If you throw exactly two heads in three tosses of a coin you win $41. If not, you pay me $29. If you played this game 713 times how much would you expect to win or lose?

Answer:

c) 13%

Step-by-step explanation:

Given information,

→ The cost of a jacket increased from the price $75.00 to $84.75.

Now we have to,

→ find the % increase of cost of jacket.

Let's solve the problem,

→ ((84.75 - 75)/75) × 100

→ (9.75/75) × 100

→ 0.13 × 100

→ 13%

Hence, the answer is 13%.

Answer:

Depends on the gravitational force. On Earth, one pound equals 4.41N.

Step-by-step explanation:

The formula for Newton's Second Law of Motion is F=ma, which is Force = mass × acceleration.

The SI unit of mass is the kilogram (kg), so we'll have to convert one pound to kilograms. For practical purposes, one pound equals 0.45kg.

The gravitational force of the Earth is 9.8m/s^2. It is worth noting that each planetary body has its own gravitational force in respect to its mass.

Force = mass × acceleration = 0.45kg × 9.8m/s^2 = 4.41N

This number is only applicable on Earth, and may and will change on a planetary body with a mass different from Earth's.

The surface area of the largest sphere that could fit into the rectangular box of dimensions 12 in x 14 in x 18 in is 324π inches²

The surface area of sphere = 324π inches²

What is a Sphere?

A sphere is symmetrical, round in shape. It is a three dimensional solid, that has all its surface points at equal distances from the center. It has surface area and volume based on its radius. It does not have any faces, corners or edges.

The Surface Area of a Sphere = 4πr²

The Volume of a Sphere = ( 4/3 ) πr³

where r is the radius of the sphere

Given data ,

Let the surface area of the Sphere be = S

Let the dimensions of the rectangular box be L x W x H

12 inches x 14 inches x 18 inches

Now , for the surface area of the sphere to have the largest surface area , the radius should be maximum

From the rectangular box , we can see that the height of the rectangle is best suited as the diameter of the sphere

So , Height of the Box = Diameter of the Sphere

And , Radius of the sphere = Height of the Box / 2

                                             = 18 / 2

Radius of the sphere = 9 inches

Now ,

Surface Area of a Sphere = 4πr²

r = 9 inches

Substituting the values in the equation , we get

Surface Area of a Sphere S = 4 x π x ( 9 )²

                                              = 4 x π x 81

                                              = 324π inches²

Therefore , the value of S is 324π inches²

Hence , The surface area of sphere = 324π inches²

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Answer:

Your answer would be 2.1.

Step-by-step explanation:

The square root of 3 is:

1.73205080757

Then since 1/3 is equal to 0.33, I added 0.33 to the square root of 3 to get:

2.06205080757

Then, I rounded it:

2.1

The expression that shows the result of applying the distributive property is 21y - 7/11 (option D).  

The distributive property states that an expression that has this form a(b + c) can be solved as a x (b + c) which becomes ab + ac.  

Thus, to solve an expression using the distributive property, multiply the term in the brackets by the term outside the brackets. Multiplication is the process of determining the product of two or more numbers. The sign that represents multiplication is x.

7(3y - 1/11)

= 7 x (3y - 1/11)

= 21y - 7/11

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Sophie determine that the function describing the cost of dinner is linear if you order X eggrolls your dinner will cost 1.50x + $10 what is the per egg roll fee?

1.50x + $10

per egg roll fee is $1.50

The time required for for the balance to reach $4635 is 5 years.

The formula for simple interest can be expressed as;

A = P( 1 + rt )

Where A is accrued amount, P is principal, r is interest rate and t is time.

Given the data in the question;

First convert the interest rate from percent to decimal

Interest rate = 0.6%

Interest rate = 0.6/100

Interest rate = 0.006

Plug the given values into the above formula and solve for time t.

A = P( 1 + rt )

t = ( 4635/4500 - 1) / 0.006

t = ( 1.03 - 1) / 0.006

t = ( 0.03) / 0.006

t = 5 years.

Therefore, the required time is 5 years.

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Answer:  1 question Solve for x

x=

3

−y−2z−10

​

Solve for y

y=−3x−2z−10

Step-by-step explanation: Steps for Solving Linear Equation

3x+y+2z=−10

Subtract y from both sides.

3x+2z=−10−y

Subtract 2z from both sides.

3x=−10−y−2z

The equation is in standard form.

3x=−y−2z−10

Divide both sides by 3.

3

3x

​

=

3

−y−2z−10

​

Dividing by 3 undoes the multiplication by 3.

x=

3

−y−2z−10

​

Answer:

  -8, -5

Step-by-step explanation:

You want the second column of matrix B given matrices A and AB.

Matrix B can be found by left-multiplying AB by A^-1, as shown in the attachment.

