What is the fractional equivalent of the repeating decimal n = 0.1515... ? Answer the questions to find out. 1. How many repeating digits does the number represented by n have? Write your answer in the space below. 2. You need to multiply n by a power of 10 to help you find the fraction. Decide on the power of 10 to multiply by, and tell how you identified that number. Write your answer in the space below. 3. Write an equation where the left side is your power of 10 times n and the right side is the result of multiplying 0.1515... by that power. Write your answer in the space bel 4. Write the original equation, n = 0.1515... underneath your equation from question 3. Then subtract the equations. 5. Write n as a fraction in simplest form.

Answer:

Chris - y marbles

Becky - x marbles

Dan - z marbles

y = 2 x

z = y + 7

x + y + z = 57

z = 2 x + 7

x + 2 x + 2 x + 7 = 57

5 x + 7 = 57

5 x = 57 - 7

5 x = 50

x = 50 : 5

x = 10,  y = 20,  z = 27

This means that Dan is not correct.

Step-by-step explanation:

Answer:

no

Step-by-step explanation:

you can start by setting the equation to "?+ ? + ? = 57"

this is because we know for sure that all of the marbles combined is 57

then you can say that b is a variable to show how many marbles Becky has

so now your equation is "? + ? + b = 57"

we know that Chris has two times as many marbles as Becky, so that is like saying "Chris = b + b".... this is the same as 2b

we can put that into the equation and get "? + 2b + b = 57"

Dan has seven more marbles than Chris so its like saying "Dan = 2b + 7"

we can put this into the equation and get "2b + 7 + 2b + b = 57"

you solve this equation to get b = 10

this means that Becky has 10 marbles, Chris has 20, and Dan has 27

(we know this by plugging in the value of b into the equations for Dan and Chris)

Now back to the original question: Dan said that he can give some marbles to Becky in order to make them all have the same amount of marbles, is Dan right?

the answer is no

Dan can only give seven marbles to Becky because if he gives seven marbles to Becky, Dan and Chris will have the same amount, 20. But Becky will only have 17.

Answer:

1st one

Step-by-step explanation:

Since 6 = 225, when going to 12 it would be 450, meaning the last one is wrong. when going up to 18, it would be 675, meaning that the 3rd one is wrong. It also means that the second one is wrong because it goes to 20 but has the same value as going to 18. Through process of elimination, the 1st option is correct

The probability that Eli's playlist will still be playing at 11 p.m. is approximately 0, indicating it's very unlikely for the playlist to be still playing at that time.

To find the probability that Eli's playlist will still be playing at 11 p.m., we need to calculate the cumulative probability up to 11 p.m. based on the average length and standard deviation of the songs.

First, let's convert the given time into minutes for easier calculation. 11 p.m. is 60 minutes after 9:50 p.m., so it corresponds to 70 minutes.

Next, we need to calculate the mean (average) length of a song in minutes. The average length in seconds is given as 197 seconds, so we divide it by 60 to get the average length in minutes:

Mean (μ) = 197 seconds / 60 = 3.28 minutes

The standard deviation (σ) is given as 33 seconds, which also needs to be converted to minutes:

Standard Deviation (σ) = 33 seconds / 60 = 0.55 minutes

Now, we can use these values to calculate the probability using the Normal distribution.

We want to find P(X > 70), where X represents the length of a song.

Using the Z-score formula:

Z = (X - μ) / σ

where Z is the standard score or Z-score, X is the value we're interested in, μ is the mean, and σ is the standard deviation.

Plugging in the values:

Z = (70 - 3.28) / 0.55 ≈ 126.87

To find the probability, we need to calculate the area under the curve to the right of the Z-score. We can use a Z-table or a calculator to find this value.

Assuming a standard normal distribution, the probability can be calculated as follows:

P(Z > 126.87) = 1 - P(Z < 126.87)

Using a Z-table or a calculator, we can find that P(Z < 126.87) is virtually 1 (it's extremely close to 1), so:

P(Z > 126.87) ≈ 1 - 1 ≈ 0

Therefore, the probability that Eli's playlist will still be playing at 11 p.m. is approximately 0, indicating it's very unlikely for the playlist to be still playing at that time.

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a. To find the relationship between Q and p, we can express Q as a function of p using the equation Q = e^(-BQ).

b. Expressing p as a function of Q, we have p = e^(-BQ).

c. To differentiate e^(-BQ) with respect to Q, we use the chain rule. The derivative is dp/dQ = -B * e^(-BQ).




The log-linear demand for a product can be expressed as ln(Q) = -BQ, where Q represents the quantity demanded and B is a constant coefficient. In order to find the relationship between price (p) and quantity (Q) and calculate the derivative dp/dQ, let's follow the steps below:

a. Express Q as a function of p:

To find the relationship between Q and p, we need to exponentiate both sides of the equation ln(Q) = -BQ. This gives us:

Q = e^(-BQ).

Now, we can solve for Q in terms of p by substituting p for Q:

p = e^(-Bp).

To calculate dp/dQ, we differentiate the expression with respect to Q:

dp/dQ = d/dQ(e^(-BQ)).

b. Express p as a function of Q and find dp/dQ:

To express p as a function of Q, we start with the equation p = e^(-Bp) and solve for p:

p = e^(-BQ).

To find dp/dQ, we differentiate the expression with respect to Q:

dp/dQ = d/dQ(e^(-BQ)).

c. Show mathematical steps for differentiation:

To differentiate e^(-BQ) with respect to Q, we can use the chain rule. Let's denote f(Q) = e^(-BQ), then:

df/dQ = (df/dQ)(dQ/dQ) = (d/dQ(e^(-BQ))) * 1 = -B * e^(-BQ).

Therefore, dp/dQ = -B * e^(-BQ).

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The natural length of the spring is 10 cm.

When the spring is stretched from 12 cm to 16 cm, the work done is 24 J. This means that the spring constant is 24 J / (16 cm - 12 cm) = 600 N/m.

When the spring is stretched from 16 cm to 20 cm, the work done is 40 J. This means that the additional work done to stretch the spring from 16 cm to 20 cm is 40 J - 24 J = 16 J.

The additional work done is equal to the work done to stretch the spring over a distance of 4 cm. The force required to stretch the spring over a distance of 4 cm is 16 J / 4 cm = 4 J/cm.

The spring constant is equal to the force required to stretch the spring divided by the distance over which the spring is stretched. The spring constant is 4 J/cm / 600 N/m = 0.00067 m = 0.67 mm.

The natural length of the spring is equal to the distance at which the spring is not stretched. The natural length of the spring is 140 mm - 4 cm = 10 cm.

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While the sum of two independent Bernoulli random variables might resemble a binomial distribution intuitively, it is not a true binomial distribution unless the probabilities of success are equal.

The sum of two random variables that follow different Bernoulli distributions with varying probabilities of success does not have a binomial distribution because the conditions for a binomial distribution are not met.

To understand this, let's consider two independent Bernoulli random variables: X with probability of success p1 and Y with probability of success p2, where p1 and p2 are not equal. The sum Z = X + Y represents the total number of successes in two independent trials.

In a binomial distribution, all the trials should be identical, meaning they must have the same probability of success (let's call it p). This allows us to define a fixed number of trials (n) and calculate the probability of obtaining a specific number of successes (k). The probability mass function (PMF) of a binomial distribution is given by:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k),

where C(n, k) represents the binomial coefficient (n choose k).

In our case, since the probabilities of success for X and Y are different (p1 and p2, respectively), we cannot directly apply the binomial PMF formula. The random variable Z does not satisfy the condition of having a fixed number of trials with a single probability of success.

However, we can still analyze the distribution of Z using the probability mass function (PMF) or cumulative distribution function (CDF) approach. By considering all possible outcomes of X and Y and their respective probabilities, we can determine the distribution of Z. It would be a discrete distribution that depends on the specific values of p1 and p2.

Therefore, while the sum of two independent Bernoulli random variables might resemble a binomial distribution intuitively, it is not a true binomial distribution unless the probabilities of success are equal.

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Answer:

the third answer

5+18 *dont know if that 8 or 5 sorry*

Step-by-step explanation:

Answer:

Triangle CBD = Triangle DAC by rule SSS

Step-by-step explanation:

Line segment CD bisects line segment AD.

Given that, triangles ΔABC ≅ ΔBAD so that C and D lie in the opposite semi-planes of segment AB.

Two triangles are said to be congruent if pairs of their corresponding sides and their corresponding angles are equal. They are of the same shape and size.

According to the question ΔABC ≅ ΔBAD.

So, the sides of triangles are congruent.

They are, AB ≅ BA, AC ≅ BD and BC ≅ AD

Similarly, the following angles are corresponding

∠ABC ≅ ∠BAD

By vertical angle theorem, we have the following corresponding angles:

∠AEC ≅ ∠BED

∠EAC ≅ ∠EBD

Notice that points A and D are common in the above angles

So, we have AE ≅ BE

Hence, line segment CD bisects line segment AD.

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"Your question is incomplete, probably the complete question/missing part is:"

Triangles ΔABC ≅ ΔBAD so that C and D lie in the opposite semi-planes of segment AB. Prove that segment CD bisects segment AD.

Answer:

A

Step-by-step explanation:

the line hits the point between the 6 and 8 notch marks so the y-intercept is (0,7).

a line increasing goes upward from left to right, so the line is increasing from x = -10 to x = -2 if you follow the notches down/up.

then you follow where the line starts decreasing (downward left to right) and you see its from the points x = -2 to x = 10.

i hope this helps :))

Answer:

in easy words 3/4÷

6 / /6

Answer:

ratio of girls to boys = 14:10 or 7:5 (simplified)

ratio of boys to class = 10:24 or 5:12 (simplified)

Step-by-step explanation:

Answer:

This means the cost of the item to you is $57.75. You will pay $57.75 for a item with original price of $82.50 when discounted 30%. In this example, if you buy an item at $82.50 with 30% discount, you will pay 82.50 - 24.75 = 57.75 dollars.

Answer:

The answer “10m + 5 > 100”

x2 ≈ 17.969712 is the approximate solution of ln(x) = 9 - x using Newton's method with x0 = 10.

To obtain an approximate solution of ln(x) = 9 - x using Newton's method, we start with an initial guess x0 = 10 and iterate until convergence.

The formula for Newton's method is:

x_(n+1) = x_n - f(x_n) / f'(x_n)

First, let's obtain the derivative of f(x) = ln(x) - 9 + x.

The derivative of ln(x) is 1/x, so:

f'(x) = 1/x - 1

Now, we can plug the values into the Newton's method formula to obtain x2:

x1 = x0 - (f(x0) / f'(x0))

   = 10 - ((ln(10) - 9 + 10) / (1/10 - 1))

   = 10 - ((ln(10) + 1) / (-9/10))

   ≈ 10 - (2.30259 + 1) / (-0.9)

   ≈ 10 - 3.30259 / (-0.9)

   ≈ 10 + 3.669544 / 0.9

   ≈ 10 + 4.077271

   ≈ 14.077271

Now, using x1 as the new approximation, we repeat the process:

x2 = x1 - (f(x1) / f'(x1))

   = 14.077271 - ((ln(14.077271) - 9 + 14.077271) / (1/14.077271 - 1))

   ≈ 14.077271 - ((2.64748 + 1) / (-0.93644))

   ≈ 14.077271 - (3.64748 / -0.93644)

   ≈ 14.077271 + 3.892441

   ≈ 17.969712

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The elasticity of substitution measures the substitutability between inputs or goods and is calculated based on the ratio of prices or consumption and the marginal rate of substitution.

The elasticity of substitution is a concept used in economics to measure the degree to which one input can be substituted for another in the production process or consumption choices. It quantifies the responsiveness of the relative changes in the ratio of inputs to the relative changes in their marginal rates of substitution. The elasticity of substitution helps economists understand the flexibility of producers or consumers in adjusting their input or consumption mix in response to changes in relative prices or preferences.

The elasticity of substitution (σ) is calculated using the following formula:

σ = (d ln(α₁/α₂))/(d ln(MRS₁₂))

Where:

α₁/α₂ represents the ratio of input prices or consumption prices.

MRS₁₂ represents the marginal rate of substitution between the two inputs or goods.

The interpretation of the elasticity of substitution depends on its value.

1. If the elasticity of substitution (σ) is greater than 1, it implies a high degree of substitutability between inputs or goods. In other words, producers or consumers can easily adjust their mix of inputs or consumption choices in response to changes in relative prices or preferences. A higher σ indicates a more elastic substitution pattern.

2. If the elasticity of substitution (σ) is equal to 1, it implies a constant elasticity of substitution. This suggests a linear relationship between inputs or goods, where the proportionate change in one input or good is equal to the proportionate change in the other input or good.

3. If the elasticity of substitution (σ) is less than 1, it implies a low degree of substitutability between inputs or goods. In this case, producers or consumers face constraints in adjusting their input or consumption mix. A lower σ indicates a less elastic substitution pattern.

Understanding the elasticity of substitution is crucial for various economic analyses. For instance, in production, a higher elasticity of substitution implies that firms can more easily adjust their production techniques by substituting one input for another. This has implications for cost minimization and efficiency. In consumption, the elasticity of substitution helps explain how consumers respond to changes in prices or preferences by adjusting their consumption mix.

In summary, the elasticity of substitution measures the substitutability between inputs or goods and is calculated based on the ratio of prices or consumption and the marginal rate of substitution. Its interpretation depends on its value, with values greater than 1 indicating high substitutability, equal to 1 indicating constant elasticity, and less than 1 indicating low substitutability. The elasticity of substitution provides insights into production decisions, cost minimization, and consumption choices.

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Answer:

a or c

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

The rocket better weigh more after it is fueled. So the weight must be 6.1*10^4 after fueling.

6.1 * 10^4 - 4.8*10^4

The easiest way to do this is to take it out of scientific notation.

61000 - 48000 = 13000 kg

If you insist on scientific notation, it is 6.1*10^4 - 4.8*10^4 = 1.3 * 10^4 which makes the answer C

a) The function f(x-4)+5 represents a horizontal shift of 4 units to the right and a vertical shift of 5 units upward.

b) The function g(x+3)-8 represents a horizontal shift of 3 units to the left and a vertical shift of 8 units downward.

c) The function k(x+9)-4 represents a horizontal shift of 9 units to the left and a vertical shift of 4 units downward.

Shift notation is used to describe the horizontal and vertical shifts of a function. The number inside the parentheses indicates the horizontal shift, while the number outside the parentheses indicates the vertical shift.

A negative value inside the parentheses shifts the graph to the right, while a positive value shifts it to the left. A positive value outside the parentheses shifts the graph upward, and a negative value shifts it downward. Additionally, a negative value inside the parentheses reflects the graph over the x-axis.

Shift notation provides a way to describe how a function is transformed horizontally and vertically. When given a function in the form f(x+a)+b, the value of "a" inside the parentheses represents the horizontal shift. If "a" is positive, the graph of the function will shift to the left by that amount. Conversely, if "a" is negative, the graph will shift to the right.

The value of "b" outside the parentheses represents the vertical shift. If "b" is positive, the graph will shift upward by that amount. If "b" is negative, the graph will shift downward.

In the case of a negative value for "a" (e.g., f(x-4)), the graph will be reflected over the x-axis. This means that any points on the original graph with a y-coordinate of "y" will now have a y-coordinate of "-y" on the reflected graph.

Taking the examples provided, let's interpret the shift notation:

a) f(x-4)+5: This means the graph of f(x) will shift 4 units to the right and 5 units upward.

b) g(x+3)-8: The graph of g(x) will shift 3 units to the left and 8 units downward.

c) k(x+9)-4: The graph of k(x) will shift 9 units to the left and 4 units downward.

By using shift notation, we can easily describe the transformations applied to a function, indicating both horizontal and vertical shifts.

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Answer:  see answers below

Step-by-step explanation:

(i) The first leaf of the tree is:  black = 5/9 and white = 4/9

   That means that there are 5 black marbles out of 9 total marbles and 4 white marbles out of 9 total marbles.

Total marbles = 9

Black marbles = 5

White marbles = 4

*******************************************************************************************

(ii)  

P(B₂/B₁)

The probability that the 2nd marble is black given that the 1st marble was black.

P(W₂/B₁)

The probability that the 2nd marble is white given that the 1st marble was black.

P(B₂/W₁)

The probability that the 2nd marble is black given that the 1st marble was white.

P(W₂/W₁)

The probability that the 2nd marble is white given that the 1st marble was white.

***********************************************************************************************

                (iii)  Outcomes            (iv)   Probability        

                         (B, B)                    (5/9) x (1/2) = 5/18

                         (B, W)                    (5/9) x (1/2) = 5/18

                         (W, B)                    (4/9) x (5/8) = 5/18

                         (W, W)                  (4/9) x (3/8) = 3/18

                                                    Check:  Total = 18/18 = 1  [tex]\checkmark[/tex]

**********************************************************************************************

(iv)  Dependent

     Once the first ball is drawn, there is one less ball for the second draw.  Therefore, the second draw is dependent on the first draw.

Answer:

(0,-1)

Step-by-step explanation:

Answer:

(0,-1)

Step-by-step explanation:

Sarah will have approximately 365,531.2 lbs of usable forage as part of her sustainable management plan.

The first step to calculate the total annual production on Sarah's ranch is to determine the production from each plant community.

For the rhizomatous wheat/green needlegrass community, which covers 61% of the ranch, the production is 1000 lbs/acre. Therefore, the total production from this community is:

1000 lbs/acre x 61% x 11,845 acres = 721,045 lbs/year

For the Big Sagebrush community, which covers 29% of the ranch, the production is 500 lbs/acre. Therefore, the total production from this community is:

500 lbs/acre x 29% x 11,845 acres = 170,925 lbs/year

For the blue grama sod community, which covers 10% of the ranch, the production is 600 lbs/acre. Therefore, the total production from this community is:

600 lbs/acre x 10% x 11,845 acres = 71,070 lbs/year

To find the total annual production on Sarah's ranch, we add up the production from each community:

721,045 lbs/year + 170,925 lbs/year + 71,070 lbs/year = 962,040 lbs/year

Now, moving on to why Sarah cannot use all of the plant biomass produced. One reason is that some of the biomass is needed to maintain healthy range condition. Removing all the biomass can lead to overgrazing and degradation of the range. Additionally, leaving some biomass behind ensures there is enough plant material for wildlife habitat, soil stabilization, and regrowth.

If Sarah decides to use 38% of her total biomass produced, the amount of usable forage can be calculated as follows:

38% x 962,040 lbs/year = 365,531.2 lbs/year

Therefore, Sarah will have approximately 365,531.2 lbs of usable forage as part of her sustainable management plan.

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Answer: -880.75

Step-by-step explanation:

Step 1: Simplify 20.25 - 912 - 912 to -891.75

-891.75+11−891.75+11

Step 2: Simplify.

-880.75

Answer:

-880.75

Step-by-step explanation:

The expression can be rewritten as log_5((y^6)/(x^6))  by applying properties of   logarithms

To rewrite the expression as a single logarithm, we can apply the properties of logarithms:

Start with the given expression: 6 * log_5(y) - 3 * log_5(x^2)

Use the power rule of logarithms: log_b(a^c) = c * log_b(a)

Applying this rule to the expression, we get: log_5(y^6) - log_5((x^2)^3)

Simplify the expression inside the second logarithm: log_5(y^6) - log_5(x^6)

Apply the quotient rule of logarithms: log_b(a) - log_b(c) = log_b(a/c)

Using this rule, we can combine the logarithms: log_5((y^6)/(x^6))

Therefore, the expression 6 * log_5(y) - 3 * log_5(x^2) can be rewritten as log_5((y^6)/(x^6)).

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Answer:

3:37

Step-by-step explanation:

Since it started 18 minutes before it ended, you need to subtract 18 minutes from 3:55 which makes the starting time 3:37 P.M

Answer:

3:37

Step-by-step explanation:

If you subtract 18 from 55, you get 37.

Given information, we are required to find the Joint Probability Mass Function of (X, Y), where X and Y are the smaller and larger number of points, respectively, when two dice are rolled.

The sample space of rolling two dice is {1, 1}, {1, 2}, {1, 3}, {1, 4}, {1, 5}, {1, 6}, {2, 1}, {2, 2}, {2, 3}, {2, 4}, {2, 5}, {2, 6}, {3, 1}, {3, 2}, {3, 3}, {3, 4}, {3, 5}, {3, 6}, {4, 1}, {4, 2}, {4, 3}, {4, 4}, {4, 5}, {4, 6}, {5, 1}, {5, 2}, {5, 3}, {5, 4}, {5, 5}, {5, 6}, {6, 1}, {6, 2}, {6, 3}, {6, 4}, {6, 5}, {6, 6}. Let A = {1, 2, 3, 4, 5, 6} be the sample space of a dice, which means the probability of each outcome is 1/6.

Now, we need to calculate the probability of rolling i and j, where X is the smaller number, and Y is the larger one. Therefore, P (X = i, Y = j) = P (i, j) - P (i, i) - P (j, j) if i≠j, where P (i, j) represents the probability of rolling i and j.

However, if i = j, then P (X = i, Y = i) = P (i, i). For i=1,2,3,4,5,6, P (X = i, Y = i) = 1/6.

We can also write P (X = i, Y = i) = P (X = i)P (Y = i). Therefore, P (X=i, Y=j)=P(i,j)−P(i,i)−P(j,j)={1/36 if i≠j}{1/18 if i=j}.

(b) X and Y are not independent since knowing X affects Y. If X is known to be 2, then Y can only be in the range of 3 to 6. Therefore, P(Y=5|X=2) ≠ P(Y=5). This shows that X and Y are not independent.

(c) Let p(i) represent the probability mass function of X, which is the probability of the smaller number being i. For i = 1, 2, 3, 4, 5, 6, P(X=i)=P(X=i,Y>i)+P(X=i,Y=i)={5/36 if i=1}{4/36 if i=2}{3/36 if i=3}{2/36 if i=4}{1/36 if i=5}{0 if i=6}

(d) The required probability of P(Y=5|X=2) = P(X=2,Y=5)/P(X=2). The probability of X=2 is P(X=2) = 4/36 = 1/9. Since X=2, the favorable outcome is {(2, 5)}, therefore, P(X=2,Y=5) = 1/36. The required probability is P(Y=5|X=2) = P(X=2,Y=5)/P(X=2) = (1/36)/(1/9) = 1/4 = 0.25. Hence, the probability that Y=5 when X=2 is 0.25.

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The quadratic function in standard form with zeros -2 and 8 is:

f(x) = (x + 2)(x - 8) = x^2 - 6x - 16

The standard form of a quadratic function is ax^2 + bx + c = 0, where a, b, and c are real numbers. The zeros of a quadratic function are the values of x that make the function equal to 0. In this case, the zeros are -2 and 8.

To find the quadratic function, we can use the following steps:

1. Write the quadratic function in factored form. The factored form of a quadratic function with zeros a and b is (x - a)(x - b). In this case, the zeros are -2 and 8, so the factored form is:

(x + 2)(x - 8)

2. Expand the factored form to get the standard form. Expanding the factored form gives us the standard form:

f(x) = x^2 - 6x - 16

Therefore, the quadratic function in standard form with zeros -2 and 8 is f(x) = x^2 - 6x - 16.

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Answer:

12 or 13

Step-by-step explanation: