Answer:
1) The null and alternative hypotheses.
H0: Hours of sleep per night is independent of age.
Ha: Hours of sleep per night is not independent of age.
Test Statistics χ²=4.009
The corresponding p-value for the test at χ²= 4.009 is 0.2604
Step-by-step explanation:
1) The null and alternative hypotheses.
H0: Hours of sleep per night is independent of age.
Ha: Hours of sleep per night is not independent of age.
2) The data is
≤ 39 ≥ 40 Total
6 hours 36 34 70
6.9-7 hours 60 57 117
7- 7.9 hours 79 77 156
8 hours or more 65 92 157
Total 240 260 500
3) The expected values are computed as follows
260×70/500=36.4
240×117/500 =56.16
260×117/500 =60.84
240×156/500 =74.88
260×156/500 =81.12
240×157/500=75.36
260×157/500 =81.64
4) The squared distances are calculated as
{(36 - 33.6)^2}/{ 33.6} = 0.171
{(34 - 36.4)^2}{ 36.4} = 0.158
{(60 - 56.16)^2}/{ 56.16} = 0.263
{(57 - 60.84)^2}/{ 60.84} = 0.242
{(79 - 74.88)^2}/{ 74.88} = 0.227
{(77 - 81.12)^2}/{ 81.12} = 0.209
{(65 - 75.36)^2}/{ 75.36} = 1.424
{(92 - 81.64)^2}{ 81.64} = 1.315
5) The significance level is set at α=0.05 for df = (4 - 1) (2 - 1) =3
degrees of freedom.
6) The critical region for this test is χ² = χ² >7.815
7) Test Statistics
χ²=i=∑(O ij −Eij )2/Eij
=0.171+0.263+0.227+1.424+0.158+0.242+0.209+1.315
= 4.009
8) Conclusion
As the calculated value χ² =4.009 does not lie in the critical region ≤χ² =7.815, null hypothesis is not rejected.
Therefore, we conclude that there is not enough evidence to accept the alternate hypothesis , at the α=0.05 significance level.
The p-value for the test at χ²= 4.009 is 0.2604
An item cost $480 before tax , and tge sales tax is $9.60
Answer:
0.02 ; 2%
Step-by-step explanation:
Given :
Cost of item = $480
Tax amount on item = $9.60
The sales tax rate = tax amount on item / cost of item
Sales tax rate = $9.60 / $480 = 0.02
As a percentage :
0.02 * 100% = 2%
[tex]2 \sqrt{3 = } [/tex]
13. The line y = -2x +1 is reflected in the line y = 2. Write the equation of the image.
After reflecting the line in the y-axis, the slope of the line will be positive 2 and the y-intercept remain unchanged.
so the equation of the image is y = 2x + 1.
What is the line of reflection?A reflection over a line is a transformation in which each point of the initial figure (the pre-image) has an image that is on the opposite side of the reflection line from the original point and is situated at the same distance from the reflection line. The pre-size image's and shape are replicated in a reflection.
The line of reflection is typically expressed as y = m x + b y=mx+by, equals, m, x, plus, b. What need I do to draw the line of reflection? The starting points in the figure are all perpendicularly separated from the line of reflection by the same amount as the starting points in the image.
To reflect a line in the y-axis, we need to negate the slope of the line.
The line y = -2x +1 has a slope of -2 and y-intercept of 1.
After reflecting the line in the y-axis, the slope of the line will be positive 2 and the y-intercept remain unchanged.
so the equation of the image is y = 2x + 1.
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2 points How Did I Do? The cost of renting a car is $42 /week plus $0.25 /mile traveled during that week. An equation to represent the cost would be y=42+0.25x , where x is the number of miles traveled.
The equation to represent the cost of renting the car, given the cost per week and the cost per mile, is y = 42 + 0.25x.
How to formulate the equation ?The total cost of renting the car at any given point, would be:
= Cost to rent per week + ( Cost per mile x Number of miles driven)
If we assume the number of miles driven is denoted by x, then the equation becomes :
= 42 + 0. 25 x
If we further take y to be the total cost, the equation then becomes :
y = 42 + 0. 25 x
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Find the volume of the
triangular prism.
2.8 cm
9 cm
4.2 cm
The volume of the triangular prism is
cm?
Answer:
52.92
Step-by-step explanation:
Please help ! It's timed! (More questions)
Answer:
Q2 : y= -2x+9
Q4: y= 2x+8
Jenny's dog weighs 38 kilograms. There are about 2.2 pounds in 1 kilogram. About how many pounds does Jenny’s dog weigh?
Answer:
83.6 pounds
Step-by-step explanation:
1 kg = 2.2 pounds
38 x 2 = 76
.2 x 38 = 7.6
76 + 7.6 is 83.6
Answer:
83.6 pounds
Step-by-step explanation:
1 kg = 2.2 pounds
38 x 2 = 76
.2 x 38 = 7.6
76 + 7.6 is 83.6
Which function does this graph represent?
A. F(x) = 3(x + 1)^2 + 2
B. F(x) = -3(x + 1)^2 + 2
C. F(x) = -3(x + 1)^2 - 2
D. F(x) = 3(x - 1)^2 + 2
Answer:
c
Step-by-step explanation:
common sense, duh.
Please solve the ques below:
Answer:
510 miles
Step-by-step explanation:
A B
Rate 80 120
Time x x - 2
Distance
Distance = rate x time
A's distance
d = 80x
B's distance
d = 120(x -2)
The distances equal each other when B catches up to A. Set the equations equal to each other and solve for the time
80x = 120(x -2) Distribute the 120
80x = 120x - 240 Subtract 120x from both sides
-40x = -240 Divide both sides by -40
x = 6
After 6 hours, B caught up with A. Substitute 6 for t and find the distance. You can use A or B.
d= 80x
d = 80(6)
d = 480
We need to add another 30 miles to get to the next town.
480 + 30 = 510
Can someone help me out
Convert 17 yards to feet. Use the rate suggested by the equation 3 feet1 yard.
Answer:
51 ft
Step-by-step explanation:
Answer:
Answer is 51 feet or 51'..........
Determine if each of the following statements are true or false (HELP!!! ARE MY ANSWERS CORRECT?)
Answer:
yes
Step-by-step explanation:
write in terms of i
Answer:
[tex]2i \sqrt{15} [/tex]
Step-by-step explanation:
...................
What is the image of the point (0,4) after a rotation of 180 degrees counterclockwise about the origin?
The image point of (0, 4) is (0, -4).
What is Cartesian plane?The intersection of the x- and y-axes creates the two-dimensional coordinate plane known as the cartesian plane. The origin is the point at where the x- and y-axes cross perpendicularly.
The Cartesian coordinate point (x, y) indicates that the distance from the origin is x in the horizontal direction and y in the vertical direction. The point is to the right of the origin if the sign of x is positive; otherwise, it is to the left.
Given points (0, 4)
to find image of the point (0,4) after a rotation of 180 degrees,
The initial coordinates (x, y) of a point become when we rotate it by 180 degrees around the origin (-x, -y).
So,
-0 is just 0 (since 0 is both negative and positive)
-(4) is -4
This makes our new point (0, -5).
Hence the image of point is (0, -4).
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Question 3 of 10 Which of the following best describes the graph below? +2 54 -3 -2 -1 1 O A. It is a one-to-one function. O B. It is a function, but it is not one-to-one. O C. It is not a function. D. It is a many-to-one function.
Answer:
It is a one-to-one function
Answer: one to one function
Step-by-step explanation:
brainlest for firs peep to answer
Answer:
8/3 is the answer
Answer:
8/3 multiply 3(denominator) and 2(whole number) then add the 2(numerator)
hope this helps
have a good day :)
Step-by-step explanation:
How do I even do this?
Answer:
going to have to to get the house ready
You have a budget of $1,900 per week for employees. Employees are paid $11 per hour and work 40 hours per week. Ignore overhead, how many employees can you hire?
