You and your friend are playing a game. The two of you will continue to toss a coin until the sequence HH or TH shows up. If HH shows up first, you win. If TH shows up first, your friend wins. What is the probability of you winning?

Answer:

(a) Candy's initial sum as a terms of x is $6x

(b) x = $60

(c) $350

Step-by-step explanation:

The given parameters are;

The ratio in which Aliyah, Brenda and Candy share the sum of money = 3:5:6

The amount Candy later gives Aliyah = $100

The amount Candy later gives Brenda = $50

The new ratio of the sum of the shared money between Aliyah, Brenda and Candy = 2:3:3

(a) Whereby Aliyah has $3x at the start, we have;

Total sum of mony = Y

Amount of Aliyah's initial share = Y × 3/(3 + 5 + 6) = Y×3/14

Therefore, Y×3/14 = $3x

x = Y×3/14 ÷ 3 = Y/14

Amount of Candy's initial share = Y × 6/14

Therefore Candy's initial sum as a terms of x = $6x

(b) Given that Aliyah's and Candy's initial sum as a function of x are   $3x and $6x, therefore, in the ratio 3:5:6, Brenda's  initial sum as a function of x = $5x

Which gives;

Total amount of money = $14x

With

6x - 150, 3x + 100, and 5x + 50, the ratio =is 2:3:3

Therefore, we have;

14·x × 2/(2 + 3 + 3) = (6·x - 150)

14·x × 2/(8) = (6·x - 150)

14·x × 1/4 = (6·x - 150)

7·x/2 = (6·x - 150)

12·x - 300 = 7·x

12·x - 7·x = 300

5·x = 300

x = $60

(b) The final amount of money with Brenda = 5x + 50 = 5 × 60 + 50 = $350

The final amount of money with Brenda = $350.

Answer:

Hey there!

In this problem, 2 is known as the base.

Let me know if this helped :)

Answer:

The Base

Step-by-step explanation:

The base in a power is the number being raised to the exponent's power. It is the bigger number in the power.

2 is being raised to the third power. This means that 2 is the base of the power.

3 would be the exponent in the power.

Brainilest Appreciated.

Answer:

0.9375

Step-by-step explanation:

Given the following :

Number of coin tosses = 7

Probability that number of heads obtained will be between 2 and 7 inclusive?

x = 2,3,4,5,6,7

Probability (P) = number of required outcomes / total possible outcomes

For a coin toss = 1 Head (H), 1 tail (T)

P(H) = 1 / 2

P(X) = C(7,x) * (1/2)^7

P(X) = C(7, x) / 0.5^-7

P(X) = [C(7,2) + C(7, 3)+ C(7,4) +C(7,5) + C(7,6) +C(7,7)] / 128

P(X) = (21 + 35 + 35 + 21 + 7 + 1) / 128

P(X) = 120 / 128

P(X) = 0.9375

Answer:

(x+9)(x+9)

Step-by-step explanation:

To factor this expression, we first need to put into standard form, that is, [tex]ax^2 + bx + c[/tex].

So it becomes [tex]x^2 + 18x + 81[/tex]

Now we need to find two numbers that:

A. When multiplied get us c (81)

B. When added get us b (18)

9 and 9 match those requirements, so out product of two binomials for this becomes (x+9)(x+9).

Hope this helped!

Answer:

Isabelle spent $52.50 more on Erasers than rulers.

Step-by-step explanation:

Step 1

Find the quantity of each stationery bought in fraction

Let us represent the total fraction of what Isabelle bought as: x

1/3x = quantity of pencils bought

5/8 of the remainder = quantity of erasers bought

The remainder = x - 1/3x = 2/3x

5/8 of 2/3x = 5/8 × 2/3x = 5/12x

Hence, 5/12x = quantity of erasers bought

The rest is rulers

1 - (1/3 + 5/12)

1 - (4 + 5/12)

1 - 9/12

1 - 3/4

= 1/4x

Hence, 1/4 = quantity of rulers bought.

Step 2

We find the number of stationeries that Isabelle bought.

