an unbiased coin is tossed until a head appears and then tossed until a tail appears. if the tosses are independent, what is the probability that a total of exactly n tosses will be required?

Answers

Answer 1

The Probability that a total of exactly n tosses will be required is (1/2)^(n-1)

To find the probability that a total of exactly n tosses will be required, we need to consider the different sequences of tosses that would result in exactly n tosses.

For a total of exactly n tosses, there are two possibilities: the head appears on the (n-1)th toss and the tail appears on the nth toss, or the head appears on the nth toss.

Let's calculate the probabilities for each case:

The head appears on the (n-1)th toss and the tail appears on the nth toss:

The probability of getting a head on any toss is 1/2, and the probability of getting a tail on any toss is 1/2.

Therefore, the probability of this case is (1/2)^(n-1) * (1/2) = 1/2^n.

The head appears on the nth toss:

The probability of getting a head on the nth toss is (1/2)^n.

To find the overall probability for a total of exactly n tosses, we sum the probabilities of the two cases:

P(n) = (1/2)^(n-1) * (1/2) + (1/2)^n

= (1/2)^n + (1/2)^n

= 2 * (1/2)^n

= (1/2)^(n-1)

Therefore, the probability that a total of exactly n tosses will be required is (1/2)^(n-1)

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Answer 2

The probability that a total of exactly n tosses will be required is (1/2)^n, and the total probability of the event is 1/2.

Let's consider the case where a total of exactly n tosses are required. This means that the first n-1 tosses must all result in tails, and the nth toss must be a head, followed by a sequence of one or more tails. The probability of this sequence of tosses occurring is:

P(n) = (1/2)^(n-1) * (1/2) * (1/2)^(n-1) = (1/2)^n

So the probability of requiring exactly n tosses is (1/2)^n.

Now we need to sum this probability over all possible values of n to get the total probability of the event. We can express this as an infinite series:

P = Σ (1/2)^n, n=2 to infinity

To evaluate this series, we can use the formula for the sum of an infinite geometric series:

S = a/(1-r)

where a is the first term and r is the common ratio. In this case, a = (1/2)^2 = 1/4 and r = 1/2, so we have:

P = Σ (1/2)^n, n=2 to infinity = 1/4/(1-1/2) = 1/2

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Related Questions

A random sample of n = 4 scores is obtained from a normal population with m = 30 and s = 8. what is the probability that the sample mean will be smaller than m = 22?

Answers

the probability that the sample mean will be smaller than m = 22 is 0.02275.

For the given question,

A z-score measures exactly how many standard deviations a data point is above or below the mean. It allows us to calculate the probability of a score occurring within our normal distribution and enables us to compare two scores that are from different normal distributions.

Here sample size, n = 4

mean, μ = 30

standard deviation, σ = 8

The probability that the sample mean will be smaller than m = 22 is

z = [tex]\frac{m-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]

⇒ z =[tex]\frac{22-30}{\frac{8}{\sqrt{4} } }[/tex]

⇒ z = [tex]\frac{22-30}{\frac{8}{2} }[/tex]

⇒ z = [tex]-\frac{8}{4}[/tex]

⇒ z = -2

Refer the Z table for p value,

Thus for P(z < -2) is 0.02275.

Hence we can conclude that the probability that the sample mean will be smaller than m = 22 is 0.02275.

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Tas
The three points marked on the graph are
the vertices (corners) of a parallelogram.
10
9
y
8
7
6
5
4
3
2
1
A
1 2
C
2
B
3 4 5 6 7 8 9
10
What are the coordinates of the fourth
vertex?

Answers

Answer: (8,10)

Step-by-step explanation:

To go from A to C, we go right 2 units and up 6 units.

So, if we let the fourth vertex be D, then to go from B to D, we must also go right 2 units and up 6 units from B.

Therefore, the answer is (8, 10).

how to simplify cos(6x) + 1

Answers

cos(6x) +1
= 32cos^6(x)−48cos^4(x)+18cos^2(x)

You want to retire on the equivalent of $50,000 per year in today's money. inflation is expected to be 3%. you will retire in 30 years. you will earn 10% annually on your investments from not till retirement and you will earn 8% during retirement (which is expected to last 20 years). how much do you need to save per month in order to fund this retirement?

