Dario puts 44 marbles in a box in which 14 are red, 12 are blue, and 18 are yellow. If Dario picks one marble at random, what is the probability that he selects a red marble or a yellow marble?

Answer:

c.

[tex] - 1 < - 0.25 < 0 < 0.5 < 1.5[/tex]

Answer:

a) 0.0645 = 6.45% probability that the 90 orders can be filled without reordering components.

b) 0.4062 = 40.62%  probability that the 100 orders can be filled without reordering components.

c) 0.9034 = 90.34% probability that the 100 orders can be filled without reordering components

Step-by-step explanation:

For each component, there are only two possible outcomes. Either it is defective, or it is not. The components can be assumed to be independent. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

3% of the components are identified as defective

This means that [tex]p = 0.03[/tex]

a. If the manufacturer stocks 90 components, what is the probability that the 90 orders can be filled without reordering components?

0 defective in a set of 90, which is [tex]P(X = 0)[/tex] when [tex]n = 90[/tex]. So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{90,0}.(0.03)^{0}.(0.97)^{90} = 0.0645[/tex]

0.0645 = 6.45% probability that the 90 orders can be filled without reordering components.

b. If the manufacturer stocks 102 components, what is the probability that the 100 orders can be filled without reordering components?

At most 102 - 100 = 2 defective in a set of 102, so [tex]P(X \leq 2)[/tex] when [tex]n = 102[/tex]

Then

[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{102,0}.(0.03)^{0}.(0.97)^{102} = 0.0447[/tex]

[tex]P(X = 1) = C_{102,0}.(0.03)^{1}.(0.97)^{101} = 0.1411[/tex]

[tex]P(X = 2) = C_{102,2}.(0.03)^{2}.(0.97)^{100} = 0.2204[/tex]

[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0447 + 0.1411 + 0.2204 = 0.4062[/tex]

0.4062 = 40.62%  probability that the 100 orders can be filled without reordering components.

c. If the manufacturer stocks 105 components, what is the probability that the 100 orders can be filled without reordering components?

At most 105 - 100 = 5 defective in a set of 105, so [tex]P(X \leq 5)[/tex] when [tex]n = 105[/tex]

Then

[tex]P(X \leq 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{105,0}.(0.03)^{0}.(0.97)^{105} = 0.0408[/tex]

[tex]P(X = 1) = C_{105,0}.(0.03)^{1}.(0.97)^{104} = 0.1326[/tex]

[tex]P(X = 2) = C_{105,2}.(0.03)^{2}.(0.97)^{103} = 0.2133[/tex]

[tex]P(X = 3) = C_{105,3}.(0.03)^{3}.(0.97)^{102} = 0.2265[/tex]

[tex]P(X = 4) = C_{105,4}.(0.03)^{4}.(0.97)^{101} = 0.1786[/tex]

[tex]P(X = 5) = C_{105,5}.(0.03)^{5}.(0.97)^{100} = 0.1116[/tex]

[tex]P(X \leq 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = 0.0408 + 0.1326 + 0.2133 + 0.2265 + 0.1786 + 0.1116 = 0.9034[/tex]

0.9034 = 90.34% probability that the 100 orders can be filled without reordering components

Answer:

430 cm³

Step-by-step explanation:

= 11 × 10 × 2

= 220 cm³

= 10 × 3 × (9-2)

= 210 cm³

= 220 + 210

= 430 cm³

Answer:

430 cubic centimeters

Step-by-step explanation:

Lets start by separating both figures. Start with the one in the back, which is the bigger one.

Given:

Length = 10 cm

Width = 3 cm

Height = 9 cm

This is a rectangle and the volume of a rectangle is L x W x H. Therefore,

Volume = 10 x 3 x 9 = 270 cubic centimeters

Now we move on to the second figure.

Given:

Length = 10 cm  (Given from the other rectangle)

Width = 8 cm (We do 11 - 3 since we separated the rectangles)

Height = 2 cm

Using the same formula we get the following.

Volume = 10 x 8 x 2 = 160 cubic centimeters

____

Finally, we add both volumes back since we separated the figures in the beginning.

Volume = 270 + 160 = 430 cubic centimeters

Answer:

8.26 or 8.3 (If Rounded)

Step-by-step explanation:

When I'm dealing with problems involving fractions. I turn the fractions to decimals. So, on a calculator, just do 3/4, you'll get 0.75.

Then, the problem would be 6.2 ÷ 0.75 = 8.26

Answer:

Step-by-step explanation:

100 bro

Answer:

522.0

Step-by-step explanation:

10*6=60

60*8.7=522.0

or you can take out the zero either way that's the answer

Answer:

522.0

Step-by-step explanation:

Step-by-step explanation:

10*6=60

60*8.7=522.0

or you can take out the zero either way that's the answer

Answer:

9 ft and 26 ft

we will take as x the width, then

P rect. = 2(A+B)

A = 2x + 8 | 2×x, because there is b twice less, and + 8, because there is at 8 longer

B = x

70 = 2(2x + 8 + x)

70-16 = 4x + 2x

54= 6 x

54/6 = 9 => B = 9; A = 2×9+8 = 26

Please put the Brainlest

Answer:

3000/1800 = 5/3

Step-by-step explanation:

3 kilograms is 3000 grams = 3000/1800 simplified to the smallest is 5/3

sorry if this isn't what you're looking for

Answer:

ΔABC ~ ΔEFD

Step-by-step explanation:

ΔABC ~ ΔEFDc

Answer:

I'm a cat, I'm a kitty cat, and a meow meow meow, and a meow meow meow

Answer:

C

Step-by-step explanation:

Answer:

2.5%

Step-by-step explanation:

% = (faulty batteries / total batteries) x 100

= (3/120) x 100

= 0.025 x 100

= 2.5

the answer is,

541.42%

I think this is the answer.

