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2 years ago

I need an explanation on how to work this out

Mathematics

1 answer:

Cerrena [4.2K]2 years ago

6 0

Answer:

Step-by-step explanation:

We have to substitute r and s with the values given:

Now we can make an equation with our new values:

(6×1/4)+(14×1/4)

Now we do one bracket at a time (I put brackets to show that you need to do them separately, you don't need to have brackets)

1.5+3.5=5

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Solving Quadratic Equations A B C D

mixas84 [53]

I believe that it’s B.

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3 years ago

Sunshine High School claims that 72% of its students complete their homework on a daily basis. Ms. Carter surveyed 80 students a

Ulleksa [173]

Answer: z equals 0.60 minus 0.72 all over the square root of the quantity 0.72 times 0.28 over 80

Step-by-step explanation:

let p be the population proportion of students complete their homework on a daily basis.

As per given , we have

p= 0.72

sample size : n= 80

Sample proportion : $\hat{p}=0.60$

Test statistic for proportion:

$z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}$

i.e.

$z=\dfrac{0.60-0.72}{\sqrt{\dfrac{0.72(1-0.72)}{80}}}$

i.e.

$z=\dfrac{0.60-0.72}{\sqrt{\dfrac{0.72(0.28)}{80}}}$

That is , z equals 0.60 minus 0.72 all over the square root of the quantity 0.72 times 0.28 over 80

6 0

3 years ago

A small rocket is fired from a launch pad 10 m above the ground with an initial velocity left angle 250 comma 450 comma 500 righ

jonny [76]

Let $\vec r(t),\vec v(t),\vec a(t)$ denote the rocket's position, velocity, and acceleration vectors at time $t$ .

We're given its initial position

$\vec r(0)=\langle0,0,10\rangle\,\mathrm m$

and velocity

$\vec v(0)=\langle250,450,500\rangle\dfrac{\rm m}{\rm s}$

Immediately after launch, the rocket is subject to gravity, so its acceleration is

$\vec a(t)=\langle0,2.5,-g\rangle\dfrac{\rm m}{\mathrm s^2}$

where $g=9.8\frac{\rm m}{\mathrm s^2}$ .

a. We can obtain the velocity and position vectors by respectively integrating the acceleration and velocity functions. By the fundamental theorem of calculus,

$\vec v(t)=\left(\vec v(0)+\displaystyle\int_0^t\vec a(u)\,\mathrm du\right)\dfrac{\rm m}{\rm s}$

$\vec v(t)=\left(\langle250,450,500\rangle+\langle0,2.5u,-gu\rangle\bigg|_0^t\right)\dfrac{\rm m}{\rm s}$

(the integral of 0 is a constant, but it ultimately doesn't matter in this case)

$\boxed{\vec v(t)=\langle250,450+2.5t,500-gt\rangle\dfrac{\rm m}{\rm s}}$

and

$\vec r(t)=\left(\vec r(0)+\displaystyle\int_0^t\vec v(u)\,\mathrm du\right)\,\rm m$

$\vec r(t)=\left(\langle0,0,10\rangle+\left\langle250u,450u+1.25u^2,500u-\dfrac g2u^2\right\rangle\bigg|_0^t\right)\,\rm m$

$\boxed{\vec r(t)=\left\langle250t,450t+1.25t^2,10+500t-\dfrac g2t^2\right\rangle\,\rm m}$

b. The rocket stays in the air for as long as it takes until $z=0$ , where $z$ is the $z$ -component of the position vector.

$10+500t-\dfrac g2t^2=0\implies t\approx102\,\rm s$

The range of the rocket is the distance between the rocket's final position and the origin (0, 0, 0):

$\boxed{\|\vec r(102\,\mathrm s)\|\approx64,233\,\rm m}$

c. The rocket reaches its maximum height when its vertical velocity (the $z$ -component) is 0, at which point we have

$-\left(500\dfrac{\rm m}{\rm s}\right)^2=-2g(z_{\rm max}-10\,\mathrm m)$

$\implies\boxed{z_{\rm max}=125,010\,\rm m}$

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3 years ago

66) A farmhouse shelters 13 animals. Some are cows and some are chickens. Altogether there are 38

yuradex [85]

Answer:

9 cows and 1 chicken ( plz help me)

Step-by-step explanation:

6 0

3 years ago

BRAINLIESTTT ASAP!! PLEASE HELP ME :)

Tju [1.3M]

Answer:

Choice C.

Step-by-step explanation:

A parallelogram is a quadrilateral with two pairs of opposite parallel sides.

There is a theorem that states that opposite sides of a parallelogram are congruent.

In this case, sides AB and CD are opposite sides.

Sides BC and AD are opposite sides.

Side CD is opposite side AB, so they are congruent.

Answer:

Choice C.

CD = AB; Opposite sides of parallelograms are congruent.

5 0

3 years ago