5. Which of the following are vertical angles?
2 3
A. 1 and 6
8
7
6
B. 4 and 7
C. 1 and 5
D. 3 and 8

The most probable number of heads becomes more and more likely as the number of tosses increases.

Let's denote the probability of observing tails as q (which is 1/2 for a fair coin). Then the probability of observing exactly n heads in 4n tosses is given by the binomial distribution:

p(n) = (4n choose n) * (1/2)^(4n)

where (4n choose n) is the number of ways to choose n heads out of 4n tosses. We can express this in terms of the most probable number of heads, which is 2n:

p(n) = (4n choose n) * (1/2)^(4n) * (2^(2n))/(2^(2n))

= (4n choose 2n) * (1/4)^n * 2^(2n)

where we used the identity (4n choose n) = (4n choose 2n) * (1/4)^n * 2^(2n). This identity follows from the fact that we can choose 2n heads out of 4n tosses by first choosing n heads out of the first 2n tosses, and then choosing the remaining n heads out of the last 2n tosses.

Now we can express the ratio p(n)/p(2n) as:

p(n)/p(2n) = [(4n choose 2n) * (1/4)^n * 2^(2n)] / [(4n choose 4n) * (1/4)^(2n) * 2^(4n)]

= [(4n)! / (2n)!^2 / 2^(2n)] / [(4n)! / (4n)! / 2^(4n)]

= [(2n)! / (n!)^2] / 2^(2n)

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

where (2n-1)!! is the double factorial of 2n-1. Note that (2n-1)!! is the product of all odd integers from 1 to 2n-1, which is always less than or equal to the product of all integers from 1 to n, which is n!. Therefore,

p(n)/p(2n) = (2n-1)!! / (n!)^2 / 2^n <= n! / (n!)^2 / 2^n = 1/(n * 2^n)

As n increases, the denominator n * 2^n grows much faster than the numerator (2n-1)!!, so the ratio p(n)/p(2n) approaches zero. This means that the probability of observing n heads relative to the most probable number of heads becomes vanishingly small as n increases, which is consistent with the intuition that the most probable number of heads becomes more and more likely as the number of tosses increases.

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The four step to graphing the linear inequalities are: Always begin by separating the variable y from the inequality's left side, Replace the inequality symbol with the equality symbol, In XY plane, graph the boundary line from step 2, The final step is to shade a portion or one side of the border line.

In the given question we have to explain the 4 steps in graphing linear inequalities.

Step 1: Always begin by separating the variable y from the inequality's left side.

Step 2: Replace the inequality symbol with the equality symbol.

Step 3: In XY plane, graph the boundary line from step 2.

Step 4: The final step is to shade a portion or one side of the border line.

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Answer:

The missing fraction is 6/12

(you can further simplify this but the question requires that you don't do that)

Step-by-step explanation:

To add fractions easily, their denominators should have the same value, so the denominator should be 12,

Then, to get 16 in the numerator, we need to find a number that on adding to 10, gives 16, or,

10 + x = 16

x = 16 - 10

x = 6

So, the numerator should be 6

so we get the fraction, 6/12

We can also solve it in an alternate way,

\(10/12 + x = 16/12\\x = 16/12 - 10/12\\x = (16-10)/12\\x = 6/12\)

Answer:

the second one!

Step-by-step explanation:

Answer: 6

Step-by-step explanation:

When solving this problem, it is important to remember the rules for when we add a negative and subtract a negative. When we add a negative (+ -), we are essentially going to keep the sign attached to the number. In this case, we would still subtract. When subtracting a negative (- -), the signs cancel out, so will add the number instead. With that in mind, we can rewrite the equation and solve it as follows:

13 - 12 + 5

1 + 5

6

Hope this helps!

Answer:

ok

Step-by-step explanation:

Answer:

alright lol

Step-by-step explanation:

16.  Valid

Reason: congruency can be represented by the symbol ≅ hence  the statement still reads <1 and <2 are congruent.

17. Invalid

Reason: A rectangle also has four right angles, It is only a square when all the sides are equal.

18. Valid

Reason: congruency can be represented by the symbol ≅ hence the statement still reads <JKM and <MKL are congruent.

19. Valid

Reason: The conclusion of the battery dying is in support of the premise giving which is leaving the light on when the car is off.

20.Valid

Reason: The conclusion, Dante obtained a part time job is in line with the premise that obtaining a pert time job, is a way to afford a car payment

21. Valid

Reason: The premise which has that selling 75% of the prom tickets will make the prom hold at country club is fulfilled, hence the prom will be held at the country club

An argument is vailed when the premises or conditions of the argument are all true. when some part of the argument is not true then it will lead to invalid conclusion.

