A fair coin is tossed 29 times. what is the probability that at most 27 heads occur?

Answer:

21 seconds

Step-by-step explanation:

First let's find out how long it would take for them to have the same score.

160 + 5s = 100 + 8s

160 = 100 + 3s

60 = 3s

20 = s

Since it takes 20 seconds to get the same score and Raul get's more points every second, it would take 21 seconds for Raul to take the lead.

Interest is Rs.96  and Total amount payback is Rs.3096.

Principal (P) = Rs.3000

Rate of  interest (R) = 1.6%

Number of years (N) = 2 yrs

Simple interest = PNR/100

= (3000*1.6*2)/100

=(9600/100

=96Rs

Total Amount (A) = P+I

=3000+96

=3096Rs

The principal, or initial balance of your account, is where interest is calculated. This could be the initial sum of a loan or an investment. The simplest way to compute interest is as a percentage of the principal .Only relatively short-term loans frequently include one-time basic interest charges. Interest is frequently paid on a daily, monthly, quarterly, or annual basis for loans with longer terms. In that scenario, interest would be consistently earned.

Hence, the interest for the above principle is 96Rs and the total amount to be payback is 3096Rs.

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Answer:

A linear pair of angles is formed when two lines intersect. Two angles are said to be linear if they are adjacent angles formed by two intersecting lines. The measure of a straight angle is 180 degrees, so alinear pair of angles must add up to 180 degrees

So, x + y = 180

x = 1/3(y)

1/3(y) + y = 180

4/3(y) = 180

y = 135

Answer:

Point H, Point D, Point G, Point F

In tape diagram, The number of visits Juan must make to earn a free movie ticket

20 + 7.5V = 125

What is a tape diagram in math?

How a tape diagram appears?

represents the number of visits Juan must make to earn a free movie ticket

20 + 7.5V = 125

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When 2 men pushes car with mass 1800 kg and their combined horizontal forces are 1000 N, then frictional force acting on the car is 550 N.

The situation can be depicted in the attached picture. F1 and F2 are the horizontal forces of both men, while Fr is the frictional force. Remember that a frictional force is always the opposite of the direction of velocity.

Apply the 2nd Newton law of motion:

∑F = m.a

Where:

∑F = resultant of forces

m = mass of object

a = acceleration

In this situation, ∑F = F1 + F2 - Fr

The given parameters:

m = 1800 kg

a =  0.25 m/s²

F1 + F2 = 1000 N

Substitute these parameters into the  2nd Newton law:

F1 + F2 - Fr = m.a

1000 - Fr = 1800 . (0.25)

1000 - Fr  = 450

Fr = 1000 - 450 = 550 N

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The total price for a 24 ounce package, with a unit price of 13.5 cents per ounce, is $3.24.

Unit price is defined as the price or the cost per unit of the item. The importance of the unit price is that it allows the buyer to understand how the total price has been calculated. By multiplying the unit price by the total weight of the item will give the total price of that item.

total price = unit price x total weight

If the total weight of the package is 24 ounces and its unit price is 13.5 cents per ounce, multiplying will give the total price.

total price = unit price x total weight

total price = 13.5 cents per ounce(24 ounces)

total price = 324 cents

total price = $3.24

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The location point of S if RS is 7 will be 4

When two vectors are added using the vector addition postulate, it is known as the vector sum.

Suppose that R and S are points on the number line. If RS=7 and R lies at -3, then;

RS = S - R

Given the following

RS = 7

R = -3

Substitute

7 = S  - (-3)

7 = S + 3

S = 7 - 3

S = 4

Hence the location point of S if RS is 7 will be 4

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Answer: <LMO and <LMJ

Step-by-step explanation:

Supplementary angles add up to a straight line, a 180 degree angle is called a straight angle. Supplementary angles add up to 180 degrees.

Answer: <LMO and <LMJ since they add up to the line OMJ

A(0,-3), B(3,-2), C(1, -1) (B) is  the coordinates of ΔA'' B'' C'' after a reflection in the x -axis and a rotation of 180.

What does the term "coordinates" mean?

A 180 degree clockwise rotation will change the coordinates as follows (x,y) --> (-x,-y)

A(-3, 0), B(-2, 3), C(-1, 0) -->

A(3, 0), B(2, -3), C(1, -1)

Reflection across the line y=-x will change the coordinates as follows (x,y) --> (-y,-x)

A(3, 0), B(2, -3), C(1, -1) -->

A(0,-3), B(3,-2), C(1, -1) (B)

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An equiangular triangle is also an example of an acute triangle is a True statement.

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.

