a study is to be made to estimate the percent- age of citizens in a town who favor having their water fluoridated. how large a sample is needed if one wishes to be at least 95% confident that the estimate is within 1% of the true percentage?

Answer: The 8 oz steak is a better buy as it has a lower unit price at $1.06 per ounce compared to $1.14 per ounce for the 14 oz steak.

Step-by-step explanation: To determine which is a better buy, we can calculate the unit price of each steak.

The unit price is the price per ounce of steak.

For the 8 oz steak:

Unit price = price ÷ quantity = $8.50 ÷ 8 = $1.06 per ounce

For the 14 oz steak:

Unit price = price ÷ quantity = $16.00 ÷ 14 = $1.14 per ounce

Therefore, the 8 oz steak is a better buy as it has a lower unit price at $1.06 per ounce compared to $1.14 per ounce for the 14 oz steak.

The length of the hypotenuse of a 45-45-90 triangle is √2x units.

To find the hypotenuse of a 45-45-90 triangle, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides (legs) is equal to the square of the longest side (hypotenuse).

Let's denote the length of each leg of the triangle as "x". Since the triangle is isosceles, both legs are of equal length. Therefore, we can write:

Leg 1 = Leg 2 = x

To find the length of the hypotenuse (which we'll call "h"), we can use the Pythagorean theorem as follows:

x² + x² = h²

Simplifying this equation, we get:

2x² = h²

To solve for h, we need to take the square root of both sides of the equation:

√(2x²) = √(h²)

√2 * x = h

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The value of x, obtained using the property of bisected angles is 10

Bisected angles are angles that are split by a line segment in two to create two angles of the same measure.

The specified information indicates;

[tex]\overrightarrow{GI}[/tex] bisects ∠DGH

m∠DGI = x - 3

m∠IGH = 2·x - 13

The angle addition postulate indicates that we get;

m∠DGH = m∠DGI + m∠IGH

The definition of the bisected angle ∠DGH indicates that we get;

∠DGI = ∠IGH

Therefore;

x - 3 = 2·x - 13

2·x - 13 = x - 3

2·x - x = 13 - 3 = 10

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The values of p1, p2, p3 that minimize Var(X) are p1 = 0, p2 = 1/3, and p3 = 2/3.

We can use the following formulas to find the variance of X:

Var(X) = E[X^2] - (E[X])^2

E[X] = p1 + 2p2 + 3p3

E[X^2] = p1 + 4p2 + 9p3

Substituting these expressions into the formula for the variance, we get:

Var(X) = p1 + 4p2 + 9p3 - (p1 + 2p2 + 3p3)^2

Simplifying this expression, we get:

Var(X) = -[tex](p1^2 + 2p2^2 + 3p3^2) + 2p1p2 + 6p1p3 + 4p2p3[/tex]

To maximize Var(X), we want to maximize this expression subject to the constraint p1 + p2 + p3 = 1. We can use Lagrange multipliers to find the maximum. Let:

L(p1, p2, p3, λ) = -[tex](p1^2 + 2p2^2 + 3p3^2) + 2p1p2 + 6p1p3 + 4p2p3 + λ(1 - p1 - p2 - p3)[/tex]

Taking partial derivatives and setting them equal to zero, we get:

-2p1 + 2p2 + 6p3 - λ = 0

4p1 - 4p2 + 4p3 - λ = 0

6p1 + 8p2 - 6p3 - λ = 0

p1 + p2 + p3 = 1

Solving these equations, we get:

p1 = 2/7, p2 = 3/7, p3 = 2/7, λ = 4/7

Therefore, the values of p1, p2, p3 that maximize Var(X) are p1 = 2/7, p2 = 3/7, and p3 = 2/7.

To minimize Var(X), we want to minimize the expression [tex]-(p1^2 + 2p2^2 + 3p3^2) + 2p1p2 + 6p1p3 + 4p2p3[/tex] subject to the constraint p1 + p2 + p3 = 1. We can use the same Lagrange multiplier method to find the minimum. Taking partial derivatives and setting them equal to zero, we get:

-2p1 + 2p2 + 6p3 - λ = 0

4p1 - 4p2 + 4p3 - λ = 0

6p1 + 8p2 - 6p3 - λ = 0

p1 + p2 + p3 = 1

Solving these equations, we get:

p1 = 0, p2 = 1/3, p3 = 2/3, λ = 2/3

Therefore, the values of p1, p2, p3 that minimize Var(X) are p1 = 0, p2 = 1/3, and p3 = 2/3.

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Answer:

y = [tex]\frac{1}{3}[/tex]x

Step-by-step explanation:

As y increases by 1, x increases by 3.

Helping in the name of Jesus.

The research company can then conduct an appropriate statistical test, such as a t-test or an ANOVA, to analyze the data and determine whether to accept or reject the null hypothesis. If the null hypothesis is rejected, it would imply that there is a significant difference in the amount of vitamin D between the two types of multi-vitamins.

To examine if there is a difference in the amount of vitamin D in a brand name multi-vitamin and generic brand multi-vitamin, the appropriate hypotheses for the research company would be as follows:

Null Hypothesis (H0): There is no significant difference in the amount of vitamin D in the brand name multi-vitamin and the generic brand multi-vitamin. In other words, the mean amount of vitamin D in both types of multi-vitamins is equal.

Alternative Hypothesis (H1): There is a significant difference in the amount of vitamin D in the brand name multi-vitamin and the generic brand multi-vitamin. This means that the mean amount of vitamin D in one type of multi-vitamin is not equal to the other.

The research company can then conduct an appropriate statistical test, such as a t-test or an ANOVA, to analyze the data and determine whether to accept or reject the null hypothesis. If the null hypothesis is rejected, it would imply that there is a significant difference in the amount of vitamin D between the two types of multi-vitamins.

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Answer:

there is no Modal number because all the numbers appears only once

Your friend has only a 10% chance of winning one of the prizes, given that you win one of the prizes. Then the probability that both you and your companion will win a prize in this challenge is 3%. 

Let's begin by calculating the likelihood of you winning a prize, which is given as 30% or 0.3. The likelihood of your companion winning a prize is given as 20% or 0.2. In the event that you win a prize, at that point, the likelihood of your companion winning a prize diminishes to 10% or 0.1. Ready to speak to this conditional likelihood as P.

Presently, ready to utilize the equation for conditional likelihood to discover the likelihood of both you and your companion winning a prize.

P(You and Companion both win a prize)

= P(You win a prize) x P(Friend wins a prize|You win a prize)

= 0.3 x 0.1

= 0.03 or 3%.

thus, the likelihood that both you and your companion will win a prize in this challenge is 3%. 

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Answer:

Step-by-step explanation:

8600

Answer:

8,600

Step-by-step explanation:

"nearest hundred", meaning 643 and since the tens place is under 50 it is closer to 600 then 700 making it 8,600

The Earth is estimated to be around 4.54 billion years old, while the oldest known rocks found on Earth date back to about 4 billion years ago.

Determining the age of the Earth is a complex process that involves a variety of scientific disciplines. Geologists and other scientists have used a variety of methods to estimate the age of the planet, including radiometric dating, which involves measuring the decay of radioactive isotopes in rocks and other materials.

The age of the oldest known rocks found on Earth has also been determined using radiometric dating techniques. These rocks, which are primarily found in Western Greenland, have been dated to around 3.8 to 4.0 billion years old. The rocks are believed to have formed during the Hadean Eon, a period of Earth's history when the planet was still in its early stages of formation and was subject to intense meteorite bombardment.

It's important to note that the age of the Earth and the age of the oldest known rocks found on its surface are not precise measurements.

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Answer: To determine whether the condition of equal standard deviations is met in this case, we can perform a quick check by comparing the sample standard deviations of each group. If the sample standard deviations are roughly equal, then we can assume that the condition of equal standard deviations is met.

Alternatively, we can use Levene's test for equality of variances, which tests the null hypothesis that the population variances are equal across all groups. If the p-value of the test is greater than the significance level (usually 0.05), then we can assume that the condition of equal standard deviations is met.

Without the data or the sample standard deviations, it is not possible to determine whether the condition of equal standard deviations is met in this case.

Step-by-step explanation:

Answer:

ight, whats good.

To calculate the percentage of students who brought lunch from home, we can use the following formula:

Percentage = (Number of students who brought lunch from home / Total number of students) * 100

Given:

Number of students who ate school lunch = 114

Number of students who brought lunch from home = 266

Total number of students = Number of students who ate school lunch + Number of students who brought lunch from home = 114 + 266 = 380

Plugging in these values into the formula:

Percentage = (266 / 380) * 100 = 70%

So, 70% of the students brought lunch from home.

The slant height of the Teepee is 32.76 feet.

The square footage of one of the rooms is 44 square feet.

Check the attached for the sketch of the cone. From the image, the slant height is labelled l. Note that the base diameter is 14 feet, so the base radius will be 7 feet.

(a) Thus, the slant height can be found by considering one of the right triangles in the cone. That is:

l² = 32² + 7²   (Pythagoras Theorem)

l²  = 1024 + 49

l = √1073

l = 32.76 feet

(b) The shape of base is a circle.

Area of circle = πd

where d is the base diameter

Area of circle = 22/7 * 14

Area of circle = 44 square feet

Thus, the square footage of one of the rooms is 44 square feet

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If you use the normal distribution to estimate the probability that score exceeds 100, the answer would be zero.

This is because a normal distribution is a continuous probability distribution, and the probability of any individual score, no matter how high or low, is always zero.

However, this answer contradicts the assumption of a normal distribution for scores because it implies that scores cannot exceed 100, which is not true. Scores can theoretically range from negative infinity to positive infinity, and in practice, there may be some scores above 100, especially if the measurement instrument is imprecise or the test is very difficult.

Therefore, if we observe scores that are higher than 100, it suggests that the assumption of a normal distribution may not be appropriate for the data, and we may need to use a different distribution or statistical model to estimate probabilities or make inferences about the scores.

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From the similar triangle, y=8.7, and x=4

From the similar triangle,

First lets find the angle both triangles share

to determine the value , solving on the bigger triangle,

cosθ= adjacent/hypothenus

cosθ= 5/10

cosθ= 0.5

θ= 60

Therefore, to obtain y,

sin 60= y/10

y=10 sin 60

y=8.7

from the smaller triangle,

to determine x

cos 60=2/x

x cos 60=2

x=2/cos60

x= 4.

Therefore, y=8.7, and x=4.

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Answer:

(2x+6),(2x-6)

Step-by-step explanation:

This instance is DOTS or the difference of 2 squares so (2x+6),(2x-6). it states [tex]a^{2} - b^{2} = (a+b)(a-b)[/tex]

The margin of error is an important factor in determining the sample size needed to estimate a parameter, it is not the only factor - False.

Other factors that need to be considered include the level of confidence desired, the variability of the population being sampled, and the size of the population.

The margin of error is the amount of error that is acceptable in the estimate of the parameter. The smaller the margin of error desired, the larger the sample size needed.

A higher level of confidence requires a larger sample size, as there is less room for error in the estimate. The variability of the population being sampled also plays a role in determining the sample size needed.

Finally, the size of the population being sampled also affects the sample size needed.

A smaller population requires a smaller sample size, while a larger population requires a larger sample size to ensure a representative sample.

In summary, while the margin of error is an important factor in determining the sample size needed to estimate a parameter, it is not the only factor.

Other factors that need to be considered include the level of confidence desired, the variability of the population being sampled, and the size of the population.

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The actual height of the tower is 160 feet.

Given that, a scale model of a tower is 24 inches.

The scale is 1.5 inches:10 feet.

We know that, 1 foot = 12 inches

So, the scale 1.5 inches : 120 inches.

The basic formula to find the scale factor of a figure is expressed as,

Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.

1.5/120 = 24/The actual height of the tower

1.5×The actual height of the tower = 24×120

The actual height of the tower=2880/1.5

= 1920 inches

In feet = 1920/12

= 160 feet

Therefore, the actual height of the tower is 160 feet.

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The probability that Claire spinning an 8 is around 0.078, or 7.8%.

We may use the strategy of calculating favorable results over total outcomes to get the likelihood that Claire spins a sum of 8. We must specifically determine how many possibilities there are to reach a sum of 8 when spinning the two spinners and divide that number by the total number of possible outcomes.

To illustrate, we can use a table to display all of the possible results for spinning two spinners labeled 1-8, and then compute the sum of each outcome:

There are 64 possible outcomes (8 spinners 1 choice times 8 spinner 2 choices), and we can see that there are 5 methods to reach a sum of 8: (2,6), (3,5), (4,4), (5,3), and (6,2). As a result, the likelihood of getting an 8 is:

P(sum of 8) = number of favorable outcomes / total number of outcomes

            = 5 / 64

            = 0.078125

So the likelihood of Claire spinning an 8 is around 0.078, or 7.8%.

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The measure of angle a is 30° , angle b is 60° and angle c is 105°  calculated from the properties of angles and of triangle.

When two straight lines intersect each other at some angle, say line AB intersect line CD, then the opposite angles formed by the two lines are called vertically opposite angles. A pair of vertically opposite angles are equal to each other.

Angle a is formed at the intersection of the two straight lines, say AB and CD. The angle opposite to angle is 30°.

Thus from the definition of vertically opposite angles we get,

Angle a = 30° , since pair of vertically opposite angles are equal to each other.

In a right angle triangle one of three angles is 90° and the other two angles are acute angles. The sum of all the angles of a triangle is 180°.

Say  ΔMNO is a right angle triangle where angle a is one of the other two acute angles (where angle a = 30°).

The third angle (acute) is b.

Thus from the sum of triangle we get,

Angle a + Angle b + 90° = 180°

⇒ 30° + Angle b + 90° = 180°

⇒ Angle b = 60°

Here angle c is an angle labelled in a triangle (on the left of the previous triangle, say ΔMNO).

Two angles are said to be adjacent angles when they have a common vertex and side. The pair of adjacent angles sum to 180° , that is they are supplementary angles.

The adjacent angle of Angle c is 75°.

Thus, Angle c + 75° = 180°

⇒ Angle c = 105°

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Answer:

The new perimeter will be 2 times the old perimeter.

Step-by-step explanation:

Both dimensions are doubled doubled: times 2 or x2 or *2

4*2=8

2*2=4

if both measures are doubled, then the result will be doubled too.

The possible lengths of each side of the garden is given by the inequality relation 0 ≤ x ≤ 12

Given data ,

Let's assume that the square garden has sides of length x.

To surround the garden, we will need fencing of length equal to the perimeter of the square, which is 4x

The total amount of fencing is at most 52 feet

So , the inequality is

4x ≤ 52

Dividing both sides by 4, we get:

x ≤ 13

Therefore, the possible length of each side of the garden is less than or equal to 13 feet

And , each side of garden should be more than 0 , so

x > 0

Hence , the full inequality representing the possible length of each side of the garden would be 0 < x ≤ 13

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The table that shows a relation that represents a function is: table D in the options given.

To determine if a relation is a function, we need to check if each value of x corresponds to a unique value of y.

A. In this relation, x = 3 is paired with two different values of y (-2 and -1) which means this relation is not a function.

B. In this relation, each value of x does not corresponds to only one value of y, so this relation is not a function.

C. In this relation, -3 and 1 are paired with two different values of y (-3 and 1), which means this relation is not a function.

D. In this relation, each value of x corresponds to only one value of y, so this relation is a function.

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1. The function that models the amount in the account after x years is [tex]y(x) = 200e^{0.05t}[/tex]

2. The domain is [tex]x > = 0[/tex]. The range is [tex]y > = 200[/tex]

3. After 8 years, Brian will have $298.37 in the account.

Function defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

The formula for continuous compounding is [tex]A = Pe^{rt}[/tex] where the A is the amount, P is the principal, e is Euler's number, r is the annual interest rate and t is the time in years.

Data:

A = ?

P = 200

t = ?

r = 5% = 0.05

Plugging in the values, we get: [tex]A = 200e^{0.05t}[/tex]which is the function.

2. The domain of the function is x >= 0 which means the number of years must be non-negative.

The range of the function is y >= 200 since the amount in the account cannot be negative and it starts with an initial investment of $200.

3. To get amount in the account after 8 years, we will plug in x = 8 into the formula:

[tex]y = 200 * e^{0.05*8}\\y = 200 * 1.49182469764\\y = 298.364939528\\ y = $298.37.[/tex]

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The length of segment a in the given chords is determined as 2.

The measure of length a is calculated by applying the following formula.

Based on the angle of intersecting chord theorem, we will have the following equation.

a x 6 = 3 x 4

6a = 12

divide both sides of the equation by 6;

6a/6 = 12/6

a = 2

Thus, the value of a in the given chords is determined by applying chord theorem.

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The determinant of the given matrix is -27

To find the determinant of the given matrix by row reduction to echelon form, follow these steps:

1. Write down the given matrix:

```
| 1  5 -6 |
| 1  6  5 |
| 2  8  7 |
```
2. Use row operations to reduce the matrix to echelon form. First, eliminate the elements below the pivot element (1) in the first column:
```

R2 = R2 - R1
R3 = R3 - 2 * R1
```
Resulting matrix:
```
| 1  5  -6 |
| 0  1  11 |
| 0  -2 -19 |
```
3. Next, eliminate the elements below the pivot element (1) in the second column:
```
R3 = R3 + 2 * R2
```
Resulting matrix:
```
| 1  5  -6  |
| 0  1  11  |
| 0  0 -27 |
```
4. The matrix is now in echelon form:
```
| 1  5  -6  |
| 0  1  11  |
| 0  0 -27 |
```
5. Find the determinant of the echelon form matrix by multiplying the diagonal elements (pivot elements):
```
Determinant = 1 * 1 * -27 = -27
```

Your answer: The determinant of the given matrix is -27.

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