Answer:
3/11
Step-by-step explanation:
In the above question, we have the following information
Total number of balls = 12
White balls = 4
Blue balls = 3
Red balls = 5
We are to find the chance of probability that if we select 3 balls, all the three are selected.
Hence,
Probability ( all the three balls are selected) = P(White ball) × P(Blue ball) × P( Red ball)
Probability ( all the three balls are selected) = 4/12 × 3/11 × 5/10
= 60/1320
= 1/22
The number of ways by which we can selected all the three balls is a total of 6 ways:
WBR = White, Blue, Red
WRB = White, Red, Blue
RBW = Red, Blue, White
RWB = Red, White, Blue
BRW = Blue, Red, White
BWR = Blue, White, Red
Therefore, the chance that all three are selected :
1/22 × 6 ways = 6/22 = 3/11
48. A map is drawn to a scale of 1cm to represent 50km. If the actual distance between two villages is 480km, what is the distance on the map?
Set up a ratio:
1/50 = x/480
Cross multiply:
50x = 480
Divide both sides by 50:
X = 9.6
The distance on the map is 9.6 cm
The red blood cell counts (in millions of cells per microliter) for a population of adult males can be approximated by a normal distribution, with a mean of million cells per microliter and a standard deviation of million cells per microliter. (a) What is the minimum red blood cell count that can be in the top % of counts? (b) What is the maximum red blood cell count that can be in the bottom % of counts?
Answer:
(a) Minimum red blood cells 5.744 million cells per micro liter
(b) Maximum red blood cells 5.068 million cells per micro liter.
Step-by-step explanation:
Z-score formula is = [tex]\frac{x-u}{Standard deviation}[/tex]
Z-score = [tex]\frac{x-5.5}{0.4}[/tex]
The value of z-score is 0.61 so then x will be;
x = 5.744
The minimum red blood cells count that can in top is 27% of count which is 5.744 million cells per micro liter.
Z-score = [tex]\frac{x-5.5}{0.4}[/tex]
The value of z-score is 0.14 so then x will be;
x = 5.068
The maximum red blood cells count that can be in top is 14% of count which is 5.068 million cells per micro liter.
(PLEASE HELP ITS URGENT)
What is the measure of angle x?
A) 60°
B) 30°
C) 45°
D) 90°
Answer:
B
Step-by-step explanation:
Reason...sum of angles in a triangle is equal to 180⁰
R+V+T=180⁰
60⁰+90⁰+x⁰=180⁰
150⁰+x⁰=180⁰
x⁰=180⁰-150⁰
:. x⁰=30⁰
===================================================
Explanation:
Ignore lines VS and SU. They're unnecessary clutter.
Triangle VRT is a right triangle with angles T = x, R = 60, V = 90
For any triangle, the angles must add to 180
T+R+V = 180
x+60+90 = 180
x+150 = 180
x = 180-150
x = 30
Or you could note that R+T = 90 Solves to T = 30 since triangle VRT is a right triangle. The rule with any right triangle is that the acute angles are always complementary (aka they add to 90 degrees).
Help me out!! Anyone
Answer:
4:10
Step-by-step explanation:
if they have to wait for plane B and it arrives every 10 mins then 4:10 is the anser
Someone help again:/
Determine two pairs of polar coordinates for the point (4, -4) with 0° ≤ θ < 360°.
Answer:
[tex] \sqrt{4 {}^{2} + ( - 4) {}^{2} } [/tex]
[tex] \sqrt{32} [/tex]
and the angle
[tex] \tan( \alpha ) = - 4 \div 4 = - 1[/tex]
and since the sin component is -ve, we have our angle on 4th quadrant, which equals 315 degrees
Options:
Determine two pairs of polar coordinates for the point (-4, 4) with 0° ≤ θ < 360°. (5 points)
Group of answer choices
(4 , 135°), (-4 , 315°)
(4 , 45°), (-4 , 225°)
(4 , 315°), (-4 , 135°)
(4 , 225°), (-4 , 45°)
Step-by-step explanation:
The guy asking forgot to provide the options you can comment the awnswe in the comments just do it before brainly turns off comments to try and prevent people from learning
−(−49) = −49 true or false?
