what is the sample size need to reduce the margin of error to 3.1% for a 95% confidence interval given that the proportion is unknown.

Answer:

5.6

Step-by-step explanation:

11*7=77

11.8*7= 82.6

82.6-77=5.6

The minutes that have passed, m, when Tank A contains the following amounts of water will be:

151 liters = 3 minutes

191.5 liters = 7.5 minutes

270.25 liters = 16.25 minutes

p liters = (p-124) / 9 min

It should be noted that for 151 lit = (151 - 124)/9 = 3 min

Also, for 191.5 lit = (191.5-124) /9

= 67.5/9 = 7.5 min = 7 min 30 sec

It should be noted that for 270.25 lit = (270.25 - 124)/9 = 146.25/9 = 16.25 = 16 min 15 sec

For p lit = (p-124) / 9 min

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Tank A initially contained 124 liters of water. It is then filled with more water, at a constant rate of 9 liters per minute.

How many minutes have passed, m, when Tank A contains the following amounts of water?

151 liters

191.5 liters

270.25 liters

p liters

Follow • 1

Answer:

X30

Step-by-step explanation:

Answer: inscribed angle

Answer:

the above answer is correct

Step-by-step explanation:

I got it right on the test

Answer:

false

Step-by-step explanation:

Answer:

equal

Step-by-step explanation:

3(x+2)=3x+6

3x+6=3x+6

-3x -3x

6=6

Answer:

a) 7/12 or 58.333%

b) red: 33.333% or 4/12   white: 25% or 3/12

Step-by-step explanation:

Answer:

The inverse function is 1/5x

Step-by-step explanation:

f(x) = 5x

We want to find the inverse

y = 5x

Exchange x and y

x = 5y

Solve for y

Divide by 5

1/5x = y

The inverse function is 1/5x

The expense function consists of two parts: the monthly payment for the car loan and the monthly cost of depreciation. The monthly payment can be calculated using the following formula: P = (r(PV)) / (1 - (1+r)^(-n)) = $1,062.66 per month. The depreciation function will be a straight line from $54,000 to $0 over a period of 10 years (or 120 months).

A depreciation function is a mathematical model that explains how the worth of an object decreases over time. It denotes the pace at which the worth of an asset depreciates over time.

In the given question,

a. The expense function will consist of two parts: the monthly payment for the car loan and the monthly cost of depreciation. The monthly payment can be calculated using the following formula:

\(P = (r(PV)) / (1 - (1+r)^(-n))\)

where P is the monthly payment, r is the monthly interest rate (4.875%/12 = 0.40625%), PV is the present value of the loan (54,000 - 8,000 = 46,000), and n is the total number of payments (4 years x 12 months per year = 48). Plugging these values into the formula, we get:

\(P = (0.0040625(46000)) / (1 - (1 + 0.0040625)^(-48)) = $1,062.66 per month\)

The depreciation function will be a straight line from $54,000 to $0 over a period of 10 years (or 120 months), so the monthly depreciation can be calculated as:

d = (54000 - 0) / 120 = $450 per month

Therefore, the expense function E(x) and depreciation function D(x) are:

E(x) = 1062.66 + 450x

D(x) = 450x

where x is the number of months since the car was purchased.

b. The graph of the expense function and depreciation function on the same axes is attached.

c. At the intersection point (around 66 months), the monthly loan payment becomes greater than the monthly depreciation cost, meaning that Winnie is paying more each month than the car is depreciating. After 66 months, the expense function is increasing faster than the depreciation function, so the total value of the car is decreasing rapidly. By the end of 120 months, the car will have depreciated to a value of $0 and Winnie will have paid a total of $62,719.20 in loan payments.

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Using equation of 39.4 inches.,  the height of the candle after 26 hours will be 39.4 inches.

The graph of a linear function is a straight line. Both the independent and dependent variables of a linear function are one. X and Y are the independent and dependent variables, respectively.

Assume the candle will be 12 cm tall after 20 hours.

Use the formula: y - y1 = m(x - x1) where m = -.0.4; x = 18; y = 21.8 to find the point/slope:

y - 21.8 = -0.4 (x - 18)

The equation (y = length after x hours) is

y - 21.8 = -0.4 (x - 18)

y - 21.8 = -0.4 x + 7.2

y = -0.4x + 29

y = -0.4x + 29

the candle's height after 26 hours

After 15 hours, y = - 0.4(26) + 29

y = 10.4 + 29

y = 39.4 inches.

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The mathematical expression of the statement "Ten more than the sum of m and n" is 10 + m + n

To do this, we simply analyze the statements one after the other.

We have:

Combine both expressions:

10 + m + n

Hence, the mathematical expression is 10 + m + n

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The length of the required chord is approximately equal to 11.8 units.

In Mathematics and Geometry, the chord of a circle refers to a line segment that typically join any two (2) points on a circle.

Based on the equation of the circle, the radius can be determined as follows;

x² + y² = 36

Radius, r = √36

Radius, r = 6 units.

By applying Pythagorean's theorem, side OA can be calculated as follows;

6² - 1² = OA²

OA² = 36 - 1

OA = √35

OA = 5.9

Length of chord = 2 × OA

Length of chord = 2 × 5.9

Length of chord = 11.8 units.

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The tangent function is periodic and the period of the tangent function is π.

Since y=tan x is a many-one function and tan x has a periodic function with period π, the graph of the tangent function repeats itself at regular intervals of length units.

Because the tangent function is an odd function and the graph of y=tan x is symmetric about the origin.

Since its range is from -∞ to ∞, the tangent function is an unbounded function.

In a complete circular rotation, it make Two cycles. In the factors of π, it repeats its interval. Example, π, 2π, 3π.

The period of the tangent function is π.

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Answer:

\(m < 1 = 36\)

\(m < 2 = 56\)

\(m < 3 = 124\)

\(m < 4 = 88\)

\(m < 5 = 36\)

The z-test statistic for the given hypothesis test is -2.45. The test statistic value lies in the critical region, which indicates that we reject the null hypothesis.


Given,
n = 250 and
x = 39
We know that,
z = (x - μ) / (σ / √n)  ----(1)
The formula for finding μ, the mean of the population proportion, is:
μ = np
Where n is the sample size and p is the population proportion.
Here,
n = 250 and
p = 0.11
So, μ = (250) (0.11) = 27.5
The formula for finding σ, the standard deviation of the population proportion, is:
σ = √[ np(1-p) ]
σ = √[ (250) (0.11) (0.89) ]
σ = 4.83
Using the values found for μ and σ in equation (1) yields:
z = (39 - 27.5) / (4.83 / √250)
z = 11.5 / 0.305
z = -2.45 (rounded to two decimal places)
Therefore, the z-test statistic for the given hypothesis test is -2.45. The test statistic value lies in the critical region, which indicates that we reject the null hypothesis.

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The vocabulary terms have been matched to the correct definitions as follows;

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(a) The power series solution for the Associated Laguerre Equation must terminate because the equation satisfies the necessary termination condition for a polynomial solution.

(b) The general expression for the power series coefficients in terms of the first coefficient can be obtained by using recurrence relations derived from the differential equation.

(a) The power series solution for the Associated Laguerre Equation, when expanded as a polynomial, must terminate because the differential equation is a second-order linear homogeneous differential equation with polynomial coefficients. Such equations have polynomial solutions that terminate after a finite number of terms.

(b) To find the general expression for the power series coefficients in terms of the first coefficient, one can use recurrence relations derived from the differential equation. These recurrence relations relate each coefficient to the preceding coefficients and the first coefficient. By solving these recurrence relations, one can express the coefficients in terms of the first coefficient and obtain a general expression.

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1. The probability of selecting exactly one tank with high-viscosity material is 0.

2. The probability of selecting at least one tank with high-viscosity material is 1.

3. The probability of selecting exactly one tank with high-viscosity material and exactly one tank with high impurities is 0.25.

1. The probability of selecting exactly one tank with high-viscosity material is calculated by the binomial distribution formula, P(X = n) = (nCx)p^x(1-p)^n-x, where n is the number of trials, x is the number of successes, and p is the probability of success. In this case, n = 4, x = 1, and p = 24/24 = 1. Therefore, P(X = 1) = (4C1)1^1(1-1)^4-1 = 0.

2. The probability of selecting at least one tank with high-viscosity material is calculated by the complement rule, P(X > 0) = 1 - P(X = 0). In this case, P(X > 0) = 1 - (4C0)1^0(1-1)^4-0 = 1.

3. The probability of selecting exactly one tank with high-viscosity material and exactly one tank with high impurities is calculated by the binomial distribution formula, P(X = n) = (nCx)p^x(1-p)^n-x, where n is the number of trials, x is the number of successes, and p is the probability of success. In this case, n = 8, x = 2, and p = 24/24 = 1. Therefore, P(X = 2) = (8C2)1^2(1-1)^8-2 = 0.25.

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Answer:

(-6, 2)

Step-by-step explanation:

\(M=\left(\frac{-8-4}{2}, \frac{-6+10}{2} \right)=(-6, 2)\)

As per the unitary method, a family would typically receive an allotment of 160 acres, which is equivalent to one-quarter of a section.

To determine the number of acres a family would receive under the Dawes Act, we need to consider the concept of "sections" and the specific provisions outlined in the Act.

Typically, a family was granted a "homestead" or an allotment, which was a specific portion of land within the reservation. The size of the allotment varied, but the most common allocation was 160 acres, which is equivalent to one-quarter of a section. This allocation was intended to provide enough land for a family to cultivate and sustain themselves.

To better understand the mathematical aspect, let's break it down:

1 section = 640 acres

1/4 section = 160 acres

Therefore, a family under the Dawes Act would typically receive an allotment of 160 acres, which is one-quarter of a section. However, it's essential to note that the actual size of the allotment could vary based on the specific circumstances of the family and the reservation.

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Complete Question:

The term section is a land unit used in surveying that equals 640 acres, or one square mile. according to the Dawes act, how many acres does a family get?

A good residual plot should have the points randomly scattered around the horizontal line with no discernible pattern.

This indicates that the model is well fit to the data. The residuals should also be equally distributed on either side of the horizontal line. This can be seen as the sum of the residuals being equal to 0, or mathematically expressed as the sum of the residuals (e) being equal to 0, where \(e = y - ŷ\), where y is the observed value and ŷ is the predicted value. The equation can be expressed as Σe=0.

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Answer:710.4

Step-by-step explanation:

Answer:

Step-by-step explanation:

Simplify the left side.

Multiply both numerator and denominator by the conjugate of the denominator:

Compare this to the right side to get:

Answer:

X - X * 0.15 = 0.85X

X * 0.85 = X - X * 0.15

Both of these expressions can be used to find the price of any lawnmower pre-tax this weekend. The first expression calculates the price by subtracting 15% of the original price from the original price, and the second expression calculates the price by multiplying the original price by 85%.

Based on the data and probability, the number of yellow cotton balls in the bag is 154.

Given that,

Tori's scout troop got a new bag of 500 cotton balls in assorted colors to use for crafts.

She randomly grabbed some cotton balls out of the bag, looked at them, and put them back in the bag.

Total number of cotton balls = 500

The colors she grabbed are :

pink, yellow, blue, yellow, pink, pink, blue, yellow, pink, blue, blue, yellow, pink.

Out of 13 picks, number of yellow balls got = 4

Probability of getting yellow ball = 4/13

Number of yellow balls in 500 balls = 4/13 × 500 = 153.846 ≈ 154

Hence the number of yellow cotton balls in the bag is 154 balls.

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Answer: True

Step-by-step explanation: Every triangle has exactly three medians, one from each vertex, and they all intersect each other at the triangle's centroid. In the case of isosceles and equilateral triangles, a median bisects any angle at a vertex whose two adjacent sides are equal in length. The concept of a median extends to tetrahedra.

Answer:

True

Step-by-step explanation:

Given a metal rod of length 31 cm placed in a magnetic field of strength 2.3 T, oriented perpendicular to the field, you need to consider the following:

1. The metal rod is 31 cm in length.
2. The magnetic field strength is 2.3 T (tesla).
3. The rod is positioned perpendicular to the magnetic field, which means that the angle between the rod and the magnetic field is 90 degrees.

In this scenario, the rod is placed in such a way that it experiences the full effect of the magnetic field due to its perpendicular orientation.

When a metal rod of length 31 cm is placed in a magnetic field of strength 2.3 T, oriented perpendicular to the field, it will experience a force. The force on the rod will be given by the formula F = BIL, where B is the magnetic field strength, I is the current flowing through the rod, and L is the length of the rod.

Since the rod is not connected to a circuit, there is no current flowing through it. Therefore, the force on the rod will be zero. However, if a current is passed through the rod, it will experience a force perpendicular to both the magnetic field and the direction of the current flow. The magnitude of the force will depend on the strength of the magnetic field, the current flowing through the rod, and the length of the rod.

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Step-by-step explanation:

f(x) = -x + 1

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

Answer:

The answer is x=0. Believe me that's right.

Using the inscribed angle theorems, the measure of the indicated angles are:

1. m∠BOA = 26°

2. m∠BDA = 13°

3. m∠BCA = 13°

Based on the inscribed angle theorem, the following relationships are established:

Given:

Intercepted arc BA = 26°

1. ∠BOA is central angle

Thus:

m∠BOA = 26° (inscribed angle theorems)

2. ∠BDA is inscribed angle.

m∠BDA = 1/2(30) = 13° (inscribed angle theorems)

3. m∠BCA = m∠BDA = 13° (inscribed angle theorems)

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