A multiple-choice examination has 10 questions, each with four possible answers, only one of which is correct. Suppose that one of the students who takes the examination answers each of the questions with an independent random guess. What is the probability that he answers at least six questions correctly?​

Based on the number of seats on the balcony, the number of seats in the theatre are 600 seats.

The balcony is said to have 120 seats and these are 1/5 of the total seats in the theatre.

The total number of seats in the theatre are:

= Number of seats on balcony / Proportion of seats this represents

Solving gives:

= 120 ÷ 1/5

= 120 ÷ 0.2

= 600 seats

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The number of students that were absent is; 24

Let the total number of students be x .

The number of students which were absent = ¹/₃x.

Number of students which were present = ²/₃x

Thus;

Number of students who attended math's test = ¹/₂x

Number of students who attended physics test = ¹/₄x

No. of students who attended both tests = 6

A denotes number of students who attended math's test

B denotes number of students who attended physics test

Thus;

n(A) = ¹/₂x

n(B) = ¹/₄x

n(A ∩ B) = 6

n(A∪B) = number of students which were present

Thus;

n(A ∪ B) = n(A) + n(B) − n(A∩B)

²/₃x = ¹/₂x + ¹/₄x − 6

²/₃x = ³/₄x - 6

³/₄x - ²/₃x = 6

x = 72

Thus, number of students that were absent = ¹/₃ * 72

Number of students that were absent = 24

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Answer:

Step-by-step explanation:

(1) The sum of the interior angles of a polygon is [tex]180(n-2)[/tex] degrees, where n is the number of sides. In this case, n=5, so the sum is 180(5-2)=540 degrees, meaning the first statement is false.

(2) Since the angles add to 540 degrees, dividing this amongst the five equal angles, we get that each angle measures 108 degrees, so this statement is true.

(3) By definition, all angles of a regular polygon are congruent.

(4) A hexagon has 6 sides, but this polygon has only 5 sides, so this statement is false.

(5) This is true. (See statement (1)).

Answer:

Options B, C, E

Step-by-step explanation:

Using the figure given, The one equation that matches with the diagram is 3x=30-6.  The diagram that matches the equation circled is given in the image attached.

From the above, we can see that the equation that matches with the diagram are:

Note that for 3(x+6)=30

3x +  18 = 30

3x = 30-18

3x = 12

x = 12/3

x = 4

Then fixing x into the equation =

3(x+6)=30

3(4+6)=30

Therefore , 12 + 18 will give us 30 and the answer is straight forward. The same applies for 30=3x+6 and 6+3x=30 as the answer is straight forward.

But the one equation that does not matches with the diagram is 3x=30-6 because its output is not straight forward.

3x =30-6

3x = 24

x = 24/3

x = 8

Fixing 8 into the equation

3x = 30-6

3(8) = 24

=24 is the  answer and not 30

Therefore, Using the figure given, The one equation that matches with the diagram is 3x=30-6.

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Answer:

D

Step-by-step explanation:

i just took a test with that question

Answer: 2041 meters

A bicycle wheel is a circular object.

The circumference of a circle is 2π(radius)

Here given:

Hence find the length for each revolution:

Then for 1000 revolutions:

Answer:

⇒ [tex]\frac{21}{2}[/tex]

or

⇒ [tex]10 \frac{1}{2}[/tex]

Step-by-step explanation:

3 3/4 = 15/4

2 4/5 = 14/5

⇒[tex](\frac{15}{4} *\frac{5}{5} )(\frac{14}{5} *\frac{4}{4} )[/tex]

⇒[tex]\frac{75}{20} *\frac{56}{20}[/tex]

⇒[tex]\frac{4200}{400}[/tex]

⇒ [tex]\frac{21}{2}[/tex]

or

⇒ [tex]10 \frac{1}{2}[/tex]

Answer:

Exact form: -3/2

Decimal Form: -1.5

Step-by-step explanation:

Hello there!

We need to find out the slope of the given two coordinates/points, that are:

Solution:

We'll need to use the formulae that is used to find out the slope,that is:

[tex] \pink{\star}\boxed{\rm \: Slope = \cfrac{y_2 -y_1}{x_2 - x_1}} \pink{\star}[/tex]

According to this question,here:

So substitute them accordingly:

[tex] \rm \: m = \cfrac{ - 6 -( 6)}{8 - 0} [/tex]

Simplify using PEMDAS rule.

[tex] \rm \: m = \cfrac{ - 12}{8} [/tex]

-12/8 could be canceled.

[tex] \rm \: m = \cfrac{ - 6}{4} [/tex]

-6/4 could also be canceled.

[tex] \boxed{ \rm \: m = \cfrac{ - 3}{2} \: or \: - \cfrac{3}{2} }[/tex]

Or it could be represented as decimal:

[tex] \boxed{ \rm \: m = - 1.5}[/tex]

Hence , the slope m will be -3/2 or -1.5

[tex] \rule{225pt}{2pt}[/tex]

Answer:

Place the squares on the rectangle.

Step-by-step explanation:

Hello!

The area of the 1cm by 1cm square is 1 square cm.

