PLEASE HELP ASAP!!!

How many different ways can 6 students be seated in a row?

inna [77]

$6!=720$
....................

6 0

3 years ago

Find the prime factorization of 70

Alekssandra [29.7K]

Answer:

2*5*7

Step-by-step explanation:

2*5=10

10*7=70

8 0

3 years ago

An airplane travels 6111 kilometers against the wind in 9 hours and 7911 kilometers with the wind in the same amount of time. Wh

natima [27]

Answer:

Speed of the plane in still air: $779\; {\rm km \cdot h^{-1}}$ .

Windspeed: $100\; {\rm km \cdot h^{-1}}$ .

Step-by-step explanation:

Assume that $x\; {\rm km \cdot h^{-1}}$ is the speed of the plane in still air, and that $y\; {\rm km \cdot h^{-1}}$ is the speed of the wind.

When the plane is travelling against wind, the ground speed of this plane (speed of the plane relative to the ground) would be $(x - y)\; {\rm km \cdot h^{-1}}$ .
When this plane is travelling in the same direction as the wind, the ground speed of this plane would be $(x + y)\; {\rm km \cdot h^{-1}}$ .

The question states that when going against the wind ( $v = (x - y)\; {\rm km \cdot h^{-1}}$ ,) the plane travels $6111\; {\rm km}$ in $9\; {\rm h}$ . Hence, $9\, (x - y) = 6111$ .

Similarly, since the plane travels $7911\; {\rm km}$ in $9\; {\rm h}$ when travelling in the same direction as the wind ( $v = (x + y)\; {\rm km \cdot h^{-1}}$ ,) $9\, (x + y) = 7911$ .

Add the two equations to eliminate $y$ . Subtract the second equation from the first to eliminate $x$ . Solve this system of equations for $x$ and $y$ : $x = 779$ and $y = 100$ .

Hence, the speed of this plane in still air would be $779\; {\rm km \cdot h^{-1}}$ , whereas the speed of the wind would be $100\; {\rm km \cdot h^{-1}}$ .

3 0

1 year ago

Isabel’s car gets 33.5 miles per gallon. Her gas tank holds 15.1 gallons of gas how many miles can Isabel drive on a full tank o

bagirrra123 [75]

Isabel can drive 505.85 miles with a gas tank that holds 15.1 gallons of gas

<em><u>Solution:</u></em>

Given that, Isabel’s car gets 33.5 miles per gallon

Her gas tank holds 15.1 gallons of gas

To find: Number of miles can Isabel drive on a full tank of gas

Let "x" be the miles drive with 15.1 gallons of gas

From given,

1 gallon = 33.5 miles

15.1 gallon = x miles

This forms a proportion and we can solve the sum by cross multiplying

$1 \times x = 15.1 \times 33.5\\\\x = 505.85$

Thus Isabel can drive 505.85 miles on a full tank of gas

6 0

3 years ago

Of all of the individuals who develop a certain rash, suppose the mean recovery time for individuals who do not use any form of

VashaNatasha [74]

Answer:

z(s) is in the rejection region. We reject H₀. We dont have enought evidence to support that the cream has effect over the recovery time

Step-by-step explanation:

Sample information:

Size n = 100

mean x = 28,5

Population information

μ₀ = 30

Standard deviation σ = 8

Test Hypothesis

Null Hypothesis H₀ x = μ₀

Alternative Hypothesis Hₐ x < μ₀

We assume CI = 95 % then α = 5 % α = 0,05

As the alternative hypothesis suggest we should develop a one tail-test on the left ( we need to find out if the cream have any effect on the rash), effects on the rash could be measured as days of recovery

A z(c) for 0,05 from z-table is: z(c) = - 1,64

z(s) = ( x - μ₀ ) / σ/√n

z(s) = ( 28,5 - 30 ) / 8/√100

z(s) = - 1,5 * 10 / 8

z(s) = - 1,875

Comparing z(s) and z(c)

|z(s)| < |z(c)| 1,875 > 1,64

z(s) is in the rejection region. We reject H₀. We dont have enought evidence to support that the cream has effect over the recovery time

3 0

3 years ago