Answer:(a) Proportion of attendeees having a room mate and studying for at least five hours a week = (26+14)/100 = 0.4
Proportion of attendeees not having a room mate and studying for at least five hours a week = (20+10)/100 = 0.3
(b) The expected table of students, if there was no association between number of hours spent studying and having a room mate is as below:
No Roommate One Roommate Totals
Three 13.5 16.5 30
Five 20.7 25.3 46
More than five 10.8 13.2 24
Totals 45 55 100
In the above table, 13.5 is derived as 30*45/100; 16.5 is derived as 30*55/100; 20.7 is derived as 46*45/100 and so on.
Since the actual observed data are different, there seems to be some association, but we can't be sure if the association is postitive or negative .
(c) We have the Null Hypothesis, H0: No of hours spent studying and whether they have a roommate have no association.
and the Alternate Hypothesis, H0: No of hours spent studying and whether they have a roommate have an association.
We do the chi-square test in Excel, using the function CHITEST().
The p-value = 0.797
Since the p-value is high, we cannot reject the Null Hypothesis and conclude that there is no association between No of hours spent studying and having a roommate.
Step-by-step explanation:
Proportion with a roommate and study for at least 5 hours per week is 0.34
Proportion without a roommate and study for at least 5 hours per week is 0.36
How to calculate the valueProportion with a roommate and study for at least 5 hours per week
= (20 + 14) / 100 = 34 / 100
= 0.34
Proportion without a roommate and study for at least 5 hours per week
= (26 + 10) / 100 = 36 / 100
= 0.36
Among attendees with no roommates, 46 out of 45 (approximately 1.02) proportionally studied for at least 5 hours per week.
Among attendees with one roommate, 40 out of 55 (approximately 0.73) proportionally studied for at least 5 hours per week.
From these calculations, we can infer that a higher proportion of attendees without a roommate studied for at least 5 hours per week compared to those with one roommate. This suggests a potential negative association between having a roommate and studying for at least 5 hours per week.
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A number with 100 digits is given. the first two digits of that number are 2 and 9 . how many digits has a square of that number?
The square of the given number will have 199 digits.
How to find the number digits in the square of the given number?A number with hundred digits is given.
The first two digits of the given number are 2 and 9.
We can use the following formula to find the total number of digits in the square of a number.
2n - 1
Where n is the total number of digits in the given number.
Let us take a number with 2 digits:
29*29 = 841 { 2*2 - 1 = 3}
We can see that the square of the 2-digit number has 3 digits in it.
Let us take a number with 3 digits:
299*299 = 89401 { 2*3 - 1 = 5}
We can see that the square of the 3-digit number has 5 digits in it.
Similarly, we can find the number of digits in the square of a 100-digit as shown below:
2n - 1 = 2*100 - 1
= 200 - 1
= 199
Therefore, we have found that the square of the given number will have 199 digits.
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Solve for x |2x+1|=-13
Answer:
no solution
Step-by-step explanation:
Your question is in the form:
absval of something
= a NEGATIVE number
The absolute value is always positive. So it can never be negative.
There are no values that x can be that will make this math sentence true.
It's not really a trick question, but the course/teacher/book/program just wants you to recognize that an absolute value CANNOT be negative.
In order for a gear to work in a piece of machinery, the radius of the gear, r, must be greater than 4 cm, but not exceed 4.1 cm. Which compound inequality represents the situation?
r > 4 and r ≤ 4.1
r > 4 or r ≤ 4.1
r < 4 and r ≥ 4.1
r < 4 or r ≥ 4.1
The compound inequality represents the situation is r > 4 and r ≤ 4.1
Compound inequalityRadius of the gear = rr must be greater than 4 cmr > 4
r must not exceed 4.1 cmr ≤ 4.1
Therefore, r > 4 and r ≤ 4.1 is the compound inequality which represent the situation.
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Its A: r > 4 and r ≤ 4.1
PLS HELP!!
Reproduce the definition of theoretical probability.
Theoretical Probability = a/b
Answer:
Step-by-step explanation:
a = number of successful events
b = total number of events.
PLEAS HELP I think I know the answer but im only 50% sure
x =x=x, equals
^\circ
∘
degrees
In the given diagram, the value of x is 90°
Calculating anglesFrom the question, we are to determine the value of x
In the given diagram,
Using the linear pair theorem, we can write that
x + 90° = 180°
x = 180° - 90°
x = 90°
Hence, the value of x is 90°
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Working her way through college kathy works two part time jobs for a total of 22 hours a week. job a pays $6.20 per hour, and job b pays $6.50 per hour. how many hours did she work at each job the week that she made $140.60? (round to two decimal places if necessary.)
