A tangent to a circle at point A is given, and point A is an endpoint of a chord, which is the same length as radius of the circle. What is the measure of angle between the tangent and the chord?
PLS HELP SQDANCEFAN!!!!! I NEED HELP I DON'T GET IT :((((
Answers
Answer:
30°
Step-by-step explanation:
Call the other end of the chord point B and the center of the circle point O. Then triangle AOB is an equilateral triangle, since OA = OB = AB.
Angle OAB is the internal angle of that triangle, so is 60°. Since OA is perpendicular to the tangent line (makes an angle of 90°), The angle between the tangent line and the chord must be ...
90° - 60° = 30°
___
The other way you know this is that central angle AOB is 60°, and the tangent-to-chord angle is half that, or 30°.
_____
One way to remember the angle relationship between a tangent line and a chord is this:
Consider a point C on long arc AB. The measure of inscribed angle ACB is half the measure of central angle AOB, no matter where C is on the circle. (If C happens to be on the short arc AB, then central angle AOB is a reflex angle, but the relationship still holds.) Consider what happens when C approaches A. The angle at vertex C is still the same: 1/2 the measure of central angle AOB. This remains true even in the limit when points A and C become coincident and line AC is a tangent at point A.
Related Questions
USA Today reported that approximately 25% of all state prison inmates released on parole become repeat offenders while on parole. Suppose the parole board is examining five prisoners up for parole. Let x = number of prisoners out of five on parole who become repeat offenders. x 0 1 2 3 4 5 P(x) 0.211 0.378 0.216 0.162 0.032 0.001 (a) Find the probability that one or more of the five parolees will be repeat offenders. (Round your answer to three decimal places.) How does this number relate to the probability that none of the parolees will be repeat offenders? This is the complement of the probability of no repeat offenders. These probabilities are not related to each other. This is twice the probability of no repeat offenders. This is five times the probability of no repeat offenders. These probabilities are the same. (b) Find the probability that two or more of the five parolees will be repeat offenders. (Round your answer to three decimal places.) (c) Find the probability that four or more of the five parolees will be repeat offenders. (Round your answer to three decimal places.) (d) Compute μ, the expected number of repeat offenders out of five. (Round your answer to three decimal places.) μ = prisoners (e) Compute σ, the standard deviation of the number of repeat offenders out of five. (Round your answer to two decimal places.) σ = prisoners
Answers
Answer:
a) 0.789, this is the complement of the probability of no repeat offenders; b) 0.411; c) 0.033; d) μ = 1.429; e) σ = 9.58
Step-by-step explanation:
For part a,
The probability that no parolees are repeat offenders is 0.211. This means the probability of at least one is a repeat offender is the complement of this event. To find this probability, subtract from 1:
1-0.211 = 0.789.
For part b,
To find the probability that 2 or more are repeat offenders, add together the probability that 2, 3, 4 or 5 parolees are repeat offenders:
0.216+0.162+0.032+0.001 = 0.411.
For part c,
To find the probability that 4 or more are repeat offenders, add together the probabilities that 4 or 5 parolees are repeat offenders:
0.032+0.001 = 0.033.
For part d,
To find the mean, we multiply each number of parolees by their probability and add them together:
0(0.211)+1(0.378)+2(0.216)+3(0.162)+4(0.032)+5(0.001)
= 0 + 0.378 + 0.432 + 0.486 + 0.128 + 0.005 = 1.429
For part e,
To find the mean, we first subtract each number of parolees and the mean to find the amount of deviation. We then square it and multiply it by its probability. Then we add these values together and find the square root.
First the differences between each value and the mean:
0-1.429 = -1.429;
1-1.429 = -0.429;
2-1.429 = 0.571;
3-1.429 = 1.571;
4-1.429 = 2.571;
5-1.429 = 3.571
Next the differences squared:
(-1.429)^2 = 2.0420
(-0.429)^2 = 0.1840
(0.571)^2 = 0.3260
(1.571)^2 = 2.4680
(2.571)^2 = 6.6100
(3.571)^2 = 12.7520
Next the squares multiplied by the probabilities:
0(2.0420) = 0
1(0.1840) = 0.1840
2(0.3260) = 0.652
3(2.4680) = 7.404
4(6.6100) = 26.44
5(12.7520) = 63.76
Next the sum of these products:
0+0.1840+0.652+0.7404+26.44+63.76 = 91.7764
Lastly the square root:
√(91.7764) = 9.58
Probabilities are used to determine the outcomes of events.
