Step-by-step explanation:
The probability of success = 8/(8 + 17) = 8/25 = 0.32.
Let X be the random variable denoting the number of successes (number of times the individual won a prize) in four picks.
Hence, X ~ Bin(4, 0.32).
Thus, P(X = 1) =
Ben is spending his summer driving across the country. He is going to spend the first day
1 answer:
Answer:
The graph of the data presented is shown in the attached image to this solution.
It shows that the relationship between distance travelled in miles and the time take in hours is D = 55t
Step-by-step explanation:
The distance travelled with the corresponding time taken are presented in the table
Note: D - Distance travelled (miles)
t - Time (hours)
D | t
55 | 1
110 | 2
165 | 3
220 | 4
275 | 5
330 | 6
We are then told to plot these distance travelled on a graph with the time taken.
The distance travelled is plotted on the y-axis and the time in hours is plotted on the x-axis.
The image of the graph of this function will be attached to this answer
It is evident that the graph shows the relationship between the distance travelled and time taken to be D = 55t
Hope this Helps!!!
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It translates to which solves to
after dividing both sides by 78. This means n is equal to 4 or it can be larger than 4.
Answer:
1) c ║ d by consecutive interior angles theorem
2) m∠3 + m∠6 = 180° by transitive property
3) ∠2 ≅ ∠5 by definition of congruency
4) t ║ v Corresponding angle theorem
5) ∠14 and ∠11 are supplementary Definition of supplementary angles
6) ∠8 and ∠9 are supplementary Consecutive interior angles theorem
Step-by-step explanation:
1) Statement Reason
m∠4 + m∠7 = 180° Given
m∠4 ≅ m∠6 Vertically opposite angles
m∠4 = m∠6 Definition of congruency
m∠6 + m∠7 = 180° Transitive property
m∠6 and m∠7 are supplementary Definition of supplementary angles
∴ c ║ d Consecutive interior angles theorem
2) Statement Reason
m∠3 = m∠8 Given
m∠8 + m∠6 = 180° Sum of angles on a straight line
∴ m∠3 + m∠6 = 180° Transitive property
3) Statement Reason
p ║ q Given
∠1 ≅ ∠5 Given
∠1 = ∠5 Definition of congruency
∠2 ≅ ∠1 Alternate interior angles theorem
∠2 = ∠1 Definition of congruency
∠2 = ∠5 Transitive property
∠2 ≅ ∠5 Definition of congruency.
4) Statement Reason
∠1 ≅ ∠5 Given
∠3 ≅ ∠4 Given
∠1 = ∠5 Definition of congruency
∠3 = ∠4 Definition of congruency
∠5 ≅ ∠4 Vertically opposite angles
∠5 = ∠4 Definition of congruency
∠5 = ∠3 Transitive property
∠1 = ∠3 Transitive property
∠1 ≅ ∠3 Definition of congruency.
t ║ v Corresponding angle theorem
5) Statement Reason
∠5 ≅ ∠16 Given
∠2 ≅ ∠4 Given
∠5 = ∠16 Definition of congruency
∠2 = ∠4 Definition of congruency
EF ║ GH Corresponding angle theorem
∠14 ≅ ∠16 Corresponding angles
∠14 = ∠16 Definition of congruency
∠5 = ∠14 Transitive property
∠5 + ∠11 = 180° Sum of angles on a straight line
∠14 + ∠11 = 180° Transitive property
∠14 and ∠11 are supplementary Definition of supplementary angles
6) Statement Reason
l ║ m Given
∠4 ≅ ∠7 Given
∠4 = ∠7 Definition of congruency
∠2 ≅ ∠7 Alternate angles
∠2 = ∠7 Definition of congruency
∠2 = ∠4 Transitive property
∠2 ≅ ∠4 Definition of congruency
∠2 and ∠4 are corresponding angles Definition
DA ║ EB Corresponding angle theorem
∠8 and ∠9 are consecutive interior angles Definition
∠8 and ∠9 are supplementary Consecutive interior angles theorem.
Answer:
In February, 423 daytime minutes is used
Step-by-step explanation:
Let the base plan charges be x
And cost per daytime minute be y
In December,
x + 510y = 92.25------------------(1)
In January,
x + 397y = 77.56---------------------(2)
Subtracting eq(2) from eq(1)
x + 510y = 92.25
x + 397y = 77.56
-------------------------------
0 + 113y = 14.69
-------------------------------
y = \frac{14.69}{113}
y = 0.13----------------------------------(3)
Substituting (3) in (1)
x + 510(0.13) = 92.25
x + 66.3 = 92.25
x = 92.25 - 66.3
x = 25.95
So In February
base plan + (daytime minute)(cost per daytime minute) = 80.9
25.95 + (daytime minute)(0.13) = 80.9
(daytime minute)(0.13) = 80.9 - 25.95
(daytime minute)(0.13) = 54.95
(daytime minute) =
daytime minutes = 422.69
daytime minute