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On a coordinate plane, parallelogram P Q R S is shown. Point P is at (negative 2, 5), point Q is at (2, 1), point R is at (1, ne

Oksanka [162]

Answer:

The perimeter is $(8\sqrt{2}+2\sqrt{10})\ units$

Step-by-step explanation:

we know that

A parallelogram is a quadrilateral where both pairs of opposite sides are parallel and equal

so

In this problem

PS=QR ----> equation A

SR=PQ ----> equation B

The perimeter of parallelogram PQRS is

P=PQ+QR+SR+PS ----> equation C

substitute equation A and equation B in equation C

$P=2SR+2QR$

we have

$QR=\sqrt{10}\ units$

$SR=4\sqrt{2}\ units$

substitute in the formula of perimeter

$P=2(4\sqrt{2})+2(\sqrt{10})$

$P=(8\sqrt{2}+2\sqrt{10})\ units$

7 0

1 year ago

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The center of a circle is located at (3, 8), and the circle has a radius that is 5 units long. What is the general form of the e

inna [77]

Answer:

The general equation of a circle is x² + y² - 6x - 16y + 48 = 0 .

Step-by-step explanation:

The standard form of equation of circle.

$(x - h)^{2} + (y - k)^{2} = r^{2}$

Where (h,k) is the centre of a circle and r is the radius.

As given

The center of a circle is located at (3, 8), and the circle has a radius that is 5 units .

Put in the formula

$(x - 3)^{2} + (y - 8)^{2} = 5^{2}$

(By using the formula (a - b)² = a² + b²- 2ab)

As 5² = 25

x² + 9 - 6x + y² + 64 - 16y = 25

x² + y² - 6x - 16y + 9 + 64 = 25

x² + y² - 6x - 16y + 73 = 25

x² + y² - 6x - 16y + 73 - 25 = 0

x² + y² - 6x - 16y + 48 = 0

(As the general equation of a circle are in the form x² + y² + Ax +By + F =0 Where A,B and C are constant .)

Therefore the general equation of a circle is x² + y² - 6x - 16y + 48 = 0 .

6 0

1 year ago

A pharmaceutical company proposes a new drug treatment for alleviating symptoms of PMS (premenstrual syndrome). In the first sta

Akimi4 [234]

Answer:

95% confidence interval for p, the true proportion of all women who will find success with this new treatment is [0.238 , 0.762].

Step-by-step explanation:

We are given that a pharmaceutical company proposes a new drug treatment for alleviating symptoms of PMS (premenstrual syndrome).

In the first stages of a clinical trial, it was successful for 7 out of the 14 women.

Firstly, the pivotal quantity for 95% confidence interval for the true proportion is given by;

P.Q. = $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion of women who find success with this new treatment = $\frac{7}{14}$ = 0.50

n = sample of women = 14

Here for constructing 95% confidence interval we have used One-sample z proportion statistics.

So, 95% confidence interval for the true proportion, p is ;

P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5%

level of significance are -1.96 & 1.96}

P(-1.96 < $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < 1.96) = 0.95

P( $-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < ${\hat p-p}$ < $1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.95

P( $\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < p < $\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.95

95% confidence interval for p = [ $\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ , $\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ]

= [ $0.50-1.96 \times {\sqrt{\frac{0.50(1-0.50)}{14} } }$ , $0.50+1.96 \times {\sqrt{\frac{0.50(1-0.50)}{14} } }$ ]

= [0.238 , 0.762]

Therefore, 95% confidence interval for p, the true proportion of all women who will find success with this new treatment is [0.238 , 0.762].

4 0

2 years ago

Large flower pots weigh 28 pounds each.

LiRa [457]

Answer:

The correct answer is: 980 pounds

Step-by-step explanation:

1 flower pot = 28 pounds

1 crate = 35 pots

∴ 1 crate = 35 pots × 28 pounds = 980 pounds

5 0

1 year ago

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Mr. Itol's assistant takes twice as long to complete a computer task as Mr. Itol. If it takes both experts 6 hours to complete t

earnstyle [38]

His assistant would have to take 4 hour 30 minutes while Mr. Itol would take 1 hour 30 minutes.

3 0

2 years ago

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