The probability that one or more are repeat offenders is 0.789The probability that two or more are repeat offenders is 0.411The probability that four or more are repeat offenders is 0.033The standard deviation of repeat offenders is 1.093The expected number of repeat offenders is 1.429The table is given as:
[tex]\left[\begin{array}{ccccccc}x &0 &1 &2 &3 &4 &5 &P(x) &0.211 &0.378 &0.216& 0.162 &0.032 &0.001\end{array}\right][/tex]
(a) Probability that one or more are repeat offenders
This is represented as: [tex]P(x \ge 1)[/tex]
Using the complement rule, we have:
[tex]P(x \ge 1) = 1 - P(x = 0)[/tex]
So, we have:
[tex]P(x \ge 1) = 1 - 0.211[/tex]
[tex]P(x \ge 1) = 0.789[/tex]
The probability that one or more are repeat offenders is 0.789
(b) Probability that two or more are repeat offenders
This is represented as: [tex]P(x \ge 2)[/tex]
Using the complement rule, we have:
[tex]P(x \ge 2) = 1 - P(x = 0) - P(x = 1)[/tex]
So, we have:
[tex]P(x \ge 2) = 1 - 0.211 - 0.378[/tex]
[tex]P(x \ge 2) = 0.411[/tex]
The probability that two or more are repeat offenders is 0.411
(c) Probability that four or more are repeat offenders
This is represented as: [tex]P(x \ge 4)[/tex]
So, we have:
[tex]P(x \ge 4) = P(x = 4) + P(x = 5)[/tex]
[tex]P(x \ge 4) = 0.032 + 0.001[/tex]
[tex]P(x \ge 4) = 0.033[/tex]
The probability that four or more are repeat offenders is 0.033
(d) The expected number of repeat offenders
This is calculated as:
[tex]\mu = \sum x \times P(x)[/tex]
So, we have:
[tex]\mu = 0 \times 0.211+ 1\times 0.378 + 2 \times 0.216 + 3 \times 0.162 + 4 \times 0.032 + 5 \times 0.001[/tex]
[tex]\mu = 1.429[/tex]
The expected number of repeat offenders is 1.429
(e) The standard deviation
This is calculated as:
[tex]\sigma= \sqrt{\sum (x^2 \times P(x)) - \mu^2}[/tex]
[tex]\sum (x^2 \times P(x))[/tex] is calculated as:
[tex]\sum (x^2 \times P(x)) = 0^2 \times 0.211+ 1^2 \times 0.378 + 2^2 \times 0.216 + 3^2 \times 0.162 + 4^2 \times 0.032 + 5^2 \times 0.001[/tex]
[tex]\sum (x^2 \times P(x)) = 3.237[/tex]
So, we have:
[tex]\sigma= \sqrt{\sum (x^2 \times P(x)) - \mu^2}[/tex]
[tex]\sigma = \sqrt{3.237 - 1.429^2}[/tex]
[tex]\sigma = \sqrt{1.194959}[/tex]
[tex]\sigma = 1.093[/tex]
The standard deviation of repeat offenders is 1.093
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A community organization surveyed 40 members to determine if they world vote yes or no for the proposition a in the next election
Twelve of the surveyed members said they would vote yes there are a total of 240 members in the community organization how many members are expected to vote yes
Answers
Answer:
72 members
Step-by-step explanation:
Total surveyed members = 40
members voting yes = 12
probability of the members voting yes = 12/40 = 3/10
It is observed that, out of every 'n' members, n*(3/10) members are expected to vote yes:
Therefore,
number of members expecting to voye yes out of 240 are = 240 * 3/10
=> 24 * 3 = 72 members
What is the slope of the line given by the equation y = -5x? Enter your answer as an integer or fraction in lowest terms. BTW can you tell me how you got the answer for future reference
Answers
Answer:
slope = - 5
Step-by-step explanation:
given the equation of a line in the form
y = mx ← m is the slope
y = - 5x is in this form with slope m = - 5
If P(A) = 0.25, then the probability of the complement of A is
0.65
0.75
-0.25
0.25
Answers
Answer:
P(A') = 0.75
Step-by-step explanation:
We are given that the probability P(A) = 0.25 and we are to determine the probability of the complement of A.
