The circumference, C, of a circle is Crd, where d is the diameter.
Solve Crd for d.
O A. d-
OB. d=C-n
O C. d-C
R
OD. d = nC

a. The MRS is constant (not diminishing) at 1/3.

U(x,y) = 3x + y

The MRS for this utility function can be found by taking the partial derivative of x concerning y:

MRS = ∂U/∂y / ∂U/∂x = 1 / 3

The MRS is constant (not diminishing) at 1/3.

b. The MRS is diminishing because as y increases, the MRS decreases.

U(x,y) = x * y

The MRS for this utility function can be found by taking the partial derivative of x concerning y:

MRS = ∂U/∂y / ∂U/∂x = 1 / y

The MRS is diminishing because as y increases, the MRS decreases.

c. The MRS is diminishing because as y increases, the MRS decreases.

U(x,y) = x * y

The MRS for this utility function can be found by taking the partial derivative of x concerning y:

MRS = ∂U/∂y / ∂U/∂x = 1 / y

Similar to the previous case, the MRS is diminishing because as y increases, the MRS decreases.

d. The MRS depends on the ratio of y to x and can vary.

U(x,y) = x^2 - y^2

The MRS for this utility function can be found by taking the partial derivative of x concerning y:

MRS = ∂U/∂y / ∂U/∂x = -2y / 2x = -y / x

The MRS depends on the ratio of y to x and can vary. It is not necessarily diminishing.

e. The MRS depends on the values of x and y and can vary.

U(x,y) = x + y / (x * y)

The MRS for this utility function can be found by taking the partial derivative of x concerning y:

MRS = ∂U/∂y / ∂U/∂x = -1 / (y^2) + 1 / (x^2 * y)

The MRS depends on the values of x and y and can vary. It is not necessarily diminishing.

Now let's move on to the second part of the question:

For parts a, b, and c, we need more specific information about the utility functions, such as the values of α and β, to calculate the demand curves for x and y, the indirect utility function, and the expenditure function.

To show that the demand curve is homogeneous in degree zero in terms of income and prices, we need the specific functional form of the utility functions and information about the prices of x and y. Please provide the necessary details for parts A, b, and c to continue the analysis.

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Answer:

Your answer is A

Step-by-step explanation:

The reason is because 1/10 is 3 muffins so if it was 7/10 it would be 21 8/10 is 24 and 9/10 is 27 and 10/10 is 30 muffins

Answer: The answer is 30

Step-by-step explanation:

You do 21 x 10 and the answer is on top of 7: 120/7

Then do 120 divided by seven and there is your answer.

The total profit received by both Satyam and Rajan is approximately Rs. 8295 (Satyam's profit) + Rs. 4483.30 (Rajan's profit) = Rs. 12778.30.

Let's break down the information given and calculate the total profit received by both Satyam and Rajan.

1. Satyam's investment:

- Satyam initially invested Rs. 40000.

- After 2 years, Satyam withdrew 25% of the amount, which is 0.25 * Rs. 40000 = Rs. 10000.

- Therefore, Satyam's remaining investment after the withdrawal is Rs. 40000 - Rs. 10000 = Rs. 30000.

2. Rajan's investment:

- Rajan invested 25% less than Satyam initially, which is 0.75 * Rs. 40000 = Rs. 30000.

- After 2.5 years, Rajan added Rs. 5000 to his initial investment, so his total investment became Rs. 30000 + Rs. 5000 = Rs. 35000.

3. Profit calculation:

- Rajan received a profit of Rs. 8295 after 6 years.

- Satyam's investment remained constant at Rs. 30000 for the entire 6 years.

To calculate the profit received by Satyam, we need to find the proportion of his investment to Rajan's investment:

Satyam's proportion = Satyam's investment / (Satyam's investment + Rajan's investment)

                  = Rs. 30000 / (Rs. 30000 + Rs. 35000)

                  = 0.46 (approx.)

Now, we can calculate the profit received by Satyam:

Satyam's profit = Satyam's proportion * Total profit

              = 0.46 * Rs. 8295

              = Rs. 3811.70 (approx.)

Finally, we can calculate the profit received by Rajan:

Rajan's profit = Total profit - Satyam's profit

             = Rs. 8295 - Rs. 3811.70

             = Rs. 4483.30 (approx.)

Therefore, the total profit received by both Satyam and Rajan is approximately Rs. 8295 (Satyam's profit) + Rs. 4483.30 (Rajan's profit) = Rs. 12778.30.

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According to Erikson's psychosocial theory, infants go through the first stage of development known as "trust versus mistrust" from birth to 18 months.

During this stage, infants learn to trust or mistrust the world based on the quality of care they receive from their primary caregivers. Jack's mom checking on him every time he cries to see if he needs to be fed or changed is demonstrating a nurturing and attentive caregiving style, which fosters trust in the infant. By consistently meeting Jack's basic needs, his mother is helping him develop a sense of trust and security in the world around him.

This stage is crucial for the child's later development because if they develop a sense of mistrust, it can lead to feelings of anxiety and insecurity in their future relationships. Conversely, if they develop a sense of trust, it can lead to feelings of security and confidence in their future relationships. Therefore, it is essential for caregivers to provide a consistent and nurturing environment to help infants develop a sense of trust.

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To estimate f(62) based on the given information, we can use linear approximation. Linear approximation uses the tangent line to approximate the function value near a known point.

The equation of the tangent line at x = 58 is given by:

y - f(58) = f'(58)(x - 58)

Substituting the given values, we have:

y - 37 = -102(x - 58)

Now, let's solve for y when x = 62:

y - 37 = -102(62 - 58)

y - 37 = -102(4)

y - 37 = -408

y = -408 + 37

y = -371

Therefore, based on the linear approximation, we estimate that f(62) is approximately -371.

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Answer:

Step-by-step explanation:

The answer is the difference between Total water and Ocean Water.

Fresh water = Total Water - Ocean Water

Total Water  =   361

Ocean Water = 335        Subtract

Fresh water   =    26       millions of Km^2

Answer:

the odds against Zahra climbing to the top are,

B. 4:1

Step-by-step explanation:

Since she has climbed 7 times in 28 attempts,

the probability of a successful climb is,

P = 7/28

P = 1/4

So, the odds against Zahra climbing to the top are 4:1

a. The​ most three sum the probabilities for k = 0 to 3.

b. A sum the probabilities for k = 2 to 4.

c. The mean of the random variable Y= 3.15

d. The standard deviation of Y= 1.179

To solve these probability questions, use the binomial distribution formula the probability of an event (p) is 0.35, and 9 trials (n) representing the traffic fatalities.

P(Y = 3) = C(n, k) × p²k ×(1 - p)²(n - k)

= C(9, 3) × (0.35)³ × (1 - 0.35)²(9 - 3)

= 84 × 0.35³ × 0.65³

= 0.265

P(Y ≥ 3) = P(Y = 3) + P(Y = 4) + P(Y = 5) + ... + P(Y = 9)

= ∑[k = 3 to 9] C(9, k) × (0.35)²k * (1 - 0.35)²(9 - k)

To calculate this, to sum the probabilities for k = 3 to 9 using the formula above.

P(Y ≤ 3) = P(Y = 0) + P(Y = 1) + P(Y = 2) + P(Y = 3)

= ∑[k = 0 to 3] C(9, k) × (0.35)²k × (1 - 0.35)²(9 - k)

to sum the probabilities for k = 0 to 3.

P(2 ≤ Y ≤ 4) = P(Y = 2) + P(Y = 3) + P(Y = 4)

= ∑[k = 2 to 4] C(9, k) × (0.35)²k × (1 - 0.35)²(9 - k)

the probabilities for k = 2 to 4.

Mean (μ) = n × p

= 9 × 0.35

= 3.15

The mean represents the expected value of Y, which is the average number of traffic fatalities involving an intoxicated or alcohol-impaired driver or nonoccupant.

Standard Deviation (σ) = √(n × p × (1 - p))

= √(9 × 0.35 × 0.65)

=1.179

The standard deviation measures the spread or variability of the random variable Y.

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The given system of equations is expressed as

y = x + 5

y = x + 1

We would apply the method of substitution. It means that

x + 5 = x + 1

x - x = 1 - 5

0 = - 4

We know that 0 is not equal to - 4. Therefore, there is no solution

Answer:

Step-by-step explanation:

Given the graph of the equation y = -2. To determine how the line will look like on Cartesian plane, first we must understand the following;

The standard form of equation of a line is y = mx+c where m is the slope and c is the intercept. Comparing this standard form to the given equation shows that the equation is in slope-intercept form.

It can also written as y = 0x-2. This shows that slope  m = 0 and the y-intercept c = -2. The graph can be graphed as y = 0x-2

The line will be an horizontal line drawn on the negative y-axis at the coordinate x = 0 and y = -2. The line will therefore be parallel to the x axis

Check the attachment for the graph.

The graph of the equation \(\boldsymbol{y=-2}\) is a line parallel to the \(\boldsymbol{x-}\)axis

A graph is a pictorial representation of data or values in a well - organized manner.

The graph of the equation passes through a point \(\boldsymbol{(a,b)}\) if it satisfies it.

The graph of the equation of the form \(\boldsymbol{x=a}\) is parallel to the \(\boldsymbol{y-}\)axis.

The graph of the equation of the form \(\boldsymbol{y=a}\) is parallel to the \(\boldsymbol{x-}\)axis.

So, the graph of the equation \(\boldsymbol{y=-2}\) is a line parallel to the \(\boldsymbol{x-}\)axis

Option 1) is correct.

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Answer:

The answer is C. (-2, 7)

Good luck :)

Answer: We can solve this problem using the standard normal distribution and standardizing the variable X.

Let Z be a standard normal variable, which is obtained by standardizing X as:

Z = (X - μ) / σ

where μ is the mean of X and σ is the standard deviation of X.

In this case, X is normal with mean μ = 3.6 and variance σ^2 = 0.01, so its standard deviation is σ = 0.1.

Then, we have:

Z = (X - 3.6) / 0.1

To find C such that P(X <= c) = 5%, we need to find the value of Z for which the cumulative distribution function (CDF) of the standard normal distribution equals 0.05. Using a standard normal table or calculator, we find that:

P(Z <= -1.645) = 0.05

Therefore:

(X - 3.6) / 0.1 = -1.645

X = -0.1645 * 0.1 + 3.6 = 3.58355

So C is approximately 3.5836.

To find C such that P(X > c) = 10%, we need to find the value of Z for which the CDF of the standard normal distribution equals 0.9. Using the same table or calculator, we find that:

P(Z > 1.28) = 0.1

Therefore:

(X - 3.6) / 0.1 = 1.28

X = 1.28 * 0.1 + 3.6 = 3.728

So C is approximately 3.728.

To find C such that P(-c < X < c) = 95%, we need to find the values of Z for which the CDF of the standard normal distribution equals 0.025 and 0.975, respectively. Using the same table or calculator, we find that:

P(Z < -1.96) = 0.025 and P(Z < 1.96) = 0.975

Therefore:

(X - 3.6) / 0.1 = -1.96 and (X - 3.6) / 0.1 = 1.96

Solving for X in each equation, we get:

X = -0.196 * 0.1 + 3.6 = 3.5804 and X = 1.96 * 0.1 + 3.6 = 3.836

So the interval (-c, c) is approximately (-0.216, 3.836).

Answer:

This is not possible, since probabilities cannot be negative. Therefore, there is no value of e that satisfies the given condition

Step-by-step explanation:

We can use the standard normal distribution to solve this problem by standardizing X to Z as follows:

Z = (X - μ) / σ = (X - 3.6) / 0.1

Then, we can use the standard normal distribution table or calculator to find the values of Z that correspond to the given probabilities.

P(X <= c) = P(Z <= (c - 3.6) / 0.1) = 0.05

Using a standard normal distribution table or calculator, we can find that the Z-score corresponding to the 5th percentile is -1.645. Therefore, we have:

(c - 3.6) / 0.1 = -1.645

Solving for c, we get:

c = 3.6 - 1.645 * 0.1 = 3.4355

So, the value of c such that P(X <= c) = 5% is approximately 3.4355.

Similarly, we can find the value of d such that P(X > d) = 10%. This is equivalent to finding the value of c such that P(X <= c) = 90%. Using the same approach as above, we have:

(d - 3.6) / 0.1 = 1.28 (the Z-score corresponding to the 90th percentile)

Solving for d, we get:

d = 3.6 + 1.28 * 0.1 = 3.728

So, the value of d such that P(X > d) = 10% is approximately 3.728.

Finally, we can find the value of e such that P(-e < X < e) = 90%. This is equivalent to finding the values of c and d such that P(X <= c) - P(X <= d) = 0.9. Using the values we found above, we have:

P(X <= c) - P(X <= d) = 0.05 - 0.1 = -0.05

This is not possible, since probabilities cannot be negative. Therefore, there is no value of e that satisfies the given condition

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To find the value of the car after 1 year, subtract the amount it depreciates from the value of the car:

20,025 - 1,385 = 18,640

After 1 year the car is valued at $18,640

Answer:

$18640

Step-by-step explanation:

For year 1: Depreciated  value is $1385.

We will minus that amount from the actual worth of car i.e. $20,025

So,

= $20,025 - $1385

= $18640

Hope this helps you.

Answer:

Step-by-step explanation:

Given: Kite WXYZ

Prove: That at least one of the diagonals of a kite decomposes the kite into 2 congruent triangles.

A diagonal is a straight line from one vertex to another of a given shape or figure.

Considering diagonal WY of the kite,

<WYZ ≅ <WYX (diagonal WY is the bisector of <Y)

<ZWY ≅ <XWY (diagonal YW is the bisector of <W)

WZ ≅ WX (congruent property)

YZ ≅ YX (congruent property)

Thus,

ΔWYZ ≅ ΔWYX (Angle-side-Angle congruent property)

Therefore, the given kite can be decompose into 2 congruent triangles (ΔWYZ and ΔWYX).

It is Given that two lines segment, AC and BD bisect each other at C.

The missing statement is ∠ACB ≅ ∠ECD

Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.

Given two lines segment, AC and BD bisect each other at C.

We have to prove that ΔACB ≅ ΔECD

In triangle ACB and ECD

AC=CE    (Given)

BC=CD   (Given)

so, as seen in options the angle ∠ACB ≅ ∠ECD due to vertically opposite angles

hence, the missing statement is ∠ACB ≅ ∠ECD

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Answer:

C.∠ACB ≅ ∠ECD

Step-by-step explanation:

The dog's running speed of 5 km/hr can be converted to approximately 3.125 mi/hr by multiplying it by the conversion factor of 1 mi/1.6 km. Rounding to the nearest thousandth, the dog can run at about 3.125 mi/hr.

To convert the dog's running speed from kilometers per hour (km/hr) to miles per hour (mi/hr), we need to use the conversion factor of 1.6 km = 1 mi.First, we can convert the dog's speed from km/hr to mi/hr by multiplying it by the conversion factor: 5 km/hr * (1 mi/1.6 km) = 3.125 mi/hr.

However, we need to round the answer to the nearest thousandth (three decimal places). Since the digit after the thousandth place is 5, we round up the thousandth place to obtain the final answer.

Therefore, the dog can run at approximately 3.125 mi/hr.

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Answer:

320 square inches

Step-by-step explanation:

10*8=80

80*4=320

final answer: 320 square inches

Answer: the night temperature was 3 degrees below the afternoon temperature

Step-by-step explanation:

Step-by-step explanation:

5x+2+x-26+30=360

6x+2=360

X=59.67 approximately 60

Answer:

319 pages and a half

Step-by-step explanation:

If the distance an athlete throws a hammer follows a normal distribution with mean= 50 feet and standard deviation= 5 feet, then the probability he throws it between 50 feet and 60 feet is 0.4772

To find the probability he throws it between 50 feet and 60 feet, follow these steps:

Hence, the probability he throws a hammer between 50 feet and 60 feet is 0.4772

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Answer:

- 2

Step-by-step explanation:

Using the rules of exponents

\(a^{m}\) ⇔ \(\frac{1}{a^{m} }\)

0.25 = \(\frac{1}{4}\) = \(\frac{1}{2^{2} }\) = \(2^{-2}\)

Answer:

\( \huge{= \frac{ {a}^{2} - {b}^{2} }{ {a}^{2b} + {ab}^{2} }} \)

Step-by-step explanation:

\(\huge{ \frac{ {a}^{2} - {b}^{2} }{ {a}^{2b} + {ab}^{2} } \div \frac{ {a}^{2b} - {ab}^{2} }{ {a}^{2b} - {ab}^{2} }} \)

\( \huge{\frac{ {x}^{2} - {b}^{2} }{ {a}^{2b} + {ab}^{2} } \div 1}\)

\( \huge{\boxed{\green{= \frac{ {a}^{2} - {b}^{2} }{ {a}^{2b} + {ab}^{2} }}}} \)

Answer:

Rational numbers

Step-by-step explanation:

A rational number is a number that can be written as a ratio. That means it can be written as a fraction, in which both the numerator (the number on top) and the denominator (the number on the bottom) are whole numbers. The number 8 is a rational number because it can be written as the fraction 8/1.

Answer:

The volume is multiplied by 8.

Step by step explanation:

Let the length equal l, the width equal w, and the height equal h for the original rectangular prism.

The volume of a right rectangular prism with length l, width w, and height h is V=lwh.

Therefore, the volume of the original prism is lwh.

The new rectangular prism has dimensions that are twice those of the original rectangular prism: the length equals 2l, the width equals 2w, and the height equals 2h.

To calculate the volume of the rectangular prism, substitute the doubled values into the formula for the volume of a rectangular prism.

V=2l·2w·2h

Simplify.

V=8lwh

The new volume is 8lwh.

If the length, width, and height of a right rectangular prism are doubled, the volume is multiplied by 8.

Therefore, the new volume is the original volume multiplied by 8.

The sample standard deviation is 12.13 (rounded to 2 decimal places) .

Sample variance (s²) and sample standard deviation (s) are the two measures of variability of a set of data. They are the estimators of population variance (σ²) and population standard deviation (σ) when the data used in the calculation is a sample of the population.

Here, we have to find the sample variance and standard deviation of the following set of data:7, 45, 14, 49, 32, 22, 30, 31, 33, 32.Sample variance and standard deviation formulae:

The sample variance formula is given by:s² = Σ (xi - X)² / (n - 1)

where,X is the sample mean;xi is the ith data value;n is the sample size.

The sample standard deviation is given by:

s = √(Σ (xi - X)² / (n - 1))

where,X is the sample mean;xi is the ith data value;n is the sample size.

Now, let's use these formulae to calculate the sample variance and standard deviation of the given data set.Sample mean,

X = (7 + 45 + 14 + 49 + 32 + 22 + 30 + 31 + 33 + 32) / 10

  = 285 / 10

   = 28.5

So, the sample mean is 28.5.

Now, calculating the sample variance:

s² = Σ (xi - X)² / (n - 1)s²

   = [(7 - 28.5)² + (45 - 28.5)² + (14 - 28.5)² + (49 - 28.5)² + (32 - 28.5)² + (22 - 28.5)² + (30 - 28.5)² + (31 - 28.5)² + (33 - 28.5)² + (32 - 28.5)²] / (10 - 1)s²

  = (440.5 + 210.5 + 290.5 + 420.5 + 12.25 + 37.25 + 5.25 + 6.25 + 17.25 + 12.25) / 9s²

  = 146.875

Thus, the sample variance is 146.875 (rounded to 2 decimal places).

Now, calculating the sample standard deviation:

s = √(Σ (xi - X)² / (n - 1))

s = √(146.875)s = 12.13

Thus, the sample standard deviation is 12.13 (rounded to 2 decimal places) .

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Answer:

A

Step-by-step explanation:

24.8 x 7 = 173.6