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2 years ago

Niamh runs 6 km in 30-minutes what is the average speed in km h

Mathematics

2 answers:

mylen [45]2 years ago

6 0

Answer:

12 km/hr

Step-by-step explanation:

SIZIF [17.4K]2 years ago

4 0

Step-by-step explanation:

Speed = Distance / Time

given distance = 6km

time = 30 minutes = 30/60 hr = 1/2hr

speed =

$\frac{6}{\frac{1}{2} } \\ = 6 \div \frac{1}{2} \\ = 6 \times 2 \\ = 12 \frac{km}{h}$

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Andre is setting up rectangle tables for a party. He can fit 6 chairs around a single table. Andre lined up 10 tables end to end

IRINA_888 [86]

If there is one table (t=1) then 6 chairs (c=6) can be placed around the table, 2 along the length on each side and 1 at each end.
When t=2, and the tables are end to end (joined at their width) c=10, that is, 4 chairs on each side of the double table and 1 at each end. Each time a table is added c increases by 4 so we can write c=4t+2 the constant 2 being the single chair at each end. If the tables are separated then c=6t.

5 0

2 years ago

Sample Response: The two conditional probabilities are not equal because each has different given events. P(A|D) has event D as

Ivan

The conditional probability illustrates that's there's a 2/8 that the event A occurs.

<h3>How to illustrate the probability?</h3>

It should be noted that probability simply means the likelihood of the occurence of an event.

In this case, it can be delivered that P(AID) and P(DIA) aren't equal.

Hence, P(D|A) has event A as its given event, resulting in 2/8 for a probability.

Learn more about probability on:

brainly.com/question/24756209

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7 0

1 year ago

In a random sample of students who took the SAT test, 427 had paid for coaching courses and the remaining 2733 had not. Calculat

Dvinal [7]

Answer:

The 95% confidence interval for the proportion of students who get coaching on the SAT is (0.1232, 0.147).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the z-score that has a p-value of $1 - \frac{\alpha}{2}$ .

427 had paid for coaching courses and the remaining 2733 had not.

This means that $n = 427 + 2733 = 3160, \pi = \frac{427}{3160} = 0.1351$

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a p-value of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1351 - 1.96\sqrt{\frac{0.1351*0.8649}{3160}} = 0.1232$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1351 + 1.96\sqrt{\frac{0.1351*0.8649}{3160}} = 0.147$

The 95% confidence interval for the proportion of students who get coaching on the SAT is (0.1232, 0.147).

8 0

3 years ago

Noah uses 1/2 of a cup of vinegar in his salad dressing recipe. How much vinegar would Noah use to make 3 1/6 recipes? Write you

saul85 [17]

Answer:

1 7/12 cups

Step-by-step explanation:

1/2 x 3 1/6 = 1/2 x 19/6 = 19/12 or 1 7/12

6 0

2 years ago

Read 2 more answers

A rock thrown vertically upward from the surface of the moon at a velocity of 36m/sec reaches a height of s = 36t - 0.8 t^2 met

Verdich [7]

Answer:

a. The rock's velocity is $v(t)=36-1.6t \:{(m/s)}$ and the acceleration is $a(t)=-1.6 \:{(m/s^2)}$

b. It takes 22.5 seconds to reach the highest point.

c. The rock goes up to 405 m.

d. It reach half its maximum height when time is 6.59 s or 38.41 s.

e. The rock is aloft for 45 seconds.

Step-by-step explanation:

Velocity is defined as the rate of change of position or the rate of displacement. $v(t)=\frac{ds}{dt}$
Acceleration is defined as the rate of change of velocity. $a(t)=\frac{dv}{dt}$

The rock's velocity is the derivative of the height function $s(t) = 36t - 0.8 t^2$

$v(t)=\frac{d}{dt}(36t - 0.8 t^2) \\\\\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'\\\\v(t)=\frac{d}{dt}\left(36t\right)-\frac{d}{dt}\left(0.8t^2\right)\\\\v(t)=36-1.6t$

The rock's acceleration is the derivative of the velocity function $v(t)=36-1.6t$

$a(t)=\frac{d}{dt}(36-1.6t)\\\\a(t)=-1.6$

b. The rock will reach its highest point when the velocity becomes zero.

$v(t)=36-1.6t=0\\36\cdot \:10-1.6t\cdot \:10=0\cdot \:10\\360-16t=0\\360-16t-360=0-360\\-16t=-360\\t=\frac{45}{2}=22.5$

It takes 22.5 seconds to reach the highest point.

c. The rock reach its highest point when t = 22.5 s

Thus

$s(22.5) = 36(22.5) - 0.8 (22.5)^2\\s(22.5) =405$

So the rock goes up to 405 m.

d. The maximum height is 405 m. So the half of its maximum height = $\frac{405}{2} =202.5 \:m$

To find the time it reach half its maximum height, we need to solve

$36t - 0.8 t^2=202.5\\36t\cdot \:10-0.8t^2\cdot \:10=202.5\cdot \:10\\360t-8t^2=2025\\360t-8t^2-2025=2025-2025\\-8t^2+360t-2025=0$

For a quadratic equation of the form $ax^2+bx+c=0$ the solutions are

$x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$\mathrm{For\:}\quad a=-8,\:b=360,\:c=-2025:\\\\t=\frac{-360+\sqrt{360^2-4\left(-8\right)\left(-2025\right)}}{2\left(-8\right)}=\frac{45\left(2-\sqrt{2}\right)}{4}\approx 6.59\\\\t=\frac{-360-\sqrt{360^2-4\left(-8\right)\left(-2025\right)}}{2\left(-8\right)}=\frac{45\left(2+\sqrt{2}\right)}{4}\approx 38.41$

It reach half its maximum height when time is 6.59 s or 38.41 s.

e. It is aloft until s(t) = 0 again

$36t - 0.8 t^2=0\\\\\mathrm{Factor\:}36t-0.8t^2\rightarrow -t\left(0.8t-36\right)\\\\\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}\\\\t=0,\:t=45$

The rock is aloft for 45 seconds.

5 0

3 years ago