How many vertices does a hexagonal prism have?
Answers
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Find the size of angle x.
Corey tosses 4 fair coins. What is the probability that all four coins will land tails up?
Find the y-intercept and x-intercept of the line -x+2y=4
What is pi/π used for in math?
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The value of \(x\) that makes the equation true is
To find the value of \(x\) that makes the equation true, you need to simplify the equation and solve for \(x\). Let's break down the steps:
1. **Distribute the -5 on the left side:**
2. **Move the constant term (100) to the right side by subtracting 100 from both sides:**
3. **Finally, divide both sides by -5 to solve for \(x\):**
To verify, substitute \(x = 13\) back into the original equation:
The equation is true when \(x = 13\).
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Answer:
x=13
Step-by-step explanation:
Divide both sides by -5 then solve the equation for x
48
88
70
84
82
66
84
82
64
44
72
90
70
86
104
58
84
72
60
90
108
62
52
72
86
66
104
78
82
96
54
68
76
72
88
102
74
68
74
78
66
72
90
62
100
92
84
76
72
(a) Construct frequency distribution.
(b) Compute mode, median and mean of the frequency distribution.
(c) The lower and upper quartile of the frequency distribution.
Answers
Answer:
The answers are in the explanation.
Step-by-step explanation:
a)
X1 -Absolute frecuency -cumulative absolute frequency -Relative frecuency
44 1 1 0.021
48 1 2 0.021
52 1 3 0.021
54 1 4 0.021
58 1 5 0.021
60 1 6 0.021
62 2 7 0.042
64 1 8 0.021
66 3 12 0.063
68 2 14 0.042
70 2 16 0.042
72 6 22 0.126
74 2 24 0.042
76 2 26 0.042
78 2 28 0.042
80 1 29 0.021
82 3 32 0.063
84 4 36 0.084
86 2 38 0.042
88 2 40 0.042
90 3 43 0.063
92 1 44 0.021
96 1 45 0.021
100 1 46 0.021
102 1 47 0.021
104 2 49 0.042
108 1 50 0.021
Total: 50 50 1
- b) Mean: is the number average = 3806/48 = 78.12
- Median: is the number or average number of half = 76
- Mode: Is the number that appears most frequently = 72
- c) Lower quartile: 67
- Upper quartile: 84
a. What is the probability that he must stop at both signals?
b. What is the probability that he must stop at the first signal but not at the second one?
c. What is the probability that he must stop at exactly one signal?
Answers
Answer: a. 0.05
b. 0.40
c. 0.85
Step-by-step explanation:
Let F= Event that a certain motorist must stop at the first signal.
S = Event that a certain motorist must stop at the second signal.
As per given,
P(F) = 0.45 , P(S) = 0.5 and P(F or S) = 0.9
a. Using general probability formula:
P(F and S) =P(F) + P(S)- P(F or S)
= 0.45+0.5-0.9
= 0.05
∴ the probability that he must stop at both signals = 0.05
b. Required probability = P(F but (not s)) = P(F) - P(F and S)
= 0.45-0.05= 0.40
∴ the probability that he must stop at the first signal but not at the second one =0.40
c. Required probability = P(exactly one)= P(F or S) - P(F and S)
= 0.9-0.05
= 0.85
∴ the probability that he must stop at exactly one signal = 0.85
Final answer:
The probability of stopping at both signals is 0.225, the probability of stopping at the first one but not the second one is 0.225. The probability of stopping at exactly one signal is 0.675.
Explanation:
The probability theory can be used to answer these questions. The probabilities of stopping at various traffic signals can be calculated using some assumptions about the independence of the events.
- The probability of the motorist having to stop at both signals can be found by multiplying the individual probabilities, assuming that these are independent events. So, P(stop at both signals) = P(stop at first signal) * P(stop at second signal) = 0.45 * 0.5 = 0.225.
- The probability of him stopping at the first signal but not at the second one is again found by multiplying the probability of stopping at the first by the probability of not having to stop at the second. Therefore, P(stop at first, not at second) = 0.45 * (1 - 0.5) = 0.225.
- To find the probability that the driver must stop at exactly one signal, we can subtract the probability of stopping at both signals from the probability of stopping at least one signal. So, P(stop at one signal) = P(stop at at least one signal) - P(stop at both signals) = 0.9 - 0.225 = 0.675.
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B. -1
C. -2
D. 5
Answers
Answer:
1
Step-by-step explanation:
The y intercept is when x =0
We need to use the second equation
-x+1 since -2 < 0 <3
0+1
The y intercept is 1
Answers
Answer:
Step-by-step explanation:
speed=distance/time
20 minutes=1/3 hours
=3*3/1
=1miles/hour
9miles per hour since 20 minute / 60 hour = 0.333333
D=s/t
D=3/0.33333
D=9 miles per second
Answers
Answer:
(0, 1).
Method 1 (Substitution):
Substituting our two y's, we get the following:
Thus, the only set of solutions is (0, 1). A quick sketch (either by hand or on Desmos) can confirm this.
Method 2 (Elimination):
We have two equations. We'll let the top one be equation 1 and the bottom one be equation 2. Eliminating as many variables as we can, we subtract (2) from (1) to get:
0 = 3x => x = 0.
So the only set of solutions is (0, 1).
Method 3 (Gaussian elimination):
We can place this in an augmented matrix and row reduce.
Row reducing this gives us:
This tells us that the only solution for x is x = 0 (since we read this as "3x = 0") and thus, the only solution we get is (0, 1).