Answer:
Tema = 26 years
Juma = 13 years
Abdul = 26 years
Step-by-step explanation:
Let their ages be represented as:
Tema = x
Juma = y
Abdul = z
From the question, we are told that:
Juma is twice as old as Abdul
y = 2z
z = y/2
= 0.5y
And Juma is a half times as old as Tema.
y = 1/2x
y = 0.5x
x = y/0.5
x = 2y
Hence,
x + y + z = 65
2y + y + 2y = 65
= 5y = 65
y = 65/5
y = 13 years
Since y = Zuma's age, Zuma is 13 years old
From the above question
Since 2y = z
y = 13
2 × 13 = z
z = 26
Since z = Abdul's age, Abdul is 26 years old
From the above question
x = 2y
y = 13 years
x = 2 × 13 years
x = 26 years.
Since x = Tema's age
Tema is 26 years.
Therefore, their present ages are:
Tema = 26 years
Juma = 13 years
Abdul = 26 years
Answer:
The radius of the circle P = 2√10 = 6.325
Step-by-step explanation:
∵ AB is a tangent to circle P at A
∴ (AB)² = BC × BE
∵ BC = 8 , AB = 12 , ED = 6
∵ BE = ED + DC + CB
∴ BE = 6 + CD + 8 = 14 + CD
∴ (12)² = 8 × (14 + DC) ⇒ (12)²/8 = 14 + CD ⇒ CD = (12)²/8 - 14
∴ CD = 4
Join PC and PE (radii)
In ΔBDC and ΔPDE ⇒ ∵ ∠PDC = Ф , ∴ ∠PDE = 180 - Ф
Use cos Rule:
∵ r² = (PD)² + (DC)² - 2(PD)(DC)cosФ
∴ r² = 16 + 16 - 32cosФ = 32 - 32cosФ ⇒ (1)
∵ r² = (PD)² + (DE)² - 2(PD)(DE)cos(180 - Ф) ⇒ cos(180 - Ф) = -cosФ
∴ r² = 16 + 36 + 48cosФ = 52 + 48cosФ ⇒ (2)
∵ (1) = (2)
∴ 32 - 32 cosФ = 52 + 48cosФ
∴ 32 - 52 = 48cosФ + 32cosФ
∴ -20 = 80cosФ
∴ cosФ = -20/80 = -1/4
∴ r² = 32 - 32(-1/4) = 32 + 8 = 40
∴ r = √40 = 2√10 = 6.325
(0,6),(4,10),(1,7), all you need to do is find a random y value and add 6 to it to get the x value.
Answer:
There is not sufficient evidence to support the claim that there is a linear correlation between the heights and pulse rates of women
Step-by-step explanation:
The correlation coefficient between the variables h(height in inches) and pulse rates (in beats per minute) is 0.202
Sample size n=40
Level of significane alpha = 0.01
Create null and alternate hypothesis as:
H0: r=0
Ha: r not equal 0
(Two tailed test at 1% significance level)
Sample r = 0.202
r difference = 0.202
test statistic t = 
df =n-2 =38
t critical value for 0.01 and df =38 is 2.704
Since our test statistic lies below 2.704, we accept null hypothesis
There is not sufficient evidence to support the claim that there is a linear correlation between the heights and pulse rates of women