Answer:
a) 12/24 * 11/24*10/24
b) 1 - 12/24 * 11/24*10/24
c) 12/24 * 11/24 *12/24
Step-by-step explanation:
Total number of bottles = 12 + 5+7 = 24
a. The probability that all (exactly three) bottles are strawberry flavored is: 212
12/24 * 11/24*10/24
b. The probability that at least one of the three bottles are strawberry flavored is:
1 - P (no strawberry bottle)
1 - (12/24*11/24*10/24)
c. The probability that exactly 2
12/24 * 11/24 *12/24
calculate the interest paid when 4920 is invested at 13% p.a simple interest for eight years
Answer:
I'll setup the problem and you can do the calculations
Step-by-step explanation:
The formula for simple interest:
I = P*r*t
I = interest
P = principle or amount invested
r = interest rate per period (period is a year)
t = number of periods
P = 4920
r = .13
t = 8
if you have questions, send a comment
Here we have been provided with the principal , rate of interest and time period for which the sum of rupees is invested.
Principal (P) = Rs.4920Rate (r) = 13% Time (T) = 8 yearsNow here we know that simple Interest is calculated by the formula,
[tex]\bf{\boxed{\bf{S.I.\: = \: \dfrac{P \times R \times T}{100}}}} \: \red\bigstar[/tex]Here in this formula,
P is PrincipalR is rate of interestT is timePutting there values in the formula,
[tex]\longrightarrow \: \sf{S.I. \: = \: \dfrac{4920 \times 13 \times 8}{100} }[/tex]
[tex]\longrightarrow \: \sf{S.I. \: = \: \dfrac{492 \times 13 \times 8}{10} }[/tex]
[tex]\longrightarrow \: \sf{S.I. \: = \: \dfrac{492 \times 13 \times \cancel{8}}{ \cancel{10}} }[/tex]
[tex]\longrightarrow \: \sf{S.I. \: = \: \dfrac{492 \times 13 \times 4}{ 5} }[/tex]
[tex]\longrightarrow \: \sf{S.I. \: = \: \dfrac{492 \times 52}{ 5} }[/tex]
[tex]\longrightarrow \: \sf{S.I. \: = \: \dfrac{25584}{ 5} }[/tex]
[tex] \longrightarrow \: \sf{S.I. \: = \: \cancel\dfrac{25584}{ 5} }[/tex]
[tex] \longrightarrow \: \orange{\boxed{\bf{S.I. \: = \: 5116.8}}}[/tex]
[tex]\underline{\bf{Henceforth, \: interest \: paid \: is \: of \: Rs.5116.8}}[/tex]
Use the table, which shows the number of pounds of skim milk, y , consumed per
person in the United States in year x. Let x represent the number of years since
1980.
a. Use the model y = 2x + 23 to estimate the number of pounds
consumed in 1994. Is this linear interpolation or linear
extrapolation?
b. Use the model y = 2x + 23 to estimate the number of pounds consumed in
1999. Is this linear interpolation or linear extrapolation?
x y
1980 26.9
1985 27.4
1990 42.8
1992 46.2
1995 53.9
1996 55.7
Answer:
Step-by-step explanation:
the formula doesn't work for the answers shown,
y = 2x +23 for 1980 should be 23 not 26.9
something is missing in your question
Find the missing angle measurement.
Answer:
54°
Step-by-step explanation:
54°
Answer:
the missing angle is 54
Step-by-step explanation:
so first we need two triangle angles to get our measurement and we know straight lines add up to 180 so
180-123=57
57+69(other angle)=126
all triangle angles add up to 180 so subtract the two other angles to get your result
180-126=54
54 is your anwser
What is the sum of the rational expressions below?
15/7x+12/7x
Answer:
27 / (7x)
Step-by-step explanation:
Since the denominators are the same, we can add the numerators
15 12
----- + ---------
7x 7x
27
----
7x
Interpret the results of the chi-square test.A die is rolled 180 times and the following data are obtained.Number Frequency 1 31 2 34 3 26 4 16 5 32 6 41A chi-square test was conducted to determine, at the 5% significance level, whether or not the die is loaded (i.e., that the six numbers are not equally likely).Carry out the hypothesis test.