According to the Complement Rule of any probability, the sum of the probabilities of an event and its complement must be equal to 1.
So for for the event A,
P(A) + P(A') = 1
0.25 + P(A') = 1
P(A') = 1 - 0.25
P(A') = 0.75
The probability of an event and its complement add up to 1. Therefore, if P(A) = 0.25, the probability of the complement of A is 0.75.
Explanation:In the field of probability theory, the probability of an event and its complement always add up to 1. Therefore, if P(A) = 0.25, then the probability of the complement of A is 1 - 0.25 = 0.75.
This is because the complement of A, denoted by A', includes all outcomes that are not in A. So, all probabilities in the sample space (which has a total probability of 1) must either be in A or in A'. Therefore, P(A) + P(A') = 1.
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What is the area of this triangle? Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth.
The figure contains a triangle. One side is 12 centimeters. A second side is 8 centimeters. The angle between the given sides is 65 degrees.
Answers
Area=1/2absinx
Area=1/2(8)(12)sin65
Area=39.7cm^2
Answer:
The area of the triangle is 43.5 cm².
Step-by-step explanation:
Since, the area of a triangle is,
[tex]A=\frac{1}{2}\times s_1\times s_2\times sin \theta[/tex]
Where, [tex]s_1[/tex] and [tex]s_2[/tex] are adjacent sides and [tex]\theta[/tex] is the included angle of these sides,
Given,
[tex]s_1=12\text{ cm}[/tex]
[tex]s_2=8\text{ cm}[/tex]
[tex]\theta = 65^{\circ}[/tex]
Hence, the area of the given triangle is,
[tex]A=\frac{1}{2}\times 12\times 8\times sin 65^{\circ}[/tex]
[tex]=\frac{96\times 0.90630778703}{2}[/tex]
[tex]=\frac{87.0055475555}2}=43.5027737778\approx 43.5\text{ square cm}[/tex]
Suppose that a and b are integers, a ≡ 11 ( mod 19), and b ≡ 3 ( mod 19 ) .find integer c with0 ≤ c ≤ 18 such that
a.c ≡ 13 a ( mod19).
b.c ≡ 8 b( mod19).
c.c ≡ a − b( mod19).
d.c ≡ 7 a + 3 b( mod19).
e.c ≡ 2 a 2 + 3 b 2 ( mod19). f) c ≡ a 3 + 4 b 3 ( mod19).
Answers
To find the integer c that satisfies the given congruences, we can use the properties of modular arithmetic. For each congruence, we substitute the given values of a and b and simplify the congruences to solve for c. The possible values of c are then determined using the Chinese Remainder Theorem when appropriate.
Explanation:To find the integer c that satisfies the given congruences, we can use the properties of modular arithmetic:
a) To find c such that a.c ≡ 13a (mod 19), we divide both sides of the congruence by a. This gives us c ≡ 13 (mod 19).
b) To find c such that b.c ≡ 8b (mod 19), we divide both sides of the congruence by b. This gives us c ≡ 8 (mod 19).
c) To find c such that c.c ≡ a - b (mod 19), we square both sides of the congruence. This gives us c^2 ≡ (a - b)^2 (mod 19). Since we know a ≡ 11 (mod 19) and b ≡ 3 (mod 19), we substitute these values and simplify the congruence to c^2 ≡ 8 (mod 19). To solve this quadratic congruence, we can use the Chinese Remainder Theorem to find the two square roots of 8 modulo 19, which are 7 and 12. Therefore, c ≡ 7 (mod 19) or c ≡ 12 (mod 19).
