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3 years ago

Find f(0) and f(2) for the given exponential function. f(x) = (1/2)^-x

1 answer:

8 0

For 0 it will equal 1 because anything to the 0th power is 1 except 0 to the 0.

For 2, It will equal for because when you raise a fraction to the negative power you flip it and that gets rid of the negative number so then you will have 2 to the second and you will get 4.

f (0) = 1, f (2) = 4

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1 year ago

Erica earn money by tutoring and babysitting. She always tutors for 5 hours each week and the amount she babysits changes from w

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I hope this helped!

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2 years ago

An urn contains 3 red and 7 black balls. Players A and B take turns (A goes first) withdrawing balls from the urn consecutively.

andrey2020 [161]

Answer:

The probability that A selects the first red ball is 0.5833.

Step-by-step explanation:

Given : An urn contains 3 red and 7 black balls. Players A and B take turns (A goes first) withdrawing balls from the urn consecutively.

To find : What is the probability that A selects the first red ball?

Solution :

A wins if the first red ball is drawn 1st,3rd,5th or 7th.

A red ball drawn first, there are $E(1)= ^9C_2$ places in which the other 2 red balls can be placed.

A red ball drawn third, there are $E(3)= ^7C_2$ places in which the other 2 red balls can be placed.

A red ball drawn fifth, there are $E(5)= ^5C_2$ places in which the other 2 red balls can be placed.

A red ball drawn seventh, there are $E(7)= ^3C_2$ places in which the other 2 red balls can be placed.

The total number of total event is $S= ^{10}C_3$

The probability that A selects the first red ball is

$P(A \text{wins})=\frac{(^9C_2)+(^7C_2)+(^5C_2)+(^3C_2)}{^{10}C_3}$

$P(A \text{wins})=\frac{36+21+10+3}{120}$

$P(A \text{wins})=\frac{70}{120}$

$P(A \text{wins})=0.5833$

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3 years ago

A rug is to be centered in a room so that the border around it is of a consistent width on all four sides. If the room is 10 ft

aleksley [76]

Answer:

The width of the border can be 9 feet or 3.5 feet.

Step-by-step explanation:

Let the width be x

Length of room = 10 feet

Breadth of room = 15 feet

Length of rug = 10-2x

Breadth of rug = 15-2x

Area of rug = $(10-2x)(15-2x)$

We are given that the area of the rug is 24 square feet.

So, $(10-2x)(15-2x)=24$ ---A

$150-20x-30x+4x^2=24$

$150-24-50x+4x^2=0$

$126-50x+4x^2=0$

$2(x-9)(2x-7)=0$

$x=9,\frac{7}{2}$

$x=9,3.5$

Substitute x =9 in A

$(10-2(9))(15-2(9))=24$

$24=24$

LHS = RHS

Substitute x = 3.5

$(10-2(3.5))(15-2(3.5))=24$

$24=24$

LHS = RHS

So, The width of the border can be 9 feet or 3.5 feet.

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3 years ago

The sum of three consecutive even numbers is 24 , find the numbers.

Sergeeva-Olga [200]

Answer:

three consecutive even integers whose sum is 24 are 6, 8 and 10.

8 0

3 years ago

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