Answer:

s = 53

Step-by-step explanation:

Bianca graphs the data in the table and finds that the trend line is :

s = 2.2 f + 4.7

We need to find the score when there are 22 free thrown in a game. Put f = 22 in the above equation.

s = 2.2(22) + 4.7

= 53.1

pr

s = 53

Hence, there is 53 score when f = 22.

Answer:

c

Step-by-step explanation:

Answer:

The second one charges $35 more then the first one.

The Step-by-step explanation:

The first one 50+15=65

THe next one 80+20=100

100-65=35

Answer:

the total number of students in 6th grade would be 350

Step-by-step explanation:

I hope this helps! ^^

☁️☁️☁️☁️☁️☁️☁️☁️

Answer:

550a + 590b = 1275

Step-by-step explanation:

We use the following relation to solve this question:

[tex]v = \frac{d}{t}[/tex]

In which v is the velocity, d is the distance and t is the speed.

In this question, we find the distance, so we use:

[tex]d = v*t[/tex]

A plane is flying to Metro City. The plane started its journey 1275 miles from Metro City.

This means that [tex]d = 1275[/tex].

Write an equation in standard form to represent the situation if the plane travels a hours at 550 mph and b hours at 590 mph.

This means that [tex]v*t = 550a + 590b[/tex].

Which equation is correctly written in standard form to represent this scenario?

[tex]d = v*t[/tex]

1275 = 550a + 590b

550a + 590b = 1275

Answer:

-1x+4

Step-by-step explanation:

-1/2 times 2x equals -1x. -1/2 times -8 equals 4.

Answer:

x would be 54 degrees

Step-by-step explanation:

Since x lies on a straight line, and it gives you the other angle (126) just subtract 180 and 126.

180 - 126 = 54

Answer:

Leg= Leg- hypotenuse

Step-by-step explanation:

5 suquared= 25

13 squared= 169

25+169 =194

194 square root is 13.9

How to determine each side of a right triangle

if leg a is the missing side, then transform the equation to the form when a is on one side, and take a square root: a = √(c² - b²)

if leg b is unknown, then. b = √(c² - a²)

for hypotenuse c missing, the formula is. c = √(a² + b²)

Answer:

13.9 (rounded)

Step-by-step explanation:

The pathaegorean theorem is A²+B²= C²

5²=25

13²= 169

169+25=194

√194=13.9

Answer: 10

Step-by-step explanation:

All you have to do to get the bottom number is add the numbers already there

Answer:

The width is equal to 12 meters

Step-by-step explanation:

The Volume equals length x width x height. In our case, we know the length and the height so we can find the width the following way...

V = (l)(w)(h)

[tex]w = \frac{V}{(l)(h)}[/tex]

[tex]w = \frac{288}{(4)(6)}[/tex]

[tex]w = \frac{288}{24}[/tex]

w = 12 m

Answer:

∫[tex]6x^5(x^6-2)\,dx[/tex] = [tex]\frac{1}{2}(x^6-2)^2+C[/tex]

Step-by-step explanation:

To find:

∫[tex]6x^5(x^6-2)\,dx[/tex]

Solution:

Method of substitution:

Let [tex]x^6-2=t[/tex]

Differentiate both sides with respect to [tex]t[/tex]

[tex]6x^5\,dx=dt[/tex]

[use [tex](x^n)'=nx^{n-1}[/tex]]

So,

∫[tex]6x^5(x^6-2)\,dx[/tex] = ∫ [tex]t\,dt[/tex] = [tex]\frac{t^2}{2}+C_1[/tex] where [tex]C_1[/tex] is a variable.

(Use ∫[tex]t^n\,dt=\frac{t^{n+1} }{n+1}[/tex] )

Put [tex]t=x^6-2[/tex]

∫[tex]6x^5(x^6-2)\,dx[/tex] = [tex]\frac{1}{2}(x^6-2)^2+C_1[/tex]

Use [tex](a-b)^2=a^2+b^2-2ab[/tex]

So,

∫[tex]6x^5(x^6-2)\,dx[/tex] = [tex]\frac{1}{2}(x^6-2)^2+C_1=\frac{1}{2}(x^{12}+4-4x^6)+C_1=\frac{x^{12} }{2}-2x^6+2+C_1=\frac{x^{12} }{2}-2x^6+C[/tex]

where [tex]C=2+C_1[/tex]

Without using substitution:

∫[tex]6x^5(x^6-2)\,dx[/tex] = ∫[tex]6x^{11}-12x^5\,dx[/tex] = [tex]\frac{6x^{12} }{12}-\frac{12x^6}{6}+C=\frac{x^{12} }{2}-2x^6+C[/tex]

So, same answer is obtained in both the cases.

Answer:

3

Step-by-step explanation:

The square root of 9 is 3

Answer:

2(3x+5)

6x+10

Step-by-step explanation:

W= x

L= 2x+5

2(x) + 2(2x+5)

Answer:

that will be 725.10 im not sure

Answer:

The answer is 770.9 and cant be rounded to the nearest tenth.