Answers

$662.18 needs to be saved per month.

$90,000 now at 3% inflation will become 90000*1.03^30 after 30 years.

i.e.  $218,454 is required in retirement years (for 20 years)

Calculating the PV of these payments at 7% is calculated as below.

FV = 0

1/y = 7%

n=20; PMT = 218454; calculate PV = $2,314,305

Now we want to get $2,314,305 at the start of retirement by saving per year. Enter the following in the financial calculator to get the per month amount.

FV = 2314305; PV = 0; n= 12*30; 1/y = 12%/12; calculate PMT  = $662.18

So $662.18 needs to be saved per month.

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10 points to you if you help me
and brainlyist

Answers

Answer:

Step-by-step explanation:

For the frequency distribution, count the numbers that satisfy each category.

79 to 83: 4 (81, 82, 83, 81)

84 to 88: 3 (87, 88, 86)

89 to 93: 7 (92, 93, 93, 93, 90, 90, 91)

94 to 98: 1 (97)

For the historagram, raise the bars at the bottom of the histogram to the numbers above (4, 3, 7, 1; in this order)

pls help me on this one :((

Answers

Answer:

The answer is B) b

Step-by-step explanation:

According to the Trapezoid area formula, the area of the trapezoid is [(2d+a+b) × c] ÷ 2, however the area also equals (d+b) × c.

So d+(a+b)/2=d+b

(a+b)/2=b

a+b=2b

a=b

hope this helps <3

SOMEONE PLEASE HELP!!! Find the area of the sector. Round your answer to the nearest tenth.

Answers

Answer:

398.2 cm^2

Step-by-step explanation:

[tex]\frac{270}{360}[/tex] * [tex]169\pi[/tex] ≈398.2 cm^2

A river flows at 2m/s . Juan's boat can travel twice as fast down the river as it can go up the river. how fast the boat go in still water? ​

Answers

Using proportions, it is found that the boat can go 6 m/s in still water.

What is a proportion?

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, we have that:

Down the river, the speed is v + 2.Up the river, the speed is v - 2.

He goes twice as fast down the river, hence:

v + 2 = 2(v - 2).

v + 2 = 2v - 4

2v - v = 2 + 4

v = 6.

The boat can go 6 m/s in still water.

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How many minutes are equal to 2 hours 20 minutes? how many minutes are equal to 2 hours 20 minutes? 100 120 220 240 none of these

Answers

Answer:

None of the answers

Step-by-step explanation:

There are 60 minutes in one hour so to find the number of minutes in two hrs we multiply 2 by 60: 2*60 = 120 minutes

We then add the extra 20 minutes: 120+20 = 140 minutes

None of the answers include 140 minutes.

HELP! what is this? what’s the answer?!

Answers

D. not continuous at X=0

if you trace the function you'll find a jump in the graph. To be continuous the line can't have any breaks in it. In this example, it's discontinuous when X=0

A local salesman receives a base salary of $975 monthly. He also receives a commission of 6% on all sales over $1200. How much would he have to sell in a month if he needed to have a monthly income of $2500

Answers

He has to sell in a month $26616.67.

Given that a local salesman receives a base salary of $975 monthly and he also receives a commission of 6% on all sales over $1200.

A numerical assertion wherein two articulations are delivered equivalent to each other is known as an algebraic condition.

Let the Sales amount be s.

We have:

Sales over 1,200 is written as

s-1200

6% is also 0.06  as a decimal,

so according to question, we have

0.06(s - 1200) + 975=2500

Now, we will apply the distributive property a(b+c)=ab+ac, we get

0.06s-0.06×1200+975=2500

Further, we want to simplify the left-hand side, we get

0.06s-72+975=2500

0.06s+903=2500

Furthermore, we will subtract 903 from both sides, we get

0.06s+903-903=2500-903

0.06s=1597

Now, we will divide both sides with 0.06, we get

0.06s/0.06=1597/0.06

s=26616.67

Hence, he have to sell in a month if he needed to have a monthly income of $2500 is $26616.67.

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15 athletes are assigned to one of three teams. Each team will have five athletes. The teams are different, so it matters who gets assigned to which team. How many ways are there to assign the athletes to the teams

Answers

Answer:

There is only one way to assign the athletes to the team by giving 5 athletes to each team

Which of the statements below is true for the following set of numbers?42,10,36,51,70,28

Answers

Answer:

statement 1(one)

Step-by-step explanation:

1) (x-y)(y-2)(x+2) / 2x^2+4yz+6 =
2) 4(x+y)(x-y)(y-x) / t+d+m =
3) ( √25+√9 / 2 ) + √21675 =
4) (9x^2+3x+27)(3+6y)(4+6y) / 1+2a+38+4c+2000z =
5) (x^2+6x+5) / (x+2)(x+6) =
^^^Simplify
6) (xy/m) + (xm/y) - (m/x) = 63 x=
Isolate

Could anyone help me with these?

Answers

See below for the solution to each expression

How to solve the expressions?

Expression 1

The expression is given as:

(x-y)(y-z)(x+z)/(2x^2+4yz+6)

Expand the numerator

(x^2 - y^2 -xz + yz)(x + z)/(2x^2+4yz+6)

Further, expand the numerator

(x^3 - xy^2 - x^2z + xyz + x^2z - y^2z - xz^2 + yz^2)/(2x^2+4yz+6)

Evaluate the like terms

(x^3 - xy^2  + xyz - y^2z - xz^2 + yz^2)/(2x^2+4yz+6)

Hence, the equivalent expression of (x-y)(y-z)(x+z)/(2x^2+4yz+6) is (x^3 - xy^2  + xyz - y^2z - xz^2 + yz^2)/(2x^2+4yz+6)

Expression 2

The expression is given as:

4(x+y)(x-y)(y-x)

Apply the difference of two squares

4(x^2 - y^2)(y - x)

Expand the expressions in the brackets

4(x^2y - x^3 - y^3 + xy^2)

Open the bracket

4x^2y - 4x^3 - 4y^3 + 4xy^2

Hence, the equivalent expression of 4(x+y)(x-y)(y-x) is 4x^2y - 4x^3 - 4y^3 + 4xy^2

Expression 3

The expression is given as:

(√25+√9/2) + √21675

Take the square roots of 25, 9 and 21675

(5 +3/2) + 5√867

Evaluate the sum

13/2 + 5√867

Hence, the equivalent expression of (√25+√9/2) + √21675 is 13/2 + 5√867

Expression 4

The expression is given as:

(9x^2+3x+27)(3+6y)(4+6y) /1+2a+38+4c+2000z

Factor out 3 and 2 from the numerator

3(3x^2 +x + 9) * 3(1 + 2y) * 2(2 + 3y)/1+2a+38+4c+2000z

This gives

18(3x^2 +x + 9)(1 + 2y)(2 + 3y)/1+2a+38+4c+2000z

The expression cannot be further simplified.

Hence, the equivalent expression of (9x^2+3x+27)(3+6y)(4+6y) /1+2a+38+4c+2000z is 18(3x^2 +x + 9)(1 + 2y)(2 + 3y)/1+2a+38+4c+2000z

Expression 5

The expression is given as:

(x^2+6x+5)/(x+2)(x+6)

Factorize the numerator

(x + 1)(x + 5)/(x + 2)(x + 6)

Hence, the equivalent expression of (x^2+6x+5)/(x+2)(x+6) is (x + 1)(x + 5)/(x + 2)(x + 6)

Expression 6

6) (xy/m) + (xm/y) - (m/x) = 63

Factor out x

x(y/m + m/y) - m/x = 63

Evaluate the sum

x(y^2 + m^2)/y - m/x = 63

Multiply through by xy

x^2(y^2 + m^2) - my = 63xy

Add my to both sides

x^2(y^2 + m^2)  = 63xy + my

The above implies that the variable x cannot be isolated from the equation

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Find the polar coordinates in radians from the given rectangular coordinates (-11, -3).

Answers

the polar coordinates are:

(√130, 285.3°)

How to find the polar coordinates?

For rectangular coordinates (x, y), the polar coordinates are:

[tex]R = \sqrt{x^2 + y^2}[/tex]

For the angle θ we need to notice that if both coordinates are negative, like in this case, we would be on the fourth quadrant, then:

θ = arctan(y/x) + 270°

In this case, we have:

x = -11

y = -3

Then:

[tex]R = \sqrt{(-11)^2 + (-3)^2} = \sqrt{130} \\\\\theta = arctan(-3/-11) + 270\° = 285.3\°[/tex]

Then the polar coordinates are:

(√130, 285.3°)

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what is the coefficient of (3y^2 + 9)5

Answers

The coefficient of (3y² + 9)5 is 15.

A polynomial is of the form a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² + ... + aₙ₋₁x + aₙ.

Here, x is the variable, aₙ is the constant term, and a₀, a₁, a₂, ..., and aₙ₋₁, are the coefficients.

a₀ is the leading coefficient.

In the question, we are asked to identify the coefficient of (3y² + 9)5.

First, we expand the given expression:

(3y² + 9)5

= 15y² + 45.

Comparing this to the standard form of a polynomial, a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² + ... + aₙ₋₁x + aₙ, we can say that y is the variable, 15 is the coefficient, and 45 is the constant term.

Thus, the coefficient of (3y² + 9)5 is 15.

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Jake started biking to the coffee shop traveling 8 mph, after some time the bike got a flat so Jake walked the rest of the way, traveling 4 mph. If the total trip to the coffee shop took 9 hours and it was 60 miles away, how long did Jake travel at each speed

Answers

Jake travel to the coffee shop by bike with speed of [tex]8mph[/tex] is  [tex]56mile[/tex] and when bike got a flat so Jake walked [tex]4mile[/tex]

How to find the speed by biking and walking ?

let [tex]b[/tex] = time spent biking

then   [tex]8-b[/tex] =time spent walking

Write distance equation

[tex]dist=speed *time[/tex]

So bike distance [tex]+[/tex] walk distance [tex]=60mile[/tex]

[tex]8b+4(8-b)=60\\8b+32-4b=60\\4b=60-32\\b=28/4\\\\b=7hrs[/tex]

Then [tex]8-7=1 hrs[/tex] spent walking.

For cross check the answer find that actual distance for each

[tex]8(7)=56mi\\4(1)=4mi\\-------\\total distance=60mile[/tex]

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An integrated transcriptomic and epigenomic analysis identifies CD44 gene as a potential biomarker for weight loss within an energy-restricted program

Answers

An integrated transcriptomic and epigenomic analysis identifies the CD44 gene as a potential biomarker for weight loss within an energy-restricted program: TRUE

What is an integrated transcriptomic and epigenomic analysis?Because of the interindividual variability in response to weight-loss treatments, new predictive biomarkers are needed to improve the efficacy of weight-loss programs. The goal of this work is to find new genes that distinguish individual responses to a weight-loss dietary regimen by combining mRNA expression and DNA methylation arrays.Different expression and DNA methylation profiles were found in LR versus HR. The integrative analysis of the array data found four genes that were differentially methylated and expressed between groups: CD44, ITPR1, MTSS1, and FBXW5. In LR, CD44 expression was higher and DNA methylation levels were lower than in HR.

Therefore, the statement "an integrated transcriptomic and epigenomic analysis identifies the CD44 gene as a potential biomarker for weight loss within an energy-restricted program" is TRUE.

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Complete question:

An integrated transcriptomic and epigenomic analysis identifies the CD44 gene as a potential biomarker for weight loss within an energy-restricted program. TRUE or FALSE

Which expression is equivalent to startfraction 3 x superscript negative 6 baseline y superscript negative 3 baseline over 15 x squared y superscript 10 baseline endfraction? assume x not-equals 0, y not-equals 0.

Answers

The correct expression is 1 Over 5 x Superscript minus 8 Baseline y Superscript minus 13 Baseline endFraction.

Given expression [tex](3x)^-6*y^-3/ 15x^2*y^10[/tex]

Lets simplify the equation:

[tex]= > (3x)^-6*y^-3/ 15x^2*y^10\\=1/5 x^-8*y^-13[/tex]

Expression:

An expression is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division. The structure of an expression is: Expression is (Number/Variable, Math Operator, Number/Variable)

Hence the correct expression is 1 Over 5 x Superscript minus 8 Baseline y Superscript minus 13 Baseline EndFraction.

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Select the correct answer from the drop-down menu.
Compare the steps for constructing a perpendicular line to line ABthrough point C using a reflective device and using paper.
.C
A
When using paper to construct the perpendicular line, the paper is folded so that
line ABwill lie exactly on top of each other.
When using a reflective device to construct a line perpendicular to line AB, set one end of the device to coincide with
then swing the other end of the device so the reflection of line ABcoincides with
All rights reserved.
Reset
Next
and the two sides of
and

Answers

The  C is perpendicular to AB

When using paper, the paper perpendicular te construct to is folded so that AB is divided equally and the two sides of. line AB will lie exactly on top of each other.

When using a reflective device to construct a live perpendicular to line AB, set One end of the device to coincide with point C, and then swing the other end of the device so that the reflection of line AB coincides with the midpoint of AB

The question is incomplete hence the complete question is shown here

Select the correct answer from the drop-down menu. Compare the steps for constructing a perpendicular line to line  through point  using a reflective device and using paper. , When using paper to construct the perpendicular line, the paper is folded so that and the two sides of line  will lie exactly on top of each other. When using a reflective dewice to construct a line perpendicular to line  , set one end of the device to coincide with , and then swing the other end of the device so the reflection of line  coincides with.

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Answer:

I toke the test, I think the first one is A and  B coincide

Step-by-step explanation:

Can you help me,pls

Answers

Answer:

  x^4 +2 +x^-4

Step-by-step explanation:

The square of a binomial is a form worthy of memorization.

  (a +b)² = a² +2ab +b²

Application

Here, you have a binomial with a=x² and b=1/x². Using these values in the pattern, we have ...

  [tex]\left(x^2+\dfrac{1}{x^2}\right)^2=(x^2)^2+2(x^2)\dfrac{1}{x^2}+\left(\dfrac{1}{x^2}\right)^2\\\\=\boxed{x^4+2+\dfrac{1}{x^4}}[/tex]

Tom has x bags of apples. he buys 8 times more and sells 12. write the amount he has left as an algebraic expression:

Answers

Answer:

Step-by-step explanation:

x times 8 +12

8x+x=9x-12

Answer = 9x-12

WILL. GIVE BRAINLIEST IF RIGHT!!​

Answers

Answer:

The class and exam medians are almost the same.

Step-by-step explanation:

The median of a box-and-whisker plot is the line inside the box.

• As we can see, the medians of  class and median are very similar, both around 85. This is why the first option is correct.

•The second option is incorrect because the exam median is not much higher than the class median; the difference is very small.

• The third option is incorrect because exam does not have the lowest median. In fact, exam median is slightly higher than class median.

• The fourth option is incorrect because outliers do not affect the median.

I need help solving this problem

Answers

Answer:

Please see the picture below.

Step-by-step explanation:

One cupcake weighs 3 1/2 ounces how many cupcakes are there in 28 ounce package

Answers

Using division, the 8 cupcakes are there in 28 ounce package if one cupcake weighs 3 1/2.

According to the question,

One cupcake weighs 3 1/2 ounces. In order to find the number of cupcakes are there in 28 ounce package.

1 cupcake = 7/2 ounces

x cupcakes = 28 ounces

28 = 7/2 * x [cross multiplication]

x = (28*2)/7     [Using division]

x = 8

Hence, using division, the 8 cupcakes are there in 28 ounce package if one cupcake weighs 3 1/2.

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what is 23,578 times 39,344

Answers

927,652,832.

Hope this helps

Answer:927652832

Step-by-step explanation:

using long multiplication step by step multiply.


The expression 40x²-65x + 50 represents the sum of the interior angles of a regular pentagon in degrees. If the
interior angles of the pentagon are equal, which expression represents the measure of two angles?

Answers

Answer:

[tex]16x^2-26x+20[/tex]

Step-by-step explanation:

Since it represents the sum of interior angles, the angle is essentially: [tex]angle + angle + angle + angle + angle[/tex], and there are 5 angles since a pentagon has 5 interior angles. To find what one interior angle is, we simply divide the polynomial by 5, to do this we can just divide each coefficient by 5 (distributing the division): [tex]\frac{40x^2-65x+50}{5} = \frac{40x^2}{5} - \frac{65x}{5} + \frac{50}{5}[/tex] this simplifies to: [tex]8x^2-13x+10[/tex]. This represents what one of the interior angles is. Since we want an expression measuring two of the angles, we simply multiply this polynomial by 2, to do this we just multiply each coefficient by 2 (distributing the 2): [tex]2(8x^2-13x+10) = 16x^2-26x+20[/tex] which is the solution

1)Convert the following binary numbwers into decimal number(only a,b,c,f,i)

Answers

#1

(11)_2(1×2⁰+1×2¹)_10(1(1)+1(2))_10(1+2)_10(3)_10

#b

(110)_2(0+1×2¹+1×2²)_10(2+4)_10(6)_10

#c

(111)_2(1×2⁰+1×2¹+1×2²)_10(1+2+4)_10(7)_10

#f

(10011)_2(1×2⁰+1×2¹+0+0+1×2⁴)_10(1+2+16)_10(19)_10

#i

(10110101)_2(1×2⁰+0+1×2²+0+1×2⁴+1×2⁵+0+1×2⁷)_10(1+4+16+32+128)_10(181)_10

Answer:

a) 3₁₀

b) 6₁₀

c) 7₁₀

f) 19₁₀

i) 181₁₀

Step-by-step explanation:

Binary to Decimal Conversion (Positional Notation Method)

Multiply each digit by the base (2) raised to the power dependent upon the position of that digit in the binary number. Sum all the values obtained for each digit.Express the number as a decimal number by placing subscript 10 after it.

For a binary number with 'n' digits:

The right-most digit is multiplied by 2⁰The left-most digit is multiplied by [tex]\sf 2^{n-1}[/tex]

For example, to convert the binary number 111001₂ into a decimal:

[tex]\begin{array}{ c c c c c c}1 & 1 & 1 & 0 & 0 & 1\\\downarrow & \downarrow & \downarrow & \downarrow & \downarrow & \downarrow \\2^5 & 2^4 & 2^3 & 2^2 & 2^1 & 2^0\\\end{array}[/tex]

Multiply each digit by the base (2) raised to the power as indicated above and sum them:

[tex]=(1 \times 2^5)+(1 \times 2^4)+(1 \times 2^3)+(0 \times 2^2)+(0 \times 2^1)+(1 \times 2^0)[/tex]

[tex]= 32+16+8+0+0+1[/tex]

[tex]= 57[/tex]

Finally, express as a decimal number ⇒ 111001₂ = 57₁₀

Question (a)

[tex]\begin{aligned}\implies 11_2 & = (1 \times 2^1)+(1 \times 2^0)\\& = 2+1\\& = 3\end{aligned}[/tex]

Therefore, 11₂ = 3₁₀

Question (b)

[tex]\begin{aligned}\implies 110_2 & = (1 \times 2^2)+(1 \times 2^1)+(0 \times 2^0)\\& = 4+2+0\\& = 6\end{aligned}[/tex]

Therefore, 110₂ = 6₁₀

Question (c)

[tex]\begin{aligned}\implies 111_2 & = (1 \times 2^2) +(1 \times 2^1)+(1 \times 2^0)\\& =4+2+1\\& = 7\end{aligned}[/tex]

Therefore, 111₂ = 7₁₀

Question (f)

[tex]\begin{aligned}\implies 10011_2 & =(1 \times 2^4)+(0 \times 2^3)+ (0 \times 2^2) +(1 \times 2^1)+(1 \times 2^0)\\& =16+0+0+2+1\\& = 19\end{aligned}[/tex]

Therefore, 10011₂ = 19₁₀

Question (i)

[tex]\phantom{)))}10110101_2 \\\\=(1 \times 2^7)+(0 \times 2^6)+(1 \times 2^5)+(1 \times 2^4)+(0 \times 2^3)+ (1 \times 2^2) +(0 \times 2^1)+(1 \times 2^0)\\\\=128+0+32+16+0+4+0+1\\\\= 181[/tex]

Therefore, 10110101₂ = 181₁₀

HELP!!!!!!QUICK!!!!!!!

Answers

Help with what? I don’t see anything.

Find the measure of the arc or central angle indicated. Assume that lines which appear to be diameters are actual diameters.

Answers

Answer:

? = 120°

Step-by-step explanation:

the central angle is the same as the arc that subtends it , that is

? = 120°

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