We can solve for the area by placing multiple of those squares in the larger rectangle.

If we place it, we get 15 placed squares, with a total area of 15 square cm. This relies on the meaning of area, as we are simply measuring the number of square cm taken up by the object.

We would place 3 rows of 5 squares, representing a height of 3 cm (side length of 3 squares), and a length of 5 cm (side length go 4 squares).

This also proves the area formula A = L * W, as we multiple the side lengths to find the number of square units.

Answer: 920.3 ft

Step-by-step explanation:

[tex]\tan 7^{\circ}=\frac{113}{x} \\ \\ x(\tan 7^{\circ})=113 \\ \\ x=\frac{113}{\tan 7^{\circ}} \approx \boxed{920.3 \text{ ft}}[/tex]

Answer:

A.

Step-by-step explanation:

the correct answer is A. y=|x-2|+3.

For more details see the attachment.

Answer:

135

Step-by-step explanation:

3b + B = 180

4b = 180. ÷4

b = 45

a = 135

Answer:

1298 mi

Step-by-step explanation:

In 5 hours, a jet would travel 5 times the distance that it would if it were to travel for one hour. This means that 590 is five times the distance of one hour. So, 590 divided by 5 is 118, so the jet travels 118 miles in one hour(this is basically the speed).

We can do the reverse to find how far it can travel in 11 hours given the jet travels 118 miles an hour. Using the same logic, the jet would travel 118 in each of the 11 hours, which is 118 x 11: 1298 mi.

Answer:

(2,0)

Step-by-step explanation:

The intersecting points of the two lines is the solution for the two equations.

(2,0) is the solution.

The other root is 1 and the value of the coefficient q is 12.

A quadratic equation is a second-order polynomial equation in a single variable x. ax²+bx+c=0. with a ≠ 0 .

Given:

x²-13x+q=0

when x= 12

So, 12²-13*12+q=0

144-156+q=0

-12+q=0

q=12

Now, x²-13x+12=0

x²-12x-x+12=0

x(x-12) - 1(x-12)=0

(x-1)(x-12)=0

x=1, 12

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Answer:

51 pounds, 48 pounds, 44 pounds and 40 pounds in that chronological order.

Answer:

X=60°

Step-by-step explanation:

Because the sum of angle of all side of a triangle is 180°

and

if that goes on

the equation become

x°+75°+45°=180°

x°+120°=180°

x°=180°-120°

x°=60° hence prove

Answer:

b

Step-by-step explanation:

because it is 4 dolls and x is the amount of dollars 1 doll is and 4x dolls are less then 102, the only answer that makes sense is b

The answer is B. I will choose to explain by process of elimination. It is not A because it is not less than or equal to, it is just less than. Therefore, we can also eliminate C. It is not D because it is four dolls that cost the same so it is 4x instead of 4+x. I hope I helped!

(f+g)(x)  

= f(x) + g(x)

= 4x^2 +5x -3 + 4x^3 -3x^2 +5

= 4x^3+x^2+5x+2

Answer:

it’s C, 5.2

hope i helped

ur wlcm :)

correct me if im wrong

Answer:

a negative linear association (C)

Re-Written Problem [Formatted]

Teams with varying numbers of players are playing a group card game. the time taken by each team to complete one game is given in the table. What is the relationship between the two variables?

Numbers of players on team are going to be 1, 2 , 3, 4, 5.

time taken to complete game (in minutes) 32, 26, 20, 14, 8

(Select the correct answer)

A. Positive linear association

B. Exponential relationship

C. Negative linear association

D. No relationship

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

Step-by-step explanation:

Lower x values (numbers of players on team) are correlated with higher y values (time taken to complete game)

[note: I know which values are x and y because of a cause-and-effect relationship. x causes y. number of players causes a change in minutes {it wouldn't make sense for the number of time it took to cause the number of players} ]

So, if we were to graph this relationship, we would see a downward-slope / negative slope of a line, because greater x-values are associated with lower y-values.

So, you would see a negative line, showing a negative linear association.

Using it's formula, it is found that the mean of the discrete random variable is given by:

B. 30.47.

The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.

Hence, considering the table, the mean of the discrete distribution is:

E(X) = 23 x 0.16 + 25 x 0.09 + 26 x 0.18 + 31 x 0.12 + 34 x 0.24 + 38 x 0.21 = 30.47.

Hence option B is correct.

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Since 7y is common to both factors, hence the GCF of the expression is 7y. The factored form will be 7y(3x + 2)

The greatest common factor is the value that will divide an expression without leaving a remainder.

Given the expression 21xy + 14y

Find the factors

21xy = 7 * 3 * x * y

14y = 7 * 2* y

Since 7y is common to both factors, hence the GCF of the expression is 7y. The factored form will be 7y(3x + 2)

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Answer:

El número equivalente de 25/50 es 1/2

Step-by-step explanation:

Answer:

81

Step-by-step explanation:

for example log2 8=3 is the same as 2^3=8, so if you switch around the variables from your question, your able to do 3^4, which is 81

Answer: $5.99 is the answer hope this helps!