Tell whatever the ordered pair is a solution of the given system.

What is the total number of possible 4-letter arrangements of the letters m-a-t-h if each letter is used exactly once in each ar

MariettaO [177]

9514 1404 393

Answer:

24

Step-by-step explanation:

The number of permutations of 4 items is 4! = 24.

math, maht, mtah, mtha, mhat, mhta,

amth, amht, atmh, athm, ahmt, ahtm,

tmah, tmha, tamh, tahm, thma, tham,

hmat, hmta, hamt, hatm, htma, htam

7 0

3 years ago

The bakers at Healthy Bakery can make 350 bagels in 10 hours. How many bagels can they bake in 23 hours? What was that rate per

cluponka [151]

Answer:

In 23 hours they make 80.5 bagels. The unit rate is 3.5 bagels per hour

Step-by-step explanation:

Divide 10 hours by 10 hours to get 1 hour.

Divide 350 bagels by 10 to get the unit rate (which is 3.5)

Multiply the unit rate by 23, and you get 80.5 hours.

8 0

3 years ago

If a cannonball is shot directly upward with a velocity of 160 ft per second, its height above the ground after t seconds is gi

Contact [7]

Step-by-step explanation:

If a cannonball is shot directly upward with a velocity of 160 ft per second. Its height as a function of time is given by :

$h(t)=160t-16t^2$ .......(1)

t is in seconds

(a) Velocity is given by :

$v=\dfrac{dh}{dt}\\\\v=\dfrac{d(160t-16t^2)}{dt}\\\\v=(160-32t)\ ft/s$

Acceleration is given by :

$a=\dfrac{dv}{dt}\\\\a=\dfrac{d(160-32t)}{dt}\\\\a=-32\ ft/s^2$

(b) For maximum height put $\dfrac{dh}{dt}=0$

i.e.

$160-32t=0\\\\t=5\ s$

Put t = 5 s in equation (1). So,

$h(5)=160t-16t^2\\\\h(5)=160(5)-16(5)^2\\\\h(5)=400\ ft$

(c) When the ball reaches ground, its height is equal to 0. So,

h(t) = 0

$160t-16t^2=0\\\\t(160-16t)=0\\\\t=0,t=10\ s$

Hence, this is the required solution.

4 0

3 years ago

a study timed left-handed and right-handed people to see how long it took them to hit a buzzer. the data is shown below: the six

Effectus [21]

The z or t score to be used is (0.422,0.978)

How to find the critical value ?

Critical probability (p*) = 1 - (Alpha / 2), where Alpha is equal to 1 - (the confidence level / 100), is the unit statisticians use to determine the margin of error within a set of data in statistics.

The critical value for α = 0.13 is $z_{c} = \frac{z_{1} - \alpha }{2}$

The corresponding confidence interval is computed as shown below

$CI = (X1_{1} - X_{2}- z_{c} \sqrt{\frac{a_{1}^{2}}{n_{1} } + \frac{a_{2}^{2}}{n_{2} }} , X1_{1} - X_{2}+z_{c} \sqrt{\frac{a_{1}^{2}}{n_{1} } + \frac{a_{2}^{2}}{n_{2} }} )$