The second column of matrix B is ...

  [tex]\left[\begin{array}{c}-8\\-5\end{array}\right][/tex]

If Samuel answers 9 questions wrong, his score will be 55 points, and if he answers x questions wrong his score is:

f(x) = 100 - x*5

We know that there are 100 points available, and each question gives 5 points, then the number of questions is given by the quotient:

100/5 = 20

There are 20 questions.

So, if you answer 9 wrong, then you answer:

20 - 9 = 11  correctly

Then your score is:

11*5 = 55

Your score will be 55 points.

And again, each answer gives 5 points, so if you answer x questions wrong your score will be the linear equation:

f(x) = (20 - x)*5

f(x) = 100 - x*5

Where x is an integer between 0 and 20.

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The order of the energy levels starting from the highest is:

3. Can hold a maximum of 32 electrons

1. Can hold a maximum of 18 electrons.

2. Can hold a maximum of eight electrons.

4. Can hold a maximum of two electrons.

When a shell gets bigger, it can retain more electrons, and has greater electron energies the further it is from the nucleus.

Two electrons can fit in the first shell, which is closest to the nucleus. Eight electrons can fit in the second shell. 18 electrons can fit in the third shell then 32 electrons can fit inside of the last shell.

The shell that can contain 32 electrons has the highest energy level

Following this relationship, it shows that the arrangement is done using the number of electrons to arrive at 3,  1,  2,and 4

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The total change in yards where the team started is 3x

The given parameters in the question are:

Yards per play = unknown

Number of plays = 3 consecutive plays

Represent the yards per play with x

So, we have

Yards per play = x

The total change in yards is the amount of yard per play multiplied by the number of plays

This is represented as

Total change = Yards per play * Number of plays

Substitute the known values in the above equation So, we have the following equation

Total change = x * 3

Evaluate

Total change = 3x

Hence, the total change is 36 yards

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The Perimeter of CED AC is 34 in. AB is 26 in. BD is 28 in. P is 57 in.

A parallelogram is the name given to a quadrilateral in geometry. In a parallelogram, the opposing sides are parallel and of equal length. The rhombus, rectangle, and square are just a few shapes that are parallelograms.

Having two sets of parallel sides makes a quadrilateral a parallelogram. A parallelogram has opposite sides that are the same length and angles that are the same size. Additionally, the internal angles on the same transverse side are supplementary. 360 degrees are equal to the total of all internal angles.

Two parallel pairs of sides make up a parallelogram, a quadrilateral. Four right angles form a parallelogram called a rectangle. Rhombus: An equal-length parallelogram with four sides.

The diagonals of a parallelogram bisect each other AC = 2 CE

Substitute AC= 34 into AC = 2 CE 34 = 2CE

Calculate 34 = 2 CE CE = 17

The diagonals of a parallelogram bisect each other BD = 2DE

Substitute BD= 28 into BD = 2DE  28 = 2DE

Calculate 28 = 2 DE DE = 14

Opposite sides of parallelogram are congruent AB = CD

Substitute AB = 26 into AB = CD CD = 26

Perimeter of a triangle PΔCDE = CE + CD + DE

Substitute  CE = 17 DE = 14 CD = 26 PΔCDE = CE + CD + DE

PΔCDE = 17+ 26 + 14

PΔCDE = 57

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Answer: Yes

Step-by-step explanation:

Because if you keep going it will reach 86, since it's added by 4, so 18, 22, 26, 30, 34, 38, 42, 46, 50, 54, 58, 62, 66, 70, 74, 78, 82, 86.

The distance of all the side of ΔABC and ΔA'B'C' are equal which makes them congruent triangles.

What is congruent triangles?

When all 3 corresponding sides and every one 3 corresponding angles area unit equal in size, 2 triangles area unit aforementioned to be congruent.

Main Body:

First let us find the co-ordinates of both the triangles.

A= (3,5)

B = (-2, 3)

C= (-4,-1)

A' =(10,-5)

B'= (5, -3)

C' =(3,1)

Distance between two points =  d=√((x₂ – x₁)² + (y₂ – y₁)²).

In ΔABC

Distance of side AB =  √((3 –(-2) )² + (5 –3 )²)

                                 = √5² +2²

                                 = √29

Distance of side BC = √((-2-(-4) )²+ (3 -(-1 )²)

                                 = √20

Distance of side CA = √((3-(-4) )² + (5-(-1) )²)

                                 = √7² + 6²

                                 = √85

Distance of side A'B' = √((10 -5)² + (-5-(-3))²

                                   = √(5² +2²)

                                   = √29

Distance of side B'C' = √ ((5-3)² + (-3 -1)² )

                                  = √ (2)² +4²

                                  = √20

Distance of side C'A' = √((10-3)² + ( -5-1)²)\

                                   = √(7)² + 6²

                                   = √85

This shows each side of ΔABC is equal to side of ΔA'B'C'.

hence the triangles are congruent.

