A student takes an exam containing 16 true or false questions. If the student guesses, what is the probability that he will get exactly 14 questions right

Answers

Answer 1

Answer:

0.001831055

Step-by-step explanation:

Here, n = 16, p = 0.5, (1 - p) = 0.5 and x = 14

As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X = 14)

P(x =14) = 16C14 * 0.5^14 *(1-0.5)^2

               = 120 * 0.5^14 *(1-0.5)^2

= 0.001831055


Related Questions

In a class of 70 pupils, 36 like tasty time , 34 like ice-
cream, 6 like both tasty time }
draw a Venn diagram to show the data.
find how
many
like neither tasty time nor ice-cream

Answers

Step-by-step explanation:

I think this might be the correct answer

The number of pupils that like neither tasty-time nor ice cream is 6 if in a class of 70 pupils, 36 like tasty time, 34 like ice cream, 6 like both tasty times.

What is the Venn diagram?

It is defined as the diagram that shows a logical relation between sets.

The Venn diagram consists of circles to show the logical relation.

We have:

In a class of 70 pupils, 36 like tasty time, 34 like ice cream, 6 like both tasty time.

Total = 70 pupils

Number of like tasty time = 36

Number of like ice cream = 34

Number of like both = 6

Let x be the total number of pupils that like neither tasty-time nor ice cream

The number of pupils that like ice cream only =  34 - 6 = 28

The number of pupils that like tasty-time only = 36 - 6 = 30

From the Venn diagram:

28 + 30 + 6 + x = 70

x = 70 - 64

x = 6

Thus, the number of pupils that like neither tasty-time nor ice cream is 6 if in a class of 70 pupils, 36 like tasty time, 34 like ice cream, 6 like both tasty times.

Learn more about the Venn diagram here:

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How many 4-digit passcodes can be created if each digit can be any number, 0-9?
6,561
10,000
40
5,040

Answers

Answer:

6,561

that's a good number

0 thru 9 is 10 numbers.

Each digit can be 1 of 10 numbers:

Total combinations = 10 x 10 x 10 x 10 = 10,000

Answer: 10,000

The length of a rectangle is twice its width. If the area of the rectangle is 72in², find its perimeter

Answers

Let breadth be x

Length=2x

[tex]\\ \sf\longmapsto Area=Length\times Breadth[/tex]

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

[tex]\\ \sf\longmapsto 2x^2=72[/tex]

[tex]\\ \sf\longmapsto x^2=\dfrac{72}{2}[/tex]

[tex]\\ \sf\longmapsto x^2=36[/tex]

[tex]\\ \sf\longmapsto x=\sqrt{36}[/tex]

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

Length=6×2=12inBreadth=6in

[tex]\\ \sf\longmapsto Perimeter=2(L+B)[/tex]

[tex]\\ \sf\longmapsto Perimeter=2(12+6)[/tex]

[tex]\\ \sf\longmapsto Perimeter=2(18)[/tex]

[tex]\\ \sf\longmapsto Perimeter=36in[/tex]

!!!!PLEASE HELP!!!!
What is the following quotient?
2
√13+ /11
O 13-2./11
13+ 11
6
13+ V11
12
√13 - 1

Answers

(D)

Step-by-step explanation:

Multiply and divide the fraction by the conjugate:

[tex]\dfrac{2}{\sqrt{13}+\sqrt{11}}×\dfrac{\sqrt{13}-\sqrt{11}}{\sqrt{13}-\sqrt{11}}[/tex]

[tex]= \dfrac{2(\sqrt{13} - \sqrt{11})}{(\sqrt{13})^2 - (\sqrt{11})^2}[/tex]

[tex]=\dfrac{2(\sqrt{13} - \sqrt{11})}{2}[/tex]

[tex]=\sqrt{13} - \sqrt{11}[/tex]

A hunter walks 400m Up a hill which slopes at an angle of 20 to the horizontal. Calculate,correct to the nearest metre, the: a. horizontal distance he covered b.vertical height through which he rises.​

Answers

let y be the horizontal distance and x the vertical

y/400 = cos 20

y=400 cos20

y=376m

x/400 =sin20

x=400sin20

x=137m

4) If the perimeter of a square is 48cm",
What is the length of each side?
Simplify your answer.