Answer:
Step-by-step explanation:
From the given information:
Null and alternative hypothesis is:
[tex]\mathbf{H_o: \text{The die is not loaded i.e. six numbbers are equally alike}}[/tex]
[tex]\mathbf{H_a: \text{The die is loaded i.e. six numbbers are not equally alike}}[/tex]
Numbers Observed Expected (O - E) (O-E)^2 (O-E)^2/E
Frequency (O) Frequency (E)
1 31 30 1 1 0.03
2 34 30 4 16 0.53
3 26 30 -4 16 0.53
4 16 30 -14 196 6.53
5 32 30 2 4 0.13
6 41 30 11 121 4.03
Total 180 [tex]X^2= \sum (\dfrac{O-E}{E})^2=11.78[/tex]
degree of freedom = n - 1
= 6 - 1
= 5
Critical value at [tex]X^2_{0.05/2,5} =11.07[/tex]
Since the calculated [tex]X^2 \ is \ > X^2_{0.025/5}[/tex] , then we reject [tex]H_o[/tex]
Conclusion: Accept the alternative hypothesis.
The information provided gives sufficient evidence for us to conclude that the given die is loaded.
Two similar trapezoids have areas 225 and 400. If the height of the smaller trapezoid is 12, find the height of the larger trapezoid.
Answer:
Step-by-step explanation:
HELP ME WITH THIS QUESTION PLEASE!!
Answer:
give me a heart first and then ill answer
Step-by-step explanation:
You deposit $200 each year for 10 years into a sinking fund that pays 6% interest compounded annually what is the future value of your fund
Answer:
FV= $2,636.16
Step-by-step explanation:
Giving the following information:
Annual deposit (A)= $200
Number of periods (i)= 10 years
Interest rate (i)= 6%
To calculate the future value, we need to use the following formula:
FV= {A*[(1+i)^n-1]}/i
A= annual deposit
FV= {200*[(1.06^10) - 1]} / 0.06
FV= $2,636.16
A pyramid and a cone are both 10 centimeters tall and have the same
volume. What statement must be true about the two solids?
A. The vertical cross-sections of the pyramid and cone at the same
width must have the same area.
B. The cross-sections of the pyramid and cone are the same shape.
C. The area of the cross-sections of the pyramid and cone are
multiples of each other.
D. The horizontal cross-sections of the pyramid and cone at the
same height must have the same area.
Answer:
D the horizontal cross-section of the pyramid and cone at the same height must have the same area
The coordinates for three vertices of a rectangle are (0٫4)٫(8٫4) and (8٫1). What is the coordinates of the fourth vertex ? A : (1٫0) B : (8٫0) ٫ C : (0٫1) D : (0٫8)
Answer:
(0, 1): Answer D
Step-by-step explanation:
The three given vertices are (0٫ 4)٫(8٫ 4) and (8٫ 1). Note that the x-coordinates of two of these are both 8. The remaining x-coordinate of the fourth vertex is 0. Since the figure is a rectangle, there are two sets of parallel sides. If one side is x = 8, the opposite vertical side must be x = 0, since the remaining coordinate is 0. This side is a vertical line segment. The fourth and last vertex is at the intersection of x = 0 and y = 1; (0, 1): Answer D.
Simplify 5√-32
a.-2
b.-4
c.2
d.16
IF YOU HELP ME ILL give U 2$ AFTER UR DONE
Triangle ABC is defined by the points A(-2, 4), B(6,2), and C(1,-1). Using what you know about the distance formula, what type of triangle would ABC be?
Answer:
LOL i dont need money jus mark me brainliest :P
Step-by-step explanation:
[tex]distance = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]
[tex]AB = \sqrt{(6--2)^2 + (2-4)^2} = \sqrt{8^2 + 2^2} = \sqrt{68}\\\\BC = \sqrt{(1-6)^2 + (-1-2)^2} = \sqrt{5^2 + 3^2} = \sqrt{34}\\\\AC= \sqrt{(1--2)^2 + (-1-4)^2}} = \sqrt{3^2 + 5^2 } = \sqrt{34}[/tex]
[tex]Clearly, this\ satisfies \ the\ Pythagoras\ theorem : AC^2 = AB^2 + BC^2[/tex]
[tex](\sqrt{68})^2 = (\sqrt{34} )^2 + (\sqrt{34} )^2\\\\68 = 34 + 34 \\68 = 68\\Hence\ satisfies .[/tex]
Therefore, the triangle ABC is a right angle triangle.
Handrail should be mounted 34 inches minimum and 38 inches maximum above ramps. Which inequality represents the required height?
Answer:
[tex]34 \leq x \leq 38[/tex]
Step-by-step explanation:
34 inches minimum
This means that x has to be at least 34, that is:
[tex]x \geq 34[/tex]
38 inches maximum
This means that x can be at most 38, that is:
[tex]x \leq 38[/tex]
Which inequality represents the required height?
The intersection of 34 minimum and 38 maximum is:
[tex]34 \leq x \leq 38[/tex]
1st Coordinate Point: (1.4)
2nd Coordinate Point: ( 6 , 6)
(X,Y,) =
(X,Y)=
M = (Y-Y.) =(X-X)
Can someone please help me on this work I really need help I will but you brainly
Answer:
-3 1/4 is the answer for this question
An elevator has a placard stating that the maximum capacity is 1610 lb---10 passengers. So, 10 adult male passengers can have a mean weight of up to 1610 divided by 10 = 161 pounds. If the elevator is loaded with 10 adult male passengers, find the probability that it is overloaded because they have a mean weight greater than 161 lb. (Assume that weights of males are normally distributed with a mean of 165 Ib and a standard deviation of 35 lb). Does this elevator appear to be safe?
The probability the elevator is overloaded is:____.
Answer:
The probability is "0.6406", this elevator isn't appear to be safe
Step-by-step explanation:
The given values are:
Mean,
[tex]\mu=165[/tex]
Standard deviation,
[tex]\sigma=35[/tex]
Number of male passengers,
[tex]n = 10[/tex]
Now,
⇒ [tex]z=\frac{161-165}{\frac{\sigma}{\sqrt{10} } }[/tex]
[tex]=\frac{161-165}{\frac{35}{\sqrt{10} } }[/tex]
hence,
The probability will be:
= [tex]P(\bar {x}>161)[/tex]
= [tex]P(z > -0.3614)[/tex]
= [tex]0.6406[/tex]
High school students from track teams in the state participated in a training program to improve running times. Before the training, the mean running time for the students to run a mile was 402 seconds with standard deviation 40 seconds. After completing the program, the mean running time for the students to run a mile was 368 seconds with standard deviation 30 seconds. Let X represent the running time of a randomly selected student before training, and let Y represent the running time of the same student after training. Which of the following is true about the distribution of X-Y?a. The variables X and Y are independent, therefore, the meanis 34 seconds and the standard deviation is 10 seconds.b. The v ales X and Y are independent therefore, the meanis 34 seconds and the standard deviation is 50 secondsc. The variables X and Y are not independent, therefore, the standard deviation is 50 seconds and the mean cannot be determined with the information given.d. The variables and are not independent, therefore, the meanis 3 seconds and the standard deviation cannot be determined with the information givene. The variables X and Y We not independent, therefore, neither the mean nor the standard deviation can be determined with the informantion given.
Answer:
b. The values X and Y are independent therefore, the mean is 34 seconds and the standard deviation is 50 seconds
Step-by-step explanation:
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Before the training, the mean running time for the students to run a mile was 402 seconds with standard deviation 40 seconds.
This means that [tex]\mu_X = 402, \sigma_X = 40[/tex]
After completing the program, the mean running time for the students to run a mile was 368 seconds with standard deviation 30 seconds.
This means that [tex]\mu_Y = 368, \sigma_Y = 30[/tex]
Which of the following is true about the distribution of X-Y?
They are independent, so:
[tex]\mu = \mu_X - \mu_Y = 402 - 368 = 34[/tex]
[tex]\sigma = \sqrt{\sigma_X^2+\sigma_Y^2} = \sqrt{40^2+30^2} = 50[/tex]
This means that the correct answer is given by option b.
The values X and Y are independent therefore, the mean is 34 seconds and the standard deviation is 50 seconds.
What is the subtraction between normal variables?
The two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Before the training, the mean running mean time for the students to runing a mile was 402 seconds with standard deviation 40 seconds.
That is the [tex]\mu_x=402 , \sigma_x=40[/tex]
That is the after completing the program, the mean running time for the students to run a mile was 368 seconds with standard deviation 30 seconds.
That is [tex]\mu_y=368,\sigma_y=30[/tex]
which of the following is true about the distribution of X-Y?
They are independent
Therefore we get,
[tex]\mu=\mu_x-\mu_y=402-368=34[/tex]
[tex]\sigma=\sqrt{\sigma_x^2-\sigma_y^2}\\\sigma=\sqrt{40^2-30^2}\\\sigma =50[/tex]
Therefore the option b is correct.
To learn more about the distribution visit:
https://brainly.com/question/24756209
This means that the correct answer is given by option b.
Jane and her friend Maria both invest in the stock market. The probability that Jane makes money in a given week is .6. The probability that Jane and Maria both make money in a given week is .48. What is the probability that Maria makes money in a given week if Jane also makes money in that same week
Answer:
.8
Step-by-step explanation:
Probability is the ratio of the number of possible outcome to the number of total outcome.
Given that the probability that Jane makes money in a given week is .6 and the probability that Jane and Maria both make money in a given week is .48. Then the probability that Maria makes money in a given week...
Let the probability that Jane makes money in a given week be p(j) and that Maria makes money in a week be p(m) then
p(j) = .6 and
p(j) * p(m) = .48
.6 * p(m) = .48
p(m) = .48/.6
= .8
An airline promotion to business travelers is based on the assumption that no more than two-thirds of business travelers use a laptop computer on overnight business trips. a. State the hypotheses that can be used to test the assumption. H 0: p Select H a: p Select b. What is the sample proportion from an American Express-sponsored survey that found 359 of 535 business travelers use a laptop computer on overnight business trips (to 4 decimals)?
Answer:
a) The null hypothesis is [tex]H_0: p \leq \frac{2}{3}[/tex] and the alternate hypothesis is [tex]H_1: p > \frac{2}{3}[/tex].
b) The sample proportion is 0.6710.
Step-by-step explanation:
Question a:
An airline promotion to business travelers is based on the assumption that no more than two-thirds of business travelers use a laptop computer on overnight business trips.
At the null hypothesis, we test if the proportion is two-thirds or less, that is:
[tex]H_0: p \leq \frac{2}{3}[/tex]
At the alternate hypothesis, we test if the proportion is of more than two-thirds, that is:
[tex]H_1: p > \frac{2}{3}[/tex]
b. What is the sample proportion from an American Express-sponsored survey that found 359 of 535 business travelers use a laptop computer on overnight business trips (to 4 decimals)?
359 out of 535 is 359/535 = 0.6710.
The sample proportion is 0.6710.
given the number line which inequality has the solution shown below
0.4x + 7 < 1
0.5x + 6 > 3
0.3x + 8 < 3
0.2x + 5 > 2
Answer:
D
Step-by-step explanation:
When you simplify the expression you start by subtracting 5 from both sides. This gives you 0.2x > -3. Then to isolate "x" you divide both sides by 0.2. This gives you x > -15, which is shown in the number line.
I will make you brainlist
Answer:
for what? do you need a question answered?
I have 3 pictures please check them out
Point C(6, 10) is dilated and end up at the image pointC C(10.5, 17.5) . What was the scale factor that was used for the dilation?
Answer:
Step-by-step explanation:xyyxxyduxuxifg icicuddididif uicidididciifificvidid idodididix ididididix ifidididix
A sphere and a cylinder have the same radius and height. The volume of the cylinder is 18 cm
What is the volume of the sphere?
Answer:
12 cm³
Step-by-step explanation:
the volume of the sphere = 4/3 πr³
the volume of the cylinder (h=2r)= πr².2r
= 2πr³
the volume ratio of S : C =
4/3 πr³ : 2 πr³
= 4/3 : 2
= 4 : 6
= 2 : 3
so, the volume of the Sphere =
2/3 × 18 = 12 cm³
Answer:
Solution given:
radius [r]=height[h]
volume of cylinder=πr²h
18cm³=πr³
again
volume of sphere
=4/3 πr³
=4/3*18=24cm³
the volume of the sphere:24cm³
100 POINTS IF YOU GUESS RIGHT PLEASE HELP
Answer:
5 and 3Step-by-step explanation:
Let the numbers be x and y.
We have:
x + y = 8x - y = 2Sum the two and find x:
2x = 10x = 5Find y:
y = 5 - 2y = 3Let the numbers be a and b
a+b=8a-b=2Add both
2a=10a=5Put in first one
5+b=8b=3Which choices are equivalent to the fraction below? Check all that apply.
Answer:
Step-by-step explanation:
It's A and B happy learning
Use the angle relationship in the figure below to solve for x. Assume that lines a and b are parallel and the given angles are given in degrees.
9514 1404 393
Answer:
x = 5°
Step-by-step explanation:
The marked angles are "alternate exterior angles," hence congruent.
2x +90° = x +95°
x = 5° . . . . . . . . . . . . subtract (x+90°) from both sides
There are______
Pairs of integers satisfying a÷b = -2
Answer:
There are only 1
Pairs of integers satisfying a÷b = -2
Step-by-step explanation:
Answer:
[tex]all \: positive \: integers \: in cluding \: 1[/tex]
so I dont really know how many
Step-by-step explanation:
eg
[tex] \frac{ - 2}{1} \\ \frac{ - 4}{2} \\ \frac{6}{ - 3} \\ = - 2[/tex]
they are all equal to negative 2
The greatest power failure in the history of Dallas, Texas lasted
13 hours. How many minutes did this power failure last?
Answer:
its 780 minutes
Step-by-step explanation:
multiply 13 by 60
Simplify the expression. Write your answer as a power.
(3.8^3)^4
The simplified expression is
What is the radius of a sphere with a volume of 62770 m, to the nearest tenth of a
meter?
Answer:
24.65
Step-by-step explanation: