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2 years ago

What does it mean to be proportional?

Mathematics

1 answer:

rusak2 [61]2 years ago

8 0

Answer:

in my words proportional means having equal portions lets say you cut a pizza into 4 separate pieces if you had 1 piece that was half and three pieces random that is not proportional but if you have 4 quarters that is proportional

Step-by-step explanation:

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A poll reported that 66% of adults were satisfied with the job the major airlines were doing. Suppose 20 adults are selected at

NARA [144]

Answer:

0.5640

Step-by-step explanation:

n = 12 (number of adults)

p = 0.65 (probability that an adult is satisfied with the job the major airlines were doing.

x = number of adults out of 11 who were satisfied.

P( x = 5) = 11C5 (0.65)^5 (0.35)^6 = 0.0986

P( x < 3) = P(x=0)+P(x=1)+P(x=2)

P( x =0) = 11C0 (0.65)^0 (0.35)^11 = 0.0000

P( x =1) = 11C1 (0.65)^1 (0.35)^10 = 0.0002

P( x =2) = 11C2 (0.65)^2 (0.35)^9 = 0.0018

Add: P( x < 3) = 0.0020

P( x ≥ 8) = P(x=8)+P(x=9)+P(x=10)+P(x=11)

P( x =8) = 11C8 (0.65)^8 (0.35)^3 = 0.2254

P( x =9) = 11C9 (0.65)^9 (0.35)^2 = 0.1395

P( x =10) = 11C10 (0.65)^10 (0.35)^1 = 0.0518

P( x =11) = 11C11 (0.65)^11 (0.35)^0 = 0.0087

add:

P( x ≥ 8) = 0.4254

P(x=4)+P(x=5)+P(x=6)+P(x=7)

P( x =4) = 11C4 (0.65)^4 (0.35)^7 = 0.0379

P( x =5) = 11C5 (0.65)^5 (0.35)^6 = 0.0985

P( x =6) = 11C6 (0.65)^6 (0.35)^5 = 0.1830

P( x =7) = 11C7 (0.65)^7 (0.35)^4 = 0.2428

Add: 0.5640

8 0

2 years ago

Please I need help with differential equation. Thank you

Inga [223]

1. I suppose the ODE is supposed to be

$\mathrm dt\dfrac{y+y^{1/2}}{1-t}=\mathrm dy(t+1)$

Solving for $\dfrac{\mathrm dy}{\mathrm dt}$ gives

$\dfrac{\mathrm dy}{\mathrm dt}=\dfrac{y+y^{1/2}}{1-t^2}$

which is undefined when $t=\pm1$ . The interval of validity depends on what your initial value is. In this case, it's $t=-\dfrac12$ , so the largest interval on which a solution can exist is $-1\le t\le1$ .

2. Separating the variables gives

$\dfrac{\mathrm dy}{y+y^{1/2}}=\dfrac{\mathrm dt}{1-t^2}$

Integrate both sides. On the left, we have

$\displaystyle\int\frac{\mathrm dy}{y^{1/2}(y^{1/2}+1)}=2\int\frac{\mathrm dz}{z+1}$

where we substituted $z=y^{1/2}$ - or $z^2=y$ - and $2z\,\mathrm dz=\mathrm dy$ - or $\mathrm dz=\dfrac{\mathrm dy}{2y^{1/2}}$ .

$\displaystyle\int\frac{\mathrm dy}{y^{1/2}(y^{1/2}+1)}=2\ln|z+1|=2\ln(y^{1/2}+1)$

On the right, we have

$\dfrac1{1-t^2}=\dfrac12\left(\dfrac1{1-t}+\dfrac1{1+t}\right)$

$\displaystyle\int\frac{\mathrm dt}{1-t^2}=\dfrac12(\ln|1-t|+\ln|1+t|)+C=\ln(1-t^2)^{1/2}+C$

$2\ln(y^{1/2}+1)=\ln(1-t^2)^{1/2}+C$

$\ln(y^{1/2}+1)=\dfrac12\ln(1-t^2)^{1/2}+C$

$y^{1/2}+1=e^{\ln(1-t^2)^{1/4}+C}$

$y^{1/2}=C(1-t^2)^{1/4}-1$

I'll leave the solution in this form for now to make solving for $C$ easier. Given that $y\left(-\dfrac12\right)=1$ , we get

$1^{1/2}=C\left(1-\left(-\dfrac12\right)^2\right))^{1/4}-1$

$2=C\left(\dfrac54\right)^{1/4}$

$C=2\left(\dfrac45\right)^{1/4}$

and so our solution is

$\boxed{y(t)=\left(2\left(\dfrac45-\dfrac45t^2\right)^{1/4}-1\right)^2}$

3 0

2 years ago

Suppose triangle ABC is reflected over the x-axis. If the distance between point A and A’ is 14, what is the distance between th

andreyandreev [35.5K]

Given:

The triangle ABC is reflected over the x-axis.

The distance between point A and A’ is 14.

To find:

The distance between the x-axis and A’.

Solution:

If a figure is reflected across the x-axis then the corresponding parts are mirror image of each other about the x-axis.

It means the distance between A and x-axis is same as the distance between x-axis and A'.

The distance between point A and A’ is 14.

Let d be the distance between the x-axis and A’. Then,

$d+d=14$

$2d=14$

$d=\dfrac{14}{2}$

$d=7$

Therefore, the correct option is 1.

7 0

2 years ago

10 men and 12 women will be seated in a row of 22 chairs. What is the probability that all men will be seated side by side in 10

-BARSIC- [3]

Answer:

The correct option is 4.

Step-by-step explanation:

It is given that 10 men and 12 women will be seated in a row of 22 chairs.

Total possible ways to arrange n terms is n!.

Similarly,

Total possible ways to place 22 people on 22 chairs = 22!

$\text{Total outcomes}=22!$

It is given that all men will be seated side by side in 10 consecutive positions.

Total possible ways to place 10 people on 10 chairs = 10!

Let 10 men = 1 unit because all men will be seated side by side in 10 consecutive positions. 12 women = 12 units because women can any where.

Total number of units = 12 + 1 = 13.

Total possible ways to place 13 units = 13!

Total possible ways to place 10 men and 12 women, when all men will be seated side by side in 10 consecutive positions is

$\text{Favorable outcomes}=10!\cdot 13!$

The probability that all men will be seated side by side in 10 consecutive positions

$P=\frac{\text{Favorable outcomes}}{\text{Total outcomes}}=\frac{10!\cdot 13!}{22!}$

Therefore the correct option is 4.

5 0

2 years ago

Write an equivalent expression in standard form for (x−4)(2x2−3x+9)

Yuri [45]

Answer:

its 21

Step-by-step explanation:

21 21 21 21 21

7 0

2 years ago