Plane P cuts sphere o in a circle that has diameter
20. If the diameter of the sphere is 30, how far is the
plane from O?
Answers
Answer:
5√5 ≈ 11.18 units
Step-by-step explanation:
The Pythagorean theorem can be used to find the unknown leg of a triangle with hypotenuse 15 and one leg 10:
d = √(15^2 -10^2) = 5√(3^2 -2^2) = 5√5
The plane is 5√5 units from the center of the sphere.
Related Questions
Ryan randomly draws equal sized cards labeled with letters A, B, C, D and F from a hat and records the results in the table. Find the theoretical and experimental probabilities of randomly drawing a card that is labeled with the letter C. Frequency A 36, B 50, C 111, D 59, F 44 total 300
Answers
Answer:
We have 5 cards, and if we assume that the probability of selecting a given card at random is the same for all the cards, then the probability of randomly drawing the card C out of the 5 cards is equal to:
P = 1/5 = 0.20
Now, for the experimental probability, we can see that out of 300 draws, 111 times he drew the card C.
The experimental probability is:
Pe = 111/300 = 0.37
You can see that the experimental probability is bigger than the theoretical one, this may happen for two things.
Not enough draws: as the number of draws, we should expect to see that the experimental probability gets closer and closer to the theoretical one.
The cards have some difference: There is a chance that card C has a difference with the other cards, and this difference makes that when Ryan draws a card has a bigger probability of drawing this one.
23. A popular brand of AAA batteries has an effective use time of 12.3 hours, on average. A startup company claims that their AAA batteries last longer. The startup company tested 24,000 of their new batteries and computed a mean effective use time of 12.32 hours. Although the difference is quite small (72 seconds—or just over a minute), the effect was statistically significant (P-value < 0.0001).
It is appropriate to conclude which of the following?
A) The startup company has strong evidence that their AAA batteries last longer, on average.
B) The startup company has moderate evidence that their AAA batteries last longer, on average.
C) The startup company has proved that their AAA batteries last longer, on average.
D) None of the answer choices are correct. With such a large sample size, statistically significant results may not be of any practical importance.
Answers
Answer:
Option B
Step-by-step explanation:
Although the difference is quite small (72 seconds—or just over a minute), the effect was statistically significant (P-value < 0.0001).
Since the P-value was less than 0.0001, the null hypothesis in this case can be rejected (H₀: ∪=12.3), concluding that the startup company has moderate/enough evidence that their AAA batteries last longer, on average.
Answer:
Step-by-step explanation:
We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
µ = 12.3
For the alternative hypothesis,
µ > 12.3
This is a right tailed test.
The decision rule is to accept the null hypothesis if the significance level is lesser than the p value and reject the null hypothesis if the significance level is greater than the p value.
Let us assume a significance level of 0.05.
Since alpha, 0.05 > than the p 0.0001, then we would reject the null hypothesis.
The correct option would be
A) The startup company has strong evidence that their AAA batteries last longer, on average.
What is the area of this parallelogram?
6 cm
2 cm
Answers
Answer:
12
Step-by-step explanation:
Area= base*height
Area= 6*2
Answer:
12cm
Step-by-step explanation:
hight & Base=6 cm & 2 cm
Formula for area: hight×base=6 cm×2 cm
12cm
A vendor at a street fair sells popcorn in cones, all of height 9 inches. The
sharing-size cone has 3 times the radius of the skinny-size cone. About how
many times more popcorn does the sharing cone hold than the skinny cone?
Answers
Answer:
The sharing cone holds about 9 times more popcorn than the skinny cone.
Step-by-step explanation:
The volume of a cone is given by the following formula:
[tex]V = \frac{\pi r^{2}h}{3}[/tex]
In which r is the radius and h is the height.
Two cones:
Both have the same height.
The sharing-size cone has 3 times the radius of the skinny-size cone.
Skinny:
radius r, height h. So
[tex]V_{sk} = \frac{\pi r^{2}h}{3}[/tex]
Sharing size:
radius 3r, height h. So
[tex]V_{sh} = \frac{\pi (3r)^{2}h}{3} = \frac{9\pi r^{2}h}{3} = 3\pi r^{2}h[/tex]
About how many times more popcorn does the sharing cone hold than the skinny cone?
[tex]r = \frac{V_{sh}}{V_{sk}} = \frac{3\pi r^{2}h}{\frac{\pi r^{2}h}{3}} = \frac{3*3\pi r^{2}h}{\pi r^{2}h} = 9[/tex]
The sharing cone holds about 9 times more popcorn than the skinny cone.
What is the value of sin(A)
Answers
Answer:
6/10
Step-by-step explanation:
In a Monopoly market, a firm is a price maker since there are no close substitutes to the product. You are asked to find the company's Proft-Maximization point. Fixed Costs remains at $1,000.00. Calculate the revenue, profit (any), and costs on the graph,
Answers
Avc= vc/q
Afc= Fc/ q
Mc= Change TC/ change q
Tc= vc+ fc
Vc= tc/ fc
Mr= change tr/ change q
P≠ mr
A pollen grain is 3/10 to the third power centimeters wide. In an illustration, the pollen grain is 6 centimeters 10 wide. How much larger is the illustration than the actual pollen?
Answers
Answer:
The illustration is approximately 226 times larder than the actual pollen grain.
Step-by-step explanation:
First of all, we have to write out the size of the actual pollen grain in a manner that is easy for us to work with.
This will be
[tex](\frac{3}{10}) ^{3}=0.027cm[/tex] wide
The original width of the pollen is 0.027 cm.
Next,
We can take the width of the illustration to be 6.10 cm wide.
After this,
To get the magnification factor, we will have to use the formula
Magnification = illustrated size/ actual size
This will be the magnification = [tex]6.10/0.027[/tex] = 255.92 times
Hence, the illustration is approximately 226 times larder than the actual pollen grain.
Solve: 3(x - 6) = -12
Answers
Answer:
x=2
Step-by-step explanation:
3*2=6
6-6=0
-12
The physical plant at the main campus of a large state university recieves daily requests to replace fluorescent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 52 and a standard deviation of 5. Using the empirical rule, what is the approximate percentage of lightbulb replacement requests numbering between 47 and 52
Answers
Answer:
34% of lightbulb replacement requests numbering between 47 and 52
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 52
Standard deviation = 5
Between 47 and 52:
52 is the mean and 47 is one standard deviation below the mean.
By the Empirical Rule, 68% of the measures are within 1 standard deviation of the mean.
Since the normal distribution is symmetric, of those, 34% are within 1 standard deviation below the mean and the mean(47 and 52) and 34% are within the mean and one standard deviation above the mean(52 and 57).
So
34% of lightbulb replacement requests numbering between 47 and 52
Determine the range of the following function {(-1,4)(0,6)(7,8)(2,-5)}
A) {-1,4,0,6}
B) {-1,0,7,8}
C) {4,6,8,-5}
D) {7,8,2,-5}
Answers
Answer:
C
Step-by-step explanation:
The range of a function is all of the y values of every point. In this case, that is 4, 6, 8, -5 (C). Hope that helps!
Answer:
The answer is C
Step-by-step explanation: 4 and 6 are the medium numbers. -5 and 8 and the lowest and highest nuumbers.
8 x
105 is how many times as great as 8 x 10-l?
10 4
10 6
10 -4
10 -6
Answers
Answer:
10 6
................
Can you send the integers worksheet question and answer for 6th grade
Answers
Find the area of the shape plssss help
Answers
ok so find the area of thesquare then triangles and then add them tiriange area is 1/2 times base times heightso 1/2 times 2 times 2 which is 4 divided by 2 which is 2 same with the other traingle so your total area for the traingles is 4. The area for the square is 2 times 2 which is 4. add them up yiouget the whole shape is 8 units squared Answer: 8 units squared
Step-by-step explanation:
Simplify 3 + 5(x - 4)
Answers
Answer:
5x - 17
Step-by-step explanation:
3 + 5x - 20
= 5x - 17
What do scientist mean by flattening the curve and why is it important?
Answers
Answer:
MRCORRECT has answered the question
Step-by-step explanation:
Inhibiting new infections to reduce the number of cases at any given time—known as "flattening the curve"—allows healthcare services to better manage the same volume of patients.
Answer:
I believe it means to slow down the virus spreading to other people and to stay safe, avoid contact, and wash your hands to stop too many people from going into the hospital.
Step-by-step explanation:
A wall in Marcus’s bedroom is 8 2/5 feet high and 16 2/3 feet long. If he paints 1/2 of the wall blue, how many square feet will be blue?
Answers
77 feet^2
Explanation:
Area of the wall is
8 2/5 × 18 1/3
42/5 × 55/3
14/5 × 55/1
14/1 × 11/1 = 154 feet^2
The area we want is half of this
77 feet^2
Hope this helps and answer you question
In the equation m = k + 3, m is the:
Answers
Answer:
Step-by-step explanation:
m is the dependent variable; it represents the value of a linear function of k:
m = f(k) = k + 3
Solve the problem 5x+(x+6)+3x
Answers
what how am I solving do I simplify
Write a recursive formula for the sequence
-1,-2,-3,-4...
Answers
Answer:
f(1) = -1
f(n) = f(n-1) -1
Step-by-step explanation:
The first term is -1. Each term is 1 less than the previous. These equations say that.
f(1) = -1
f(n) = f(n-1) -1
Giving brainliest to CORRECT answer.
Answers
Answer:
B) (-3,4)
Step-by-step explanation:
I graphed the function on the graph below to show you that vertex of the function.
If this answer is correct, please make me Brainliest!
The answer is B because it appears on my graphing calculator as this.
Compute: 10:00 - 2:30
Answers
Answer:
4 hr and 30 minutes?
Step-by-step explanation:
You didnt really specify soo. 11 12 1 2 2:30
1hr 2hr 3hr 4hr 30 min
Answer:7:30
Step-by-step explanation:
where is the point (0, –4) located
Answers
4 points below the origin
Charles’s law states that if the pressure of a dry gas is held constant, then the volume V of the gas and its temperature T, measured in degrees Kelvin, satisfy the relationship V=cT, where c is a constant. Which of the following best describes the relationship between the rate of change, with respect to time t, of the volume and the rate of change, with respect to time t, of the temperature?
a) dV/dt = T dc/dt
b) dV/dt = c * dT/dt
c) dV/dT = c
d) 1 = c * dT/dV
Answers
Answer:
b) dV/dt = c * dT/dt
Step-by-step explanation:
Differentiating the equation with respect to time, you have ...
V = cT
dV/dt = c·dT/dt . . . . matches choice B
What Value if n makes the equation true
1/2(n + 4)=6
Answers
N=8
1/2 x (8+4) = 6
1/2 x 12 = 6
The lengths of pregnancies are normally distributed with a mean of 250 days and a standard deviation of 15 days.
a. Find the probability of a pregnancy lasting 308 days or longer?
b. If we stipulate that a baby is premature if the length of the pregnancy is in the lowest 8% (8th percentile), find the length that separates premature babies from those who are not premature.
Answers
Answer:
a) 0.005% probability of a pregnancy lasting 308 days or longer
b) The pregnancy length that separates premature babies from those who are not premature is 229 days.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 250, \sigma = 15[/tex]
a. Find the probability of a pregnancy lasting 308 days or longer?
This is 1 subtracted by the pvalue of Z when X = 308. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{308 - 250}{15}[/tex]
[tex]Z = 3.87[/tex]
[tex]Z = 3.87[/tex] has a pvalue of 0.99995
1 - 0.99995 - 0.00005
0.005% probability of a pregnancy lasting 308 days or longer
b. If we stipulate that a baby is premature if the length of the pregnancy is in the lowest 8% (8th percentile), find the length that separates premature babies from those who are not premature.
The 8th percentile is X when Z has a pvalue of 0.08. So it is X when Z = -1.405.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.405 = \frac{X - 250}{15}[/tex]
[tex]X - 250 = -1.405*15[/tex]
[tex]X = -1.405*15 + 250[/tex]
[tex]X = 229[/tex]
The pregnancy length that separates premature babies from those who are not premature is 229 days.
Need help please no dumb answers I gotta turn it in in five min help a girl out please
Answers
Answer:
boo just search the formula dud
its A though
convert the decimal 0.085to a percent
Answers
Answer:
8.5%
Step-by-step explanation:
Answer:
8.5%
Step-by-step explanation:
0.085
1: Ignore the 0 and take the numbers that is 85
2: Add a percent
3: Answer is 8.5%
Hope this helps.
Children in 50 Households
Number of Children Number of
Households
0
5
1
11
2
13
3
10
4
9
5
2
Using a proportion, what can you infer about the number of households in her town that have more than thre
About 242 households have more than three children.
About 269 households have more than three children.
About 296 households have more than three children.
About 565 households have more than three children.
Answers
Answer:I think it’s 269 because when you do 1,350 divided by 50 it’s 27 then you add 9+2 to get 11/50 then you do 27x11 which gives you 270 and the closest answer to that is 269
Step-by-step explanation:
Answer:
About 296 households have more than three children.
Step-by-step explanation:
I got it right on edge
Please help asap! Will give brainliest! Please read the question then answer correctly! No guessing.
Answers
Answer:
A. x - 4
D. x + 8
Step-by-step explanation:
To find the two binomial that are factors of the trinomial, you split the middle term into two:
[tex]x^2[/tex] + 4x - 32
[tex]x^2[/tex] - 4x + 8x - 32
Group:
([tex]x^2[/tex] - 4x) (8x - 32)
Take out GCF (Greatest Common Factor):
x(x - 4) 8(x - 4)
(x + 8) (x - 4)
What is the median for the given set of data?
[40, 54, 22, 30, 55, 13, 33}
A)
32
B)
33
C)
40
D)
42
Answers
13 22 30 33 40 54 55
