Please see the figure. We'll first work out half the area of the rounded triangle, half the unshaded part, then double it, then subtract it from the big square.
Half the area is the circular sector PTQ (with center P, arc TQ) minus the right triangle PUT.
A/2 = area(sector PTQ) - area(triangle PUT)
The triangle is half of equilateral triangle PQT, so a 30/60/90 right triangle so we know the sides are in ratio 1:√3:2 so
TU = (7/2)√3
area(PUT) = (1/2) (7/2)(7/2)√3 = (49/8)√3
area(sector PTQ) = (angle TQP / 360°) πr^2
We know angle TQP is 60° because TQP is equilateral. r=7.
area(sector PTQ) = (60°/360°) π (7²) = 49π/6
Putting it together,
A/2 = area(sector PTQ) - area(triangle PUT)
A = 2(49π/6 - (49/8)√3)
A = 49(π/3 - √3/4) square cm
I hate ruining a nice exact answer with an approximation, but they seem to be asking.
A ≈ 30.095057615914535
Check:
I'm not sure how to check it. I'd estimate it's about 25% bigger than equilateral triangle PQT with area (√3/4)7² ≈ 21.2, so around 27. 30 seems reasonable.
Now the real area we seek is the big square PQRS minus A, so
area = 7² - 30.095057615914535 = 18.904942384086 sq cm
They want square meters for some reason; we scale by (1/100)²
Answer: 0.00189 square meters
Answer:
p value = 0.03514
Step-by-step explanation:
Hypotheses would be
(left tailed test at 10% level of significance)
Here p stands for the sample proportion of mothers smoked more than 21 cigarettes during their pregnancy.
Sample size =130
persons who smoked = 2
Sample proportion =
Assuming H0 to be true
Std error=
p difference = -0.0346
Test statistic z=-1.81
p value = 0.03514
Since p is less than 0.10, significance level, we reject H0
<em>Note: you may have unintentionally missed to add the complete question. Therefore, after a little research, I am able to find the complete question which I am attaching to solve your query, which anyways would clear your concept. </em>
The complete Question:
Keenan gives Tisha half of his strawberries. Tisha keeps 4 of the strawberries she got from Keenan and gives the rest to Suvi.
a) Write an expression for the number of strawberries Tisha gives to Suvi. Use k for the number of strawberries Keenan started with.
b) Could Keenan have started with 6 strawberries? Use your expression to explain why or why not.
Answer:
Part a)
An expression for the number of strawberries Tisha gives to Suvi will be:<em> </em>
Part b)
Keenan could not have started with 6 strawberries
Step-by-step explanation:
Part a) <em>Write an expression for the number of strawberries Tisha gives to Suvi. Use k for the number of strawberries Keenan started with.</em>
Let be the total number of strawberries which Keenan has.
So,
is the number of strawberries Keenan gave to Tisha.
As Tisha keeps 4 strawberries and gives the rest to Suvi. Let be the number of strawberries which Suvi has.
So,
Therefore, an expression for the number of strawberries Tisha gives to Suvi will be:<em> </em>
b) Could Keenan have started with 6 strawberries? Use your expression to explain why or why not.
Considering the expression for the number of strawberries Tisha gives to Suvi
Putting in the expression
Solving the expression
∵
So, Keenan would have started with 6 strawberries, then Suvi would have -1 strawberries. Since, strawberries cannot be negative as Suvi cannot have negative number of strawberries.
Therefore, Keenan could not have started with 6 strawberries.
Keywords: word problem, expression
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Answer:
108 x 25² divided by 2⁶ x 5² is equal to
Step-by-step explanation:
Given;
108 x 25² divided by 2⁶ x 5²
The expression is simplified as follows;
Therefore, 108 x 25² divided by 2⁶ x 5² is equal to