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Rus_ich [418]
3 years ago
8

The circumference of a circular mat is 13π feet. What is the area, in square feet, of the mat? Express your answer in terms of π

Mathematics
1 answer:
qaws [65]3 years ago
6 0

\bf \textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=13\pi \end{cases}\implies 13\pi =2\pi r\implies \cfrac{13\pi }{2\pi }=r\implies \boxed{\cfrac{13}{2}=r} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \textit{area of a circle}\\\\ A=\pi r^2\qquad \qquad \implies A=\pi \left(\cfrac{13}{2} \right)^2\implies A=\pi \left( \cfrac{13^2}{2^2} \right)\implies A=\cfrac{169}{4}\pi

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Solve mathematics question, in photo. :)
Jlenok [28]
(0,4) is the correct answer.
7 0
3 years ago
Three-fourths of a number increased by one-half is equal to fourteen. Find the number.
ivanzaharov [21]

Three-fourths of a number increased by one-half

= 3/4 x + 1/2

So three-fourths of a number increased by one-half is equal to fourteen:

3/4 x + 1/2 = 14

Multiply both sides by 4

3x + 2 = 56

Subtract 2 from both sides

3x = 54

Divide both sides by 3

x = 18

Answer: The number is 18

8 0
3 years ago
Read 2 more answers
7x-3=-3+7x i neep help answer this please
erica [24]

Answer:

All real numbers are solutions.

Step-by-step explanation:

Let's solve your equation step-by-step.

7x− 3 = − 3 + 7x

Step 1: Simplify both sides of the equation.

7x − 3 = −3 + 7x

7x + −3 = −3 + 7x

7x − 3 = 7x − 3

Step 2: Subtract 7x from both sides.

7x− 3 −7x = 7x −3 −7x

−3 = −3

Step 3: Add 3 to both sides.

−3 + 3 = −3 + 3

0 =  0

7 0
3 years ago
Read 2 more answers
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Semenov [28]
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5 0
2 years ago
A newspaper published an article about a study in which researchers subjected laboratory gloves to stress. Among 260 vinyl​ glov
yawa3891 [41]

Answer:

Step-by-step explanation:

pop 1 n₁ = 260, p₁ = 58% = 0.58

pop 2 n₂ = 260, p₂ = 8% = 0.08

Null hypothesis: p₁ ≤ p₂

Alternative hypothesis: p₁ > p₂

The test statistic : p₁-p₂ / √{p-sample (1 - p-sample) (1/n₁ + 1/n₂)}

where p-sample is sample proportion = p₁n₁ +p₂n₂ / n₁+n₂

Thus, p-sample = 0.58x260 +0.08x260 / 260+260 =150.8+20.8 / 520 = 171.6 / 520 = 0.33.

Thus, the test statistic is (0.58 - 0.08) / √[0.33 (1-0.33) (0.0038+0.0038)

  = 0.5 / √[0.33(0.67) (0.0076)

= 0.5 / √0.00168036

= 0.5 / 0.04099

= 12.20

P = P(Z>12.20) = 1-P(Z≤12.20) at a significance level of 0.1= the p-value is less than the hypothesized thus, we have sufficient evidence to reject the null hypothesis and concluding that vinyl gloves have a greater virus leak than latex gloves.

5 0
3 years ago
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