Answers

Answer:

If the total perimeter of square is 48 cm, then the length of one side is equal to 48 divided by 4, since all sides of a square are the same.

So, the correct answer is 12.

Let me know if this helps!

The length of each side is 12cm.

Explanation:

The perimeter of a square is calculated by the formula:

P = 4a , where  P = perimeter, and a = length of any side, all sides being equal in a square.

From the given data we write:

48 = 4a

Divide both sides by

4.12 = a

The length of each side is 12cm.

f (x) = 3r + 6. Find the inverse of f(x).

Answers

Answer:

The inverse is 1/3x -2

Step-by-step explanation:

f (x) = 3x + 6

y = 3x+6

Exchange x and y

x = 3y+6

Subtract 6 from each side

x-6 = 3y+6-6

x-6 = 3y

Divide by 3

1/3x - 6/3 = y

1/3x -2 = y

The inverse is 1/3x -2

Help very confusing to me???!

Answers

Answer:

Heyy mate... here's ur ans ;)

they asked us to apply pythagarus theorem becoz that theorem proves

that it is rectangle so lets get started

( p - perpendicular / b - base / h - hypotenuse )

a) =>

B = 8.1 m

P = 6.3 m

H = 10.15m

Now applying thm => H^2=p^2+b^2

(8.1)^2 + (6.3)^2 = (10.15)^2

65.61 + 39.69 = 103.02

so now LHS = 105.3 and RHS = 103.02 hence

LHS not equal to RHS

so is not rectangle

b) =>

B = 14.4

P = 5.2

H = 15.31

Now applying thm => H^2=p^2+b^2

(5.2)^2 + (14.4)^2 = (15.31)^2

27.04 + 207.36 = 234.39

LHS = 234.4 and RHS = 234.39

just taking approximation rhs is 234.4

hence

LHS = RHS

so it is a rectangle

please mark it brainliest <3

1.) Three numbers form a geometric sequence whose common ratio is 0.5. If the first is reduced to 10 more than one quarter its value, the second decreased by 10, and the third increased by 10 more than twice its value, the resulting three numbers form an arithmetic sequence. Determine the original three numbers.

Answers

Let x be the first number in the sequence, so the first three numbers are

{x, 0.5x, 0.5²x}

Then

{x/4 + 10, 0.5x - 10, 2(0.5²x) + 10}

is arithmetic, so there is some constant c such that

0.5x - 10 = x/4 + 10 + c   ==>   x/2 - 10 = x/4 + 10 + c

2(0.5²x) + 10 = 0.5x - 10 + c   ==>   x/2 + 10 = x/2 - 10 + c

Solve the second equation for c :

x/2 + 10 = x/2 - 10 + c

c = 20

Substitute this into the first equation and solve for x :

x/2 - 10 = x/4 + 10 + 20

x/4 = 40

x = 160

Then the terms are

{160, 80, 40}

write your answer in simplest radical form​

Answers

Answer:

n = 8√2

Step-by-step explanation:

From the question given above, the following data were obtained:

Angle θ = 60°

Opposite = 4√6

Hypothenus = n =?

The value of n can be obtained by using the sine ratio as illustrated below:

Sine θ = Opposite / Hypothenus

Sine 60 = 4√6 / n

√3/2 = 4√6 / n

Cross multiply

n × √3 = 2 × 4√6

n × √3 = 8√6

Divide both side by √3

n = 8√6 / √3

Rationalise

n = 8√6 / √3 × (√3/√3)

n = 8√(6×3) / 3

n = 8√18 / 3

Recall

√18 = √(9×2) = √9 × √2 = 3√2

Thus,

n = 8√18 / 3

n = 8 × 3√2 / 3

n = 8√2

2. About how much is 123.1 do you weigh in pounds? Estimate if you don't know☺ Find an online converter and find out how many kilograms that is.​

Answers

Answer:

123.1 pounds is vary long, and I don't want to repeat, so 55.8372207 repeat.