Use the distributive property to write an
expression that is equivalent to each expression. If
you get stuck, consider drawing boxes to help
organize your work.
D. 8(-x-1/2)
e. -8(-x-3/4y+7/2
Answer:
D. -8x-4
E. 8x+6y-28
Step-by-step explanation:
D. 8(-x-1/2) = -8x-4
E. -8(-x-3/4y+7/2 = 8x+6y-28
Suppose that a box contains 6 cameras and that 3 of them are defective. A sample of 2 cameras is selected at random. Define the random variable X as the number of defective cameras in the sample. Write the binomial probability distribution for X . Round to two decimal places.
Answer:
X ~ Binom (n = 6, p = 0.50)
Step-by-step explanation:
We are given that a box contains 6 cameras and that 3 of them are defective.
A sample of 2 cameras is selected at random.
Let X = Number of defective cameras in the sample.
The above situation can be represented through binomial distribution;
[tex]P(X=r)= \binom{n}{r}\times p^{r} \times (1-p)^{n-r} ;x = 0,1,2,3,......[/tex]
where, n = number of trials (samples) taken = 2 cameras
x = number of success
p = probabilitiy of success which in our question is probability that
cameras are defective, i.e. p = [tex]\frac{3}{6}[/tex] = 0.50
So, X ~ Binom (n = 2, p = 0.50)
Now, the binomial probability distribution for X is given by;
[tex]P(X=r)= \binom{6}{r}\times 0.5^{r} \times (1-0.5)^{6-r} ;r = 0,1,2[/tex]
Here, the number of success can be 0, 1, or 2 defective cameras.
Help please!!! Tyyyyy
Answer:
D) 60 degree
Step-by-step explanation:
Let's connect the remaining diagonal, which forms a triangle containing angle x.
As a property of regular hexagon, all diagonals are equal.
=> The formed triangle is a regular triangle and it has three equal angles, which are 60 degrees.
Find x.
60°
45°
6
—————
Answer:
Step-by-step explanation:
Melissa, Brian, and shen have a total of $85 in their wallets. Brian has 3 times what Shen has. Shen has $10 less than Melissa. How much do they have in their wallets?
Answer:
Shen has $15, Brian has $45, and Melissa has $25
Step-by-step explanation:
Let x represent how much money Shen has.
Since Brian has 3 times what Shen has, his amount can be represented by 3x.
Since Shen has $10 less than Melissa, Melissa's amount can be represented by x + 10.
Create an equation to represent the situation, and solve for x:
x + 3x + x + 10 = 85
5x + 10 = 85
5x = 75
x = 15
So, Shen has $15 in their wallet.
Find how much Brian has by multiplying this by 3:
15(3) = $45
Find how much Melissa has by adding 10 to this:
15 + 10 = $25
Shen has $15, Brian has $45, and Melissa has $25.
What is the volume of a sphere, to the nearest cubic inch, if the radius is 16 inches? Use π = 3.14.
Answer:
vol = 17,148 cu. in.
Step-by-step explanation:
vol = 4 / 3 * pi * r³
vol = 4 / 3 *3.14 * 16³
vol = 17,148 cu. in.
Answer:
The answer is
17149 cubic inchesStep-by-step explanation:
Volume of a sphere is given by
[tex]V = \frac{4}{3} \pi {r}^{3} [/tex]
where r is the radius of the sphere
π = 3.14
From the question
r = 16 inches
Volume of the sphere is
[tex]V = \frac{4}{3} (3.14) {16}^{3} [/tex]
V = 17148.586
We have the final answer as
V = 17149 cubic inches to the nearest cubic inch
Hope this helps you
A recent survey of 1090 U.S. adults selected at random showed that 623 consider the occupation of firefighter to have very great prestige. Estimate the probability (to the nearest hundredth) that a U.S. adult selected at random thinks the occupation of firefighter has very great prestige.
Answer:
0.572
Step-by-step explanation:
From the question,
We have
n = 1090 of US adults
x = 623 selected from this population at random who consider the occupation to be one of great prestige
So we have that
The probability of X = x/n
= 623/1090
= 0.572
We conclude that 0.572 is the probability that a US adult selected at random thinks the occupation has great prestige.
The movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer
Janet and Michelle begin walking at the same time from the same point. Janet walks directly north, and Michelle walks directly ea
10 km apart, Michelle has walked 2 km farther than Janet has walked. How far has Michelle walked?
08 km
06 km
12 km
10 km
9514 1404 393
Answer:
(a) 8 km
Step-by-step explanation:
Let m represent the distance (in kilometers) Michelle has walked. Then Janet walked a distance of (m-2). These distances are at right angles, so the distance between them can be found using the Pythagorean theorem.
m² +(m -2)² = 10²
m² +m² -4m +4 = 100
2m² -4m = 96 . . . . . . subtract 4, collect terms
m² -2m +1 = 49 . . . . . divide by 2 and add 1
(m -1)² = 7² . . . . . . .write as squares
m -1 = 7 . . . . . . positive square root
m = 8
Michelle walked 8 km.
simplify -3(2g - 6) +4g
-3-2g+6+4g
3+2g
hope it helps
Answer:
-2g + 18
Step-by-step explanation:
-3(2g - 6) + 4g
First we use distributive property.
-3 × 2g = -6g
-3 × -6 = 18
now we have
-6g + 18 + 4g
Now we combine the like terms
-6g + 4g = -2g
Finally we have
-2g + 18
and they are not like terms so we leave them and the equation is solved.
Which compound inequality could this graph be the solution of?
-4 ≤ x ≤ 6
x ≥ -4
3x ≥ -12
3x + 12 ≥ 0
3x + 14 ≥ 2
6 ≥ x
6 - x ≥ 0
1 - x ≥ -5
A. 3x + 14 ≥ 2 and 1 - x ≥ -5
Researchers recorded that a certain bacteria population declined from 450,000 to 900 in 30 hours at this rate of decay how many bacteria will there be in 13 hours
Answer:
30,455
Step-by-step explanation:
Exponential decay
y = a(1 - b)^x
y = final amount
a = initial amount
b = rate of decay
x = time
We are looking for the rate of decay, b.
900 = 450000(1 - b)^30
1 = 500(1 - b)^30
(1 - b)^30 = 0.002
1 - b = 0.002^(1/30)
1 - b = 0.81289
b = 0.1871
The equation for our case is
y = 450000(1 - 0.1871)^x
We are looking for the amount in 13 hours, so x = 13.
y = 450000(1 - 0.1871)^13
y = 30,455
what's the formula for sum of
geometric progression
Answer:
Hello,
Step-by-step explanation:
[tex]u_1\ is\ the \ first\ term\ of\ the\ gp\\q\ is \ the\ common\ ratio\\\\\\\boxed{u_n=u_1*\dfrac{q^n-1}{q-1} }[/tex]
You make 85,000 per year and your company matches 50 cents for every dollar you deposit into your 401k plan, up to 8% of your salary.
Answer:
The question is incomplete, below is a possible match for the complete question:
You make $85,000 per year and your company matches 50 cents for every dollar you deposit into your 401k plan, up to 8% of your salary. Complete parts (a) through (c) below.
(a) If you contribute $200 every month to your 401k, what will your company contribute each month?
The company will contribute $ (Type an integer or a decimal rounded to two decimal places as needed.)
(b) If you contribute $830 every month to your 401k, what will your company contribute each month?
The company will contribute $ (Type an integer or a decimal rounded to two decimal places as needed.)
(c) What is the maximum amount of money the company will contribute to your 401k each year?
The maximum amount that the company will contribute each year is $
(Type an integer or a decimal rounded to two decimal places as needed.)
Answer:
a.) The company will contribute $100
b.) The company will contribute $415
c.) maximum amount the company will be willing to contribute = $6,800 per year
Step-by-step explanation:
First, let us calculate the maximum amount the company will be willing to pay into the 401k plan yearly:
Annual salary = $85,000
Monthly salary = $7083.3333
maximum amount = 8% = 8/100 = 0.08 of salary
maximum amount = 0.08 × 7083.3333 = $566.67
a.) If you contribute $200 every month.
Since $200 is less than the maximum amount that the company will be willing to contribute, let us calculate how much the company is willing to contribute:
Company matches 50 cents for every dollar you deposit
1 dollar deposited = 50 cents from company
but 1 cent = $0.01
∴ 50 cents = 0.01 × 50 = $0.5
$1 deposited = $0.5 from company
∴ $200 deposited = 0.5 × 200 = $100 contributed by company
Therefore, if you contribute $200 every month, your company will contribute $100 each month.
from this example, we can see that the company is willing to contribute half of every amount you deposit every month ($100 = half of $200), hence, subsequently, we will use this for calculations.
b.) If you contribute $830 every month, the company will be willing to contribute half this amount, which is:
half of $830 = 830 ÷ 2 = $415
Therefore, if you contribute $830 per month, your company will contribute $415 per month.
c.) The maximum amount the company will be willing to contribute each year = 8% of salary per year
= [tex]= \frac{8}{100}\times 85,000 \\ =0.08\ \times\ 85,000 = \$6,800[/tex]
Therefore, the company will be willing to contribute $6,800 per year.
What is the radius of the circle whose center is the
origin and that passes through the point (5,12)?
Answer:
13 units
Step-by-step explanation:
Use the equation of a circle, (x - h)² + ( y - k )² = r², where (h, k) is the center and r is the radius.
Plug in the values and solve for r:
(5 - 0)² + (12 - 0)² = r²
25 + 144 = r²
169 = r²
13 = r
. In statistics, a data set has the following characteristics: (Choose all that apply) A:A data set is a collection of similar data. B:A data set can contain only quantitative data. C:A data set is any piece of descriptive or quantitative information on any object of study. D:A data set contains data all of which have some common characteristic.
Answer:
A. A data set is a collection of similar data.
D. A data set contains data all of which have some common characteristic.
At the beginning of a basketball season, the Spartans won 35 games out of 98 games. At this rate, how many games will they win in a normal 116 game season?
Kelvin wants to know whether he skied without falling more than twice as long as anyone else in his family. His dad tells him that he can check by using the inequality 2f < 223, where f is the time skied in seconds for each person. Plug the values for the time skied by each person into the inequality to find the answer.
Lori 55
Vanessa 265
Devon 172
Celia 112
Arnold 356
Answer:
Kelvin did not skied without falling more than twice as long as anyone else in his family.
Step-by-step explanation:
The inequality representing the event where Kelvin skied without falling more than twice as long as anyone else in his family is:
[tex]2f<223[/tex]
Here 223 is the time for Kelvin.
Check for Lori as follows:[tex]2f<223[/tex]
[tex]2\times 55=110<223[/tex]
Kelvin skied without falling more than twice as long as Lori.
Check for Vanessa as follows:[tex]2f<223[/tex]
[tex]2\times 265=530>223[/tex]
Kelvin skied without falling less than twice as long as Vanessa.
Check for Devon as follows:[tex]2f<223[/tex]
[tex]2\times 172=344>223[/tex]
Kelvin skied without falling less than twice as long as Devon.
Check for Celia as follows:[tex]2f<223[/tex]
[tex]2\times 112=224>223[/tex]
Kelvin skied without falling less than twice as long as Celia.
Check for Arnold as follows:[tex]2f<223[/tex]
[tex]2\times 356=712>223[/tex]
Kelvin skied without falling less than twice as long as Arnold.
Thus, Kelvin did not skied without falling more than twice as long as anyone else in his family.
Answer:
Yes, Kevin skied 2x as long as Lori.
Step-by-step explanation:
Kevin's time was 223 seconds; Lori's time was 110 seconds.
110^2 = 220 or 110 multiplied by 2 equals 220 or 110 x 2 = 220 or
110 * 2 = 220
Thus, Kevin indeed, skied twice as long as Lori.
(4m-n-3). 12n13
8m 20
Answer:
24n^7/m^16
Step-by-step explanation:
Just simplify and rewrite what ever you get simplify again 2 times and now make the calculation as you see every big number is a whole number and is a pair.
2
7) through: (-3,0), slope
3
Answer:
Step-by-step explanation:
Point-slope equation for line of slope m that passes through (x₀, y₀):
y-y₀ = m(x-x₀)
Slope =3 and (x₀, y₀)=(-3,0)
y = 3(x+3)
y = 3x+ 9
:::::
Slope-intercept equation for line of slope m and y-intercept b:
y = mx+b
m=1 and b= -4:
y = x-4
The Centers for Disease Control and Prevention (CDC) report that gastroenteritis, or stomach flu, is the most frequently reported type of recreational water illness. Gastroenteritis is a viral or bacterial infection that spreads through contaminated food and water. Suppose that inspectors wish to determine if the proportion of public swimming pools nationwide that fail to meet disinfectant standards is different from 10.7%, which was the proportion of pools that failed the last time a comprehensive study was done, 2008.
A simple random sample of 30 public swimming pools was obtained nationwide. Tests conducted on these pools revealed that 26 of the 30 pools had the required pool disinfectant levels.
Does this sample meet the requirements for conducting a one-sample z ‑test for a proportion?
a. No, the requirements are not met because the population standard deviation is not known.
b. No, the requirements are not met because the sample has fewer than 10 failures, which violates the condition for approximating a normal distribution.
c. No, the requirements are not met because the sample is not random, even though the number of successes and the number of failures are both at least 10, ensuring that the distribution is approximately normal.
d. Yes, the requirements are met because the sample size is more than 30, ensuring that the distribution is approximately normal.
e. Yes, the requirements are met because the number of successes and the number of failures of this random sample are both at least 10, ensuring that the distribution is approximately normal.
b. No, the requirements are not met because the sample has fewer than 10 failures, which violates the condition for approximating a normal distribution.
Step-by-step explanation:
from the question, the number of successes is equal to 30
and it is more than the number of failures
for us to conduct this test such as the z test the data we are using should be a random sample from the population that we are interested in. the population should be at least as big as the sample by 10 times. first of all We need to check if the mean of the sample is normally distributed.
if 26 are successes out of a sample of 30, then failures would be 4. therefore option b is correct.
Are you able to find tri-sector (equally divided by 3) rays for an arbitrary angle with straightedge-and-compass construction?
Answer:
Step-by-step explanation:
No, it is an ancient problem which has been proved to be impossible (in 1837), at least not for an arbitray angle.
However, we can trisect certain angles, such as 90 degrees, but rather than trisection, we are just constructing 30 degree angles.
For further reading, google "angle trisection"
Factor.
x2 - 7x + 10
(x - 10)(x + 1)
(x + 1)(x - 10)
(x - 5)(x - 2)
(x + 5)(x + 2)
Answer:
The answer is option C
Step-by-step explanation:
x² - 7x + 10
To factor the expression rewrite - 7x as a difference
That's
x² - 5x - 2x + 10
Factor out x from the expression
x( x - 5) - 2x + 10
Factor - 2 from the expression
x(x - 5) - 2( x - 5)
Factor out x - 5 from the expression
The final answer is
( x - 2)(x - 5)Hope this helps you
Suppose that a sample mean is .29 with a lower bound of a confidence interval of .24. What is the upper bound of the confidence interval?
Answer:
The upper bound of the confidence interval is 0.34
Step-by-step explanation:
Here in this question, we want to calculate the upper bound of the confidence interval.
We start by calculating the margin of error.
Mathematically, the margin of error = 0.29 -0.24 = 0.05
So to get the upper bound of the confidence interval, we simply add this margin of error to the mean
That would be 0.05 + 0.29 = 0.34