Answer:
Step-by-step explanation:
This is a test of 2 independent groups. Let μ1 be the mean dissolution time for disk-shaped ibuprofen tablets and μ2 be the mean dissolution time for oval-shaped ibuprofen tablets.
The random variable is μ1 - μ2 = difference in the mean dissolution time for disk-shaped ibuprofen tablets and the mean dissolution time for oval-shaped ibuprofen tablets.
We would set up the hypothesis.
a) The null hypothesis is
H0 : μ1 = μ2 H0 : μ1 - μ2 = 0
The alternative hypothesis is
H1 : μ1 ≠ μ2 H1 : μ1 - μ2 ≠ 0
This is a two tailed test.
For disk shaped,
Mean, x1 = (269.0 + 249.3 + 255.2 + 252.7 + 247.0 + 261.6)/6 = 255.8
Standard deviation = √(summation(x - mean)²/n
n1 = 6
Summation(x - mean)² = (269 - 255.8)^2 + (249.3 - 255.8)^2 + (255.2 - 255.8)^2+ (252.7 - 255.8)^2 + (247 - 255.8)^2 + (261.6 - 255.8)^2 = 337.54
Standard deviation, s1 = √(337.54/6) = 7.5
For oval shaped,
Mean, x2 = (268.8 + 260 + 273.5 + 253.9 + 278.5 + 289.4 + 261.6 + 280.2)/8 = 270.7375
n2 = 8
Summation(x - mean)² = (268.8 - 270.7375)^2 + (260 - 270.7375)^2 + (273.5 - 270.7375)^2+ (253.9 - 270.7375)^2 + (278.5 - 270.7375)^2 + (289.4 - 270.7375)^2 + (261.6 - 270.7375)^2 + (280.2 - 270.7375)^2 = 991.75875
Standard deviation, s2 = √(991.75875/8) = 11.1
b) Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is
(x1 - x2)/√(s1²/n1 + s2²/n2)
Therefore,
t = (255.8 - 270.7375)/√(7.5²/6 + 11.1²/8)
t = - 3
c) The formula for determining the degree of freedom is
df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²
df = [7.5²/6 + 11.1²/8]²/[(1/6 - 1)(7.5²/6)² + (1/8 - 1)(11.1²/8)²] = 613.86/51.46
df = 12
We would determine the probability value from the t test calculator. It becomes
p value = 0.011
d) Since alpha, 0.05 > than the p value, 0.011, then we would reject the null hypothesis. Therefore, we can conclude that at 5% significance level, the mean dissolve times differ between the two shapes
Omar has three t shirts: one red, one green and one yellow. He has two pairs of shorts one black and red.
-How many different outfits can Omar put together?
-What is the probability of Omar’s outfits including a red T-shirt or red shorts?
Answer:
Omar can put together 6 outfits.
66.67% probability of Omar’s outfits including a red T-shirt or red shorts
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
-How many different outfits can Omar put together?
For each t-shirt, that are two options of shorts.
There are 3 t-shirts.
3*2 = 6
Omar can put together 6 outfits.
What is the probability of Omar’s outfits including a red T-shirt or red shorts?
Red t-shirt and red shorts
Red t-shirt and black shorts
Green shirt and red shorts
Yellow shirt and red shorts
4 desired outcomes.
4/6 = 0.6667
66.67% probability of Omar’s outfits including a red T-shirt or red shorts
Please help. I’ll mark you as brainliest if correct!!!!
Answer:
a= 2/5
b= -3/5
Step-by-step explanation:
We need to multiply the numerator and denominator by -i (conjugate) to cancel out i in the denominator
[tex]\frac{(3+2i)(-i)}{5i(-i)}[/tex]
This simplifies to:
[tex]\frac{-3i+-2i^{2} }{-5i^{2} }[/tex]
This further simplifies to:
[tex]\frac{-3i +2}{5}[/tex]
Can be rewritten as:
[tex]\frac{2}{5} +-\frac{3}{5} i[/tex]
a = 2/5
b = -3/5
If f(x)=x³-2x², which expression equivalent to f(i)?
Answer:
f(x) = x³ - 2x²
=>
f(i) = i³- 2i²
Hope this helps!
:)
what is the midpoint of the segment shown below?