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Using the z-distribution to test the hypothesis, it is found that:

a) The conclusion is that there is not enough evidence to conclude that the percentage has changed from 2016.

b) A Type II error would mean finding that there is not enough evidence that the percentage is significantly below 58.1% when in fact it is.

At the null hypothesis, it is tested if the proportion is the same as in 2016, that is:

[tex]H_0: p = 0.581[/tex]

At the alternative hypothesis, it is tested if the proportion is different, hence:

[tex]H_1: p \neq 0.581[/tex]

A Type II error is the non-rejection of a false null hypothesis, that is, finding that there is not enough evidence that the percentage is significantly below 58.1% when in fact it is.

The equation calculating the test statistic is:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

In which the variables are listed as follows:

For this problem, the value for these variables is given as follows:

[tex]\overline{p} = \frac{586}{1048} = 0.559, n = 1048, p = 0.581[/tex]

Hence the test statistic is:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

[tex]z = \frac{0.559 - 0.581}{\sqrt{\frac{0.581(0.419)}{1048}}}[/tex]

z = -1.44.

The critical value for a two-tailed test is with a significance level of 0.05 is:

|z| = 1.96.

The absolute value of the test statistic is of |z| = 1.44 < 1.96, meaning that there is not enough evidence to conclude that the percentage has changed from 2016.

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In order to estimate the mean per capita income at the 90% level of confidence with an error of at most $0.42. The sample size would be 85

Information form the question

the mean income is $28

the standard deviation is known to be $5.5

the mean per capita income at the 90% level of confidence

an error of at most $0.42

This is given as from margin of error:

This is the term refers to the minimum error that is to be allowed

Margin of error, E = Zc * √(SD²/n)

n = sample size

n = SD x (Zc/E)²

SD = standard deviation

Zc = would be the critical value at 90 percent level of confidence = 1.65

plugging in the values

n = 5.5 x (1.65/0.42)²

n = 0.25 x 15.4337

n = 84.8854

n = 85

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The lower and upper limit of the 95% confidence interval is 183.2 and 196.0 unit.

What is a confidence interval ?

When you run your experiment again or resample the population in the same way, you can expect your estimate to fall within a certain range of values a certain percentage of the time. This is known as the confidence interval.

Main Body:

Given in question :

x- bar = 189.6

standard deviation = 10

C.I. = 95% =0.95

N=12

so, degree of freedom (D.F) = N-1 = 11

confidence  level (α) = (1- C.I.)/2

                                  = 0.025

according to t- distribution table for d.f = 11 and α= 0.025  , my result is 2.201

Now dividing standard deviation by square root of samples, we get

= 10/√12= 2.887

Lower limit = Mean - 2.201*2.887

                  = 189.6- 6.354

                  = 183.246

Upper limit = Mean + 2.201*2.887

                  = 189.6 + 6.354

                  = 195.954

Hence the result is 183.2 and 196.

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The required change in height of the missile is 16100 feet.

Given that,
A missile was fired from a submarine from 200 feet below sea level. If the missile reached a height of 15900 feet before exploding, the change in the altitude of the missile is to be determined.

Change in defined as when the object is in one state but after a certain period of time, the state of the object changes is called change of the state.

here,
The height attained by the missile above sea level is 15900 feet.
The height attained by the missile below the seal level is 200 feet.
Change in height = 15900- (-200) = 15900 + 200 = 16100.

Thus, the required a change in height of the missile is 16100 feet.

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The answer to the inequality is  -55 < 49. That is -55 is less than 49.

What is inequality?

This refers to the relationship between two values that are not equal. It can be represented with the following symbols; < less than,> greater than, ≥ greater than or equal to,≤ less than or equal to, and  ≠ not equal to.

The given equation States that;

5(11 − ) < + 49

5*11- < +  49

-55  < +49

Therefore, -55 is less than 49.

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⇒ let us first write the given equation in the form

[tex]ax^{2} +bx+c=0[/tex]

⇒[tex]49x^{2} -64=0[/tex]

⇒ Note in this case bx=0

Let us factorize the equation...49 is a square number and 64 is also a square number ..This equation is a difference of two squares which can be written as:

[tex](7x-8)(7x+8)=0[/tex]

⇒The answer is (7x-8)(7x+8)=0

Answer:

[tex]\frac{11}{221}\approx{0.0498}\approx{4.98\%}[/tex]

Step-by-step explanation:

Two cards are drawn randomly from a well-shuffled deck of cards without replacement. Find the probability of getting both face cards in succession.

