where do you put a decimal on 64

1. Price constraint: Pc = $8

2. when Pc = $8, C ≈ 10.22, and S ≈ 40.88.

Price constraint: Pc = $9

3. when Pc = $9, C = 9.2, and S = 36.8.

Price constraint: Pc = $2

4. When Pc = $2, C ≈ 30.67, and S ≈ 122.68.

To graph Susan's consumption curve and budget constraints, we'll use the given information:

The price of a cup of coffee is denoted as Pc = $8.

The price of a spoonful of sugar is denoted as Ps = $0.25.

Susan's budget for coffee and sugar combined is $92.

Let's start by plotting the consumption curve for prices re = Sl, rc = 32, and rc = So. We'll calculate the number of cups of coffee (C) and the number of spoonfuls of sugar (S) corresponding to each price point.

Price constraint: Pc = $8

Since Susan spends exactly four spoonfuls of sugar (S) for each cup of coffee (C), we can express S in terms of C: S = 4C.

Using the budget constraint equation, we have: 8C + 0.25S = 92.

Substituting S = 4C into the equation: 8C + 0.25(4C) = 92.

Simplifying the equation: 8C + C = 92.

Combining like terms: 9C = 92.

Solving for C: C = 92 / 9, approximately 10.22.

Therefore, when Pc = $8, C ≈ 10.22, and S ≈ 40.88.

Price constraint: Pc = $9

Using the same approach, we substitute the new price into the equation.

9C + 0.25(4C) = 92.

Simplifying the equation: 9C + C = 92.

Combining like terms: 10C = 92.

Solving for C: C = 92 / 10, which is exactly 9.2.

Therefore, when Pc = $9, C = 9.2, and S = 36.8.

Price constraint: Pc = $2

Applying the same method:

2C + 0.25(4C) = 92.

Simplifying the equation: 2C + C = 92.

Combining like terms: 3C = 92.

Solving for C: C = 92 / 3, approximately 30.67.

Therefore, when Pc = $2, C ≈ 30.67, and S ≈ 122.68.

Now, we can plot these points on a graph with the number of cups of coffee (C) on the horizontal axis and the number of spoonfuls of sugar (S) on the vertical axis:

Consumption curve: Connect the three plotted points (10.22, 40.88), (9.2, 36.8), and (30.67, 122.68).

Budget constraint for Pc = $8: Plot the point (10.22, 40.88) and draw a straight line from the origin to that point.

Budget constraint for Pc = $9: Plot the point (9.2, 36.8) and draw a line from the origin to that point.

Budget constraint for Pc = $2: Plot the point (30.67, 122.68) and draw a line from the origin to that point.

Make sure to label the axes and the curves accurately.

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After doing the equitation the at rate of $15 per week.

How to do graph representation?

Graph representation is a way of visualizing data as a graph or chart. It is used to easily identify relationships between data points and to illustrate trends in the data. Graphs can be used to present data in a variety of ways, such as bar graphs, line graphs, pie charts, scatter plots and more. Graphs are especially useful when trying to compare two or more sets of data and to highlight any patterns or trends that may exist. Additionally, graphs are often used to represent numerical data in a more visually appealing way. By using graphs, it is easier to identify relationships, trends and outliers in the data. Graphs also help to make data easier to interpret and understand.

Carson owes = $110

At rate of $15 per week.

The graph representation will follows:

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The correct answer is (b) The central limit theorem is applicable for the sample mean.

The condition that the population size be at least 10 times the sample size is necessary to ensure that the sample mean follows a normal distribution, as required by the central limit theorem. The central limit theorem states that the sample mean will be approximately normally distributed, regardless of the underlying population distribution, as long as the sample size is large enough. In this case, the condition is necessary to ensure that the sample size is sufficiently large for the central limit theorem to be applicable. Options (a), (c), (d), and (e) are not the correct answers because they do not directly relate to the condition that the population size be at least 10 times the sample size.

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The commission earned are R41123.17, R47931.67 and R15024.09

The VAT included prices are given as:

R271 800,00; R316 800,00 and R99 300,00.

The VAT rate is 12.36%.

So, the price before VAT is calculated as:

VAT included = Price without VAT * (1 + 12.36%)

This gives

VAT included = Price without VAT * 1.1236

So, we have:

Price without VAT = VAT included/1.1236

For the three cars, we have:

Price without VAT = R271 800.00/1.1236 = R241901

Price without VAT = R316800.00 /1.1236 = R281951

Price without VAT = R99300.00/1.1236 = R88377

Hence, the prices of the cars before VAT was added are R241901, R281951 and R88377

This is calculated as:

Commission = Price * 17%

So, we have:

Commission = R241901 * 17% = R41123.17

Commission = R281951 * 17% = R47931.67

Commission = R88377 * 17% = R15024.09

Hence, the commission earned are R41123.17, R47931.67 and R15024.09

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Now, price of desk in furniture store

= $169 + (24% of $169)

= $169 + (24/100 × $169)

= $169 + $4056/100

= $169 + $40.56

= $209.56

Hence, answer is $209.56.

Answer:For random variable X~N(3,0.75), what is the probability that X takes on a value within two standard deviations on either side of the mean?

Step-by-step explanation:

Answer:

Mean: 20

Median: 16

Mode: No mode

Step-by-step explanation:

For the mean:

44 + 4 + 27 + 5 = 80

80/4 = 20

For the median:

5 + 27 = 32

32/2 = 16

For the mode:
None of the numbers are repeated.

Using Conditional probability,

The probability that after a fair coin is tossed 5 times that the result will contain 3 'heads' given that the first toss was a 'head' is 3/5.

A fair coin is tossed five times .

so, total possible outcomes = 2⁵ = 32

Let A: head observed on first toss

B: 3 heads observed.

Probability that the first toss was head (p) = 1/2

we have to find out probability that on 5 tosses result contain 3 heads given that first toss wss head .

Using Binomial Probability distribution

P (X= x) = ⁿCₓ (p)ˣ (q)⁽ⁿ⁻ˣ⁾

x = 3 , n = 5

we get , P(B) = P(X= 3 ) = ⁵C₃(1/2)³(1/2)²

=> P(B) = 10 ×(1/2)⁵= 5/16

since the first toss is fixed as a head.

P(A ∩ B) =P( X₁ = 1 and X₂+ X₃ + X₄ + X₅) = P(X₁= 1)P(X₂+X₃+X₄+X₅)

= 1/2 × ⁴C₂ (1/2)⁵ = 3 (1/2)⁴

The required probability is , Conditional probability P(B/A) = P(A ∩ B)/P(A)

= 3(1/2)⁴/ 5/16 = 3/5

Hence , the required probability is 3/5.

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The steps to condensing the expressions
2loga(4)+3loga(X-4)loga(4)

Log(x+3)+log(x-3) is given below.

To condense the   expressions, we can apply the  properties of logarithms. Here are the condensed forms of the given expressions.

2loga (4) + 3loga(X - 4) - loga 4 )  

By using the product and quotient rules of logarithms, we can simplify this expression as follows

2 loga( 4) + 3 loga( X-4) - log a(4)

= loga(4 ²) + loga((X-4)³) -  loga (4) = loga (16 ) + loga((X-4)³) - loga (4)

Combining the logarithms  using the power rule and quotient rule we have

= loga(16(X-4)³/4)

log(x+3) + log (x-3)

By using the product rule of logarithms, we can combine these logarithms

log (x +3) +log (x - 3) = log ((x +3 )(x -3 ))

Simplifying further, we get

= log (x² - 9 )

So this means that the condensed forms of the given expressions are

2loga( 4) + 3loga(X -4) - loga (4) = loga(16 (X-4) ³/4)

log (x+ 3) + log(x- 3) = log(x² - 9)

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Oliver's result of 85.4° for angle A is wrong. This is because the sum of angles of a triangle should add up to 180°.

Triangles are classified according to the lengths of their sides and the measure of their angles.

In this triangle, we have two angles, angle A and angle B. If angle A is 85.4°, then angle B must be 94.6°. But, the angles of a triangle should add up to 180°, which is not the case here.

We can solve for angle A using the Law of Cosines:

Cos A = (b² + c² - a²)/2(bc)

A = \(cos^{-1}[(15^2 + 10^2 - 12^2)/2(15)(10)]}\)

A = \(cos^{-1}(0.6)}\)

A = 36.86°

Therefore, the correct size of angle A is 36.86°. Oliver's result of 85.4° is incorrect.

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The correct answer is the Beta-binomial model. Bayesian analysis is a statistical approach that incorporates prior knowledge or beliefs about a parameter of interest and updates it based on observed data using Bayes' theorem.

In the case of a binary choice, where the outcome can be either yes or no, Bayesian analysis seeks to estimate the probability of success (yes) based on available information.

The Beta-binomial model is a commonly used model in Bayesian analysis for binary data. It combines the Beta distribution, which represents the prior beliefs about the probability of success, with the binomial distribution, which describes the likelihood of observing a specific number of successes in a fixed number of trials.

The Beta distribution is a flexible distribution that is often used as a prior for modeling probabilities because of its ability to capture a wide range of shapes. The Beta distribution is characterized by two parameters, typically denoted as alpha and beta, which can be interpreted as the number of successes and failures, respectively, in the prior data.

The binomial distribution, on the other hand, describes the probability of observing a specific number of successes in a fixed number of independent trials. In the context of Bayesian analysis, the binomial distribution is used to model the likelihood of observing the data given the parameter of interest (probability of success).

By combining the prior information represented by the Beta distribution and the likelihood information represented by the binomial distribution, the Beta-binomial model allows for inference about the probability of success in a binary choice.

The other options mentioned, such as the Normal-normal model and the Gaussian model, are not typically used for binary data analysis. The Normal-normal model is more suitable for continuous data, where both the prior and likelihood distributions are assumed to follow Normal distributions. The Gaussian model is also suitable for continuous data, as it assumes that the data are normally distributed.

In summary, the Beta-binomial model is the appropriate model for Bayesian analysis of a binary choice because it effectively combines the Beta distribution as a prior with the binomial distribution as the likelihood, allowing for inference about the probability of success in the binary outcome.

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Answer:

answer is 2.30 using sine =opp/hyp

Answer:

The first one; NM = 8.

Step-by-step explanation:

\(2(x+3)=3x+1\\2x+6=3x+1\\x=5\\\)

JN and NM are equal. Plug in 5 to x + 3 and solve to get 8.

There are 1,048,576 ways a student can answer the 15 questions.

To determine the total number of ways a student can answer the 15 questions, we need to consider the number of possible ways to answer each type of question and then multiply them together. There are 10 true-false questions, and for each question, there are two possible answers (true or false). Therefore, the number of ways to answer these questions is 2^10, which is equal to 1024.

There are 5 multiple-choice questions, and each question has 4 possible choices. Therefore, the number of ways to answer these questions is \(4^5\), which is equal to 1024.

To determine the total number of ways a student can answer all 15 questions, we multiply the number of ways to answer the true-false questions by the number of ways to answer the multiple-choice questions:

Total number of ways = \(2^{10} \times 4^5\)

= 1024 x 1024

= 1,048,576

This means that a student has a vast number of possible ways to answer the questions, and they should carefully consider their choices to ensure that they answer them correctly.

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The area of the triangle whose vertices are (-3, 5), (3, -6), and (7, 2) is 14.

To find the area of a triangle given the coordinates of its vertices, we can use the formula:

Area = 1/2 * |(x1y2 + x2y3 + x3y1) - (y1x2 + y2x3 + y3x1)|

where (x1,y1), (x2,y2), and (x3,y3) are the coordinates of the three vertices.

Substituting the given coordinates, we get:

Area = 1/2 * |(-3*-6 + 32 + 75) - (5*3 - (-6)7 + 2(-3))|

= 1/2 * |(-18 + 6 + 35) - (15 + 42 - 6)|

= 1/2 * |23 - 51|

= 1/2 * |-28|

= 14

Therefore, the area of the triangle is 14 square units.

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The work done by the force can be found to be 206. 45 foot-pounds.

To find the work done by the force, the formula is:

Work = Force × Distance × cos (θ)

The angle was 55° , the distance was 20 feet and the force was 18 pounds. This is included in the question and so can be used to find the work done to be :

= 18 × 20 × cos ( 55 °)

= 18 × 20 × 0. 573576

= 206. 44568

= 206. 45 foot - pounds

In conclusion, the work done by the force was approximately 206. 45 foot - pounds.

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The work that is done by the force is 280.2 J.

When a force acts on an object and causes it to move a specific distance, the amount of energy that is transmitted is known as the work done. It is described as the result of the amount of force that is exerted on an item and the distance that the object moves in the force's direction.

We have;

W = FdCosθ

W = work done

F = force

d = distance

θ = Angle turned

F = 18 Ib = 80.1 N

d = 20 feet = 6.1 m

θ = 55°

W = 80.1 N * 6.1 m * Cos 55

= 280.2 J

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Answer:

the answer is 12 degrees

The measure of angle ACB when the secant BC and the tangent AC intersect is 12°

When a secant and a tangent meet outside the circle, thwe product of the length of the secant and its external segment equals the square of the length of the tangent segment.

Therefore,

arc XA = 2(64) = 128 degrees.

Hence,

m∠C = 1 / 2 (152 - 128)

m∠C = 1 / 2 (24)

m∠ACB = 12°

Therefore, angle ACB is 12 degrees.

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Answer:

C

Step-by-step explanation:

Here, we want to select the correct statement that best defines if the given points are a function

We have this answer as;

The ordered pairs do not represent a function because one input value has two different output values

What they are trying to say here is that for us to have a function, no x-value should have 2 y-values although a y-value can have 2 x-values

But according to the points given, a certain x-value has 2 y-values which does not make the relation correct as a function

Answer: 12.5%

Step-by-step explanation:

Formula for Half Life

N = N₀ \((\frac{1}{2} ^{\frac{t}{t_{1/2} } } )\)

N = number of isotopes after

N₀ = Initial Isotopes

t = number of years

\(t_{1/2}\) =  half life years

Given

t=6000

\(t_{1/2}\) = 2000

Percent is part out of the whole  = remaining/starting amoung

Percent fraction =  \(\frac{N}{N_{0} }\)

\(\frac{N}{N_{0} } = \frac{1}{2} ^{\frac{t}{t_{1/2} } }\)

\(\frac{N}{N_{0} } = \frac{1}{2} ^{\frac{6000}{2000 } }\)

\(\frac{N}{N_{0} } =\) .125 =12.5%

Answer:

2.09 is the answer now what

Answer:

Step-by-step explanation:

The zero of a function is also known as the x-intercept of a function. The x-intercept of a function exists where y = 0. So we will begin by setting each of those lines = 0:

4x - 20 = 0     and     -1/2x + k = 0 and then solve each for x:

4x = 20 so

x = 5 and

-1/2x = -k and

1/2x = k so

x = 2k. Now we set the 2 x expressions equal to each other and solve for k:

5 = 2k so

k = 5/2

The value of the K in the given equation is 5/2.

The zero of a function is also known as the x-intercept of a function.

The x-intercept of a function exists where y = 0. So we will begin by setting each of those lines = 0:

4x - 20 = 0     and  

-1/2x + k = 0 and then solve each for x:

The substitution method is the algebraic method to solve simultaneous linear equations. As the word says, in this method, the value of one variable from one equation is substituted in the other equation.

4x = 20 so

x = 5 and

-1/2x = -k and

1/2x = k so

x = 2k. Now we set the 2 x expressions equal to each other and solve for k

5 = 2k so

k = 5/2

Therefore the value of the K in the given equation is 5/2.

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If the incenter, circumcenter, centroid, and orthocenter are always inside the triangle, the correct answer is an acute triangle (option B).

In an acute triangle, all three angles are less than 90 degrees. The incenter, which is the center of the inscribed circle, lies inside the triangle. The circumcenter, which is the center of the circumscribed circle, also lies inside the triangle.

The centroid, which is the point of intersection of the medians, is located inside the triangle as well. Finally, the orthocenter, which is the point of intersection of the altitudes, is inside the triangle in an acute triangle.

In contrast, a right triangle has one angle measuring 90 degrees, an obtuse triangle has one angle greater than 90 degrees, and an isosceles triangle has two equal side lengths. These types of triangles may have some of the points (incenter, circumcenter, centroid, orthocenter) located outside the triangle.

Therefore, the correct answer is option B, acute triangle.

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Answer:

1,608.5 cm³

Step-by-step explanation:

radius = 16 : 2 = 8 cm

base area = 8² · π = 64 ·π = 201.06193 cm²

Volume = 201.06193 · 8  = 1,608.495439 cm³

In a manufacturing process where the probability of a defect in an aluminum beverage can is 0.00004, we are interested in finding the probabilities associated with producing a certain number of defective cans out of a total of 100,200 cans.

In this scenario, we can use the binomial distribution to calculate the probabilities. The binomial distribution is used to model situations where there are a fixed number of independent trials (can production) with two possible outcomes (defective or non-defective).

Let's denote X as the random variable representing the number of defective cans. The probability mass function of the binomial distribution is given by:

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

where n is the total number of cans produced, p is the probability of a defective can, and C(n, k) is the binomial coefficient.

a) To find the probability of exactly x defective cans, substitute the values into the formula mentioned above: P(X = x) = C(100200, x) * (0.00004)^x * (1 - 0.00004)^(100200 - x).

b) To find the probability of at most x defective cans, we need to calculate the cumulative probability: P(X ≤ x) = P(X = 0) + P(X = 1) + ... + P(X = x).

c) To find the probability of more than x defective cans, we can subtract the cumulative probability from 1: P(X > x) = 1 - P(X ≤ x).

By plugging in the appropriate values and performing the calculations, we can determine the desired probabilities associated with producing a certain number of defective cans out of 100,200 cans.

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i) Swornima's annual income is: Rs 6,24,000.

ii) The tax rebate for Swornima is: Rs 12,400.

iii) Swornima should pay Rs 0 as her annual income tax after applying the 10% rebate.

(i) The parameters given are:

Monthly basic salary = Rs 48,000

Dashain allowance (1 month's salary) = Rs 48,000

The Total annual income is expressed by the formula:

Total annual income = (Monthly basic salary × 12) + Dashain allowance

Thus:

Total annual income = (48000 × 12) + 48,000

Total annual income = 576000 + 48,000

Total annual income = Rs 624000

(ii) We are told that she is entitled to a 10% rebate on her income tax.

10% rebate on income has Income tax slab rates in the range:

Rs 500001 to Rs 700000

Thus:

Income taxed at 10% = Rs 624,000 - Rs 500,000

Income taxed at 10% = Rs 1,24,000

Tax rebate = 10% of the income taxed at 10%

Tax rebate = 0.10 × Rs 124000

Tax rebate = Rs 12,400

(iii) The annual income tax is calculated by the formula:

Annual income tax = Tax on income from Rs 5,00,001 to Rs 7,00,000 - Tax rebate

Annual income tax = 10% of (Rs 624,000 - Rs 500,000) - Rs 12,400

Annual income tax = 10% of Rs 124,000 - Rs 12,400

Annual income tax = Rs 12,400 - Rs 12,400

Annual income tax = Rs 0

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a) The amount of water in the tank will be 0 after 5 minutes.

b) As time increases, the amount of water decreases at a rate of -60 L/min.

Here we can see a graph of a linear function that relates the amount of water in an aquarium (vertical axis) with the time (horizontal axis).

The amount of water in the aquarium will reach the 0 liters mark when the line intercepts the x-axis.

We can see that happens for x =  5 minutes

b) We can see that as we move to the right (time flows to the right in that graph) the line goes downwards. This means that the amount of water on the tank decreases as the time increases.

We can see that in 5 minutes, the amount of water goes from 300 lites to 0 liters, so the rate at which the water comes out of the tank is:

R = 300L/5min = 60 liters per minute.

It should actually be written with a negative sign so we are 100% clear that it means that the water is coming out from the tank, so the rate is:

R = -60 L/min

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Answer: 12/16

Step-by-step explanation: 3 x 4 = 12 and 4 x 4 = 16

Answer:

42.68

Step-by-step explanation:

21.34 * 2= 42.68