Step-by-step explanation:

If you have any questions regarding my answer, tell me them in the comments, and I will come answer them for you. Have a good day.

Which side of XYZ is the longest?

A. xy
B. xz
C. yz
D. cannot be determined​

Answers

Answer:

the answer is x because its small

Answer:

Step-by-step explanation:

It’s Xy

Find the sum of ∑4/k=1 (-4k)

Answers

Answer:

Hello,

Answer C: -40

Step-by-step explanation:

[tex]\displaystyle \sum_{k=1}^4\ (-4k)\\\\=-4*\sum_{k=1}^4\ k\\\\=-4*4*\dfrac{1+4}{2} \\\\=-4*5*2\\\\=-40\\[/tex]

Find the value of
[tex] {z}^9{ \times {z}^10 = {z}^x [/tex]

Answers

Step-by-step explanation:

Just use the Law of Indices.

Identify the transformed function that represents f(x) = ln x stretched vertically by a factor of 17, reflected across the x-axis, and shifted by 19 units left.
A. g(x) = −17ln (x + 19)
B. g(x) = 17ln (x − 19)
C. g(x) = 17ln (x + 19)
D. g(x) = −17ln (x − 19)

Answers

Answer:

b

Step-by-step explanation:

ANSWER. EXPLANATION. The given logarithmic function is. The transformation,. stretches the graph of y=f(x) vertically by a factor of c units ...

4 votes

ANSWER[tex]y = - 3 ln(x - 7) [/tex]EXPLANATIONThe given logarithmic function is [tex]f(x) = ln(x) [/tex]The transformation, [tex]y = - cf(x - k)[/tex]stretches

find the missing length indicated ​

Answers

Answer:  240

============================================================

Explanation:

Let y be the length of the vertical dashed red line in the drawing. More specifically, this dashed line is an altitude.

Along the top, the entire segment is 400 units long. The right piece is 144 units long, so the left piece is 400-144 = 256 units long.

The triangles are similar, allowing us to set up a proportion like so:

144/y = y/256

144*256 = y*y

36864 = y^2

y^2 = 36864

y = sqrt(36864)

y = 192

So this is the length of that vertical dashed red line.

--------------------------------

Now shift your attention solely on the smaller triangle on the right side. It is a right triangle with legs 144 and 192. The hypotenuse is x.

We can use the pythagorean theorem to find x.

a^2 + b^2 = c^2

c = sqrt( a^2 + b^2 )

x = sqrt( 144^2 + 192^2 )

x = 240

240.

Let y be the length of the vertical dashed red line in the drawing. More specifically, this dashed line is an altitude.

Along the top, the entire segment is 400 units long. The right piece is 144 units long, so the left piece is 400-144 = 256 units long.

The triangles are similar, allowing us to set up a proportion like so:

144/y = y/256

144*256 = y*y

36864 = y^2

y^2 = 36864

y = sqrt(36864)

y = 192

So this is the length of that vertical dashed red line.

Now shift your attention solely to the smaller triangle on the right side. It is a right triangle with legs 144 and 192. The hypotenuse is x.

We can use the Pythagorean theorem to find x.

a^2 + b^2 = c^2

c = sqrt( a^2 + b^2 )

x = sqrt( 144^2 + 192^2 )

x = 240

What is Pythagorean Theorem?

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2.

Learn more about the Pythagorean theorem at

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Reaner Recycling collected 7/4 tons of aluminum last Saturday. If 7 ton of
aluminum can be shredded each day, how many days will it take to process what
was collected on Saturday?

Answers

Answer:

1/4

Step-by-step explanation:

since 7 tonnes can be shredded per day you need o divide the amount you have by 7

so 7/4 /7 = 1/4

so it will  take 1/4 days

Answer:

[tex] \frac{1}{4} [/tex]

Step-by-step explanation:

Make a ratio

7 : 1

7/4:x

Cross multiple

7x = 7/4

Then make x a subject formula

x =1/4

Find the value of each determinant

Answers

Answer:

−4304

Step-by-step explanation:

1. The given determinant is :

[tex]\begin{vmatrix}7 &31 \\ 142& 14\end{vmatrix}[/tex]

We need to find its determinant . It can be solved as follows :

[tex]\begin{vmatrix}7 &31 \\ 142& 14\end{vmatrix}=7(14)-142(31)\\\\=-4304[/tex]

So, the value of determinant is equal to −4304.