d) To find c such that c.c ≡ 7a + 3b (mod 19), we substitute the given congruences for a and b into the congruence and simplify to obtain c^2 ≡ 7(11) + 3(3) ≡ 4 (mod 19). Similar to part (c), we use the Chinese Remainder Theorem to find the square roots of 4 modulo 19, which are 2 and 17. Therefore, c ≡ 2 (mod 19) or c ≡ 17 (mod 19).
e) To find c such that c.c ≡ 2a^2 + 3b^2 (mod 19), we substitute the given congruences for a and b into the congruence and simplify to obtain c^2 ≡ 2(11^2) + 3(3^2) ≡ 2(121) + 3(9) ≡ 149 ≡ 2 (mod 19). Therefore, c ≡ ±4 (mod 19).
f) To find c such that c ≡ a^3 + 4b^3 (mod 19), we substitute the given congruences for a and b into the congruence and simplify to obtain c ≡ 11^3 + 4(3^3) ≡ 11^3 + 4(27) ≡ 11^3 + 4(8) ≡ 11 + 32 ≡ 17 (mod 19). Therefore, c ≡ 17 (mod 19).
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Determine the nature of the roots:
Answers
Answer:
A
Step-by-step explanation:
Nature of roots is determined by using the Discriminant, D, which is:
[tex]D=b^2-4ac[/tex]
If
D > 0, there are 2 real unique solutions
D = 0, there are 2 real equal solutions
D < 0, there are no real solutions
Note: a is the coefficient of x^2, b is the coefficient of x, and c is the independent term (the constant)
Now, for our quadratic expression, a = 3, b = 12, & c = -3. Plugging it in the discriminant formula, we get:
[tex]D=b^2-4ac\\D=(12)^2-4(3)(-3)\\D=180[/tex]
Thus, D > 0 , which means there are 2 distinct real solutions. Answer choice A is right.
(2CQ) Write the repeating decimal as a fraction .15
Answers
Answer:
c. [tex]\frac{5}{33}[/tex]
Step-by-step explanation:
The given decimal is [tex]0.\bar {15}[/tex]
Let [tex]y=0.\bar {15}...(1)[/tex]
Multiply equation (1) by 100.
[tex]100y=15.\bar {15}...(2)[/tex]
Subtract equation (1) from equation (2)
[tex]\Rightarrow 100y-y=15.\bar {15}-0.\bar {15}[/tex]
[tex]\Rightarrow 99y=15[/tex]
Divide both sides by 99.
[tex]\Rightarrow y=\frac{15}{99}[/tex]
Simplify;
[tex]\Rightarrow y=\frac{5}{33}[/tex]
The recurring decimal 0.15 can be converted to the fraction 5/33.
To convert the repeating decimal 0.15 to a fraction, follow these steps:
Let x be the repeating decimal: x = 0.151515...
Express this equation by multiplying both sides by 100 to shift the decimal point two places: 100x = 15.151515...
Next, subtract the original equation from this new equation: 100x - x = 15.151515... - 0.151515...
This simplifies to: 99x = 15
Solve for x by dividing both sides by 99: x = 15/99
Simplify the fraction by dividing the numerator and the denominator by their greatest common divisor (GCD), which is 3: x = 5/33
Therefore, the repeating decimal 0.15 can be expressed as the fraction 5/33.
If ~ p: Two parallel lines never intersect. What is p? Two parallel lines always intersect. Two parallel lines never intersect. Two parallel lines sometimes intersect. None of the above
Answers
Answer:
Two parallel lines never intersect.
Step-by-step explanation:
The definition of a parallel line is: 2 lines that are exactly the same, but will not touch each other.
Answer with explanation:
~p means other line is Similar to p.
If there are two parallel lines , it means Perpendicular distance between the two lines is always constant, if measured by taking a point anywhere on the line.
⇒Two Parallel lines never intersect.
