Answer:
WE reject the Null and conclude that one of the drug is more effective than the other.
Step-by-step explanation:
Given :
Diet 1 3.4 10.9 2.8 7.8 0.9 5.2 2.5 10.5 7.1 7.5
Diet 2 11.9 13.1 11.6 6.8 6.8 8.8 12.5 8.6 17.5 10.3
This is a matched pair sample :
The hypothesis :
H0 : μd = 0
H1 : μd ≠ 0
Hence, we intun the difference between the two groups of value :
Difference, d = -8.9,-2.2,-8.8,1,-5.9,-3.6,-10,1.9,-10.4,-2.8
The test statistic :
dbar ÷ (Sd/√n)
dbar = mean of difference = Σd / n = - 49.7 / 10 = - 4.97
Standard deviation of difference, Sd = 4.51
Test statistic :
-4.97 ÷ (4.51/√10)
Test statistic = - 3.485
The sample size, n = 10
df = n - 1 ; 10 - 1 = 9
Critical value (0.10, 9) = 1.833
If Test statistic > |Critical value |
Since 3.486 > 1.833 ; WE reject the Null and conclude that one of the drug is more effective than the other
The product of two rational numbers is 47/42 and one of them is -11/21, find the other number
answer:
another number is -47/22
explanation:
let one number be x and the other be y
-11/21 × y = 47/42
y = -47/22
Answer:
- [tex]\frac{47}{22}[/tex]
Step-by-step explanation:
let n be the other number , then
- [tex]\frac{11}{21}[/tex] × n = [tex]\frac{47}{42}[/tex] ( divide both sides by - [tex]\frac{11}{21}[/tex] )
n = [tex]\frac{\frac{47}{42} }{-\frac{11}{21} }[/tex]
= [tex]\frac{47}{42}[/tex] × - [tex]\frac{21}{11}[/tex] ( cancel 21 and 42 )
= [tex]\frac{47}{2}[/tex] × - [tex]\frac{1}{11}[/tex]
= - [tex]\frac{47}{22}[/tex]
What is the smallest number that becomes 600 when rounded to the nearest hundred?
A. 545
B. 550
C. 555
D. 590
Answer:
B. 550
Step-by-step explanation:
550 is the smallest number that becomes 600 when rounded to the nearest hundred
Angelica’s bouquet of a dozen roses contains 5 white roses. The rest of the roses are pink what fraction of the bouquet is pink? There are 12 roses in a dozen.
A. 5/12
B. 7/12
C. 5/7
D. 7/5
Answer:
7/12
Step-by-step explanation:
There are 12 roses - 5 white = 7 pink
7 pink / 12 total
*20 points*
how do you get the weighted average from this table?
Answer:
it is
[(2+3+4+6)-2*4]:4=1.75
I THINK
Step-by-step explanation:
Why wouldn't you use division to find an equivalent fraction for 7/15
Answer:
This depends whether you want to make the fraction bigger or smaller.
Step-by-step explanation:
If you want to the the fraction into something smaller than it already is, you would use division because when you divide something, you get a smaller number.
However, if you want to make the fraction bigger, then you would multiply.
Hope this helps! :)
Answer:
Because 7 is a prime number which means it can only divide by itself and one so you cannot divide seven but you can divide 15.
Step-by-step explanation:
John has a cylindrical propane tank that measures 8" in diameter and 8" tall If John
buys a new cylindrical propane tank that is twice as wide and half as tall as his
current tank, how much larger will the volume of the new tank be?
Answer:
2 times as large
Step-by-step explanation:
For the original cylinder, we can say that the volume of a cylinder is equal to V= πr²h. For this cylinder, we can say that V = π * radius² * height. The radius is equal to 1/2 of the diameter, so the original radius is 8/2 = 4. Therefore, the volume of the original cylinder is V = π * radius² * height = π * 4² * 8 = π * 16 * 8 = π * 128
For the new cylinder, "twice as wide" means that the diameter is twice as big as the original one. Half the height means that the height is halved. The new diameter is therefore 8 * 2 = 16 (meaning that the new radius is 16/2=8) while the new height is 8/2 = 4. The new volume is thus
V = π * radius² * height = π * 8² * 4 = π * 64 * 4 = π * 256
To see how much larger the new tank volume is, we can divide (new tank volume) by (old tank volume), resulting in
π * 256 / (π *128) = 2
Area of a circle whose circumference is 100ft
Answer:
A≈795.77ft²
Step-by-step explanation:
C=100ft
Area of circle=C^2/4pie
100/4×22/7≈795.77472ft²
△DOG ~△?
Complete the similarity statement and select the theorem that justifies your answer.
**If they are not similar, select "none" for both parts
9514 1404 393
Answer:
nonenoneStep-by-step explanation:
The reduced side ratios, shortest to longest are ...
AC : AT : CT = 8 : 9 : 15
OD : OG : DG = 5 : 6 : 10
These are different ratios, so the triangles are not similar.
Not sure how to do this
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
Please help me solve this question ?
Answer:
Hi,
If you don't know how to derivate, i can show you using
lim (f(x+h)-f(x))/h if h ->0
Step-by-step explanation:
[tex]f(x)=2x^2+3x-2\\\\f'(x)=4x+3\\\\f'(1)=4*1+3=7\\\\f'(3)=4*3+3=15\\\\f'(5)=4*5+3=23\\[/tex]
Step-by-step explanation:
18
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.
Learn more about ratios here:
https://brainly.com/question/32531170?
#SPJ3
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)
Mr. Lock bought 6 quarts of oil for his car. He spent $16.02. How much was each quart of oil?
Answer:
2.67
Step-by-step explanation:
To solve this problem do 16.02 / 6.
I hope this answer helps you out! Brainliest woudl be appreciated.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.
Which of the following illustrates the truth value of the given statements? A triangle has four sides, and a rectangle has three sides. T F → F F T → F T T → T F F → F
Answer:
F F → F
Step-by-step explanation:
The statement is given as:
A triangle has four sides, and a rectangle has three sides.
It is again a false statement since a triangle is a polygon with three sides and a rectangle is a polygon with four sides.
Hence, the answer is:
F F → F
PLEASE ANSWER THIS !!!!
Answer:
option D
Step-by-step explanation:
Area of the square is 100 m² so each side is √100 = 10 m and half the area is 50 m²
Area of one quarter of the circle is ¼πr² = ¼π(10²) = 25π
The shaded area is thus (25π - 50) m²
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
The mean length of time, per week, that students at a certain school spend on their homework is 24.3 hours, with a standard deviation of 1.4 hours. Assuming the distribution of study times is normal, what percent of students study between 22.9 and 25.7 hours
Answer:
Approximately 68% of students study between 22.9 and 25.7 hours.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean of 24.3 hours, standard deviation of 1.4 hours.
What percent of students study between 22.9 and 25.7 hours?
22.9 = 24.3 - 1.4
25.7 = 24.3 + 1.4
Within 1 standard deviation of the mean, so:
Approximately 68% of students study between 22.9 and 25.7 hours.
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?
9514 1404 393
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