(1, 2) (1,-5)
A. (1, -3/2)
B. (2, -3/2)
C. (2, -3)
D. (1, -3)
Answer:
The answer is A (1,-3/2)
Step-by-step explanation:
Add both x coordinates, divide by 2
Add both y coordinates, divide by 2
Sick computers: Let V be the event that a computer contains a virus, and let W be the event that a computer contains a worm. Suppose
P(V) = 0.47, P(W) = 0.37, P(Vand W) = 0.01
(a) Find the probability that the computer contains either a virus or a worm or both.
(b) Find the probability that the computer does not contain a worm
Part 1 of 2
(a) Find the probability that the computer contains either a virus or a worm or both.
The probability that the computer contains either a virus or a worm or both is
Х
5
Part 2 of 2
(b) Find the probability that the computer does not contain a worm
The probability that the computer does not contain a worm is
Х
Answer:
0.83
0.63
Step-by-step explanation:
P(V or W) = P(V) + P(W) − P(V and W)
P(V or W) = 0.47 + 0.37 − 0.01
P(V or W) = 0.83
P(not W) = 1 − P(W)
P(not W) = 1 − 0.37
P(not W) = 0.63
a. the probability that the computer contains either a virus or a worm or both is 0.83
b. The probability that the computer does not contain a worm is 0.63.
Calculation:(a)
The probability is
P(V or W) = P(V) + P(W) − P(V and W)
P(V or W) = 0.47 + 0.37 − 0.01
P(V or W) = 0.83
(b) The probability is
P(not W) = 1 − P(W)
P(not W) = 1 − 0.37
P(not W) = 0.63
Learn more about the probability here: https://brainly.com/question/16096170
Triangle JKL was dilated using the rule D Subscript M, one-third. The image, triangle J'K'L', is the result of the dilation. Point M is the center of dilation. Triangle J K L is dilated to form smaller triangle J prime K prime L prime. The length of M L prime is 2.5. What is L'L? 5 units 7.5 units 10 units 12.5 units
Answer: the answer is A 5 units
The length of L'L in the dilated figure is 5 units.
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.
Dilation is the increase or decrease in size of a figure.
Triangle JKL was dilated by 1/3 with M as the center of dilation to form J'K'L'.
Given that ML' = 2.5 units, hence:
L'L = (2.5 * 3) - 2.5 = 5 units
The length of L'L in the dilated figure is 5 units.
Find out more on transformation at: https://brainly.com/question/1620969
Arlinda says there is a linear relationship between the price (p) of 500ml soft drink and the number sold (x). The formula is x = ap + b where a and b are constants. At N$20 she sells 1500 of the 500ml soft drinks but the quantity sold falls by 200 of the 500ml soft drinks when she increases the price by 50%. At what price will 600 of the 500ml energy drinks be sold?
Answer: 600 of the 500ml energy drinks be sold be sold at $45
Step-by-step explanation:
The linear relationship between the price (p) of 500ml soft drink and the number sold (x) is expressed as
x = ap + b
At N$20 she sells 1500 of the 500ml soft drinks. This means that the first equation would be
1500 = 20a + b - - - - - - - - -1
the quantity sold falls by 200 of the 500ml soft drinks when she increases the price by 50%. This means that the new quantity sold is 1500 - 200 = 1300
The price at which they were sold is
20 + (50/100 × 20) = $30
The second equation would be
1300 = 30a + b - - - - - - - - -2
Subtracting equation 2 from equation 1, it becomes
200 = - 10a
a = 200/- 10 = - 20
Substituting a = - 20 into equation 2, it becomes
1300 = 10 × - 20 + b
1300 = - 200 + b
b = 1300 + 200 = 1500
The linear relationship becomes
x = - 20p + 1500
If x = 600, then
600 = - 20p + 1500
- 20p = 600 - 1500 = - 900
p = - 900/ - 20
p = $45
PLEASE ANSWER THIS , I WILL MAKE U BRAINLIEST IF RIGHT
Answer:
hope this helps you
Lindsay needs to make some house repairs in four years that will cost $8,000. She has some money in an account earning 8% annual interest. How much money needs to be in the account today so she will have enough to pay for the repairs
Answer:
$5,882
Step-by-step explanation:
To calculate the money Lindsay needs today, you can use the following formula to calculate the present value:
PV=FV/(1+i)^n
PV= present value
FV= future value= $8,000
i= interest rate= 8%
n= number of periods= 4
PV= 8,000/(1+0.08)^4
PV=8,000/1.08^4
PV=8,000/1.36
PV= 5,882
According to this, Lindsay will need to have $5,882 in the account today so she will have enough to pay for the repairs in four years.
NEED THE ANSWER PLS TIMER
Angela was given this expression to simplify. Negative 2 (2 x + 1) minus 3 (x + 3). Consider her steps in simplifying: 1. Negative 2 (2 x) + (negative 2) (1) + negative 3 (x) + (negative 3) (3). 2. Negative 4 x + negative 2 + negative 3 x + negative 9. 3. Negative 7 x minus 11.
Which statements are true about the steps Angela used? Check all that apply.
In step 1, she distributed –2 through the parentheses.
In step 1, she distributed 3 through the parentheses.
In step 2, she added the factor to the value inside the parentheses.
In step 2, she multiplied the factor to the value inside the parentheses.
In step 3, she combined like terms.
9514 1404 393
Answer:
In step 1, she distributed –2 through the parentheses.In step 1, she distributed 3 through the parentheses.In step 2, she multiplied the factor to the value inside the parentheses.In step 3, she combined like terms.Step-by-step explanation:
In step 1 Angela used the distributive property to eliminate both sets of parentheses. In step 2, she found each of the products she indicated in step 1. In step 3, she combined like terms.
Answer:
the answer is a,d,e
Step-by-step explanation:
A rhombus is a quadrilateral with four congruent sides. The perimeter of rhombus WXYZ is less than 32 inches. Which inequality can be used to find all possible side lengths, s, for rhombus WXYZ? s squared greater-than 32 s squared less-than 32 4 s less-than 32 4 s greater-than 32
Answer:
4s< 32
Step-by-step explanation:
Congruent sides mean they are all the same length
Let the length be s
Perimeter means add the sides
s+s+s+s < 32
4s< 32
Answer:
4s>32
Step-by-step explanation:
your welcome dears
Please answer this correctly
Answer:
Set the height of the bar to 5
Step-by-step explanation:
Since there are 5 quantities between 20-29, So set the height up to 5
Leroy is 22 years old. His car averages 31 miles
per gallon. His car payments are $165.32 per
month, and he has 36 more payments to
make. How old will he be when he pays off his
car?
Answer:
he will be 25
Step-by-step explanation:
36 monthly payments left/12 payments a year = 3 years. 22 + 3 = 25
Entrance to a prestigious MBA program in India is determined by a national test where only the top 10% of the examinees are admitted to the program. Suppose it is known that the scores on this test are normally distributed with a mean of 420 and a standard deviation of 80. Parul Monga is trying desperately to get into this program. What is the minimum score that she must earn to get admitted?
Answer:
The minimum score that she must earn to get admitted is 523.
Step-by-step explanation:
As the scores are normally distributed, we can calculate the probability using the z-score.
The distribution has a mean of 420 and a standard deviation of 80.
We have to calculate the z-score z* that satisfies:
[tex]P(z>z^*)=0.1[/tex]
This happens for z*=1.28155.
Then, we can calculate the score as:
[tex]X=\mu+z\cdot\sigma=420+1.28155\cdot 80=420+102.524=522.524[/tex]
What’s the correct answer for this?
Answer:
C
Step-by-step explanation:
Measure of Arc FED = 51+79
= 130°
Since the measures of arcs and angles are the same
Hence
<FED = 130°
What is the value of p ?????
Answer:
d) 50
Step-by-step explanation:
40 + 90 + p = 180
p = 50
Ania kupiła w księgarni dwie książki i zapłaciła 37,20, a jurek za swoje zapłacił trzy razy więcej. Ile zapłacił jurek
Answer:
111.60
Question:
Ania bought two books in a bookstore and paid 37.20, and Jurek paid three times more for his. How much did Jurek pay?
Step-by-step explanation:
This is a question on multiplying decimals by natural numbers.
Number if books bought by Ania = 2
Cost for the two books = 37.20
Jurek paid = 3 times the amount Ania paid
Amount Jurek paid = 3×37.20
To multiply decimals with whole numbers, first multiply without the decimals
3×3720 = 11160
3 has no decimal place
37.20 has 2 decimal place
Therefore the answer would be in two decimal place = 111.60
So 3× 37.2= 111.60
Please answer this correctly
Answer: 363 cm squared
Step-by-step explanation:
So we can split the shape into 1 triangle and 3 rectangles.
We can start with the top right rectangle which is a 4 by 5.
