2.5p3, r, plus, 2, point, 5, p gives the cost (in dollars) of
r
rr roses and
p
pp petunias.
What is the cost of
7
77 roses and
8
88 petunias?
Answer:
$41
Step-by-step explanation:
Fill in the values of the variables and do the arithmetic.
3r +2.5p = 3(7) +2.5(8) = 21 +20 = 41
7 roses and 8 petunias cost $41.
At a candy store, 3 giant lollipops sell for $7.59 and 2 small packets of bubblegum cost $4.82. Which is a better buy?
A new concert venue just opened in downtown Atlanta and they are in the process of deciding how many tickets they can sell for each show. The venue has three levels, two general admission levels that only have standing room, and one level with 180 seats. The first level of standing room is a square with one side measuring 75’. The second level, also standing room, is a rectangle measuring 130’ by 60’ ft. The third level has 180 seats. The venue thinks each person will occupy 2.25 square feet.
(A) How many tickets should they sell?
Answer:
[tex]6147\:Tickets[/tex]
Step-by-step explanation:
Area of the first level [tex]=75 X 75=5625 \:ft^2[/tex]
Area of the second level [tex]=130 X 60=7800 \:ft^2[/tex]
Total Area of Standing Room [tex]=5625+7800=13425 \:ft^2[/tex]
Since each person will occupy 2.25 square feet.
Number of Persons that will occupy the standing room
[tex]= 13425 \div 2.25\\=5966.7 \approx 5767\:persons[/tex]
Therefore the number of Tickets that should be sold
=Number of seats + Number for standing Room
=180+5967
[tex]\approx 6147\:tickets[/tex]
Therefore, the concert venue should sell 6,147 tickets.
By calculating the total square footage available in the venue, and then dividing by the space each person occupies, it's determined that the venue can sell roughly 6046 tickets per show.
Explanation:The main task is to calculate the total available space, in square feet, in the concert venue. For the standing room areas, we first calculate the total square footage of each level by multiplying the dimensions of each space. For the first level, the area of a square is calculated by squaring the side length, so 75' x 75' = 5625 sq. ft. For the second level, the area of a rectangle is calculated by multiplying the length by the width, so 130' x 60' = 7800 sq. ft. The seated area already specifies the number of people it can accommodate, so no calculation for square footage is needed. Altogether, the venue has 5625 + 7800 + 180 = 13605 sq ft. available.
The next step is to divide the total square footage by the space taken up by each person to find out how many people can be accommodated. We divide 13605 by 2.25, obtaining 6046.67, but since we can't sell a fraction of a ticket, we should round down to the nearest whole number. Therefore, the venue can sell roughly 6046 tickets per show.
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La suma de tres términos consecutivos a partir a 55(sin incluirlo) vale 738.Encontrar n
The first of three consecutive terms after 55, which sum up to 738, is found to be 245 by setting up an equation and solving for n.
Explanation:The student's question involves finding a variable, n, which represents the first of three consecutive terms, given that the sum of the three terms is 738 and that the sequence starts with a term after 55.
Let's denote the three consecutive terms as n, n+1, and n+2, where n is the first term that comes after 55. Since the sum of the terms is given as 738, we can formulate the following equation:
\(n + (n+1) + (n+2) = 738\)
Combining like terms, we get:
\(3n + 3 = 738\)
To find n, we'll subtract 3 from both sides of the equation and then divide by 3:
\(3n = 738 - 3\)
\(3n = 735\)
\(n = 245\)
Therefore, the first of the three consecutive terms is 245.
What function is graphed below?
y = cot(x)-2
y=tan(x)-2
y = cot(x)+2
y=tan(x)+2
Answer:
d
Step-by-step explanation:
The function y = tan(x) + 2 is shown in the provided graph option fourth is correct.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
The missing figure is in the picture please refer to the picture.
As we have a trigonometric function.
In the picture, the graph of a tanx is shown but 2 units up.