Using Algebraic equation, Kathy worked 22 hours at job A and 12 hours at job B, the week she made US $ 140.60.
Let's review all the information given for solving this question:
Rate per hour of Job A = US$ 6.20
Rate per hour of Job B = US$ 6.50
Earnings received by Kathy during the week = US$ 140.60
Total time worked by Kathy during the week = 22hours
Hours at job A = x
Hours at job B = 22 -x
In order to find how many hours Katy worked at each job: This is the Algebraic equation that we'll use:
6.20x + 6.50 (22 - x) = 140.60
6.20x + 143- 6.50x = 140.60
-0.3x = 140.60 - 143
-0.3x = - 2.4
x = -(2.4)/-(0.3)
x = 14.3/0.3 = 8 (Dividing by 0.3 at both sides)
Kathy worked 8 hours at job A.
Hours at job B = 22 - x. Put x = 11 we get
Hours at job B = 22 -11
= 11
Hence, using Algebraic equation Kathy worked 22 hours at job A and 12 hours at job B, the week she made US $ 140.60.
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3. Find the missing side lengths. Leave the answers as radicals in simplest form.
Answer:
x = y = 6.5[tex]\sqrt{2}[/tex]
Step-by-step explanation:
the triangle is isosceles, both base angles are 45° then the 2 legs are congruent , that is x = y
using the sine ratio in the right triangle and the exact value
sin45° = [tex]\frac{\sqrt{2} }{2}[/tex] , then
sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{13}[/tex] = [tex]\frac{\sqrt{2} }{2}[/tex] ( cross- multiply )
2x = 13[tex]\sqrt{2}[/tex] ( divide both sides by 2 )
x = y = 6.5[tex]\sqrt{2}[/tex]
Which pairs of triangles appear to be congruent? Check all that apply. 2 A. Triangles 1 and 2 B. Triangles 2 and 3 C. Triangles 1 and 4 D. Triangles 1 and 3 E. Triangles 3 and 4 Triangles 2 and 4 A
Pairs of triangles appear to be congruent are :
Triangles 2 and 3. Option B
Triangles 2 and 4. Option D
Triangles 3 and 4. Option E
What are congruent triangles?Congruent triangles can be defined as the pairs of triangles with same measurement
Triangles 2 and 3 :
After observing triangles 2 and 3 it appears that triangle is congruent to triangle .
Option C
Triangles 2 and 4
After observing triangles 2 and 4 it appears that triangle 2 is congruent to triangle 4 .
Option D
E. Triangles 3 and 4
After observing triangles 3 and 4. They are congruent
Option E
Hence, Option B, D and E are correct of the triangles
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Answer:
Triangles 3 and 4
Triangles 1 and 4
Triangles 1 and 3
Step-by-step explanation:
if this is wrong tell me so i can edit the answer, but this is what i got
Sheree’s brother gave samuel his collection of stamps when she left for college. at that time, the value of the collection was $420. eight years later, the stamp collection was worth $980. what is the rate of change?
The rate of change of stamp collection was $57.5 per year.
Rate is comparison of two related quantities.
Often the second quantity is time (per second, per hour, etc) but it can be anything.
Can be in the style "this per that" or as a single number calculated using division.
Example: Sam makes 3 pancakes every 6 minutes, that is a rate of:
• 3 pancakes per 6 minutes
• 0.5 pancakes per minute
• 30 pancakes per hour
• an hourly rate of 30
By formula the rate of change = Change in cost/ Time taken
=( $980 - $420)/ 8years
= $460/ 8 years
= $57.5 per year
Thus the rate of change of stamp collection was $57.5 per year.
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There are seven roads that lead to the top of a hill. How many different ways are there to reach the top and come back ( you dont have to go on the same road there and back)?
Answer:
49 different ways
Step-by-step explanation:
If there are seven roads that lead to the top, you have seven possible choices to go to the top of the hill.
Then, to come back to the start, you also have seven possible choices (seven roads), and you can pick any road.
So, if you have seven ways to go up and seven ways to go down, the number of different ways of going to the top and coming back is the product of these numbers of possible choices.
N(total) = N(up) * N(down)
N(total) = 7 * 7
N(total) = 49 different ways
Brainliest pls and tysm!
10 cm
7 cm
8 cm
SA =
7 cm
2 cm
[?] cm²
6 cm
If you'd like,
you can use a
calculator.
Step-by-step explanation:
as the graphic shows, there are 2 objects : 1 block and 1 triangular shaped half-block.
the block is
7cm × 6cm × 2cm
the half-block is
8cm × 7cm × 6cm
with 10cm being the length of the tilted "roof" area.
the 2 sides facing each other are not visible to the observer, so, they are not part of the surface area of the composite figure.
let's start with the block :
top and bottom 7×2
front and back 6×2
no left (fully covered by the half-block)
right 6×7
that gives us :
2 × 7×2 = 2×14 = 28 cm²
2 × 6×2 = 2×12 = 24 cm²
6×7 = 42 cm²
in total : 94 cm²
the half-block :
top 10×7
bottom 8×7
front and back (triangles) 8×6/2
no left (due to being a half-block)
no right (fully covered by the block)
that gives us :
10×7 = 70 cm²
8×7 = 56 cm²
2 × 8×6/2 = 2×24 = 48 cm²
in total : 174 cm²
so, the complete surface area of the composite figure is
94 + 174 = 268 cm²
What is the area of this trapezoid?
Answer:
315
Step-by-step explanation:
In 2015, around ____ percent of the world’s population had an internet connections.
What was the purpose of the coordinate graphing system described by Descartes in his book Discourse on Method?
O to use algebraic methods to solve geometric problems
O to prove the universe was Sun-centered
O to represent equations for the queen of Sweden
O to prove his own existence
The purpose of the coordinate graphing system described by Descartes in his book "Discourse on Method" is to use algebraic methods to solve geometric problems. That is option A.
What is coordinate graphing system?The coordinate graphing system is used on graphical systems to describe the relationship or location between two points on different axes such as X and y axis.
According to Descartes in his book "Discourse on Method" he developed a connection between Algebra and geometry.
Therefore, the main purpose for the coordinate graphing system is to use algebraic methods to solve geometric problems.
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Answer:
The answer that you are looking for is A.
Have a great day!
Step-by-step explanation:
Please mark me brainliest!
Paul has four paper strips of the same length. He glues two of them together with 4 cm overlap, and the new strip is 36 cm long. He wants to make a 30cm long strip with the other two strips how long should the overlap be?
Answer:
maybe the answer ris 36×4 and then 30×4 and subtract the result?!?!
Find the volume of the composite figure. Round to the nearest tenth if necessary.
The volume of the composite figure shown in the picture is equal to 375 cubic meters.
What is the volume of the composite figure?
The volume is the space occupied by a solid, the volume of the composite figure is sum of the volumes of the two elements, the one is a square prism and the other, a triangular prism. The volume of the entire figure is:
V = (5 m)² · (13 m) + (1/2) · (5 m)² · (4 m)
V = 375 m³
The volume of the composite figure shown in the picture is equal to 375 cubic meters.
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I need help finding values of x,y,z. I want to know if there is an answer apart from 0, since that is what I need to find. Thanks and look at the pic.
Answer:
They all equal zero
Step-by-step explanation:
A number cannot equal itself times any number that isn't zero, unless it itself is zero.
If the ratio of y to x is equal to 3 and the sum of y and x is 80, what is value of y
Answer:
y = 60
Step-by-step explanation:
Step 1: Make sense of the given"The ratio of y to x is 3"
This means that, [tex]y\div x=3[/tex]
"The sum of y and x is 80"
This means, [tex]x+y=80[/tex]
Step 2: Make use of the factsIf [tex]y\div x=3[/tex], then [tex]y = (3*x)[/tex].
We can plug this into the other equation by substitution:
[tex]x + (3 * x)=80[/tex]
This simplifies to:
[tex]4x = 80[/tex]
Which we can solve out and get:
[tex]x=20[/tex].
We solved for x, but we need the value of y.
So, we go back to the equation we first derived: "[tex]y = (3*x)[/tex]".
And now we substitute the value of x, into this.
[tex]y = (3 * (20))[/tex]
By solving this out, we get:
[tex]y=60[/tex]
So, the value of y is 60.
A couple quick algebra 1 questions for 50 points!
Only answer if you know the answer, quick shout-out to Subtomex0, tysm for the help!