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The equation that he used to find n, the number of gallons of water he should remove is 3.52 / (22 - n) = 24 / 100. Option C is correct.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Amount of ammonia in the solution 16%  x 22 gallons  =  3.52 gallons

The proportion of ammonia remains the same as the water evaporates, but the total composition of the solution is decreased by the amount of water that evaporates.

Quantity of ammonia = 3.52 gallons

Quantity of water after evaporation = 22 - n

Composition of ammonia after evaporation of water, 24% = 24/100

Now the percentage of ammonia after evaporates
Quantity of ammonia / Remaining water = 24%
3.52 / (22 - n) = 24 / 100

Thus, the equation that he used to find n, the number of gallons of water he should remove is 3.52 / (22 - n) = 24 / 100.

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A linear programming problem with two decision variables can be solved by a graphical solution method. In this method, the constraints and the objective function of the linear programming problem are graphed on a two-dimensional coordinate plane, and the optimal solution is found at the intersection of the feasible region (the area defined by the constraints) and the level curve of the objective function.

The graphical solution method is a simple and intuitive way to solve linear programming problems with few decision variables, but it becomes impractical as the number of decision variables and constraints increase. In such cases, more complex algorithms, such as the simplex method or interior point methods, are used to find the optimal solution.

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Solve for y

Subtract 4x both sides

Divide by 3 into both sides

Answer:

Answer:

V = 1/32 yd^3

Step-by-step explanation:

To find the volume

V= l*w*h  where l is length, w is width, and h is height

V = 1/4 * 1/4 * 1/2

V = 1/32 yd^3

The equation or system of equations that can be used to determine the number of cats and dogs Bea has in her pet shop is d = 2c - 5 d + 3 = c + 3. We can solve the system of equations using substitution and plug it back into either equation to find the value of d, which is 8 cats and 10 dogs.

The equation or system of equations that can be used to find the number of cats and dogs Bea has in her pet shop is:

d = 2c - 5

d + 3 = c + 3

No, Bea's Pet Shop could not initially have 15 cats and 20 dogs. This is because the equation or system of equations states that the number of dogs is five less than twice the number of cats, which would mean that 15 cats would result in 25 dogs, which is not equal to 20.

To determine algebraically the number of cats and the number of dogs Bea initially had in her pet shop, we can use the equation or system of equations that we previously created.

d = 2c - 5

d + 3 = c + 3

We can solve the system of equations using substitution:

d = 2c - 5

d + 3 = c + 3

d + 3 = c + 3

d = c + 3

2c - 5 = c + 3

2c = c + 8

c = 8

Once we determine the value of c, we can plug it back into either equation to find the value of d:

d = 2(8) - 5

d = 15 - 5

d = 10

Therefore, Bea initially had 8 cats and 10 dogs in her pet shop.

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The complete question is: At Bea's Pet Shop, the number of dogs, d, is initially five less than twice the number of cats, c. If she decides to add three more of each, the ratio of cats to dogs will be – Write an equation or system of equations that can be used to find the number of cats and dogs Bea has in her pet shop. Could Bea's Pet Shop initially have 15 cats and 20 dogs? Explain your reasoning. Determine algebraically the number of cats and the number of dogs Bea initially had in her pet shop.​

Answer:

2079

Step-by-step explanation:

is the correct answer 2079

Using the law of cosines, it is found that the length of side AB is of AB = 13.

The law of cosines states that we can find the angle C of a triangle as follows:

\(c^2 = a^2 + b^2 - 2ab\cos{C}\)

in which:

For this problem, the parameters are:

C = 120, a = 8, b = 7.

Hence:

\(c^2 = a^2 + b^2 - 2ab\cos{C}\)

\(c^2 = 8^2 + 7^2 - 2(8)(7)\cos{120^\circ}\)

\(c^2 = 169\)

\(c = \sqrt{169}\)

c = 13.

Hence AB = 13.

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Answer: 27 students

Step-by-step explanation:

First take 45 + 90 = 135 students total

20% = 0.2

Then take 135 times 0.2 = 27 students

Answer:

X=7

y= -8

Step-by-step explanation:

4x+y+(x-y)=20+15

4x+y+x-y=35

plus y and minus y cancels out.

4x+X= 35

5x=35

X= 7

Substitute X=7 in any equation

x-y=15

7-y=15

y=-8

It will take Tom and Nelson 1.875 hours, or 1 hour and 52.5 minutes, to complete the report working together.

To solve this problem, we can use the concept of work done. Let's assume that a report is a unit of work, and Tom and Nelson each do a fraction of the work in one hour.

Tom can do the entire report in 3 hours, which means he can do 1/3 of the report in one hour. Similarly, Nelson can do 1/5 of the report in one hour.

If they work together, the fraction of the report they can do in one hour is the sum of their individual fractions:

1/3 + 1/5 = 8/15

So, together they can do 8/15 of the report in one hour. To find out how long it will take them to do the entire report working together, we can use the formula:

time = work ÷ rate

where work is 1 (the whole report) and rate is 8/15 (the fraction of the report they can do in one hour).

time = 1 ÷ (8/15)

time = 1.875 hours

Therefore, it will take Tom and Nelson 1.875 hours, or 1 hour and 52.5 minutes, to complete the report working together.

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The choice of the type and dimensions of the measuring geometry in TPA (Thermal Performance Analysis) is influenced by several factors such as measurement accuracy, sensitivity to heat transfer variations, sample size, spatial resolution, and practical considerations.

Here are the steps to explain why the dimensions of the measuring geometry are often 25mm and 50mm probe in TPA:

Step 1: Measurement Accuracy and Resolution

The dimensions of the measuring geometry should be chosen to ensure sufficient accuracy and resolution in the measurements. Larger probe dimensions may provide more accurate results due to better averaging of temperature variations, while smaller probe dimensions can provide higher resolution for detecting localized temperature variations. Therefore, a balance needs to be struck between accuracy and resolution.

Step 2: Sensitivity to Heat Transfer Variations

The choice of probe dimensions in TPA is also influenced by the sensitivity of the system to heat transfer variations. Larger probe dimensions can capture a wider area and average out local variations, providing a more representative measurement of the overall heat transfer performance. On the other hand, smaller probe dimensions can detect localized variations and provide more detailed information about specific regions.

Step 3: Sample Size and Spatial Resolution

The dimensions of the measuring geometry should be suitable for the size and scale of the system being analyzed. If the sample size is large or if there are significant spatial variations in the heat transfer, larger probe dimensions may be more appropriate to cover a representative area. However, if the sample size is small or if there are fine-grained spatial variations, smaller probe dimensions can provide higher spatial resolution.

Step 4: Practical Considerations

Practical considerations also play a role in determining the dimensions of the measuring geometry. For instance, the size of the available equipment or probes may limit the choice of dimensions. Standardized probe sizes, such as 25mm and 50mm, are commonly used in TPA, as they are readily available and widely accepted in the industry.

The choice of the type and dimensions of the measuring geometry in TPA, such as 25mm and 50mm probes, is determined by factors such as measurement accuracy, sensitivity to heat transfer variations, sample size, spatial resolution, and practical considerations. The specific dimensions should strike a balance between accuracy and resolution, considering the characteristics of the system being analyzed and the available equipment.

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Answer:

the modulus of a complex number z = a + bi is:

Izl= √(a²+b²)

The fact that n is complex does not mean that n doesn't has a real part, so we must write our numbers as:

m = 2 + 6i

n = a + bi

Im + nl = 3√10

√(a² + b²+ 2²+ 6²)= 3√10

√(a^2 + b^2 + 40) = 3√10

squaring both side

a²+b²+40 = 3^2*10 = 9*10 =90

a²+b²= 90 - 40

a²+b²=50

So,

|n|=√(a^2 + b^2) = √50

The modulus of n must be equal to the square root of 50.

now

values a and b such

a^2 + b^2 = 50.

for example, a = 5 and b = 5

5²+5²=25+25= 50

Then a possible value for n is:

n = 5+5i

Answer:

9) 5.8

10) 27.9

11) 37.1

12) 16.8

Step-by-step explanation:

For this you need to know SOH (sine = opposite/adj) CAH (cos = adj/hypo) and TOA (tan = opp/adj).

For 9, you have one side 15 and one angle 21 degrees.  We can see that relative to the 21 degrees the side lengths, x and 15, are the Opposite and the Adjacent. So we label them "x=O" and "15=A". This means we have Tangent(21) = Opposite "x" /Adjacent "15"

We then evaluate tan21=x/15.

1) To get rid of the fraction multiply 15 on both sides to get 15*tan21=x.

2) Use a calculator to get the answer 5.8 (5.7579..)

For 10, it is the same process but with cosine. You have one side 19 and one angle 47 degrees. We can see that relative to the 21 degrees the side lengths, x and 19, are the Hypotenuse and the Adjacent. So we label them "x=H" and "19=A". This means we have Cosine(47) = Adjacent "19" / Hypotenuse "x"

We then evaluate cos47=19/x.

1) To get rid of the fraction multiply x on both sides to get x*cos47=19.

2) Divide by cos47 on both sides to isolate x. This will be x=47/cos21

3) Use a calculator to get the answer 27.9 (27.8593...)

For 11, refer to how I did question 9 on how it's tan68 = 15/x.

Then refer to question 10 on what to do if x is the denominator (isolate the x).

You should end up with x=15/tan68 which is 37.1 (37.1263...)

Finally for 12, it's the same but for sine (sin=opp/hyp).

You should get that the opp=15 and hypo=x.

That means sin63=15/x which is then x=15/sin63

Answer is 16.8 (16.834...)

Answer:

0.13 in²

Step-by-step explanation:

Given that,

→ Diameter = 0.4 in

→ Radius (r) = 0.4/2 = 0.2

Formula we use,

→ πr²

The area of the circle will be,

→ πr²

→ (22/7) × 0.2 × 0.2

→ 0.12571428571

→ [ 0.13 in² ]

Hence, area of circle is 0.13 in².

Answer:

Answer: 0.3 square inches

Step-by-step explanation:

The formula to find the area of a circle is

\(area \: of \: circle \: = \pi {r}^{2}\)

Let pi be (3.14), the radios as given in the question is (0.4 ÷ 2 = 0.2). Therefore;

\(\pi {r}^{2} = \\ (3.14) \: {(0.2)}^{2} \\ 3.14 \times 0.04 = \\ 0.1256\: or \: 0.13\: {inches}^{2}\)

It takes a train going 50 mph approximately 11/2 miles to stop safely.

The distance a train takes to come to a stop can be determined by several factors, including the speed of the train, the weight of the train, the condition of the brakes and the track, and the reaction time of the engineer.

In general, a train going 50 mph will take about 1 1/2 miles or 8,000 feet to stop safely. This is because a train moving at 50 mph is traveling at about 75 feet per second, and it takes a significant distance to slow down a heavy object moving at such a high speed. It's important to note that this is an estimation, and the actual stopping distance may vary depending on the specific conditions.

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The properties of the mean and median to determine which

are the correct mean and median for the following histogram. The answer is Mean is 3.5; median is 3.1.

Mean

\(\mu=& \varepsilon x \cdot P(x)\)

= 0(0.04)+1(0.08)+2(0.125)+3(0.24) +4(0.15)+5(0.14)+6(0.12)+7(0.05)

= 0+0.08+0.25+0.72+0.6+0.7+0.72+0.35

= 3.42 [Approx: 3.5]

Mean =3.5 of median 3.1.

A data set's mean (average) is calculated by summing all of the numbers in the set, then dividing by the total number of values in the set. When a data collection is ranked from least to greatest, the median is the midpoint. The number that appears most frequently in a data collection is called the mode.

The median is computed by sorting the scores into numerical order, dividing the total by 2, rounding the result up if the number of scores is odd to determine the median position, or by averaging the median position and the position after it, if the number of scores is even.

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Answer:

42 Pots

Step-by-step explanation:

Because 256 divided by 6 is 42

Hope this helped

:)

Answer:

The mean is 11

Step-by-step explanation:

To find the mean, add up all the scores and divide by the number of scores

( 5+9+11+16+18+7)/6 =

66/6

11

Answer:

11

Step-by-step explanation:

5 + 9 + 11 + 16 + 18 + 7 = 66

66 / 6 = 11

Answer:

L= 16 m

W= 12 m

Step-by-step explanation:

let us define the parameters of the parallelogram

let the length be L

and the width be W

given that the W= L-4

perimeter= 72 meters

We know that the perimeter of a parallelogram is given as

\(P=2L + 2W\)

Substituting W= L-4 for W we have

\(72=2L + 2(L-4)\\\\72= 2L+2L-8 \\\\72= 4L-8\\\\4L= 72-8\\\\4L= 64\)

Divide both sides by 4 we have

\(L= 64/4\\\\L= 16 m\)

From w= L-4 we can find w by setting L= 16

W= 16-4

W= 12 m

Answer:

 (b+3)+b=51

"b" is a smaller number, that is 24.

So a larger numer is 27

Step-by-step explanation:

L = b +3

L+b = 51

(b+3) + = 51

2b + 3 = 51 >> subtract 3 to both sides

2b = 48 >> divide by 2 to both sides

b = 24

Larger = b + 3= 24 + 3= 27

Parametrization of equations x=x(t), y=y(t) for f(x)=x^8−x^2−6 from (5,−4) to (9,−1) is that parametrization does indeed connect the points (5, -4) and (9, -1).

A parametrization for the curve that connects the points (5, -4) and (9, -1) given by the function f(x) = \(x^8 - x^2 - 6.\)

To do this, we can use the parameter t to represent points on the curve as follows:

x(t) = 5 + 4t, since we want x to start at 5 and end at 9, so we need to add 4 to x over the interval [0, 1].

Substituting this into our function f(x), we get:

y(t) = f(x(t)) = \((5 + 4t)^8 - (5 + 4t)^2 - 6\).

Therefore, our parametrization is:

x(t) = 5 + 4t

y(t) = (5 + 4t)^8 - (5 + 4t)^2 - 6

To verify that this parametrization does indeed connect the points (5, -4) and (9, -1), we can check that x(0) = 5, x(1) = 9, y(0) = f(5) = -4, and y(1) = f(9) = -1.

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