In a deck of 52 cards, there are three face cards (J, Q, and K) in each of four suits (clubs, diamonds, hearts, and spades). That means there are 12 face cards in total (J♣, Q♣, K♣, J♦, Q♦, K♦, J♥, Q♥, K♥, J♠, Q♠, K♠).

The probability of drawing a face card the first time, then, is 12 out of 52.

There is now one less face card in the deck, as well as one less card in the deck. Therefore, the probability of drawing a face card a second time is 11 out of 51.

The probability, then, of drawing two face cards in succession is:

[tex]\frac{12}{52}\times{\frac{11}{51}}=\frac{132}{2652}=\frac{11}{221}\approx{0.0498}\approx{4.98\%}[/tex]

1. An algebraic expression that represents each purchase is as follows:

2. Supposing that x has the same value in both expressions written above, the two algebraic expressions are not equivalent because the slope of expression A is greater than the slope of expression B.

3. The cost of a soccer ball in relation to the cost of a baseball cannot be represented by the algebraic expression 4 + 5x because it is given that the cost of a soccer ball is $15, and no number can substitute the x variable to equate the two.

An algebraic expression is a combination of terms (variables and constants) using the mathematical operations of addition, subtraction, multiplication, division, etc.

a) 15x + 4(6) = 15x + 24

b) 4(6) + 5x = 24 + 5x or 5x + 24

c) Cost of a soccer ball = $15

Cost of a baseball = $6

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Soccer balls = $15 each

Baseballs=$6 each

Sweat socks =$5 per pair

Answer:

45

Step-by-step explanation:

the pattern adds 3 if you look at it care fully

The value of the function  (f - g)(x) is x² + 3x + 5

A function is defined as a relation between a set of inputs having one output each.

In a simpler terms, a function relates input and output.

Therefore, let's solve the function (f - g)(x)

f(x) =  √16x⁴

g(x) = 3x² - 3x - 5

Therefore,

(f - g)(x) = f(x) - g(x)

(f - g)(x) = √16x⁴ - (3x² - 3x - 5)

(f - g)(x) = √16x⁴ - 3x² + 3x + 5

(f - g)(x) = 4x² - 3x² + 3x + 5

Therefore,

(f - g)(x) = x² + 3x + 5

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The distance between the two points (3, π/6) and (2, π/3) in polar coordinates is 1.614 units

The points are (3, π/6) and (2, π/3)

The polar coordinate system is the system that represent a point by a distance from a fixed reference point and angles from a reference direction

The distance between the two points

d = [tex]\sqrt{r_1^2+r_2^2-2r_1r_2cos(theta_1-theta_2)}[/tex]

(3, π/6) is the coordinates of first point

(2, π/3) is the coordinates of second point

Substitute the values in the equation

d = [tex]\sqrt{3^2+2^2-2(3)(2)cos(\pi/6 - \pi /3)}[/tex]

d = [tex]\sqrt{9+4-12(\frac{\sqrt{3} }{2} )}[/tex]

d = [tex]\sqrt{13-6\sqrt{3} }[/tex]

d = 1.614 units

Hence, the distance between the two points (3, π/6) and (2, π/3) in polar coordinates is 1.614 units

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The inequality will be represented by p ≥ 33 for at least 15 points.

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relation between variables and the numbers.

Mark must score at least 11 points to have an average of 10 points per game.

The average of a set of data is its sum, divided by the number of data points in the set. If p is the number of points Mark scores in his next game, and he wants his average at least 15, then the relation is ...

 (8+14+10+20+5++p)/6 ≥ 15

 57 +p ≥ 90 . . . . . . . . . multiply by 6 and simplify

 p ≥ 33

Mark must score at least 33 points in the next game to average at least 15 points per game.

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The kilograms of dough that Emmett prepare if he worked for 4 hours is 20 kilograms.

A proportional relationship simply means the relationship that has an equivalent ratio as well as a constant.

In this case, Emmett prepared 10 kilograms of dough after working 2 hours. The kilograms per hour will be:

= 10/2

= 5 kilograms per hour

Therefore, in 4 hours, the kilograms will be:

= Number of hours × 5 kilograms

= 4 × 5

= 20 kilograms

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Answer:

E and X

Step-by-step explanation:

look for the 6 then behind it

Answer:

X and E

Step-by-step explanation:

"axes" is the plural of axis. The x-axis is the flat line marked with numbers and arrows at the ends. Its labelled x on the right side.

The y-axis is the up-and-down line marked with numbers and arrows at the ends, labelled y at the top.

The origin is where the two axes cross.

Points J, E, X and P are all on the axes. But X and E are 5 units from the origin (where the lines cross) J and P are 9 units from the origin.

2, 6 and 10 were labelled on the axes, but each tick mark is an evenly spaced amount. So the 5 was unlabelled, but it is understood to be 5. See image.