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1 month ago

If y varies directly as x, and y is 400 when x is r and y is r when x is 4, what is the numeric constant of variation in this

Mathematics

2 answers:

Leona [12.6K]1 month ago

7 0

Answer:

Step-by-step explanation:

If there’s a direct correlation between variables x and y, it can be expressed as

y = kx,

where y is the dependent variable

x is the independent variable

k signifies the constant of variation

_____________________________

For the first scenario

y = 400

x = r

using y = kx, we can derive the relation:

400 = kr

To find k here:

k = 400/r

For the second scenario

y = r

x = 4

again using y = kx, the relationship is given by:

r = 4k

Solving for k:

k = r/4

Since both conditions provide the same equation, k will have the same value in both cases.

Thus, we conclude:

400/r = r/4

=> 400*4 = r*r

=> 1600 = r^2

$\sqrt{r^{2} } = \sqrt{1600} \\r = 40$

Hence, r is calculated to be 40.

Thus, k = r/4 = 40/4 = 10.

The constant of variation is confirmed to be 10, which is the correct answer.

Verification:

k = 400/r = 400/40 = 10

zzz [12.3K]1 month ago

6 0

Answer:

A. 10 on Edg2020

Step-by-step explanation:

Hope this assists!!! Wishing you a wonderful day!!!: )

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A trapezoid can indeed be a quadrilateral with only two right angles, hence Balavan's assertion is incorrect. Denna is correct as having three right angles implies the fourth angle must also be a right angle, leading to either a square or a rectangle.

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1 month ago

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f Khan had an army of 10,000 soldiers at the lowest level, how many men in total were under him in his organization? (b) If Khan

babunello [11817]

Cette question est incomplète, la question complète est;

Gengis Khan organisait ses hommes en groupes de 10 soldats dirigés par un « leader de 10 ». Dix « leaders de 10 » étaient sous un « leader de 100 ». Dix « leaders de 100 » étaient sous un « leader de 1 000 ».

(a) Si Khan avait une armée de 10 000 soldats au niveau le plus bas, combien d'hommes en tout étaient sous son commandement dans son organisation?

(b) Si Khan avait une armée de 5 763 soldats au niveau le plus bas, combien d'hommes en tout étaient sous son commandement dans son organisation?

On suppose que les groupes de 10 doivent contenir 10 si possible, mais qu'un groupe à chaque niveau peut avoir besoin de témoigner moins

Réponse:

a) = 11110 soldats

b = 6404 soldats

Explication étape par étape:

Étant donné que Khan a disposé ses hommes en groupes de 10 sous un « leader de 10 », dix « leaders de 10 » étaient supervisés par un « leader de 100 », et dix « leaders de 100 » étaient dirigés par un « leader de 1000 »

alors

a) Si Khan avait une armée de 10 000 soldats au niveau le plus bas, combien d'hommes au total étaient sous son organisation?

MAINTENANT

Nombre de soldats = 10 000

Rang le plus bas (soldat) = 10000

troisième plus haut (leader de 10) = 10000/10 = 1000

deuxième le plus élevé (leader de 100) = 1000/10 = 100

Le plus haut (Leader de 1000) = 100/10 = 10

donc le total = 10000 + 1000 + 100 + 10 = 11110 soldats

b) Si Khan avait une armée de 5 763 soldats au rang le plus bas, combien d'hommes au total étaient sous son commandement dans son organisation? On suppose que les groupes de 10 doivent contenir 10 si possible, mais qu'un groupe à chaque niveau peut avoir besoin de témoigner moins

MAINTENANT

Nombre de soldats = 5 763

Rang le plus bas (soldat) = 5763

troisième plus haut (leader de 10) = 5763/10 = 576.3 = 577 (nombre entier requis pour un humain)

deuxième le plus élevé (leader de 100) = 577/10 = 57.7 = 58

Le plus haut (Leader de 1000) = 58/10 = 5.8 = 6

donc le total = 5763 + 577 + 58 + 6 = 6404 soldats

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1 month ago

The amount of time it takes for a student to complete a statistics quiz is uniformly distributed (or, given by a random variable

Zina [12379]

Answer:

(A) 0.15625

(B) 0.1875

(C) Cannot be determined

Step-by-step explanation:

The time it takes for a student to finish a statistics quiz is uniformly distributed between 32 and 64 minutes.

Let's denote X as the duration needed for the student to complete the statistics quiz

Thus, X ~ U(32, 64)

The probability density function (PDF) for a uniform distribution is expressed as;

f(X) = $\frac{1}{b-a}$ , a < X < b where a = 32 and b = 64

The cumulative distribution function (CDF) is given by P(X <= x) = $\frac{x-a}{b-a}$

(A) The probability of a student taking longer than 59 minutes to complete the quiz = P(X > 59)

P(X > 59) = 1 - P(X <= 59) = 1 - $\frac{x-a}{b-a}$ = 1 - $\frac{59-32}{64-32}$ = $1-\frac{27}{32}$ = 0.15625

(B) The probability that a student completes the quiz between 37 and 43 minutes = P(37 <= X <= 43) = P(X <= 43) - P(X < 37)

P(X <= 43) = $\frac{43-32}{64-32}$ = $\frac{11}{32}$ = 0.34375

P(X < 37) = $\frac{37-32}{64-32}$ = $\frac{5}{32}$ = 0.15625

P(37 <= X <= 43) = 0.34375 - 0.15625 = 0.1875

= P(X = 44.74)

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1 month ago

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If there are 2.2 pounds in 1 kilogram how many pounds are there in x kilograms?

tester [12383]

Answer:

P=x/2.2

Step-by-step explanation:

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