Answer:
[tex]\textsf{2.} \quad y=\dfrac{35}{x}[/tex]
[tex]\textsf{3.} \quad y=-\dfrac{90}{x}[/tex]
[tex]\textsf{4.} \quad y=\dfrac{63}{x}[/tex]
[tex]\textsf{5.} \quad y=-\dfrac{112}{x}[/tex]
Step-by-step explanation:
If y is inversely proportional to x, then:
[tex]y \propto\dfrac{1}{x} \implies y=\dfrac{k}{x} \quad \textsf{(for some constant }k)[/tex]
Question 2
Substitute one of the given ordered pairs into the inverse variation equation and solve for k:
[tex]\implies 7=\dfrac{k}{5}[/tex]
[tex]\implies 7 \cdot 5=\dfrac{k}{5} \cdot 5[/tex]
[tex]\implies k=35[/tex]
Substitute the found value of k into the formula to create the inverse variation equation for the given ordered pairs:
[tex]\implies y=\dfrac{35}{x}[/tex]
Question 3
Substitute y = -15 and x = 6 into the formula and solve for k:
[tex]\implies -15=\dfrac{k}{6}[/tex]
[tex]\implies -15 \cdot 6=\dfrac{k}{6} \cdot 6[/tex]
[tex]\implies k=-90[/tex]
Substitute the found value of k into the formula to create the inverse variation equation for the given values:
[tex]\implies y=-\dfrac{90}{x}[/tex]
Question 4
Substitute one of the given ordered pairs into the inverse variation equation and solve for k:
[tex]\implies 9=\dfrac{k}{7}[/tex]
[tex]\implies 9 \cdot 7=\dfrac{k}{7} \cdot 7[/tex]
[tex]\implies k=63[/tex]
Substitute the found value of k into the formula to create the inverse variation equation for the given ordered pairs:
[tex]\implies y=\dfrac{63}{x}[/tex]
Question 5
Substitute one of the given ordered pairs into the inverse variation equation and solve for k:
[tex]\implies -16=\dfrac{k}{7}[/tex]
[tex]\implies -16 \cdot 7=\dfrac{k}{7} \cdot 7[/tex]
[tex]\implies k=-112[/tex]
Substitute the found value of k into the formula to create the inverse variation equation for the given ordered pairs:
[tex]\implies y=-\dfrac{112}{x}[/tex]
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slope intercept form of 3x+2y=7
Answer:
y = -1.5x + 3.5
Step-by-step explanation:
Slope intercept form is y=mx+b.
3x + 2y = 7
2y = -3x + 7
y = -1.5x + 3.5
Answer:
-3/2x+7/2=y
Step-by-step explanation:
A ball inside of a cube has a volume of 113 cubic inches. If each side of the cube measures 12.6 inches, what is the volume of air inside the cube
The volume of air inside the cube is 1887.376 cubic inches
What is Volume?The volume of a shape or an object is the amount of space in the object
How to determine the volume of air inside the cube?The given parameters are:
Volume of the ball = 113 cubic inchesThe side length of the cube = 12.6 inchesThe volume of the cube is calculated using
Volume = (Side length)^3
Substitute 12.6 for Side length
Volume = 12.6^3
Expand the exponent
Volume = 12.6 * 12.6 * 12.6
Evaluate the product
Volume = 2000.376
The volume of air inside the cube is calculated using
Volume of the air = Volume of the cube - Volume of the ball
So, we have
Air = 2000.376 - 113
Evaluate
Air = 1887.376
Hence, the volume of air inside the cube is 1887.376 cubic inches
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2 quick algebra 1 questions for 50 points!
Only answer if you know the answer, quick shout-out to Subtomex0, tysm for the help!
Answer:
t = 60/n
Step-by-step explanation:
The original equation we know is y = k/n
Since 12 people can assemble the set in 5 hours, when y is 5, n will be 12.
We can now input that value into the equation.
--> 5 = k/12
--> 5(12) = k/12 (12)
--> 60 = k
--> k = 60
The equation to represent the situation can be written as:
t = 60/n
and that is our final answer!
12 people can assemble in 5hours
So
y=k/x12=k/5k=60Equation
y=60/xOr
t=60/nConsider the series . what is the truncation error for s3? 0.002 0.008 0.992 0.998
The truncation error for s3 is 0.008
What is Truncation error?The truncation error serves as the difference between a truncated value as well as the actual value.
This truncated quantity can be a numeral having a fixed number of allowed digits.
Therefore the value of S_3=0.008
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[tex]\sqrt{x}[/tex][tex]\sqrt{x}[/tex]4-[tex]\sqrt{x}[/tex][tex]\sqrt{x}[/tex]7 -[tex]\sqrt{x}[/tex][tex]\sqrt{x}[/tex]4+[tex]\sqrt{x}[/tex]7 +[tex]\sqrt{x}[/tex]2
[tex]4x - 7x - 4x + 7 \sqrt{x} + \sqrt{x} [/tex]
[tex] - 7x + 8 \sqrt{x} [/tex]
A population has a mean of μ= 35 and a standard deviation of σ = 5. after 3 points are added to every score in the population, what are the new values for the mean and standard deviation?
The new values for the mean and the standard deviation are 38 and 5 respectively.
The mean of a population is given as [tex]\mu = \frac{\sum_{N}^{i}x_i}{N}[/tex] and its standard deviation is given as [tex]\sigma = \sqrt{\frac{\sum_{N}^{i}(x_i-\mu)^2}{N}}[/tex].
In the question, we are given that a population has a mean of μ = 35 and a standard deviation of σ = 5, and are asked for the new values for the mean and standard deviation when 3 points are added to every score in the population.
We let the new population formed be over the variable k.
Thus, [tex]k_i = x_i + 3[/tex], for all i from 1 to N.
Thus, the new mean can be calculated as:
[tex]\mu_k = \frac{\sum_{N}^{i}k_i}{N}\\\mu_k = \frac{\sum_{N}^{i}(x_i + 3)}{N}\\\mu_k = \frac{\sum_{N}^{i}x_i + 3N}{N}\\\mu_k = \frac{\sum_{N}^{i}x_i}{N} + 3\\\mu_k = \mu + 3\\\mu_k = 35 + 3 = 38 [Since, \mu = 35].[/tex]
Thus, the new mean is 38.
Thus, the new standard deviation can be calculated as:
[tex]\sigma_k = \sqrt{\frac{\sum_{N}^{i}(k_i-\mu_k)^2}{N}}\\\sigma_k = \sqrt{\frac{\sum_{N}^{i}(x_i + 3-38)^2}{N}}\\\sigma_k = \sqrt{\frac{\sum_{N}^{i}(x_i-35)^2}{N}}\\\sigma_k = \sqrt{\frac{\sum_{N}^{i}(x_i-\mu)^2}{N}} [Since, \mu = 35]\\\sigma_k = \sigma = 5.[/tex]
Thus, the new standard deviation is 5.
Thus, the new values for the mean and the standard deviation are 38 and 5 respectively.
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The function f(x) is shown in the graph.
Which type of function describes f(x)?
a) Exponential
b) Logarithmic
c) Rational
d) Polynomial
The function that describes the graph is an exponential function
How to determine the function type?From the graph, we have the following highlights:
Initially, when x increases; y seem not to increaseThen, x and y increase at the same timeFinally, y increase and x seem not to increaseThe above is the description of an exponential function
Hence, the function that describes the graph is an exponential function
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Select the correct answer. What is the approximate solution to this equation? 4lnx - 8 = 12
A. x = 148.4
B. x = 10.5
C. x = 1.61
D. x = 59,874
Answer:
Step-by-step explanation:
hello :
4lnx - 8 = 12
4lnx - 8 +8= 12+8
4lnx =20
lnx =5
coclusion : x =e^5
A. x = 148.4
What is the range of possible sizes for side x?
Answer:
Should be 3.9
Step-by-step explanation:
prove me wrong
what is an equivalent expression for 3(x-9) ?
Find the length of side DF
The length of side DF is 3.75.
Given that within the figure there are two triangles that are similar.
Congruent triangles will be triangles that have a comparable measure and shape. This infers that the comparing sides are comparable and the relating focuses are equivalent.
Two comparative triangles are given.
If two triangles are comparable at that point their comparing sides are relative and comparing points are congruent.
DF/AB=EF/BC
Substitute the values from the given figure
DF/15=6/24
Cross multiply both sides, and we get
DF×24=6×15
DF×24=90
Divide both sides by 24, we get
(DF×24)/24=90/24
DF=15/4
DF=3.75
Hence, the length of side DF from the given figure is 3.75.
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