Thus, the function y = tan(x) + 2 is shown in the provided graph option fourth is correct.
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Determine the center of the following data set by finding
the median.
Test Scores
47,50,43, 42, 42, 38, 49, 47, 42, 50
Answer:
The median of this set is 45.
Step-by-step explanation:
According to this site, if you know the coordinates of two points on a line, what form would you use to write the equation of the
line? Explain the process for writing the equation. (Site 1)
You would use the POINT SLOPE FORMULA and the Slope Formula
which is as follows ...
slope formula : [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
point slope formula: [tex]y - y_{1} = m(x - x_{1} )[/tex]
Integrate both sides of the differential equation you found for dp to obtain an equation for p. Your equation should then include a constant that depends on initial conditions. Determine the value of this constant by assuming that the pressure at some reference height y0 is p0. Express your answer in terms of quantities given in the problem introduction along with y0 and p0.
Answer:
Step-by-step explanation:
FIND THE SOLUTION BELOW
Maya picks 16 vegetables from her garden.
6 of them are carrots. The rest are cucumbers.
Then she gives away 5 cucumbers.
How many cucumbers does Maya have now?
16 - 6 = 10
10 - 5 = ?
16 + 6 = 22
22 - 5 = ?
16 - 6 = 10
10 + 5 = ?
Answer:
she has 5
Step-by-step explanation:
16 vegetables subtracted by 6 = 10 carrots
10 carrots subtracted by 5 that she gives away = 5 that she has left
In March, April, and June it rained 2 inches. In February, May, and September it rained 1 inch In August and
October, it rained 3 inches. And in January it only rained 4 inches. Which line plot represents the data?
x
x
.
X
.
X
X
X
1
2
3
4
5
✓ Done
Intro
Answer:
d
Step-by-step explanation:
What is the quotient?
StartFraction 2 m + 4 Over 8 EndFraction divided by StartFraction m + 2 Over 6 EndFraction
Answer:
3/2
Step-by-step explanation:
StartFraction 2 m + 4 Over 8 EndFraction divided by StartFraction m + 2 Over 6 EndFraction
I think you mean:
(2m + 4) / 8 divided by (m + 2)/6
=
(2m + 4)/8 times (6 / (m + 2) )
= (m + 2)/4 times 6/(m + 2)
= 6/4 = 3/2
The quotient of the given (2m + 4)/8 divided by (m +2)/6 will be 3/2.
What is a fraction?In such a fraction, the value that appears above the horizontal line is referred to as the numerator.
In another word, the fraction is the division of the two numbers but the division is not wholly complete.
In another word, if we divide two numbers by each other then the upper word is called the numerator, and a lower word is called the denominator.
It represents the number of pieces removed from the whole. The denominator of a fraction is the numerical value that comes before the brings together various.
Given that
(2m + 4)/8 ÷ (m +2)/6
⇒ (2m + 4)/8 × 6/(m +2)
⇒ 2 ×6 ÷8
⇒3/2 hence it will be the correct answer.
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Several years ago, Dirk bought some gold at a price of $710 per ounce. When he went to sell it, the gold was worth 60% more than it was when he purchased it. What was the new value of the gold?
Answer:
$1,136 per ounce.
Step-by-step explanation:
To find the new value of gold, you have to find what 60% of 710 is. You do this by converting 60% into a decimal and multiplying it by 710. This results in 0.6*710. 60% of 710 is 426. 426 + the original price of 710 is equal to 1,136.
You can also solve this problem in a condensed manner by multiplying 710 by 1.6: the 1.0 stands for the original price (710) so you don't have to add it later. The 0.6 stands for the 60% more. Multiplying 710 by 1.6 gets you 1,136, which is the new value of gold/ounce.
If I sent out 200 letters and got 80 responses. If I want 20 more responses how many more letters do I have to send out
Answer:
Step-by-step explanation:
50