The function f(x)=4x is transfored to g (x) = -8x. what type of transformation has occurred?
1 answer:
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Answer:
The surface area of the pyramid in exact form is 64 + cm²
The approximated surface area of the pyramid is 174.9 cm²
Step-by-step explanation:
The surface area of the square pyramid is the sum of the area of the base and the area of the four triangular faces
In Δ EFD
∵ m∠EFD = 90°
∵ m∠FDE = 60°
∵ ED = 8 cm
- By using sine ratio to find FE
∵ sin(∠FDE) =
∴ sin(60) =
- Multiply both sides by 8
∴ FE = 8 sin(60°)
∴ FE = cm
In Δ AED
∵ AE = ED
∵ m∠D = 60°
- In any isosceles Δ if measure of an angle is 60, then the
triangle is equilateral Δ
∴ Δ AED is an equilateral Δ
∴ AD = 8 cm
∵ The pyramid has 4 identical triangular faces
∵ Area of each Δ = × base × height
∵ AD is the base and FE is the height
∴ Area of each Δ = × 8 ×
∴ Area of each Δ = cm²
∵ Surface area of the pyramid = Area of base + 4 area of a Δ
∵ Area of base = 8²
∴ Area of base = 64 cm²
∴ Surface area of the pyramid = 64 + 4 ×
∴ Surface area of the pyramid = 64 +
The surface area of the pyramid in exact form is 64 + cm²
The approximated surface area of the pyramid is 174.9 cm²
Answer:
The calculated value Z = 1.4460 < 1.96 at 0.05 level of significance.
The null hypothesis is accepted
A local power company believes that residents in their area use more electricity on average than EIA's reported average
Step-by-step explanation:
<u><em>Step(i):-</em></u>
Given that the mean of the Population = 10,608 kWh of electricity this year.
Given that the size of the sample n = 187
Given that mean of sample x⁻ = 10737 kWh
The Standard deviation of the Population = 1220kWh
Level of significance = 0.05
The critical value (Z₀.₀₅)= 1.96
<u><em>Step(ii):-</em></u>
Null Hypothesis: H₀:μ > 10608 kWh
Alternative Hypothesis: H₁: μ < 10608kWh
Test statistic
Z = 1.4460
<u>Final answer:-</u>
The calculated value Z = 1.4460 < 1.96 at 0.05 level of significance.
The null hypothesis is accepted
A local power company believes that residents in their area use more electricity on average than EIA's reported average.