Are the two figures similar? If so, give the scale factor of the first figure to the second figure.

Answer:

d= -1/8

Step-by-step explanation:

8d+d+3d+2+4d= 16d+2

16d= -2

d= -1/8

The amount in the account 38.00 years from today will be approximately $12,399.61.

To calculate the future value of Derek and Will's deposits, we can use the formula for compound interest:

A = P(1 + r)^n

Where:

A = Future value

P = Initial deposit amount

r = Interest rate per compounding period

n = Number of compounding periods

In this case, Derek and Will are depositing $2,277.00 per year for 9.00 years, and the interest rate is 6.00%.

To calculate the future value 38.00 years from today, we need to consider that the first deposit is made 5.00 years from today. Therefore, the total number of compounding periods is 38.00 - 5.00 = 33.00 years.

Let's calculate the future value:

P = $2,277.00

r = 6.00% = 0.06

n = 33.00

A = 2277 * (1 + 0.06)^33

Using a calculator, the future value of the account after 38.00 years will be approximately:

A ≈ $12,399.61

Therefore, the amount in the account 38.00 years from today will be approximately $12,399.61.

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To solve this question, just divide.

49/60 = 0.81666666666

= 82%

Answer:

Crissy's percentage is 82% (81.67% rounded).

Step-by-step explanation:

1. 49 / 60 = 0.82 (0.81666 rounded)

2. 0.82 x 100

3. 82%

Answer:

Y = 2x + 11

Step-by-step explanation:

Hope i helped!

Answer:

\(\huge\boxed{\sf x = 80\°}\)

Step-by-step explanation:

So,

30 + 70 + x = 180

100 + x = 180

Subtract 100 to both sides

x = 180 - 100

\(\rule[225]{225}{2}\)

Answer:

80 degree

Step-by-step explanation:

Sum of all angles inside a triangle is 180.

70 + 30 + x  = 180

x = 180- 70 - 30

x = 80

A sphere thrown upward at a 45-degree angle to the horizontal in a classroom elastically bounces off the ceiling while still rising

At time t = 0, a sphere is launched with an initial velocity at a 45-degree angle to the horizontal in a classroom. The sphere follows a parabolic trajectory as it rises due to the upward component of its initial velocity and experiences the downward pull of gravity. While the sphere is still ascending, it reaches the ceiling and collides with it.

During the elastic collision, the sphere's motion is reversed. It rebounds off the ceiling, changing its direction but maintaining its kinetic energy. As a result, the sphere starts descending with the same speed it had before the collision but in the opposite direction. The angle of descent will also be 45 degrees to the horizontal, mirroring the angle of the initial launch.

Throughout the entire process, neglecting air resistance, the total mechanical energy of the sphere is conserved since the collision with the ceiling is elastic.

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There are 39 independent sets in the graph.

Given the question, an independent set in a graph is a set of mutually non-adjacent vertices in the graph. In this problem, we will count the number of independent sets in the given graph.

Using an adjacency matrix, we can calculate the degrees of all vertices, which are defined as the number of edges that are connected to a vertex.

In this graph, we can see that vertex 1 has a degree of 3, vertices 2, 3, 4, and 5 have a degree of 2, and vertex 6 has a degree of 1. 0 1 1 0 0 1 1 0 1 1 0 1 1 0 1 0 0 1 0 1 0 0 1 1 0 1

The number of independent sets in the graph is given by the sum of the number of independent sets of size k, for k = 0,1,2,...,n.

The number of independent sets of size k is calculated as follows:

suppose that there are x independent sets of size k that include vertex i.

For each of these sets, we can add any of the n-k vertices that are not adjacent to vertex i.

Therefore, there are x(n-k) independent sets of size k that include vertex i. If we sum this value over all vertices i, we obtain the total number of independent sets of size k, which is denoted by a_k.

Using this method, we can calculate the number of independent sets of size 0, 1, 2, 3, and 4 in the given graph.

The calculations are shown below: a0 = 1 (the empty set is an independent set) a1 = 6 (there are six vertices, each of which can be in an independent set by itself) a2 = 8 + 6 + 6 + 6 + 2 + 2 = 30 (there are eight pairs of non-adjacent vertices, and each pair can be included in an independent set;

there are also six sets of three mutually non-adjacent vertices, but two of these sets share a vertex, so there are only four unique sets of three vertices;

there are two sets of four mutually non-adjacent vertices) a3 = 2 (there are only two sets of four mutually non-adjacent vertices) a4 = 0 (there are no sets of five mutually non-adjacent vertices)

The total number of independent sets in the graph is the sum of the values of a_k for k = 0,1,2,...,n.

Therefore, the number of independent sets in the given graph is a0 + a1 + a2 + a3 + a4 = 1 + 6 + 30 + 2 + 0 = 39.

Bonus Question : How many independent sets are there in the graph?

There are 39 independent sets in the graph.

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Problem 2:Solution:

Let G be a graph with six vertices, labelled A, B, C, D, E, F as shown below. There are no other edges except the ones shown.

Complete the table below showing the size of the largest independent set in each of the subgraphs of G.Given graph with labelled vertices are shown below,

Given Graph with labelled vertices

Now, the subgraphs of G are shown below.

Subgraph C

Graph with vertices {A, B, C, D}

The size of the largest independent set in the subgraph C is 2.Independent set in subgraph C: {A, D}

Subgraph D

Graph with vertices {B, C, D, E}

The size of the largest independent set in the subgraph D is 2.Independent set in subgraph D: {C, E}Bonus SubgraphGraph with vertices {C, D, E, F}

The size of the largest independent set in the subgraph formed by {C, D, E, F} is 3.Independent set in subgraph {C, D, E, F}: {C, E, F}

Hence, the required table is given below;

Subgraph

Size of the largest independent setC2D2{C, D, E, F}3

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Step-by-step explanation:

We can set up an equation for this line using slope intercept form:

\(y = mx + b\)

Where \(m\) is the slope of the line and \(b\) is the y-intercept (where the line cross the Y-axis at \(x = 0\)).

We know that the slope of the line is \(-4\) so we can plug that in for \(m\), but we don't know \(b\), so we'll have to use the given point \()(-6, -10)\) to help solve for it:

\(y = -4x + b\)

\(-10 = -4(-6) + b\)

\(-10 = 24 + b\)

\(b = -34\)

This means the equation of the line is \(y = -4x - 34\). Now we can plug in the point \((-9, s)\) and solve for \(s\):

\(y = -4x - 34\)

\(s = -4(-9) - 34\)

\(s = 36 - 34\)

\(s = 2\)

Answer:

(2x*+6)(x-2)

2x(x-2)+6(x-2)

2xx+2x(-2)+6x +6(-2)

we know ;

(-). (-) = +

(-). (+) = -

(+). (-) = -

(+). (+) = +

2xx-2x(2)+6x -6(2)

2x^2  - 4x + 6x  -12

2x^2  - 2x  -12

Step-by-step explanation:

Answer:

Riley can only order 2 pizzas

Step-by-step explanation:

1. subtract delivery fee from the 20 dollars.

$20 - $6 = $14

2. Find number of pizzas with the $14 that she can use.

$14 ÷ $5 = 2 R $4

thus she can only buy 2 pizzas

and n = 2 in this case.

Answer:

3%

Step-by-step explanation:

Answer:

100%

Step-by-step explanation:

Markup % = ( Selling Price - Coast) / ( Coast) * 100

( $4 - $3) / ($3) * 100

1 * 100 = 100

The length of the shorter piece of pipe is 47 inches.

A 235-inch pipe is cut into two pieces.  One piece is four times the length of the other.

The length of the shorter piece can be found as follows:

let the length of the shorter piece be x.

Therefore,

length of the longer piece = 4x

Hence,

4x + x = 235

5x = 235

divide both sides of the equation by 5

5x / 5 = 235 / 5

x = 235 / 5

x = 47

Therefore,

length of the shorter piece = 47 inches.

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The radio station awarded all three prizes to the 300th caller.

To estimate the one caller to receive the all three prices, find the LCM of 15, 25 and 100.

LCM of 15, 25 and 100 is as follows;

3     15, 25, 100

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

4      5, 25, 100

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

5      5, 25, 25

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

5       1, 5, 5

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

         1, 1, 1

LCM = 3×4×5×5

LCM = 300

Therefore, the radio station will first award all three prizes to the 300th caller.

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The exponential distribution is a continuous probability distribution that describes the time between events in a Poisson process, where events occur continuously and independently at a constant rate. The probability density function of the exponential distribution is given by f(x) = λe^(-λx), where λ is the rate parameter.

a. To show that EX" = EXn-1, we need to use the memoryless property of the exponential distribution. This property states that the conditional probability of X > t+s given that X > s is equal to the unconditional probability of X > t, for any s,t > 0. Using this property, we can write:

EX" = E(X|X > n-1) + (n-1) = E(X) + n-1 = 1/λ + n-1

EXn-1 = E(X|X > 1) + (n-2) = E(X) + n-2 = 1/λ + n-2

Since EX" = EXn-1, we have shown that the memoryless property holds.

b. To find EX" = n!, we can use the moment generating function (MGF) of the exponential distribution, which is given by M(t) = λ/(λ-t). The nth moment of X is defined as E(X^n) = (-1)^n d^n M(t)/dt^n at t=0. Differentiating the MGF n times, we get:

E(X^n) = n!λ^n/(λ-t)^n+1 at t=0

Setting n=1, we get E(X) = 1/λ, which is the mean of the exponential distribution. Setting n=2, we get E(X^2) = 2/λ^2, which is the variance of the exponential distribution.

For n>2, we can use the formula above to find the nth moment:

E(X^n) = n!λ^n/(-1)^{n+1} = n!/(λ^n)

Therefore, for n = 1,2,3,..., we have:

EX" = E(X^n|X > n-1) = (n-1)!/(λ^n-1) = n!/λ^n

Thus, we have shown that EX" = n! for n = 1,2,3,...

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Answer:

Sure thing!

For the first equation 6v+38≤ -4

The answer would be v≤-7

and for the second equation 2(v+3)≥-2

the answer would be v≥-4

Step-by-step explanation:

6v+38≤ -4

Subtract 38 from both sides

6v+38-38≤-4-38

Simplify

6v≤-42

Divide both sides by 6

6v/6≤-42/6

Simplify

v≤-7

SAME THING FOR THE OTHER

2(v+3)≥-2

Divide both sides by 2

2(v+3)/2≥-2/2

Simplify

v+3≥-1

Subtract 3 from both sides

v+3-3≥-1-3

And finally, simplify

v≥-4

PLEASE MARK AS BRAINLIEST

The final speed v2 is √6 times the initial speed v1, when the net force is 2f1 and the object moves the same distance d while the force is being applied.

We can use the work-energy theorem to solve this problem, which states that the work done on an object by a net force is equal to the change in its kinetic energy.

When the force has magnitude f1 and the object moves a distance d, the work done is:

W = f1 * d

This work changes the kinetic energy of the object from zero to (1/2) * m * v1^2, where m is the mass of the object. Therefore, we have:

f1 * d = (1/2) * m * v1^2

Solving for v1, we get:

v1 = sqrt((2 * f1 * d) / m)

Now, when the net force has magnitude f2 = 2f1 and the object moves the same distance d, the work done is:

W = f2 * d = 2f1 * d

This work changes the kinetic energy of the object from (1/2) * m * v1^2 to (1/2) * m * v2^2, where v2 is the final speed of the object. Therefore, we have:

2f1 * d = (1/2) * m * (v2^2 - v1^2)

Solving for v2, we get:

v2 = sqrt(v1^2 + (4 * f1 * d) / m)

Substituting the expression for v1, we get:

v2 = sqrt((4 * f1 * d) / m + (2 * f1 * d) / m)

Simplifying, we get:

v2 = sqrt(6) * v1

Therefore, the final speed v2 is sqrt(6) times the initial speed v1.

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Answer:

5/15 is the probability of choosing a red marble from the box.

Step-by-step explanation:

We know that,

There are 5 red marbles and 10 green marbles in the box.

Divide the number of events by the number of possible outcomes. This will give us the probability.

P(red marble) = P(5)

Possible outcomes

5 red, 10 green -> 15 possibilities

Probability = \(\frac{5}{15}\)

Please leave a 'thanks' if this helped!

The required probability of drawing a red marble the 6th time is 1/2.

Given that,

A box contains 10 red marbles and 10 green marbles.

Sampling at random from this box five times without replacement, you have drawn a red marble all five times.

Without replacing any of the marbles.

We have to determine,

What is the probability of drawing a red marble the 6th time?

According to the question,

There are 10 red marbles and 10 green marbles,

The initial condition is to the same state at every step, so the probability to get a red marble is the same in each sampling  and is equal to the ratio of the number of red marbles to the total number of samples.

Therefore,

The probability of drawing a red marble the 6th time is,

\(P = \dfrac{10}{10+10}\\\\P = \dfrac{10}{20}\\\\P = \dfrac{1}{2}\)

Hence, The required probability of drawing a red marble the 6th time is 1/2.

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Answer:

The slope of a line in the plane containing the x and y axes is generally represented by the letter m, and is defined as the change in the y coordinate divided by the corresponding change in the x coordinate, between two distinct points on the line.

Step-by-step explanation:

Answer:

sum of ratio =3+2=5

David'share=£9900x3/5=£5940

Sum of ratio for part= 4+4+2=10

for himself=£5940x4/10=£2376

for wife=£5940x4/10=£2376

for son=£5940x2/10=£1188

his wife gets over son

£2376-£1188=£1188

Answer:

1188 pounds

Step-by-step explanation:

your welcome :)

he exponential function for the given problem is

f(y) = ((5/6) ^ y) × ((1/6) ^ (1000 - y)) × [1000! / y! (1000 - y)!]

Let Y denote the number of sixes subtracted in rolling a dice 1000 times.

Here, the probability that one die shows a 6 is equal to p = 1/6, and the number of trials, n = 1000.

So, the number of times a die does not show a 6 is (1 - p) = (5/6) per trial.

Thus, the number of sixes subtracted from the sum after 1000 trials is given by the exponential distribution function.

Mathematically, this function is defined as follows:

f(y) = ((5/6) ^ y) × ((1/6) ^ (1000 - y)) × [1000! / y! (1000 - y)!]

Therefore, the exponential function for the given problem is

f(y) = ((5/6) ^ y) × ((1/6) ^ (1000 - y)) × [1000! / y! (1000 - y)!]

where y = number of times a six is rolled and subtracted.

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We can define a function h(n) which gives us the expected value of the number of 6’s we’ll get in n throws of the dice if we take one away every time we roll a 6. The exponential equation is \(h(n) = f(n) - g(n) = \frac{n}{6} - 6 + (5/6)^n\)

Let us define a function f(n) which gives us the expected value of the number of 6’s we’ll get in n throws of a fair dice. For one roll, f(1) = 1/6. Let’s say we make n throws of the dice.

Then we can calculate the probability that none of them are 6’s: (5/6)ⁿ.

Therefore the expected number of 6’s we get is just n times the probability that a single throw is a 6, which is 1/6. Therefore f(n) = n/6.

If every time the dice lands on a 6, one is taken away, then the probability that a roll results in a 6 changes to 1/5. Therefore we can define a new function g(n) which gives us the expected value of the number of times we’ll have to throw the dice until we get a 6:

g(1) = 1/6

g(n) = (5/6)

g(n-1) + 1/6

So, we can rewrite it in a more general way as,

\(g(n) = \frac{1}{6} + \frac{5}{6}g(n-1)\)

This is a linear recursive relation with constant coefficients. We can write out the first few terms of the sequence:

\(g(1) &= 1/6\\g(2) &= 1/6 + 5/6 \cdot 1/6 = 11/36\\g(3) &= 1/6 + 5/6 \cdot 11/36 = 91/216\\\)

In general,

\(\[g(n) = \frac{1 - (5/6)^n}{1 - 5/6} = 6 - (5/6)^n\]\)

Therefore we can define a function h(n) which gives us the expected value of the number of 6’s we’ll get in n throws of the dice if we take one away every time we roll a 6:

\(h(n) = f(n) - g(n) = \frac{n}{6} - 6 + (5/6)^n\)

This is the exponential function you asked for.

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Answer:

The answer is 6

Step-by-step explanation:

(0,6)

x=0,y=6

Substituting 0 for x and 6 for y

6=2(0) + b

6=b

or

6 = 3(0)+b

6=b

Therefore, b=6

A. The solution to the congruence 3x - 107 ≡ 0 (mod 12) is x ≡ 1 (mod 12).

B. The solution to the congruence 5x + 3 - 102 ≡ 0 (mod 7) is x ≡ 6 (mod 7).

C. The solution to the congruence 66 + 9 ≡ 0 (mod 11) is x ≡ 4 (mod 11).

To solve modulo equations or congruences, we need to find values of x that satisfy the given congruence.

A. For the congruence 3x - 107 ≡ 0 (mod 12), we want to find an x such that when 107 is subtracted from 3x, the result is divisible by 12. Adding 107 to both sides of the congruence, we get 3x ≡ 107 (mod 12). By observing the remainders of 107 when divided by 12, we see that 107 ≡ 11 (mod 12). Therefore, we can rewrite the congruence as 3x ≡ 11 (mod 12). To solve for x, we need to find a number that, when multiplied by 3, gives a remainder of 11 when divided by 12. It turns out that x ≡ 1 (mod 12) satisfies this condition.

B. In the congruence 5x + 3 - 102 ≡ 0 (mod 7), we want to find an x such that when 102 is subtracted from 5x + 3, the result is divisible by 7. Subtracting 3 from both sides of the congruence, we get 5x ≡ 99 (mod 7). Simplifying further, 99 ≡ 1 (mod 7). Hence, the congruence becomes 5x ≡ 1 (mod 7). To find x, we need to find a number that, when multiplied by 5, gives a remainder of 1 when divided by 7. It can be seen that x ≡ 6 (mod 7) satisfies this condition.

C. The congruence 66 + 9 ≡ 0 (mod 11) states that we need to find a value of x for which 66 + 9 is divisible by 11. Evaluating 66 + 9, we find that 66 + 9 ≡ 3 (mod 11). Hence, x ≡ 4 (mod 11) satisfies the given congruence.

Modulo arithmetic or congruences involve working with remainders when dividing numbers. In a congruence of the form a ≡ b (mod m), it means that a and b have the same remainder when divided by m. To solve modulo equations, we manipulate the equation to isolate x and determine the values of x that satisfy the congruence. By observing the patterns in remainders and using properties of modular arithmetic, we can find solutions to these equations.

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Answer:

asking if there are any questions

Answer:

About 50% percent

Step-by-step explanation:

20 is 50 percent of 40, so 21 is about 50 percent (52.5 %)

~theLocoCoco

Answer:

52.5%

Step-by-step explanation:

21/40 = 52.5/100

52.5/100= 52.5%

im not sure but you can try :<

Human eyes have an average diameter of 24 thousandths of a meter. White blood cell size equals 0.002 millimeters in diameter. The diameter of the human eye is 12000 greater then the diameter of the white blood cell.

Given that,

Human eyes have an average diameter of 24 thousandths of a meter. White blood cell size equals 0.002 millimeters in diameter.

We have to calculate which the number is greater diameter.

By dividing the Human eyes have an average diameter of 24 thousandths of a meter. White blood cell size equals 0.002 millimeters in diameter.

We get,

\(\frac{24}{0.002}\)

=12000

Therefore, the diameter of the human eye is 12000 greater then the diameter of the white blood cell.

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Answer:

630/x+5 (remainder over divisor)

Answer:

p = 125/73

Step-by-step explanation:

−p − 13 = −43p + 23 (5p − 6)

−p − 13 = −43p + 115p − 138

−p − 13 = 72p − 138

+p            +p

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

-13 = 73p - 138

+138         +138

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

125 = 73p

/73     /73

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

125/73 = p

If you need the answer in mixed fraction, then it's --> p = 1 52/73

The solution to the given equation is p = - 1.71

To determine the solution of the given equation,

We will find the value of the variable, p, that satisfies the equation.

From the question, the given equation is

\(-p-13 = -43p+23(5p-6)\)

To solve this,

First, Clear the brackets

\(-p-13 = -43p + 115p - 138\)

Now, Collect like terms

\(-p +43p -115p = -138 + 13\)

\(73p = -125\)

Now, divide both sides of the equation by 73

\(\frac{73p}{73} = \frac{-125}{73}\)

∴ p = - 1.71

Hence, the solution to the given equation is p = - 1.71

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Answer:

Option 4.

Step-by-step explanation:

Tan(X)=perpendicular/base

Tan(X)=48/14

X=arctan(48/14)=74

Answer: 29152332 ≡ 0 (mod 3)

Step-by-step explanation:

In modular arithmetic, there is the form a ≡ b (mod m) where b is the remainder.

To solve this problem, we want to divide 29152332 by 3 and find the remainder.

29152332 ÷ 3 = 9717444

Since we get an integer with no remainder, we know the answer is 29152332 ≡ 0 (mod 3).