A box contains 35 gems, of which 10 are real diamonds and 25 are fake diamonds. Gems are randomly taken out of the box, one at a time without replacement. What is the probability that exactly 2 fakes are selected before the second real diamond is selected

Answer:

512

Step-by-step explanation:

To effectively answer the question, let us calculate the value of m. This can be obtained as follow:

m, (m² + 4), 16m

1st term (T₁) = m

2nd term (T₂) = m² + 4

3rd term (T₃) = 16m

Common ratio = T₂/T₁ = T₃/T₂

(m² + 4) / m = 16m / (m² + 4)

Cross multiply

(m² + 4)(m² + 4) = m × 16m

(m² + 4)² = 16m²

Take the square root of both side

√[(m² + 4)²] = √(16m²)

m² + 4 = 4m

Rearrange

m² – 4m + 4 = 0

Solving by Factorisation

m² – 2m – 2m + 4 = 0

m(m – 2) – 2(m – 2) = 0

(m – 2)(m – 2) = 0

(m – 2)² = 0

Take the square root of both side

m – 2 = 0

m = 2

Thus,

1st term (T₁) = m = 2

2nd term (T₂) = m² + 4 = 2² + 4 = 8

3rd term (T₃) = 16m = 16 × 2 = 32

The sequence => m, (m² + 4), 16m

Becomes

2, 8, 32

Finally, we shall determine the 5th term. This can be obtained as follow:

1st term (a) = 2

Common ratio (r) = 2nd / 1st = 8/2 = 4

5th term (T₅) =?

T₅ = ar⁴

T₅ = 2 × (4)⁴

T₅ = 2 × 256

T₅ = 512

Therefore, the 5th term is 512

Answer:

Assume you need to find distance CD, between points C(-2, 2), D(4, -4)

Use distance formula:

Answer:

C(x1,y1)=(-2, 2), D(4, -4)

D(x2,y2)=(4, -4)

we have

the length of line segment CD

=[tex]\sqrt{(x2-x1)²+(y2-y1)²}\\ \sqrt{(4+2)²+(-4-2)²}=8.48 units[/tex]

Answer:

the answer is .5 I think I'm sorry if I'm wrong

ln(2e/x)

ln2+ ln e -ln x

ln 2 + 1 - ln x

OPTION D is the correct answer

Answer:                                                                    

14 and 1

Explanation:

14 + 14 + 1 + 1 = 30

14 x 1 = 14

The perimeter is the sum of all 4 sides. Divide the perimeter in half fo the some of one length and one width:

Length + width = 15

Area is length x width

Find 2 numbers that when added equal 15 but when multiplied equal 14

15 + 0 = 15, 15 x 0 = 0

14 + 1 = 15, 14 x 1 = 14

The answer is 14 ft long by 1 ft wide

Answer:

5x+9=39

5x=39-5

5x÷5=30÷5

x=6

Answer:

See problem 1 below.

Step-by-step explanation:

Problem 1.

1. <A, <D

Given

2. <1, <3

Given

3. BC is congruent to BC

Congruence of segments is reflexive.

4. ABC, DBC

AAS

18. (5+3i) + (2-2i)

8 + 0

Answer = 8

19. (8+9i) + (5-9i) - (8-7)

17 + -4 - 1

- - = +

:. -4 + 1 = -3

17 - - 3

Answer = 20

20. (6+8i)(3-2i)

14 × 1

Answer = 14

9514 1404 393

Answer:

  1/10

Step-by-step explanation:

The product of fractions is the product of the numerators, divided by the product of the denominators.

  [tex]\dfrac{1}{2}\text{ of }\dfrac{1}{5}=\dfrac{1}{2}\times\dfrac{1}{5}=\dfrac{1\times1}{2\times5}=\boxed{\dfrac{1}{10}}[/tex]

__

Additional comment

When working with fractions and percentages, you will find that "of" often means "times."

Answer:

Hello! answer: 10

Step-by-step explanation:

you do a^2+b^2=c^2 meaning

8 × 8 + 6 × 6 will equal a number which then we have to find out the square root of that number meaning what number you can multiply by itself to get that number so...

8 × 8 = 64

6 × 6 = 36

64 + 36 = 100

√100 = 10

10 × 10 = 100 therefore the missing length is 10 hope that helps!

Answer:

4 / x¹⁴y⁸

Step-by-step explanation:

eliminate parenthese by multiplying all exponents inside parentheses by the exponent outside the parentheses:

1/2⁶ ÷ 1/4⁴ = 1/64 ÷ 1/256 which equals 256/64 or 4

x⁻⁶y⁴ ÷ x⁸y¹² = x⁻¹⁴y⁻⁸ = 1/x¹⁴ · 1/y⁸

put it all together to get:

4÷(x¹⁴y⁸)

Answer: The slope is -5/3 or -1.4

Algebra

[tex]s = \frac{y2 - y1}{x2 - x1} [/tex]

[tex]s = \frac{5}{3} [/tex]

Answer: Since he had fourteen, and he gave away six of them, he has eight left.

