What is the simplified form of the expression? 5c2-4c+3D-3+2c2d-3c+d-7

cConsider a game in which players roll a number cube to determine the number of points earned. If a player rolls a prime number,

quester [9]

Expected value = -1(1/6) + 2(1/6) + 3(1/6) - 4(1/6) + 5(1/6) - 6(1/6) = -1/6 + 2/6 + 3/6 - 4/6 + 5/6 - 6/6 = -1/6 = -0.167

4 0

3 years ago

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if there is a line and a point not on the line, then there is exactly one line through the point that intersects the given line?

arlik [135]

The answer is an intersect between both lines.

7 0

3 years ago

Craig has a rectangle wooden deck that measures 799 inches by 245 inches that he wants to put a string of lights around. What le

tino4ka555 [31]

Answer:

He should buy lights that are 2088 inches long

Step-by-step explanation:

Craig has a rectangle wooden deck that measures 799 inches by 245 inches.

Let us say the length, L, is 799 inches and the breadth, B, is 245 inches.

He wants to put a string of lights around the deck.

This means that he needs to buy the length of lights that would be equal to the perimeter of the rectangular deck.

The perimeter of a rectangle is given as:

P = 2(L + B)

Hence, the length of lights he should buy is:

P = 2(799 + 245) = 2(1044)

P = 2088 inches

He should buy lights that are 2088 inches long.

5 0

2 years ago

A tank contains 30 lb of salt dissolved in 300 gallons of water. a brine solution is pumped into the tank at a rate of 3 gal/min

sesenic [268]

$A'(t)=(\text{flow rate in})(\text{inflow concentration})-(\text{flow rate out})(\text{outflow concentration})$
$\implies A'(t)=\dfrac{3\text{ gal}}{1\text{ min}}\cdot\left(2+\sin\dfrac t4\right)\dfrac{\text{lb}}{\text{gal}}-\dfrac{3\text{ gal}}{1\text{ min}}\cdot\dfrac{A(t)\text{ lb}}{300+(3-3)t\text{ gal}}$
$A'(t)+\dfrac1{100}A(t)=6+3\sin\dfrac t4$

We're given that $A(0)=30$ . Multiply both sides by the integrating factor $e^{t/100}$ , then

$e^{t/100}A'(t)+\dfrac1{100}e^{t/100}A(t)=6e^{t/100}+3e^{t/100}\sin\dfrac t4$
$\left(e^{t/100}A(t)\right)'=6e^{t/100}+3e^{t/100}\sin\dfrac t4$
$e^{t/100}A(t)=600e^{t/100}-\dfrac{150}{313}e^{t/100}\left(25\cos\dfrac t4-\sin\dfrac t4\right)+C$
$A(t)=600-\dfrac{150}{313}\left(25\cos\dfrac t4-\sin\dfrac t4\right)+Ce^{-t/100}$

Given that $A(0)=30$ , we have

$30=600-\dfrac{150}{313}\cdot25+C\implies C=-\dfrac{174660}{313}\approx-558.02$

so the amount of salt in the tank at time $t$ is

$A(t)\approx600-\dfrac{150}{313}\left(25\cos\dfrac t4-\sin\dfrac t4\right)-558.02e^{-t/100}$

3 0

3 years ago

A school is preparing fruit baskets for a local nursing home. There are 162 apples, 108 oranges, and 180 bananas. If the baskets

kari74 [83]

To solve this exercise, we must calculate the Maximum Common Divisor (M.C.D.), which is the greatest common divisor of 62,108 and 180. We apply factor decomposition, and we obtain:

162= (3^4)(2)

108= (2^2)(3^3)

180= (2^2)(3^2)(5)

We choose the common numbers with their lowest exponent:

M.C.D.= (2)(3^2)

M.C.D.= 2x9

M.C.D.= 18

The greatest number of baskets that can be made is: 18 baskets

To know how many apples, oranges and bananas are in each basket, we must divide the greatest number of them that can be made between the total amount of apples, oranges and bananas, as shown below:

162/18= 9 apples

108/18= 6 oranges

180/18= 10 bananas

So, there are 9 apples, 6 oranges and 10 bananas in each basket.

3 0

3 years ago

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