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3 years ago

Please help! also please leave the steps!

Mathematics

1 answer:

trapecia [35]3 years ago

4 0

Answer:

The base of the rectangle = 17x

perimeter of the rectangle = 1 + 34x

Base + Height = 1 + 34x

Height + 17x = 1 + 34x

Height = 1 + 17x --------------------- Length of the vertical side

Area of rectangle = 17x * (1 + 17x)

Area = 17x + (17*x)^2

If x = 50

Area = 17(50) + (17*50) * (17 * 50)

Area = 850 + 850 * 850

Area = 850 + 722500

Area = 723,350 -------------------------- Area if x = 50

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Karla is selling tickets for a high school play. Child tickets cost $7 and adult tickets cost $13 she sells 180 tickets and coll

ycow [4]

Answer: The number of child tickets is 85 and the number of adult tickets is 95.

Step-by-step explanation:

Let C = Number of child tickets

A = Number of adult tickets.

As per given, we have

C+A=180 (i)

7C+13A=1830 (ii)

Multiply 7 to both sides of equation (ii), we get

7C+7A=1260 (iii)

Eliminate (iii) from (ii) , we get

$6A=570\\\\\Rightarrow\ A=95$

Put value of y in (i), we get

C= 85

Hence, the number of child tickets is 85 and the number of adult tickets is 95.

3 0

3 years ago

In studies for a medication, 3 percent of patients gained weight as a side effect. Suppose 643 patients are randomly selected.

timofeeve [1]

Part a)

It was given that 3% of patients gained weight as a side effect.

This means

$p = 0.03$

$q = 1 - 0.03 = 0.97$

The mean is

$\mu = np$

$\mu = 643 \times 0.03 = 19.29$

The standard deviation is

$\sigma = \sqrt{npq}$

$\sigma = \sqrt{643 \times 0.03 \times 0.97}$

$\sigma =4.33$

We want to find the probability that exactly 24 patients will gain weight as side effect.

P(X=24)

We apply the Continuity Correction Factor(CCF)

P(24-0.5<X<24+0.5)=P(23.5<X<24.5)

We convert to z-scores.

$P(23.5 \: < \: X \: < \: 24.5) = P( \frac{23.5 - 19.29}{4.33} \: < \: z \: < \: \frac{24.5 - 19.29}{4.33} ) \\ = P( 0.97\: < \: z \: < \: 1.20) \\ = 0.051$

Part b) We want to find the probability that 24 or fewer patients will gain weight as a side effect.

P(X≤24)

We apply the continuity correction factor to get;

P(X<24+0.5)=P(X<24.5)

We convert to z-scores to get:

$P(X \: < \: 24.5) = P(z \: < \: \frac{24.5 - 19.29}{4.33} ) \\ = P(z \: < \: 1.20) \\ = 0.8849$

Part c)

We want to find the probability that

11 or more patients will gain weight as a side effect.

P(X≥11)

Apply correction factor to get:

P(X>11-0.5)=P(X>10.5)

We convert to z-scores:

$P(X \: > \: 10.5) = P(z \: > \: \frac{10.5 - 19.29}{4.33} ) \\ = P(z \: > \: - 2.03)$

$= 0.9788$

Part d)

We want to find the probability that:

between 24 and 28, inclusive, will gain weight as a side effect.

P(24≤X≤28)=

P(23.5≤X≤28.5)

Convert to z-scores:

$P(23.5 \: < \: X \: < \: 28.5) = P( \frac{23.5 - 19.29}{4.33} \: < \: z \: < \: \frac{28.5 - 19.29}{4.33} ) \\ = P( 0.97\: < \: z \: < \: 2.13) \\ = 0.1494$