You can hire around 173 employees. Here's the calculation: $1,900 / ($11/hour * 40 hours/week) = 173.333..., which rounds down to 173.
Question 9 (1 point)
Which of the following has the result as dividing a number by 5/2 and then multiplying by 1/2?
a
b
Multiplying by 2
Dividing by 2
Multiplying by 5
Dividing by 5
Ос
Od
Next Page
Back
Answer:
Dividing by 5
Step-by-step explanation:
fill in the blanks to complete the equation 3/8=1/ +1/ + 1/
Answer:
1/8 + 1/8 + 1/8
Step-by-step explanation:
Please answer!!!Thanks
The swim team trains 4 days every week on monday, tuesday and thursday. The swim team spends 1/2 hours in the gym followed by 1 1/4 hours in the pool. On saturday there is no gym but the swim time is doubled. How many hours per week does the swim team train?
Answer:
6 hours
Step-by-step explanation:
The swim team trains 4 days every week, with 1/2 hour in the gym and 1 1/4 hours in the pool on Monday, Tuesday and Thursday. On Saturday, there is no gym, but the swim time is doubled, so the total swim time is 2 1/2 hours.
Therefore, the total time spent training each week is 6 hours.
1/2 hour in the gym plus 5 1/2 hours in the pool.
Answer: The swim team trains for 7 hours and 45 minutes a week.
Step-by-step explanation:
Since the swim team trains in the gym and the pool (collectively) on Monday, Tuesday and Thursday, subsequently we will be multiplying GYM TIME + POOL TIME, 3 TIMES to get the time taken for training on the three days i.e. 3 ( ½ + 1 ¼ ) and add twice the time taken in pool for Saturday i.e. 2(1 ¼ )
= 3( ½ + 5/4) + 2(5/4)
=31/4
= 7 ¾
Multiply ¾ with 60 as 1 hour = 60 minutes to get the answer in time format.
Firstly, convert mixed fractions into improper ones and find the final answer. Then, convert the final answer into Time format i.e. hours and minutes.
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Aaron had 5/7 as much money as Remus. After Aaron spent 3/5 of his money on a laptop.
Remus had $2820 more than Aaron. How much money did Remus have?
Step-by-step explanation:
let Remus' money be = y
Aaron's = 5/7 y
3/5 * 5/7 y = 3/7 y
balance= 2/7 y
y - 2/7y = 2820
5/7 y= 2820
y = 2820*7/5= 564*7 = 3948
Which of these contexts describes a situation that is impossible?
Rolling a number less than 1 on a standard six-sided die, numbered
from 1 to 6,
Spinning a spinner divided into four equal-sized sections colored
red/green/yellow/blue and landing on some color,
Winning a raffle that sold a total of 100 tickets if you bought 50 tickets,
Reaching into a bag full of 15 strawberry chews and 5 cherry chews
without looking and pulling out a strawberry or a cherry chew.
Rolling a number less than 1 on a standard six-sided die, numbered
from 1 to 6 is an impossible situation.
What is a sure event?Suppose we have a coin with sides heads and tails then the occurrence of a head or a tail is a sure event.
If we observe the given options we can conclude that Rolling a number less than 1 on a standard six-sided die, numbered from 1 to 6 is an impossible situation as we couldn't get a number less than 1 on the die not possible right?
All the other options seem possible in some different ways but the first option is an impossible situation.
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A condominium owner pays property taxes of $2,000 per year. If taxes are figured
at a rate of $1.25 for every $100 in value, what is the value of his condominium?