Option B
Katrina took a train trip to visit her aunt. By 11:15 the train had traveled 40 miles. By 1:15 the train had traveled an additional 20 miles. Katrina is now halfway to her aunt's house. At what time will she reach her aunt's house at the train's current speed? a. 6:45 c. 3:15 b. 7:15 d. 4:30
Answers
(Q6) Decide if the function is an exponential function. If it is, state the initial value and the base. y= -4.8·4^x
Answers
Answer:
D
Step-by-step explanation:
Exponential equation takes the form [tex]y=a*b^x[/tex] where
a is the initial value ( a ≠ 0), andb is the base ( b ≠ 1)The equation given in the problem can be written as [tex]y=-4.8*4^x[/tex], so it is an exponential equation, where a = -4.8 and b = 4.
Thus we can say that the initial value = -4.8 and the base is 4
The correct answer is D
Answer:
d
Step-by-step explanation:
A circle has a circumference of 150 meters. What is the measure of the radius? Round to the nearest tenth
Answers
Answer:
Step-by-step explanation:
Answer:
75 "I think"
Step-by-step explanation:
Determine the ratio of the geometric sequence: 1/10, -1/2, 5/2,...
-1/5
1/5
-5
5
Answers
Answer: third option.
Step-by-step explanation:
By definition we know tht the geometric sequences has a common ratio, which is represented with r.
This ratio can be calculated by dividing a term by the previous term.
Therefore, keeping the information above on mind, you have that the ratio r of the geometric sequence given in the problem, is the shown below:
[tex]r=\frac{-\frac{1}{2}}{\frac{1}{10}}\\\\r=-5[/tex]
Answer:
The ratio of the sequence is -5
Step-by-step explanation:
The given geometric series is ;
[tex]\frac{1}{10},-\frac{1}{2},\frac{5}{2},...[/tex]
The ratio of the geometric sequence is given by;
[tex]r=\frac{a_n}{a_{n-1}}[/tex]
[tex]r=\frac{\frac{5}{2}}{-\frac{1}{2}}[/tex]
We simplify to get;
[tex]r=-5[/tex]
The mean incubation time of fertilized eggs is 21 days. Suppose the incubation times are approximately normally distributed with a standard deviation of 1 day.(a) Determine the 20th percentile for incubation times.(b) Determine the incubation times that make up the middle 39% of fertilized eggs.
Answers
Answer:
a) 20.16; b) 20.49 and 21.51
Step-by-step explanation:
We use z scores for each of these. The formula for a z score is
[tex]z=\frac{X-\mu}{\sigma}[/tex].
For part a, we want the 20th percentile; this means we want 20% of the data to be lower than this. We find the value in the cells of the z table that are the closest to 0.20 as we can get; this is 0.2005, which corresponds with a z score of -0.84.
Using this, 21 as the mean and 1 as the standard deviation,
-0.84 = (X-21)/1
-0.84 = X-21
Add 21 to each side:
-0.84+21 = X-21+21
20.16 = X
For part b, we want the middle 39%. This means we want 39/2 = 19.5% above the mean and 19.5% below the mean; this means we want
50-19.5 = 30.5% = 0.305 and
50+19.5 = 69.5% = 0.695.
Looking these values up in the cells of the z table, we find those exact values; 0.305 corresponds with z = -0.51 and 0.695 corresponds with z = 0.51:
-0.51 = (X-21)/1
-0.51 = X-21
Add 21 to each side:
-0.51+21 = X-21+21
20.49 = X
0.51 = (X-21)/1
0.51 = X-21
Add 21 to each side:
0.51+21 = X-21+21
21.51 = X
The 20th percentile for incubation times is approximately 20.16 days. The incubation times that make up the middle 39% of fertilized eggs fall between roughly 20.5 days and 21.5 days.
Explanation:This question focuses on statistics and their application in a biological context, specifically about the incubation time of fertilized eggs. In statistics, the normal distribution is a common continuous probability distribution that is symmetric about the mean.
