Twelve residents from the city of Rocklin were randomly selected and asked "How many TVs are in your household?". The following data were obtained: 2, 3, 3, 1, 2, 5, 3, 4, 1, 2, 4, and 3.
According to Nielsen Media Research the national average is 2.7 TVs per household. Is this sufficient sample evidence to indicate that the mean number of TVs in Rocklin households is higher than the reported national average of 2.7 TVs per household? Use ! = 5% and assume that the number of TVs in Rocklin households is normally distributed.
Answer:
There isn't enough evidence to indicate that the mean number of TVs in Rocklin households is higher than the reported national average .
Step-by-step explanation:
This is a one sample mean test ;
H0 : μ = 2.7
H1 : μ > 2.7
Given the data :
2, 3, 3, 1, 2, 5, 3, 4, 1, 2, 4, 3
Sample size, n = 12
The sample mean, xbar = ΣX / n = 33/12 = 2.75
The sample standard deviation, s = 1.215 ( from calculator)
The test statistic :
(xbar - μ) ÷ (s/√(n))
T = (2.75 - 2.7) ÷ (1.215/√(12))
T = 0.05 / 0.3507402
T = 0.1426
The critical value from Tscore ;
df = 12 - 1 = 11
Critical value = 1.796
Since ; Test statistic < Critical value ;WE fail to reject the Null and conclude that there isn't enough evidence to indicate that the mean number of TVs in Rocklin households is higher than the reported national average
In the following problem, the ratios are directly proportional. Find the missing variable.
If y1 = 4, x2 = 6, and y2 = 8, what is the value of x1?
Answer:
x1 = 3
Step-by-step explanation:
first set up the proportion (write as fractions):
(y1/x1) = (y2/x2)
then fill in the variables:
4/x1 = 8/6
now cross multiply:
8 • x1 = 6 • 4
simple algebra:
8 • x1 = 24
x1 = 24/8
x1 = 3
If y1 = 4, x2 = 6, and y2 = 8, then the value of x1 is 3 which we can solve using ratios.
In a directly proportional relationship, the ratios between the corresponding values of two variables remain constant. This constant ratio is often referred to as the "proportionality constant."
In this problem, you have two pairs of values: (x1, y1) and (x2, y2). We're given that the ratios are directly proportional, which means:
x1 / y1 = x2 / y2
Plugging in the given values:
x1 / 4 = 6 / 8
Now, cross-multiply to solve for x1:
x1 * 8 = 4 * 6
x1 = 24 / 8
x1 = 3
Therefore, the value of x1 is 3.
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Mr. Cole packed 20 pounds into a suitcase, and Mrs. Cole packed 23 pounds into the same suitcase. They then had to remove 8 pounds because it was too heavy. How many pounds was their suitcase after making it lighter?
Answer:
35 lbs is the final weight
Step-by-step explanation:
20 +23 = 43 lbs
Then they had to remove 8 lbs
43 - 8 =35
35 lbs is the final weight
How many minutes will the bus take to complete the trip If a bus completes half a trip at 40 km per hour and the other half at 50 20. if the whole trip was 60 k.m. ?
Answer:
The bus will take 81 minutes to complete the trip.
Step-by-step explanation:
To determine how many minutes will the bus take to complete the trip if a bus completes half a trip at 40 km per hour and the other half at 50 km per hour, and the whole trip was 60 km, the following calculation must be performed:
60/2 = 30
30/40 = 3/4 of an hour = 45 minutes
30/50 = 3/5 of an hour = 36 minutes
45 + 36 = 81
Therefore, the bus will take 81 minutes to complete the trip.
In a mixture 60 liters, the ratio of milk and water 2:1.If this ratio is to be 1:2, then what is the quantity of water to be further added?
Answer:
Hello,
60L
Step-by-step explanation:
Quantity of water /Quantity of milk =2/1
Quantity of mixture= Quantity of water +Quantity of milk =60L
Quantity of milk =40 L
Quantity of water =20 L
Let say x the quantity of water to be added
New ratio =1/2=40/(20+x)
20+x=80 (cross products)
x=60 (L)
Help me plz 20 points to who ever gets it right
Step-by-step explanation:
2., 3., 4., 5.
yes, you had the right idea to calculate the half distances between the coordinates. just create the absolute values of the full distance before cutting it in half.
you need to remember : we have to go this half distance from one point to the other (meaning adding our subtracting the half distance to/from the starting point).
2.
(-4, 6) to (10, -10)
in x the distance is 10 - -4 = 14. half is 7.
in y the distance is |-10 - 6| = |-16| = 16. half is 8.
so the midpoint is
(-4 + 7, 6 - 8) = (3, -2)
remember, to go the half distance in the direction towards the second point (so we have to choose properly, when to use "+" and "-" depending on the change of the coordinate : from -4 to 10 we have to add, from 6 to -10 we have to subtract, of course).
3.
(-3, -8) to (-6.5, -4.5)
in x distance : -3 - -6.5 = 3.5. half is 1.75
in y distance : -8 - -4.5 = |-3.5| = 3.5. half is 1.75
midpoint is
(-3 - 1.75, -8 + 1.75) = (-4.75, -6.25)
4.
(3, 7) to (-8, -10)
x : 3 - -8 = 11. half is 5.5
y : 7 - -10 = 17. half is 8.5
midpoint is
(3 - 5.5, 7 - 8.5) = (-2.5, -1.5)
5.
(-6, -13) to (-6.4, -3.8)
x : -6 - -6.4 = 0.4. half is 0.2
y : -13 - -3.8 = |-9.2| = 9.2. half is 4.6
midpoint is
(-6 - 0.2, -13 + 4.6) = (-6.2, -8.4)
6.
(-1, 7) to (5, 1)
x : -1 - 5 = |-6| = 6. 1/3 is 2.
y : 7 - 1 = 6. 1/3 is 2.
1/3 from C to D
(-1 + 2, 7 - 2) = (1, 5)
7.
2/3 of the way from D to C is the same point as in 6. (1/3 from C to D).
again
(1, 5)
8.
2/3 of the way from C to D.
so, we need to double what we added in 6.
(-1 + 4, 7 - 4) = (3, 3)
9.
1/3 of the way from D to C is the same point as in 8. (2/3 of the way from C to D).
again
(3, 3)
10.
exactly. Pythagoras.
the square root of the sum of the squares of the coordinate differences.
distance = sqrt((x1 - x2)² + (y1 - y2)²)
11.
(6, 8) to (-1, 8)
distance = sqrt((6 - -1)² + (8 - 8)²) = sqrt(49) = 7
12.
(5, -6) to (5, 6)
sqrt((5-5)² + (-6-6)²) = sqrt(144) = 12
13.
(-2, 0) to (11, 0)
sqrt((-2 - 11)² + (0-0)²) = sqrt(169) = 13
14.
(1, -5) to (9, 1)
sqrt((1-9)² + (-5 - 1)²) = sqrt(64 + 36) = sqrt(100) = 10
15.
ST and MT are basically the same equation.
MT is half of ST.
ST equation based on 2 points :
y – yS={(yT – yS)/(xT – xS)}(x – xS)
M = (xS + (xT - xS)/2, yS +(yT - yS)/2)
so, let's put that into the general equation :
y - yM={(yT - yM)/(xT - xM)}(x - xM)
y - (yS +(yT - yS)/2) = {(yT - (yS +(yT - yS)/2))/(xT - (xS + (xT - xS)/2))}(x - (xS + (xT - xS)/2))
16.
the two corners farthest away are (5, 10) and (9, 6).
what distance from (0, 0) is now bigger ?
since it is (0, 0), we can skip the 0s and just sum up the squares of the coordinates.
5² + 10² = 125
9² + 6² = 117
so, the corner (5, 10) is the farthest away.
the ratio of sadia's age to her father's age is 3:6. The sum of their age is 96 .What is sadia's age
We have,
[tex]a:b=3:6,a+b=96[/tex]
Introduce variable [tex]x[/tex] such that [tex]a=3x,b=6x[/tex]
The sum [tex]a+b=96[/tex] is therefore [tex]9x=96\implies x=10.\overline{6}[/tex]
So,
[tex]a=3\cdot10.\overline{6}=\boxed{32}[/tex] (sadia's age)
[tex]b=6\cdot10.\overline{6}=\boxed{64}[/tex] (father's age)
Hope this helps :)
look at the image below urgent plz over 100 points
Answer: 1,526.04 yd³ (this is what i got on my calculator others may vary use any rounding you need)
VOLUME of CONE is: V= Pir² h / 3
Pi= 3.14
r= 9
h= 18
V= (3.14) x (9)² x (18)
9²= 81
3.14 x 81= 254.34 x 18= 4,578.12
4,578.12 / 3= 1,526.04 <-- answer
Help me Please I need this
there are 7 vertices in this shape
Answer:
7.
Step-by-step explanation:
The vertices are the points where the lines meet.
Look at the pattern below. If the
pattern continues, what will be
the tenth number?
3. 11, 9, 17, 15, 23, 21...
Answer:
35
Step-by-step explanation:
We are adding 8 and then subtracting 2
3, 11, 9, 17, 15, 23, 21
The 8th number is 21+8 = 29
The 9th number
Subtract 2
29-2 = 27
10th number
Add 8
27+8 = 35
First is adding 8 to get the next number then subtract 2 to get the number after.
21 is the 7th number.
8th number = 21 + 8 = 29
9th number = 29-2 = 27
10th number = 27 + 8 = 35
Answer: 35
please help
Question: 6b = 18
Answer: ?
Answer:
6b=18
b=18/6
b=3
.
.
.
.
.
.
Answer:
6b=18
b=18/6
b=3
.
Step-by-step explanation:
Part C
Based on feedback from an independent research firm, the flashlight manufacturer has decided to change the design of the flashlight. The reflector now needs to extend 4 centimeters past the center of the bulb, as shown in the diagram. In the new design, how wide will the reflector (CD) be at its widest point? Show your work.
Answer:
The answer is "18".
Step-by-step explanation:
In the given graph by concluding we observe that on the x-axis, one step is 2 units, and when we half each of the steps it will= 1 unit
[tex]\therefore\\\\CD = distance\ from\ -(8+1)\ to\ (8+1)\ = \text{distance between} -9 \ to\ 9\ = 18[/tex]
The mean output of a certain type of amplifier is 102102 watts with a standard deviation of 1212 watts. If 6363 amplifiers are sampled, what is the probability that the mean of the sample would differ from the population mean by greater than 3.43.4 watts
Answer:
0.0244 = 2.44% probability that the mean of the sample would differ from the population mean by greater than 3.4 watts.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean of 102, standard deviation of 12:
This means that [tex]\mu = 102, \sigma = 12[/tex]
Sample of 63:
This means that [tex]n = 63, s = \frac{12}{\sqrt{63}}[/tex]
What is the probability that the mean of the sample would differ from the population mean by greater than 3.4 watts?
Below 102 - 3.4 = 98.6 or above 102 + 3.4 = 105.4. Since the normal distribution is symmetric, these probabilities are equal, and thus, we find one of them and multiply by two.
Probability the mean is below 98.6.
p-value of Z when X = 98.6. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{98.6 - 102}{\frac{12}{\sqrt{63}}}[/tex]
[tex]Z = -2.25[/tex]
[tex]Z = -2.25[/tex] has a p-value of 0.0122.
2*0.0122 = 0.0244
0.0244 = 2.44% probability that the mean of the sample would differ from the population mean by greater than 3.4 watts.
10. In a group of 50 people, there are two types of professionals, engineers and managers. If 36 of them are engineers and 24 of them are managers, how many persons are both managers and engineers?
Step-by-step explanation:
The photo above is the Venn diagram
Now, the number of persons that are both managers and engineers= n
Since, Total number of persons is 50
Therefore, 50= M+n+E
M only = 36-n
E only = 24-n
Therefore, 50= 36 - n + n + 24 - n
50 = 36+24-n
50 = 60 - n
60 - n = 50
-n = 50 - 60
-n = - 10
Therefore, n = 10
Therefore, the number of persons that are both Managers and Engineers is 10persons.
Wesley is making a patio from stones of two sizes, 5 inch wide and 10 inch wide. He wants to begin and end his pattern with a 10 inch stone so there will be one more of the 10 inch stones than of 5inch stones. His patio will be 130 inches wide.
How many 10 inch stones will Wesley need for one row?
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Answer:
9
Step-by-step explanation:
If x is the number of 10-inch stones, then (x-1) is the number of 5-inch stones, and the total width is ...
10x +5(x-1) = 130
15x -5 = 130 . . . . . . . eliminate parentheses
15x = 135 . . . . . . add 5
x = 9 . . . . . . . divide by 15
Wesley will need 9 10-inch stones for one row.
Help me with this please.
Answer:
the answer should be B
Step-by-step explanation:
take the total of people who got the flu(63) and the amount of them who were vaccinated(35) and write it as a fraction. 35/63 in its simplest form is 5/9
round 32.68 to the nearest hundredth
Answer:
32.70
Step-by-step explanation:
round up
Average person who drives car in United States drives 15, 350 miles which is 50% more than an average driver in Europe. We assume that the number of yearly miles by U.S. drivers is approximately a normal random variable of standard deviation of 4200 miles. Calculate percent of drivers who traveled between 10,000 to 12,000 miles in a year.
Answer:
7,675
that is your answer
? Question
Use the drawing tools to form the correct answer on the graph.
Graph this step function:
Answer:
start on (0,1) and go up two and left three. keep going until you run out of room. then, draw a line through the points.
Step-by-step explanation:
A lawyer commutes daily from his suburban home to his midtown office. The average time for a one-way trip is 24 minutes, with a standard deviation of 3.8 minutes. Assume the distribution of trip times to be normally distributed.
(a) What is the probability that a trip will take at least ½ hour?
(b) If the office opens at 9:00 A.M. and he leaves his house at 8:45 A.M. daily, what percentage of the time is he late for work?
(c) If he leaves the house at 8:35 A.M. and coffee is served at the office from 8:50 A.M. until 9:00 A.M., what is the probability that he misses coffee?
(d) Find the length of time above which we find the slowest 10% of trips.
(e) Find the probability that 2 of the next 3 trips will take at least one half
1/2 hour.
Answer:
Step-by-step explanation:
a) Probability-Above 30 min = 5.72% = .0572
b) Probability-Above 15 min = 99.11% = .9911
c) *Probability-Between 1 - 59.49% = .4051
d) 19.136 minutes z = -1.28
a) The probability that trip will take at least 1/2 hour will be 0.0606.
b) The percentage of time the lawyer is late for work will be 99.18%.
c) The probability that lawyer misses coffee will be 0.3659.
d) The length of time above which we find the slowest 10% of trips will be 0.5438.
e) The probability that exactly 2 out of 3 trips will take at least one half
1/2 hour is 0.0103.
What do you mean by normal distribution ?
A probability distribution known as a "normal distribution" shows that data are more likely to occur when they are close to the mean than when they are far from the mean.
Let assume the time taken for a one way trip be x .
x ⇒ N( μ , σ ²)
x ⇒ N( 24 , 3.8 ²)
a)
The probability that trip will take at least 1/2 hour or 30 minutes will be :
P ( x ≥ 30)
= P [ (x - μ) / σ ≥ (30 - μ) / σ ]
We know that , (x - μ) / σ = z.
= P [ z ≥ (30 - 24) / 3.8)]
= P [ z ≥ 1.578 ]
= 1 - P [ z ≤ 1.578 ]
Now , using the standard normal table :
P ( x ≥ 30)
= 1 - 0.9394
= 0.0606
b)
The percentage of the time the lawyer is late for work will be :
P ( x ≥ 15)
= P [ z ≥ -2.368 ]
= P [ z ≤ 2.368]
= 0.9918
or
99.18%
c)
The probability that lawyer misses coffee :
P ( 15 < x < 25 ) = P ( x < 25 ) - P ( x < 15)
= P [ z < 0.263] - P ( z < -2.368)
or
= 0.3659
d)
The length of time above which we find the slowest 10% of trips :
P( x ≥ X ) ≤ 0.10
= 0.5438
e)
Let's assume that y represents the number of trips that takes at least half hour.
y ⇒ B ( n , p)
y ⇒ B ( 3 , 0.0606)
So , the probability that exactly 2 out of 3 trips will take at least one half
1/2 hour is :
P ( Y = 2 )
= 3C2 × (0.0606)² × ( 1 - 0.0606)
= 0.0103
Therefore , the answers are :
a) The probability that trip will take at least 1/2 hour will be 0.0606.
b) The percentage of time the lawyer is late for work will be 99.18%.
c) The probability that lawyer misses coffee will be 0.3659.
d) The length of time above which we find the slowest 10% of trips will be 0.5438.
e) The probability that exactly 2 out of 3 trips will take at least one half
1/2 hour is 0.0103.
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I need help this is confusing to me
Answer:i think it is b not really sure
Step-by-step explanation:
Solve for the unknown variable
4y-2=8-2y+4y
y=?
Step-by-step explanation:
I hope it helped and it is easy to understand i hope it was helpful
1)4y-2=8-2y+4y
=4y-2y+4y=8-2
2y +4y=8-2
6y+6
12
Consider the graph below, and identify the piecewise function that describes it.
Answer:
f(x)=-x when x belongs to (-infinity, 3)
f(x)=-2 when x belongs to [3, 6]
f(x)=2x-7 when x belongs to (6, infinity)
The answer pl shhaoksngausinxbbs pls
Answer:
D. 3
Step-by-step explanation:
A triangle can be defined as a two-dimensional shape that comprises three (3) sides, three (3) vertices and three (3) angles.
Simply stated, any polygon with three (3) lengths of sides is a triangle.
In Geometry, a triangle is considered to be the most important shape.
Generally, there are three (3) main types of triangle based on the length of their sides and these include;
I. Equilateral triangle: it has all of its three (3) sides and interior angles equal.
II. Isosceles triangle: it has two (2) of its sides equal in length and two (2) equal angles.
III. Scalene triangle: it has all of its three (3) sides and interior angles different in length and size respectively.
In Geometry, an acute angle can be defined as any angle that has its size less than ninety (90) degrees.
Hence, we can deduce that the greatest number of acute angles that a triangle can contain is three (3) because the sum of all the interior angles of a triangle is 180 degrees.
The bar graph shows the z-score results of four students on two different mathematics tests. The students took Test 1 and then, a month later, took Test 2. Which student had the lowest score on Test 2? Euan Felicia Dave Carla
Answer:
euan had lowest score on test 2
The student with lowest score on test 2 is Euan.
What is bar graph ?Bar graph is used for the graphical representation of data or quantities by using bars or strips.
Here,
The z-score results of four students on two different mathematics tests is represented by the given bar graph.
Calculating the scores of each students for the two tests respectively.
1) Carla
Test 1: 0.75
Test 2: -0.5
2) Dave
Test 1: -0.5
Test 2: 1
3) Euan
Test 1: 0.25
Test 2: -1
4) Felicia
Test 1: 1.25
Test 2: 1.5
Hence,
The student with lowest score on test 2 is Euan.
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Rotation 90° counterclockwise around the origin of the point (-8,1)
Tile is to be placed in an entryway, as shown below.
At $6.25 per square foot, how much does it cost to tile the entryway?
Calculate the area by using 2 rectangles:
13 x 5 = 65 square feet
5 x 4 = 20 square feet
Total area = 65 + 20 = 80 square feet.
Multiply price per square foot by total area:
6.25 x 80 = 500
Cost = $500
write your answer in simplest radical form
Answer:
x = 2 yd
Step-by-step explanation:
Angles of 45 degreees = two congruent legs
for the Pythagorean theorem
2x^2 = 8
x^2 = 4
x = 2
Find theta to the nearest tenth of a degree, if theta is between 0 degrees and 360 degrees for sin theta = 0.4649 with theta in quadrant 2
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Answer:
152.3°
Step-by-step explanation:
The arcsine function only gives angles in quadrants I and IV. Since this is a quadrant II angle, its value will be ...
θ = 180° -arcsin(0.4649) = 180° -27.7°
θ = 152.3°
You have $2,000 on a credit card that charges a 16% interest rate. If you want to pay off the credit card in 5 years, how much will you need to pay each month (assuming you don't charge anything new to the card)?
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Answer:
$48.64
Step-by-step explanation:
The monthly payment amount is given by the amortization formula ...
A = P(r/n)/(1 -(1 +r/n)^(-nt))
where P is the loan amount, r is the annual interest rate compounded n times per year for t years.
Here, you have P=2000, r=0.16, n=12 (months per year), t=5 (years), so the payment is ...
A = $2000(0.16/12)/(1 -(1 +0.16/12)^(-12·5)) = $320/(12(0.54828942))
A ≈ $48.636 ≈ $48.64
You will need to pay $48.64 each month to pay off the charge in 5 years.
