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2 years ago

A bag contains 4 red marbles, 2 blue marbles, 1 purple marble, and 3 green marbles.

Mathematics

1 answer:

STatiana [176]2 years ago

7 0

Answer:

10 outcomes

Step-by-step explanation:

The number of outcomes is the number of marbles in the bag since we are taking out one marble

4+2+1+3 = 10

There are 10 outcomes

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Nathan had an infection, and his doctor wanted him to take penicillin. Because Nathan’s father and paternal grandfather were all

Fittoniya [83]

Let events
A=Nathan has allergy
~A=Nathan does not have allergy
T=Nathan tests positive
~T=Nathan does not test positive

We are given
P(A)=0.75 [ probability that Nathan is allergic ]
P(T|A)=0.98 [probability of testing positive given Nathan is allergic to Penicillin]

We want to calculate probability that Nathan is allergic AND tests positive
P(T n A)

From definition of conditional probability,
P(T|A)=P(T n A)/P(A)
substitute known values,
0.98 = P(T n A) / 0.75
solving for P(T n A)
P(T n A) = 0.75*0.98 = 0.735

3 0

2 years ago

Find the derivative of f(x) = (1 + 6x2)(x − x2) in two ways.

ipn [44]

Using product rule;

f(x)=(1+6x²)(x-x²)

f'(x)=(12x)(x-x²) + (1-2x)(1+6x²) = 12x² -12x³ +1 +6x² -2x -12x³ = -24x³ +18x² -2x +1

Solving the bracket first;

f(x)=(1+6x²)(x-x²) = x -x² +6x³ -6x^4

f'(x)= 1 -2x +18x² -24x³ = -24x³ +18x² -2x +1

3 0

3 years ago

FREEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE Poiunts

otez555 [7]

Answer:

YAYY

Step-by-step explanation:

5 0

2 years ago

The shorter leg of a right triangle is 5 inches shorter than the longer leg. The hypotenuse is 5 inches longer than the longer l

Licemer1 [7]

Answer:

longer leg: 20 in

shorter leg: 15 in

hypotenuse: 25 in

Formulas:

<u>Pythagorean Theorem</u>

$c^2 = a^2 + b^2$

c ... hypotenuse

a ... one leg

b ... another leg

Pythagorean theorem is used in right triangles (triangles in which one angle is 90°).

Step-by-step explanation:

longer leg: x

shorter leg: x - 5

hypotenuse: x + 5

To find x (longer leg), let's use Pythagorean theorem.

$c^2 = a^2 + b^2\\(x+5)^2 = x^2 + (x-5)^2\\x^2 + 10x + 25= x^2 + x^2 -10x + 25\\x^2 + 10x = 2x^2 - 10x\\0 = x^2 - 20x$

Now let's factorize to get solutions for x.

$0 = x(x-20)$

First solution:

$x = 0$

Second solution:

$x - 20 = 0\\x = 20$

Since a side of a triangle has to be a positive number, x is equal to 20.

Now let's just substitute x back to get side lengths. From the question the lengths are in inches.

longer leg: x = 20 in

shorter leg: x - 5 = 20 - 5 = 15 in

hypotenuse: x + 5 = 20 + 5 = 25 in

6 0

1 year ago

A 7-foot tall stop sign creates a shadow that is 2 feet long. At the same time, a utility pole creates a shadow that is 10.4 fee

barxatty [35]

38.5 ft tall

is the answer to your question

plz rate 5 stars

8 0

2 years ago