Billy has a $40 gift card. She spends $10 per week. Write a linear equation for this situation.

(Hint: Use y = mx + b, where y is money remaining, m is loss per week, and b is the starting money.)

Because we know one point and an axis of symmetry, we know that the point (2, -7) must lie on the graph.

If a function has a line of symmetry at x = x₀, then we know that:

f(x₀ + x) = f(x₀ - x).

So we have symmetry around that line.

Then, if the line of symmetry is at x = 5 and we know that:

f(8) = f(5 + 3) = -7

We also must have:

f(2) = f(5 - 3) = -7

Then the point (2, - 7) must be on the graph.

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Answer:

Step-by-step explanation:

The surface area of a square pyramid = 1/2 * slant height * base perimeter + area of base

 The slant height is 5 cm

The base perimeter is 4 * 5 cm = 20 cm

The area of the base is 5 cm * 5 cm = 25 cm**2

Plugging into the formula the area =

1/2 * 5 cm * 20 cm + 25 cm**2 =

5 cm * 10 cm + 25 cm**2 =

50 cm**2 + 25 cm**2 = 75 cm**2

Answer:

-2(9+8n)

Step-by-step explanation:

open the bracket

-18-16n

factorize by -2

-2(9+8n)

Answer:

The answer is ≤-3.3

Step-by-step explanation:

If you multiply -3.3 x -2 it will give you 9.99 anything above that would go past 10.

So the answer is less than or equal to -3.3 because this number or anything below it on a number line multiplied by -3 will never go past 10.

Hope this helps!

The width of the rectangle is 9 meter.

Now, According to the question:

The perimeter of a rectangle is defined as the sum of all the sides of a rectangle. For any polygon, the perimeter formulas are the total distance around its sides. In case of a rectangle, the opposite sides of a rectangle are equal and so, the perimeter will be twice the width of the rectangle plus twice the length of the rectangle and it is denoted by the alphabet “p”.

Now, Solving the problem:

Perimeter of rectangle is 50 meter sq.

Length of the rectangle(L) is 16 meter.

We have to find the width (W) of the rectangle.

We know that,

Perimeter of rectangle is = 2 (L + W)

50 = 2(16 + W)

50 = 32 + 2W

2W = 50 - 32

2W = 18

W = 18/2

W = 9

Hence, The width of the rectangle is 9 meter.

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Answer:

There isn't much to say because there is no image with the options but, no, all these measures of desperation are affected by extreme values

Answer:

2,2,2,11,11

Step-by-step explanation:

968/2

484/2

242/2

121/11

11/11

Answer:

A=50, B=4

A is directly proportional to the square root of B

name the constant 'k'

A = k*B^0.5

50 = k*4^0.5

50=2k

k=25

=> A =25 root B

i.e, A = 25*B^0.5 (The answer should be written the way it is written in the attached picture)

A written in terms of B is 25√B.

In direct proportion if one quantity increases the other quantity also increases and vice versa.In case of inverse proportion when one quantity increases the other quantity decreases and vice versa.

According to the given question A is directly proportional to the square root of B.

∴ A = K\(\sqrt{B}\)

Given when A = 50 B = 4.

50 = K\(\sqrt{4}\)

50 = 2k

k = 25.

So, A =25√B.

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The value of the total area of the shaded region are,

⇒ 42 units²

We have to given that;

Sides of rectangle are,

AB = 9

BC = 6

Hence, The area of rectangle is,

⇒ 9 x 6

⇒ 54 units²

And, Area of triangle is,

A = 1/2 × 4 × 6

A = 12 units²

Thus, The value of the total area of the shaded region are,

⇒ 54 - 12

⇒ 42 units²

So, The value of the total area of the shaded region are,

⇒ 42 units²

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Answer: 1017.36 km²

Step-by-step explanation:

Area of Circle = πr² = 3.14×18×18 = 1017.36 km²

Answer:

x-4= 0

X= 4

from the function above

f(x) =4x^3+3x-2

4(4)^3 + 3(4) - 2

256+12- 2

==> 266

Answer:

Hiya There!!

_________________

4×⅛ = ½

_________________

“I think it’s a mistake to ever look for hope outside of one’s self.”

– Arthur Miller

Think of life as a mytery because well it sort of is! You don't know what may happen may be good or bad but be a little curious and get ready for whatever comes your way!!  ~Ashlynn

Answer:

38

Step-by-step explanation:

This might be wrong, But to my calculations it is

The diameter of the circle is approximately 60 inches.

To explain further, we can use the formula relating the central angle of a sector to the length of its intercepted arc. The formula states that the length of the intercepted arc (A) is equal to the radius (r) multiplied by the central angle (θ) in radians.

In this case, we are given the central angle (225 degrees) and the length of the intercepted arc (30π inches).

To find the diameter (d) of the circle, we need to find the radius (r) first. Since the length of the intercepted arc is equal to the radius multiplied by the central angle, we can set up the equation 30π = r * (225π/180). Simplifying this equation gives us r = 20 inches.

The diameter of the circle is twice the radius, so the diameter is equal to 2 * 20 inches, which is 40 inches. Therefore, the diameter of the circle is approximately 60 inches.

In summary, by using the formula for the relationship between central angle and intercepted arc length, we can determine the radius of the circle. Doubling the radius gives us the diameter, which is approximately 60 inches.

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a) The transition matrix for the Markov chain representing the end of a volleyball game can be constructed based on the given states. The matrix will have dimensions 6x6, with each element representing the probability of transitioning from one state to another. The transition probabilities depend on the probabilities of winning rallies for each team. The resulting transition matrix is as follows:

[ 0 0 0 0 1 0 ] [ 0 0 0 0 0 1 ] [ p 0 0 0 0 1-p ] [ 0 q 0 0 1-q 0 ] [ 0 0 0 0 1 0 ] [ 0 0 0 0 0 1 ]

In this matrix, each row represents a current state, and each column represents a possible next state. The element in the i-th row and j-th column represents the probability of transitioning from state i to state j.

b) To find the probability that the game will not be finished after three rallies when team B is serving and both teams are tied 15-15, we need to calculate the probability of being in the states "tied - B serving" after three rallies. Using the given transition matrix and probabilities p = q = 0.65, we can perform matrix multiplication to obtain the state probabilities after three transitions.

Starting with an initial state vector [0 0 0 1 0 0], representing being in the state "tied - B serving," we multiply it by the transition matrix three times to find the state probabilities after three rallies. The probability of the game not being finished is the sum of the probabilities in the states "tied - B serving," "A ahead by 1 point - A serving," and "B ahead by 1 point - B serving."

Performing the calculations, the probability that the game will not be finished after three rallies is approximately 0.1721 or 17.21%.

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The transition matrix for the Markov chain representing the end of a volleyball game, considering rally point scoring, can be derived based on the six states described: 1) tied - A serving, 2) tied - B serving, 3) A ahead by 1 point - A serving, 4) B ahead by 1 point - B serving, 5) A wins the game, and 6) B wins the game.

.

(a) To construct the transition matrix for the Markov chain, we consider the possible transitions between the six states. The matrix will have dimensions 6x6, with each element representing the probability of transitioning from one state to another. For example, the probability of transitioning from state 1 (tied - A serving) to state 2 (tied - B serving) can be calculated based on the probabilities p and q mentioned in the problem statement. By considering all possible transitions, the complete transition matrix can be obtained.

(b) In this scenario, we start with state 2 (tied - B serving) and need to find the probability that the game will not be finished after three rallies. To calculate this probability, we can use the transition matrix obtained in part (a) and perform matrix multiplication. By multiplying the initial state vector (corresponding to state 2) with the transition matrix three times, we can find the probabilities of ending up in each state after three rallies. The probability of the game not being finished after three rallies would be the sum of the probabilities in states 1 and 2, which represent tied scores.

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The equation of the circle with center (−1,−2) containing the point (0,6).

(x + 1)^2 + (y + 2)^2 = 65

Remember that the equation of a circle with radius R and center (a, b) is written as:

(x - a)^2 + (y - b)^2 = R^2

Here we know that the center of the circle is (-1, -2), then our equation is something like:

(x + 1)^2 + (y + 2)^2 = R^2

We know that our circle contains the point (0, 6), replacing these values in the equation above we get:

(0 + 1)^2 + (6 + 2)^2 = R^2

1 + 8^2 = R^2

65 = R^2

Then the circle equation is:

(x + 1)^2 + (y + 2)^2 = 65

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The length vector is 1. So the sketch vector field f is given below. So the option a is correct.

In the given question, the vector field F by drawing a diagram like this figure.

The given vector field F is:

F(x, y) = (yi + xj)/√(x^2 + y^2)

We can write the vector field as:

F(x, y) = yi/√(x^2 + y^2) + xj/√(x^2 + y^2)

Here

F(x, y) = [y/√(x^2 + y^2)]^2 + [x/√(x^2 + y^2)]^2

F(x, y) = y^2/(x^2 + y^2) + x^2/(x^2 + y^2)

F(x, y) = (y^2+ x^2)/(x^2 + y^2)

F(x, y) = 1

F(0, y) = y/|y| = ±1

F(x, 0) = x/|x| = ±1

So the length vector is 1.

So the sketch vector field f is given below:

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The complete question is:

Sketch the vector field F by drawing a diagram like this figure.

F(x, y) = (yi + xj)/√(x^2 + y^2)

Answer:

(-4, 3)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define Systems

6x + 8y = 0

-7x + y = 31

Step 2: Rewrite Systems

-7x + y = 31

Step 3: Redefine Systems

6x + 8y = 0

y = 7x + 31

Step 4: Solve for x

Substitution

Step 4: Solve for y

The optimal allocation is x = -1/2, y = 3/2, with a shadow price of 1.50.

To maximize profit, the firm needs to determine the optimal allocation of inputs x and y within the budget constraint of $100.

Let's assume the firm uses 'a' units of input x and 'b' units of input y. Since each unit of x costs $2 and each unit of y costs $3, the total cost constraint can be expressed as:

2a + 3b ≤ 100

To maximize profit, we need to differentiate the profit function P(x, y) with respect to both inputs and set the derivatives equal to zero:

∂P/∂x = 2y - 3 = 0 ---> y = 3/2

∂P/∂y = 2x + 1 = 0 ---> x = -1/2

However, x and y cannot have negative values, so these values are not feasible. To find the feasible values, we can substitute the values of x and y into the cost constraint:

2(-1/2) + 3(3/2) = 0 + 9/2 = 9/2 ≤ 100

This constraint is satisfied, so the feasible allocation is x = -1/2 and y = 3/2.

To find the shadow price, we need to determine the rate at which the maximum profit would change with respect to a one-unit increase in the budget constraint. We can do this by finding the derivative of the profit function with respect to the cost constraint:

∂P/∂(2a + 3b) = λ

Where λ represents the shadow price or the marginal value of an additional dollar in the budget. In this case, λ is the shadow price.

Taking the derivative of the profit function with respect to the cost constraint:

∂P/∂(2a + 3b) = ∂(2xy - 3x + y)/∂(2a + 3b) = 0

2y - 3 = 0 ---> y = 3/2

Thus, the shadow price (λ) is 3/2 or 1.50 when rounded to two decimal places.

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Answer:

Step-by-step explanation:

Ceiling area:  (28 ft)(16 ft) =           448 ft^2

End areas:  2(16 ft)(8 ft) =               256 ft^2

Long wall areas:  2(28 ft)(8 ft) =     448 ft^2

Total area (not incl. floor area) =  1152 ft^2

Answer:

D-a solar eclipse that happens every 18 months

Step-by-step explanation:

hope this helped helped,

have a great day!!

Answer:

1,500

Step-by-step explanation:

a + 5d = 39 (1)

a + 18d = 78 (2)

Subtract (1) from (2) to eliminate a

18d - 5d = 78 - 39

13d = 39

d = 39/13

d = 3

Substitute d = 3 into (1)

a + 5d = 39 (1)

a + 5(3) = 39

a + 15 = 39

a = 39 - 15

a = 24

Sum of the first 25 terms

Sn = n/2[2a + (n – 1)d]

S25 = 25/2{2*24 + (25-1)3}

= 12.5{48 + (24)3}

= 12.5{48 + 72)

= 600 + 900

= 1,500

S25 = 1,500

The probability of picking a cast member who sold more than 30 tickets is 2/5

Given that one cast member will be picked at random from the 20 cast members who sold tickets to receive a prize. We have to determine the probability of picking a cast member who sold more than 30 tickets.

To find the probability of picking a cast member who sold more than 30 tickets, we need to count the number of cast members who sold more than 30 tickets. Let A be the event of picking a cast member who sold more than 30 tickets. The number of cast members who sold more than 30 tickets is 8. Therefore, P(A) = 8/20 = 2/5.

The probability of picking a cast member who sold more than 30 tickets is 2/5.Answer: 2/5.

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Answer:

yes

Step-by-step explanation:

Answer: Hi, for these type of questions I can help you! I

Step-by-step explanation: hi, my answers are  correct but wont always give you a 100%. for any questions contact me and my legal team!

Answer:

$305.9022863 or $305.90 (rounded to 2 decimal places)

Step-by-step explanation:

It is a compound interest, meaning an interest accumulates on an initial amount every period. The formula  

A= P(1+R)^n

A= the total amount P=Initial amount       R= rate  n=time period

P=$100 R=15% or 0.15(decimal)  n=8 (years)  

A= 100 (1.15)^8

A= 100(3.059022863)

A=305.9022863

The amount you will have after 8 years is $220

The formula for calculating simple interest is expressed as:

SI =PRT

P is the principal = $100

T is the time = 8 years

R is the rate. = 15%

SI = 100 * 8 * 0.15
SI = $120

Amount after 8years = $100 + $120
Amount after 8years = $220

Hence the amount you will have after 8 years is $220

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Answer:

$1361.68

Step-by-step explanation:

15000 > 10000

so she gets the 8.5%

so she gets 108.5% of her salary

x/1255 = 108.5/100

1255(108.5) = 136,167.5

136,167.5/100 = 1361.68

The property of real numbers illustrated by each equation depends on the specific equation. However, some common properties of real numbers include the commutative property, associative property, distributive property, identity property, and inverse property.

The property of real numbers illustrated by each equation depends on the specific equation. However, there are several properties of real numbers that can be applied to equations:

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Answer:

X-Intercept: (4, 0), Y-Intercept: (0, -12)

$$f(x) = \begin{cases}\lambda e^{-\lambda x} &\quad x \geq 0\\0 &\quad x < 0\end{cases}$$where λ is the scale parameter of the distribution.

This was the probability density function (pdf) of an exponential distribution. The cumulative distribution function (cdf) is given by:$$F(x) = \begin{cases}1 - e^{-\lambda x} &\quad x \geq 0\\0 &\quad x < 0\end{cases}$$The mean and variance of an exponential distribution are:$$\mu = \frac{1}{\lambda}$$$$\sigma^2 = \frac{1}{\lambda^2}$$We are given that the lifetime of a digital watch is a random variable with exponential distribution. Let X be the lifetime of the watch and let λ be the scale parameter of the distribution. We are given that the probability that the watch will work after 4 years is 0.3. In other words, we want to find P(X > 4).Using the cdf of the exponential distribution, we have:$$P(X > 4) = 1 - P(X \leq 4) = 1 - F(4) = 1 - (1 - e^{-4\lambda}) = e^{-4\lambda}$$$$e^{-4\lambda} = 0.3$$$$-4\lambda = \ln(0.3)$$$$\lambda = \frac{\ln(0.3)}{-4} = 0.693147$$Therefore, the scale parameter of the exponential distribution is λ ≈ 0.693147. Answer more than 100 words:Given that the probability that the watch will work after 4 years is 0.3, we have found that the scale parameter of the exponential distribution is λ ≈ 0.693147. Using this value of λ, we can find the mean and variance of the lifetime of the watch. The mean is given by:$$\mu = \frac{1}{\lambda} = \frac{1}{0.693147} \approx 1.44$$Therefore, we expect the watch to last for about 1.44 years on average. The variance is given by:$$\sigma^2 = \frac{1}{\lambda^2} = \frac{1}{0.693147^2} \approx 2.00$$Therefore, the lifetime of the watch has a relatively high degree of variability, with a variance of about 2.00. In conclusion, we have found that the lifetime of a digital watch is a random variable with exponential distribution, and we have used the given probability to find the scale parameter of the distribution. We have also calculated the mean and variance of the distribution, which tell us the average lifetime of the watch and the degree of variability in its lifetime.

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The rate parameter of the exponential distribution for the lifetime of the digital watch is 0.2663.

To find the parameters of the exponential distribution, we can use the information provided.

Let X be the lifetime of the digital watch, and λ be the rate parameter of the exponential distribution.

Given that the probability that the watch will work after 4 years is 0.3, we can use the exponential survival function:

S(t) = e^(-λt)

We know that S(4) = 0.3.

Plugging in the values, we have:

e^(-4λ) = 0.3

To solve for λ, we can take the natural logarithm (ln) of both sides:

ln(e^(-4λ)) = ln(0.3)

-4λ = ln(0.3)

Now, we can solve for λ:

λ = -ln(0.3) / 4

λ = -ln(0.3) / 4

= 0.2663

Hence, the rate parameter of the exponential distribution for the lifetime of the digital watch is 0.2663.

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