Answer:

A= -4269

B= 1768

C= 647.36

Step-by-step explanation:

Graph y=|x|+5, how does it compare to parent graph y=|x|

Answers

9514 1404 393

Answer:

  it is shifted 5 units upward

Step-by-step explanation:

The y-coordinate is a measure of the distance above the x-axis. When 5 is added to a y-coordinate, the point is shifted 5 units upward.

The function y = |x| +5 adds 5 units to the y-value of every point of the graph of y = |x|. The graph of y=|x|+5 is shifted 5 units upward from the parent graph.

if 25 liters of milk can make 8 tin of cheese how many liters of milk would b needed to make 11 tin of cheese? ​

Answers

Answer:

Step-by-step explanation:

34.375 Liters of milk make 11 tins of cheese. Assuming that milk is available in whole liters only, 35 Liters of milk are needed.

how many cubic meters of gravel are in the back of a full dump truck that measures 7m wide by 4m tall by 16m long​

Answers

Answer:

Step-by-step explanation:

Assuming the gravel reaches the top of the walls and no higher, the volume is 7×4×16 = 448 m³

Answer:

hello thereee

now vol of truck = l b h = 7 * 4 * 16 = 448 m^3

( 448m^3 is final ans...

glad for brainliest.... hope that helps <3

2. A dolphin leaps 5 feet in the air at the same time an orca whale dives 12 feet below the water. How far apart are the whale and the dolphin?​

Answers

They are 17 feet apart.
Hope this helps
17 feet, hope u can answ

Which shapes are quadrilaterals?
1. Scalene right triangle
2. Obtuse scalene triangle
3. Isosceles right triangle
4. Hexagon
5. Pentagon
6. Right trapezoid
7. Venn diagram

Answers

Hey there! I'm happy to help!

A quadrilateral is any polygon (enclosed shape) with four sides. Let's see what each of these shapes are.

Scalene right triangle - the prefix tri- means three  (tricycle, tripod, triple, etc.), and all triangles have three sides, so this is not a quadrilateral.Obtuse scalene triangle - once again a triangle, so not a quadrilateral.Isosceles right triangle - would you look at that, another triangle! Not a quadrilateral.Hexagon - a hexagon is a six-sided polygon (hex=six), so this is not a quadrilateral.Pentagon - a pentagon is a five-sided polygon (pent=five, like Pentatonix!). Not a quadrilateralRight trapezoid - a trapezoid is a quadrilateral with at least one pair of parallel sides!Venn diagram - a Venn diagram is a compare and contrast chart made of two overlapping circles (ZERO sides), so this is not a quadrilateral.

So, the only shape on your list that is a quadrilateral is 6. right trapezoid.

Have a wonderful day! :D

Complete the equation describing how x
and y are related.
х у
y = [ ? ]x
-2
-1
0
1
2
3
-6
-3
0
3
6
9
Enter the answer that
belongs in [?]

Answers

Answer:

y=3x

Step-by-step explanation:

-6/-2=3, -3/-1=3, 3/1=3. 6/2=3

what is the maximum number of students among whom 100 orange ,150 cirtrus, and 250 guavas can be equally distirbuted ? what is the share of each fruits for a student?​

Answers

Answer:

Hello,

Step-by-step explanation:

HCF(100,150,250)=50*HCF(2,3,5)=50*1=50

Part of each fruits for a student:

2 oranges, 3 cirtrus and 5 guavas.

Find the area enclosed in the graph of
x² + y² 16x + 32y.