There are many types of triangles such that right-angle triangles, equilateral triangles, and much more.

An equiangular triangle is a triangle whose all angles are the same and since all angles are the same so by geometrical constraint all sides must be the same so it will also be an equilateral triangle.

In an equilateral triangle, all interior angles are 60°, and since an acute angle triangle is a triangle in which all angles must be less than 90°.

So an equiangular triangle will be an acute triangle.

Hence "An equiangular triangle is also an example of an acute triangle is a True statement".

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The co-ordinates of point B is (4, -5).

Let the endpoints of a line segment be [tex]x_{1}[/tex], [tex]y_{1}[/tex], and [tex]x_{2}[/tex], [tex]y_{2}[/tex]. The midpoint is equal to half of the sum of the two points' x-coordinates and half of the sum of the two points' y-coordinates.

Point at A ([tex]x_{1}[/tex], [tex]y_{1}[/tex]) = (8,1)

Point at B ([tex]x_{2}[/tex], [tex]y_{2}[/tex]) = (x,y)

The mid point AB is M (2,-2)

Using the mid point formula:
( [tex]\frac{x_{1} +x_{2} }{2}[/tex], [tex]\frac{y_{1} +y_{2} }{2}[/tex] ) = ( x,y )

[tex]\frac{8 +x_{2} }{2}[/tex] = 2

8 + [tex]x_{2}[/tex] = 4

[tex]x_{2}[/tex] = - 4

And

[tex]\frac{1 + y_{2} }{2}[/tex] = -2

1 + [tex]y_{2}[/tex] = -4
[tex]y_{2}[/tex] = - 5

So, the co-ordinate of point B is (4, -5).

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Answer: (8w) - 6 = 7

Step-by-step explanation:

         To write an equation, we will look at the phrase given.

Six less than ➜ - 6

the product of ➜ multiplication

is equal to 7 ➜ = 7

Six less than the product of 8 and a number is equal to 7.

(8w) - 6 = 7

Calculating the likelihood of experiments happening is one of the branches of mathematics named as probability. The probability that none of the 2 vials have hairline cracks is 0.0565.

The study of probabilities, which exists defined by the ratio of favorable occurrences to probable cases, exists comprehended as probability.

The probability that there won't be any hairline cracks = 13/53

If you choose two vials at random from the delivery

Probability (avoiding hairline cracks) = 13 - 1/53 - 1

Probability (avoiding hairline cracks) = 12/52

To find the chance that neither of the two vials has a hairline crack is

(13/53) × (12/52) = 0.2452 × 0.2307

= 0.0565

The probability that none of the 2 vials have hairline cracks is 0.0565

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A scatter plot is a series of points plotted on horizontal and vertical axes. If there is no correlation between variables, the points appear randomly scattered on the coordinate plane. The points will be clustered around a straight line if the correlation is high. A scatter chart is a data visualization tool that helps show trends.

The scatter plot shows not only the magnitude of the correlation but also the direction of the correlation.

As the vertical (or Y-axis) variable increases, the correlation is positive as the horizontal (or X-axis) variable increases.

The correlation is negative if the y-axis variable decreases and the x-axis variable increases, or vice versa.

The correlation is zero if none of the above criteria can be established.

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Answer: 100 times

Explanation: 6 times 100 would be 600 so 600 would be 100 times bigger than 6.

Vertically Stretching and Compressing

It multiplies a function by a positive constant that yields a position whose graph is vertically stretched or compressed relative to the original function's graph. If the constant is greater than 1, it will stretch vertically. If the constant is between 0 and 1, vertical compression is done and you will get vertical compression.

Vertical compression occurs when you multiply the function by a rational scaling factor. The base of the function graph remains the same even when the graph is compressed vertically. Only initial values ​​are affected.

Solution

Y=x

Multiplying the right side by ½

Y= (1/2) *X

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A triangle's exterior angle is always greater than its two remote interior angles. The exterior angle ∠1 is greater than ∠3, ∠5, ∠7, and ∠8.

According to the exterior angle inequality theorem, the measure of any exterior angle of a triangle is greater than the measure of either of the opposite interior angles. The adjacent interior angle and the exterior angle are supplementary. A triangle's exterior angles add up to 360º.

A triangle's exterior angle is always greater than its two remote interior angles.

Since, angle 1 is an exterior angle of Δ ABE,

m∠1 > m∠3 and m∠4

Since, angle 1 is an exterior angle of Δ ABD,

m∠1 > m∠5

Since, angle 1 is an exterior angle of Δ ABC,

m∠1 > m∠7 and m∠8

Therefore, ∠1 is greater than ∠3, ∠5, ∠7, and ∠8.

The complete question is:

Use the Exterior Angle Inequality Theorem to list all of the angles that satisfy the stated condition.

a. Measures less than m ∠ 1 .

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Answer:

4.24-(8*2)/4)=

4.24- 4= 0.24

The relationship between the ∠1 and ∠5 is that both are corresponding angles

Given,

The angles = ∠1 and ∠5

Here,

∠1 and ∠5 are lies on the same side of the two lines and on the same side of the transversal

So, ∠1 and ∠5 are corresponding angles

Hence, The relationship between the ∠1 and ∠5 is that both are corresponding angles

The complete question is:

Classify the relationship between the pair of angles as alternate interior, alternate exterior, corresponding, or consecutive interior angles.

∠1 and ∠5

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The discriminant of the quadratic equation is q · (q + 8) < 0. The solution set of this inequality is (0, - 8).

The nature of the roots of quadratic equations of the form a · x² + b · x + c = 0 can be inferred by the understading of its discriminant under the following condition:

b² - 4 · a · c < 0

Where a, b, c are the coefficients of the polynomial.

If we know that a = 2 · q, b = q and c = - 1, then the equation of the discriminant is:

q² - 4 · (2 · q) · (- 1) < 0

q² + 8 · q < 0

And by algebraic handling, we find the set of possible values of q:

q · (q + 8) < 0

The solution set of this inequality is (0, - 8).

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The number of meters away that dolphins cab hear sounds underwater will be 0.0024 m

From the information, Dolphins can hear sounds underwater that are 24 kilometers away.

The number of meters away that dolphins can hear sounds underwater will be:

= 24 / 1000

= 0.0024 m

Therefore, the correct option is D.

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The equation which represents the situation is 13 = 2x − 5 while Bernadette ran 9 miles so option (A) will be correct.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

Given that,

Andrew ran 5 miles less than two times the number of miles Bernadette ran.

If Bernadette ran x miles then,

13 = 2x - 5 is the correct representation.

Now,

2x -  5 = 13

2x = 18

x = 9 miles.

Hence " The number of miles that Bernadette ran is 9 miles while the equation of constraint is 13 = 2x − 5".

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The simplest version is one that utilizes fundamental algebraic and mathematical ideas, such as exponents.  The simplified equation of (7/2c) - (2/c²) is (7c - 4)/(2c²).

Let the expression be (7/2c) - (2/c²)

Taking LCM of the denominator

⇒ (7/2c²) - (4/2c²)

simplifying the above equation, we get

⇒ (7c - 4)/(2c²)

Simplifying a mathematical expression means putting it in the most basic form. Typically, the simplest version is one that utilizes fundamental algebraic and mathematical ideas, such as exponents. The phrase is intended to be made simpler by eliminating any repetition or duplication.

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The correct statements are:

Check all that applies:

A The integer −21 represents the sale of 21 books.

True

B After Monday's sales, 26 copies are available.

False

Saturday = 45 - 21

= 24 books available

Monday = 25 - 14

= 11 books available

Total books available = 24 + 11

= 35 copies available

C The integer 25 represents the new shipment.

True

D After Monday's sales, 35 copies are available.

True

E The integer 14 represents the sale of 14 books.

False

Therefore, option A, C and D are the correct statements.

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hi

let take two points :  

( 0; -1)  and  (4 ;  2)

here is  a = 0 ; f(a) = -1

            b = 4   ; f(b) = 2

Slope is  :   f(a) -f(b)   / a-b

let's apply :   -1 - 2  / 0-4   =    -3/-4   =  3/4

Slope is   3/4

if you want to check result, you can calculate the coordonate of an other point and see if it match.

here I read that      there is a point on the line for  -4 ; -4  

here  I can read that  Y axis  value for   X = 0  is  -1  

as a line is defined  by :   mx+p  

with m =  slope  and p  value for  x = 0

so  : p = - 1

with   m =  3/4  ;   x = -4  and   p = -1  

I can test my line equation   and see if it match the result  :

3/4 ( -4)  - 1 =   -12/4 - 1 =   -3 -1 = -4  

Result match what I see on the graph, so previous result is correct.  

:  Slope is  3/4

ps :  if line grows, the slope can only be  positive. if line decrease, slope is negative, if line is constant, then slope is  still and equal 0

By combining the like terms, the simplified form of the expression 0.5x-x is -0.5x

Given,

The algebraic expression = 0.5x-x

Combine the like terms

0.5x-x=(0.5-1)x

= -0.5x

Simplified form is -0.5x

Hence, By combining the like terms, the simplified form of the expression 0.5x-x is -0.5x

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