What is the chance of getting 3 of the same cards in a row in a 52 cards deck?

Answer:

0.0016 = 0.16% probability that the lot will pass inspection.

Step-by-step explanation:

For each bulb, there are only two possible outcomes. Either it is defective, or it is not. The probability of a bulb being defective is independent of any other bulb, which means that the binomial probability distribution is used 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.

Sample of 18 light bulbs

This means that [tex]n = 18[/tex]

30% of the bulbs in the lot are defective.

This means that [tex]p = 0.3[/tex]

What is the probability that the lot will pass inspection?

It will pass inspection if there are no defective bulbs, that is, we have to find P(X = 0). So

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

[tex]P(X = 0) = C_{18,0}.(0.3)^{0}.(0.7)^{18} = 0.0016[/tex]

0.0016 = 0.16% probability that the lot will pass inspection.

Answer:

14cm²

Step-by-step explanation:

3x2=6,

3x2=6,

2x1=2,

6+6+2=14 cm^2

Answer:

B

Step-by-step explanation:

i did the test and it was correct, ur welcome

Answer:

[tex]\angle P[/tex]

Step-by-step explanation:

Given

[tex]\triangle PRQ = \triangle TSU = 90^o[/tex]

[tex]PQ = 20[/tex]     [tex]QR = 16[/tex]    [tex]PR = 12[/tex]

[tex]ST = 30[/tex]       [tex]TU = 34[/tex]    [tex]SU = 16[/tex]

See attachment

Required

Which sine of angle is equivalent to [tex]\frac{4}{5}[/tex]

Considering [tex]\triangle PQR[/tex]

We have:

[tex]\sin(P) = \frac{QR}{PQ}[/tex] --- i.e. opposite/hypotenuse

So, we have:

[tex]\sin(P) = \frac{16}{20}[/tex]

Divide by 4

[tex]\sin(P) = \frac{4}{5}[/tex]

Hence:

[tex]\angle P[/tex] is correct

Answer:

A or <P

Step-by-step explanation:

on edge 2021

Answer:

5:12

Step-by-step explanation:

125:300 simplified = 5:12

I hope this helps

Answer:

0.26684

Step-by-step explanation:

Given that :

Mean, μ = 62.5

Standard deviation, σ = 1.96

P(Z ≥ 63.72)

The Zscore = (x - μ) / σ

P(Z ≥ (x - μ) / σ)

P(Z ≥ (63.72 - 62.5) / 1. 96) = P(Z ≥ 0.6224)

P(Z ≥ 0.6224) = 1 - P(Z < 0.6224)

1 - P(Z < 0.6224) = 1 - 0.73316 = 0.26684

Answer:

A one solution

Step-by-step explanation:

4(x - 5) = 3x + 7

Distribute

4x - 20 = 3x+7

Subtract 3x from each side

4x-3x-20 = 3x+7-3x

x -20 = 7

Add 20 to each side

x -20+20 = 7+20

x = 27

There is one solution

Answer:

Step-by-step explanation:

Let's simplify that before we make the decision, shall we? We'll get rid of the parenthesis by distribution and then combine like terms.

4x - 20 = 3x + 7 and combining like terms and getting everything on one side of the equals sign:

1x - 27 = 0. Since that x has a power of 1 on it (linear), that means we have only 1 solution. If that was an x², we would have 2 solutions; if that was an x³, we would have 3 solutions, etc.

Answer:

The slope is undefined.

Step-by-step explanation:

The line must pass through the points (10,-3) and (10,-8), meaning that it must be vertical. The slope of a line is undefined if the line is vertical.

Answer:

n+3

Step-by-step explanation:

1/2 × 2(n+3)=n +3

I hope this helps

Answer:

9/10

Step-by-step explanation:

The first two digit number is 10 and the last is 99. That's a total of 99-10+1 numbers in all. That simplifies to 90. (Just like if we wanted to see how many numbers was 3,4,5, we would do 5-3+1=3 to get the total number.

Anyways, let's consider first how many 2 digjt numbers whose digits are equal. You have 11 22,33,44 55,66,77,88,99 which is 9 numbers total.

So the amount of 2 digits number whose digits differ is 90-9=81.

The probability that a 2 digit number have different digits is 81/90.

This can reduce. Divide top and bottom by 9 giving 9/10.

If y (0) = -1/3, then

-1/3 = 1 / (1 + C e ⁻⁰)

Solve for C :

-1/3 = 1 / (1 + C )

-3 = 1 + C

C = -4

So the particular solution to the DE that satisfies the given initial condition is

[tex]\boxed{y=\dfrac1{1-4e^{-x}}}[/tex]

Work Shown:

[tex]7x^2*\sqrt{2x^4}*6\sqrt{2x^{12}}\\\\7*6x^2*\sqrt{2x^4*2x^{12}}\\\\42x^2*\sqrt{4x^{4+12}}\\\\42x^2*\sqrt{4x^{16}}\\\\42x^2*\sqrt{(2x^8)^2}\\\\42x^2*(2x^8)\\\\42*2x^{2+8}\\\\84x^{10}\\\\[/tex]

So that's why the answer is choice C

The requirement that x is nonzero isn't technically necessary. The original expression simplifies to choice C even when x = 0 is the case. Also, we don't have issues such as division by zero errors that could arise. It's a bit curious why your teacher put in that condition.

Answer:

C.

Step-by-step explanation:

7x²×sqrt(2x⁴)×6×sqrt(2x¹²)

we see right away that as constant multiplication factor we have 7×6 = 42.

and then we get from each sqrt expression a sqrt(2), which leads to sqrt²(2) = 2 and therefore 42×2=84.

the only answer option with 84 is C.

now, to be completely sure, and to get some practice, let's look at the other parts :

sqrt(2x⁴) = sqrt(2)×sqrt(x⁴) = sqrt(2)×x²

sqrt(2x¹²) = sqrt(2)×sqrt(x¹²) = sqrt(2)×x⁶

=>

7x²×sqrt(2)×x²×6×sqrt(2)×x⁶ =7×6×2×x²×x²×x⁶ = 84x¹⁰

perfect. C is confirmed.

Answer:

x² - √3x / x² - 3

Step-by-step explanation:

To Do :-

Solution :-

We need to rationalize ,

Multiply numerator and denominator by x-√3 :-

Tanθ =sin /cos

tan θ = 5/2 / y

tan (30°) = 5/2 /y

[tex]y = \frac{5 \sqrt{3} }{2} [/tex]

y=4.33

Answer:

It is a ray because there are two points with a line passing through them which is extenging on one side but not on the other.

Answer: Number 1 is 150

Step-by-step explanation: If you put 72 / 48% in your calculator, you will get your answer.

Answer:

yeah, teachers kinda suck

qualitative

Step-by-step explanation:

b cos the question is in quality format

Answer:

cutee!

SUP???

Hiii friend :]

cuteee~!

prettyyy

Answer:

[tex]a = 4, -4[/tex]

Step-by-step explanation:

Step 1:  Plug in -4 for c

[tex]-a^{2} + c^{2}[/tex]

[tex]-a^{2} + (-4)^{2}[/tex]

[tex]-a^{2} + 16[/tex]

Step 2:  Solve for a

[tex]-a^{2}+16-16=0-16[/tex]

[tex]-a^{2}/-1 = -16/-1[/tex]

[tex]a^{2} = 16[/tex]

[tex]\sqrt{a^{2}} = \sqrt{16}[/tex]

[tex]a = 4, -4[/tex]

Answer:  [tex]a = 4, -4[/tex]

Step-by-step explanation:

|a+b|=✓(a²+b²)

|a|+|b|=a+b

||a+b|| ≤ ||a||+|b||

Answer:

dC=3.5

DC is between 3.475 and 3.525

Step-by-step explanation:

So let dx=1 since the change there is a change in 1 unit.

Find dC/dx by differentiating the expression named C.

dC/dx=0.05x+3

So dC=(0.05x+3) dx

Plug in x=10 and dx=1:

dC=(0.05×10+3)(1)

dC=(0.5+3)

dC=3.5

Let D be the change in cost-the triangle thing.

Since dx=1 we only want the change in unit to be within 1 in difference.

So this means we want it to be from x=9 to x=1] ot from x=10 to x=11.

Let's do from x=9 to x=10 first:

DC=C(10)-C(9)

DC=[0.025×10^2+3×10+4]-[0.025×9^2+3×9+4]

DC=[2.5+30+4]-[0.025×81+27+4]

DC=[36.5]-[2.025+31]

DC=[36.5]-[33.025]

DC=3.475

Now let's do from x=10 to x=11

DC=[0.025×11^2+3×11+4]-[0.025×10^2+3×10+4]

DC=[0.025×121+33+4]-[36.5]

DC=[3.025+37]-[36.5]

DC=[40.025]-[36.5]

DC=3.525

So DC, the change in cost where the change in unit is 1, is between 3.475 and 3.525.

9514 1404 393

Answer:

  (b)  0 = -78

Step-by-step explanation:

Subtracting 6 times the first equation from the second will give ...

  (4x +15y) -6(2/3x +5/2y) = (12) -6(15)

  0 = -78

Answer:

the answer is b

Step-by-step explanation:

Answer:

(-2,2) and (-3,-4)

Step-by-step explanation:

by graphing the line and parabola, you should get this graph

9514 1404 393

Answer:

  B.  x^2/3^2 + y^2/4^2 = 1

Step-by-step explanation:

The graph looks like a circle, but is not. It is a unit circle scaled by a factor of 3 in the x-direction and a factor of 4 in the y-direction. Thus, its equation is ...

  (x/3)^2 +(y/4)^2 = 1

  x^2/3^2 +y^2/4^2 = 1

Answer:

I am pretty sure it is B.

Step-by-step explanation:

This is a line with a positive slope, therefore we can discard c and d.

the sign < will mean that the shaded in area will be on your right side.

Answer:

5 bags of cement are required.

Step-by-step explanation:

Since to make concrete, the ratio of cement to sand is 1: 3, if cement and sand are sold in bags of equal mass, to determine how many bags of cement are required to make concrete using 15 bags of sand the following calculation must be done:

Cement = 1

Sand = 3

3 = 15

1 = X

15/3 = X

5 = X

Therefore, 5 bags of cement are required.

Answer:

21

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp/ adj

tan 60 = x / 7 sqrt(3)

7 sqrt(3)  tan 60 = x

7 sqrt(3) sqrt(3) = x

7*3 = x

21 = x

Answer:

x=60

Step-by-step explanation:

There are different ways to find x but this is what I found easiest.

To solve first note that AOD and CFB are vertical angles; this means that they are congruent. AOD consists of two angles with the measurements of 90 and x. CFB consists of two angles with the measurements of 30 and 2x. So, to find x set add the adjacent angles and set them equal to the other pair of angles. The equation would be [tex]90+x=30+2x[/tex]. First, subtract x from both sides; this makes the equation [tex]90=30+x[/tex]. Then, subtract 30 from both sides. This gives the final answer, x=60.

If f(x) = 7/(1 + x), then

f (2) = 7/3

f '(x) = -7/(x + 1)²   ==>   f ' (2) = -7/9

f ''(x) = 14/(x + 1)³   ==>   f '' (2) = 14/27

f '''(x) = -42/(x + 1)⁴   ==>   f ''' (2) = -14/27

Then the Taylor series of f(x) about a = 2 is

7/3 + 1/1! (-7/9) (x - 2) + 1/2! (14/27) (x - 2)² + 1/3! (-14/27) (x - 2)³

= 7/3 - 7/9 (x - 2) + 7/27 (x - 2)² - 7/81 (x - 2)³