The cost of the stationery is

a Pencil: $1.20

an eraser: $1

a ruler: $0.50.

Total amount spent on stationery = 169.50

We have this equation

1.20 × 1/3x + 1 × 5/12x + 0.50 × 1/4x = 169.50

0.4x + 0.4166666667x + 0.125x =

169.50

0.9416666667x = 169.50

x = 169.50 /0.9416666667

x = 179.99999999

Approximately , the number of stationeries that Isabelle bought = x = 180

Step 3

Find the number and the amount spent on each stationery that Isabelle bought

a) i) Quantity of pencils bought = 1/3 x

x = 180

= 1/3 × 180

= 60 pencils

ii) Amount spent on pencils

If 1 pencil = $1.20

60 pencils =

60 × 1.20 = $72

b) i) Quantity of Erasers bought = 5/12x

x = 180

= 5/12 × 180

= 75 pencils

ii) Amount spent on Eraser

If 1 pencil = $1

75 pencils =

75 × 1 = $75

c) i) Quantity of rulers bought = 1/4 x

x = 180

= 1/4 × 180

= 45 pencils

ii) Amount spent on pencils

If 1 pencil = $0.50

45 pencils =

45 × 0.50 = $22.50

Step 4

We were asked to calculate how much more did she spend on erasers than rulers.

In step 3, the amount spent on Erasers = $75

the amount spent on ruler = $22.5

The difference in the amount spent = $75 - $22.5

= $52.5

Therefore, Isabelle spent $52.50 more on Erasers than rulers.

Answer:

The future value of the car after 5 years is $36,249.5

Step-by-step explanation:

Given the value at which a car depreciates, we are interested in finding the value of the car after a period of 5 years.

To find the value, we make use of an exponential equation;

The exponential equation to use is;

FV = PV(1 - r)^n

where FV is the future value of the car which is what we want to calculate

PV is the present value of the car which is $55,000

r is the depreciation percentage = 8% = 8/100 = 0.08

n is the number of years.

So now, we input these values into the formula;

FV = 55,000(1 -0.08)^5

FV = 55,000(0.92)^5

FV = $36,249.5

Answer:

8 10 12 14 16

Step-by-step explanation:

8+2=10, 10+2=12, 12+2=14, 14+2=16

Answer:

tokyo

Step-by-step explanation:

Answer:

2 hours and 5 minutes

Step-by-step explanation:

50/40=1.25 km/m

100*1.25=125 minutes

125 minutes= 2.08 hours= 2 hours and 5 minutes

Answer:

The answer to the nearest hundredth is 0.07 liters per minute

Step-by-step explanation:

In this question, we are told to express the given metric in liters per minute.

The key to answering this question, is to

have the given measurements in the metric in which we want to have the answer.

Hence, we do this by converting milliliters to liters and seconds to minute.

Let’s start with milliliters;

Mathematically;

1000 milliliters = 1 liters

10 milliliters = x liters

x * 1000 = 10 * 1

x = 10/1000

x = 1/100

x = 0.01 liters

For the seconds;

We need to convert the seconds to minutes;

Mathematically;

60 seconds = 1 minute

8.5 seconds = y minutes

60 * y = 8.5 * 1

y = 8.5/60

y = 0.14167 minutes

Now, our rate of flow is liters per minute, that means we have to divide the volume by the time;

Hence, we have ;

0.01/0.14167 = 0.070588235294

Which to the nearest hundredth is 0.07

Answer:

3x-4y=65

3x=65+4y

x=(65+4y)/3, when y=4

x=(65+4*4)/3

x=(65+16)/3

x=81/3

x=27

Answer:

x = 27

Step-by-step explanation:

3x - 4y = 65

Let y= 4

3x - 4(4) = 65

3x -16 = 65

Add 16 to each side

3x-16+16 = 65+16

3x = 81

Divide by 3

3x/3 =81/3

x=27

Answer:

1/4

Step-by-step explanation:

What is the ratio of the length of to DE the length of BC

The perimeter of a sector is given by:

P = [tex]\frac{\theta}{360}**2\pi r[/tex]

Where [tex]\theta[/tex] is the angle it subtends from the center and r is the radius of the circle.

For Sector ADE, the radius (r) = r/2 and the angle  [tex]\theta[/tex]  = β. Therefore:

Perimeter of DE = [tex]\frac{\beta}{360}**2\pi (\frac{r}{2} )=\frac{\beta}{360}(\pi r)[/tex]

For Sector ABC, the radius (r) = r and the angle  [tex]\theta[/tex]  = 2β. Therefore:

Perimeter of BC = [tex]\frac{2\beta}{360}**2\pi r=\frac{2\beta}{360}(2\pi r)=\frac{\beta}{360}*(4\pi r)[/tex]

The ratio of the length of to DE the length of BC =

Answer:

1/4

Step-by-step explanation:

Answer:

This is an experiment because a treatment was applied to a group.

Step-by-step explanation:

There are two groups, The first group used the computer program while the second group did not therefore this is an experiment. An experiment involves changing an independent variable to see how it affects a dependent variable. The dependent variable in this case  determining the effect of a new computer program on learning while the independent variables was testing with the computer program and not testing with the program.

Answer:

(1) B

(2) D

Step-by-step explanation:

(1)

Let the quadratic function be:

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

For the point, (0,-1),

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

[tex]-1=(a\times0)+(b\times0}+c\\-1=c\\c=-1[/tex]

Then the equation is:

[tex]y = ax^{2} + bx -1[/tex]

For the point (-1, -8) ,

[tex]y = ax^{2} + bx -1[/tex]

[tex]-8=(a\times (-1)^{2})+(b\times -1)-1\\-8=a-b-1\\a-b=-7...(i)[/tex]

For the point (1, 2) ,

[tex]y = ax^{2} + bx -1[/tex]

[tex]2=(a\times (1)^{2})+(b\times 1)-1\\2=a+b-1\\a+b=3...(ii)[/tex]

Add the two equations and solve for a as follows:

[tex]a-b=-7\\a+b=3\\\_\_\_\_\_\_\_\_\_\_\_\_\_\_\\2a = -4\\a = -2[/tex]

Substitute a = -2 in (i) and solve for b as follows:

[tex]a-b=-7\\-2-b=-7\\b=5[/tex]

Thus, the quadratic function is:

[tex]f(x)=-2x^{2}+5x-1[/tex]

The correct option is (b).

(2)

The ordered pairs are:

(5, 7), (7, 11), (9, 14), (11, 18)

Represent them in an XY table as follows:

X : 5 | 7 | 9 | 11

Y : 7 | 11 | 14 | 18

Compute the difference between the Y values as follows:

Diff = 11 - 7 = 4

Diff = 14 - 11 = 3

Diff = 18 - 14 = 4

Now compute the difference between the Diff values:

d = 3 - 4 = -1

d = 4 - 3 = 1

Since the differences between the differences of the y-values is not consistent, the ordered pairs do not represent a quadratic equation.

The correct option is D.

Answer:

1,080 meters squared.

Step-by-step explanation:

Let's say the breadth of the rectangle is x. That means the length of it is 6/5x.

The perimeter is 132 meters. The formula for the perimeter is 2 times the breadth plus two times the length.

2(x) + 2(6/5x) = 132

2x + 12/5x = 132

10/5x + 12/5x = 132

22/5x = 132

22x = 660

x = 30.

That means that the breadth of the rectangle is 30 meters, and the length is (6/5) * 30 = 6 * 6 = 36 meters.

The formula for the area of the rectangle is the breadth times the length, so the area is 36 * 30 = 1,080 meters squared.

Hope this helps!

Answer:  D) right 9 units

Step-by-step explanation:

The Vertex form of a quadratic equation is: y = a(x - h)² + k     where

        → h is the horizontal shift (+ is right, - is left)

        → k is the vertical shift (+ is up, - is down)

y = f(x - 9)

            ↓

           h=9

Since h is positive, the graph moves 9 units to the RIGHT

Answer:

The graph of y = f(x) will shift right 9 units.

Step-by-step explanation:

If the -9 is inside the parenthesis, the graph g(x) shifts 9 points to the right.

Answer:

5/14, 7/10, 11/15, 5/6, 19/21.

Step-by-step explanation:

Covert the fractions to decimal form:

5/14 = 0.357

7/10 = 0.7

5/6 = 0.833

11/15 = 0.733

19/21 = 0.905.

So in ascending order this is:

5/14, 7/10, 11/15, 5/6, 19/21.

Answer:

Step-by-step explanation:

to arrange in ascending order, we need to convert them into like fractions

to convert them into like fractions, we need to find the LCM of the denominators

the LCM of the denominators ( 14, 10, 6, 15 and 21 ) is 210

5/14 × 15/15 = 75/210

7/10 × 21/21 = 147/210

5/6 × 35/35 = 175/210

11/15 × 14/14 =154/210

19/21 × 10/10 = 190/210

75/210 < 147/210 < 154/210 < 175/201 < 190/210

∴ 5/14 < 7/10 < 11/15 < 5/6 < 19/21

Hope this helps

plz mark as brainliest!!!!!!!

Answer:

12

563 - (563x0.25) = 422.25 -> 422

16

422 -(422x0.25) = 316.5 -> 317

20

317 - (317x0.25) = 237.75 -> 238

24

238 - (238x0.25) = 178.5 -> 179

28 (continue the step by step process)

134.25 -> 134

32

100.5 -> 101

36

75.75 -> 76

40

57

44

42.75 -> 43

48

32.25 -> 32

52

24

56

18

Step-by-step explanation:

the time interval has to keep skipping by four hours because the medicine is filtered in that amount of time.

The multiplying by 0.25 part must be done first in order to show how much the kidney has filtered.

after this, you need to subtract that from how many milligrams of medicine are left in your system

note that if you do not subtract, you will only be showing how much the kidney has filtered. the question asks for how much is left in the SYSTEM overall, so subtracting is quite necessary to completely answer the question.

I hope this helped.

Answer:

O P=20($1.50)

They will make $3,000 if they sell 100 boxes of chocolates

Step-by-step explanation:

It is multiplication because it is $1.50 per each chocolate bar, and since there is 20 per box, we need to find the profit for the entire box

using that info, we find that each box of chocolates is 30 dollars

multiplied by 100 boxes is $3000.

There are four pairs (m,n) that work: (5,10), (6,6), (8,4), and (12,3).

Answer:

The answer is most likely 1/3

The correct option D. 3.  The slope of AD, where A is (-2, 4), B is (-6, 2), and C is (3, -1), is 1/3 using the slope formula.

Given points :

[tex]A(-2, 4)\\B(-6, 2)\\C(3, -1)[/tex]

To find the slope of AD,  to determine the slope of the line passing through points A and D.

Calculate the slope of the line passing through points A and D using the formula:

slope [tex]= (y_2 - y_1) / (x_2 - x_1).[/tex]

First, let's find the slope of BC using the coordinates of points B and C:

Slope of BC [tex]= (y_2- y_1 / (x_2- x_1)\\[/tex]

Plugging the coordinates of points B and C gives:

[tex]= (-1 - 2) / (3 - (-6))[/tex]

On adding gives:

[tex]= (-3) / (9)[/tex]

On dividing both numerator and denominator by 3

[tex]= -1/3[/tex]

Since A is the altitude to BC, it is perpendicular to BC.

The slope of a line perpendicular to another line is the negative reciprocal of the slope of that line.

Therefore, the slope of AD will be the negative reciprocal of -1/3.

Negative reciprocal of -1/3 = -1 / (-1/3) = 3

Hence, the slope of AD is 3. The option is D. 3

Learn more about slopes here:

https://brainly.com/question/29147363

#SPJ4

Answer:

Step-by-step explanation:

Yes you can just write them with denominator 1,

So 3 = 3/1 and -6 = -6/1.

Answer:

Yes.

Step-by-step explanation:

ALL real numbers can be written as fractions, and since integers fall under the category of real numbers, it is official that they can be written as fractions.

I am joyous to assist you at any time.

Answer:

Step-by-step explanation:

step one:

Given the sample space, which is the value of individual number of colored balls in the bin

Red balls=5

Yellow balls=3 and

Green balls= 4

And the sample size is the sum of all the colored balls in the bin

The sample size S= {5+3+4}= 12

step two:

The probability of choosing a red ball in an event can be expressed as, the total number of the red balls over the total number of balls in the bin

P(r)= 5/12

Hence the probability of selecting a red ball in one event 5/12

Answer:

Step-by-step explanation:

To find the value of h use the formula for finding the slope of a line

That's

[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]

Where ( x1, y1) and (x2 ,y2) are the points

From the question

slope = - 3

The points are [4,-9] and [-3,h]

Substitute these values into the equation

We have

[tex] - 3 = \frac{h + 9}{ - 3 - 4} [/tex]

[tex] - 3 = \frac{h + 9}{ - 7} [/tex]

Cross multiply

That's

- 3(-7) = h + 9

21 = h + 9

h = 21 - 9

We have the final answer as

Hope this helps you

Answer:

-3.5

Step-by-step explanation:

The problem you have stated is (y-z)/z where y=-2 and z = 4/5. To solve, substitute the values of y and z into the problem. Then, you have (-2-4/5)/4/5. (-2-4/5) simplifies to -14/5 so then you have (-14/5)/4/5. To divide, multiply -14/5 by 5/4 {multiplying by the reciprocal}. That equals -70/20 which is equal to -3.5

Answer:

[tex]\large\boxed{-3.5}[/tex]

Step-by-step explanation:

(y - z) ÷ z          y = -2 and z = 4/5

Substitute in the given values for y and z into the equation

(y - z) ÷ z  

(-2 - 4/5) ÷ 4/5

Subtract inside the parenthesis (-2 - 4/5)

-2.8 ÷ 4/5

Convert 4/5 into a decimal (in this case that can be done by multiplying both the numerator and denominator by 20)

4/5 = (4 * 20) / (5 * 20) = 80 / 100

80 / 100

Divide numerator and denominator by 10

8/10 = 0.8

Substitute into previous equation

-2.8 ÷ 4/5 = -2.8 ÷ 0.8

Divide

[tex]\large\boxed{-3.5}[/tex]

Hope this helps :)

Answer:

Option (B)

Step-by-step explanation:

From the picture attached,

NL and KM are the two lines intersecting at a point P.

Therefore, ∠KPN ≅ LPM [Vertical angles]

In ΔPLM,

m∠LPM + m∠PML + m∠PLM = 180° [Property of a triangle]

m∠LPM + 70° + 60° = 180°

m∠LPM + 130° = 180°

m∠LPM = 180° - 130°

m∠LPM = 50°

Therefore, m∠KPN = 50° [vertical angles]

Option (B) will be the correct option.

The value of KPN will be 50°.

It should be noted that the sum of the angles that are in a triangle is 180°.

Therefore, looking at the angles, the measure of KPN will go thus:

KPN + 70° + 60° = 180°

KPN + 130° = 180°

KPN = 180° - 130°

KPN = 50°

Therefore, KPN will be 50°.

Read related link on:

https://brainly.com/question/17226102

Answer:

[tex]\boxed{m=7.5}[/tex]

Step-by-step explanation:

Hey there!

Cross multiply the given info

60 = 8m

Divide both sides by 8

m = 7.5

Hope this helps :)

Answer:

--1-- (of set 23456)

2   4

5 3

 6

--2-- (of set 23456)

2   3

5 4

 6

--3-- (of set 23456)

2   5

6 3

 4

--4-- (of set 23456)

2   3

6 5

 4

--5-- (of set 23456)

3   5

4 2

 6

--6-- (of set 23456)

3   2

4 5

 6

--7-- (of set 23456)

3   6

5 2

 4

--8-- (of set 23456)

3   2

5 6

 4

--9-- (of set 23456)

3   5

6 4

 2

--10-- (of set 23456)

3   4

6 5

 2

--11-- (of set 23456)

4   5

3 2

 6

--12-- (of set 23456)

4   2

3 5

 6

--13-- (of set 23456)

4   6

5 3

 2

--14-- (of set 23456)

4   3

5 6

 2

--15-- (of set 23456)

5   4

2 3

 6

--16-- (of set 23456)

5   3

2 4

 6

--17-- (of set 23456)

5   6

3 2

 4

--18-- (of set 23456)

5   2

3 6

 4

--19-- (of set 23456)

5   6

4 3

 2

--20-- (of set 23456)

5   3

4 6

 2

--21-- (of set 23456)

6   5

2 3

 4

--22-- (of set 23456)

6   3

2 5

 4

--23-- (of set 23456)

6   5

3 4

 2

--24-- (of set 23456)

6   4

3 5

 2

--1-- (of set 34567)

3   5

6 4

 7

--2-- (of set 34567)

3   4

6 5

 7

--3-- (of set 34567)

3   6

7 4

 5

--4-- (of set 34567)

3   4

7 6

 5

--5-- (of set 34567)

4   6

5 3

 7

--6-- (of set 34567)

4   3

5 6

 7

--7-- (of set 34567)

4   7

6 3

 5

--8-- (of set 34567)

4   3

6 7

 5

--9-- (of set 34567)

4   6

7 5

 3

--10-- (of set 34567)

4   5

7 6

 3

--11-- (of set 34567)

5   6

4 3

 7

--12-- (of set 34567)

5   3

4 6

 7

--13-- (of set 34567)

5   7

6 4

 3

--14-- (of set 34567)

5   4

6 7

 3

--15-- (of set 34567)

6   5

3 4

 7

--16-- (of set 34567)

6   4

3 5

 7

--17-- (of set 34567)

6   7

4 3

 5

--18-- (of set 34567)

6   3

4 7

 5

--19-- (of set 34567)

6   7

5 4

 3

--20-- (of set 34567)

6   4

5 7

 3

--21-- (of set 34567)

7   6

3 4

 5

--22-- (of set 34567)

7   4

3 6

 5

--23-- (of set 34567)

7   6

4 5

 3

--24-- (of set 34567)

7   5

4 6

 3

Step-by-step explanation:

This javascript code is extremely brute-force, but it does the job:

function checkIfInSet(i, set) {

   return i.toString().split('').sort().join('') === set;

}

function checkIfMagic(s) {

   return (parseInt(s[0]) + parseInt(s[1]) == parseInt(s[3]) + parseInt(s[4]))

}

function printMagic(s) {

   console.log(`${s[0]}   ${s[4]}`);

   console.log(` ${s[1]} ${s[3]}`);

   console.log(`  ${s[2]}\n`);

}

function checkSet(set) {

   let counter = 1;

   for(let i=1; i<99999; i++) {

       if (checkIfInSet(i, set) && checkIfMagic(i.toString())) {

           console.log(`--${counter++}-- (of set ${set})`);

           printMagic(i.toString());

       }

   }

}

checkSet('23456');

checkSet('34567');

Answer: [tex]x=\dfrac{25}{21}[/tex]

Step-by-step explanation:

Area of parallelogram = Base x height

If two parallelograms are similar, then their corresponding sides are proportional.

That means, [tex]\dfrac{\text{Area of first parallleogram}}{\text{Area of second parallleogram}}=\dfrac{\text{height of first parallelogram}}{\text{height of second parallelogram}}[/tex]

[tex]\Rightarrow \dfrac{3x+5}{9x}=\dfrac{16}{20}\Rightarrow \dfrac{3x+5}{9x}=\dfrac{4}{5}\\\\\Rightarrow 5(3x+5)=4(9x)\\\\\Rightarrow\ 15x+25 = 36x\\\\\Rightarrow\ 36x-15x=25\\\\\Rightarrow\ 21x = 25\\\\\Rightarrow\ x=\dfrac{25}{21}[/tex]

Hence, [tex]x=\dfrac{25}{21}[/tex]