A bug starts at a vertex of an equilateral triangle. On each move, it randomly selects one of the two vertices where it is not currently located, and crawls along a side of the triangle to that vertex. Given that the probability that the bug moves to its starting vertex on its tenth move is m/n, where m and n are relatively prime positive integers, find m + n.

(a) The area of the shaded region is 0.2709.

(b) The area of the shaded region is 0.3520.

(c) The area of the shaded region is 0.5555.

(d) The area of the shaded region is 0.6197

What is standard normal curve?

The horizontal axis is approached but never touched by the standard normal curve as it extends indefinitely in both directions. The center of the bell-shaped standard normal curve, which has a z=0 slope, is. Nearly all of the standard normal curve's area lies between z = 3 and z = 3.

The shaded area under the standard normal curve are,

1) Find,  P[Z > 0.61 ]

= P[Z > 0.50]

= 1 - P[Z < -0.50]

= 1 - 0.7291 ( use z table)

=   0.2709

The area of the shaded region is 0.2709.

2) Find,  P[Z < -0.38 ]

= P[Z < -0.38 ]

= 0.3520 ... ( use z table)

The area of the shaded region is 0.3520.

3) Find,  P( -0.58 < Z < 0.98 )

= P(Z < 0.98 ) - P(Z < -0.58 )

= 0.8365 - 0.2810 ......(using z-table)

= 0.5555

The area of the shaded region is 0.5555.

4) Find ,  P( -0.11 < Z > 0.98 )

= 1 - P(Z < 0.98 ) - P(Z < -0.11 )

= 1 - ( 0.8365 - 0.4562 ) ......(using z-table)

= 1 - 0.3803

= 0.6197

Hence, the area of the shaded region is 0.6197.

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The probability of the following event. The first die is 3 or the sum is 6 would be 1/4.

What is the probability?

Probability refers to a possibility that deals with the occurrence of random events.

All events must have a probability of occuring at least once, or 1.

The proportion of positive outcomes to all outcomes is referred to as the probability formula.

Let's assume that the blue die came up first among the two.

A = the amount of times we roll a first-die and get a 3.

B is the quantity of times a total of six occurs.

Now Locate 3 on the blue die and notice there are 6 occurrences when this happens which corresponds to the 6 other possibilities for the red die. So we have A = 5.

Also,there are 5 occurrences of the sum "6" in the table. So B = 5.

We have A+B = 5+5 = 10 occurrences of either the first die is 3 or the sum is 6.

However, we have to subtract off 1 because we double counted "6" when adding A and B.

So in reality we have 10-1 = 9 times this happens.

This is out of 36 total ways to roll two dice.

Therefore, the probability of the following event.

The first die is 3 or the sum is 6 would be 9/36 = 1/4

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The point estimate for sales when advertising is $3000 is $5412.

Based on the given information, the estimated regression equation is Ŷ = 12 + 1.8x, where Ŷ is the estimated value of the dependent variable (sales), x is the value of the independent variable (advertising), and the constants 12 and 1.8 are the coefficients of the regression equation.

If advertising is $3000, then the point estimate for sales (in dollars) is the value of Ŷ when x = 3000. Substituting this value into the estimated regression equation, we get:

Ŷ = 12 + 1.8 * 3000 = 12 + 5400 = 5412

So, the required amount is $5412.

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Injective function is a type of function which relates an element of a given set with a distinct element of another set. An injective function is also referred to as a one-one function.

Let's start by listing supposition and their respective reasons.

Suppose,

g О f is injective then f : A → B is also injective.

As we are dealing with injective functions, we can rightly proceed.

The functions f(x) = f(y) when x,y ∈ A

g(f(x)) = g(f(y))

Given the fact that g О f ,then x = y

Thus, we can say that since g О f , f : A is an injective function too (one to one function)

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A quasi-experiment with one treatment and one control group that measures the dependent variable only nonequivalent control group posttest only design.

The quasi experiment design is defined as the attempt to produce the cause and effect relationship by using different types of criteria except randomization

The dependent variable is the variable that the value of this variable affected by the other variables

The treatment is defined as the any independent variable that affected by the experimenters.

Here the quasi-experiment with one treatment and one control group that measures the dependent variable only once.

Therefore, this is a nonequivalent control group posttest only design

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The required measure of the angle ∠VYW is given as 59°.

Given that,
A Right angle is shown, where the measure of the complementary angle ∠VYW is to be determined.

orientation of one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.

here,
For complementary angle,
∠TYV + ∠VYW = 90
31 + ∠VYW = 90
∠VYW = 59°

Thus, the required measure of the angle ∠VYW is given as 59°.

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His bottom line was a gain from selling and 3% commission is $257.50.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

The cost price of 200 shares of BUI is (19.50×200) = $3900.

The selling price of 200 shares of BUI is (20.75×200) = $4150.

The net gain is (4150 - 3900) = $250 and with 3% commission it is,

= (103/100)×250.

= $257.50.

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To make the similar cake for 8 persons , the number of cups of both flour and milk will be needed is [tex]4\frac{2}{3}[/tex] cups .

In the question ,

it is given that ,

number of cups of milk needed  to make the cake is = 1 cup

number of cups of flour needed  to make the cake is = [tex]2\frac{1}{2}[/tex] = 5/2 cups .

So , the total is = cups of milk + flour

= 1 + 5/2 = 7/2

So , for 6 persons , 7/2 cups of milk and flour is needed .

for 1 person 7/12 cups of milk and flour is needed .

and for 8 persons = 8×7/12 cups of milk and flour is needed .  

= 14/3

= [tex]4\frac{2}{3}[/tex] cups .

Therefore , the number of cups of milk and flour needed is  [tex]4\frac{2}{3}[/tex] cups .

The given question is incomplete , the complete question is

A recipe calls for 1 cup of milk for every [tex]2\frac{1}{2}[/tex] cups of flour to make a cake that would feed 6 persons. How many cups of both flour and milk will be needed to make a similar cake for 8 persons ?

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the two numbers x and y for which x2y is that value, as well as the highest possible value .P at any solutions found in part d, as well as the endpoints of the domain found as The maximum value of P is =4092, The values of x and y are x=64, y=32.

a. Solve x+y=96 for y.

y=96-x

b. In the equation P=x2y, replace the variable to be maximized with the outcome from part a.

P=x^2(96-x)

c. Find the domain of the function P found in part b.

Dom(P)=[0,96]

d. Find dP/dx. Solve the equation dP/dx=0.

dP/dx=2x(96-x)-x^2=0

Solve the equation

x=0,96

e. Evaluate P at any solutions identified in part d, as well as the endpoints of the domain found in part c.

P(0)=0

P(64)=4096

P(96)=0

f. provide the maximum value of P, as well as the two numbers x and y for which x2y is that value.

The maximum value of P is 4096

The values of x and y that maximize P are x=64, y=32

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Answer:

have her do the number times each number every time so if the number is seven and there is a four on top, add or multiply or subtract 7 by 4

Step-by-step explanation:

If we suppose that x is equal to 0, then the value of y is 2(0)+3y = 3, and y is equal to 1. Therefore, (0,1) is one of the answers to this equation.

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance.

Equations come in a variety of forms, including linear, quadratic, cubic, etc.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation.

To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. The statement is not an equation if there is no "equal to" symbol in it.

According to our question-

The formula is 2x + 3y = 3. There are an infinite number of solutions to this equation.

We must first enter any random value for any variable, followed by the matching value for the other variable, in order to find any solution to this equation.

Now, if we suppose that x is equal to 0, then the value of y is 2(0)+3y = 3, and y is equal to 1. Therefore, one of the solutions to this equation is (0,1).

Hence, If we suppose that x is equal to 0, then the value of y is 2(0)+3y = 3, and y is equal to 1. Therefore, (0,1) is one of the answers to this equation.

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Complete question-

Find the one of the solution of 2x + 3y = 3?

Answer: 4x

Step-by-step explanation:

Combine like terms

3x + x

4x

Hope this helps!

Answer:

  4x

Step-by-step explanation:

You want to "solve" 3x +x.

Start by understanding the meaning of 3x. The coefficient of 3 tells you how many instances of x you have. The term 3x is a representation of repeated addition:

  3x = x + x + x . . . . . . . . x is included in the sum 3 times

The sum 3x + x can be written out as ...

  3x + x = (x + x + x) + x

This is fully equivalent to ...

  3x + x = x + x + x + x

We recognize the sum on the right includes 4 instances of x, so can be written using a coefficient as ...

  x + x + x + x = 4x

This means ...

  3x + x = 4x

If we use the distributive property, we can also get there this way:

  3x + x = 3x + 1x = (3 +1)x = 4x

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The triangle is an isosceles trianlge. Then the value of the variable 'x' will be 19.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.

The two triangular legs and their opposing angles are congruent in an isosceles triangle.

In the event that the air conditioner is harmonious to CB, the proportion of point A = (3x + 18), and the proportion of point C = (2x - 8)

Then the equation is given as,

∠A + ∠B + ∠C = 180°

3x + 18 + 3x + 18 + 2x - 8 = 180

8x + 28 = 180

8x = 152

x = 19

The triangle is an isosceles trianlge. Then the value of the variable 'x' will be 19.

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The sample type is option (D) Systematic random sample

Here they randomly select one of the first 25 users each day and show them a message asking for a donation

They also show the message to every 25th user from that point on

The random sample is the selecting one from a large population

The systematic random sample is defined as the probability sampling method from a large population, the random samples are selected periodically. The periodical selection of random variable means the random variables are selected in regular interval.

Here the random samples are selected as one of the first 25 users each day

Therefore, the random sample is systematic random sample

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A concentric square and circle intersect at 8 points. the area of A2, A6 is (3/4)s²

Generally, let's call the side length of the square s and the radius of the circle r.

We can set up the following equation:

(s/2)² + (r/2)² = (5/8) * s²

We can rearrange this equation to solve for r:

(r/2)² = (5/8)s² - (s/2)²

Evaluate the exponents

This gives

r²/4 = 5/8s² - s²/4

Multiply through by 4

So, we have

r² = 5/2s² - s²

Evaluate the like terms

This gives

r² = 3/2s²

Take the square roots of both sides

So, we have

r = s√(3/2)

Since A1, A3, A5, and A7 are the vertices of the square, the area of this region is (s/2)²,

When expanded, this gives

Area = 1/4s².

The area of A2, A6 can be found by subtracting the area of A1, A3, A5, and A7 from the area of the entire square.

This gives us:

A2, A6 = s² - (1/4)s²

Evaluate

A2, A6 = (3/4)s²

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Answer:

10 hours

Step-by-step explanation:

Amount used:

1 hour of use would be

1/3 of 24 = 6 hours used of the total

8/24 of 24 would be 8 hours used of the total

14 total hours would be used out of a 24 hour totals, so that leaves 10 hours of battery use left.

I am not feeling real confident about this.

Answer:

------------------------------------

24 hours of idle use time is equivalent to 3 hours of active use.

If it was in use for 1 hour, it is equivalent  to:

Since it is included in the 9 hours, it is equivalent to:

Battery life left:

Answer:

y=5x

Step-by-step explanation:

Because we already know we need atleast 5 quarters to complete a full load (Wash and dry) so we would multiply that number by how many loads were doing (x) and y is the amount we need. For example five loads is y=5x5 and then we can find y which would be y=25

The probability that at most 2 of the next 10 callers have to wait more than 8 minutes is the sum of the probabilities of 0, 1, or 2 callers having to wait for more than 8 minutes which is 0.810

The probability that at most 2 of the next 10 callers having to wait can be defined using the expression :

P(X ≤ 2) = P(0) + P(1) + P(2)

Using the individual probabilities given by the histogram attached :

P(X ≤ 2) = 0.181 + 0.345 + 0.284

P(X ≤ 2) = 0.810

Therefore, the probability that at most 2 callers have to wait more than 8 minutes is 0.810

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Answer:

$292.36

Step-by-step explanation:

To calculate the total amount Nadia will have to pay the bakery to deliver the éclairs, you need to determine how many boxes of éclairs she will need to order and then add the delivery charge.

First, you need to determine how many éclairs Nadia will need to order to feed all of her guests. Since there are 8 éclairs per box and Nadia has 76 guests in addition to herself and Elizabeth, a total of 78 people, she will need to order 78 / 8 = <<78/8=9.75>>9.75 boxes of éclairs.

To calculate the total cost of the éclairs, you can multiply the number of boxes needed by the cost per box: 9.75 boxes * $24 per box = $<<9.75*24=234>>234.

To calculate the total delivery charge, you can multiply the number of boxes needed by the delivery charge per box: 9.75 boxes * $5.95 per box = $<<9.75*5.95=58.36>>58.36.

To find the total amount Nadia will have to pay the bakery, you can add the cost of the éclairs to the delivery charge: $234 + $58.36 = $<<234+58.36=292.36>>292.36.

Therefore, Nadia will have to pay the bakery a total of $292.36 to deliver the éclairs.

Answer:

[tex]\boxed{292.4625}.[/tex]

Step-by-step explanation:

To determine the total amount Nadia will have to pay the bakery to deliver the eclairs, you will need to first calculate the total number of eclairs that are needed. Since Nadia and Elizabeth will both be attending the party, and there will be a total of 76 friends attending, the total number of people at the party will be 76 + 2 = 78.

Next, you will need to determine how many boxes of eclairs Nadia will need to order. Since each box contains 8 eclairs, and there are 78 people at the party, Nadia will need to order 78 / 8 = <<78/8=9.75>>9.75 boxes of eclairs.

Since the bakery charges $24 per box of eclairs and Nadia needs to order 9.75 boxes, the cost for the eclairs will be 24 * 9.75 = $<<24*9.75=234>>234.

In addition to the cost of the eclairs, Nadia will also need to pay a delivery charge of $5.95 per box. Since Nadia needs to order 9.75 boxes, the delivery charge will be 5.95 * 9.75 = $<<5.95*9.75=58.4625>>58.4625.

To find the total amount Nadia will have to pay the bakery, you will need to add the cost of the eclairs and the delivery charge. The total amount Nadia will have to pay the bakery will be: $234 + $58.4625 = $<<234+58.4625=292.4625>>292.4625. Answer: \boxed{292.4625}.

a) The probability that at least one of the two young adults selected is living in his or her parent’s home is; 0.74.

b) The probability both young adults selected are living on their own is; 0.26

We are given the events as;

M = the event a male young adult is living in his parent’ home

F = the event a female young adult is living in her parent’ home

We are also given that;

Probability that a male young adult is living in his parent’ home; P(M) = 0.56

Probability that a female young adult is living in her parent’ home; P(F) = 0.42

a) The probability that at least one of the two young adults selected is living in his or her parent’ home is;

P(at least one of the two young adults selected is living in his or her parents home) = P(M or F) = P(M) + P(F) - P(M and F)

= 0.56 + 0.42 - 0.24 = 0.74.

B) The probability both young adults selected are living on their own which means neither is living with their parents is;

P(neither living with parents) = 1 - P(M or F)

= 1 - 0.74 = 0.26.

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Answer:

The answer is 65 degrees fahrenheit.

Step-by-step explanation:

Answer: $72

Step-by-step explanation:

x = money M had before he bought the hat

0.25x = 18

x = 18/.25 = 72

5.3 ? I think.

The mixed number ver is -5 32/97

Yes Rhombuses are special parallelograms is true statement. Yes square is also a special rhombus. True square is a specific type of parallelogram.

What is parallelograms?

A parallelogram is a geometric shape with sides that are parallel to one another in two dimensions. It is a type of polygon with four sides (also known as a quadrilateral) in which each parallel pair of sides is the same length.

A parallelogram has adjacent angles that add up to 180 degrees.

rhombuses is a quadrilateral with all the four sides having equal lengths.

In a rhombus, the opposite sides are parallel and equal. Hence, it is a parallelogram.

So  rhombuses are special parallelograms this statement is true.

A square is a special rhombus Yes that is true

The sides of a square and a rhombus are both the same length. A rhombus only has its opposite angles equal, whereas a square has all of its angles at 90 degrees.

why is a parallelogram not the same type of quadrilateral is a trapezoid?

Since they both have four sides, it is obvious that a trapezoid and a parallelogram are quadrilaterals. There are at least one set of parallel sides in a trapezoid. Two sets of parallel sides make up a parallelogram. Therefore, a trapezoid is not a parallelogram if it has only one pair of parallel sides.

a square is a specific type of parallelogram this statement is true.

A square is a quadrilateral in two dimensions that has four equal sides and four equal angles. It is a unique parallelogram with equal angles and sides.

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Explanation:

Let point C represent the center of the planet.

Segment QC is 2810 miles long as it's one of the radii.

Segment DC is 1970+2810 = 4780 miles long after adding on the height of the mountain.

Triangle DQC is a right triangle. That allows us to use a trig ratio to determine theta. Specifically we'll use cosine.

cos(angle) = adjacent/hypotenuse

cos(theta) =  QC/DC

cos(theta) = 2810/4780

theta = arccos(2810/4780)

theta = 53.9942734 degrees approximately

A full 360 degree rotation takes 24 hours. We take a fraction of that to find how many hours it takes for that planet to rotate so point P ends up where point Q is currently located.

(theta/360)*24 = (53.9942734/360)*24 = 3.599618

That's the number of approximate hours it takes. Multiply that by 60 to determine how many minutes it takes.

3.599618*60 = 215.97708

Then that rounds to the final answer 215.98 minutes.

Answer:

$226

Step-by-step explanation:

1. define the variable x

x = # of days to rent the carpet cleaner

2. substitute x for 7 days

c(7) = 30(7) + 16

3. solve

c(7) = 210 + 16

c(7) = 226

For 7 days, Rhonda will have to rent the carpet cleaner for $226.

The ordered pair in the set of numbers are 1.5 and 5.5. Option C is correct here.

The equation would have to be in the form of y = mx + b

We have b = 7, this is when x ix 0. It is the value of y

Using the pair (0, 7) and (1, 6)

The slope would be : (6 - 7)/(1 - 0)

= -1 / 1 = -1

we would put -1 in the slope equation

where m = -1 and b = 7

Hence y =  -x + 7

Next we would have to use (0, 1) and (1, 4)

similarly,  (4 - 1)/(1 - 0)

= 3 / 1

= 3

we would have to substitute the value of 3 iun the slope equation using b as 1

y = 3x + 1

Since we have two equations given as

y = -x + 7

y = 3x + 1 => Eqn. 2

We would have to solve the simultaneous linear equation as follows, put the value of 1 in 2

-x + 7 = 3x + 1

take the like terms

Collect like terms

4x = 6

x = 1.5

put the value of x in the first equation

y = -x + 7

y = -1.5 + 7

= 5.5

Hence the pair is given as  1.5 and 5.5

Option c is right.

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Range is the measure of variability which is not dependent on the exact value of each score.

In terms of variability, range is independent of the exact value of each score, and in terms of central tendency, median is the measure that is independent of the exact values of each score.

What is a range?

Range is basically the difference of the highest and the lowest value of a series. The range has nothing to do with the exact value of each score. It just considers the highest and the lowest values of any given class for its calculation.

Range= highest value- Lowest value

That is the reason, why, Range is the independent measure of variability.

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In coin changing problem,  the greedy strategy fails for the denominations 25, 20, 10, 5, and 1 cents.

The greedy algorithm for the coin change problem (pay a certain amount with the fewest number of coins feasible) is effective. It always chooses the coin with the largest denomination that does not exceed the remaining sum, and it consistently determines the right answer for certain coin sets.

But for certain set of denominations, it fails. For example take a sum of 44 cents then by greedy algorithm, first taking the highest denominations one 25 cent is taken and now 19 is remaining. So now one 10 cent is taken, and 9 is remaining. Now, one 5 cent is taken and four 1 cent is taken. So total we get 7 coins.

Now let us deviate from greedy algorithm and take two 20 cents, now 4 is remaining. So now four 1 cent is taken, this sums up only 6 coins. So this is a much optimal solution than the one obtained by greedy algorithm.

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Slope: −34

y-intercept: (0,−14)

[IF ITS WRONG TELL ME]