Answer:
Step-by-step explanation:
m = 2 ; x1 = -3 ; y1 = -1
Slope- point form: y - y1 = m(x -x1)
y - [-1] = 2(x - [-3])
y + 1 = 2(x + 3)
y + 1 = 2x + 3*2
y + 1 =2x + 6
y = 2x + 6 - 1
y = 2x + 5 This is slope intercept form : y = mx + b
The total number of members should be the sum of the number of men, x, and women, y, and that should be equal to 150. In mathematical equation that should be,
<em>x + y = 150</em>
If we are to note that there are 34 more men than women in the team, we can say that,
y = x - 34
The equation then would become,
x + (x - 34) = 150
The value of x from the equation is equal to 92. With this, the number of the women is equal to 58.
You know the adjacent and you need to find the opposite, so you would use tangent. Your equation would look like this; tan 26°= x/28. You would need to multiply both sides by 28 to simplify it to this; 28*tan 26°= x
Solving this, you would get an answer of 13.7
Answer: the qualifying time in seconds is about 25.3
Step-by-step explanation:
Since the personal best finishing times for a particular race in high school track meets are normally distributed, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = personal best finishing times for a particular race.
µ = mean finishing time
σ = standard deviation
From the information given,
µ = 24.6 seconds
σ = 0.64 seconds
The probability value for the top 15% of finishing time for runners to qualify would be (1 - 15/100) = (1 - 0.15) = 0.85
Looking at the normal distribution table, the z score corresponding to the probability value is 1.04
Therefore,
1.04 = (x - 24.6)/0.64
Cross multiplying by 0.64, it becomes
1.04 × 0.64 = x - 24.6
0.6656 = x - 24.6
x = 0.6656 + 24.6
x = 25.3 seconds