Step-by-step explanation:
the tax rate gives us a ratio of tax amount to value.
this ratio (in our case 1.25/100) is constant for any value.
therefore, when we know how many $1.25 units are in $2000, we know that there are exactly as many $100 units in the value.
in other words, we multiply
1.25/100 × f/f
so that the numerator reaches the total of $2000 of taxes. and then the enumerator gives us the total value.
f = 2000 / 1.25 = 1600
so, we get
1.25/100 × 1600/1600 = 2000 / 160000
so, the value of the condominium is
value = $160,000
. Darlene is making punch. She pours 4 quarts 2 cups of apple juice into a bowl. Then she pours 3 quarts 1 cup of grape juice into the bowl. How much juice is in the bowl now? A 1 quart 1 cup B 7 quarts 1 cup © 7 quarts 3 cups D 8 quarts 1 cup
Answer:
C. 7 quarts 3 cups
Step-by-step explanation:
First you add 4 quarts, with 3 quarts to get 7 quarts. Then, you add 1 cup with 2 cups to get 3 cups.
Step-by-step explanation:
7 quarts 3 cups..........
Can y’all help me on question 14?!
Answer:
A. 4
Step-by-step explanation:
3(4)=12
12=12
........
Mathematics, 17.03.2021 23:50 burners
In a class of 80 students,40 study physics,48study mathematics and 44 study chemistry,20 study physics and mathematics,24 study physics and chemistry and 32 study only two of the three subjects. Of every student studies at least one of the three subjects. Find ; 1.The number of students who study all the three subjects.2.The number of students who study only mathematics and chemistry.
9514 1404 393
Answer:
10 study all three8 study only math and chemStep-by-step explanation:
1. Adding the numbers of those who study a given subject counts ...
once -- those who study only one subjecttwice -- those who study exactly two subjectsthree times -- those who study all three subject.That total is 40 +48 +44 = 132. When we subtract from this the total number of students, we get 132 -80 = 52, the number who study exactly 2 subjects plus twice the number who study all three.
From this, we can subtract the number who study exactly 2 subjects, leaving twice the number who study all three. 52 -32 = 20. So, 10 students study all three subjects.
__
2. Adding the numbers of those who study physics and another subject, we have 20+24 = 44. Subtracting twice the number who study all three gives the total of those how study only two subjects, one of which is physics. That total is 44 -20 = 24. So, of those 32 who study exactly two subjects, the remaining 32 -24 = 8 must be students who study only math and chemistry.
_____
It may be helpful to see the matrix of equations the problem statement describes. If we use the variables m, p, c, mp, mc, pc, mpc in that order to represent numbers of 1-subject, 2-subject, and 3-subject students, the augmented matrix looks like this.
[tex]\left[\begin{array}{ccccccc|c}1&1&1&1&1&1&1&80\\0&1&0&1&0&1&1&40\\1&0&0&1&1&0&1&48\\0&0&1&0&1&1&1&44\\0&0&0&1&0&0&1&20\\0&0&0&0&0&1&1&24\\0&0&0&1&1&1&0&32\end{array}\right][/tex]
The solution is m=20, p=6, c=12, mp=10, mc=8, pc=14, mpc=10. The bold values are the ones this question is asking about.
you can use a calculator if you want. No links please help this is very important i will give you brain thing if its correct
Answer:
C
Step-by-step explanation:
12.3+0.25=12.55
Answer:
C 12.55
Step-by-step explanation:
They are the same unit so 0.25ml+12.3ml=12.55ml
hope it helps :)
Can anybody awnser the table for me!!
The table is completed as shown below and total earnings of Lori is found.
What exactly is total earnings of a person?
The wages paid for both regular working hours and other working hours, including extra work or tips are referred to as total earnings.
Consider Tuesday
Hours worked = 4
Base salary = 4 × 7 ( $7 per hour given)
= $28
Tips = 18% of food sales = 0.18 × 300 = $54
Total earnings on Tuesday = 28 + 54 = $82
In the similar way the table can be completed as below.
1) The total earnings of Lori for the week = 82+138.9+218.5+173 = $612.4
2) Total earnings in a year = 52 × 612.4 = $31844.8
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13 cm
L
5 cm
Calculate the perimeter
Answer:
36
Step-by-step explanation:
permeter is solved by doing length+length+width+width so therefore you would do 13+13+5+5 which equals 36 as your answer