Answer:
(1) 2π - x² = 0 (2) x = 2.5 cm (3) perimeter = 10 cm
Step-by-step explanation:
(1)The area of the circular coin without the inner square removed is πr² where r = 3 cm is the radius of the coin. So, the area of the coin without the inner square removed is πr² = π(3 cm)² = 9π cm²
The area of the square of x sides removed from its center is x².
The area A of the each face of the coin is thus A = 9π - x²
Since the area of each face of the coin A = 7π cm²,
then
7π = 9π - x²
9π - 7π - x² = 0
2π - x² = 0
(2) Solve the equation 2π - x² = 0
2π - x² = 0
x² = 2π
x = ±√(2π)
x = ± 2.51 cm
Since x cannot be negative, we take the positive answer.
So, x = 2.51 cm
≅ 2.5 cm
(3) Find the perimeter of the square
The perimeter of the square, p is given by p = 4x
p = 4 × 2.51 cm
= 10.04 cm
≅ 10 cm
The probablity that the sample's mean length is greate than 6.3 inches is0.8446.
Given mean of 6.5 inches,standard deviation of 0.5 inches and sample size of 46.
We have to calculate the probability that the sample's mean length is greater than 6.3 inches is 0.8446.
Probability is the likeliness of happening an event. It lies between 0 and 1.
Probability is the number of items divided by the total number of items.
We have to use z statistic in this question because the sample size is greater than 30.
μ=6.5
σ=0.5
n=46
z=X-μ/σ
where μ is mean and
σ is standard deviation.
First we have to find the p value from 6.3 to 6.5 and then we have to add 0.5 to it to find the required probability.
z=6.3-6.5/0.5
=-0.2/0.5
=-0.4
p value from z table is 0.3446
Probability that the mean length is greater than 6.3inches is 0.3446+0.5=0.8446.
Hence the probability that the mean length is greater than 6.3 inches is 0.8446.
Learn more about probability at brainly.com/question/24756209
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<span>First we need to find the GCF (greatest common factor)</span>
<span>Factors of 42 are:
1, 2, 3, 6, 7, 14, 21, 42</span>
<span>Factors of 48 are:
1, 2, 3, 4, 6, 8, 12, 16, 24, 48</span>
<span>GCF is 6</span>
<span>To simplify you divide numerator and denominator into the GCF</span>
<span>42 ÷ 6 = 7</span>
<span>48 ÷ 6 = 8</span>
<span>42/48 = 7/8</span>
<span>Hope this helps. :)
</span>
Answer:
A
Step-by-step explanation:
1/2r +1/2= -2/7r -29/7 Subtracting 1/2 from both sides
1/2r +1/2 - 1/2= -2/7r -29/7- 1/2
1/2r = -2/7r - 29(2)-7/14
1/2r = -2/7r -65/14
Point-slope:
y-y1= m(x-x1)
Plug in what you know.
y1= 1 and x1= -8
y-1= 2/5(x-(-8)
y-1= 2/5(x+8)
Distribute.
y-1=.4x+ 3.2 <- that is the final answer
I hope this helps!
~kaikers