Answers

Answer:

3

256

sq.units

Step-by-step explanation:

Both parabolas cut each other at (0,0) and (16,16)

Area enclosed by these parabolas

=∫

0

16

4

x

dx−∫

0

16

16

x

2

dx

=[

3

2×4×x

3/2

]

0

16

−[

16×3

x

3

]

0

16

=

3

2×4

4

3

4

4

=

3

256

sq. units

HELP NEEDED PLEASE :(
Identify the center and the radius of a circle that has a diameter with endpoints at (5, 8)
and (7,6).

Answers

Answer:

Centre is,

((5+7)/2,(8+6)/2)

or, (12/2,14/2)

or, (6,7)

radius is,

[√{(5-7)²+(8-6)²}]/2

= [√(2²+2²)]/2

= [√(4+4)]/2

= [√8 ]= [2√2]/2 = √2

The center of a circle = (6, 7)

the radius of a circle = [tex]\sqrt{2}[/tex] units

What is the distance formula?

"The distance between two points [tex](x_1,y_1),(x_2,y_2)[/tex] is given by  [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_2)^2}[/tex]"

What is midpoint formula?

"The coordinates of the midpoint of the line segment having endpoints [tex](x_1,y_1),(x_2,y_2)[/tex] is given by [tex]m=(\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )[/tex] "

What is diameter of circle?

"It is the line segment through the center and touching two points on its edge. "

For given question,

The diameter of circle has endpoints at (5, 8) and (7,6).

Let [tex](x_1,y_1)=(5,8),(x_2,y_2)=(7,6)[/tex]

First we find the length of the diameter of the circle.

Using the distance formula,

[tex]\Rightarrow d=\sqrt{(x_2-x_1)^2+(y_2-y_2)^2} \\\\\Rightarrow d=\sqrt{(7-5)^2+(6-8)^2} \\\\\Rightarrow d=\sqrt{2^2+(-2)^2}\\\\\Rightarrow d=\sqrt{4+4}\\\\\Rightarrow d=2\sqrt{2}~units[/tex]

We know that the diameter = 2 × radius

⇒ radius (r) = [tex]\frac{2\sqrt{2} }{2}[/tex]

⇒ r = [tex]\sqrt{2}[/tex] units

We know that the midpoint of the diameter is the center of the circle.

Using midpoint formula the center of the circle would be,

[tex]\Rightarrow O=(\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )\\\\\Rightarrow O=(\frac{5+7}{2} ,\frac{8+6}{2} )\\\\\Rightarrow O=(\frac{12}{2} ,\frac{14}{2} )\\\\\Rightarrow O=(6,7)[/tex]

Therefore, the center of the circle is (6,7)

Hence, the center of a circle = (6, 7)

the radius of a circle = [tex]\sqrt{2}[/tex]

Learn more about the distance formula and mid-point formula here:

https://brainly.com/question/11231122

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8. Solve the following triangle for all missing sides and angles.

Part 1: Find the measure of angle B

Part 2: Use the law of sines to find the length of side A

Part 3: Use any method to find the length of side c

Answers

Answer:

Parte1 :

∡B= 180 - (42 + 83)= 55°

Parte2 :

Using the law of sines : [tex]\frac{sin 42}{a} = \frac{sin 55}{175}[/tex] ⇔ [tex]a = sin42 \frac{175}{sin 55}[/tex] ⇔ a= 142.95

Parte3 :

Using the same law : [tex]c = sin 83\frac{a}{sin 42}[/tex]  or  [tex]c= sin 83\frac{175}{sin 55}[/tex]  ⇔ c= 212.04

Need help plz + will give brainlest

Thanks in advance

Answers

Answer:

it is  D.

Step-by-step explanation:

An exponential function f(x) = ab^xpasses through the points (0, 2) and (3, 54). What are the values of a and
b?
a=
b =

Answers

Answers:

a = 2

b = 3

=======================================================

Explanation:

Plug in x = 0 and y = 2 to find that

y = a*b^x

2 = a*b^0

2 = a*1

2 = a

a = 2

Then plug in x = 3 and y = 54 to determine the value of b

y = a*b^x

y = 2*b^x

54 = 2*b^3

2b^3 = 54

b^3 = 54/2

b^3 = 27

b = (27)^(1/3)

b = 3

So we have y = a*b^x update to y = 2*3^x

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