Mr. Andrews has a classroom of 45 students. He wants to divide them equally into 5 teams for a group project.

Solve the following equation for x: 6(4x+5)= 3(x+8)+3. Round to the nearest hundredth.

gavmur [86]

6(4x + 5) = 3(x + 8) + 3
24x + 30 = 3x + 24 + 3
24x + 30 = 3x + 27
24x - 3x = 27 - 30
21x = - 3
x = -3/21
x = - 0.143 <==

8 0

2 years ago

Read 2 more answers

What is PA <br> Enter your answer in the box

SSSSS [86.1K]

Answer:

3

Step-by-step explanation:

P is the in-center

⇒PA=PE=PD because they are in-radius of the in-circle

We know that, tangent segments drawn from a point outside the circle are always equal in length

⇒DK=EK=7.2

In right triangle PKE,

using Pythagoras' Theorem : $PK^{2}=PE^{2}+KE^{2}$

⇒ $PE^{2}=PK^{2}-KE^{2}$

⇒ $PE=\sqrt{PK^{2}-KE^{2} }$

⇒ $PE^{2}=\sqrt{7.8^{2}-7.2^{2}} }$

⇒ $PE=3$

Therefore, $PA=3$

3 0

2 years ago

A bus travels on an east-west highway connecting two cities A and B that are 100 miles apart. There are 2 services stations alon

melamori03 [73]

Answer:

51/4

Step-by-step explanation:

To begin with you have to understand what is the distribution of the random variable. If X represents the point where the bus breaks down. That is correct.

X~ Uniform(0,100)

Then the probability mass function is given as follows.

$f(x) = P(X=x) = 1/100 \,\,\,\, \text{if} \,\,\,\, 0 \leq x \leq 100\\f(x) = P(X=x) = 0 \,\,\,\, \text{otherwise}$

Now, imagine that the D represents the distance from the break down point to the nearest station. Think about this, the first service station is 20 meters away from city A, and the second station is located 70 meters away from city A then the mid point between 20 and 70 is (70+20)/2 = 45 then we can represent D as follows

$D(x) =\left\{ \begin{array}{ll} x & \mbox{if } 0\leq x \leq 20 \\ x-20 & \mbox{if } 20\leq x < 45\\ 70-x & \mbox{if } 45 \leq x \leq 70\\ x-70 & \mbox{if } 70 \leq x \leq 100\\ \end{array}\right.$

Now, as we said before X represents the random variable where the bus breaks down, then we form a new random variable $Y = D(X)$ , $Y$ is a random variable as well, remember that there is a theorem that says that

$E[Y] = E[D(X)] = \int\limits_{-\infty}^{\infty} D(x) f(x) \,\, dx$

Where $f(x)$ is the probability mass function of X. Using the information of our problem

$E[Y] = \int\limits_{-\infty}^{\infty} D(x)f(x) dx \\= \frac{1}{100} \bigg[ \int\limits_{0}^{20} x dx +\int\limits_{20}^{45} (x-20) dx +\int\limits_{45}^{70} (70-x) dx +\int\limits_{70}^{100} (x-70) dx \bigg]\\= \frac{51}{4} = 12.75$

3 0

3 years ago

(1) Area: 35 y² +13y-12

Fiesta28 [93]

Answer:

35y2+13y−12

=35y2+28y−15y−12

=7y(5y+4)−3(5y+4)

=(7y−3)(5y+4)

Therefore, the possible length and breadth are 7y-3 units and 5y+4 units

6 0

1 year ago

In a recent survey of 974 voters, 724 indicated that they were in favor of a new city park, while the other 250 voters said that

Marrrta [24]

250/974 = x/40,000...250 opposed to 974 total = x opposed to 40,000 total
cross multiply because this is a proportion
974x = 10,000,000
x = 10,000,000/974
x = 10266.94 rounds to 10,267 <==

3 0

2 years ago