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2 years ago

F is directly proportional to a.If F = 42 when a 7 finda when F = 18

Mathematics

2 answers:

horrorfan [7]2 years ago

7 0

Answer:

a=3

Step-by-step explanation:

The formula for direct proportion is

f = ka

Let f= 42 and a = 7

42 = k*7

Divide each side by 7

42/7 = k7/7

6 =k

f = 6a

Let f = 18

18 = 6a

Divide each side by 6

18/6 = 6a/6

3 =a

crimeas [40]2 years ago

4 0

Answer:

a = 3

Step-by-step explanation:

Given that F is directly proportional to a, then the equation relating them is

F = ka ← k is the constant of proportion

To find k use the condition F = 42 when a = 7, thus

42 = 7k ( divide both sides by 7 )

6 = k

F = 6a ← equation of proportion

When F = 18, then

18 = 6a ( divide both sides by 6 )

3 = a

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A quality control engineer tests the quality of produced computers. suppose that 5% of computers have defects, and defects occur

11111nata11111 [884]

(a) 0.059582148 probability of exactly 3 defective out of 20

(b) 0.98598125 probability that at least 5 need to be tested to find 2 defective.

(a) For exactly 3 defective computers, we need to find the calculate the probability of 3 defective computers with 17 good computers, and then multiply by the number of ways we could arrange those computers. So

0.05^3 * (1 - 0.05)^(20-3) * 20! / (3!(20-3)!)

= 0.05^3 * 0.95^17 * 20! / (3!17!)

= 0.05^3 * 0.95^17 * 20*19*18*17! / (3!17!)

= 0.05^3 * 0.95^17 * 20*19*18 / (1*2*3)

= 0.05^3 * 0.95^17 * 20*19*(2*3*3) / (2*3)

= 0.05^3 * 0.95^17 * 20*19*3

= 0.000125* 0.418120335 * 1140

= 0.059582148

(b) For this problem, let's recast the problem into "What's the probability of having only 0 or 1 defective computers out of 4?" After all, if at most 1 defective computers have been found, then a fifth computer would need to be tested in order to attempt to find another defective computer. So the probability of getting 0 defective computers out of 4 is (1-0.05)^4 = 0.95^4 = 0.81450625.

The probability of getting exactly 1 defective computer out of 4 is 0.05*(1-0.05)^3*4!/(1!(4-1)!)

= 0.05*0.95^3*24/(1!3!)

= 0.05*0.857375*24/6

= 0.171475

So the probability of getting only 0 or 1 defective computers out of the 1st 4 is 0.81450625 + 0.171475 = 0.98598125 which is also the probability that at least 5 computers need to be tested.

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2 years ago

If week 1=5, week 2=3, week 3=7, week 4=5 what will week 5 be?

olga2289 [7]

Answer: 11

Step-by-step explanation:

The sequence goes +4, +1, +5, +1... so obviously the next number will be +6. So, 5+6=11

The answer is week 5=11

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1 year ago

Mr. Matthew is testing the online popularity of his custom made belts and wallets that were marketed differently. Some items wer

Tomtit [17]

See the attached figure
===========================
After 3 days, the total number of belts sold will be the same as the total number of wallets sold. The number of belts and the number of wallets Mr. Matthew sold after this many days is 27.

======================================================
Explanation of the answer:
The equation that represents the number of belts sold = 3^x ⇒⇒⇒ blue graph

The equation that represents the number of wallets sold = 4x+15 ⇒⇒⇒ red graph

The point of intersection represents the total number of belts sold will be the same as the total number of wallets sold.

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2 years ago

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Noah is running a portion of a marathon at a constant speed of 6 mph. Complete the table to predict how long it would take him t

ycow [4]

Answer:

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Step-by-step explanation:

Noah's running speed = 6 mph.

Use formula $D=v\cdot t,$ where

D is the distance,

v is the speed,

t is the time.

If $t=1$ hour, then $D=6\cdot 1=6$ miles.

If $t=\dfrac{1}{2}$ hour, then $D=6\cdot \dfrac{1}{2}=3$ miles.

If $t=1\dfrac{1}{3}$ hours, then $D=6\cdot 1\dfrac{1}{3}=6\cdot \dfrac{4}{3}=8$ miles.

If $t=1\dfrac{1}{2}$ hours, then $D=6\cdot 1\dfrac{1}{2}=6\cdot \dfrac{3}{2}=9$ miles.

If $t=9$ hours, then $D=6\cdot 9=54$ miles.

If $t=4\dfrac{1}{2}$ hours, then $D=6\cdot 4\dfrac{1}{2}=6\cdot \dfrac{9}{2}=27$ miles.

So, the table is

$\begin{array}{cc}\text{Time}&\text{Distance}\\ \\1&6\\ \\\dfrac{1}{2}&3\\ \\1\dfrac{1}{3}&8\\ \\1\dfrac{1}{2}&9\\ \\9&54\\ \\4\dfrac{1}{2}&27\end{array}$

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2 years ago

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Now, we can use the height to figure out the volume of a cone. The volume of a cone is $V = pi * r^2 * \frac{h}{3}$
R is 2 again and h is 2.87
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2 years ago

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F is directly proportional to a.If F = 42 when a 7 finda when F = 18​

F is directly proportional to a.If F = 42 when a 7 finda when F = 18