Step-by-step explanation:

The number sentence shows the number of apples Austin has left is 14 - 6 and equal to 8.

A way to express or represent numbers is through the number system.

The Number System includes any of the several sets of symbols and the rules for using them to represent numbers.

As per the given,

Total number of apples = 14

Number of apples that make a pie = 6

Left = 14 - 6 = 8

Hence "The number sentence shows the number of apples Austin has left is 14 - 6 and equal to 8".

For more about the number system,

https://brainly.com/question/22046046

#SPJ2

Answer:

75%

88.89%

Step-by-step explanation:

Given :

Mean = 70

Standard deviation = 12

Since the data is said to be extremely skewed, we apply Chebyshev's theorem rather than the empirical rule :

The minimum proportion of observation between 46 and 94

Chebyshev's theorem :

1 - 1 / k²

k = number of standard deviations from the mean

k = (94 - 70) / 12 = 24 / 12 = 2

Hence, we have ;

1 - 1/2²

1 - 1/4

1 - 0.25 = 0.75

Hence, The minimum proportion of observation between 46 and 94 is 75%

Between 36 and 106 :

k = (106 - 70) / 12 ;

k = 36/12 = 3

Hence,

1 - 1/3² = 1 - 1/9 = 8/9 = 0.8888 = 88.89%

The minimum proportion of observation between 34 and 106 is 88.89%

9514 1404 393

Answer:

  3/7

Step-by-step explanation:

The fraction is ...

  [tex]24\text{ g to }56\text{ g}=\dfrac{24\text{ g}}{56\text{ g}}=\dfrac{3}{7}\cdot\dfrac{8\text{ g}}{8\text{ g}}=\boxed{\dfrac{3}{7}}[/tex]

Answer:

3 / 7

Step-by-step explanation:

Fraction :-

24 g to 56 g

= 24 g / 56 g

= 3/7 + 8 g / 8 g

= 3/7

Answer:

wheres the photo

Step-by-step explanation:

Answer:

combined discount is 40%

Answer:

first day =64%

the second day = 36%

Answer:

Step-by-step explanation:

Answer:

V = 29.31 cm^3

Step-by-step explanation:

The volume of a cone is given by

V = 1/3 pi r^2 h

V = 1/3 (3.14) (2)^2 (7)

V =29.30666

Rounding to the nearest hundredth

V = 29.31 cm^3

Answer:

(-10, -8)

Step-by-step explanation:

4u

Each component of vector u is multiplied by 4. So

u = (3, 1)

4u = (4*3, 4*1) = (12,4).

v – 4u

Subtraction of the components of vector v by the components of the vector 4u. So

v - 4u = (2, -4) - (12, 4) = (2-12, -4 - 4) = (-10, -8)

The value is (-10, -8)

Answer: left 7 units, up 4 units, and vertical compression

Step-by-step explanation:

Given

The function is [tex]y=x^2[/tex]

First shift it to the left by 7 units, so the function becomes

[tex]y=(x+7)^2[/tex]

Now compress it to make it one-third

[tex]y=\dfrac{1}{3}(x+7)^2[/tex]

Now, sift the graph upward by 4 units

[tex]y=\dfrac{1}{3}(x+7)^2+4[/tex]

Thus , the conditions are left 7 units, up 4 units, and vertical compression.

Answer:

hlw its jess your ans is here ↑ ↓

:- 150 rotation and the other 30 rotation about the same point is equivalent to 150+30 = 180

rotation about that point

Answer:

9 people can go to the amusement park.

Answer:

x = 5

Step-by-step explanation:

Note the equal sign, what you do to one side, you do to the other. Isolate the variable, x.

Add 3 and subtract 2x from both sides of the equation:

4x (-2x) - 3 (+3) = 2x (-2x) + 7 (+3)

4x - 2x = 7 + 3

2x = 10

Next, isolate the x by dividing 2 from both sides of the equation:

(2x)/2 = (10)/2

x = 10/2

x = 5

5 is your answer for x.

~

Answer:

x=5

Step-by-step explanation:

4x-3=2x+7

Subtract 2x from each side

4x-2x-3=2x-2x+7

2x -3 = 7

Add 3 to each side

2x-3+3=7+3

2x = 10

Divide by 2

2x/2 =10/2

x = 5

Answer:

A. 5:12   B. 12:51

Step-by-step explanation:

. Use the smaller hand as the hour hand and the bigger hand to track each minute.

Answer:

If A > B (A is greater than B), A will be on the right side of B, and B will be on the left side of A on a number line.

Step-by-step explanation:

This is because as you keep on going right on a number line, the numbers keep getting greater. Same idea vise versa (left side gets lesser). Therefore, if A is greater than B, it will be to the right of B on a number line. Look below for an example:

Answer:

yea i dont know this one bro

Step-by-step explanation:

Answer:

Rule:-15

Step-by-step explanation:

36,21,6,-9,-24,-39,-54,-69...