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1 year ago

R is inversely proportional to A R = 12 when A = 1.5 a) Work out the value of R when A = 5 b) Work out the value of A when R = 9

Mathematics

1 answer:

lapo4ka [179]1 year ago

5 0

Answer:

a) R = 3.6

b) A = 2

Step-by-step explanation:

To find the value, start by modeling the inverse proportionality by using the base equations with the original givens.

y = k/x

12 = k/1.5

18 = k

Now we use that to model the equation

R = 18/A

And we can now use that to solve parts a) and b)

R = 18/A

R = 18/5

R = 3.6

R = 18/A

9 = 18/A

2 = A

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Patrick’s living room must be 6 units wide.

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2 years ago

Data sets A and B are dependent. Find sd.Assume that the paired data came from a population that is normally distributed.A. 1.73

marusya05 [52]

Complete question :

A : 2.7, 3.7, 5.6, 2.6, 2.7

B : 5.1, 4.0, 3.9, 3.8, 5.2

Data sets A and B are dependent. Find sd.Assume that the paired data came from a population that is normally distributed.A. 1.73B. 1.21C. 1.32D. 1.89

Answer: A.1.73

Step-by-step explanation:

Given the data:

A : 2.7, 3.7, 5.6, 2.6, 2.7

B : 5.1, 4.0, 3.9, 3.8, 5.2

Difference betweenA and B (A - B) :

Xd = (A - B) = - 2.4, -0.3, 1.7, - 1.2, - 2.5

Sum of (A - B) = Σ Xd = (-2.4 + (-0.3) + 1.7 + (-1.2) + (-2.5) = - 4. 7

Md = ΣXd / n = - 4.7 / 5 = - 0.94

Xd - Md = (-2.4 + 0.94), (-0.3 + 0.94), (1.7 + 0.94), (-1.2 + 0.94), (-2.5 + 0.94)

(Xd - Md) = - 1.46, 0.64, 2.64, - 0.26, - 1.56

(Xd - Md)^2 = (-1.46)^2 + 0.64^2 + 2.64^2 + (-0.26)^2 + (-1.56)^2

Σ(Xd - Md)^2 = (2.1316 + 0.4096 + 6.9696 + 0.0676 + 2.4336) = 12.012

Standard deviation = √[Σ(Xd - Md)^2 / (n-1)]

Standard deviation= √12.012 / 4

Standard deviation = 1.7329

Standard deviation= 1.73

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2 years ago

Find the sum of the first 63 terms of –19, -13, -7 …

boyakko [2]

The Given Sequence is an Arithmetic Sequence with First term = -19

⇒ a = -19

Second term is -13

We know that Common difference is Difference of second term and first term.

⇒ Common Difference (d) = -13 + 19 = 6

We know that Sum of n terms is given by : $S_n = \frac{n}{2}(2a + (n - 1)d)$

Given n = 63 and we found a = -19 and d = 6

$\implies S_6_3 = \frac{63}{2}(2(-19) + (63 - 1)6)$

$\implies S_6_3 = \frac{63}{2}(-38 + (62)6)$

$\implies S_6_3 = \frac{63}{2}(-38 + 372)$

$\implies S_6_3 = \frac{63}{2}(334)$

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The Sum of First 63 terms is 10521

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2 years ago

Find the area of the triangle with the given measurements. Round the solution to the nearest hundredth if necessary. A = 46°, b

horrorfan [7]

We will use the law of cosines
side a² = b² + c² -2bc • cos(A)
side a² = 729 + 196 -2*27*14 * cos (46)
side a² = 925 -(756 * 0.69466)
side a² = 399.83704 
side a = 19.995925585 
We could round that to 20
a = 20 b = 27 c =14

We can calculate a triangle's area when we know all 3 sides by using Heron's Formula
area = square root (s • (s - a) • (s - b) • (s - c))

where s is the semi-perimeter 
semi-perimeter = (side a + side b + side c) ÷ 2
s = (20 + 27 + 14) / 2
s = 30.5
Now we use Heron's Formula
area = square root (s • (s - a) • (s - b) • (s - c))
area = square root (30.5 • (30.5 - 20) • (30.5 - 27) • (30.5 - 14))
area = square root (30.5 • (10.5) • (3.5) • (16.5))
area = square root (18494.4375)
 area = 135.9942553934 which rounds to
136 square feet
Source:
http://www.1728.org/triang.htm

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1 year ago

Which of the following could be the ratio of the length of the longer leg of a 30-60-90 triangle to the length of its hypotenuse

Aliun [14]

Answer:

Option C is correct.

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Step-by-step explanation:

This is the special right angle triangle 30°-60°-90° as shown below in the figure.

The side opposite the 30° angle is always the shortest because 30 degrees is the smallest angle.

The side opposite the 60° angle will be the longer leg, because 60 degrees is the mid-sized degree angle in this triangle.

Finally , the side opposite the 90° angle will always be the largest side(Hypotenuse) because 90 degrees is the largest angle.

In 30°−60°−90° right triangle,

the length of the hypotenuse is twice the length of the shorter leg,also
the length of the longer leg is $\sqrt{3}$ times the length of the shorter leg.

Then:

the sides are in proportion i.e, $1:\sqrt{3} :2$

Therefore, the ratio of the length of the longer leg to the length of its hypotenuse is: $\sqrt{3} : 2$

7 0

2 years ago

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