Answer:
The angle the wire now subtends at the center of the new circle is approximately 145.7°
Step-by-step explanation:
The radius of the arc formed by the piece of wire = 15 cm
The angle subtended at the center of the circle by the arc, θ = 68°
The radius of the circle to which the piece of wire is reshaped to = 7 cm
Let 'L' represent the length of the wire
By proportionality, we have;
L = (θ/360) × 2 × π × r
L = (68/360) × 2 × π × 15 cm = π × 17/3 = (17/3)·π cm
Similarly, when the wire is reshaped to form an arc of the circle with a radius of 7 cm, we have;
L = (θ₂/360) × 2 × π × r₂
∴ θ₂ = L × 360/(2 × π × r₂)
Where;
θ₂ = The angle the wire now subtends at the center of the new circle with radius r₂ = 7 cm
π = 22/7
Which gives;
θ₂ = (17/3 cm) × (22/7) × 360/(2 × (22/7) × 7 cm) ≈ 145.7°.
Approximately 22.360679775
b) five more than m
"m in addition to 5"= m+5
Answer:
x = -5/3
Step-by-step explanation:
Combine like terms: 2x + 3x = 5x - 1 (on the left) -6 + 2x (on the right) (5x - 1 = -6 + 2x)
Get X on one side: Isolate +2x by subtracting 2x on both sides (5x - 2x = 3x) (3x - 1 = -6) Isolate -1 by subtracting 1 on both sides (3x = -5) Isolate 3x by dividing 3 on both sides.
I hope I explained it correctly
Answer:
There is no sufficient evidence to support the executive claim
Step-by-step explanation:
From the question we are told that
The population proportion is 
The sample proportion is 
The sample size is 
The level of significance is 
The null hypothesis is 
The alternative hypothesis is 
Generally the test statistics is mathematically evaluated as
=> 
=> 
The p-value is mathematically represented as
Form the z-table
=> 
=> 
Given that 
we fail to reject the null hypothesis
Hence we can conclude that there is no sufficient evidence to support the executive claim
