Answer:
7
Step-by-step explanation:
g(x) = -3x - 5
g(-4) = -3(-4) - 5
g(-4) = 12 - 5
g(-4) = 7
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Answer
(a) The probability that at most two police cruisers will drive through the neighborhood is 0.2642
(b) he probability of having 4 police is 0.2642
Step-by-step explanation:
(a) To get the probability that at most two police cruisers the neighborhood we have to consider the probability, of having 2 police, 3 police , 4 police , 5 , 6 or 7 police. All that possibilities meet my condition,
We have to add the probalities of the different possibilities to know the total probability
P=0.1839 +0.0613 +0.0153 +0.0031+ 0.0005 +0.0001=0.2642
(b) If we suppose that 2 police sighted in the neighborhoof and we are looking the probability of having 4 police , that means that 2 o more are random distribuited,
So, again , the probabily we are looking for is to have 2 o more police. Is the same calculus we made in the previus exercice.
The total amount of x values of dimes and q values of quarters is equal to 6.35. From the given, the number of dimes may also be expressed as, 3q + 3. The equation that best represent the given is,
(3q + 3)(0.1) + q(0.1) = 6.35
![\large\underline{\bf \red{Step \:by\: Step \:Explanation:}}](https://tex.z-dn.net/?f=%5Clarge%5Cunderline%7B%5Cbf%20%5Cred%7BStep%20%5C%3Aby%5C%3A%20Step%20%5C%3AExplanation%3A%7D%7D)
Given two equations are :
- 2x = - y + 6.
- -4 x + 3y = 8 .
We may write them as ,
- 2x + y - 6 = 0 .................(i)
- 4x - 3y + 8 = 0 ...............(ii)
Multiplying equⁿ (i) by 2 :
⇒ 2(2x + y - 6 ) = 0.
⇒ 4x + 2y - 12 = 0 .....................(iii) .
<u>Subtra</u><u>ct</u><u> </u><u>equ</u><u>ⁿ</u><u> </u><u>(</u><u>ii</u><u>)</u><u> </u><u>from</u><u> </u><u>equⁿ</u><u> </u><u>(</u><u>iii</u><u>)</u><u> </u><u>:</u><u>-</u>
⇒ 4x + 2y - 12 = 0
ㅤ- 4x + 3y - 8 = 0 [ Sign changes ]
__________________
⇒ 5y - 20 = 0.ㅤㅤㅤㅤㅤ
⇒ 5y = 20.
⇒ y = 20/5.
⇒ y = 4
Put this value in (i) to obtain x .
⇒ 2x + y - 6 = 0.
⇒ 2x +4 - 6 = 0.
⇒ 2x - 2 = 0.
⇒2x = 2 .
⇒ x = 2/2.
⇒ x = 1 .
<u>Hence</u><u> </u><u>the</u><u> </u><u>value</u><u> of</u><u> x</u><u> is</u><u> </u><u>1</u><u> </u><u>&</u><u> </u><u>y</u><u> </u><u>is</u><u> </u><u>4</u><u>.</u>
![\boxed{\purple{\bf\pink{\dag}\:Hence\:the\: correct\: option\:is\:[b]\:(1,4)}}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cpurple%7B%5Cbf%5Cpink%7B%5Cdag%7D%5C%3AHence%5C%3Athe%5C%3A%20correct%5C%3A%20option%5C%3Ais%5C%3A%5Bb%5D%5C%3A%281%2C4%29%7D%7D)
Answer:
![\boxed{\text{160 ft}}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Ctext%7B160%20ft%7D%7D)
Step-by-step explanation:
The angle of depression from the ranger at point A and the angle of elevation from the fire on the ground at Point C are congruent (interior opposite angles).
The distance from the ranger up in the tower to the fire on the ground is the hypotenuse AC of the right triangle ABC.
sin 30 = 80/AC
AC = 80/sin30 = 80/0.5 = 160 ft
The distance is ![\boxed{\textbf{160 ft}}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Ctextbf%7B160%20ft%7D%7D)