4*5 = 20 cm squared
We can now do the horizontal rectangle. We need to find the dimensions firs by subtracting 4 from 31 to find the length and add 4 and 5 to find the height.
This means the dimensions are 27 by 9.
27 * 9 = 243 cm squared
Now the final square toward the bottom left will be a 10 by 7.
10 * 7 = 70 cm squared.
Now for the final piece is the triangle in the bottom left. We need to first find the height which we can determine by taking the the right hand side values of 10 , 4 and 5 and adding those together then subtracting that number by 13 to get the missing length that will add to 6 to find the height.
10 + 4 + 5 = 19
19 - 13 = 6
6 + 6 = 12
Now that we have the height and base of the triangle we solve for the area.
0.5 * 5 * 12 = 30 cm squared
Now we add all the areas together to find the total area.
20 + 243 + 70 + 30 = 363 cm squared
Classify the following triangle. Check all that apply.
35°
10.1
7
102"
6
O A. Isosceles
O B. Equilateral
O c. Obtuse
O D. Right
O E. Scalene
F. Acute
Answer: obtuse and scalene
Step-by-step explanation:
Answer:
Obtuse And Scalene
Step-by-step explanation:
trust me!
~I will mark as BRANLIEST and give you 55 points if you answer correctly.
Answer:
The lines would intersect at: (6, -4)
Step-by-step explanation:
I graphed both lines.
Answer:
(4,-2)
Step-by-step explanation:
The equation for the graphed line is [tex]y=\frac{1}{2} x-4[/tex] as it has a slope of [tex]\frac{1}{2}[/tex] and a y-intercept of -4.
Now that we have the two equations, we can set them equal to each other to find the x-value at which they intersect
[tex]\frac{1}{2} x-4=-x+2[/tex]
First, we can add 4 to each side
[tex]\frac{1}{2} x=-x+6[/tex]
Then we can add x to each side
[tex]\frac{3}{2} x=6[/tex]
Now we need to divide both side by [tex]\frac{3}{2}[/tex], which is the same thing as multiplying by [tex]\frac{2}{3}[/tex]
[tex]x=6*\frac{2}{3} \\\\x=\frac{12}{3} \\\\x=4[/tex]
Now that we have the x-value, we can plug it into one of the equations to see the y-value for where they intersect.
[tex]y=-x+2\\\\y=-(4)+2\\\\y=-2[/tex]
This means that the coordinates for the intersection of these two lines would be [tex](4,-2)[/tex]
Dustin is buying carpet for the living room. How many square feet of carpet will he need to buy?
Complete Question:
Dustin is buying carpet for the living room. If the length of the room is 21 ft and the width
is 11 ft, how many square feet of carpet does he need to buy?
Answer:
231 ft²
Step-by-step explanation:
==>GIVEN:
Length of room (L) = 21 ft
Width of room (W) = 11 ft
==>REQUIRED:
Square feet of carpet to be bought = area of the rectangular room
==>SOLUTION:
The room to be covered with carpet is rectangular in shape. In order to ascertain the square feet of carpet to be bought, we need to calculate the area of the room by using the formula for area of rectangle.
Thus, area of rectangle (A) = Length (L) × Width (W)
A = 21 × 11
A = 231 ft²
Square feet of carpet to be bought = 231 ft²
A tank contains 24 gallons of water when all of a sudden the water begins draining at a constant rate of 2 gallons per hour. Let t represent the number of hours since the water began draining and let v represent the volume of water in the tank.
Required:
a. Write a formula that expresses v in terms of t.
b. As t increases from 3 to 6, v varies from _________ to _________
Answer:
a) [tex]V(t) = 24 - 2t[/tex]
b) As t increases from 3 to 6, v varies from 18 gallons to 12 gallons.
Step-by-step explanation:
The volume of the tank in terms of the time can be described by the following equation:
[tex]V(t) = V(0) - at[/tex]
In which V(0) is the initial volume and a is the hourly decrease rate.
a. Write a formula that expresses v in terms of t.
The tank initially contains 24 gallons of water, which means that [tex]V(0) = 24[/tex]
Drains at a constant rate of 2 gallons per hour, so [tex]a = 2[/tex]
Then
[tex]V(t) = V(0) - at[/tex]
[tex]V(t) = 24 - 2t[/tex]
b. As t increases from 3 to 6, v varies from _________ to _________
[tex]V(t) = 24 - 2t[/tex]
[tex]V(3) = 24 - 2*3 = 18[/tex]
[tex]V(6) = 24 - 2*6 = 12[/tex]
So as t increases from 3 to 6, v varies from 18 gallons to 12 gallons.
Show that an implicit solution of 2x sin2(y) dx − (x2 + 10) cos(y) dy = 0 is given by ln(x2 + 10) + csc(y) = C. Differentiating ln(x2 + 10) + csc(y) = C we get 2x x2 + 10 + dy dx = 0 or 2x sin2(y) dx + dy = 0. Find the constant solutions, if any, that were lost in the solution of the differential equation. (Let k represent an arbitrary integer.)
Answer:
Step-by-step explanation:
[tex]2xsin(2y)dx-(x^2+10) cosy dy =0\\\\\frac{2x}{x^2 + 10}dx= \frac{cosy}{sin(2y)}[/tex]
Take integration both side (apply substitution for the left hand side, apply sin(2y) = 2 sin(y) cos(y) for the right hand side) you will have the condition.
Problem solved
Select all fractions that are equal to 3/4
3/4, 6/8, 9/12, 12/16 , 15/20, 18/24, 21/28, 24/32 , 27/36, 30/40, 33/44, 36/48 , 39/52, 42/56, 45/60, 48/64 , 51/68, 54/72, 57/76, 60/80, ect..
I hope this is what you are looking for :)
Solve for m:
-3(1 – 5m) = — 38 + 8m
Answer:
m = - 5
Step-by-step Explanation:
[tex]-3(1-5m)=-38+8m \\ \\ - 3 + 15m = - 38 + 8m \\ \\ 15m - 8m = 3 - 38 \\ \\ 7m = - 35 \\ \\ m = \frac{ - 35}{7} \\ \\ \huge \purple{ \boxed{m = - 5}}[/tex]
Answer:
-5
Step-by-step explanation:
Find the volume of the cone.
Please help
Answer:1232m^3
Step-by-step explanation:
1/3 *22/7*7^2*24
1232m^3
Which is the graph of f(x) = 2(3)^x?
Answer: The graph is:
Oliver had $43 on the day before his birthday. After he received some money for his birthday, he had $68. Write an equation to find how much money Oliver received for his birthday.
Answer:
$25
Step-by-step explanation
If oliver had $43 before his birthday he was given (+) an amount of money, in order to find out how much money was given you need to reverse the equation (-) $68-$43= $25
Simplify (1+√3) (2-√3).
Answer:
[tex] \sqrt{3} - 1[/tex]
Step-by-step explanation:
[tex](1 + \sqrt{3} )(2 - \sqrt{3} ) \\ 2 - \sqrt{3} + 2 \sqrt{3} - 3 \\ = \sqrt{3} - 1[/tex]
Q 4.6: In a survey of 1,000 adults living in a big city, 540 participants said that they prefer to get news from the Internet, 330 prefer to watch news on TV, and 130 are rarely interested in the current news. We want to test if the proportion of people getting the news from the Internet is more than 50%. By generating the randomization distribution, we find that the p-value is 0.0057. Choose the correct statement interpreting the p-value.
Answer:
Option E is correct.Step-by-step explanation:
In a survey of 1,000 adults living in a big city, 540 participants said that they prefer to get news from the Internet, 330 prefer to watch news on TV, and 130 are rarely interested in the current news. We want to test if the proportion of people getting the news from the Internet is more than 50%. By generating the randomization distribution, we find that the p-value is 0.0057. Choose the correct statement interpreting the p-value.
A.If the proportion of people getting the news from the Internet is not equal to 0.5 then there is a 0.0057 chance of seeing the sample proportion as extreme as the survey results.
B. If the proportion of people getting the news from the Internet is not equal to 0.54 then there is a 0.0057 chance of seeing the sample proportion as extreme as the survey results.
C. If the proportion of people getting the news from the Internet is equal to 0.54 then there is a 0.0057 chance of seeing the sample proportion less extreme compared to the survey results. р
D. If the proportion of people getting the news from the Internet is equal to 0.54 then there is a 0.0057 chance of seeing the sample proportion as extreme as the survey results.
E. If the proportion of people getting the news from the Internet is equal to 0.5 then there is a 0.0057 chance of seeing the sample proportion as extreme as the survey results.
The correct interpretation of P value will be:
if the proportion of people getting the news from internet is equal to 0.5 then there is a 0.0057 chance of seeing the sample proportion as extreme as survey results.
Option E is correct.