Find x . Please and thank you

Answer:

0.2992 = 29.92% probability of obtaining at least 8 failures.

Step-by-step explanation:

For each dice, there are only two possible outcomes. Either a failure is obtained, or a success is obtained. Trials are independent, 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.

A success is 5 or 6.

A dice has 6 sides, numbered 1 to 6. Since a success is 5 or 6, the other 4 numbers are failures, and the probability of failure is:

[tex]p = \frac{4}{6} = 0.6667[/tex]

10 normal six sided dice are thrown.

This means that [tex]n = 10[/tex]

Find the probability of obtaining at least 8 failures.

This is:

[tex]P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10)[/tex]

So

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

[tex]P(X = 8) = C_{10,8}.(0.6667)^{8}.(0.3333)^{2} = 0.1951[/tex]

[tex]P(X = 9) = C_{10,9}.(0.6667)^{9}.(0.3333)^{1} = 0.0867[/tex]

[tex]P(X = 10) = C_{10,10}.(0.6667)^{10}.(0.3333)^{0} = 0.0174[/tex]

Then

[tex]P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10) = 0.1951 + 0.0867 + 0.0174 = 0.2992[/tex]

0.2992 = 29.92% probability of obtaining at least 8 failures.

Answer:

The t distribution can be used when finding a confidence interval for the population mean whenever the sample size is small.

Hence, the correct option is A.

To estimate the population mean we use a t-distribution to calculate the confidence interval. When we use a t-distribution the sample standard deviation is used to estimate the population standard deviation

Answer:

ok so if we add this up we get that there is 14 kids in the class who have been polled and 2/14 or 1/7 likes hamlet so the chance is 1 out of 7

The experimental probability that the next student to respond likes Hamlet best is [tex]\frac{1}{6}[/tex] .

Thus, the experimental probability that the next student to respond likes Hamlet best is [tex]\frac{1}{6}[/tex] .

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Answer:

c)  y = 8[tex]\sqrt{3}[/tex]

Step-by-step explanation:

in a 30-60-90° Δ the ratio of the sides, respectively, is 1: [tex]\sqrt{3}[/tex] : 2

if the side opposite the 30°∡ is 8 then 'y' is 8[tex]\sqrt{3}[/tex] and 'x' is 16

Answer:

20

Step-by-step explanation:

The numbers whose product are to be obtained :

(–24.98)(–1.29)

To use front end approximation, numbers are rounded to the greatest place value :

For :

(-24.98) is rounded to - 20 (4 is rounded here to 0)

(-1.29) is rounder to - 1 (2 is rounded to 0)

Then, the product of the two numbers will be :

-20 * - 1 = 20

Answer:

2x - 3

Step-by-step explanation:

3x-1 - (x+2)

3x-1 -x -2

2x - 3

Answer:

x = + 5/4 or x = - 5/4

Step-by-step explanation:

[tex]4 x^2 = 6\frac{1}{4}\\\\4 x^2 = \frac{25}{4}\\\\x^2 =\frac{25}{16}\\\\x = \pm \frac{5}{4}[/tex]

Answer:

it is b

Step-by-step explanation:

Answer:

it is b

Step-by-step explanation:

Answer:

solution,

x+41+59=180⁰ ( the sum of total angle of triangle is 180⁰)

or, x+ 100=180

or, X=180-100

so , X=80

Step-by-step explanation:

let us check

59+41+80=180

Answer:

(4, -4)

Step-by-step explanation:

Using the midpoint formula;

M(X,Y) = {(ax1+bx2)/a+b, (ay1+by2)/a+b}

X = (ax1+bx2)/a+b

Y = (ay1+by2)/a+b

Substitute

X = 4(2)+2(8)/4+2

X = 8+16/6

X = 24/6

X = 4

Also

Y = 4(-3)+2(-6)/6

Y = -12-12/6

Y = -24/6

Y = -4

Hence the required partition is (4, -4)

Answer:

slope = 4/3

Step-by-step explanation:

(-1 , 1) = (x1 , y1)

(2 , 5) = (x2 , y2)

slope (m) = y2 - y1/x2 - x1

=5 - 1/2 - (-1)

=4 /2+1

=4/3

Answer:

Two solutions

Step-by-step explanation:

The number of points of intersections represents the number of solutions to the system of equations. Since the parabola intersects the circle at two points, there are two solutions to the circle.

Furthermore, these two points of intersection are exactly the solutions to the system of equations. Finding the coordinates of the points of intersection will give you the solutions to the system of equations.

Answer:

x = 4/5 is the one x value that is not permitted.  The domain of (fog)(x) is

(-infinity, 4/5) ∪ (4/5, infinity)

Step-by-step explanation:

(fog)(x) is the "composition" of f and g.  We start with f(x) and replace x with g(x), which is 5x - 4:

              3

f(x) = x - ------- becomes

               x

                                          3            

f(5x - 4) =     [5x - 4]  -  ------------

                                      [5x - 4]

To identify the domain, consider the value or values of x for which the denominator shown above is zero:  5x - 4 = 0, or 5x = 4, or x = 4/5

The domain of the composite function (f·g)(x) in interval notation is (-∞,0)∪(0,∞).

The domain and range are defined for a relation and they are the sets of all the x-coordinates and all the y-coordinates of ordered pairs respectively.

The given functions are f(x)= x-3/x and g(X)=5x-4.

Now, (f·g)(x)=f(x)×g(x)

= (x-3/x)(5x-4)

(f·g)(x)= 5x²-15-4x+12/x

Find the domain by finding where the expression is defined.

Interval Notation: (-∞,0)∪(0,∞)

Set-Builder Notation:{x|x≠0}

Therefore, the domain of the composite function (f·g)(x) in interval notation is (-∞,0)∪(0,∞).

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Answer:

b

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠ 1 is an exterior angle of the triangle , then

∠ 1 = 30° + 39° = 69°

Answer:

option b:  69°

Step-by-step explanation:

the sum of the interior angles of a triangle is 180c.

that is, 39 + 30 + x = 180

                          x = 180 - 39 - 30

                          x = 111°

∠ 1 + x = 180°            [ straight line angles ]

∠1 + 111° = 180°

∠1 = 180 - 111 = 69°

Let

We know that in a rectangle

☆ Perimeter=2(Length+Breadth)

[tex]\\ \sf\longmapsto 2(x+2x)=432[/tex]

[tex]\\ \sf\longmapsto 2x+4x=432[/tex]

[tex]\\ \sf\longmapsto 6x=432[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{432}{6}[/tex]

[tex]\\ \sf\longmapsto x=72[/tex]

[tex]\\ \sf\longmapsto 2x=2(72)=144[/tex]

☆Area=Length×Breadth

[tex]\\ \sf\longmapsto Area=144\times 72[/tex]

[tex]\\ \sf\longmapsto Area=10368cm^2[/tex]

Answer:

it's B

Step-by-step explanation:

I'm quite sure it is. Hope it helps u

Answer:

x = 32 and BEC = 43

Step-by-step explanation:

3X + 41 = 137

3X = 96

X = 32

FOR BEC:

137 + 137 = 274

360-274=86 ( ANGLES AROUND A POINT ADD UP TO 360)

86/2 = 43

BEC/AED = 43 ( VERTICALLY OPPOSITE ANGLES ARE EQUAL)

hope this helps good luck!

Answer:

? = 10

Step-by-step explanation:

13 - (10) = 7-4 ....... 2×2 =4

3 = 3

Answer:

6 degrees

Step-by-step explanation:

[tex] - 4 + 10 = 6[/tex]

Answer:

6 degrees

Step-by-step explanation:

Answer:

7√10 / 10.

Step-by-step explanation:

7/√10

Multiply top and bottom by √10:

= 7√10 / 10

Answer:

The given relation is presented as follows;

[tex]\dfrac{1}{a} + \dfrac{1}{b} +\dfrac{1}{c} = \dfrac{1}{a + b + c}[/tex]

Where 'a', 'b', and 'c' are member of real numbers, we have;

a⁹, b⁹, and c⁹ are also member of real numbers

When a⁹ = x, b⁹ = y, and c⁹ = z

By the above relationship, we have;

[tex]\dfrac{1}{x} + \dfrac{1}{y} +\dfrac{1}{z} = \dfrac{1}{x + y + z}[/tex]

Substituting x = a⁹, y = b⁹, and z = c⁹, we get;

[tex]\dfrac{1}{a^9} + \dfrac{1}{b^9} +\dfrac{1}{c^9} = \dfrac{1}{a^9 + b^9 + c^9}[/tex]

Step-by-step explanation:

Step-by-step explanation:

[tex]1) \\ - 2 \leqslant x \leqslant 1 \\ 2) \\ - 3 > x \geqslant 2 \\ 3) \\ x> 0[/tex]

[tex]4) \\ x \leqslant - 3 \\ 5) \\ - 4 \leqslant x \geqslant 1[/tex]

[tex]6) \\ - 2< x \leqslant 0[/tex]

Answer:

55 mph

Step-by-step explanation:

Answer:

138 Degrees

Step-by-step explanation:

Because it is adjacent to the 42 degrees, just subtract 42 from 180 to get 138 degrees.

Answer:

D+42*=180*

D=180-42

138

Step-by-step explanation:

mark as brainiest please

Answer:

y-acis

Step-by-step explanation:

the function graph is symmetric about

- y-axis when it is an even function

-the origin ehen it is an even function

A symmetrical graph about the x-axis is not a function graph

f(×) is a even if and only if f(×) =f(×)

f(×) is a odd if and only f(×)=f(×)

We have the function r(0) = 4cos (50)

(only symmetry about the y-acis or about the origin)

Check r(-0)

r(-0) = 4cos (5-0) = 4cos (-50 = 4 cos (50)

Used cos (-× = cos ×

We have r(0). Therefore the graph of r(0) is symmectric about the y-axis.

Answer:

positive slope

Step-by-step explanation:

when a graph is sloping to the right it means it has a positive . the gradient of this straight is positive .

gradient of the line is greater than 0

The slope of the line is m = 2

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( 1 , 3 )

Let the second point be Q ( 0 , 1 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 3 - 1 ) / ( 1 - 0 )

m = 2

Therefore , the value of m is 2

Hence , the slope is 2

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Answer:

as x --> oo, f(x) = oo (infinite)

as x -- -oo, f(x) = 3

Answer:

Any real number.

Step-by-step explanation:

I dunno what you're asking, but Im assuming you need what a equals to.

[tex]a+5(2a-1)+3=11a-2\\a+10a-5+3=11a-2\\11a-2=11a-2\\[/tex]

The answer is any real number.