(a) The 20th percentile of the normal distribution can be found using the z-table or a calculator that has the capability. Using the formula Z = (X - μ) / σ, where Z is the Z-score, X is the value in the data set, μ is the mean, and σ is the standard deviation, a Z-score associated with the 20th percentile is approximately -0.84. So the incubation time in days for the 20th percentile is (0.84 * 1) + 21 = 20.16 days.
(b) Similarly, to find the incubation times that make up the middle 39% of the fertilized eggs, note that since this is symmetric, this implies the incubation times falls between the 30.5 percentile and the 69.5 percentile. Using the formula Z = (X - μ) / σ and the Z-table, the Z-scores associated with these percentiles are approximately -0.5 and 0.5 respectively. Hence the incubation time falls between (0.5 * 1) + 21 = 20.5 days and (0.5 * 1) + 21 = 21.5 days
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Tom bought 5 t-shirts from a store. After he bought the t-shirts, his account balance showed a change of −$65.25. What would have been the change to Tom's account balance had he bought only 1 t-shirt from the store?
Answers
Answer:
It would be $13.05
Step-by-step explanation:
Since you're dividing negative $65.25 with a negative number of 5 stores. The five stores are negative because he bought from those stores. So, when dividing the 2 negatives you get a positive $13.05.
If Tom has bought only one t-shirt the change to Tom's account balance
would have been - $13.05.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, Tom bought 5 t-shirts from a store.
After he bought the t-shirts, his account balance showed a change of
- $65.25.
Assuming all 5 t-shirts cost the same so the cost of 1 t-shirt would be
= - (65.25/5).
= - 13.05 dollars.
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Can someone please help me
Answers
Answer:
1. The marked answer is correct.
2. The only equivalent equation is the 2nd one: x^2 -12x +36 = 28
Step-by-step explanation:
The square of a binomial is ...
(x -a)^2 = x^2 -2ax +a^2
This tells you the constant term in the perfect square trinomial is the square of half the x-coefficient.
1. The x-coefficient is -8, so half that is -4. The square of -4 is 16. To complete the square, the added constant term must be 16, the marked answer.
___
2. The x-coefficient is -12, so the square of half that is (-6)^2 = 36. Adding 36 to the equation gives ...
x^2 -12x +36 = 28 . . . . . . matches the 2nd choice
_____
The rule that makes algebra work is this: whatever you do on one side of the equal sign must also be done on the other side.
If you add 36 on one side of the equation, you must add 36 on the other side. Of course addition of signed numbers is done in the usual way: 36 + (-8) = 28.
Find the measure of angle B.
A) 90
B) 180
C) 120
D) 60
Answers
Answer:
C) 120 degrees
Step-by-step explanation:
m<A + m<B + m<C = 180
45 + m<B + 15 = 180
m<B + 60 = 180
m<B = 120
The answer is C) 120
A student stands 50 feet away from the front of a building and measures the angle of elevation to the top of the building. From the student's eye level 5 feet off the ground, the angle of elevation to the top of the building is 30^\circ. Approximately, what is the height of the building?
Answers
Answer:
The height of the building is approximately [tex]34\ ft[/tex]
Step-by-step explanation:
Let
h------> height of the building from the student's eye level
H----> height of the building from the ground (H=h+5 ft)
we know that
[tex]tan(30\°)=\frac{h}{50}[/tex]
[tex]h=tan(30\°)(50)=28.87\ ft[/tex]
Find the height of the building H
[tex]H=h+5=28.87+5=33.87\ ft[/tex]
The height of the building is approximately [tex]34\ ft[/tex]
-------------------------------------------------------------------
Answers
Answer:
[tex]\large\boxed{x\approx0.52}[/tex]
Step-by-step explanation:
[tex]2^{5x}=6\Rightarrow\log_22^{5x}=\log_26\qquad\text{use}\ \log_ab^n=n\log_ab\\\\5x\log_22=\log_26\qquad\text{use}\ \log_aa=1\\\\5x=\log_26\qquad\text{divide both sides by 5}\\\\x=\dfrac{\log_26}{5}\\\\\log_26\approx2.585\\\\x\approx\dfrac{2.585}{5}\to\boxed{x\approx0.52}[/tex]
A manager at a local manufacturing company has been monitoring the output of one of the machines used to manufacture chromium shells. Past data indicate that if the machine is functioning properly, the length of the shells produced by this machine can be modeled as being normally distributed with a mean of 118 centimeters and a standard deviation of 6.3 centimeters. Suppose 10 shells produced by this machine are randomly selected. What is the probability that the average length of these 10 shells will be between 116 and 120 centimeters when the machine is operating "properly?"
Answers
Answer:
0.6826
Step-by-step explanation:
To solve this, we find the z scores for both sample means. We then us a z table to find the area under the curve to the left of (probability less than) each z score, and subtract them to find the area between them.
The formula we use, since we are using sample means, is
[tex]z=\frac{\bar{X}-\mu}{\sigma \div \sqrt{n}}[/tex]
Our x-bar will be 116 in the first z-score and 120 in the second; our mean, μ, is 118; our standard deviation, σ, is 6.3; and our sample size, n, is 10:
[tex]z=\frac{116-118}{6.3\div \sqrt{10}}=\frac{-2}{1.9922}\approx -1.0039\\\\z=\frac{120-118}{6.3\div \sqrt{10}}=\frac{2}{1.9922}\approx 1.0039[/tex]
Using a z table, we see that the area under the curve to the left of -1.00 is 0.1587. The area under the curve to the left of 1.00 is 0.8413. This makes the area between them
0.8413-0.1587 = 0.6826.
To solve this statistics problem, calculate the z-scores for the lengths 116 cm and 120 cm, using the given mean, standard deviation, and sample size. Then, use a z-table to find the probabilities associated with these z-scores. The difference between these probabilities will give the likelihood of the machine producing shells between these lengths.
Explanation:This problem is essentially a question about probability in statistics, specifically relating to the normal distribution. Given that the machine is operating properly, and assuming that the lengths of the shells it produces are normally distributed with a mean of 118 cm and a standard deviation of 6.3 cm, we want to find the probability that the average length of 10 randomly selected shells is between 116 and 120 cm.
First, we need to find the z-scores corresponding to the lengths of 116 cm and 120 cm. The formula for the z-score is (X - μ)/σ, where X is the measurement (in this case, the average length of the shells), μ is the mean, and σ is the standard deviation. However, in this scenario, due to the application of the Central Limit Theorem, we must use σ/sqrt(N) as the standard deviation for the distribution of sample means, where N=10. Therefore, for 116 cm we get Z1 = (116 -118) / (6.3/ sqrt(10)) and for 120 cm we get Z2 = (120 - 118) / (6.3/sqrt(10)).
Once the Z-scores are calculated, we can use Z-tables (commonly found in statistics textbooks or online) to find the probabilities associated with these z-scores. Subtract the probability of Z1 from the probability of Z2 to get the desired range probability.
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Susan collected 1,470 stickers and placed them in her sticker book if there are 35 stickers on each page of her sticker book how many pages of stickers does Susan have
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All you need to do is divide 1470 by 35, which is 42.
A rectangular prism has the dimensions 8 feet by 3 feet by 5 feet. What is the surface area of the prism?
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Answer:
A=158
Step-by-step explanation: SA = 2 × l × w + 2 × l × h + 2 × w × h
Answer: Option D
(D) 158 square feet
Step-by-step explanation:
A=2(wl+hl+hw)=2·(3·8+5·8+5·3)=158ft²
Please help me out............
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3x+3=6x-57
60=3x
3x=60
60÷3=20
x=20
Joel gives 1/3 of his baseball cards to his sister. what is a fraction equivalent to 1/3
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If you multiply the numerator and the denominator by the same number, it will be equal to 1/3.
For example:
1/3 * 3/3 = 3/9
1/3 * 8/8 = 8/24
Answer:
2/6, 3/9, and 4/12
Step-by-step explanation:
Any fraction where you can divide both the numerator and the denominator by the same number to get 1/3 also equals 1/3.
For example: 2/6
When you divide both numbers by 2, you get 1/3. Which means they are equivalent fractions (or equal).
In Las Vegas, Nevada, stores charge a 4.6\%4.6%4, point, 6, percent state sales tax and a 3.65\%3.65%3, point, 65, percent county sales tax. Yuki is purchasing a handbag priced at \$220$220dollar sign, 220 before tax. How much sales tax does Yuki pay for her handbag purchase? \$
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Answer:
18.15
Step-by-step explanation:
Percent means per hundred, so we can convert 4.6% and 3.65% to equivalent decimals.
4.6%= 4.6 divided by 100 = 0.046
3.65%= 3.65 divided by 100 = 0.0365
Since both sales tax rates apply to $220, we can add the two rates.
0.046 + 0.0365= 0.0825
0.0825 x 220 = 18.15
And so, Yuki pays$18.15 in sales tax for her handbag purchase.
Helen has some pens and some square tiles .Each pen is 130mm longet . The sides of each tile are 13mm long . Helen lays ten pens end to end to make a straight line . She makes a line of tiles which is the same length as the line of pens . How many tiles does she use?
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Answer:
100
Step-by-step explanation:
The total length of ten pens laid end-to-end is
10 pens × 130 mm/1 pen = 1300 mm
The number of tiles needed to stretch the same length is
1300 mm × 1 tile/13 mm = 100 tiles
Helen uses 100 tiles.
If a plane can travel 500 miles per hour with the wind and 420 miles per hour against the? wind, find the speed of the wind and the speed of the plane in still air.
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Answer:
plane velocity (with wind) = 500 mph
plane velocity (against wind) = 420 mph
velocity difference divided by 2 = 40
plane velocity = 500 - 40 = 460 mph
Step-by-step explanation:
To show that polygon ABCDE is congruent to polygon FGHIJ, a must be used to make the two polygons coincide. A sequence of two transformations that can be used to show that polygon ABCDE is congruent to polygon FGHIJ is
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Is there answer choices?
(Q9) Decide if the function is an exponential growth function or exponential decay function, and describe its end behavior using limits. y=0.8^x
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Answer:
C
Step-by-step explanation:
A function in the form [tex]y=a*b^x[/tex] is an exponential function. If
a > 0, and b > 1 -- this is exponential growth functiona > 0, and 0 < b < 1 -- this is exponential decay functionThe given function can be written as [tex]y=1*0.8^x[/tex], so a > 0 and 0 < b < 1, hence this is exponential decay function.
For end behavior, we take limits from -∞ and from ∞. If we do that we can see that C is the correct answer. Also, looking at the graph explains it. Attached is the graph.
From the graph, as we move towards negative infinity, the graph goes towards positive infinity and as we move towards positive infinity, the graph goes towards 0.
Based on the experimental probability, predict the number of times that you will roll a 5 if you roll the number cube 300 times.
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Rolling a 5 in 300 rolls: Probability of 1/6 [tex]*[/tex] 300 ≈ 50 times.
Sure, let's break it down step by step:
1. Understand Experimental Probability : Experimental probability is based on actual outcomes from an experiment or trial. It's calculated by dividing the number of favorable outcomes by the total number of outcomes.
2. Identify the Probability of Rolling a 5 : Since a standard number cube has 6 faces numbered 1 through 6, each face has an equal probability of 1/6 of showing up in a single roll.
3. Calculate the Probability of Rolling a 5 : The probability of rolling a 5 is 1/6, since there's one favorable outcome (rolling a 5) out of the total 6 possible outcomes.
4. Use Probability to Predict Outcomes : To predict how many times you'll roll a 5 in 300 rolls, multiply the probability of rolling a 5 by the total number of rolls.
Let's calculate:
Probability of rolling a 5 = 1/6
Total number of rolls = 300
Number of times you'll roll a 5 = (Probability of rolling a 5) * (Total number of rolls)
= (1/6) [tex]*[/tex] 300
≈ 50
So, based on experimental probability, you can predict that you will roll a 5 approximately 50 times if you roll the number cube 300 times.